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https://www.physicsforums.com/threads/basic-intergrate-question-x-3.353701/ | # Basic intergrate question x 3
1. Nov 11, 2009
### ming2194
1. The problem statement, all variables and given/known data
2. Relevant equations
above
3. The attempt at a solution
1)
needs some hints here.
may i treat e^2x as (e^x)2 and then apply the formula to get the answers?
2)
i didnt write a full attempt but it is the flow of my thought.
did my attempt correct? or in fact there are other easier way to get the answers?
3)
this one i just wonder whether my work is correct or not. (shown in pic)
thx a lots.
2. Nov 11, 2009
### Gib Z
1) Assuming the formula is for the standard form $\int \frac{1}{\sqrt{x^2-1}} dx$, no you can not treat it that simply. You could try letting u=e^x.
2) Your method will work. I've tried some things and that seems to be the most elementary.
3) That is pretty much the correct evaluation of the "net area" but strictly the integral does not converge at all because the integrand is not well defined over the interval of integration.
3. Nov 11, 2009
### Staff: Mentor
For 3, as Gib Z already noted, the integrand is undefined at a point in the interval. For this problem you need to split the integral into two improper integrals:
$$\lim_{a \rightarrow 1^-} \int_0^a \frac{dx}{x - 1}~+~\lim_{b \rightarrow 1^+} \int_b^3 \frac{dx}{x - 1}$$
Evaluate each integral and take the limit. There's no guarantee that either improper integral will converge, though.
4. Nov 11, 2009
### ming2194
actually how can i know when the question is asking me using improper integral? or it's needed to decide by myself?
and for 2), i worked out the answer and found it's damn long and complex. so how can i check whether im correct?
1)
thx again.
5. Nov 11, 2009
### Staff: Mentor
I think this is wrong, which you can confirm by differentiating your final result. How did you go from this integral:
$$\int \frac{du}{\sqrt{u^4 - 4u^2}}$$
to this?
$$ln(u^2 + \sqrt{u^4 - 4u^2}) + C$$
I would have left the integral like this:
$$\int \frac{du}{u\sqrt{u^2 - 4}}$$
and worked toward a trig substitution, with sec($\theta$) = u/2. | 2017-08-21 19:10:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7107401490211487, "perplexity": 793.3851172444744}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109470.15/warc/CC-MAIN-20170821172333-20170821192333-00068.warc.gz"} |
https://quant.stackexchange.com/questions/65779/best-books-on-portfolio-construction/67872 | # Best books on portfolio construction?
I am a master of finance student and although I understand the basics and the theory of portfolio construction I am still struggling when it comes to the practical side of things, i.e. building a real-world portfolio, with real-world assets, real-world data, etc. and the challenges that come with it. I was wondering if someone on here would be able to point me to some good books that would help me get started, and that ideally also include programming applications and examples. Thanks.
• Hi: maybe you're under the impression that there's some secret techniques involved but they're really aren't. I would check out maybe Rudd and Clasing's text on portfolio theory. It's not an exact book for your needs but based on what you described, I don't know if there is such a book like that. For quants, 3 steps might be: 1) build some objective function, 2) add constraints 3) use an optimization routine to retrieve the weights of the resulting portfolio. Jun 30 at 0:13
• I did some searching and it appears that DataCamp also offers a very basic yet informative, concise, and hands-on portfolio analytics course. I'll drop the link here in case someone is interested: learn.datacamp.com/courses/intermediate-portfolio-analysis-in-r. Jun 30 at 12:13
I can list a couple of things that are very reasonable to start off with. As written in the above comment, you will not be able to find any "secret sauce" in books and journals. You will, however, be able to find some good ideas that are commonly shared in the industry.
### "Free" applied course: Portfolio optimization with R
There exists a course called portfolio optimization with R taught by Prof. Daniel P. Palomar at the Hong Kong University of Science and Technology (HKUST). The course is very applied and teaches you the basics of R (if you're new to it), common time-series analysis, and of course, portfolio optimization. He has made all of his slides and R sessions available on his webpage (see above link), and much of his code are also imbedded into his slides. This makes it easy to reproduce many of the portfolio setups and problems that he walks through in his course. In general, the course teaches you about:
• Markowitz portfolio framework.
• Robust portfolio optimization.
• Portfolio optimization under alternative risk-measures (VaR, Downside risk, CVaR).
• Risk parity portfolio.
• Factor models.
• Black-Litterman model.
I believe this would be a good starting point if you're looking for very applied teaching materials.
### Journal of portfolio management
The Journal of portfolio management is a great source to scavenge for new ideas revolving about portfolio management, cost-schemes, alternative investment strategies etc. The papers are often co-authored by people in the industry together with professors in academia. Again, many of the papers are very applied and contain minimal mathematics. Therefore, you sometimes need some background knowledge before completely understanding the paper and the authors methodology. Nevertheless, if you have access to the journal through your university, you're in luck! | 2021-11-29 21:45:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4285486340522766, "perplexity": 855.2267355622738}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00382.warc.gz"} |
https://mathoverflow.net/questions/335557/do-the-odd-cycles-of-a-graph-define-a-matroid | # Do the Odd Cycles of a Graph Define a Matroid?
An Odd Cycle Transversal is a set of vertices that, when removed from a graph, renders it bipartite.
Question:
does the collection of "critical" sets of vertices, whose removal renders a graph bipartite, resemble a Matroid, i.e. will a greedy strategy yield a critical vertex set of minimal cardinality?
I am looking for a proof deciding the matroid property that either affirm the success of the greedy strategy or for a proof of at least the existence of instances, where the greedy strategy doesn't yield a minimal set of vertices whose removal renders the graph bipartite; a concrete counter example would be more than I dare to hope for in that case.
By a critical set of vertices, in this context, I mean a set of vertices whose removal renders a graph bipartite, but none of its proper subsets has that property.
By the greedy strategy I mean repeatedly removing a vertex that is on a maximal number of odd cycles in the graph resulting from previous greedy vertex deletions.
Please note that the question is not as to whether it is efficiently possible to determine the number of odd cycles on which a vertex; it is rather assumed that that information comes from a kind of oracle or whatever celestial being you prefer.
Take large $$n$$, and consider complete bipartite $$K_{n, n}$$ with parts $$V_0, V_1$$ together with an additional disjoint triangle $$T$$, and connect all vertices of $$T$$ with two vertices $$v, u \in V_0$$ pairwise. Odd cycles in this graph consist of paths in $$K_{n, n}$$ between $$v$$ and $$u$$ extended by a two-vertex path in $$T$$, together with $$O(1)$$ odd cycles confined to $$\{v, u\} \cup T$$. One can see that:
• $$v$$ and $$u$$ are contained in all odd cycles except for $$O(1)$$;
• vertices of $$T$$ and other vertices of $$K_{n, n}$$ are contained in at most $$2 / 3 + o(1)$$ fraction of all odd cycles.
A smallest OCT consists of two vertices of $$T$$, yet the greedy algorithm WLOG will first take $$v$$, and then will proceed to delete at least two other vertices (since the remaining graph contains $$K_4$$, namely, the union of $$u$$ and $$T$$). | 2020-11-26 01:13:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8586991429328918, "perplexity": 168.05604138717112}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141185851.16/warc/CC-MAIN-20201126001926-20201126031926-00002.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/how-do-you-solve-2-6-x-4x | # How do you solve 2 (6-x)<4x?
Mar 9, 2016
$2 < x$
#### Explanation:
Expand the brackets
$12 - 2 x < 4 x$
Add $2 x$ to both sides
$12 < 6 x$
Divide both sides by 6
$2 < x$ | 2020-07-05 15:34:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9461715817451477, "perplexity": 5318.566594114394}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655887377.70/warc/CC-MAIN-20200705152852-20200705182852-00490.warc.gz"} |
http://physics.stackexchange.com/questions/linked/20289?pagesize=50&sort=hot | 158 views
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https://wiki.ubc.ca/Level_Curves | # Level Curves
Example 1:
Question: Find the level curves of heights C = -1, 0, 1 for f(x,y) = x+y+1
Solution:
For height C = -1 ( Yellow Line )
f(x,y) = x+y+1 = -1
x+y+1 = -1
y = -2-x
slope = -1
y-intercept = -2
For height C = 0 ( Blue Line )
x+y+1 = 0
y = -1-x
For height C = 1 ( Red Line )
x+y+1 = 1
y = -x
This is the graph that refers to Example 1.
Example 2:
Question: Find the level curves of heights C = 4, 1, 0, and -1 for f(x,y) = ${\displaystyle x^{2}+y^{2}}$
Solution:
For height C = 4 ( Blue Circle )
${\displaystyle x^{2}+y^{2}=4}$
${\displaystyle x^{2}+y^{2}=2^{2}}$
For height C = 1 ( Red Circle )
${\displaystyle x^{2}+y^{2}=1}$
${\displaystyle x^{2}+y^{2}=1^{2}}$
For height C = 0 ( Yellow Dot )
${\displaystyle x^{2}+y^{2}=0}$
Only solution is x = 0, y = 0.
For height C = -1
${\displaystyle x^{2}+y^{2}=-1}$
Does not exist because ${\displaystyle x^{2}+y^{2}}$ has to be greater than equal to 0.
This is the graph that refers to Example 2. | 2022-06-30 04:16:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3396950364112854, "perplexity": 1611.878180659719}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103661137.41/warc/CC-MAIN-20220630031950-20220630061950-00170.warc.gz"} |
https://codereview.stackexchange.com/questions/15521/simplify-raphael-js-code-display-text-in-div-on-click-event | # Simplify Raphael JS code: display text in DIV on click event
I've been working with the RaphaelJS 'australia map' example that displays text in a DIV when a state is clicked on. However I'm having difficulty working with it to create different events and functions.
I want to be able to duplicate the 'display text' function for two different element onClick events (i.e. have two different buttons (elements) that do the same thing). But the current code is a bit too complicated for me. Can somebody please help me simplify the code that displays the text in a DIV when an element is clicked on.
Any help would be much appreciated - this is what I'm currently working with jsfiddle.
window.onload = function () {
var R = Raphael("paper", 532, 500);
var attr = {
fill: "#0B0",
stroke: "#fff",
"stroke-width": 3,
};
var ctx = {};
ctx.btn_1 = R.path("M 180,130 L 340,130, L 392,212, L 128,212 z").attr(attr);
ctx.btn_2 = R.path("M 128,212 L 392,212, L 435,280, L 85,280 z").attr(attr);
var current = null;
for (var state in ctx) {
(function (st, state) {
st[0].style.cursor = "pointer";
st[0].onmousedown = function () {
current && (document.getElementById(current).style.display = "");
st.toFront();
R.safari();
document.getElementById(state).style.display = "block";
current = state;
};
})(ctx[state], state);
}
};
## migrated from stackoverflow.comSep 11 '12 at 12:59
This question came from our site for professional and enthusiast programmers.
• That is actually reasonably compact, straightforward code. Which part were you hoping to simplify, exactly? One thought: if the click handler is what you're focusing on, you can always declare the function independently and assign it by variable name, rather than reproducing it inline repeatedly. – Kevin Nielsen Sep 10 '12 at 16:38
• The part of code I'm hoping to simplify is the click handler (starting from var current = null; to the end of the code). The problem I'm having is trying to rebuild the click handler code - or even calling the function to be used elsewhere. – user1619342 Sep 11 '12 at 9:04
• @MarkThomas I'll try codereview too, thanks. – user1619342 Sep 11 '12 at 9:06
• You could user Paper.set and make an array of elements. I wouldn't add it to the context as class property. And btw, you can add 'cursor': 'pointer' to your attr. And at last: Don't use for..in, because it's very vulnerable, try Google :) – Dan Lee Sep 11 '12 at 9:41
• Great, thanks Dan Lee. I'll look into those more. Google to the rescue! :) – user1619342 Sep 13 '12 at 9:51
I agree with tiffon it's better to extract a function, but I don't agree with the rest of their edits, so here's what I would have done (I also kept the style intact).
var initPath = (function () {
var currentEl;
function init(el, path) {
path.attr({
fill: "#0B0",
stroke: "#fff",
"stroke-width": 3,
});
path[0].style.cursor = "pointer";
path[0].onmousedown = function () {
currentEl && (currentEl.style.display = "");
path.toFront();
path.paper.safari();
el.style.display = "block";
currentEl = el;
};
}
return init;
})();
var R = Raphael("paper", 532, 500);
var paths = {
'btn_1': R.path("M 180,130 L 340,130, L 392,212, L 128,212 z"),
'btn_2': R.path("M 128,212 L 392,212, L 435,280, L 85,280 z")
};
for (var id in paths) {
initPath(document.getElementById(id), paths[id]);
}
};
Firstly, I think st and state were confusing names, so I changed them to be path and id, respectively, and then changed id to el to avoid additional lookups.
I separated the infrastructure (current and initPath) from the usage (R, paths and the loop).
I also think an object literal looks better than a series of assignments, so I changed that.
Finally, I like it better if I move initPath and currentEl into a closure of their own—after all, they don't depend on window.onload anymore.
I left the inner init a named function so it is named in a stack trace, if there is an error.
I gave it a shot.
window.onload = function () {
var R = Raphael("paper", 532, 500),
attrs = {
fill: "#0B0",
stroke: "#fff",
"stroke-width": 3,
cursor: "pointer"
},
paths = [
{id: 'btn_1', p:"M 180,130 L 340,130, L 392,212, L 128,212 z"},
{id: 'btn_2', p:"M 128,212 L 392,212, L 435,280, L 85,280 z"}
],
current,
max,
i;
for (i = 0, max = paths.length; i < max; i++) {
initPath(paths[i].p, attrs, paths[i].id);
}
function initPath(pathStr, attrs, targetId) {
var path = R.path(pathStr).attr(attrs),
txElm = document.getElementById(targetId);
path.click(function (e) {
if (current) {
if (current === txElm) {
return;
}
current.style.display = '';
}
current = txElm;
current.style.display = 'block';
this.toFront();
R.safari();
});
}
}
Integrated Dan Lee's comments and defined a function instead of making a new closure in each loop iteration.
• I see absolutely no problem with using for... in to enumerate object properties, Google did not help. The original click logic was idiomatic JavaScript, not sure why you changed it. Also, OP doesn't use jQuery ([0] comes from Raphaël). – Dan Jan 7 '14 at 0:55 | 2019-11-13 16:00:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31736165285110474, "perplexity": 6772.404053675651}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667262.54/warc/CC-MAIN-20191113140725-20191113164725-00119.warc.gz"} |
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# Jing's Journal: Quest for 800
Author Message
Manager
Joined: 07 Sep 2007
Posts: 121
Followers: 3
Kudos [?]: 16 [0], given: 0
Jing's Journal: Quest for 800 [#permalink]
### Show Tags
12 Oct 2007, 04:19
Hey guys,
I've decided to start a topic to track my progress in preparation for the GMAT. I hope the added public accountability will keep me focused on my studies.
My Background
I just graduated, and my current goal is to get accepted at a top Masters program in quantitative finance. Because most of these programs take GMAT in place of GRE, GMAT seemed more practical because taking it would also knock out the test for B-School in the future.
So, a week ago, I committed myself to taking the test.
Current Progress
Princeton Review - Cracking the GMAT - Great primer! Gets you started with the right mentality of how to tackle the GMAT. Reading this guide raised my target score from 720+ to 800, because they show you that all the elements of the test can be learned. I was scoring about 50% in Verbal before reading this! Recommended read.
- Finished strategies and tips sections
- Completed practice problem sets (Q: 17/20, V: 18/20) [Careless mistakes]
- Easy and Medium Questions
- - - 50/53 Quant (1 bad assumption PS, 2 misread questions PS&DS)
- - - 44/52 Verbal (6 SC, 2 RC)
- (Medium-Hard and Hard Questions)
- (Take practice tests)
Kaplan GMAT Premier Program - So far so good, but I heard a lot of negatives about this program.
- Online Diagnostic Quiz (95%) [2 careless mistakes: 1 DS, 1 RC]
- CR Practice Quiz (41/50) [Wow, made some dumb mistakes especially close to the end. Really disappointed in myself. Note-to-self: Read CR answers more clearly.]
- SC Practice Quiz (43/50) [Learned mistakes as I went, 100% on last 20]
Strunk & White: The Elements of Style - Great reference for the fundamentals of good writing. Clear understanding of the fundamentals is key for SC.
- (Finish book)
Barron's GMAT CD - Crap; completely unrepresentative of the real GMAT questions.
OG11: GMAT Review
- Diagnostics Quiz - T_T
- - - Quant: 43/48 (1PS, 4DS)
- - - Verbal: 46/52 (2RC, 2CR, 2SC)
(Kaplan GMAT 800)
(1000 SC, RC, CR)
(1000 DS, PS)
Weaknesses to Fix
1. Spending too much time on Quant questions (Having 2-3 questions left when time runs out)
2. Reluctance to reread RC and CR passages when unsure of answer
3. Only around 80% confident of answer to some SC
4. Careless errors! Need to work on mental stamina!
Conclusion
GMATPrep1: 760 (51Q, 41V)
GMATPrep2: 770 (50Q, 45V)
GMAT Test: 780 (50Q, 48V)
Detailed write-up here: http://www.gmatclub.com/forum/t55399
Last edited by JingChan on 13 Nov 2007, 00:03, edited 16 times in total.
Kaplan GMAT Prep Discount Codes Optimus Prep Discount Codes Veritas Prep GMAT Discount Codes
Director
Joined: 11 Jun 2007
Posts: 931
Followers: 1
Kudos [?]: 148 [0], given: 0
### Show Tags
12 Oct 2007, 10:58
you are doing super well so far! Kaplan is trash and Princeton Review is good start although not enough for a higher score. i would recommend all of the Original Guide books (11th ed/ math/verbal) and the MGMAT books to your list. The GMATclub math challenges are also great once you have mastered the basics. I like Powerscore for CR and of course gmatclub forums for stimulating discussions. as for timing, have you looked into the GMATPrep / PowerPrep CAT's?
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19
Kudos [?]: 371 [0], given: 0
Re: Jing's Journal: Quest for 800 [#permalink]
### Show Tags
12 Oct 2007, 12:24
JingChan wrote:
Hey guys,
I've decided to start a topic to track my progress in preparation for the GMAT. I hope the added public accountability will keep me focused on my studies.
My Background
I just graduated, and my current goal is to get accepted at a top Masters program in quantitative finance. Because most of these programs take GMAT in place of GRE, GMAT seemed more practical because it would also knock out the test for B-School in the future.
So, a week ago, I committed myself to taking the test.
Current Progress
Princeton Review - Cracking the GMAT - Great primer! Gets you started with the right mentality of how to tackle the GMAT. Reading this guide raised my target score from 720+ to 800. Recommended read.
- Finished strategies and tips sections
- Completed practice problem sets (Q: 17/20, V: 18/20) [Careless mistakes]
- (Take practice tests)
Kaplan GMAT Premier Program - So far so good, but I heard a lot of negatives about this program.
- Online Diagnostic Quiz (95%) [2 careless mistakes: 1 DS, 1 RC]
Strunk & White: The Elements of Style - Great reference for the fundamentals of good writing. Clear understanding of the fundamentals is key for SC.
- (Finish book)
(OG: GMAT Review)
(Kaplan GMAT 800)
(1000 SC, RC, CR)
(1000 DS, PS)
Weaknesses to Fix
1. Spending too much time on Quant questions (Having 2-3 questions left when time runs out)
2. Reluctance to reread RC and CR passages when unsure of answer
3. Only around 80% confident of answer to some SC
4. Careless errors! Need to work on mental stamina!
Bro u seem to understand the GMAT very well. Showin us old Gmatclubbers, newbies can still own .
Id def. stay away from Kaplan. Its just not very good material.
Try MGMAT materials.
GMATPrep.
OG 11
OG Verbal
OG Quant.
GMATClub Challenges
CR in the OG's will seem like kindergarden to you though.
Good luck!
Manager
Joined: 07 Sep 2007
Posts: 121
Followers: 3
Kudos [?]: 16 [0], given: 0
### Show Tags
12 Oct 2007, 12:30
Thanks for the suggestions so far! I will make note of them.
Manager
Joined: 07 Sep 2007
Posts: 121
Followers: 3
Kudos [?]: 16 [0], given: 0
### Show Tags
12 Oct 2007, 19:16
I went through a "practice test" consisting of the easy and medium question sets for both Quant and Verbal in Princeton Review to gauge my performance.
50/53 Quant (1 bad assumption PS, 2 misread questions PS&DS) - 69 minutes (1.3 min/q)
44/52 Verbal (6 SC, 2 RC) - 75 minutes (1.4 min/q)
Really need to focus/relax more during SC. Grammar is much harder to evaluate when you have time pressure. RC mistakes were from the same line of thought, I should have went back and looked at the passage.
Time was pretty bad, especially since these were the easy and medium questions. It didn't help that people were chattering in the bookstore that I was in. Though, I suppose it's probably a good way to train myself to better ignore distractions.
Senior Manager
Joined: 11 Sep 2005
Posts: 324
Followers: 2
Kudos [?]: 185 [0], given: 0
### Show Tags
13 Oct 2007, 22:53
Again a good one from a GMATClubber...thanks for sharing this!
Keep us updated!
Director
Joined: 31 Mar 2007
Posts: 585
Followers: 9
Kudos [?]: 60 [0], given: 0
### Show Tags
14 Oct 2007, 15:39
Nice work Jing, keep it up.
I would recommend eventually just going to OG + Paper Tests + GMATPrep before you write the real thing. Once you start doing a lot of OG you will notice that a lot of Kaplan, Princeton, McGraw, etc questions are formulated incorrectly and fail to properly eliminate subjectivity in the answers (which really, really pisses you off!). Anyways just a tip.
Also if you find you get tired, try doing 150 questions in 150 mins and simulating the same mix of questions (a few DS, then a few PS, a few DS, few PS, then RC, etc) (or just doing 2 paper tests in a row as fast as you can).
Best of luck!
Manager
Joined: 07 Sep 2007
Posts: 121
Followers: 3
Kudos [?]: 16 [0], given: 0
### Show Tags
16 Oct 2007, 14:30
Just finished taking the diagnostics quiz at the beginning of OG11.
Kinda iffy scores, need to work on consistency.
Quant: 43/48
Verbal: 46/52
Breakdowns:
PS 23/24
DS 20/24
CR 15/17
RC 15/17
SC 16/18
When I score each section there are always a couple questions where I'm like "how did i get that wrong?"
Consistently scoring about 9 out of 10 questions no matter what type of question. I think my flaw is concentration.
Senior Manager
Joined: 11 Sep 2005
Posts: 324
Followers: 2
Kudos [?]: 185 [0], given: 0
### Show Tags
17 Oct 2007, 11:46
Hi JingChan
i've jotted down some points on prep-materials i'm following and few concerns if u would share ur thoughts on that, it will really b helpful! Below is the link...
http://www.gmatclub.com/forum/t53976
Thanks
Current Student
Joined: 18 Jun 2007
Posts: 408
Location: Atlanta, GA
Schools: Emory class of 2010
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### Show Tags
17 Oct 2007, 13:39
JingChan wrote:
Just finished taking the diagnostics quiz at the beginning of OG11.
Kinda iffy scores, need to work on consistency.
Quant: 43/48
Verbal: 46/52
Breakdowns:
PS 23/24
DS 20/24
CR 15/17
RC 15/17
SC 16/18
When I score each section there are always a couple questions where I'm like "how did i get that wrong?"
Consistently scoring about 9 out of 10 questions no matter what type of question. I think my flaw is concentration.
JingChan, you're going to do very well. If I remember my diagnostic scores from OG11 correctly they were very similar to yours, and I did that in my final week of preparation. I remember the diagnostic being a fairly good representation of how the mix of problems will be on the test. If you keep working like you are, you very well could join the elusive 800 club.
Director
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Posts: 585
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### Show Tags
17 Oct 2007, 16:00
Jing -- that's the main problem, focus. I find that as you do more and more questions, you progressively get more and more tired. Do you get the 'brain buzz'? That fuzzy/warm feeling in your brain? That's what I get, then nothing makes sense and it's hard to focus... I find doing a lot of questions in a row helps (like 150 in a row, in 2 hours) helps train the brain.
Keep up the good work
Manager
Joined: 07 Sep 2007
Posts: 121
Followers: 3
Kudos [?]: 16 [0], given: 0
### Show Tags
31 Oct 2007, 20:56
Wow, haven't updated this in a long time.
I've been going through the OG11 and doing about 60-80 questions a day. Have to really step up my studying hardcore because I need to write the test soon to be able to work on applications.
Here's my scores so far:
PS: 165/170 (97%)
DS: 88/90 (98%)
RC: 50/57 (88%)
SC: 79/100 (79%)
CR: 64/70 (91%)
I'm not sure how this will translate exactly to a percentile score on the GMAT.
I'm hoping to push all the percentages up to at least 90%, my biggest obvious flaw has been SC. Do any of you guys have suggestions on how to rock the SC? I have a feeling that my approach to answering those questions is flawed, and that I'm missing the fundamentals.
Best,
J
Manager
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Posts: 121
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### Show Tags
31 Oct 2007, 21:01
Jing -- that's the main problem, focus. I find that as you do more and more questions, you progressively get more and more tired. Do you get the 'brain buzz'? That fuzzy/warm feeling in your brain? That's what I get, then nothing makes sense and it's hard to focus... I find doing a lot of questions in a row helps (like 150 in a row, in 2 hours) helps train the brain.
Keep up the good work
Yeah man, I always get that burnout after I do about 50-80 questions. I's zone out while reading passages and I'd have to mentally kick myself back into concentration mode to get through it. The bright side is that the actual test itself only has about 80 questions, so as long as you can do 80 without your eyes glazing over, you're probably okay.
Doing 150... is nuts. Lol. But I'm sure it's great for training stamina. I'll probably do a few marathon question rounds as I start winding down to test day.
-J
Manager
Joined: 07 Sep 2007
Posts: 121
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### Show Tags
07 Nov 2007, 16:36
GMATPrep 1: 740 (51Q, 39V)
Although this score is lower than I'd like. I actually ran out of time on verbal with ~8 questions to go, getting them all wrong (which is supposedly really bad for your score). Haha, I'm usually very fast with verbal (~1 min a question), but I was distracted by my parents during that section.
Math section was fine, I finished with 11+ minutes to go.
So, even though my score is lower than great, I'm feeling pretty confident about the test.
I purposely did not review my answers, and will go and retake the test in a more isolated environment to hopefully get a better approximation.
And I'm saving GMATPrep 2 for the day before the test.
Scheduled my GMAT for this Sunday at 9am. (Only time available within the next two weeks at my closest center.)
---
Edit: So I retook the GMATPrep 1 test after my family went to sleep.
Score: 760 (51Q, 41V)
Missed 2 questions on Quant (careless errors), but 11 on Verbal! Score is still too low for my liking.
And I believe 9 of the ones I got wrong were all SC!
I pretty much got all the SC wrong, but did fine on every other type of question. It seems that some days I can go 20-30 SC questions in a row and not miss a single one, but other days I miss 1 out of 5. On this test, however, I probably missed 2 out of 3. Horrid.
Really need to step up my SC game if I am to write this test on Sunday... 3 days away. Gonna do straight SC1000s for the next 2 days.
Senior Manager
Joined: 02 May 2004
Posts: 311
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### Show Tags
09 Nov 2007, 08:14
JingChan wrote:
Jing -- that's the main problem, focus. I find that as you do more and more questions, you progressively get more and more tired. Do you get the 'brain buzz'? That fuzzy/warm feeling in your brain? That's what I get, then nothing makes sense and it's hard to focus... I find doing a lot of questions in a row helps (like 150 in a row, in 2 hours) helps train the brain.
Keep up the good work
Yeah man, I always get that burnout after I do about 50-80 questions. I's zone out while reading passages and I'd have to mentally kick myself back into concentration mode to get through it. The bright side is that the actual test itself only has about 80 questions, so as long as you can do 80 without your eyes glazing over, you're probably okay.
Doing 150... is nuts. Lol. But I'm sure it's great for training stamina. I'll probably do a few marathon question rounds as I start winding down to test day.
-J
I think the Powerscore Sentence Correction book is better than Manhattan GMAT's-it starts from the beginning and gives examples/problems throughout and explains the concepts in more depth. Definitely worth the $$..I am a native English speaker and never learned proper grammar-never really counted for me in school since I was in a honors classes-teachers focused more on content ideas than correct form. Manager Joined: 07 Sep 2007 Posts: 121 Followers: 3 Kudos [?]: 16 [0], given: 0 [#permalink] ### Show Tags 09 Nov 2007, 19:46 jamesrwrightiii wrote: I think the Powerscore Sentence Correction book is better than Manhattan GMAT's-it starts from the beginning and gives examples/problems throughout and explains the concepts in more depth. Definitely worth the$$\$..I am a native English speaker and never learned proper grammar-never really counted for me in school since I was in a honors classes-teachers focused more on content ideas than correct form.
Yeah, that must have been my problem, too. I never remember rigorous training in correct grammatical form, and I'm a native speaker who went to a Governor's school.
Thanks for the advice, but it's a little late for me; I'm taking the test in 1.5 days. I've just decided to use the SC1000 and ram the question type into my head by doing as many as I can each day. After studying, I know all the rules, I just need to take what I know and apply it to the questions.
Cheers,
J
Manager
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### Show Tags
10 Nov 2007, 23:37
GMATPrep #2: 770 (50Q, 45V)
Disappointed at the 50Q, I missed 7 questions!
Verbal was kicking, I'd be happy with a 45V anyday.
Practices have been okay, tomorrow is game day- going to sleep early tonight.
-Jing
Senior Manager
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### Show Tags
11 Nov 2007, 00:20
good luck
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# Jing's Journal: Quest for 800
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2016-08-24 14:08:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31337970495224, "perplexity": 6591.342845206706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982292330.57/warc/CC-MAIN-20160823195812-00049-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://ask.sagemath.org/answers/23734/revisions/ | # Revision history [back]
In particular, give a name to your object and use the automatic TAB-completion to get the list of available methods. In this way, you can learn about the methods .degree and .variables by hitting the TAB key after toto.
sage: sage: R = BooleanPolynomialRing(3, 'x')
sage: sage: x, y, z = R.gens()
sage: too = x+z
sage: sage: too.v # (pressing TAB key here)
too.variable too.vars_as_monomial
too.variables too.version
sage: too.variables()
(x0, x2)
sage: len(toto.variables())
2
In particular, give a name to your object and use the automatic TAB-completion to get the list of available methods. In this way, you can learn about the methods .degree and .variables by hitting the TAB key after toto.
sage: sage: R = BooleanPolynomialRing(3, 'x')
sage: sage: x, y, z = R.gens()
sage: too = x+z
sage: sage: too.v # (pressing TAB key here)
too.variable too.vars_as_monomial
too.variables too.version
sage: too.variables()
(x0, x2)
sage: len(toto.variables())
len(too.variables())
2
In particular, give a name to your object and use the automatic TAB-completion to get the list of available methods. In this way, you can learn about the methods .degree and .variables by hitting the TAB key after toto.too.
sage: sage: R = BooleanPolynomialRing(3, 'x')
sage: sage: x, y, z = R.gens()
sage: too = x+z
sage: sage: too.v # (pressing TAB key here)
too.variable too.vars_as_monomial
too.variables too.version
sage: too.variables()
(x0, x2)
sage: len(too.variables())
2 | 2021-10-26 03:41:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23665419220924377, "perplexity": 7042.774035948742}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587794.19/warc/CC-MAIN-20211026011138-20211026041138-00425.warc.gz"} |
https://www.appropedia.org/Installing_RTM_Software_on_Linux | Radiative Transfer Modelling software is fun stuff! Decoding cryptic fortran docs is such a great time. So here's me spoiling all that fun for you, (hopefully) making it easy. Or at least easier.
I got it all going on a dual-core 64-bit AMD processor running a fresh install of Ubuntu 12.04. Most of this should be applicable to other platforms and linux-based operating system. Maybe even some other unix-based systems.
## The Software
• RRTM, by Atmospheric and Environmental Research, Inc.
• SMARTS, The Simple Model of the Atmospheric Radiative Transfer of Sunshine by Dr. Christian Gueymard.
• SBDART, Santa Barbara DISORT
## System
### Installing Fortran Compilers
All three RTM programs are written in Fortran, so you'll need a Fortran compiler! And actually make that three different Fortran compilers because you're awesome.
#### fort77
SBDART is written in FORTRAN77, so we need a compiler which compiles FORTRAN77 code. No kidding. Ubuntu doesn't have one by default so we need to install it.
1. Check if you already have it! Open up a terminal (ctrl-alt-t) and type the following command: f77. If the output looks like this:
The program 'fort77' is currently not installed. You can install it by typing:
sudo apt-get install fort77
Then you don't have it yet; proceed with the following instructions. If it says
gfortran: fatal error: no input files
compilation terminated
1. Install it! Type sudo apt-get install gfortran into the terminal.
2. Input your password at the prompt. I assume that your account has administrative power over the computer. If you installed Ubuntu yourself, you should have no issue. If you're using a machine administrated by someone else, you may need to talk to them.
3. You may encounter a confirmation asking you to confirm that you do, indeed, wish to download and install the compiler, something like
After this operation, 2,986 kB of additional disk space will be used.
Do you want to continue [Y/n]?
If that's still true, type 'Y' and hit enter. fort77 (and its dependencies) will install. That's it. Yep, installing programs in Ubuntu rocks.
#### gfortran
Guess what? gfortran installs in exactly the same way as fort77!
1. Check if it's there gfortran
2. If not, install it sudo apt-get install gfortran
Boom.
(Tip: basically anything you want in linux installs this way. SBDART doesn't because it's a very obscure piece of software which isn't in Ubuntu's repository. But a shocking wealth of software is readily available from the repository!)
#### PGILinux Fortran
I had no luck compiling RRTM with either gfortran or fort77, but they have a makefile specifically for The Portland Group's fortran compiler. It's not free, but there is a free trial period; good enough for our purposes. (note to self: look into the license I agreed to and see if there are any extra stipulations on the use of the trial version...)
1. Create a PGI account.
2. Download the compiler. I went with PGI Accelerator Fortran Workstation with Target 64-bit & 32-bit, for linux, obviously. It's massive. Find something to do while it downloads.
3. Extract the files somewhere, and then open a terminal and navigate there. I extracted them into a folder in my home directory that I named pgi, so for me that meant opening up a terminal (ctrl-alt-t), and typing cd ~/pgi.
4. The installer must be run with "root privileges", so you have to put sudo before the command. sudo ./install ... enter your password...
5. The EULA will show up in the terminal. Press Spacebar to move down page-by-page, and when you are satisfied, either accept or decline the terms at the end.
6. Assuming you accepted, You should now have a choice of type of installation. Choose the first (by entering the number 1), unless you think you might need a network install. That would be out of the scope of this document.
7. Leave the default installation directory (again unless you feel it needs to be changed, in which case I can't help you and you could have easily written this document); press enter.
8. I am running on an AMD processor, so I chose to install the ACML. I don't know if it will actually work since my operating system is running on a virtual machine, but it doesn't seem to hurt... I'll leave this one up to your judgement, however do note that there is an additional license agreement for the ACML.
9. The next screen was asking about ACML versions... I left it at the default (just hit enter)
10. I also have a nvidia video card (again, maybe this is not applicable anyway since I'm in a virtual machine), so chose to also install the CUDA stuff. Don't really know what it is... using the GPU to run parts of your code maybe? Again, there is yet another license agreement for CUDA.
11. I also installed the OpenACC drivers. The OpenACC site was down, but the Wikipedia page on it said it was about parallel computing, so I figured I'd get it, even though I think I'll be using OpenMP for the purposes it fills. Guess what? There's another license to agree to!
12. Java, I chose yes... and I'm starting to remember that I'm only getting this compiler so I can compile one already-made program once and then it expires in two weeks... accept another license...
13. Hey, now it's finally installing!
14. Do you wish to update/create links in the 2012 directory? (y/n) I picked y
15. It then installs all that extra crap I agreed to...
16. Do you wish to install MPICH1? (y/n) Since I'm already installing everything, y
17. Remote execution method? (rsh,ssh) ssh
18. Do you want the files in the install directory to be read-only? (y/n) y
Installation complete.
Celebrate!
And then test it
phil@ubuntu:~/pgi$pgf90 No command 'pgf90' found, did you mean: Command 'pdf90' from package 'pdfjam' (universe) pgf90: command not found Nooooooooooo Don't panic, bash just doesn't know where to find it yet. Let's try it with the absolute path: phil@ubuntu:~/pgi$ /opt/pgi/linux86-64/12.4/bin/pgf90
pgf90-Warning-No files to process
Ok, now is the time to celebrate.
I decided not to bother adding that directory to my PATH or anything, since I just need it for this one build. So we're done!
No, not actually. We need to get our license files.
Get the hostid by opening a terminal and typing ifconfig eth0. My output looked like this:
phil@ubuntu:/opt/pgi/linux86-64/12.4/bin$/sbin/ifconfig eth0 eth0 Link encap:Ethernet HWaddr 00:0c:29:30:4c:1e inet addr:192.168.65.128 Bcast:192.168.65.255 Mask:255.255.255.0 inet6 addr: fe80::20c:29ff:fe30:4c1e/64 Scope:Link UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1 RX packets:608040 errors:0 dropped:0 overruns:0 frame:0 TX packets:310314 errors:0 dropped:0 overruns:0 carrier:0 collisions:0 txqueuelen:1000 RX bytes:913047840 (913.0 MB) TX bytes:17318408 (17.3 MB) It's that HWaddr part that we need, in my case 00:0c:29:30:4c:1e. Keep that code handy, and head over to https://www.pgroup.com/license/trialkey.php and copy it in. You should get a page with a link called "Save trial keys as a file on my computer". Click it, and you should be presented with the option to save a file called license.dat. Save it. Now move it to the right place... sudo cp ~/Downloads/license.dat /opt/pgi/license.dat (you may have to enter a password for sudo, since /opt is protected) And now, finally, at long last, we're there. Done. ## Installing SBDART ### Get the code Get the SBDART source code. It's all in one file. Either right-click that link and Save link as..., or open it up in the browser, and then select File -> Save As.... Save it somewhere convenient, like on your desktop. Or somewhere better, like inside a folder called sbdart in your home directory. ### Compile SBDART If you don't already have a terminal open, hit ctrl-alt-t to get one. Navigate to the directory where you put the sbdart code (so cd ~/Desktop if you saved it on the desktop, or cd ~/sbdart if you saved it in a folder called sbdart in your home directory. If this is confusing, you may wish to brush up on your linux terminal skills.) I like to double-check I'm in the right place by typing ls, which should simply return sbdart.f if you're in the right directory (there may be other things listed there as well, just make sure sbdart.f is in there!). To compile sbdart, enter this command: f77 sbdart.f -o sbdart It should output a couple hundred lines of stuff very quickly to the terminal, and then leave you back at a prompt after a couple moments. Get a directory listing again to see if it worked (ls), and if you now see sbdart sbdart.f, then you're done! ## Installing SMARTS SMARTS is a little trickier than SBDART to get up and running (the source code is more than just a single file like SBDART!), but still very simple. ### Grab the code First you'll need to register with NREL. They'll email you a username and password to download the source. Then you can grab the code here. At this time of writing, the current version is 2.9.5, which is available for linux in a 3MB .tar.gz file. ### Make it go Extract that file somewhere, like say a new folder called smarts in your home directory. Make the executable, executable! After I extracted SMARTS, I found I couldn't execute the program. This is what my try looked like: phil@ubuntu:~/smarts/SMARTS_295_Linux$ ./smarts295
bash: ./smarts295: No such file or directory
Bizarre. It's there -- I can see it with ls. ll shows that it's set to executable, so doing chmod +x smarts295 had no effect. I don't know why it doesn't work, but they give us the source code, so grab the gfortran compiler (see above) and let's go!
Navigate into the Source_code directory. For me that meant
cd ~/smarts/SMARTS_295_Linux/Source_code
Compile
gfortran smarts295.f -o smarts
It should complete in a couple moments. Move our new executable back out of the Source_code folder
mv smarts ../
Go up a level to try it out...
cd ../
./smarts
phil@ubuntu:~/smarts/SMARTS_295_Linux$./smarts *********************************** Welcome to SMARTS, version 2.9.5! ***********************************$ SMARTS_295> Use standard mode with default input file?
[If YES (or Y), execution will start immediately
using the default input file smarts295.inp.txt]
(Y/N) ==>
Hooray, we're done, it seems to work!
## Installing RRTM
There are four versions of RRTM, as you can see here. We wanted the Short-Wave version, and the stand-alone model, so RRTM_SW. Get the code via the Code and Examples link on the left frame. Here is a direct link to that page (it's frame-less so that link loses all the page navigation).
Grab the source code and makefiles. They'll prompt you for your email address, name, etc. If you really don't want to part with that info, they don't validate the fields (you could just enter a, b, c. But be nice).
Extract that archive somewhere. I made a new folder in my home directory called (you guessed it) rrtm.
Copy the appropriate makefile up a level in order to use it
phil@ubuntu:~$cd ~/rrtm/rrtm_sw/makefiles phil@ubuntu:~/rrtm/rrtm_sw/makefiles$ cp make_rrtm_sw_linux_pgi ../
phil@ubuntu:~/rrtm/rrtm_sw/makefiles$cd ../ phil@ubuntu:~/rrtm/rrtm_sw$ ls
linux_pgi_pgf90_dbl.o make_rrtm_sw_linux_pgi src
makefiles rrtm_sw_instructions update_rrtm_sw_v2.5.txt
At this point make sure you've installed the PGLinux Fortran compiler. See a couple sections up in this document for help with that.
If you remember, bash didn't know where to find the executable pgf90 after we installed it, and since we haven't fixed that issue, it's easier to just edit the makefile. Lets open it up in gedit:
phil@ubuntu:~$cd ~/rrtm/rrtm_sw/ phil@ubuntu:~/rrtm/rrtm_sw$ gedit make_rrtm_sw_linux_pgi
Now find the lines where it says FC = pgf90 and CDOTO = $(PLATFORM)_$(FC)_dbl.o
###############################
# Set variables
###############################
PLATFORM = linux_pgi
VERSION = v2.5
FC = pgf90
FCFLAG = -fast -r8 -i8
OUTPUT = rrtm_sw_$(PLATFORM)_$(VERSION)
CPATH = src
CDOTO = $(PLATFORM)_$(FC)_dbl.o
And change them to FC = /opt/pgi/linux86-64/12.4/bin/pgf90 and CDOTO = $(PLATFORM)_pgf90_dbl.o, respectively. ############################### # Set variables ############################### PLATFORM = linux_pgi VERSION = v2.5 FC = /opt/pgi/linux86-64/12.4/bin/pgf90 FCFLAG = -fast -r8 -i8 OUTPUT = rrtm_sw_$(PLATFORM)_$(VERSION) CPATH = src CDOTO =$(PLATFORM)_pgf90_dbl.o
And finally....
phil@ubuntu:~/rrtm/rrtm_sw$make -f make_rrtm_sw_linux_pgi ----------------- rrtm_sw_linux_pgi_v2.5 Makefile ----------------- This Makefile was designed for the linux_pgi platform. It uses the /opt/pgi/linux86-64/12.4/bin/pgf90 compiler, with the following options: -fast -r8 -i8 The object files used are as follows: rrtm.o RDI1MACH.o rtrdis.o rrtatm.o setcoef.o taumoldis.o ErrPack.o util_linux_pgi.o extra.o LINPAK.o disort.o cldprop.o k_g.o rrtm_sw_linux_pgi_v2.5 make in progress ... NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. PGF90-W-0155-The type of FLOAT is now double precision with -r8 (src/setcoef.f: 140) 0 inform, 1 warnings, 0 severes, 0 fatal for setcoef NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.45 hours. PGF90-W-0155-The type of FLOAT is now double precision with -r8 (src/disort.f: 473) 0 inform, 1 warnings, 0 severes, 0 fatal for disort NOTE: your trial license will expire in 14 days, 7.45 hours. NOTE: your trial license will expire in 14 days, 7.44 hours. PGF90-W-0155-The type of FLOAT is now double precision with -r8 (src/cldprop.f: 155) 0 inform, 1 warnings, 0 severes, 0 fatal for cldprop NOTE: your trial license will expire in 14 days, 7.44 hours. NOTE: your trial license will expire in 14 days, 7.44 hours. NOTE: your trial license will expire in 14 days, 7.44 hours. ================= Makefile done ================= phil@ubuntu:~/rrtm/rrtm_sw$ ls
linux_pgi_pgf90_dbl.o make_rrtm_sw_linux_pgi~ src
makefiles rrtm_sw_instructions update_rrtm_sw_v2.5.txt
make_rrtm_sw_linux_pgi rrtm_sw_linux_pgi_v2.5
phil@ubuntu:~/rrtm/rrtm_sw\$ ./rrtm_sw_linux_pgi_v2.5
INVALID INPUT_RRTM
WOOOOOOOOOOOOHOOOOOOOOOOO!!!! Now is celebration time.
Page data
Authors Philip Schleihauf 2012 CC-BY-SA-4.0 No main image Philip Schleihauf (2012). "Installing RTM Software on Linux". Appropedia. Retrieved August 9, 2022.
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http://www.physicsforums.com/showthread.php?p=2442736 | # Lorentz contraction
by matheinste
Tags: contraction, lorentz
P: 687
Quote by matheinste All this emphasises my point. With such levels of disagreement, quote and counter quote, reference and counter reference do not help or give any learners confidence in the answers. A clear and carefully presented analysis should speak for itself. The answer cannot depend on who we care to believe. Break or not break is a discusson I would not get involved in. With such "eminent" names being cited as references with different conclusions no-one would, or should, take notice of anything someone at my level has to say. Matheinste.
I was aware of the fracture for solving this problem.
I gave both sides to the problem, one by doing the integral in the instantaneous frame of the rockets and rope here
http://www.mathpages.com/home/kmath422/kmath422.htm
And, the other by viewing the problem from the launch frame using the constant acceleration equations of SR here
http://math.ucr.edu/home/baez/physic...SR/rocket.html
http://arxiv.org/PS_cache/physics/pd.../0411233v1.pdf
http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf
Then, I began analyzing the problem but Jesse does not want me to so I am going to stop.
P: 1,060
Quote by cfrogue I was aware of the fracture for solving this problem. I gave both sides to the problem, one by doing the integral in the instantaneous frame of the rockets and rope here http://www.mathpages.com/home/kmath422/kmath422.htm And, the other by viewing the problem from the launch frame using the constant acceleration equations of SR here http://math.ucr.edu/home/baez/physic...SR/rocket.html http://arxiv.org/PS_cache/physics/pd.../0411233v1.pdf http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf Then, I began analyzing the problem but Jesse does not want me to so I am going to stop.
Hello cfrogue,
I can asure you that my remarks were not aimed at you personally. I was commenting generally on the confusion amomg people, many of which I assume, are well versed in relativity.
My position is that from what I have read I believe that the correct answer is that the string breaks. However, I am as yet not confident in my ability to explain the reasons to anyone else, which of course is the acid test of understanding. I am also aware that there are variations on the scenario and so we may not all be singing from the same songbook.
Matheinste.
P: 8,430
Quote by cfrogue Obviously, I was talking about the instantaneous frame of the rockets.
That wasn't too obvious, because earlier you had suggested you wanted to focus on the launch frame when you said: "But, the launch frame in and of itself presents a problem." And "instantaneous frame of the rockets" is still too vague, the instantaneous frame at any given instant is an inertial frame so there will be no gravitational force in this frame, I think what you really mean is an accelerating frame whose definitions of distance and simultaneity at each moment match those of the instantaneous inertial frame at the same moment.
Quote by cfrogue And, these are not my ideas.
I never suggested the idea of gravity in an accelerating frame was "your idea", but it is your own reasoning that leads you to the conclusion there is some doubt about whether the string breaks, since you have not pointed to any papers that mirrored your argument that the original paper failed to consider the "back side" (and you still haven't explained what you meant by that phrase), or that there is any disagreement among physicists that the string will break in the standard version of the problem.
Quote by cfrogue Well, the article did not state that CERN changed its mind. Further, I am not in a position to claim that CERN would look at a problem casually. Finally, there is no literature that I am aware of that says CERN backed away from its decision on the rope.
You're talking as though "CERN" as an institution issued some official position about the rope not breaking, but this is obviously not the case--the article clearly states that Bell just took an "informal and non-systematic" poll of his colleagues at CERN, and that most of them thought it wouldn't break. He adds that many of them changed their mind (i.e. 'backed away from their decision') after further reflection, and I also quoted a paper that said "Though many of Bell's CERN colleagues originally thought the thread would not break, it is now universally agreed that it, indeed, will."
If you think there is any dispute among modern physicists about what would happen in this thought-experiment, you need to post some actual peer-reviewed literature, not a reference to an informal poll taken back when the idea was totally new. I am quite confident that there is no actual dispute about the fact that the stress increases, although as I said there could be types of accelerations where the stress increases but the string doesn't break (maybe because in certain types of accelerations the stress would approach a fixed limit rather than increasing without bound).
Quote by cfrogue Here is the x for constant acceleration. It is in the links I posted. x(t) = c^2/a ( sqrt( 1 + (a t/c)^2 ) -1 ) Now, by adding 0, ie choosing the back back to initialize at 0 and x0 for the front rocket, you can readily see the x(t) is based only on a and t from the launch frame. Thus, the launch from will not see a deviation with the distance between the rockets.
Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant.
P: 1,060
Quote by Al68 Assuming that the distance between two objects would be equal to the length of a rope stretched between them, what is the difference between "length contraction" and "space contraction"? It seems to me that if the "space between objects does not contract" then a rope stretched between them would not be contracted either. It's not like a rope would stretch between two objects in their rest frame, but only reach part way as viewed from a different frame, because the rope contracted while the distance between the objects didn't.
I think that the in LET the space between solid objects is considered not to contract and the contraction of solid objects is due to stresses or other effects between the interatomic forces. There are of course all the other complications with local time etc. required to make the theory work. In Einsteins' formulation everything contracts.
The reason I asked for confirmation of this is that some commentators on the paradox claim that the break/non-break outcomes are a result of the two differing approaches. I believe that the differing outcomes are due to faulty reasoning on the part of one side or the other. If the claims of those commentators are correct, then there would be an experimental method to decide between the formulations. If the two formulations are generally accepted, by proponents of both formulations , to be experimentally induistinguishable I would consider such claims for the reasons of the differring outcomesto be invalid.
Matheinste.
P: 687
Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant
.
This peer reviewed paper proves the string contracts and that is the reason for the string to break. See theorem 3.
http://arxiv.org/PS_cache/arxiv/pdf/...902.2032v2.pdf
P: 82
Quote by cfrogue Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant.
No - the point is that the stress in the string will be continually increasing because its length in the launch frame is remaining constant.
Imagine two rockets separated by d=1 light-second, whereby the rockets are connected by a rope. In the launch frame the rockets accelerate simultaneously up to a velocity of 0,8c and therefore the distance between the rockets will remain the same. However, because of length contraction the rope (not the distance between the rockets) tends to get contracted to $$d/\gamma=0,6$$ light-seconds. This generates stresses within the rope, so it will break.
On the other hand, the observers within the rockets will note that the acceleration of the rockets was not simultaneous, so the calculation shows that after the acceleration the distance between the rockets is increased to $$d\cdot\gamma=1,67$$ light-second. Now, because the proper length of the rope is still 1 light-second, the rope will also break in the (new) rocket-frame.
So in both frames the rope will break.
Regards,
P: 687
Quote by Histspec No - the point is that the stress in the string will be continually increasing because its length in the launch frame is remaining constant. Imagine two rockets separated by d=1 light-second, whereby the rockets are connected by a rope. In the launch frame the rockets accelerate simultaneously up to a velocity of 0,8c and therefore the distance between the rockets will remain the same. However, because of length contraction the rope (not the distance between the rockets) tends to get contracted to $$d/\gamma=0,6$$ light-seconds. This generates stresses within the rope, so it will break. On the other hand, the observers within the rockets will note that the acceleration of the rockets was not simultaneous, so the calculation shows that after the acceleration the distance between the rockets is increased to $$d\cdot\gamma=1,67$$ light-second. Now, because the proper length of the rope is still 1 light-second, the rope will also break in the (new) rocket-frame. So in both frames the rope will break. Regards,
Here is a peer reviewed paper just published Oct 18, 2009
Bell’s paradox was that his intuition told him the cable would break, yet there was no change in the distance between the ships in system S. He suggested resolving the paradox by stating that a cable between the ships would shorten due to the contraction of a physical object proposed by Fitzgerald and Lorentz, while the distance between the ships would not change. This resolution however contradicts special relativity which allows no such difference in any measurement of these two equal lengths.
Conclusion:
For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between
them continually increases.
http://arxiv.org/PS_cache/arxiv/pdf/...906.1919v2.pdf
P: 82
Quote by cfrogue Here is a peer reviewed paper....
Arxiv preprints are not necessarily "peer reviewed".
P: 687
Quote by Histspec Arxiv preprints are not necessarily "peer reviewed".
Oh.
How do you tell if they are not reviewed?
Mentor P: 15,575 If they don't also show up in a peer-reviewed journal.
PF Patron Sci Advisor P: 1,772 In the case of the article in question http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)
P: 687
Quote by DrGreg In the case of the article in question http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)
I have a question.
From what I have seen, all calculations agree the launch frame observer believes there is no distance differential between the two ships.
Is this correct as far as you know?
P: 1,060
Quote by DrGreg In the case of the article in question http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)
On page 3 the author seems to be using the fact that Lorentz transforms (coordinate transforms) do not induce stress in an object as proof that Lorentz contraction, in the original Lorentzian use of the term, do not either.-----"-One other point to be considered is whether strains and stresses can be induced by Lorentz contraction, as is contended in Refs. [1,2,4,5]. Our answer to this is clear from the previous discussion. Just as a 3D rotation of an object does not induce strain, a 4D rotation (Lorentz transformation) will not induce strain and consequent stress."--------
Also the fact that he describes the apparent relativistic contraction of length as illusory is a bit unusual.-------"And, just as the “shortening” of a stick that is rotated in three dimensions is an illusion, we now can see that the “shortening” of a stick that is rotated in four dimensions by a Lorentz transformation is also illusory."----------
I have not read the rest of the article closely yet but the above points disturb me a little.
Of course it may just be my reading of the text that is in error.
Matheinste.
P: 8,430
Quote by cfrogue
Quote by JesseM Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant.
This peer reviewed paper proves the string contracts and that is the reason for the string to break. See theorem 3.
http://arxiv.org/PS_cache/arxiv/pdf/...902.2032v2.pdf
I don't know what you mean by "theorem 3"--what page are you looking at? In any case, looking over the paper, in equation 3.12 at the bottom of p. 11 they explicitly show that the length of the string does not change in the frame where the ships have identical coordinate accelerations (and started accelerating simultaneously). I'm sure you won't find any physicists who dispute this very obvious and trivial point.
Quote by cfrogue Here is a peer reviewed paper just published Oct 18, 2009 Bell’s paradox was that his intuition told him the cable would break, yet there was no change in the distance between the ships in system S. He suggested resolving the paradox by stating that a cable between the ships would shorten due to the contraction of a physical object proposed by Fitzgerald and Lorentz, while the distance between the ships would not change. This resolution however contradicts special relativity which allows no such difference in any measurement of these two equal lengths. Conclusion: For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between them continually increases. http://arxiv.org/PS_cache/arxiv/pdf/...906.1919v2.pdf
This paper does not dispute Bell's claim that the cable would break! Instead it calls for a rethinking of the reason the cable breaks...the author's argument seems to be that the only physical way of defining an object's length is by looking at its own rest frame, so that treating "length contraction" as a change in length is overly confusing...from p. 3:
This suggests the need for a definition of “length” that is the same for any state of uniform motion. This would correspond to the use in relativity of “proper time” and “invariant mass” for time and mass, but the terms “proper length” and “invariant length” have already been used in the literature with other meanings. The term we recommend for length is “rest frame length”, which we define as the length a moving object has after a Lorentz transformation to its rest system. If length is to be considered a physical attribute of an object, then this physical attribute should be the rest frame length. This length, of course, would not be changed by uniform motion.
The author then points out that the "rest frame length" of the cable or string does grow as the ships accelerate, even though the distance between them in the observer's frame does not change, and that this should be seen as the true reason a cable or string would break, not length contraction:
Although the spaceships are accelerating, the system S′ is a Lorentz system moving at constant velocity. Since each ship is instantaneously at rest in this system, the length d′ = gamma*d is the rest frame distance between the ships. As such, it is the physical distance between the ships. If there were an inextensible cable between the ships, it would snap at the start of motion of the ships. An elastic cable would stretch until it reached its maximum possible length dMax, at which point it would snap.
PF Patron
P: 1,772
Quote by cfrogue I have a question. From what I have seen, all calculations agree the launch frame observer believes there is no distance differential between the two ships. Is this correct as far as you know?
Yes.
There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18.
If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest).
Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break.
I think this agrees with what everyone else has been saying in this thread and what the quoted paper says.
There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is).
P: 687
Quote by DrGreg Yes. There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18. If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest). Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break. I think this agrees with what everyone else has been saying in this thread and what the quoted paper says. There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is).
OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame?
In other words, does the launch frame conclude the distance does not change yet the string contracts?
P: 8,430
Quote by cfrogue OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame? In other words, does the launch frame conclude the distance does not change yet the string contracts?
In the launch frame the string won't experience any change in length until it snaps. As I've said, the stress in the string will increase though. I think when people cite "Lorentz contraction" as an explanation for the string breaking, what they're getting at is that the string "wants" to contract but can't because it's attached to the ships...it may be easier to make sense of this if we think of a spring rather than a string, since you may remember from classical mechanics that springs have a "rest length" that they naturally assume when nothing is pulling or pushing on them (the rest length minimizing the stress in the spring), and that when they are pulled to a greater length than the rest length they pull back with greater and greater force, as if they are "trying" to return to that length (and obviously if you pull a spring far enough past its rest length, it'll snap). If you had two identical springs traveling alongside each other, one attached to the two ships and one with its ends free whose length was equal to its rest length, then the length of the free spring would grow shorter and shorter as seen by the launch frame as its velocity increased, which implies that the spring attached to the ships, whose length does not change in this frame, is being extended farther and farther past its own natural rest length.
P: 687
Quote by JesseM In the launch frame the string won't experience any change in length until it snaps. As I've said, the stress in the string will increase though. I think when people cite "Lorentz contraction" as an explanation for the string breaking, what they're getting at is that the string "wants" to contract but can't because it's attached to the ships...it may be easier to make sense of this if we think of a spring rather than a string, since you may remember from classical mechanics that springs have a "rest length" that they naturally assume when nothing is pulling or pushing on them (the rest length minimizing the stress in the spring), and that when they are pulled to a greater length than the rest length they pull back with greater and greater force, as if they are "trying" to return to that length (and obviously if you pull a spring far enough past its rest length, it'll snap). If you had two identical springs traveling alongside each other, one attached to the two ships and one with its ends free whose length was equal to its rest length, then the length of the free spring would grow shorter and shorter as seen by the launch frame as its velocity increased, which implies that the spring attached to the ships, whose length does not change in this frame, is being extended farther and farther past its own natural rest length.
Well, the SR acceleration equations indicate the distance between ther ships will not change.
From the POV of the rest observer, what is the math to indicate the space remains constant but a rod will contract if allowed between the two ships.
All these links show what happens from the POV of the accelerating ships.
I want to concentrate on the math from the rest/launch frame's POV.
Also, this paper seems to say something different.
4 Conclusion
We have seen that the physical length of an object is the rest frame length as
measured in the instantaneous rest frame of the object. For two spaceships
having equal accelerations, as in Bell’s spaceship example, the distance between
the moving ships appears to be constant, but the rest frame distance between
them continually increases. This means that a cable between the two ships must
eventually break if the acceleration continues.
http://arxiv.org/PS_cache/arxiv/pdf/...906.1919v2.pdf
Related Discussions Special & General Relativity 9 Special & General Relativity 8 Special & General Relativity 64 Introductory Physics Homework 4 General Physics 13 | 2013-12-08 18:44:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5112828612327576, "perplexity": 600.2513591016881}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163791972/warc/CC-MAIN-20131204132951-00026-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/732746/integrating-sinx-on-a-unit-circle | Integrating sin(x) on a unit circle
I am trying to integrate $\int\int_{D} sin(x)$ where $D$ is a unit circle centered at $(0,0)$.
My approach is to turn the area into the polar coordinate so I have $D$ as $0\leq r\leq1$ , $0 \leq \theta \leq 2\pi$.
Which turns the integral into:
$$\int^{2\pi}_{0}\int^{1}_{0} \sin(r\cos(\theta)) |r| drd\theta$$ and it is not integrable.
I also tried the Cartesian approach by evaluating:
$$\int^{1}_{0}\int^{\sqrt{1-x^2}}_{0} \sin(x) dydx$$ which is also not integrable
Which direction or method should I use to integrate this problem?
Edit* Thank you so much for the answers, I agree that because of symmetry, the answer is zero. The hint says don't do too work work also lol.
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What about symmetry considerations...? – Andrew D. Hwang Mar 30 '14 at 17:36
Aside: $D$ is the unit disc: the unit circle is the loop around the boundary of the disc. – Hurkyl Mar 30 '14 at 18:53
UW questions....lol – Jing Apr 3 '14 at 15:45
2 Answers
By symmetry, the integral is $0$.
Remark: In the Cartesian version, the integral of the post integrates over the quarter disk in the first quadrant.
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Thank you! I appreciate your answer. – tkhu Mar 30 '14 at 20:40
You are welcome. – André Nicolas Mar 30 '14 at 20:49
Additional: From a complex analysis approach we have $\int_{|z|=1} \sin(z) \ dz = 0$, since $f(z)=\sin(z)$ is analytic on the unit circle.
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Thank you for your answer, it's great to have a deeper understanding of the question too. – tkhu Mar 30 '14 at 20:42 | 2016-07-02 04:08:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.946522057056427, "perplexity": 488.9792785174059}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783404826.94/warc/CC-MAIN-20160624155004-00057-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/386129/horizontal-spacing-commands | # Horizontal spacing commands
What is the difference between math mode horizontal spacing and text mode horizontal spacing?
Actually, I want to understand, why are few commands used in math mode only (say : and \;) while commands like \quad , \qquad are used in math mode as well as in text mode?
Spacing commands for text mode can also be used in math mode, but not conversely, unless you load amsmath (for a couple of them).
The LaTeX kernel defines \, \: and \; for \mskip\thinmuskip, \mskip\medmuskip and \mskip\thickmuskip respectively. For reference
• \, is the space between an ordinary symbol and an operator or conversely (like in 2\sin x) or after a punctuation symbol;
• \: is the space around a binary operation symbol (like in a+b);
• \; is the space around a relation symbol (like in a>b).
However, the LaTeX kernel defines \, to be also used in text mode, inserting a kern of width 0.1667em (3/18-th of an em). If amsmath is loaded, also \: and \; can be used in text mode, inserting kerns of 0.2222em (4/18-th of an em) and 0.2777em (5/18-th of an em). These width are the same natural widths of the math mode spacings, expressed in em units (but the em can differ).
Specific math mode spacing indeed uses mu units, where 18mu is the same as 1em in the math symbol font. Such units can only be used as arguments to \mskip or \mkern, which is legal only in math mode. On the other hand, standard units and \hskip or \kern can appear in math mode as well as in text mode (and em will refer to the font current when math mode was started).
This explains why \quad and \qquad can be used in math mode: they will add 1em of space referring to the current text font. In some rare occasions \hspace can turn out to be useful (notice the emphasis, though). | 2020-02-18 21:11:44 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9934836030006409, "perplexity": 2797.0624562336548}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143815.23/warc/CC-MAIN-20200218210853-20200219000853-00333.warc.gz"} |
http://mathoverflow.net/feeds/question/15041 | Is there a matrix C so that the trace of C^n is dense in R? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T10:18:51Z http://mathoverflow.net/feeds/question/15041 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/15041/is-there-a-matrix-c-so-that-the-trace-of-cn-is-dense-in-r Is there a matrix C so that the trace of C^n is dense in R? Hej 2010-02-11T22:16:46Z 2010-02-12T08:45:56Z <p>I am looking for a matrix C so that the sequence tr(C^n) is dense in the set of real numbers. Equivalently (in the 2 by 2 case), find a complex number z so that the sequence z^n+w^n is dense in R where w is the conjugate of z. </p> http://mathoverflow.net/questions/15041/is-there-a-matrix-c-so-that-the-trace-of-cn-is-dense-in-r/15042#15042 Answer by Richard Kent for Is there a matrix C so that the trace of C^n is dense in R? Richard Kent 2010-02-11T22:26:47Z 2010-02-12T01:12:17Z <p>(Oops, the rescaling part is bogus in the below. So this only works for C with determinant 1.)</p> <p>In the 2-by-2 case, the answer is no. (Something like this argument should go through in general).</p> <p>After rescaling, we can assume the matrix has determinant 1. If C is elliptic (real trace between -2 and 2), then all powers are elliptic, so that's no good. If it's parabolic (trace equal to -2 or 2), then all powers all parabolic, again no good. If it's loxodromic, the traces of the powers have real part going to infinity with n, and so they can't be dense.</p> http://mathoverflow.net/questions/15041/is-there-a-matrix-c-so-that-the-trace-of-cn-is-dense-in-r/15052#15052 Answer by Victor Miller for Is there a matrix C so that the trace of C^n is dense in R? Victor Miller 2010-02-11T23:37:02Z 2010-02-11T23:54:33Z <p>In answer to the question as to whether $\text{tr}(C^n)$ is dense in $(-2,2)$: Choose $z=\exp(2 \pi i \theta)$ where $\theta$ is irrational, and let $C$ be the diagonal matrix with $z$ and $\overline{z}$ on the diagonal. By Weyl's criterion , the fractional parts of $n \theta$ are equidistributed modulo 1, and thus <code>$\{z^n\}$</code> is dense in the unit circle. From this it follows easily that $\text{Re}(z^n)$ is dense in $(-1,1)$.</p> http://mathoverflow.net/questions/15041/is-there-a-matrix-c-so-that-the-trace-of-cn-is-dense-in-r/15056#15056 Answer by Bjorn Poonen for Is there a matrix C so that the trace of C^n is dense in R? Bjorn Poonen 2010-02-12T00:39:58Z 2010-02-12T00:45:26Z <p>The answer is yes, even in the $2 \times 2$ case. Let $q_1,q_2,\ldots$ be an enumeration of the rational numbers. Let $Q_j$ be the closed interval $[q_j-1/j,q_j+1/j]$. Let $I_0=[0,2\pi]$. Let $z=2e^{i \theta}$ for a $\theta \in I_0$ to be determined.</p> <p>By induction, we construct positive integers $n_1 < n_2 < \ldots$ and closed intervals $I_0 \supseteq I_1 \supseteq \cdots$ such that for each $j$, the trace $z^{n_j} + \bar{z}^{n_j}$ is in $Q_j$ whenever $\theta \in I_j$. Namely, if $n_1,\ldots,n_{j-1},I_1,\ldots,I_{j-1}$ have been determined already, then for any sufficiently large $n_j$, the set of $\theta$ such that $z^{n_j} + \bar{z}^{n_j}$ is in $Q_j$ is a union of closed intervals such that every real number is within $2\pi/n_j$ of a point inside this union and within $2\pi/n_j$ of a point outside this union, so if $n_j$ is chosen large enough, one such interval in this union will be completely contained in $I_{j-1}$ and we name it $I_j$.</p> <p>The intersection of a descending chain of closed intervals is nonempty, so we can choose $\theta$ such that $\theta \in I_j$ for all $j$. Then $\lbrace z^n+\bar{z}^n : n \ge 1 \rbrace$ contains an element of $Q_j$ for each $j$, so it is dense in $\mathbb{R}$.</p> http://mathoverflow.net/questions/15041/is-there-a-matrix-c-so-that-the-trace-of-cn-is-dense-in-r/15061#15061 Answer by George Lowther for Is there a matrix C so that the trace of C^n is dense in R? George Lowther 2010-02-12T01:36:46Z 2010-02-12T01:50:37Z <p>Bjorn has already answered this question in the affirmative, and shown that such matrices do exist. I'd like to add a further comment here though - 'almost no' matrices satisfy the required property. That is, the collection of 2x2 matrices such that Tr(C^n) is dense in R has zero Lebesgue measure.</p> <p>We know that Tr(C^n) = a^n + b^n where a,b are the roots of the characteristic polynomial of C. If a and b are both real then it is not possible for C to have the required property. The only possibility is where they are complex conjugates, a = r exp(iθ), b = r exp(-iθ) for r >1. Then, Tr(C<sup>n</sup>)=2rcos(nθ). Suppose that θ is uniformly distributed over [-π,π], so that exp(inθ) is uniformly distributed on the unit circle for each n. For any positive K, |Tr(C^n)|<K is equivalent to |cos(nθ)|<r<sup>-n</sup>K/2. The set of values of exp(inθ) for which this holds forms a pair of arcs of length r<sup> -n</sup>K (to leading order). So,</p> <p>$$\mathbb{P}(\vert{\rm Tr}(C^n)\vert\lt K)\approx r^{-n}K/\pi$$</p> <p>to leading order. Summing over n, this is finite. Then, the <a href="http://en.wikipedia.org/wiki/Borel%E2%80%93Cantelli%5Flemma" rel="nofollow">Borel-Cantelli lemma</a> says that, with probability one, |Tr(C<sup>n</sup>)|<K only finitely often. So, with probability 1, |Tr(C<sup>n</sup>)| diverges to infinity.</p> | 2013-05-22 10:18:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9582867622375488, "perplexity": 411.00705966918696}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368701577515/warc/CC-MAIN-20130516105257-00055-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/270325?ln=en | Formats
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Abstract
The production fractions of (B) over bar (0)(s) and Lambda(0)(b) hadrons, normalized to the sum of B- and (B) over bar (0) fractions, arc measured in 13 TeV pp collisions using data collected by the LHCb experiment, corresponding to an integrated luminosity of 1.67 fb(-1). These ratios, averaged over the b hadron transverse momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are 0.122 +/- 0.006 for (B) over bar (0)(s) and 0.259 +/- 0.018 for Lambda(0)(b) where the uncertainties arise from both statistical and systematic sources. The Lambda(0)(b) ratio depends strongly on transverse momentum, while the (B) over bar (0)(s) ratio shows a mild dependence. Neither ratio shows variations with pseudorapidity. The measurements are made using semileptonic decays to minimize theoretical uncertainties. In addition, the ratio of D+ to D-0 mesons produced in the sum of (B) over bar (0) and B- semileptonic decays is determined as 0.359 +/- 0.006 +/- 0.009, where the uncertainties are statistical and systematic. | 2021-06-14 07:08:04 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9764124155044556, "perplexity": 3058.217650636639}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611445.13/warc/CC-MAIN-20210614043833-20210614073833-00377.warc.gz"} |
https://events.illc.uva.nl/FOAM/posts/talk4/ | Social Welfare Loss in Hybrid Multi-Unit Auctions
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# Social Welfare Loss in Hybrid Multi-Unit Auctions
Corruption in auctions, where an auctioneer engages in bid rigging with one (or several) of the bidders, occurs rather frequently in practice, especially in the public sector (e.g., in construction and procurement auctions). We study the social welfare loss caused by corrupt auctioneers, both in single-item and multi-unit auctions.
In our model, the auctioneer may collude with the winning bidders by letting them lower their bids in exchange for a fraction \gamma \in [0, 1] of the surplus. In the most basic corruption scheme, also known as magic number cheating, all winning bidders lower their bid to the highest losing bid. More generally, we consider corruption schemes that can be related to \gamma-approximate first-price auctions, where the payments recover at least a \gamma-fraction of the first-price payments. Our goal is to obtain a precise understanding of the robust price of anarchy (POA) of such auctions.
In this talk, we review some of the techniques to analyze the POA of auctions and discuss their applications and limits to corrupt auction schemes. We derive several (tight) bounds which provide a rather fine-grained landscape of the price of anarchy, depending on the auction setting and the equilibrium notion.
Joint work with Andries van Beek and Ruben Brokkelkamp. | 2023-03-31 11:43:23 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8177341222763062, "perplexity": 2759.4873815983483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949642.35/warc/CC-MAIN-20230331113819-20230331143819-00745.warc.gz"} |
https://dmoj.ca/problem/dmpg15b6 | ## DMPG '15 B6 - Bad S'mores
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Points: 10 (partial)
Time limit: 1.4s
Memory limit: 32M
Author:
Problem type
It is time to set up camp for the night! Bob has built a nice campfire to help everybody keep warm during the night. Every tent would like to be close to the fire, but there is one small problem — Bob's s'more ingredients were expired and many people got sick eating them. As a result, every tent should be close to the washroom as well.
The campsite can be represented as a Cartesian plane.
• The campfire is located at and can provide warmth to tents of at most distance away from the fire as the crow flies (Euclidean distance).
• The washroom is located at , and can be reached by walking along the paths on the campsite.
• The paths in the campsite form a grid, such that each path can be described as a line in the form of or , where is an integer. There is a path for every integral value of , so in total the number of paths is infinite. A tent should be within walking distance along a path (Manhattan distance), such that the distance to the washroom is less than or equal to . A tent can be set up only on an integer coordinate — such that and are integers — and cannot occupy the same position as the fire or washroom.
Can you help Bob determine the maximum amount of tents that can be set up?
#### Input Specification
The first line will contain three integers, , , and . The second line will contain another three integers, , , and . and .
For at least of the marks, and .
#### Output Specification
One integer, the maximum number of tents that can be set up so that it is within range of the fire and the washroom.
#### Sample Input
2 2 2
5 2 3
#### Sample Output
4
#### Diagram for Sample Input
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https://www.fin.gc.ca/drleg-apl/wmmNov06n_4-eng.asp | # Archived - Explanatory Notes to Legislative Proposals Relating to Income Tax: 4
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Clause 118
Manufacturing and Processing Profits Deduction
ITA
125.1
Section 125.1 of the Act provides a reduced rate of corporate tax on Canadian manufacturing and processing profits.
Manufacturing and Processing Profits Deduction
ITA
125.1(1)(b)(ii)
Subsection 125.1(1) of the Act provides the basic rules for the calculation of a corporation’s manufacturing and processing profits deduction. The deduction for a given taxation year is the lesser of two amounts, one of which is the corporation’s taxable income less certain other amounts. One of these other amounts, described in subparagraph 125.1(1)(b)(ii), is the grossed up amount of the corporation’s foreign tax credits (FTCs) for the year in respect of foreign businesses. Currently, the corporation’s FTCs are grossed up by a factor of 10/4, which assumes this income was subject to tax at a rate of 40%.
Subparagraph 125.1(1)(b)(ii) is amended to adjust this factor to reflect recent reductions to income tax rates. The new factor will be 3, which implies an assumed tax rate of 33.3% on foreign source business income.
This amendment applies to the 2003 and subsequent taxation years.
Definitions
ITA
125.1(3)
Subsection 125.1(3) of the Act defines the expression "manufacturing or processing" for the purpose of section 125.1. Paragraph 125.1(3)(l) of this definition excludes any manufacturing or processing of goods for sale or lease.
The French version of subparagraphs (l)(i) and (ii) of the definition are amended to replace the word "articles" by the word "marchandises" in order to be consistent with the terminology used in the opening words of paragraph (l) of the definition. A similar amendment is made to the French version of the definition "Canadian manufacturing and processing profits" in subsection 125.1(3).
These amendments apply on Royal Assent.
Clause 119
Resource Income
"taxable resource income"
ITA
125.11
Section 125.11 of the Act has the effect of reducing the federal corporate income tax rate for income earned from resource activities from 28% to 21% by 2007. This is accomplished for the years 2003-2006 by providing a deduction against the 28% rate for income that falls within the definition of "taxable resource income". After 2006 resource income will be included in full rate taxable income and be subject to the general rate reduction rules.
Currently, a taxpayer’s "taxable resource income" is the lesser of the taxpayer’s taxable income for the taxation year and the amount calculated by the following formula: 3(A/B) + C- D. A represents the deduction taken as a resource allowance under paragraph 20(1)(v.1). B is a reduction of the resource allowance, which is being phased out between 2003 and 2006, prorated for non-calendar year-ends. C represents additions to the taxpayer’s income resulting from negative resource pools. Lastly, D is any amounts deducted from income on account of resource pools.
The definition "taxable resource income" is being amended to ensure that resource income that was earned by a Canadian-controlled private corporation (CCPC) and received a small business deduction under section 125(1) of the Act is not also eligible for this rate reduction. The result is that a taxpayer’s "taxable resource income" will now be the lesser of two amounts. The first amount is the taxpayer’s taxable income for the year less 100/16 of the amount the taxpayer deducted from tax payable pursuant to section 125(1) of the Act. The second amount is calculated by the formula 3(A/B) + C - D - E. Elements A to D are unchanged from the previous formula contained in this definition, and remain as described above. New element E is 100/16 of the amount deducted from tax otherwise payable pursuant to subsection 125(1) of the Act. This amendment ensures that resource income earned by a CCPC can only benefit from one rate reduction.
This amendment applies to taxation years that begin after February 27, 2004.
Clause 120
Canadian Film or Video Production Tax Credit
ITA
125.4
Section 125.4 of the Act sets out the rules that apply for the purpose of computing the Canadian film or video production tax credit ("CFVPTC"). Generally, this tax credit is available at a rate of 25% of qualified labour expenditures incurred by a qualified corporation for a production certified by the Minister of Canadian Heritage to be a Canadian film or video production.
Except as noted below, the amendments to subsection 125.4 generally apply in respect of productions for which development commences on or after November 14, 2003 or the first labour expenditures (as determined under subsections 125.4(1) and (2) as they applied before that date – the "old rules") of the production corporation are incurred after 2003. As well, if development commenced before November 14, 2003 and the first labour expenditures (as defined under the old rules) were incurred by the corporation in its taxation year that includes November 14, 2003, the corporation may elect to have the new rules apply. Subject to this election, corporations must continue to claim the CFVPTC under the old rules for productions that qualified under those rules. Where, in the case of a co-production, more than one qualified corporation is eligible to claim a CFVPTC in respect of the production, the election to have the new rules apply must be made jointly. A production cannot qualify under both schemes.
Definitions
ITA
125.4(1)
"assistance"
In computing the CFVPTC, qualified labour expenditures in respect of a film or video production are limited to 48% of the amount by which the cost of the production exceeds any "assistance" in respect of that cost that has not been repaid.
The definition "assistance" is amended to provide that the equity share of a production of a government or other public authority is treated in the same manner as government assistance. This could include, for example, a loan from a government agency where repayment of the loan is dependent on profit from the production.
"Canadian film or video production certificate"
A qualified corporation must file a Canadian film or video production certificate with its tax return for a taxation year in which it claims a Canadian film or video production tax credit in respect of the production. A "Canadian film or video production certificate", as defined in subsection 125.4(1) of the Act, is issued by the Minister of Canadian Heritage. The definition is amended to provide that that Minister will also certify that the public funding of the production would not be contrary to public policy and that, generally, a qualified corporation or a related taxable Canadian corporation will retain an acceptable share of revenues from the exploitation of the production in non-Canadian markets. The Minister of Canadian Heritage will issue guidelines as to how these criteria can be met.
This amendment generally applies in respect of Canadian film or video productions for which certificates are issued by the Minister of Canadian Heritage after December 20, 2002.
The definition is also amended to remove the requirement for the Minister of Canadian Heritage to provide estimates relevant to the calculation of the CFVPTC, in respect of certificates issued after 2003.
"investor"
The definition "investor" describes a person who is not actively engaged on a regular, continuous, and substantial basis in a Canadian film or video production business carried on through a permanent establishment in Canada. A CFVPTC may not be claimed in respect of a Canadian film or video production where an investor, or a partnership in which an investor has an interest, may deduct an amount in respect of the production.
The definition of investor is repealed, applicable to taxation years that end after November 14, 2003, as well as to productions in respect of which a qualifying production corporation has, in a return of income filed before November 14, 2003, claimed an amount under subsection 125.4(3) of the Act in respect of a labour expenditure incurred after 1997 in respect of the production.
"labour expenditure"
The definition "labour expenditure" describes the underlying expenditures of a qualified corporation in respect of a film or video production that will be eligible for the CFVPTC. The definition is amended concurrently with the repeal of the definition "investor" in subsection 125.4(1) and the amendment of subsections 125.4(2) and (4) of the Act, to include those production expenditures incurred by the qualified corporation for or on behalf of another person. That is, labour expenditures are no longer limited to those included in the cost to the qualified corporation of the production. The definition is also amended concurrently with the introduction of the definition "production commencement time", which represents the time after which an eligible expenditure will qualify for the CFVPTC.
Where a particular corporation is a co-producer with another qualified corporation, and that other corporation has incurred expenditures for or on behalf of the taxpayer, new paragraph 125.4(2)(d) of the Act prevents the particular corporation from claiming a CFVPTC in respect of those expenditures.
For more information on subsections 125.4(2) and (4) and the definitions "investor" and "production commencement time", refer to the commentary for those provisions.
"production commencement time"
For the purpose of the definition "labour expenditure" in subsection 125.4(1) of the Act, in order to be eligible for the CFVPTC, expenditures in respect of a film or video production must be incurred by a qualified corporation from the time that is the "final script stage" of the production. The definition "labour expenditure" is amended to instead refer to expenditures incurred after the production commencement time. The new definition "production commencement time" describes the time that is the latest of the following:
1. The time at which a qualified corporation or its parent company first incurs development labour costs for the development of property of the corporation that is script material on which a Canadian film or video production is based.
2. The first time at which the qualified corporation or its parent company acquires a right in respect of the story that is the basis of the final script. Such rights might include a published literary work, play or screenplay.
3. Two years before the date on which principal photography of the production begins.
It is intended that the in-house development labour costs of an initial draft of a script, as well as the cost of modifications, should fall within the period of production for which labour expenditures qualify for the CFVPTC. These in-house costs could include the cost to hire an independent writer to create a script on the basis of some other story or literary work for which the rights have been acquired by the corporation.
Existing conditions on eligible labour expenditures also apply to scriptwriting labour. (See, for example, amounts excluded from the definition "salary and wages" in subsection 125.4(1) of the Act, such as amounts determined by reference to profits or revenues). As well, the cost to acquire an initial script or any other right referred to above will, like other rights, not qualify. Such an expenditure represents the cost of a property, not a labour expenditure.
The new definition "script material" in subsection 125.4(1) is defined for the purpose of the definition "production commencement time".
"qualified labour expenditure"
The definition "qualified labour expenditure" describes the portion of a qualified corporation’s labour expenditures upon which it can claim a 25% investment tax credit for a Canadian film or video production. Under a formula in the definition, qualified labour expenditures in respect of a production are limited to 48% of the amount by which the cost of the production to the qualified corporation exceeds any "assistance" in respect of that cost that has not been repaid.
Variable A in the formula is amended to increase the maximum amount of labour expenditure that qualify for the CFVPTC from 48% to 60% of the cost of the production. The definition is also amended concurrently with the repeal of the definition "investor" in subsection 125.4(1) and the amendment of subsections 125.4(2) and (4) of the Act, to include in the production cost those production expenditures incurred by the qualified corporation for or on behalf of another person. That is, production expenditures are no longer limited to those included in the cost to the qualified corporation of the production.
Where the taxpayer corporation is a co-producer with another qualified corporation, and that other corporation has incurred expenditures for or on behalf of the taxpayer, those expenditures are excluded from the formula by new paragraph 125.4(2)(b) of the Act.
For more information on subsections 125.4(2) and (4) and the definition "investor", refer to the commentary for those provisions.
"salary or wages"
For the purposes of the Canadian film and video production tax credit, the definition "salary or wages", which is generally defined in subsection 248(1) of the Act, does not include an amount described in section 7 of the Act (share option benefits) or any amount determined by reference to profits or revenues.
The definition "salary or wages" is amended to provide that it also does not include an amount paid to a person in respect of services rendered by the person at a time when the person was non-resident, unless the person was at that time a Canadian citizen.
"script material"
The new definition "script material" applies for the purpose of determining the "production commencement time" of a production. Script material is written material describing the story on which the production is based and, for greater certainty, includes a draft script, original story, screen story, narration, television production concept, outline or scene-by-scene schematic, synopsis or treatment. These descriptions are terms commonly used in the film production industry.
Rules Governing Labour Expenditure of a Corporation
ITA
125.4(2)
Subsection 125.4(2) of the Act provides rules that apply for the purpose of the definition of "labour expenditure" in subsection 125.4(1). Paragraph 125.4(2)(a) provides that remuneration does not include remuneration determined by reference to profits or revenues.
Subsection 125.4(2) is amended to provide that it also applies to the definition "qualified labour expenditure" in subsection 125.4(1). In addition, paragraph 125.4(2)(a) is amended to provide that remuneration also does not included remuneration in respect of services rendered by a person at a time when the person was non-resident, unless the person was at that time a Canadian citizen.
A film or video production may be produced jointly by two or more qualified corporations. New paragraph 125.4(2)(d) of the Act is added to ensure that only one qualified corporation may claim a CFVPTC in respect of any particular expenditure. Where another qualified corporation supplies goods to or renders services for or on behalf of the taxpayer corporation, new paragraph 125.4(2)(d) provides that the related expenditure by the taxpayer is not a labour expenditure, a cost or capital cost of the production to the taxpayer. This provision does not affect the calculation of the cost of the production for other purposes of the Act.
Exception
ITA
125.4(4)
Subsection 125.4(4) of the Act provides that a Canadian film or video production tax credit is not available for a production if an investor may deduct an amount in respect of the production in computing its income for any taxation year. An investor is defined in subsection 125.4(1) to include, generally, any person, other than a prescribed person, that does not carry on a film or video production basis in Canada on a substantial basis.
Subsection 125.4(4) is amended concurrently with the repeal of the definition "investor", to deny the CFVPTC only in circumstances where the production or a person or partnership holding an interest in the production is a tax shelter investment for the purpose of section 143.2 of the Act.
However, section 1106 of the Income Tax Regulations includes a requirement that, for a film or video production to qualify as a Canadian film or video production eligible for the CFVPTC, a prescribed taxable Canadian corporation must retain worldwide ownership of copyright.
This amendment applies to taxation years that end after November 14, 2003, or if a qualifying production corporation has, in a return of income filed before November 14, 2003, claimed an amount under subsection 125.4(3) in respect of a labour expenditure incurred after 1997 in respect of the production.
Revocation of a Certificate
ITA
125.4(6)
Subsection 125.4(6) of the Act provides that a Canadian film or video production certificate in respect of a production may be revoked by the Minister of Canadian Heritage. The revocation of a certificate may occur if an incorrect statement or an omission was made in order to obtain the certificate, or if the production is not a Canadian film or video production. A revoked certificate is considered never to have been issued, so a Canadian film or video production tax credit under new subsection 125.4(3) cannot be claimed in respect of the decertified production.
Subsection 125.4(6) is amended, applicable after November 14, 2003, to clarify that a Canadian film or video production certificate may be revoked in respect of one episode of a television series without affecting the eligibility of other episodes in the series and that, in such a case, the expenditures attributable to that episode do not qualify for the CFVPTC.
Guidelines
ITA
125.4(7)
New subsection 125.4(7) of the Act, which applies in respect of Canadian film or video productions for which certificates are issued by the Minister of Canadian Heritage after December 20, 2002, requires the Minister of Canadian Heritage to issue guidelines respecting the circumstances under which new conditions in the definition "Canadian film or video production certificate" in subsection 125.4(1) are met. For further details, see the commentary for that definition.
Clause 121
Foreign Tax Credit
ITA
126(2.22)
The French version of subsection 126(2.22) of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. These amendments will come into force on Royal Assent.
Foreign Tax Credit – Dispositions Ignored
ITA
126(4.4)
Subsection 126(4.4) of the Act directs that certain dispositions and acquisitions of property be ignored for the purposes of the foreign tax credit limitations in subsections 126(4.1) and (4.2) and the definition of "economic profit" in subsection 126(7). As a consequence of the restructuring of section 132.2 of the Act, the reference in paragraph 126(4.4)(a) to paragraph 132.2(1)(f) is replaced by a reference to section 132.2.
This amendment applies to dispositions and acquisitions that occur after 1998 except that, in applying paragraph 126(4.4)(a) of the Act to dispositions and acquisitions that occur before June 28, 1999, that paragraph is to be read without reference to subsections 10(12), 10(13), 14(14) and 14(15) of the Act.
Rules of Construction
ITA
126(6)(d)
Section 126 of the Act permits a taxpayer to claim a foreign tax credit. Subsection 126(1) sets out the rules for claiming the credit in respect of foreign non-business-income tax – that is, the foreign taxes imposed on investment income and other categories of foreign source non-business income. A credit in respect of foreign taxes on business income is provided under subsection 126(2).
New paragraph 126(6)(d) applies to amounts received after February 27, 2004.
Clause 122
ITA
126.1
Section 126.1 of the Act provides certain employers with a refundable tax credit to offset the increase in the employer’s portion of 1993 unemployment insurance premiums.
This section has lapsed, and is repealed in respect of forms filed after March 20, 2003.
Clause 123
Deductions in Computing Tax
ITA
127
Section 127 of the Act permits deductions in computing tax payable in respect of logging taxes, political contributions and investment tax credits.
Logging Tax Deduction
ITA
127(2)
The amendments to the French version of subsection 172(2) of the Act correct a grammatical error. In this subsection, the expression "revenu tiré pour l’année des opérations forestières dans la province" has the meaning set out in the Regulations. However, the expression that appears in the Regulations is "revenu tiré pour l’année d’opérations forestières dans la province", which is grammatically correct. The Act is therefore amended accordingly on Royal Assent.
Contributions to Registered Parties and Candidates
ITA
127(3)
Subsection 127(3) of the Act provides a tax credit to a taxpayer in respect of amounts contributed to a registered party or to a candidate. Subsection 127(3) is amended consequential to the addition of new subsections 248(31) and (32) of the Act, to provide that the amount of a contribution that is eligible for the political contributions tax credit is to be reduced by the amount of any advantage or benefit, as defined by subsection 248(32), to which the taxpayer is entitled in respect of the contribution. This amendment is generally applicable to monetary contributions made after December 20, 2002.
It is proposed that subsections 2000(1) and (6) of the Regulationsbe amended to provide that every official receipt issued by a registered party in respect of a contribution contain, in addition to the information already prescribed, the eligible amount and the amount of the advantage, if any, in respect of the contribution.
For additional details, see the commentary to new subsections 248(31) and (32) regarding the amount of the advantage in respect of a contribution.
Allocation of Amount Contributed Among Partners
ITA
127(4.2)
Subsection 127(4.2) of the Act allows the tax benefits of political contributions made by a partnership to be flowed through to its members. Subsection 127(4.2) is amended consequential to the amendment of subsection 127(3) of the Act, applicable to contributions made after December 20, 2002, to provide the amount of a contribution that is eligible for a tax credit because of a taxpayer’s membership in a partnership.
Investment Tax Credits
ITA
127(5) to (35)
Subsections 127(5) to (35) of the Act provide rules concerning investment tax credits.
Recapture of Investment Tax Credit
ITA
127(27)
Subsection 127(27) of the Act provides for the recapture of investment tax credits in respect of property used for scientific research and experimental development (SR&ED) where the property is sold or converted to commercial use. This recapture is effected by way of an addition to tax payable of an amount equal to the lesser of
• the amount that can reasonably be considered to have been included in the taxpayer’s investment tax credit in respect of the particular property (i.e., the amount that is obtained by multiplying the amount of the qualified expenditure by the ITC rate that applied to that expenditure), and
• the amount that is obtained by multiplying the ITC rate (that applied to the qualified expenditure) by
• the proceeds of disposition of the particular property (or of property that incorporates the particular property) if the property is disposed of to a person who deals at arm’s length with the taxpayer. (See paragraph 127(27)(e) of the Act.)
• in any other case, the fair market value of the particular property (or the other property) at the time of its conversion or disposition. (See paragraph 127(27)(f) of the Act.)
Concern has been expressed about the application of subsection 127(27) of the Act in the context of shared-use equipment, only 25% or 50% of the cost of which is a "qualified expenditure" under subsection 127(9) because of subsection 127(11.5) of the Act. This concern is illustrated by the following example.
Example: Year 1: Taxpayer acquires shared-use equipment for $100. The ITC rate is 20% and the taxpayer claims an ITC for first term shared-use-equipment of$5 (20% x $25 [1/4 of its$100 cost under paragraph 127(11.5)(c)]).Year 2: Taxpayer claims an ITC for second term shared-use-equipment of $5 (20% x$25 [1/4 of its $100 cost under paragraph 127(11.5)(c)]).Year 4: Taxpayer sells the property for$80.Recapture under subsection 127(27): $10 being the lesser of:$10 (20% x $100 x 50% because the property is second term shared-use-equipment), and$16 (20% x $80 proceeds of disposition). However, in this example the$16 amount should be $8 given that only a portion (50%) of the cost of the second term shared-use-equipment is a qualified expenditure. As well, the government is concerned that subsection 127(27) should apply where the disposition or conversion relates to property acquired pursuant to an expenditure that would have been a qualified expenditure incurred in a taxation year but for the application of the 180-day-unpaid-amount rule in subsection 127(26) of the Act. To address these concerns, subsection 127(27) is amended in four respects. First, paragraphs 127(27)(b) and (c) are amended to refer to the "cost, or a portion of the cost, of the particular property" instead of to the "cost of the particular property". Second, paragraphs 127(27)(b) and (c) are amended to provide that the reference therein to a qualified expenditure included in a taxpayer’s investment tax credit be read without reference to subsection 127(26) relating to unpaid amounts. Third, consequential changes are made to the wording between paragraphs 127(27)(d) and (e) of the Act. In particular, the first of the two amounts in the "lesser of" formula is moved to new paragraph 127(27)(e). The second of these two amounts is described in amended paragraph 127(27)(f), which combines former paragraphs 127(27)(e) and (f). Fourth, paragraph 127(27)(f), which combines former paragraphs 127(27) (e) and (f), is changed to account for circumstances where the property that is disposed of or converted is first term shared-use-equipment or second term shared-use-equipment. These amendments apply to dispositions and conversions that occur after December 20, 2002. Clause 124 Labour-sponsored Venture Capital Corporations ITA 127.4 Section 127.4 of the Act provides for a tax credit for individuals (other that trusts) that acquire shares issued by a labour-sponsored venture capital corporation (LSVCC). Definitions ITA 127.4(1) "approved share" Subsection 127.4(2) of the Act allows an individual (other than a trust) a tax credit for the acquisition of an "approved share", which is defined in subsection 127.4(1) as, generally, a share issued by a prescribed LSVCC. LSVCCs prescribed for this purpose under section 6701 of the Regulations include LSVCCs registered under Part X.3 of the Act, as well as specified provincially registered LSVCCs. Paragraph (b) of the definition "approved share" excludes from the definition certain shares issued by a provincially-registered LSVCC that is not a federally-registered LSVCC. This exclusion applies only in the event that, at the time of the issue of the shares, no assistance is available in respect of the acquisition of such shares because of a suspension or termination of assistance to the LSVCC under the laws of every province in which the LSVCC is registered. Paragraph (b) of the definition "approved share" is amended to provide that an approved share does not include a share issued by a provincially-registered LSVCC (that is not a federally-registered LSVCC) if, at the time of the issue, no province under the laws of which the corporation is an LSVCC that is a prescribed LSVCC provides assistance in respect of the acquisition of the share. This amendment is provided to have the definition "approved share" better reflect the policy that a federal income tax credit be available in respect of a share issued by a provincially-registered LSVCC (that is not a federally-registered LSVCC) only if a provincial income tax credit is also available in respect of the share. Paragraph (b) of the definition will continue to apply if, at the time of the issue by such an LSVCC of a share, no assistance is available in respect of the acquisition of shares of the LSVCC because of a suspension or termination of assistance to the LSVCC under the laws of every province in which the LSVCC is registered. Amended paragraph (b) of the definition will also apply where there has not been a suspension or termination of assistance with respect to the issuance of the LSVCC’s shares generally, but assistance is not available with respect to the acquisition of a particular share. For example, if under the laws of a province under which an LSVCC is a prescribed LSVCC, a taxpayer who acquires a share is not entitled to any assistance in respect of the acquisition either because of having reached the age of 65 years or because of the province of residence of the taxpayer, the share will not be treated as an approved share. This amendment applies to acquisitions of shares that occur after 2003. "qualifying trust" Subsection 127.4(1) of the Act contains the definition of "qualifying trust". In 2000, the Act was amended to include common-law partners, but some provisions, including the English version of the definition of "qualifying trust", were overlooked. This definition is therefore amended to correct this omission. The amendment applies, in general, to the 2001 and subsequent taxation years. However, it may apply as of 1998 if the common-law partners jointly choose to be deemed as such, beginning in that year, for the purposes of the application of the Act. Clause 125 Minimum Tax ITA 127.52 Section 127.52 of the Act defines the "adjusted taxable income" of an individual for a taxation year for the purpose of determining the individual’s minimum tax liability under Division E.1 of Part I of the Act. ITA 127.52(1)(d) Paragraph 127.52(1)(d) of the Act provides that in computing an individual’s adjusted taxable income for minimum tax purposes, the total amount of capital gains and losses is to be taken into account. In some cases, because of subsection 104(21.6) of the Act (which in some cases deems a taxpayer to have realised a larger capital gain than was actually realised) more than the total amount of capital gains and losses would be taken into account. Excess capital gains are deemed by subsection 104(21.6) to have been realized in order that the inclusion rate for capital gains realized on property disposed of by a trust prior to February 28, 2000 is ¾ and property disposed of by a trust after February 27, 2000 and before October 18, 2000 is 2/3. Paragraph 127.52(1)(d) is therefore amended to ensure that only the actual amount of the gain is included in computing the alternative minimum tax. This change applies to the 2000 and subsequent taxation years. Clause 126 Returning Trust Beneficiary ITA 128.1(7) The French version of subsection 128.1(7) of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent. Clause 127 Private Corporations - "refundable dividend tax on hand" ITA 129(3)(a) Section 129 of the Act allows a private corporation that pays a taxable dividend to obtain a partial refund of the income taxes it has paid on its investment income. For this purpose, paragraph 129(3)(a) adds to the refundable dividend tax on hand of a Canadian-controlled private corporation at the end of a taxation year the least of three amounts. One of these amounts, which is described in subparagraph 129(3)(a)(ii), is 26 2/3% of a corporation’s taxable income, less income that either benefited from the section 125 small business deduction or supported a foreign tax credit (FTC). Income that supported an FTC is measured by multiplying both the corporation’s non-business- and its business-income FTCs by factors that reflect assumed Canadian tax rates. Subparagraph 129(3)(a)(ii) is amended to adjust the factor for foreign business income. The factor for business-income FTCs will become 3. This implies an assumed tax rate of 33.3%. This amendment applies to the 2003 and subsequent taxation years. Clause 128 Definition "mutual fund trust" ITA 132(6)(c) Subsection 132(6) of the Act sets out the definition "mutual fund trust". Under paragraph 132(6)(c), a trust will qualify at any time as a mutual fund trust only if at that time it meets prescribed conditions relating to the number of its unit holders, dispersal of ownership of trust units issued by it and public trading of trust units issued by it. Paragraph 132(6)(c) is amended so that the prescribed conditions that a trust may be required to satisfy in order to qualify as a mutual fund trust are not limited to those relating to ownership and trading of its units. This amendment applies to the 2000 and subsequent taxation years. The regulations setting out these prescribed conditions for a mutual fund trust are found in Part XLVIII of the Income Tax Regulations. In particular, Regulation 4801 sets out conditions that apply to a class of units issued by a trust in order for the trust to be considered a mutual fund trust. It is intended that proposed amendments to Part XLVIII of the Regulations would include the following: • The French language version would be amended to correct a technical deficiency in the use of the expression "appel public à l’épargne" ("qualified for distribution to the public"). The amendments to the French version of the Regulations would clarify that, as is the case in the English version, the defined expression in subsection 4803(2) of the Regulations applies in determining whether a class of units is qualified for distribution to the public in paragraph 4801(a) of the Regulations. • Paragraph 4801(a) of the Regulations would be amended so that subparagraph 4801(a)(ii) applies to a trust created before 2000, for its 2004 and subsequent taxation years, if the trust elects by notifying the Minister of National Revenue in writing in its return of income for the taxation year of the trust that ends in the calendar year in which the amending regulations are published in Part II of the Canada Gazette. As a result of the proposed change, if there has been a lawful distribution in a province to the public of units of a class of units of a trust created before 2000 and a prospectus, registration statement or similar document was not required under the laws of the province to be filed in respect of the distribution, the trust could rely upon subparagraph 4801(a)(ii) to meet, in its 2004 and later taxation years, the condition prescribed under paragraph 4801(a). These amendments to the Regulations would, except as described above, be proposed to apply to the 2000 and subsequent taxation years of trusts. Clause 129 Taxation Year of Mutual Fund Trust ITA 132.11(1) Section 132.11 of the Act generally allows a mutual fund trust to elect to have taxation years that end on December 15, rather than on December 31. Where a trust makes this election, each subsequent taxation year of the trust is deemed to start on December 16 of a calendar year and to end on December 15 of the following calendar year, unless any of certain events intervenes. One of the events that can intervene, and that results in an earlier year-end, is a qualifying exchange under section 132.2 of the Act. As a consequence of the restructuring of section 132.2, the reference in paragraph 132.11(1)(b) to paragraph 132.2(1)(b) is replaced by a reference to paragraph 132.2(3)(b). This amendment applies after 1998 except that, in applying the amended version of paragraph 132.11(1)(b) to taxation years that end before 2000, the paragraph is to be read as though it did not contain the words "subject to subsection (1.1)". Paragraph 132.11(1)(c) generally provides that each fiscal period of a mutual fund trust that has made an election under subsection 132.11(1) shall end no later than the end of the trust’s taxation year that ends on December 15th. The French-language version of paragraph 132.11(1)(c) is amended to clarify that the paragraph applies to each fiscal period of the trust that either begins in a taxation year of the trust that ends on December 15 because of an election under paragraph 132.11(1)(a) or that ends in a subsequent taxation year of the trust. This technical change does not represent a change in policy. This amendment applies to the 1998 and subsequent taxation years. Amounts Paid or Payable to Beneficiaries ITA 132.11(4) Subsection 132.11(4) of the Act is designed to permit distributions made in the last 16 days of a calendar year in respect of a trust’s taxation year ending on December 15 of the calendar year to be treated as if they were made at the end of that taxation year. Subsection 132.11(4) of the Act is amended so that it applies for the purpose of paragraph (i) of the definition "disposition" in subsection 248(1). As a result, in the case of a mutual fund trust that has elected under section 132.11 to have a December 15th taxation year-end, distributions from the trust in respect of a taxpayer’s capital interest made in the last 16 days of a calendar year will not result in a disposition of the interest. This amendment applies to amounts that, after 1999, are paid or have become payable by a trust. Clause 130 Mutual Fund Qualifying Exchanges ITA 132.2 Section 132.2 of the Act provides rules to allow two mutual fund trusts, or a mutual fund trust and a mutual fund corporation, to merge on a tax-deferred basis. Such a merger is referred to as a "qualifying exchange". In addition to introducing several substantive improvements to the rules in section 132.2, these amendments restructure the provision as a whole. In general terms, the section is now organized as follows: new subsection 132.2(1) sets out definitions that apply for the section; subsection (2) describes the order in which the events that make up a qualifying exchange are considered to have occurred; subsection (3) provides a set of general rules; subsection (4) deals with non-depreciable property that is transferred on the qualifying exchange; and subsection (5) deals with depreciable property that is transferred. Subsection (6) establishes the due date for the election to treat a transfer as a qualifying exchange; and subsection (7) provides authority for the Minister of National Revenue to allow that election to be amended or revoked. Despite this restructuring, the basic principles of section 132.2 remain unchanged, as do most aspects of its operation. The exceptions – the areas where these amendments change the provision substantively – have to do with depreciable property that is transferred on a qualifying exchange, and with the election to treat a transaction as a qualifying exchange. Further modifications have been made to prevent the creation of artificial or "phantom" losses, generally in circumstances where one fund holds units or shares of the other fund immediately before the transfer time. Transfers of Depreciable Property In its current form, section 132.2 does not deal comprehensively with transfers of depreciable property between mutual funds. In particular, the deemed timing of the transfer, in relation to the deemed year-end of the funds, may prevent either fund from claiming capital cost allowance (CCA) for the last taxation year that began before the qualifying exchange. The transferor has disposed of the property two moments before the end of its year, and the transferee will not acquire it until the last moment of its own year. To ensure that one CCA claim is available for that last year, new subsection 132.2(5) provides a special regime for qualifying exchanges that include transfers of depreciable property. A key aspect of these special rules is the ordering of events in accordance with new subsection 132.2(2). That subsection provides that, starting with the actual (i.e., legal) transfer of property between a transferor fund and a transferee fund that carry out a qualifying exchange, the following series of times occurs, each immediately after the previous one: Name of Time Description Reference the transfer time The actual transfer of the property between the funds takes place. definition "qualifying exchange" in 132.2(1) the first intervening time The funds are treated as having disposed of and reacquired non-transferred property (other than depreciable property). 132.2(3)(a) the acquisition time The transferee is treated as having acquired transferred property (other than depreciable property); the funds’ taxation years are treated as ending. 132.2(4)(a); 132.2(3)(b) the beginning of the funds’ first post-exchange years 132.2(3)(b) the depreciables disposition time The transferor is deemed to have disposed of any transferred property that is depreciable property. 132.2(5)(a) the second intervening time The funds are treated as having disposed of and reacquired any non-transferred property that is depreciable property. 132.2(3)(c) the depreciables acquisition time The transferee is deemed to have acquired any transferred property that is depreciable property. 132.2(5)(b) As a result of this timing, the transferor fund will be treated as owning, until after its first post-exchange year has begun, any depreciable property that is being transferred. This will ensure that the transfer does not prevent the transferor from deducting CCA in respect of property of that class, for its taxation year that ends at the acquisition time. The new rule also ensures that the transferee does not duplicate that deduction, by treating the transferee as having acquired the property only after its new taxation year has begun. This treatment of depreciable property applies, along with most aspects of the restructuring of section 132.2, to qualifying exchanges that take place after 1998. Timing of Election For section 132.2 to apply to a transfer of property between mutual funds, the definition "qualifying exchange" currently requires the funds to file their joint election in prescribed form with the Minister of National Revenue within six months after the transfer time. This timing requirement is changed to allow greater flexibility. The amended definition "qualifying exchange" requires that the funds’ election be made before the election’s "due date", defined in new subsection 132.2(6) to mean either the day that is six months after the day that includes the transfer time or any later day that the Minister accepts, on joint application by the funds. An example of a case in which the Minister might accept such an application would be one in which the Minister has already decided to accept a late filing of the funds’ returns of income for the taxation year that includes the qualifying exchange. In certain cases, mutual funds that have elected to treat a transfer as a qualifying exchange may wish to amend, or even revoke, their election. New subsection 132.2(7) allows the funds to do this, on joint application and with the permission of the Minister. New subsections 132.2(6) and (7), and the amended definition "qualifying exchange" in subsection 132.2(1), apply to qualifying exchanges that take place after June 1994. Definition "designated beneficiary" Rules of General Application ITA 132.2(3)(g)(iii) and 132.2(1)(j)(iii) New subparagraph 132.2(3)(g)(iii) of the Act applies in determining whether a person is a "designated beneficiary" (as defined in section 210 of the Act) of a trust. Under the definition designated beneficiary, certain persons or partnerships that are beneficiaries under a trust may be treated (or may cause trusts or partnerships of which they are beneficiaries or members to be treated) as designated beneficiaries under the trust, unless the relevant interest in the trust is held at all times by the person or partnership, as the case may be, or by another person exempt because of subsection 149(1) of the Act from tax, under Part I of the Act, on all of the other person’s taxable income. In a qualifying exchange, a mutual fund trust or mutual fund corporation (transferor) transfers all or substantially all of its property to another mutual fund trust (transferee) and takes back units of the transferee. Those units are then provided by the transferor to its investors in exchange for their shares or units of the transferor. New subparagraph 132.2(3)(g)(iii) ensures that, in these circumstances, the transferor is treated, for the purpose of the definition designated beneficiary, as not having held the units of the transferee. This amendment applies for qualifying exchanges that occur after 1998. A similar rule, in former subparagraph 132.2(1)(j)(iii), applies for qualifying exchanges that occurred after June 1994 and before 1999. Rules of General Application - Losses ITA 132.2(3)(f) and (g) New paragraphs 132.2(3)(f) and (g) of the Act are amended to ensure that the mutual fund merger rules do not apply inappropriately to create artificial or "phantom" losses. Although the changes reflected in these new provisions are not expected to be relevant to most qualifying exchanges, the following is a description of their purpose and effect. Under the definition "qualifying exchange" in new subsection 132.2(1), all or substantially all of the outstanding shares issued by the transferor must be disposed of to the transferor within the 60 days after the transfer time, and every person so disposing of shares of the transferor must receive only units of the transferee as consideration. The second leg of a qualifying exchange is thus a set of transactions in which the transferor’s investors replace their shares of the transferor with units of the transferee. The tax effect of those transactions are governed by paragraphs 132.2(1)(f) and (g). For clarity, these notes reflect the legislation by referring to investments in the transferor – whether a corporation or a trust – as shares, reserving the term "units" to refer to the units of the transferee mutual fund trust. Existing paragraph 132.2(1)(i) provides that if, within 60 days after the transfer time, the transferor fund disposed of units of the transferee in exchange for shares of itself, its proceeds of disposition are deemed to be nil. Since the units acquired by the transferor in return for its property are deemed, under existing paragraph 132.2(1)(h) (now new paragraph 132.2(3)(e)), also to have had a cost of nil, this provision allows the transferor to roll those units out to its investors with no tax consequences to it. New paragraph 132.2(3)(f) provides that if, within 60 days after the transfer time, the transferor fund disposes of units of the transferee in exchange for shares of itself, its proceeds of disposition will be deemed to be equal to the cost amount of the units to the transferor immediately before the disposition. This change – from nil proceeds to proceeds equal to cost amount – ensures appropriate results if the transferor held units of the transferee that were acquired otherwise than as a result of the qualifying exchange. In this situation, that first tranche of units will have a cost base that, pursuant to section 47 of the Act, will be averaged with the second tranche of units (i.e. the units that the transferor acquired in the qualifying exchange). Existing paragraph 132.2(1)(i) deems the proceeds of the disposition of the second tranche of units to be nil, an inappropriate result in that it creates a phantom loss. New paragraph 132.2(3)(f), deeming the proceeds of disposition equal to the cost amount of the units to the transferor immediately before the disposition, ensures that the transferor can still roll units of the transferee out to its investors with no tax consequences to it, and avoids the creation of a phantom loss. Existing subparagraph 132.2(1)(j)(i) provides that, where a taxpayer disposes of shares of the transferor in exchange for units of the transferee within that same 60-day period, both the taxpayer’s proceeds of disposition of the shares and the taxpayer’s cost of the units are deemed to be equal to the cost amount of the shares immediately before the transfer time. New subparagraph 132.2(3)(g)(i) provides that, where a taxpayer disposes of shares of the transferor in exchange for units of the transferee within that same 60-day period, both the taxpayer’s proceeds of disposition of the shares and the taxpayer’s cost of the units are deemed to be equal to the cost amount of the shares immediately before the disposition. This change – from measuring the cost amount of the shares immediately before the transfer time to measuring it immediately before the disposition – ensures that the transferor’s investors will not realize any gain or loss on their exchange of their shares for units of the transferee. Paragraph 132.2(3)(g) also includes a new subparagraph 132.2(3)(g)(iv) to address the disposition by certain persons or partnerships of the units in the transferee that they received on the qualifying exchange. Those affected by this new provision are those who, when they acquire the units, are affiliated with one or both of the funds. This could include, for example, the transferee itself, or a corporation it controls. The subparagraph first deems the units received in the qualifying exchange not to be identical to any other units of the transferee. This segregates the new units from the averaging effect of section 47 of the Act. Next, the subparagraph specifies the effects of disposing of the new units. If the taxpayer is the transferee, and the units cease to exist when the taxpayer acquires them (if, for example, the units are cancelled immediately on receipt), clause 132.2(3)(g)(iv)(B) provides two effects. First, to prevent any possible question in this regard, the taxpayer is deemed to have acquired those units. This ensures, among other things, that subparagraph (i) establishes the taxpayer’s cost of the units. Second, the taxpayer is treated as having disposed of those units immediately after it acquired them, for proceeds of disposition equal to the cost amount to the taxpayer of those units at that time. This ensures, for greater certainty, that a transferee that had an investment in the transferor prior to the qualifying exchange will not incur a phantom loss as a result of exchanging its shares in the transferor in return for units of itself. If the taxpayer is affiliated with one or both of the funds, but is not the transferee, clause 132.2(3)(g)(iv)(C) provides that, for the purpose of computing any gain or loss of the taxpayer from the taxpayer’s first disposition of each of those units, the proceeds of disposition of the unit will depend on whether the disposition is a renunciation or surrender of the unit or some other disposition. New subclause 132.2(3)(g)(iv)(C)(I) provides that, if the disposition is a renunciation or surrender of the unit by the taxpayer for no consideration, and is not in favour of any person other than the transferee, the taxpayer’s proceeds of disposition of that unit are deemed to be equal to that unit’s cost amount to the taxpayer immediately before that disposition. This ensures that an affiliated taxpayer will never incur a phantom loss or gain on the renunciation or surrender of the unit. If the disposition is not a renunciation or surrender of the unit described in subclause 132.2(3)(g)(iv)(C)(I), the affiliated taxpayer’s proceeds of disposition of that unit are deemed by subclause 132.2(3)(g)(iv)(C)(II) to be equal to the greater of that unit’s fair market value and its cost amount to the taxpayer immediately before that disposition. This ensures that the taxpayer will never incur a loss, including a phantom loss, on a disposition of one of those units, but may incur a gain. Two additional points should be noted with respect to the operation of new subparagraph 132.2(3)(g)(iv). • The deeming, by subclause 132.2(3)(g)(iv)(C)(II), of a taxpayer’s proceeds of disposition of the units the taxpayer acquired on the qualifying exchange applies only to the first disposition of each unit. It is possible that a taxpayer might dispose of a unit and then reacquire the same unit (under, for example, the change in residence rules in section 128.1 of the Act). The subclause will not apply to any subsequent disposition of the unit by that taxpayer. • In some circumstances, an affiliated taxpayer may have a latent loss on a share of the transferor prior to the qualifying exchange, and may wish to realize that loss. This can be done, if the affiliated taxpayer disposes of the share prior to the qualifying exchange. However, the possible application of the Act’s "superficial loss" and loss deferral rules would have to be borne in mind. New paragraphs 132.2(3)(f) and (g), together with the rest of new subsection 132.2(3), generally apply to qualifying exchanges that occur after 1998. A limited exception applies in respect of certain qualifying exchanges in respect of which a return of income, claiming the losses sought to be prevented by these amendments, was filed by the transferee mutual fund before July 18, 2005. Clause 131 Non-resident-owned Investment Corporations - Transition ITA 134.1(2) Section 134.1 of the Act was enacted, along with section 134.2, in 2001 to provide transitional relief for corporations that cease to be non-resident owned investment corporations (NROs). The essence of the relief provided in section 134.1 is to allow such a corporation to recover refundable tax by paying a dividend in its "first non-NRO year". In its current form, the section applies only in respect of dividends paid to a non-resident person or another NRO. There is, however, another kind of shareholder to whom an NRO may pay a dividend in respect of which it is appropriate to apply the section - a trust for the benefit of non-resident persons or their unborn issue. Since such a trust could, under the rules that have governed NROs themselves, have held the shares and debt of an NRO, a dividend to the trust ought to support a refund of the former NRO’s refundable tax. Subsection 134.1(2) is therefore amended to include such dividends within the section’s scope. In addition, subsections 104(10) and (11) of the Act are added to the list of provisions in subsection 134.1(2) for which a former NRO is deemed to be an NRO during its first non-NRO year. Prior to the repeal of the NRO system, a trust that received a dividend from an NRO and that did not in turn distribute the amount of the dividend to its non-resident beneficiaries was entitled to deduct that amount from the trust’s income under subsection 104(10). Subsection 104(11) then deemed the amount deducted under subsection 104(10) to have been paid to a non-resident beneficiary, with the result that Part XIII withholding tax would typically be payable. These two subsections are included in subsection 134.1(2) in order to allow a trust to benefit from these provisions in the year it receives the final payment of dividends from the former NRO. Both of these amendments apply on the same basis as section 134.1: that is, to a corporation that ceases to be an NRO because of a transaction or event that occurs, or a circumstance that arises, in a taxation year of the corporation that ends after February 27, 2000. Clause 132 Cooperative Corporations ITA 136 Section 136 of the Act provides rules that apply to cooperative corporations. Subsection 136(1) provides that a cooperative corporation that would otherwise be a private corporation is treated as a private corporation for the purposes of specified provisions of the Act. The subsection is amended to include among those provisions section 123.4 of the Act, which in effect provides reductions in corporate tax rates. This subsection is amended, for the 2001 and subsequent taxation years, to provide that a cooperative corporation that otherwise qualifies as a Canadian-controlled private corporation (CCPC) may use the special rate reduction provided for CCPCs. Subsection 136(2) of the Act sets out conditions that a corporation must meet in order to be a cooperative corporation. The condition in current paragraph 136(2)(c) has two parts: at least 90% of its members must be individuals, other cooperative corporations, or corporations or partnerships that carry on the business of farming; and at least 90% of its shares, if any, must be held by those persons or partnerships. The second part of this condition is modified to accommodate cases where the shares of a cooperative are held not only by the members themselves, but also by their registered plans (RRSPs, RRIFs, or RESPs). If shares are held by a trust that is governed by such a plan, provided a member of the cooperative is the plan’s subscriber or annuitant, as the case may be, those shares will be counted in the same way as if they were held by a member personally. Amended paragraph 136(2)(c) and new paragraph 136(2)(d), which give effect to this change, apply to the 1998 and subsequent taxation years. Clause 133 Credit Unions ITA 137(6) "member" Section 137 of the Act provides rules that apply to credit unions. Among the definitions set out in subsection 137(1) is "member," meaning essentially a member of record who is entitled to the services of the credit union. This definition is amended, for the 1996 and subsequent taxation years, to treat as a member a registered retirement savings plan, registered retirement income fund, or registered education savings plan, provided that the annuitant or subscriber under the plan is a person who meets the existing definition of "member". Credit Union not Private Corporation ITA 137(7) Subsection 137(7) of the Act provides that a credit union that would otherwise be a private corporation is treated as a private corporation for the purposes of specified provisions of the Act. The subsection is amended to include among those provisions section 123.4 of the Act, which in effect provides reductions in corporate tax rates. This amendment, which applies to the 2001 and subsequent taxation years, provides that a credit union that otherwise qualifies as a Canadian-controlled private corporation (CCPC) may use the special rate reduction provided for CCPCs. Clause 134 Deposit Insurance Corporations ITA 137.1 Section 137.1 of the Act provides rules for the taxation of deposit insurance corporations (DICs), including rules that affect the computation of income. In general terms, the premiums that a member institution pays to a DIC are deductible in computing the member’s income and are not included in computing the income of the DIC, while any assistance that the DIC provides to the member or the member’s depositors is not deductible for the DIC and is included in computing the member’s income. In certain circumstances, two or more DICs may share responsibilities toward a group of members. In such a case, it may be necessary for one DIC to pay to another an amount in respect of premiums. To ensure the appropriate tax consequences of such a payment, subsections 137.1(2) and (4) are amended. New paragraph 137.1(2)(b) excludes from the income of a DIC any amount it receives from another DIC, to the extent the amount can reasonably be considered to have been paid out of premiums or assessments received or receivable by the other DIC from its member institutions. New paragraph 137.1(4)(d), on the other hand, precludes the paying DIC from deducting the amount in computing its own income. These amendments apply to the 1998 and subsequent taxation years. Clause 135 Insurance Corporations ITA 138 Section 138 of the Act provides detailed rules relating to the taxation of insurance corporations. Insurer’s Income or Loss ITA 138(2) Subsection 138(2) of the Act provides rules for the purpose of computing the income of a life insurer resident in Canada where the life insurer carries on an insurance business in Canada and in a country other than Canada. The subsection provides that the insurer’s income from carrying on an insurance business is the amount of its income from carrying in the insurance business in Canada computed in accordance with the Act. As well, the subsection provides that the insurer’s taxable capital gains and allowable capital losses from property used or held in the course of carrying on an insurance business is the insurer’s taxable capital gains and allowable capital losses from designated insurance property. Subsection 138(2) is being amended to extend its application to non-resident insurer’s that carry on an insurance business in Canada. As well, it is being amended to provide, for greater certainty, the following: 1. In computing a multinational insurer’s income from an insurance business carried on by it in Canada, no amount is to be included in respect of the insurer’s gross investment revenue for a taxation year derived from property used or held in the course of carrying on an insurance business that is not designated insurance property of the insurer. Subsection 138(9) of the Act provides that in computing a multinational insurer’s income from an insurance business carried on by it in Canada the insurer must include its gross investment revenue for the year from its designated insurance property for the year plus the amount prescribed in respect of the insurer for the year. Designated insurance property is defined in section 2400 of the Income Tax Regulations. 2. In computing a multinational insurer’s taxable capital gains and allowable capital losses for the year from the disposition of property used or held in the course of carrying on an insurance business there is to be included the insurer’s taxable capital gains and allowable capital losses from dispositions of its designated insurance property for the year. It also provides that the insurer’s taxable capital gains and allowable capital losses for the year from the disposition of property used or held in the course of carrying on an insurance business that is its designated insurance property for the year are not to be included in computing a multinational insurer’s taxable capital gains and allowable capital losses for the year. The amendments are applicable to taxation years that end after 1999. Computation of Income of Non-resident Insurer ITA 138(11.91) Subsection 138(11.91) of the Act provides rules for the purpose of computing the income of a non-resident insurer that at any time in a particular taxation year commences to carry on business in Canada or that ceases to be exempt from tax under Part I of the Act. Paragraph 138(11.91)(f) of the English Version of the Act applies where the non-resident insurer’s capital cost of a depreciable property exceeds the property’s fair market value immediately before the commencement of the particular taxation year. To ensure that on a later disposition of the property the non-resident insurer is subject to recapture of any excess capital cost allowance claimed before the particular taxation year, this paragraph preserves the property’s capital cost, and treats the excess as having been allowed as capital cost allowance. Since it is inappropriate to provide for the recapture of capital cost allowance that was claimed when the business was not carried on in Canada or when the non-resident insurer was exempt from tax under Part I of the Act, paragraph 138(11.91)(f) of the English version of the Act is repealed. Paragraph 138(11.91)(d) of the French version of the Act is repealed for the same reason. This amendment applies to taxation years that end after 1999. Clause 136 Mark-to-market Rules ITA 142.6(1) Subsection 142.6(1) of the Act contains rules that apply where a taxpayer becomes (or ceases to be) a financial institution. This is most likely to happen where the change of status occurs because the taxpayer becomes (or ceases to be) controlled by a financial institution. If a taxation year of the taxpayer does not end immediately before the time at which its status as a financial institution changes, subparagraph 142.6(1)(a)(i) deems the taxpayer’s taxation year that would otherwise have included that time to end immediately before that time. A new taxation year begins at that time, and the taxpayer is permitted to adopt a new fiscal period. One purpose for the deemed year-end is to ensure the proper application, in taxation years in which the taxpayer is a financial institution, of the rules, commonly known as the mark-to-market rules, • in section 142.3 of the Act for specified debt obligations, and • in section 142.5 of the Act for market-to-market properties. The expressions "financial institution", "specified debt obligation" and "mark-to-market property" are defined in section 142.2 of the Act. Paragraph 142.6(1)(b) applies where a taxpayer becomes a financial institution. This paragraph generally provides for a deemed disposition at fair market value of each property held by the taxpayer that is • a specified debt obligation (other than a specified debt obligation that is a mark-to-market property to which subparagraph 142.6(1)(b)(ii) applies)[1], or • a mark-to-market property for the taxpayer’s taxation year that ends immediately before the time of the change of status[2]. This deemed disposition under paragraph 142.6(1)(b) is intended to ensure that amounts brought, because of the mark-to-market rules in sections 142.3 and 142.5, into the taxpayer’s income for the taxpayer’s subsequent taxation year (i.e., the taxation year that includes the time of the change of status) do not include gains or losses accrued before the beginning of that subsequent taxation year. Paragraph 142.6(1)(b) is amended to ensure that this is achieved in connection with mark-to-market properties. Amended paragraph 142.6(1)(b) results in the taxpayer being deemed to have disposed of, immediately before the end of its particular taxation year that ends immediately before the time of the change of status, and for proceeds equal to its fair market value at the time of that disposition, a mark-to-market property of the taxpayer • for the particular taxation year, or • for the subsequent taxation year. Paragraph 142.6(1)(c) provides for a deemed disposition of specified debt obligations (other than mark-to-market property) in the opposite situation of change of status, i.e., where the taxpayer ceases to be a financial institution. Paragraph 142.6(1)(d) provides that the taxpayer is deemed to have reacquired, at the end of the taxation year referred to in paragraph 142.6(1)(b) or (c), each property deemed by that paragraph to have been disposed of by the taxpayer, at a cost equal to the proceeds of disposition of the property. Consequential to the amendments to paragraph 142.6(1)(b), paragraph 142.6(1)(d) is amended to provide that the taxpayer is deemed to have reacquired, at the end of its taxation year that ends immediately before the time of the change of status, each property deemed by paragraph 142.6(1)(b) or (c) to have been disposed of by the taxpayer, at a cost equal to the proceeds of disposition of the property. Amended paragraphs 142.6(1)(b) and (d) apply to taxation years that end after 1998. Clause 137 Authorized Foreign Banks – Conversion ITA 142.7(8)(d) Section 142.7 of the Act provides time-limited rules to facilitate foreign banks’ transformation of certain Canadian operations, currently carried out through subsidiaries, into Canadian branches (known as "authorized foreign banks") of the foreign banks themselves. When an authorized foreign bank assumes certain debt obligations of its Canadian affiliates, subsection 142.7(8) applies to govern the tax consequences of the assumption. Subparagraph 212(1)(b)(vii) of the Act provides an exemption from Part XIII tax in respect of interest payments on certain long- and medium-term corporate debt. The exemption can depend upon, among other things, the time at which a debt is issued. New paragraph 142.7(8)(d) is added to treat, for the purpose of subparagraph 212(1)(b)(vii), a debt obligation assumed by an authorized foreign bank from its Canadian affiliate as having been issued at the time that the debt was issued by the Canadian affiliate. This amendment applies after June 27, 1999. Clause 138 Communal Organizations ITA 143 Section 143 of the Act sets out rules governing the taxation of communal organizations (referred to in that section as "congregations") that do not allow their members to own property in their own right. Election in Respect of Gifts ITA 143(3.1) Subsection 143(3.1) of the Act allows a communal organization that makes an election under subsection 143(2) of the Act to elect to have its total charitable, Crown, cultural and ecological gifts flowed through to those members (the "participating" members) of the congregation for whom an amount is included in income for the year under subsection 143(2). Subsection 143(3.1) is amended consequential to the addition of new subsection 248(31) of the Act, in respect of gifts made after December 20, 2002, to refer to the "eligible amount" of a gift made because of a person being a participating member in the communal organization. Clause 139 Limited-recourse Debt in Respect of a Gift or Monetary Contribution ITA 143.2(6.1) New subsection 143.2(6.1) of the Act describes limited-recourse debt in respect of a gift or monetary contribution made after February 18, 2003. Such an amount is an advantage under subsection 248(32) of the Act, such that it reduces the eligible amount of a gift or political contribution determined under subsection 248(31) of the Act. For additional details regarding the amount of an advantage, see the commentary to new subsection 248(32). A limited-recourse debt includes the unpaid principal of any indebtedness for which recourse is limited, even if that limitation applies only in the future or contingently. It also includes any other indebtedness of the taxpayer, related to the gift or contribution, if there is a guarantee, security or similar indemnity or covenant in respect of that or any other indebtedness. For example, if a donor (or any other person mentioned below) enters into a contract of insurance whereby all or part of a debt will be paid upon the occurrence of either a certain or contingent event, the debt is a limited-recourse debt in respect of a gift if it is in any way related to the gift. Such an indebtedness is also a limited-recourse debt if it is owed by a person dealing non-arm’s length with the taxpayer or by a person who holds an interest in the taxpayer. Information Located Outside Canada ITA 143.2(13) Subsection 143.2(13) of the Act applies where information related to an indebtedness in respect of an expenditure is located outside Canada, and the Minister of National Revenue is not satisfied that the indebtedness is not a limited-recourse amount. In such a case, the indebtedness is deemed to be a limited-recourse amount in respect of the expenditure. Subsection 143.2(13) is extended to also apply in respect of an indebtedness that relates to a gift or political contribution made after February 18, 2003. Clause 140 Expenditure – Limitations ITA 143.3 New section 143.3 of the Act reduces, if applicable, the amount of a taxpayer’s expenditure by certain amounts for the purposes of computing the taxpayer’s income, taxable income and tax payable or an amount considered to have been paid on account of the taxpayer’s tax payable. Definitions ITA 143.3(1) New subsection 143.3(1) of the Act provides definitions that apply for the purposes of section 143.3. Those definitions are: "expenditure" "Expenditure" of a taxpayer, which means an expense, expenditure or outlay made or incurred by the taxpayer, or that is a cost or capital cost of property acquired by the taxpayer. "option" "Option", which means an option, warrant or similar right, issued or granted by the taxpayer, giving the holder the right to acquire an interest in the taxpayer or in another taxpayer with which the taxpayer does not, at the time the option, warrant or similar right is issued or granted, deal at arm’s length. "taxpayer" "Taxpayer", which is defined to include a partnership. Options – limitation ITA 143.3(2) New subsection 143.3(2) of the Act provides that, in computing a taxpayer’s income, taxable income or tax payable or an amount considered to have been paid on account of the taxpayer’s tax payable, an expenditure of the taxpayer is deemed not to include any portion of the expenditure that would – if the Act were read without reference to subsection 143.3(2) – be included in determining the expenditure because of the taxpayer having granted or issued an option on or after November 17, 2005. In essence, the value of an option granted by a taxpayer is not considered to be an expenditure for income tax purposes. Corporate Shares – Limitation ITA 143.3(3) New subsection 143.3(3) of the Act provides for two reductions that apply to an expenditure that would – if the Act were read without reference to subsection 143.3(3) – include an amount because of a corporation (or another corporation not dealing at arm’s length with the corporation) having issued a share of its capital stock at any particular time on or after November 17, 2005. The reductions apply to the corporation in computing its income, taxable income or tax payable or an amount considered to have been paid on account of the corporation’s tax payable. New paragraph 143.3(3)(a) applies on the issuance of the share (other than on the exercise of an option). Generally, the corporation is to reduce the related expenditure by the amount, if any, by which (i) the fair market value of the share exceeds (ii) if the transaction under which the share is issued is a transaction to which section 85, 85.1 or 138 of the Act applies, the amount determined under that section to be the cost to the corporation of the property acquired in consideration for the issuance of the share, or (iii) in any other case, the amount of consideration that is the fair market value of the property transferred to, or the services provided to, the issuing corporation for issuing the share. In addition, under new paragraph 143.3(3)(b), if the issuance of the share is a consequence of the exercise of an option, generally the corporation is to reduce the related expenditure by the amount, if any, by which (i) the fair market value of the share exceeds (ii) that portion of the amount paid, pursuant to the terms of the option, by the holder to the issuing corporation for issuing the share. Example Facts In its 2006 taxation year, Corporation X grants an option to Y in return for$1,000 worth of paintings by a little-known Canadian artist. Corporation X does not give cash or any other consideration for the paintings. The option gives Y the right to acquire one share of Corporation X for $10,000 in 2007. (At the time the option is granted one share of Corporation X has a fair market value of$10,000.) In 2007, Y exercises the option and pays Corporation X $10,000 cash for the share. The share has a fair market value of$15,000 at the time of issue. Corporation X files its 2007 income tax return on the basis that the cost of the paintings is $5,000, representing the difference between the fair market value of the share when it was issued and the cash paid by Y for the share. Application of section 143.3 of the Act 1. On granting the option: New subsection 143.3(2) applies to clarify that there is no expenditure by Corporation X resulting from it issuing the option. 2. On the exercise of the option: When issuing the share on the exercise of the option, new paragraph 143.3(3)(b) ensures that an expenditure, if any, of Corporation X is reduced by$5,000 – being the amount by which $15,000 (the fair market value of the share – see subparagraph (b)(i)) exceeds$10,000 (the amount paid for the share – see subparagraph (b)(ii). However, and as noted in the explanatory note accompanying new subsection 143.3(5), the reductions provided for under subsections 143.3(3) and (4) do not apply to reduce an expenditure if the expenditure itself does not include an amount determined to be excesses described in those subsections.
Non-corporate Interests – Limitation
ITA
143.3(4)
New subsection 143.3(4) of the Act provides for two reductions that apply to a non-corporate taxpayer’s expenditure that would – if the Act were read without reference to subsection 143.3(4) – include an amount because the taxpayer (or another taxpayer not dealing at arm’s length with the taxpayer) issues or creates an interest in itself at any particular time on or after November 17, 2005. The reductions apply to the taxpayer in computing its income, taxable income or tax payable or an amount considered to have been paid on account of the taxpayer’s tax payable.
In general terms, under new paragraph 143.3(4)(a), if the issuance or creation of the interest in a taxpayer is not a consequence of the exercise of an option, the taxpayer is to reduce the expenditure by the amount, if any, by which
(i) the fair market value of the interest
exceeds
(ii) if the transaction under which the interest is issued or created is a transaction to which paragraph 70(6)(b), subsection 97(2), paragraph 73(1.01)(c), subsection 73(1.02), section 107.4 or 132.2 of the Act applies, the amount determined under that provision to be the cost to the taxpayer of the property acquired for the interest, or
(iii) in any other case, the amount of the consideration that is the fair market value of the property transferred to, or the services provided to, the taxpayer for the interest.
In addition, under new paragraph 143.3(4)(b), if the issuance or creation of the interest is a consequence of the exercise of an option, the taxpayer is to reduce the expenditure by the amount, if any, by which
(i) the fair market value of the interest
exceeds
(ii) the amount paid, pursuant to the terms of the option, by the holder to the taxpayer for the interest.
However, and as noted in the explanatory note accompanying new subsection 143.3(5), the reductions provided for under subsections 143.3(3) and (4) do not apply to reduce an expenditure if the expenditure itself does not include an amount determined to be excesses described in those subsections.
Clarification
ITA
143.3(5)
New subsection 143.3(5) of the Act provides four rules for greater certainty.
First, paragraph 143.3(5)(a) clarifies that subsection 143.3(2) does not reduce an expenditure that is a commission, fee or other amount for services rendered by a person as a salesperson, agent or dealer in securities in the course of the issuance of the option.
Second, paragraph 143.3(5)(b) clarifies that subsections 143.3(3) and (4) do not apply to reduce an expenditure to the extent that the expenditure does not include an amount determined to be an excess under those subsections. For example, if a corporation were to issue shares of its capital stock having a fair market value of $100 in consideration for having acquired property or services having a fair market value of$40, no excess exists under paragraph 143.3(3)(a) if the expenditure of the corporation for the property or services claimed by the corporation without reference to section 143.3 is, for income tax purposes, $40. To the extent the corporation seeks to claim an expenditure in excess of that$40, paragraph 143.3(3)(a) would reduce that excess to nil. Paragraph 143.3(5)(b) recognizes that the jurisprudence that would treat an expenditure of the type reduced by subsections 143.3(3) and (4) currently applies only to scientific research and experimental development (SR&ED) tax credits, and is limited to a single decision of the Tax Court of Canada. It may very well transpire that future jurisprudence may constrain or eliminate any such expenditure that may be considered to arise in these circumstances.
Third, paragraph 143.3(5)(c) clarifies that section 143.3 does not determined the cost or capital cost of property determined under certain tax-deferral rules. For example, if section 85 of the Act deems a transferee corporation that acquires non-depreciable capital property to do so at a cost of $100 in circumstances where the corporation issued a share of its capital stock having a fair market value of$200, this section does not decrease or increase the $100 cost for the property to the corporation, as determined under section 85. Fourth, paragraph 143.3(5)(d) clarifies that section 143.3 does not determine the amount of a taxpayer’s expenditure if the amount of the expenditure as determined under section 69 of the Act is less than an amount determined under section 143.3. Clause 141 Registered Retirement Savings Plans ITA 146 Section 146 of the Act provides rules relating to registered retirement savings plans (RRSPs). Definitions ITA 146(1) "earned income" Subsection 146(1) of the Act defines "earned income", which is relevant in determining the maximum tax-deductible contributions that a taxpayer may make to RRSPs. The definition includes references to a number of provisions that have previously been repealed or re-numbered. The definition is amended to remove these references and update the numbering, with application from the time the provisions were repealed or re-numbered. Deemed Receipt of Refund of Premiums ITA 146(8.1) Subsection 146(8.1) of the Act deals with situations in which an amount paid from a deceased individual’s RRSP to the individual’s estate would have been a "refund of premiums" if it had been paid by the RRSP to a beneficiary under the estate. An amount paid out of an RRSP as a consequence of the death of the annuitant is defined, by subsection 146(1) of the Act, to be a "refund of premiums" if the recipient was, immediately before the death of the RRSP annuitant, a spouse or common-law partner of the annuitant or a financially dependent child or grandchild of the annuitant. Subsection 146(8.1) allows the legal representative of a deceased RRSP annuitant’s estate and a qualifying beneficiary under the estate to elect jointly to have the RRSP proceeds that were paid to the estate treated as a refund of premiums received by the beneficiary from the RRSP. When such an election is made, the beneficiary may include the deemed refund of premiums in income. If a corresponding amount is used to acquire a qualifying annuity or is paid into an RRSP or registered retirement income fund of the beneficiary and certain other conditions are satisfied, the beneficiary will be entitled to an offsetting deduction under paragraph 60(l) of the Act. Subsection 146(8.1) is amended to provide that the expression "beneficiary" under a deceased RRSP annuitant’s estate has the meaning assigned by subsection 108(1) of the Act. This has the effect of extending the provisions of subsection 146(8.1) to an individual who is "beneficially interested" in a deceased RRSP annuitant’s estate (as defined in subsection 248(25)), but who is not a beneficiary under the estate. This could occur, for example, where an individual has only an indirect interest in the deceased RRSP annuitant’s estate by virtue of being a beneficiary under a trust that is a beneficiary under the estate – a structure typically contemplated in the estate planning of parents of mentally infirm children. This change applies after 1988. Where Tax Payable ITA 146(10.1) Subsection 146(10.1) of the Act provides that income earned by a trust governed by a retirement savings plan from non-qualified investments is taxable under Part I. Subparagraph 146(10.1)(b)(ii) provides that income for this purpose includes the full amount of capital gains in excess of capital losses. This subparagraph is reworded for clarity, applicable on Royal Assent. Clause 142 Home Buyers’ Plan ITA 146.01 Section 146.01 of the Act set out the requirements for the Home Buyers’ Plan (HBP), which allows the tax-free withdrawal of RRSP funds for the purchase of a home. Definitions ITA 146.01(1) "quarter" Subsection 146.01(1) of the Act contains the definition "quarter" for purposes of the rules relating to the HBP. This definition is repealed as a consequence of the repeal of subsection 146.01(8) of the Act, where this definition applied. The repeal of this definition applies for the 2002 and subsequent taxation years. Filing of Prescribed Form ITA 146.01(8) In order for an RRSP withdrawal to qualify as an HBP withdrawal, the taxpayer must make a written request in prescribed form to the RRSP issuer. The prescribed form for this purpose is the T1036. Under subsection 146.01(8) of the Act, an RRSP issuer to whom a T1036 is submitted must file the form with the Minister of National Revenue no later than 15 days after the quarter in which it was so submitted. Subsection 146.01(8) is repealed. Rather than reporting HBP withdrawals on a quarterly basis by filing the relevant T1036, RRSP issuers are instead required (by subsection 214(1) of the Regulations) to report such withdrawals on an annual basis using the T4RSP. The repeal of subsection 146.01(8) applies for the 2002 and subsequent taxation years. Clause 143 Registered Education Savings Plans - Conditions for Registration ITA 146.1(2)(g.3) and (2.3) Subsection 146.1(2) of the Act sets out the conditions that must be satisfied in order for an education savings plan to be accepted for registration. New paragraph 146.1(2)(g.3) is introduced to preclude non-residents and individuals who have not yet been assigned a Social Insurance Number (SIN) from becoming a beneficiary under a registered education savings plan (RESP) or from benefiting from RESP contributions. Specifically, paragraph 146.1(2)(g.3) requires that an education savings plan not permit an individual to be designated as a beneficiary under the plan, and not allow a contribution for an individual who is a beneficiary under the plan, unless the individual’s SIN has been provided to the promoter of the plan and the individual is resident in Canada. If an individual is designated as a beneficiary under an RESP in conjunction with the transfer of property into the plan from another RESP under which the individual was a beneficiary immediately before the transfer, the requirement that the individual be resident in Canada in order to be designated as a beneficiary does not apply. However, subject to the exceptions in new subsection 146.1(2.3), the individual’s SIN has to be provided to the promoter in order for the individual to be designated as a beneficiary under the transferee RESP. This special rule is intended primarily to accommodate transfers from an RESP to a replacement RESP after the beneficiary has ceased to be resident of Canada. (It should be noted that the transfer itself, as a contribution to an RESP, is not subject to the SIN and residency conditions that apply to ordinary contributions.) New subsection 146.1(2.3) provides two additional exceptions to the SIN condition that are primarily of relevance to RESPs that were entered into before 1999 and RESPs that replace such plans. These exceptions recognize that the Canada Revenue Agency only began requiring the beneficiary’s SIN to be provided on the application for registration for plans entered into after 1998. The first new exception allows an education savings plan that was entered into before 1999 to not require that an individual’s SIN be provided in respect of a contribution to the plan. Such contributions, however, continue to be ineligible for the Canada Education Savings Grant. It should be noted that this exception is only relevant for contributions made for existing beneficiaries under such plans. An individual without a SIN is prevented from being designated as a new beneficiary under such a plan. Under the second new exception, an education savings plan may permit a non-resident individual who does not have a SIN to be designated as a beneficiary under the plan provided that the designation is being made in conjunction with a transfer of property into the plan from another RESP under which the individual was a beneficiary immediately before the transfer. This exception is intended, in particular, to accommodate the transfer of property from an RESP that was entered into before 1999, under which the beneficiary had always been non-resident or had ceased to be resident in Canada before having been assigned a SIN, to a replacement RESP (and successive transfers). Paragraph 146.1(2)(g.3) and subsection 146.1(2.3) apply after 2003. Clause 144 Registered Retirement Income Funds ITA 146.3 Section 146.3 of the Act provides rules relating to registered retirement income funds (RRIFs). Definitions ITA 146.3(1) "annuitant" Subsection 146.3(1) of the Act contains the definition "annuitant" for purposes of the rules relating to RRIFs. Paragraph (b) of the definition allows the spouse or common-law partner of a deceased annuitant to become the successor annuitant under the RRIF, if the deceased annuitant so elected or the legal representative of the deceased annuitant consents. When this paragraph was amended by S.C. 2000, c. 12 (the Modernization of Benefits and Obligations Act, formerly Bill C-23), the word "or" in the English version was inadvertently removed. The definition is amended to correct this error, and to improve the readability of this paragraph, with the same application as the initial amendment in Bill C-23. Acceptance of Fund for Registration ITA 146.3(2) Subsection 146.3(2) of the Act outlines the conditions that must be satisfied in order for a retirement income fund to be registered as a RRIF. Paragraph 146.3(2)(c) of the English version refers to a carrier who "is a person referred to as a depository in section 146". This paragraph is amended to replace the word "depository" with the word "depositary", which is the term used in section 146. This amendment applies after 2001. Paragraph 146.3(2)(f) prohibits a RRIF from receiving property, other than property transferred from sources listed in that paragraph. The paragraph is amended so that a RRIF may receive property transferred directly from a deferred profit sharing plan (DPSP) in accordance with subsection 147(19) of the Act. This amendment is consequential on an amendment to subsection 147(19) that permits direct transfers from DPSPs to RRIFs. For more details, see the commentary to that subsection. This amendment applies after March 20, 2003. Amount Included in Income ITA 146.3(5.1) In 2000, the Act was amended to include common-law partners, but some provisions, including the English version of subsection 146.3(5.1), were overlooked. This subsection is therefore amended to correct this omission. The amendment applies, in general, to the 2001 and subsequent taxation years. However, it may apply as of 1998 if the common-law partners jointly choose to be deemed as such, beginning in that year, for the purposes of the application of the Act. Tax Payable on Income from Non-qualified Investment ITA 146.3(9) Subsection 146.3(9) of the Act provides that, if a trust governed by a RRIF acquires a non-qualified investment, any income earned by the trust from the investment is taxable under Part I. Subsection 146.3(9) is amended to clarify that income from property that was a qualified investment at the time it was acquired but later became non-qualified is also taxable in respect of the non-qualified period. This amendment, which applies to the 2003 and subsequent taxation years, is consistent with the tax treatment of income earned by RRSP trusts from non-qualified investments under subsection 146(10.1) of the Act. Subparagraph 146.3(9)(b)(ii) is reworded for clarity, applicable on Royal Assent. Clause 145 Deferred Profit Sharing Plans ITA 147 Section 147 of the Act provides rules relating to DPSPs. Acceptance of Plan for Registration ITA 147(2)(e) Subsection 147(2) of the Act sets out the conditions that a profit sharing plan must satisfy in order to be registered as a DPSP. Paragraph 147(2)(e) requires that such a plan include a provision stipulating that no right of an employee who is a beneficiary under the plan is capable of surrender or assignment. Paragraph 147(2)(e) is amended in two ways. First, it is amended to extend the application of the provision to require that the stipulation apply to all persons who have rights under a DPSP, not just employee beneficiaries. Second, it is amended to provide that the stipulation is not required to prohibit: • an assignment under a court order or written agreement relating to the division of property on the breakdown of a marriage or common-law partnership; • an assignment by a deceased individual’s legal representative on the distribution of the individual’s estate; and • a surrender of benefits to avoid revocation of the plan’s registration. These new provisions are similar to the rule in Regulation 8502(f) that applies to registered pension plans (RPPs). The new provisions are, in part, consequential on amendments to subsection 147(19) of the Act that accommodate the division of DPSP assets on the breakdown of a marriage or common-law partnership. These amendments apply after March 20, 2003. Compensation ITA 147(5.11) Subsection 147(5.1) of the Act sets out the employer contribution limits for DPSPs. In general terms, the maximum employer contributions in respect of an individual for a calendar year cannot exceed the lesser of: (i) 18% of the individual’s compensation for the year from the employer; and (ii) 1/2 of the year’s money purchase limit. For this purpose, "compensation" and "money purchase limit" are generally as defined in subsection 147.1(1). Additional cross-plan limits apply if the individual also participates in an RPP sponsored by the employer or in a DPSP or RPP sponsored by a non-arm’s length employer. If the contribution limits are not respected for a calendar year, the Minister of National Revenue may revoke the registration of the DPSP. In addition, the employer is denied a deduction for all contributions made in the year, except as expressly permitted in writing by the Minister. Subsection 147(5.11) provides a special relieving rule that applies when an employee who is a beneficiary under a DPSP terminates employment with a participating employer in a calendar year. In this circumstance, for the purposes of determining whether the contribution limits have been satisfied, the employee’s compensation can be based on the compensation for the immediately preceding year, if it is more than the compensation for the year of termination. This rule recognizes that it is common practice for an employer to make contributions to a DPSP only after its fiscal year-end, since this is when profits are determined. This can often result in employer contributions being made based (in whole or in part) on employees’ earnings in the previous calendar year, but being included in the employees’ contribution limits for the current calendar year. This in turn can give rise to over-contributions when an employee terminates employment later in the year before having earned sufficient compensation to support the contribution. However, subsection 147(5.11) generally ensures that such over-contributions do not result in adverse tax effects by allowing the contribution limits to be based on the employee’s compensation from the preceding calendar year. There are, however, two policy concerns with the approach used in subsection 147(5.11). The first concern is that the provision deals only with over-contributions that involve employees who terminate employment. It does not provide relief for similar over-contributions that arise where an employee takes an unpaid leave of absence before having earned sufficient compensation to support any contributions that the employer had already made on his or her behalf. The second concern is that the provision allows DPSP contributions to be made in situations where there is no supporting employment income. To address these concerns, subsection 147(5.11) is repealed and replaced by a broader relief mechanism in section 8301 of the Regulations. The new mechanism will provide relief in both of the situations described above by allowing over-contributions to be ignored for purposes of the DPSP contribution limits, provided the excess is refunded from the plan. The repeal of subsection 147(5.11) applies to cessations of employment that occur in 2003 and subsequent calendar years, while the new refund mechanism in the Regulations applies for 2002 and subsequent calendar years. As a result, for excess contributions relating to cessations of employment that occur in 2002, employers will be entitled to relief either by relying on existing 147(5.11) or by using the new refund mechanism. Transfer to RPP, RRSP, RRIF or DPSP ITA 147(19) Subsection 147(19) of the Act provides for the tax-free transfer on behalf of an individual of a lump sum amount from a DPSP to an RPP, an RRSP or another DPSP for the individual’s benefit. Currently, direct transfers may be made on behalf of an individual only if the individual is an employee or former employee of an employer who participated in the plan or was a spouse or common-law partner of a deceased employee as at the date of the employee’s death. A number of technical amendments are being made to subsection 147(19) to provide greater consistency with the transfer provisions that apply to RPPs. Subsection 147(19) is amended so that the direct transfer on the death of an employee may be made on behalf of a former spouse or common-law partner of the deceased employee. It is also amended to allow for direct transfers of DPSP assets to be made on behalf of a spouse or common-law partner, or former spouse or common-law partner, of an employee or former employee, where the transfer relates to a division of property arising on the breakdown of their marriage or common-law partnership. Finally, subsection 147(19) is amended to allow for direct transfers from DPSPs to RRIFs. This is primarily of relevance where the surviving spouse or common-law partner of a deceased employee is over 69 years of age and, therefore, cannot transfer the DPSP assets to an RRSP. In this regard, the French version of paragraph 147(19)(d) is amended in order to add a reference to the word "fonds". These amendments apply to amounts transferred after March 20, 2003. Clause 146 Amounts Included in Computing Policyholder’s Income ITA 148(1)(e) Subsection 148(1) of the Act requires the inclusion in income of certain amounts from the disposition of a life insurance policy, but excludes from this rule annuities described in paragraph 148(1)(e). Paragraph 148(1)(e) describes • an annuity the payment for which was deductible under paragraph 60(l) in computing the policyholder’s income, and • an annuity acquired by a policyholder in circumstances to which subsection 146(21) applies (i.e., an annuity described in paragraph 60(l) and acquired with funds paid out of the Saskatchewan Pension Plan). An annuity described in paragraph 148(1)(e) is defined, by paragraph 304(1)(b) of the Income Tax Regulations, to be a "prescribed annuity contract" and, as such, is not subject to the accrual rules set out in section 12.2 of the Act. This treatment reflects the fact that the policyholder acquiring such an annuity does so with tax-deferred funds, and is generally meant to be taxed only when amounts are paid out of the annuity. Subsection 148(1) is amended to include, in the annuities described in paragraph (e), an annuity that is a "qualifying trust annuity" with respect to a taxpayer (as defined in new subsection 60.011(2)), the payment for which was deductible by the taxpayer under paragraph 60(l). This reflects the fact that a qualifying trust annuity will typically be held by a trust, rather than by the taxpayer who is entitled to the deduction under paragraph 60(l), and ensures that it is treated, for tax purposes, in the same manner as if it were held by the taxpayer. This amendment applies after 1988. Transfer to spouse at death ITA 148(8.2) The French version of subsection 148(8.2) of the Act is amended to correct a terminology error. In effect, the term "attribué" is replaced by "distribué" so that it is clear that an interest in a life insurance policy is actually distributed to the spouse or common-law partner of the policyholder and not simply set aside for him or her. This amendment will come into force on Royal Assent. Clause 147 Eligible Funeral Arrangements ITA 148.1 Section 148.1 of the Act provides for the tax-free build-up of income earned on contributions made under an eligible funeral arrangement (EFA), which is an arrangement that provides for the pre-funding of expenses with respect to funeral and cemetery services. Contributions made to an EFA are not deductible, and income earned in an EFA accrues tax-free. Distributions from an EFA as payment for the provision of funeral or cemetery services are not taxable. Other distributions from an EFA are generally treated first as a distribution of earnings, which is taxable, then as a return of contributions, which is not taxable. Definitions ITA 148.1(1) "relevant contribution" A "relevant contribution" to a particular arrangement is the amount of any contribution that is not made by way of a transfer from another eligible funeral arrangement or the amount of any other contribution made directly to another eligible funeral arrangement that can reasonably be considered to have been transferred into the particular arrangement. Paragraph (b) of the French version of the definition "relevant contribution" refers to « l’arrangement visé à l’alinéa a) » (the arrangement referred to in paragraph (a)). This is a source of confusion as paragraph (a) refers to two arrangements: the particular arrangement and an eligible federal arrangement. For clarification purposes, the French version of the definition is reformulated in order to introduce the notion of « arrangement donné » (a particular arrangement), making it clear which arrangement is referred to in paragraph (b). This amendment applies on Royal Assent. Transfer of Funds General Discussion ITA 148.1(3) to (5) Section 148.1 is amended to provide specific rules relating to transfers from one EFA account to another. In general terms, the changes are as follows: • A new provision (paragraph 148.1(4)(a)) deems the transferred amount to be distributed to the individual from whose EFA account the amount is transferred. However, if that individual is deceased, the amount is deemed to be distributed to the individual to whose EFA account the amount is transferred. This ensures that the transfer is included in income (to the extent that it does not exceed the income accumulated in the transferor account). • A new provision (paragraph 148.1(4)(b)) deems the transferred amount to be a contribution made to the recipient EFA account other than by way of transfer. This ensures that the earnings portion of the transferred amount is not taxed again when it is distributed from the recipient EFA account. • The provision that requires EFA distributions to be included in income (subsection 148.1(3)) is amended to ensure that the determination of the amount that can subsequently be distributed from the transferor EFA account on a tax-free basis is reduced by the portion of the transferred amount that was not included in income (i.e., that portion of the transferred amount that represents a return of contributions). • A new provision (subsection 148.1(5)) provides that these new rules do not apply if the transferor and the recipient EFA accounts are in respect of the same person, the entire balance in the transferor account is transferred to the recipient account and the transferor EFA account is terminated immediately after the transfer. These changes are described in more detail below. Income Inclusion on Return of Funds ITA 148.1(3) Subsection 148.1(3) of the Act provides for an income inclusion by a taxpayer in the event that there is a distribution of funds from an individual’s EFA account to the taxpayer (otherwise than as a payment for the provision of funeral or cemetery services with respect to the individual). The amount of the income inclusion is the lesser of the distributed amount and a second amount. In general terms, this second amount is determined by the formula: A + B – C where A is the balance in the EFA account immediately before the distribution, B is the total of all payments made from the EFA account before the distribution for the provision of funeral or cemetery services, and C is the total of all "relevant contributions" in respect of the EFA account that were made before the distribution. For the purpose of the description of C, an amount is defined in subsection 148.1(1) to be a "relevant contribution" in respect of a particular EFA account if • the amount was contributed to the particular EFA account otherwise than by way of transfer from another EFA account, or • the amount was contributed to another EFA account (otherwise than by way of transfer) and subsequently transferred (either from the original or a subsequent EFA account) to the particular EFA account. The effect of subsection 148.1(3) is to include in the income of the taxpayer the lesser of the amount received and an amount which generally represents the income accumulated in the EFA account. If the amount received by the taxpayer is greater than the amount included in the taxpayer’s income, the excess generally represents a non-taxable refund of relevant contributions (represented by the variable C in the formula). The description of C is amended so that its value is reduced, in effect, by any relevant contributions previously transferred from the EFA account to another EFA account. This ensures that the amount of the transferred relevant contribution (which, by virtue of subsection 148.1(3), can be distributed from the recipient EFA account tax-free) cannot also be used to support a subsequent tax-free withdrawal from the transferor EFA account. The description of C is amended to provide that its value is determined by the formula D – E For this purpose, the value of D is the amount determined under the existing description of C. The value of E is the total of all amounts each of which is • an amount which was previously transferred from the EFA account and deemed, by new subsection 148.1(4), to be a distribution minus • the portion of the deemed distribution that was required, by subsection 148.1(3), to be included in computing a taxpayer’s income. This amendment applies to transfers made after December 20, 2002. Deemed Distribution on Transfer ITA 148.1(4) New subsection 148.1(4) of the Act contains rules that apply when an amount is transferred from one EFA account to another EFA account of the same or another person. Paragraph 148.1(4)(a) deems the transfer to be a distribution from the transferor EFA account. If the individual from whose account the amount is transferred is alive at the time of the transfer, that individual is deemed to be the recipient of the distribution. Otherwise, the recipient is deemed to be the individual to whose EFA account the amount is transferred. This deeming provision ensures that subsection 148.1(3) applies to the transfer. Consequently, the transferred amount will be included in computing the income of the deemed recipient, except to the extent that the transferred amount exceeds the income accumulated in the transferor EFA account. Paragraph 148.1(4)(b) of the Act deems the amount transferred to be a contribution made (otherwise than by way of transfer) under the recipient EFA account. This ensures that the income portion of the transferred amount (which is included in income, under subsection 148.1(3), as a distribution from the transferor account) is considered to be a "relevant contribution" in respect of the recipient EFA account (which it would not otherwise be, because of the definition "relevant contribution" in subsection 148.1(1)). This allows it to subsequently be withdrawn from the recipient EFA account on a tax-free basis. New subsection 148.1(4) applies to transfers made after December 20, 2002. Non-application of Subsection (4) ITA 148.1(5) New subsection 148.1(5) of the Act provides that new subsection 148.1(4) does not apply when the entire balance of an individual’s EFA account is transferred to another EFA account of the same individual and the transferor EFA account is terminated immediately after the transfer. Consequently, there will be no deemed distribution resulting from such a transfer. New subsection 148.1(5) applies to transfers made after December 20, 2002. The following examples illustrate the application of the amendments to subsection 148.1. Example 1 Paul sets up an EFA account for the pre-funding of his funeral expenses. He contributes$10,000 to his account, and earns $7,000 of interest in the account. Paul transfers$3,000 to an EFA account which he establishes for his daughter, Gaby. The transferred amount is deemed to be a distribution to Paul under new paragraph 148.1(4)(a). Consequently, Paul includes in his income, under subsection 148.1(3), an amount of $3,000, which is the lesser of$3,000, which is the amount distributed, and$7,000, which is the amount determined by the formula under subsection 148.1(3): A + B – C (where C = D – E) =$17,000 + $0 – ($10,000 - $0) The transfer is treated, in effect, as a distribution of a portion of the income accumulated in the plan. Under new paragraph 148.1(4)(b), the transferred amount is also deemed to be a contribution made, other than by way of transfer, to Gaby’s EFA account. Thus, the$3,000 is considered to be a relevant contribution in respect of Gaby’s EFA account, and can subsequently be withdrawn tax-free.
Example 2 The facts are the same as in Example 1, except that Paul transfers $13,000 to Gaby’s EFA. The transferred amount is deemed to be a distribution to Paul under new paragraph 148.1(4)(a). Consequently, Paul includes in his income, under subsection 148.1(3), an amount of$7,000, which is the lesser of $13,000, which is the amount distributed, and$7,000, which is the amount determined by the formula under subsection 148.1(3): A + B – C ( where C = D – E) = $17,000 +$0 – ($10,000 –$0) The transfer is treated, in effect, as a distribution of all of the income accumulated in the plan ($7,000), which is taxable, plus a return of a portion of the relevant contributions in respect of the EFA ($6,000), which is not taxable. Under new paragraph 148.1(4)(b), the transferred amount is also deemed to be a contribution made, other than by way of transfer, to Gaby’s EFA account. This has no particular significance with respect to the portion of the transfer that represents relevant contributions in respect of Paul’s EFA account, since this amount would be considered to be a relevant contribution to Gaby’s EFA account under the existing rules. However, it does have significance with respect to the portion of the transfer that represents income in Paul’s EFA account, in that it allows that portion to become a relevant contribution in respect of Gaby’s EFA account which can then be withdrawn from Gaby’s account tax-free.
Example 3 The facts are the same as in Example 2. After the transfer of $13,000, the balance in Paul’s EFA account is$4,000, all of which represents relevant contributions in respect of the account. Over the next few years, the account earns an additional $2,500 of interest. Paul then withdraws the entire balance from the account. The withdrawal is a distribution under subsection 148.1(3). Consequently, Paul includes$2,500 in his income, which is the lesser of: $6,500, which is the amount of the withdrawal, and$2,500, which is the amount determined by the formula under subsection 148.1(3): A + B – C (where C = D – E) = $6,500 + 0 - ($10,000 - $6,000) The value of E ($6,000) is the excess of the amount that was previously transferred and to which subsection 148.1(4) applied ($13,000) over the portion of that amount that was included in income under subsection 148.1(3) ($7,000).
Clause 148
Exemptions
ITA
149
Section 149 of the Act provides that no tax is payable under Part I on certain persons’ taxable income for a period in a taxation year during which the person is a person listed in that section.
Exemptions - Municipalities and Other Governmental Public Bodies
ITA
149(1)(d.5)
Paragraph 149(1)(d.5) of the Act exempts from tax, subject to an income test, the taxable income of any corporation, commission or association at least 90% of the capital of which is owned by one or more municipalities in Canada.
In accordance with the Tax Court of Canada decision in Otineka Development Corporation Limited and 72902 Manitoba Limited v. The Queen, 94 D.T.C. 1234, [1994] 1 C.T.C. 2424, an entity could be considered a municipality for the purpose of this paragraph on the basis of the functions it exercised. More recently, however, the decision in Tawich Development Corporation v. Deputy Minister of Revenue of Quebec, [1997] 2 C.N.L.R. 187 (Que. Civil Chamber), aff’d 2001 D.T.C. 5144 (Que. C.A.), a decision under the Taxation Act (Quebec), held that an entity could not attain the status of a municipality by exercising municipal functions but only by statute, letters patent or order. From a tax policy perspective, it is desired that the entities previously entitled to the exemption on the basis of the Otineka decision continue to have access to the exemption. This amendment resolves the uncertainty resulting from the two conflicting cases. The exemption in paragraph 149(1)(d.5) is therefore extended to include any corporation, commission or association at least 90% of the capital of which was owned by one or more entities each of which is a municipal or public body performing a function of government in Canada, which is consistent with the bodies described in paragraph 149(1)(c) of the Act.
This amendment applies to taxation years that begin after May 8, 2000.
Exemptions - Subsidiaries of Municipal Corporations
ITA
149(1)(d.6)
Paragraph 149(1)(d.6) of the Act exempts from tax, subject to an income test, a wholly-owned subsidiary of a corporation, commission or association referred to in paragraph 149(1)(d.5) of the Act. As a consequence of the amendment to paragraph 149(1)(d.5), the geographical boundaries of the entities referred to in subparagraphs (i) and (ii) of paragraph 149(1)(d.6) are expanded to include references to all of the entities in the amended 149(1)(d.5).
This amendment applies to taxation years that begin after May 8, 2000.
Trusts established because of the Environment Quality Act (Quebec) or the Nuclear Fuel Waste Act
ITA
149(1)(z.1) and (z.2)
New paragraph 149(1)(z.1)) exempts from tax under Part I a trust created because of a requirement imposed by section 56 of the Environment Quality Act (Quebec). That provision requires certain residual materials elimination facilities to provide financial guarantees by way of establishment of a social trust to cover certain costs after the closure of the facility. This exemption applies only where no persons are beneficially interested in the trust other than Her Majesty in right of Canada, Her Majesty in right of a province and municipalities that are exempt from taxation under subsection 149(1) of the ITA.
Similarly, new paragraph 149(1)(z.2) exempts from tax under Part I a trust created because of a requirement imposed by subsection 9(1) of the Nuclear Fuel Waste Act (NFWA). That provision requires specified entities to contribute moneys to a trust fund for the management of nuclear fuel waste. In this case, the exemption only applies where no persons are beneficially interested in the trust other than Her Majesty in right of Canada, Her Majesty in right of a province, a Crown-owned nuclear energy corporation that is exempt from taxation under subsection 149(1) of the ITA or the waste management organization that is required to be set up under the provisions of the NWFA (provided that all the shares of the waste management organization are owned by nuclear energy corporations).
These provisions ensure that the tax consequences to a municipality or Crown-owned nuclear energy corporation that is required by federal or provincial legislation to set up a trust to fund an environmental obligation are the same as if the municipality or the Crown-owned nuclear energy corporation accumulated the funds internally rather than in a trust.
These amendments apply to the 1997 and subsequent taxation years.
Income Test
ITA
149(1.2)
Subsection 149(1.2) of the Act excludes, for the purposes of paragraphs 149(1)(d.5) and (d.6) of the Act, certain income from the determination of where an entity to which either of those paragraphs applies derives its income. As a consequence of the amendment to paragraph 149(1)(d.5), a written agreement in subsection 149(1.2) is expanded to include reference to a municipal or public body.
In addition, subparagraph 149(1.2)(a)(vi) is added to clarify that the geographical boundary of a municipal or public body performing a function of government in Canada is defined to be the area described in new subsection (11).
This amendment applies to taxation years that begin after May 8, 2000.
ITA
149(1.3)
Subsection 149(1.3) of the Act provides that, for the purposes of applying paragraph 149(1)(d.5) and subsection 149(1.2) of the Act to a corporation, 90% of the capital of the corporation is considered to be owned by one or more municipalities only if the municipalities are entitled to at least 90% of the votes associated with the shares of the corporation.
As a consequence of the amendment to paragraph 149(1)(d.5), subsection 149(1.3) is amended applicable to taxation years that begin after May 8, 2000, to include reference to municipal or public bodies performing a function of government in Canada.
In addition, subsection 149(1.3) is replaced, applicable to taxation years that begin after December 20, 2002, to provide that paragraphs 149(1)(d) to (d.6) do not apply to exempt a person’s taxable income for a period in a taxation year in two cases.
First, under new paragraph 149(1.3)(a), a corporation is not exempt from tax on its taxable income for a period in a taxation year if at any time during the period the corporation has issued shares that are owned by one or more persons (other than certain tax-exempts) that, in total, give them more than 10% of the votes that could be cast at a meeting of shareholders. For this purpose, it is necessary to determine whether more than 10% of the votes could be cast at a meeting of the shareholders by a person or persons other than:
• Her Majesty in right of Canada or of a province,
• a municipal or public body performing a function of government in Canada, or
• a commission, an association or a corporation, to which any of paragraphs 149(1)(d) to (d.6) apply.
Second, under new paragraph 149(1.3)(b), a person is not exempt because of any of paragraphs 149(1)(d) to (d.6) from tax on taxable income for a period in a taxation year if at any time in the period the person is, or would be if the person were a corporation, controlled, directly or indirectly in any manner whatever, by a person (or by a group of persons that includes a person) other than:
• Her Majesty in right of Canada or of a province,
• a municipal or public body performing a function of government in Canada, or
• a commission, an association or a corporation, to which any of paragraphs 149(1)(d) to (d.6) apply.
For further details about the expression "controlled, directly or indirectly in any manner whatever", reference should be made to subsections 256(5.1) and (6) of the Act. In general, the expression refers to a controller, who has any direct or indirect influence that, if exercised, would result in control in fact of the person.
Geographical Boundaries - Body Performing Government Functions
ITA
149(11)
Subsection 149(11) of the Act is added to define, for the purposes of section 149, the geographical boundaries of a municipal or public body performing a function of government in Canada. Those boundaries are defined as encompassing the area in respect of which an Act of Parliament or an agreement given effect by an Act of Parliament recognizes or grants to the body a power to impose taxes; or if there has been no such recognition or grant, the area within which the body has been authorized by the laws of Canada or of a province to exercise that function.
For example, if a particular self-governing First Nation meets the definition of "a public body performing a function of government in Canada," it is intended that the relevant geographic boundary would delineate the area where the self-government agreement, or the statute enacting self-government powers, provides the First Nation authority to impose direct taxes. As a second example, if a particular Indian Band meets the definition of "a public body performing a function of government in Canada," it is intended that the geographic boundary of the Indian Band be the band’s reserves as defined in the Indian Act. Similarly, if a particular school board meets the definition of "a municipal or public body performing a function of government in Canada" it is intended that the geographic boundary of the school board be the area of jurisdiction of the board as defined by provincial legislation or regulation.
This amendment applies to taxation years that begin after May 8, 2000.
Clause 149
Charities
ITA
149.1
Section 149.1 of the Act provides the rules that must be met for charities to obtain and keep registered status. A registered charity is exempt from tax on its taxable income and can issue receipts which entitle its donors to claim tax relief for their donations.
Definitions
ITA
149.1(1)
Subsection 149.1(1) of the Act contains definitions that are relevant for the purposes of section 149.1.
"charitable organization"
The definition "charitable organization" provides that more than 50% of the directors, trustees, officers or similar officials of a charitable organization must deal with each other and with each of the other directors, trustees, officers or similar officials at arm’s length.
For a charity that has applied for registration after February 15, 1984 and which has been designated as a private or public foundation, the definition "charitable organization" also requires that not more than 50% of the charity’s capital be contributed by a person or group of persons not dealing with each other at arm’s length. This definition is amended to replace the "contribution" test with a "control" test. As a result, a charity will not be disqualified from being treated as a charitable organization solely because a person, or a group of persons not dealing with each other at arm’s length, has contributed more than 50% of the charity’s capital. However, such a person or group is not permitted to control the charity in any way, nor may the person or the members of the group represent more than 50% of the directors, trustees, officers and similar officials of the charity.
This amendment generally applies after 1999.
"disbursement quota"
The "disbursement quota" for a taxation year of a charitable foundation or organization is defined in subsection 149.1(1) of the Act for the purpose of determining the amount that the charity is required to spend on charitable activities or gifts to other charities. One factor in calculating the disbursement quota is a specified proportion of donations for which tax receipts are issued.
Consequential to the addition of new subsection 248(31) of the Act, the definition "disbursement quota" is to be read in respect of gifts made after December 20, 2002 and in a taxation year that begins before March 23, 2004, to provide that the amount of a gift for which a tax receipt is issued refers to the "eligible amount" of the gift. For additional information, see the commentary to new subsection 248(31).
"enduring property"
The English version of the definition "enduring property", which applies for the purpose of the definition "disbursement quota" to taxation years that begin after March 22, 2004, is amended to correct a cross-reference in its paragraph (d).
"public foundation"
The definition "public foundation" provides that more than 50% of the directors, trustees, officers or similar officials of a public foundation must deal with each other and with each of the other directors, trustees, officers or similar officials at arm’s length.
This definition requires that not more than 50% (75% in some cases) of the foundation’s capital can be contributed by a person or group of persons not dealing with each together at arm’s length. The "contribution" test in the definition is replaced by a "control" test. As a result, a foundation will not be disqualified from being treated as a public foundation solely because a person, or a group of persons not dealing with each other at arm’s length, has contributed more than 50% of the foundation’s capital. However, such a person or group is not permitted to control the foundation in any way, nor may the person or the members of the group represent more than 50% of the directors, trustees, officers and similar officials of the foundation.
This amendment generally applies after 1999.
Revocation of Registration
ITA
149.1(2), (3) and (4)
Subsections 149.1(2), (3) and (4) of the Act set out the reasons for which the Minister of National Revenue may revoke the registration of a charitable organization, a public foundation and a private foundation, respectively. These subsections are amended to permit the revocation of the registration of such entities if they make gifts (other than gifts made in the course of their charitable activities) to persons or entities that are not qualified donees. A "qualified donee" is essentially a person or entity to which a tax deductible or tax creditable donation may be made.
Accumulation of Property
ITA
149.1(9)
Subsection 149.1(8) of the Act permits a registered charity, with the approval of the Minister of National Revenue, to accumulate property over a specified period for a particular purpose. The amount of such property accumulated is deemed to have been expended in the taxation year of the charity in which it was accumulated. If in fact the charity defaults on this responsibility by not using the property for the approved purpose within the specified period, subsection 149.1(9) treats that property as income of the charity and the amount of a gift for which it issued a receipt. This affects the calculation of the disbursement quota of the charity, with the result that the amount of the property must be actually disbursed in the year following default.
Subsection 149.1(9) is amended consequential to the addition of new subsection 248(31) of the Act, in respect of gifts made after December 20, 2002, to provide that the amount of a gift for which a tax receipt is issued refers to the "eligible amount" of a gift. For additional information, see the commentary to new subsection 248(31).
Information May be Communicated
ITA
149.1(15)(b)
Section 241 of the Act prohibits the use or communication by an official of information obtained under the Act unless specifically authorized by one of the exceptions found in that section. Paragraph 149.1(15)(b) of the Act, which deals with charities, provides that, notwithstanding section 241, the Minister of National Revenue may publish a listing of all registered or previously registered charities indicating the name, location, registration number and, where the charity is no longer registered, the effective date of the revocation, annulment or termination of the charity’s registration. This provision does not currently allow for the release of similar information in respect of registered Canadian amateur athletic associations. Since taxpayers who make donations to such associations obtain the same tax relief that is available in respect of donations to registered charities and, since subsection 149.1(15) is intended to provide transparency for the benefit of potential donors, paragraph 149.1(15)(b) is amended, effective after Royal Assent to this measure, to allow for the release of such information in respect of Canadian amateur athletic associations.
Clause 150
Assessment
ITA
152
Section 152 of the Act contains rules relating to assessments and reassessments of tax, interest and penalties payable by a taxpayer and to determinations and redeterminations of amounts of tax deemed to have been paid by a taxpayer.
Provisions Applicable
ITA
152(1.2)
Subsection 152(1.2) is amended to delete the reference to section 126.1 of the Act, consequential to the repeal of that section. For additional information, see the commentary to section 126.1.
This change applies in respect of forms filed after March 20, 2003.
Determination of UI Premium Tax Credit
ITA
152(3.4)
This subsection enables a taxpayer to request the Minister of National Revenue to determine the amount deemed by subsection 126.1(6) or (7) of the Act to be an overpayment on account of the taxpayer’s liability under Part I of the Act.
This subsection is repealed consequential to the repeal of section 126.1. For additional information, see the commentary to section 126.1.
This change applies in respect of forms filed after March 20, 2003.
Notice of Determination
ITA
152(3.5)
Subsection 152(3.5) of the Act requires the Minister of National Revenue to respond to a request for a determination of the UI premium tax credit. This subsection is repealed consequential to the repeal of section 126.1. For additional information, see the commentary to section 126.1.
This change applies in respect of forms filed after March 20, 2003.
Clause 151
Withholding
Section 153 of the Act requires the withholding of tax from certain payments, described in paragarphs (a) to (t). The person making such a payment is required to remit the amount withheld to the Receiver General on behalf of the payee. Paragraph (d.1) is amended consequential to the introduction of the new Quebec Parental Insurance Plan introduced on January 1, 2006. This amendment applies to the 2006 and subsequent taxation years.
Clause 152
Instalments
ITA
157(3)
Section 157 of the Act requires a corporation to pay monthly instalments of its total tax payable under Parts I, I.3, VI, VI.1 and XIII.1 of the Act. Subsection 157(3) allows corporations to reduce each monthly instalment by 1/12 of the amount of certain tax refunds, including the "dividend refund" under section 129 of the Act. For most mutual fund corporations, the dividend refund amount is computed according to rules set out in subsection 131(5) of the Act. Paragraph 157(3)(c), which allows a mutual fund corporation to apply its dividend refund to reduce its instalments, therefore refers to subsection 131(5). However, prescribed labour-sponsored venture capital corporations (LSVCCs), which are by definition mutual fund corporations, do not use subsection 131(5) to compute their dividend refunds – instead, they use special rules in subsection 131(11) of the Act. To ensure that subsection 157(3) applies appropriately to LSVCCs, this amendment adds to paragraph 157(3)(c) a reference to subsection 131(11). The amendment applies for the 1999 and subsequent taxation years.
Clause 153
Person Acting for Another – Personal Liability
ITA
159(3)
Subsection 159(1) of the Act provides, in part, that a legal representative acting for another person is jointly and severally liable for each amount payable by the other person under the Act, to the extent that the representative has possession and control of the other person’s assets. If the representative distributes assets of the other person before obtaining a certificate from the Minister of National Revenue that the other person’s tax debts have been paid, the Minister may, under subsection 159(3) of the Act, assess the representative for the amount of the debt.
Subsection 159(3) is amended to clarify that a legal representative so assessed after December 20, 2002 is subject to interest on the assessment without any limit on the amount of interest for which the representative may be liable.
Clause 154
Tax Liability – Non-arm’s Length Transfers of Property
ITA
160
Section 160 of the Act contains rules regarding the joint and several liability of a taxpayer for the income tax liability of another person (the "tax debtor") who, when not dealing at arm’s length with the taxpayer, transferred property to the taxpayer for consideration less than its fair market value.
ITA
160(1)(e)
The amount that a taxpayer is liable to pay in respect of the transfer of property from a non-arm’s length tax debtor is determined under subsection 160(1) of the Act. The Minister may assess the taxpayer for such a liability under subsection 160(2) of the Act. Paragraph 160(1)(e) is amended, in respect of assessments made after December 20, 2002, to clarify that the assessment of the taxpayer is subject to interest, without any limit on the amount of interest for which the taxpayer may be liable.
Joint Liability Where subsection 69(11) Applies
ITA
160(1.1)
Subsection 160(1.1) of the Act provides that where subsection 69(11) of the Act applies to deem a disposition of property to have occurred at fair market value, both the person disposing of the property and the person acquiring the property are jointly and severally liable for the payment of each other’s liabilities arising under the Act as a result of that disposition.The Minister of National Revenue may assess the person for such a liability under subsection 160(2) of the Act. Subsection 160(1.1) is amended, in respect of assessments made after December 20, 2002, to clarify that the assessment of the taxpayer is subject to interest.
Joint Liability – Tax on Split Income
ITA
160(1.2)
Subsection 160(1.2) of the Act, which applies in respect of tax owing on split income, is amended in two respects.
First, paragraphs 160(1.2)(a), (b) and (d) are amended to replace the phrase "goods or services" with the phrase "property or services" as a consequence of the same changes made to paragraphs (b) and (c) of the definition "split income" in subsection 120.4(1). These amendments apply after December 20, 2002.
Second, a "postamble" is added to subsection 160(1.2) to clarify that, in respect of assessments made under subsection 160(2) after December 20, 2002, the assessment is subject to interest.
Assessment
ITA
160(2)
Subsection 160(2) of the Act allows the Minister of National Revenue to assess a taxpayer at any time in respect of liabilities arising under section 160, with such assessment having the same effect as if it had been made under section 152 of the Act. Subsection 160(2) is amended, in respect of assessments made after December 20, 2002, to clarify that the assessment is subject to interest.
Clause 155
Where Excess Refunded
ITA
160.1(3)
Subsection 160.1(3) of the Act allows the Minister of National Revenue to assess a taxpayer in respect of excess refunds and overpayments for which the taxpayer is jointly and severally liable under subsection 160.1(1), (1.1), (2.1) or (2.2) of the Act. Subsection 160.1(3) is amended, in respect of such assessments made after December 20, 2002, to clarify that such an assessment is subject to interest, except that no interest is payable to the extent that the excess refund is attributable to the overpayment of a GST tax credit or a child tax benefit.
Clause 156
Joint and Several Liability – Amounts Received out of or under RRSP
ITA
160.2(1), (2) and (3)
Subsection 160.2(1) of the Act provides that a taxpayer who receives benefits out of another person’s registered retirement savings plan is jointly and severally liable for the portion of that other person’s tax that is attributable to those benefits. Subsection 160.2(2) of the Act provides a similar result with respect to benefits received out of another person’s registered retirement income fund. The Minister may assess the taxpayer for such a liability under subsection 160.2(3) of the Act.
Subsections 160.2(1), (2) and (3) are amended, in respect of assessments made after December 20, 2002, to clarify that the assessment is subject to interest, without any limit on the amount of interest for which the taxpayer may be liable.
Joint and Several Liability in Respect of a Qualifying Trust Annuity
ITA
160.2(2.1)
New subsection 160.2(2.1) applies to annuities that are "qualifying trust annuities" with respect to a taxpayer (as defined in new subsection 60.011(2)).
A distinguishing feature of a qualifying trust annuity with respect to a taxpayer is that the annuitant thereunder is a trust under which the taxpayer is a beneficiary. Such an annuity will typically be acquired and held either by the trust that is the annuitant under the annuity, or by the estate of a deceased spouse, common-law partner, parent or grandparent of the taxpayer which acquired the annuity with proceeds received from a registered retirement savings plan or registered retirement income fund of the deceased individual or from a registered pension plan in which the deceased individual participated.
Where the cost of a qualifying trust annuity with respect to a taxpayer is deductible by the taxpayer under paragraph 60(l) and the taxpayer has not died before 2006, new section 75.2 deems amounts payable out of or under the annuity after 2005 and before the taxpayer’s death to have been received by the taxpayer. Section 75.2 also deems the taxpayer to have received, immediately before death, an amount out of or under the annuity equal to the fair market value of the annuity. By virtue of paragraph 56(1)(d.2), the taxpayer is required to include these amounts in computing income under Part I.
New subsection 160.2(2.1) provides that, where a taxpayer is deemed by section 75.2 to have received an amount from a qualifying trust annuity, the annuitant and the policyholder (which may be one and the same) are jointly and severally, or solidarily, liable for the portion of the taxpayer’s tax that is attributable to the amounts that the taxpayer is deemed to have received from the annuity. The Minister of National Revenue may reassess the annuitant and the policyholder for such a liability under subsection 160.2(3) of the Act.
Subsection 160.2(2.1) applies to assessments made after 2005.
No Limitation on Liability
ITA
160.2(2.2)
New subsection 160.2(2.2) of the Act provides that the provisions of new subsection 160.2(2.1), which make the annuitant and policyholder of a "qualifying trust annuity" with respect to a taxpayer (as defined in new subsection 60.011(2)) jointly and severally, or solidarily, liable for a portion of the taxpayer’s tax, do not limit the liability of the taxpayer under any provision of the Act. It also provides that there is no limitation on the liability of the annuitant or policyholder for the interest for which the annuitant or policyholder is liable under the Act on an assessment in respect of an amount that the annuitant or policyholder is liable to pay because of subsection 160.2(2.1).
Subsection 160.2(2.2) applies to assessments made after 2005.
Rules Applicable – Qualifying Trust Annuity
ITA
160.2(5)
New subsection 160.2(5) of the Act provides that a payment by the annuitant or policyholder of a "qualifying trust annuity" with respect to a taxpayer (as defined in new subsection 60.011(2)), on account of the annuitant’s or policyholder’s joint liability for a portion of the taxpayer’s tax, directly reduces the joint liability to the extent of the payment. However, a payment by the taxpayer on account of the taxpayer’s tax liability reduces the joint liability of the annuitant and the policyholder only to the extent that the payment reduces the total liability of the taxpayer to an amount that is less than the amount in respect of which the annuitant and policyholder were made jointly liable under subsection 160.2(2.1).
Subsection 160.2(5) applies to assessments made after 2005.
Clause 157
Liability – Amounts Received out of or under RCA Trust
ITA
160.3(1) and (2)
Subsection 160.3(1) of the Act provides that a person who receives benefits from a retirement compensation arrangement that relate to another taxpayer’s employment is jointly and severally liable for the portion of that other taxpayer’s tax that is attributable to such benefits. The Minister of National Revenue may assess the person for such a liability under subsection 160.3(2) of the Act. Subsections 160.3(1) and (2) are amended, in respect of assessments made after December 20, 2002, to clarify that such an assessment is subject to interest, without any limit on the amount of interest for which the person may be liable.
Clause 158
Liability – Transfers by Insolvent Corporation
ITA
160.4(1) to (3)
Subsection 160.4(1) of the Act applies where a transfer of property has been made by a corporation and, as a consequence of the transfer (or the transfer combined with other transactions), the corporation is precluded under subsection 61.3(3) of the Act from deducting an amount under section 61.3. Where this is the case, the transferee is jointly and severally liable with the transferor under subsection 160.4(1) for the transferor’s tax under Part I of the Act for the first taxation year of the transferor that ends after the time of the transfer and for preceding taxation years. The liability of the transferee applies up to the amount, if any, by which the fair market value of the property at the time of the transfer exceeds the fair market value of the consideration given for the property transferred.
In addition, subsection 160.4(2) of the Act provides for joint and several liability of subsequent non-arm’s length transferees for the corporation’s Part I tax if the original transferee makes a further non-arm’s length transfer and one of the reasons that the transfer was made was to prevent the enforcement of section 160.4.
Under subsection 160.4(3) of the Act, the Minister of National Revenue may assess a transferee for a liability arising under subsections 160.4(1) or (2).
Subsections 160.4(1), (2) and (3) are amended, in respect of assessments made after December 20, 2002, to clarify that such an assessment is subject to interest, without any limit on the amount of interest for which the transferee may be liable.
Clause 159
Penalties
ITA
162
Section 162 of the Act imposes penalties for infractions such as the failure to file a return for a taxation year.
Failure to Provide Identification Number
ITA
162(6)
Subsection 162(6) of the Act provides a penalty for failure by a person or partnership to provide on request their social insurance number or their business number to any person who is required to make an information return in their regard. The French version of this subsection refers to individuals instead of persons, thereby excluding corporations. The provision is therefore amended to replace the word « particulier » by the word « personne ».
This amendment applies after June 18, 1998, the date on which the penalty in subsection 162(6) was extended to corporations in respect of business numbers.
Clause 160
False Statements or Omissions – GSTC Payments
ITA
163(2)(c.1)
Subsection 163(2) of the Act imposes a penalty where a taxpayer knowingly, or in circumstances amounting to gross negligence, participates in or makes a false statement for the purposes of the Act. The penalty is determined with reference to the understatement of tax or the overstatement of amounts deemed to be paid on account of tax. Paragraph 163(2)(c.1) imposes a penalty where the false statement relates to the goods and services tax credit (GSTC).
The GSTC provisions were recently amended (S.C. 2002, chapter 9, formerly Bill C-49) to make the credit more responsive to changes in family circumstances by providing that the eligibility to the credit and the amount paid in each quarter reflect such changes that occurred before the end of the preceding quarter rather than in the preceding taxation year.
Paragraph 163(2)(c.1) is amended to reflect the new quarterly calculation of the GSTC. This amendment applies to amounts deemed to be paid during months specified for the 2001 and subsequent taxation years.
Clause 161
Refunds
ITA
164
Section 164 of the Act contains rules relating to refunds of taxes, including provisions dealing with repayments, application to other debts, and interest.
Refund of Instalment – Hardship
ITA
164(1.51) to (1.53)
New subsections 164(1.51) to (1.53) of the Act, which apply on Royal Assent, allow the Minister of National Revenue to refund excessive instalment amounts paid on account of a taxpayer’s tax liability. In order for such a refund to be made, four conditions must be met. Three of these are set out in new subsection 164(1.51). First, the taxpayer must have paid one or more instalments of tax under Part I or, where the taxpayer is a corporation, Part I.3, VI, VI.1 or XIII of the Act. Second, it must be reasonable to conclude that the total amount of the instalments the taxpayer has paid exceeds the total amount of taxes payable by the taxpayer under those Parts for the year. Third, the Minister must be satisfied that the payment of the instalments has caused or will cause the taxpayer undue hardship.
The last condition is implied in new subsection 164(1.52) of the Act. The availability of an instalment refund in a particular case is a matter of the Minister’s discretion. The final condition is therefore that the Minister agree to make the refund. Similarly, new subsection 164(1.52) makes it clear that the amount of any instalment refund is to be decided by the Minister: the Minister may refund all or any part of an excessive instalment.
New subsection 164(1.53) of the Act provides that, for the purposes of computing interest and penalties, a taxpayer that receives an instalment refund is treated as not having paid the instalment to that extent.
Refund of UI Premium Tax Credit
ITA
164(1.6)
Subsection 164(1.6) of the Act provides rules concerning refunds of the UI premium tax credit. This subsection is repealed consequential to the repeal of section 126.1. For additional information, see the commentary to section 126.1.
This change applies in respect of forms filed after March 20, 2003.
Interest on Refunds and Repayments
ITA
164(3)
Subsection 164(3) of the Act provides for the payment of interest on tax refunds. Two amendments are made to the subsection. First, the preamble of that subsection is being amended to adapt the wording to the new terminology now used elsewhere the Act. Second, the reference to section 126.1 is deleted consequential on the repeal of that section.
These changes apply in respect of forms filed after March 20, 2003.
Clause 162
Large Corporations Tax
ITA
Part I.3
Part I.3 of the Act imposes a tax (generally known as the "large corporations tax") on the amount by which a large corporation’s taxable capital employed in Canada exceeds a $50 million "capital deduction" (shared among related corporations). Definitions ITA 181(1) "financial institution" Subsection 181(1) of the Act sets out definitions for the purposes of the Part I.3 tax on large corporations. Among these is the term "financial institution," which is relevant for a number of purposes. Most importantly, corporations that are financial institutions compute their capital for the purposes of Part I.3 differently from other corporations. The status of a particular corporation is also relevant to corporations that invest in the particular corporation or hold its debt, since whether certain of those investments are counted in the investor corporation’s "investment allowance" – and thus whether they will reduce their own tax under Part I.3 – depends, in part, on whether the particular corporation is a financial institution. In addition to listing several types of corporations, the definition "financial institution" provides, in its paragraph (g), that the definition applies as well to a prescribed corporation. Currently, such corporations are prescribed under section 8604 of the Regulations. Paragraph (a) of that regulation provides that a corporation of which all or substantially all of the assets of which are shares or indebtedness of a financial institution (as defined in subsection 181(1) of the Act) to which the corporation is related, is itself prescribed to be a financial institution; the remaining paragraphs list particular corporations by name. Paragraph (g) of the definition is amended to reflect a fundamental change in the technique by which these corporations will be identified as financial institutions. Rather than listing corporations in a regulation, this new approach is to list them in a schedule to the Act. Amended paragraph (g) therefore refers to corporations that are either listed in the schedule, as per new subparagraph (g)(i), or that are described in new subparagraph (g)(ii), currently paragraph (a) of section 8604 of the Regulations. These changes to paragraph (g) of the definition apply after December 22, 1997. As a consequence to the changes to paragraph (g) of the definition, section 8604 of the Regulations is to be repealed and a schedule is added at the end of the Act. Subject to a number of deletions due primarily to name changes and amalgamations, the schedule lists those corporations that are currently prescribed under section 8604 immediately before its repeal. The schedule also lists a number of corporations that are not currently prescribed, but meet the requirements for treatment as financial institutions and have asked to be treated as such. Transitional rules for paragraph (g) of the definition ensure that corporations prescribed before the repeal of Regulation 8604 retain the status that they would have had under paragraph (g) had it not been amended to exclude prescribed corporations. As described above, a number of corporations currently not prescribed are listed in the schedule, effective as of dates that precede December 20, 2002. Transitional rules ensure that, for any taxation year that begins before December 20, 2002, no corporation that deals at arm’s length with any of these corporations will lose an investment allowance as a result the corporation’s change in status to a financial institution under paragraph (g) of the definition. Clause 163 Taxable Capital Employed in Canada ITA 181.2 Section 181.2 of the Act provides rules for determining the capital, taxable capital, taxable capital employed in Canada and investment allowance of corporations (other than financial institutions) resident in Canada for the purposes of the Part I.3 tax on large corporations. Section 181.2 is amended in two respects. First, subsections 181.2(3) and (5) of the Act are amended to clarify the effect of tiered partnerships: structures in which one partnership is a member of another partnership. Second, an amendment is made to subsection 181.2(3) to accommodate a change to the accounting presentation of redeemable preferred shares. Tiered Partnerships Subsection 181.2(3) defines the "capital" of a corporation, and in paragraph 181.2(3)(g) includes in a corporation’s capital a pro-rata share of the reserves, deferred foreign exchange gains and indebtedness of any partnership of which it is a member. To determine those amounts, the relevant paragraphs of subsection 181.2(3) are applied to the partnership in the same way as they apply to corporations. Paragraph 181.2(3)(g) is amended so that it itself applies on this basis. As a result, the proration of the reserve, deferred gain and debt amounts will carry through any number of tiered partnerships. Subsection 181.2(4) of the Act provides for the "investment allowance" by which, in broad terms, one corporation’s investment in another is excluded from the first corporation’s taxable capital. Subsection 181.2(5) determines the carrying value of an interest of a corporation in a partnership for this purpose. Subsection 181.2(5) is amended to ensure that the carrying value of an interest of a corporation in a particular partnership, for the purposes of subsection 181.2(4), includes the carrying value of an interest of the particular partnership in another partnership. These changes to paragraph 181.2(3)(g) and subsection 181.2(5) apply after December 20, 2002. Preferred Shares In general, a corporation’s tax payable under Part I.3 of the Act is computed with reference to amounts reflected in the balance sheet of the corporation, as prepared in accordance with generally accepted accounting principles (GAAP). The Canadian Institute of Chartered Accountants’ Handbook (the Handbook), which is the principal authority of GAAP in Canada, requires that a liability of a corporation in respect of a redeemable preferred share be reflected on the corporation’s balance sheet. The Handbook provides that this liability may be accounted for in one of two ways. Under the first method, the difference between the stated capital of a share and its redemption value is charged to retained earnings, which in some cases may result in the corporation having negative retained earnings or a deficit. Retained earnings are unaffected under the second method, under which a line account is set up reflecting the redemption liability of the preferred shares. Current paragraph 181.2(3)(i) of the Act allows for a reduction of a corporation’s capital, to the extent of any deficit deducted in computing the corporation’s shareholders’ equity. To accommodate the alternative presentation of a provision for the redemption of preferred shares, the paragraph is amended to refer explicitly to the amount of such a provision. This amendment applies to taxation years that begin after 1995. Clause 164 Taxable Capital Employed in Canada of Financial Institution ITA 181.3 Section 181.3 of the Act provides rules for determining the capital, taxable capital, taxable capital employed in Canada and investment allowance of a financial institution (as defined in subsection 181(1)) for the purposes of the Part I.3 tax on large corporations. Section 181.3 is amended in two respects. First, changes are made to several paragraphs of subsection 181.3(3) to accommodate a change to the accounting presentation of redeemable preferred shares. Second, a new subparagraph and a new clause are added, respectively, to paragraph 181.3(3)(c) and subparagraph 181.3(3)(d)(iv) to reflect the manner in which property and casualty insurers are required to account for claims reserves. Preferred Shares The accounting procedures described in the notes to amended section 181.2 of the Act are relevant to financial institutions as well as to other corporations, and readers may consult those notes for additional background. As in that section, the amendments introduced to section 181.3 include, in the computation of a deficit deducted in computing shareholders’ equity, the amount of any provision for the redemption of preferred shares. This inclusion is added to three specific provisions: subparagraph 181.3(3)(a)(v) in respect of financial institutions other than insurers and authorized foreign banks; subparagraph 181.3(3)(b)(iv) in respect of Canadian-resident life insurance corporations; and subparagraph 181.3(3)(c)(v) in respect of other Canadian-resident insurance companies. These amendments apply to taxation years that begin after 1995. Claims Reserves In general, a corporation is required to compute amounts relevant in determining its tax payable under Part I.3 of the Act using generally accepted accounting principles (GAAP). The Canadian Institute of Chartered Accountants’ Handbook (the Handbook), which is the principle authority of GAAP in Canada, requires that property and casualty insurers account for claims reserves on a gross basis, rather than net of reinsurance. Paragraphs 181.3(3)(c) and (d) of the Act stipulate the amounts to be included in determining the capital of an insurance corporation resident in Canada (other than a life insurance corporation) and an insurance corporation not resident in Canada, respectively. Among other things, claims reserves are required under these paragraphs to be included in computing the capital of such a corporation. New subparagraph 181.3(3)(c)(vii) and clause 181.3(3)(d)(iv)(F) allow such corporations to reduce their capital by an amount that is recoverable through reinsurance, to the extent that the amount relates to an amount that was included in capital as a claims reserve. In this way, claims reserves are included on a net of reinsurance basis under paragraphs 181.3(3)(c) and (d). New subparagraph 181.3(3)(c)(vii) and clause 181.3(3)(d)(iv)(F) apply to taxation years that begin after 1995. Clause 165 Additional Tax on Excessive Elections ITA Part III Under section 83 of the Act, a private corporation can identify a dividend as a "capital dividend," with the result that the dividend is not taxable to the shareholders who receive it. In concept, a capital dividend is a distribution of the non-taxable portion of the corporation’s capital gains, which portion is recorded in the corporation’s "capital dividend account". A similar mechanism allows mutual fund corporations and mortgage investment corporations to designate a dividend as a "capital gains dividend" – which is taxable to the shareholder, but as a capital gain. Part III of the Act (sections 184 and 185) applies a special tax to a corporation that designates as a capital dividend or a capital gains dividend an amount that exceeds the amount available to be paid as such a dividend. If the corporation obtains the consent of its shareholders, it can avoid the special tax by treating the excess amount as a separate taxable dividend. These amendments simplify Part III and update its language, reduce the rate of the special tax, and modify the requirement for shareholder consent to the recharacterization of an excessive dividend. These amendments apply to dividends that are paid by a corporation after its 1999 taxation year, with a special transitional rule for elections, described below in the notes to subsection 184(5) of the Act. Tax on Excessive Elections ITA 184(2) Subsection 184(2) of the Act applies the tax under Part III of the Act to the amount by which a dividend paid by a corporation as a capital dividend or a capital gains dividend exceeds the amount eligible to be so designated. For greater clarity, the subsection is amended to refer to the full amount of the initial dividend as the "original dividend." That term is then used elsewhere in amended Part III. The rate of tax imposed by subsection 184(2) is also changed, as part of a series of amendments that reflect recent and planned reductions in tax rates. The rate is reduced from 75% of the excess capital gains dividend to 60% of the excess. Reduction of Excess ITA 184(2.1) Subsection 184(2.1) of the Act is a transitional rule that applies to certain dividends that became payable before June 18, 1987. That subsection has lapsed and is repealed. Election to Treat Excess as Separate Dividend ITA 184(3) Subsection 184(3) of the Act allows a corporation that would otherwise be liable to tax under Part III in respect of an excessive capital dividend or capital gains dividend to treat the excess as a separate taxable dividend, and thus to avoid the tax. The subsection is amended to update and clarify its language. Concurrence with Election ITA 184(4) Subsection 184(4) of the Act sets out the requirements for shareholders’ consent to the recharacterization, under subsection 184(3), of an excessive capital dividend or capital gains dividend. This subsection is amended to update and clarify its language. Exception for Non-taxable Shareholders ITA 184(5) New subsection 184(5) of the Act provides an exception to the shareholder consent requirements of subsection 184(4). Where a corporation wishes to recharacterize an excessive dividend under subsection 184(3), and the dividend was paid on a class of shares all of the holders of which are persons all of whose taxable income is exempt from tax (for example, registered plans), the corporation need not obtain the shareholders’ consent. Instead, the only requirement imposed by new subsection 184(5) is that the corporation’s election be made within 30 months after the time that the original (excessive) dividend became payable. An election under new subsection 184(5) will be deemed to have been made in a timely manner if it is made within 90 days after these amendments receive Royal Assent. Clause 166 Revocation Tax ITA 188(1) Subsection 188(1) of the Act imposes a tax payable by a registered charity in respect of the revocation of the charity’s registration. The tax is generally equal to the total of the value of the assets of the charity plus the amount of receipted donations and inter-charity gifts received by the charity after the "valuation day" of the charity’s assets, net of certain eligible disbursements. Subsection 188(1) is amended consequential to the addition of new subsection 248(31) of the Act, in respect of gifts made after December 20, 2002, to refer to the "eligible amount" of a gift for which a receipt was issued by the charity. For additional information, see the commentary to new subsection 248(31). Clause 167 Financial Institutions Capital Tax ITA 190.13 Section 190.13 of the Act contains the rules for determining the capital of a financial institution for the purpose of Part VI of the Act. Section 190.13 is amended to accommodate a change to the accounting presentation of provisions for the redemption of preferred shares. Generally accepted accounting principles (GAAP) are relevant to the determination of amounts referred to in section 190.13. The accounting procedures described in the notes to amended section 181.2 of the Act are therefore relevant in the context of Part VI of the Act, and readers may consult those notes for additional background. As in that section, the amendments introduced to section 190.13 include, in the computation of a deficit deducted in computing shareholders’ equity, the amount of any provision for the redemption of preferred shares. This inclusion is added to two specific provisions: subparagraph 190.13(a)(v), in respect of financial institutions other than life insurers and authorized foreign banks; and subparagraph 190.13(b)(iv) in respect of Canadian-resident life insurance corporations. These amendments apply to taxation years that begin after 1995. Clause 168 Excluded Dividend – Partner ITA 191(6) Section 191 of the Act sets out a number of rules relating to the taxes imposed, under Part VI.1 of the Act, on taxable Canadian corporations that pay dividends of certain kinds. Those taxes are not payable in respect of "excluded dividends," a term defined in subsection 191(1) of the Act. Dividends paid by a corporation to a shareholder that holds a "substantial interest" in the corporation are excluded dividends. "Substantial interest" is itself defined in subsection 191(2) of the Act. In general, a shareholder has a substantial interest in a corporation if the shareholder is related to the corporation (otherwise than because of a right under paragraph 251(5)(b)) or if the shareholder’s holdings meet certain thresholds in terms of votes and value. If a shareholder has a substantial interest in a corporation, and is also a member of a partnership that holds shares of the corporation, it is appropriate that a dividend paid by the corporation to the partnership be an excluded dividend, to the extent of the shareholder’s interest in the dividend. To ensure this result, new subsection 191(6) is added to the rules that govern the Part VI taxes. The new subsection provides that a dividend paid to a partnership is, for the purposes of the "excluded dividend" definition, considered to have been paid ratably to each member of the partnership. Three technical aspects of the new rule bear special mention. First, the apportionment of the dividend among the partners is based upon each partner’s share of the partnership’s income for its last fiscal period that ended before the corporation paid the dividend. (If the dividend was paid during the partnership’s first fiscal period, the apportionment looks to that period.) Second, to ensure appropriate effects where there is more than one tier of partnerships between the dividend-paying corporation and the person that holds a substantial interest in the corporation, the new provision applies to itself. That is, if a member of a partnership is itself a partnership, the rule will treat the dividend-paying corporation as having paid a proportionate amount as a dividend not only to the second partnership, but also to that second partnership’s members. Third, in apportioning a dividend among members of a partnership, new subsection 191(6) uses the new definition of "specified proportion," which is added to subsection 248(1) of the Act. For further information, see the commentary to that amendment. New subsection 191(6) applies to dividends paid after December 20, 2002. Clause 169 Tax on Taxable Dividends ITA 191.1(1)(a) Subsection 191.1(1) of the Act provides for a tax to be paid by a corporation that has paid taxable dividends on taxable preferred shares. In the case of short-term preferred shares, paragraph 191.1(1)(a) sets the rate of the tax at 66 2/3% of the dividend. This rate produces an amount of tax equal to the amount of income tax that would have been collected had a corporate shareholder sought the same after-tax return in the form of interest. That result obtains, at the current 66 2/3 percent rate, if interest income is assumed to be taxed at 40%. As part of a series of amendments reflecting recent and planned reductions in income tax rates, the rate of tax under paragraph 191.1(1)(a) is reduced to 50% of the dividend amount. This provides the desired result on the basis of an assumed tax of 33.3% on interest income, as shown below. Dividend Interest Issuer To Holder$66.67 $100.00 191.1(1)(a) tax 33.33 n/a Total paid$100.00 $100.00 Shareholder Receives$66.67 $100.00 Part I tax NIL 33.33 After tax$66.67 $66.67 This amendment applies to the 2003 and subsequent taxation years. Clause 170 Distribution Deemed Disposition ITA 200 The French version of section 200 of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent. Clause 171 Labour-sponsored Venture Capital Corporations ITA 204.81(1), (1.1) and (1.2) Section 204.81 of the Act sets out the conditions for the registration of labour-sponsored venture capital corporations (LSVCCs). Subsection 204.81(1) permits the Minister of National Revenue to register a corporation as an LSVCC under Part X.3 if its articles satisfy specified conditions, and other requirements are met. Subparagraph 204.81(1)(c)(v) sets out the requirements of a federally-registered LSVCC’s articles regarding the circumstances in which the LSVCC may redeem shares of its capital stock. The current rule generally provides, pursuant to clause 204.81(1)(c)(v)(E), a minimum holding period of eight years for corporations that are incorporated after March 5, 1996. Clause 204.81(1)(c)(v)(E) is amended to require that the articles of a federally-registered LSVCC provide that the LSVCC shall not redeem its shares unless the redemption occurs either • more than eight years after the day on which the share was issued, or • in February or on March 1st but not more than 31 days before the day that is eight years after the day on which the share was issued. This amendment applies to corporations after February 6, 2000 regardless of when they were incorporated. However, federally-registered LSVCCs that were incorporated before March 6, 1996 may contain statements in their articles that provide that the LSVCC shall not redeem certain of its shares unless the redemption occurs more than five years after the day on which such a share was issued. New subsection 204.81(1.1) provides that in applying clause 204.81(1)(c)(v)(E), at any time before 2004, in respect of a corporation incorporated before March 6, 1996, the references in that clause to the word "eight" are replaced with references to the word "five" if, at that time, the relevant statements in the corporation’s articles refer to the word "five". This is intended to ensure that the extended (February, or March 1st) redemption provisions required of a federally-registered LSVCC’s articles apply equally to shares originally subject to a minimum five year holding period and those subject to a minimum eight year holding period. New subsection 204.81(1.2) is a transitional rule that provides a federally-registered LSVCC, incorporated before February 7, 2000, with a reasonable amount of time to amend its articles as required by clause 204.81(1)(c)(v)(E). Subsection 204.81(1.2) provides that, in applying subsection 204.81(1) at any time before 2004 to such an LSVCC, if the LSVCC’s articles comply with subclause 204.81(1)(c)(v)(E)(I) (as modified by subsection 204.81(1.1)) those articles are deemed to provide the statement required by subclause 204.81(1)(c)(v)(E)(II). New subsections 204.81(1.1) and (1.2) apply after February 6, 2000. These amendments are part of a set of amendments, announced by the Minister of Finance (News Release 2000-009, dated February 7, 2000) concerning the redemption requirements for federally-registered LSVCCs. For information on a related amendment, see the commentary to subsection 211.8(1) of the Act. Clause 172 Transfers Between Plans ITA 204.9(5) The French version of section 200 of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent. Clause 173 Foreign Property Rules ITA Part XI Part XI of the Act set out rules for a 1% per month penalty tax on excess foreign property held by deferred income plans. Part XI was repealed, effective for months that end after 2004, in Budget Implementation Act, 2005, S.C. 2005, c.30. A number of amendments are being made to Part XI that are effective prior to its repeal. Definitions ITA 206(1) "cost amount" "Cost amount" is defined in subsection 206(1) of the Act for the purposes of Part XI. The definition was introduced in 2001 to deal with arrangements that provided for trust income to be "capitalized" without the trust issuing new units. Under the definition, the cost amount otherwise determined of a taxpayer’s interest in such a trust reflects the capitalized amounts. For months that end after December 20, 2002 and before 2005, the definition is to be read to clarify that it applies to trusts under which all beneficiaries are registered plan trusts (e.g., trusts described in paragraph (e) of the definition "trust" in subsection 108(1)). "foreign property" "Foreign property" is defined in subsection 206(1) of the Act. Under paragraph (d.1) of the definition, foreign property includes certain shares and debt issued by Canadian corporations, if shares of the corporation may reasonably be considered to derive their value primarily from foreign property. Paragraph (g) of the definition treats as foreign property the indebtedness of a non-resident person other than indebtedness issued by various international organizations or indebtedness issued by an authorized foreign bank and payable at a Canadian branch of that bank. For months that end after October 2003 and before 2005, paragraphs (d.1) and (g) are to be read to provide that a mortgage obligation that is fully secured by real property situated in Canada is not foreign property. "specified proportion" Subsection 206(1) of the Act includes a definition of a partner’s "specified proportion" of a partnership for a fiscal period. To enable the definition to be used for other purposes as well, it is moved to subsection 248(1) of the Act, and is repealed in subsection 206(1), effective after December 20, 2002. Acquisition of Qualifying Security ITA 206(3.1) The French version of subsection 206(3.1) of the Act is amended to correct an erroneous reference. The reference to subparagraph 206(2)(a)(iii), which does not exist in the French version of the Act, is replaced by a reference to subparagraph 206(2)(a)(ii). This amendment applies to months that end after 1997, which corresponds to the application of the last amendment to subsection 206(3.1). Clause 174 Tax Payable by Recipient of an Ecological Gift ITA 207.31 Section 207.31 of the Act imposes a tax on charities and Canadian municipalities where, without the approval of the Minister of the Environment, they dispose of or change the use of property donated to them as an ecological gift. The tax is equal to 50% of the amount that is the fair market value of the property at the time of the disposition or change in use as determined for the purposes of section 110.1 or 118.1 of the Act. Section 207.31 is amended, in respect of dispositions of or changes of use of property after July 18, 2005, to clarify that it also applies to a public body performing a function of government in Canada. For more information, refer to the commentary for subsection 118.1(1) and paragraph 149(1)(d.5). Clause 175 Tax on Designated Income of Certain Trusts ITA Part XII.2 Part XII.2 of the Act imposes a special tax on the designated income (as defined in subsection 210.2(2) of the Act) of certain trusts that are resident in Canada with respect to distributions to non-residents and other designated beneficiaries. One of the objectives of Part XII.2 tax is to prevent the minimization of tax on specified Canadian-source income that would otherwise arise where a Canadian trust’s income is distributed to a non-resident and is subject only to Part XIII tax. Part XII.2 tax is also meant to discourage transactions between taxable and tax-exempt beneficiaries designed to allow taxable income earned by a trust to be flowed-through to tax-exempt beneficiaries after the acquisition of a trust unit by the tax-exempt beneficiary from the taxable beneficiary. Definitions and Application ITA 210 Section 210 of the Act defines "designated beneficiary" for the purpose of Part XII.2. Section 210 is amended so that a number of definitions that apply for the purposes of Part XII.2 are now found in new subsection 210(1). In addition, new subsection 210(2) replaces section 210.1 of the Act, which is being repealed. Definitions ITA 210(1) New subsection 210(1) of the Act contains the definitions "designated beneficiary" (previously found in section 210 of the Act) and "designated income" (previously found in subsection 210.2(2) of the Act). These definitions apply in Part XII.2. "designated beneficiary" Under paragraphs (a) and (b) of the definition "designated beneficiary", a designated beneficiary includes, respectively, a non-resident person and a non-resident-owned investment corporation. Under paragraph (c) of the definition, a person exempt from tax under Part I of the Act is treated as a designated beneficiary because of owning an interest in a trust (acquired from a beneficiary under the trust) unless, generally speaking, no taxable entity previously owned that interest. Under paragraph (d) of the definition, a trust is a designated beneficiary of another trust if a beneficiary of the trust includes, generally, either a person or partnership described in any of paragraphs (a), (b), (c) or (e) of the definition or another trust (other than a testamentary trust resident in Canada). Under paragraph (e) of the definition, a partnership is a designated beneficiary of a trust if a member of the partnership is a person described in paragraph (a), (b) or (d) of the definition, another partnership or a person exempt from tax under Part I by reason of subsection 149(1) of the Act. The opening words of the definition "designated beneficiary" are amended so that the references in the definition to a "trust" under which there may be a designated beneficiary are references to a "particular trust". Paragraph (c) of the definition "designated beneficiary" is amended to clarify that a designated beneficiary of a particular trust includes, except as provided in subparagraphs (c)(i) and (ii) of the definition, a person who is, because of subsection 149(1), exempt from tax under Part I on all or part of their taxable income and who acquired an interest in the particular trust after October 1, 1987 directly or indirectly from a beneficiary under the particular trust. Paragraph (d) of the definition "designated beneficiary" is amended so that a designated beneficiary of a particular trust includes another trust (in this commentary referred to as the "other trust") having as a beneficiary any one of the following persons or partnerships: • under subparagraphs (d)(i) and (ii) of the definition, a non-resident person (including a trust) or a non-resident-owned investment corporation; • under subparagraphs (d)(iii) of the definition, any trust, other than • a testamentary trust (however, note that if the testamentary trust were non-resident, the other trust would be treated as a designated beneficiary of the particular trust because of subparagraph (d)(i)), • a mutual fund trust, • a trust that is exempt because of subsection 149(1) from tax under Part I on all or part of its taxable income (however, note that under subparagraph (d)(iv), described below, such a trust may cause the other trust to be a designated beneficiary of the particular trust), and • a trust none of the beneficiaries under which is, at that time, a designated beneficiary under it and whose interest, at that time, in the other trust was held, at all times after the day on which the interest was created, either by it or by persons who were exempt because of subsection 149(1) from tax under Part I on all of their taxable income; • under subparagraph (d)(iv) of the definition, a person (including a trust) or partnership that • is a designated beneficiary under the other trust because of paragraph (c) of the definition (i.e., a person who is, because of subsection 149(1), exempt from tax under Part I on all or part of their taxable income and who acquired an interest in the particular trust after October 1, 1987 directly or indirectly from a beneficiary under the particular trust) or because of paragraph (e) of the definition, or • would, based on the assumptions set out it in clause (d)(iv)(B), be a designated beneficiary under the particular trust because of paragraph (c) or (e) of the definition. Note that a person or partnership that is a beneficiary of the other trust need only be described in any of one of subparagraphs (d)(i) to (iv) in order for the other trust to be a designated beneficiary of the particular trust. Note also that references in paragraph (d) of the definition to the expression "resident in Canada" are removed as these are unnecessary given that paragraph (a) of the definition provides that a non-resident person is a designated beneficiary. Paragraph (d) of the definition is also amended to provide that the other trust will not be treated, under that paragraph, as a designated beneficiary of the particular trust if it is a testamentary trust, a mutual fund trust, or a trust that is exempt because of subsection 149(1) from tax under Part I on all or part of its taxable income. However, these excluded trusts may be treated as designated beneficiaries of the particular trust under paragraphs (a) or (c) of that definition (e.g., a non-resident testamentary trust). Amended paragraph (e) of the definition provides, in new subparagraph (e)(i), that a designated beneficiary of a particular trust includes a particular partnership any of the members of which is another partnership. However, no such other partnership will cause the particular partnership to be a designated beneficiary under the particular partnership if • all such other partnerships are Canadian partnerships (as defined in subsection 102(1) of the Act), • the interest of each such other partnership in the particular partnership is held, at all times after the day on which the interest was created, by the other partnership or by persons who were exempt because of subsection 149(1) from tax under Part I on all of their taxable income, • the interest of each member, of each such other partnership, that is a person exempt because of subsection 149(1) from tax under Part I on all or part of its taxable income was held, at all times after the day on which the interest was created, by that member or by persons who were exempt because of subsection 149(1) from tax under Part I on all of their taxable income, and • the particular partnership’s beneficial interest in the particular trust is held, at all times after the day on which the interest was created, by the particular partnership or by persons who were exempt because of subsection 149(1) from tax under Part I on all of their taxable income. Under subparagraphs (e)(ii) to (iv), a particular partnership will be a designated beneficiary under a particular trust if any one of the partnership’s members is a non-resident person, a non-resident-owned investment corporation, or a specified person. For this purpose, a specified person means a trust that is a designated beneficiary of the particular trust because of paragraph (d) of the definition or a trust that would be such a designated beneficiary on the following assumptions: the other trust were at that time a beneficiary under the particular trust whose interest as a beneficiary under the particular trust were • acquired from each person or partnership from whom the particular partnership acquired its interest as a beneficiary under the particular trust, and • held at all times after the later of October 1, 1987 and the day on which the particular partnership’s interest as a beneficiary under the particular trust was created, by the same persons or partnerships that held at those times that interest of the particular partnership. New subparagraph (e)(v) of the definition provides that a particular partnership will be a designated beneficiary of a particular trust if any of the members of the particular partnership is a person exempt because of subsection 149(1) from tax under Part I on all or part of its taxable income, unless the interest of the particular partnership in the particular trust was held, at all times after the day on which the interest was created, by the particular partnership or by persons who were exempt because of subsection 149(1) from tax under Part I on all of their taxable income. Note that, for the purposes of the definition "designated beneficiary", a new rule in section 132.2 applies in respect of certain trust units acquired by a beneficiary under a "qualifying exchange" (as defined in subsection 132.2(1)). For more detail, see the commentary on section 132.2. Note as well that paragraph 210.2(3)(b) is amended to ensure that subsection 210.2(3) does not apply to a non-resident person that would be a designated beneficiary under the trust if the definition "designated beneficiary" in subsection 210(1) were read without reference to its paragraph (a). This amendment applies to the 1996 and subsequent taxation years. This amendment applies to the 1996 and subsequent taxation years. "designated income" The tax under Part XII.2 of the Act is calculated by reference to a trust’s "designated income" (as determined under subsection 210.2(2)). Subsection 210.2(2) is being replaced (for more detail, see the commentary below) and the definition "designated income" is now found in subsection 210(1) of the Act. Paragraphs (a), (b) and (d) of the new definition "designated income" in subsection 210(1) are largely unchanged from the equivalent provisions found in repealed subsection 210.2(2). Paragraph (c) of the new definition replaces paragraph 210.2(2)(b). Under subparagraph (c)(i), designated income is calculated by reference to taxable capital gains and allowable capital losses from dispositions of the trust’s taxable Canadian property. Subparagraph (c)(ii) provides that a trust’s designated income is also calculated by reference to taxable capital gains and allowable capital losses from a disposition by the trust of particular property (other than property described in any of subparagraphs 128.1(4)(b)(i) to (iii) of the Act). In this context, particular property (or property for which the particular property is a substitute) must be property (referred to in this commentary as the "transferred property") that was transferred to a particular trust in circumstances in which subsection 73(1) or 107.4(3) of the Act applied. This condition will be met whether the particular trust is the trust in respect of which the designated income is being determined, or any other trust to which the transferred property was transferred in circumstances in which subsection 73(1) or 107.4(3) applied and that subsequently transferred, directly or indirectly, the property to the trust in respect of which the designated income is being determined. In addition, clauses (c)(ii)(A) and (B) of the definition require • that it be reasonable to conclude that the transferred property was, at a particular time, transferred to the particular trust in anticipation of the emigration of a person beneficially interested at the particular time in the particular trust and that a person (whether the anticipated person or another) beneficially interested at that time in the particular trust subsequently ceases to reside in Canada, or • at the particular time that the transferred property was transferred to the particular trust, that the terms of the particular trust satisfy the conditions in subparagraph 73(1.01)(c)(i) or (iii) of the Act and that it be reasonable to conclude that the transfer was made in connection with the cessation of residence, on or before that time, of a person who was, at that time, beneficially interested in the particular trust and a spouse or common-law partner, as the case may be, of the transferor of the transferred property to the particular trust. These amendments generally apply for the 1996 and subsequent taxation years. Subparagraph (c)(ii) of the definition as described above applies, in effect, to dispositions, of property by a trust, that occur after December 20, 2002. Application of Part XII.2 ITA 210(2) and 210.1 Section 210.1 of the Act provides a list of types of trusts to which Part XII.2 does not apply. Section 210.1 is being repealed. The list of types of trusts to which Part XII.2 does not apply is now found in new subsection 210(2). New subsection 210(2), consequential on the amendments to the definition "designated beneficiary" (described in the commentary above), also clarifies that it applies only to determine to which trusts the special Part XII.2 tax does not apply. Subsection 210(2) does not apply, for example, to determine whether a trust referred to in that subsection may have a designated beneficiary. This amendment applies to the 1996 and subsequent taxation years. Clause 176 Amateur Athlete Trusts ITA 210.2(2) Subsection 210.2(1.1) of the Act extends the tax under Part XII.2 to amateur athlete trusts, which are provided for in section 143.1, in circumstances where amounts are distributed by such trusts to non-resident beneficiaries. Subsection 210.2(1.1) of the Act is amended by renumbering it as subsection 210.2(2). In addition, the reference in that subsection to section 210.1 is, given that section’s renumbering as subsection 210(2), replaced with a reference to subsection 210(2). The amended subsection also replaces the existing reference to the phrase "36% of 100/64" with the numerical equivalent of "56.25%". Finally, the provision is amended to clarify that Part XII.2 tax applies to a trust for a particular taxation year of the trust on the amount that is required by subsection 143.1(2) to be included in computing the income under Part I for a taxation year of a beneficiary under the trust, only if • the beneficiary is at any time in the particular taxation year a designated beneficiary under the trust, and • the particular taxation year ends in that taxation year of the beneficiary. This amendment applies to the 1996 and subsequent taxation years. Clause 177 Part XII.4 ITA 211.6(1) Part XII.4 imposes a special tax on qualifying environmental trusts, as defined under subsection 248(1). Subsection 211.6(1) is the charging provision of Part XII.4. It requires a qualifying environmental trust to pay a tax equal to 28% of its income for the year. Subsection 211.6(1) is amended to provide that a trust that is described by new paragraphs 149(1)(z.1) or (z.2), even if it is a qualifying environmental trust, is not subject to Part XII.4 tax. This amendment applies to the 1997 and subsequent taxation years. Clause 178 Recovery of Labour-sponsored Funds Tax Credit ITA Part XII.5 Part XII.5 of the Act (sections 211.7 to 211.9) provides for a special tax that is designed to recover the federal tax credit under section 127.4 of the Act with respect to the original acquisition of a share issued by a labour-sponsored venture capital corporation (LSVCC). This tax applies where there is a disposition of an "approved share", as defined in subsection 127.4(1) of the Act. Disposition of Approved Share ITA 211.8(1) Subsection 211.8(1) of the Act provides that the special tax under Part XII.5 generally applies where shares in a federally-registered LSVCC that qualify for the federal LSVCC tax credit are redeemed prior to the expiry of a minimum period. In the case of shares the "original acquisition" (as defined in subsection 127.4(1) of the Act) of which occurred before March 6, 1996, there is no recovery of the tax credit for a share redeemed more than five years after the day on which the share was issued. For shares the original acquisition of which occurs after March 5, 1996, the recovery generally applies where a share is redeemed less than eight years after the day on which it was issued. Subsection 211.8(1) is amended so that there is no Part XII.5 tax in respect of the redemption by a federally-registered LSVCC of a share the original acquisition of which was after March 5, 1996, if the redemption occurs on a day that is in February or on March 1st of a calendar year and that day is no more than 31 days before the day that is eight years after the day on which the share was issued. For a share the original acquisition of which occurred before March 6, 1996, the circumstances in which there is no recovery of the tax credit are extended to include the redemption of the share on a day that is in February or on March 1st of a calendar year if that day is no more than 31 days before the day that is five years after the day on which the share was issued. This amendment applies to redemptions, acquisitions, cancellations and dispositions that occur after November 15, 1995. This amendment is part of a set of amendments, announced by the Minister of Finance (News Release 2000-009, dated February 7, 2000) concerning the redemption requirements for federally-registered LSVCCs. The set of amendments is intended to accommodate taxpayers wishing to acquire new LSVCC shares in the first 60 days of a year using the proceeds from the redemption of LSVCC shares. Other related changes include amendments to section 204.81 of the Act. For additional information, see the commentary on those provisions. Example 1 On February 2nd, 1998 a federally-registered LSVCC redeemed 200 Class A shares owned by Charles. The original acquisition by Charles of the shares was on March 1, 1993, the same day on which the shares were issued. The issuing LSVCC was incorporated on December 1, 1992. The LSVCC’s Articles comply with the applicable registration requirements. Results: 1. Under new clause (i)(C) of the description of B in paragraph 211.8(1)(a), there will be no recovery of the tax credit on the redemption of the 200 shares because the original acquisition of the shares was before March 6, 1996 and the redemption occurred on a day in February not more than 31 days before the day that is five years after the day on which the shares were issued. 2. Because of new subsection 204.81(1.2), subsection 204.81(6) of the Act would not apply to allow the Minister of National Revenue to revoke the LSVCC’s registration solely because of the redemption. Example 2 On February 15, 2005 a federally-registered LSVCC redeemed 200 Class A shares owned by Marguerite. The circumstances of the redemption are not described in any of the provisions, described in clauses 204.81(1)(c)(v)(A) to (D) of the Act, of the LSVCC’s articles. The original acquisition by Marguerite of the first 100 shares was on March 1, 1997, although the shares were issued on March 12th, 1997. The original acquisition by Marguerite of the second 100 shares was on February 29, 2000, the same day on which the shares were issued. The LSVCC was incorporated on May 1, 1996. Results: 1. Under new subparagraph (i.1) of the description of B in paragraph 211.8(1)(a), there will be no recovery of the tax credit on the redemption of the first 100 shares because the redemption occurred in February on a day not more than 31 days before the day that is eight years after the day on which the shares were issued. Subparagraph (i) of the description of variable B in paragraph 211.8(1)(a) does not apply because the original acquisition of the shares was not before March 6, 1996. 2. Under new subparagraph (i.1) of the description of B in paragraph 211.8(1)(a), there will be a recovery of the tax credit on the redemption of the second 100 shares because the redemption occurred less than eight years after the day on which the share was issued and more than 31 days before the day that is eight years after the day on which the shares were issued. 3. Because of new subsection 204.81(1.2), subsection 204.81(6) would not apply to allow the Minister of National Revenue to revoke the LSVCC’s registration solely because of the redemption of the first 100 shares. However, the early redemption by the corporation of the second 100 shares, in violation of the provisions of its articles described in clause 204.81(1)(c)(v)(E), authorizes the Minister of National Revenue to revoke the LSVCC’s registration under subsection 204.81(6). Clause 179 Taxation of Non-residents ITA Part XIII Part XIII of the Act applies a tax on certain amounts paid by a person resident in Canada to a non-resident person. Non-resident Withholding Tax – Interest ITA 212(1)(b)(iv) Paragraph 212(1)(b) of the Act both applies tax under Part XIII of the Act to interest paid or credited by a person resident in Canada to a non-resident person and includes a number of exemptions from the tax. One of these, in subparagraph 212(1)(b)(iv), is for interest payable to an arm’s length person who holds a valid "certificate of exemption". These certificates, issued by the Minister of National Revenue under the authority provided by subsection 212(14) of the Act, are generally available to foreign pension entities, charities and certain other tax-exempt entities. In its current form, subparagraph 212(1)(b)(iv) applies only to interest on a "bond, debenture or similar obligation." Since this restriction may unduly limit the scope of the provision, it is broadened to encompass all forms of indebtedness. It should be noted, however, that no change is made to the requirement that the Canadian-resident payer of the interest and the non-resident recipient deal at arm’s length. This amendment applies to the 1998 and subsequent taxation years. ITA 212(1)(b)(xii) Subparagraph 212(1)(b)(xii) provides an exemption for interest payable under certain securities lending arrangements by registered or licensed securities dealers resident in Canada. Given the current definition of "securities lending arrangement" in subsection 260(1) of the Act, this exemption is only available to dealers who are dealing at arm’s length with the other parties to the arrangements. Consequential to the amendments to the definition of "securities lending arrangement" in subsection 260(1), which now includes certain arrangements between non-arm’s length parties, the amendment to subparagraph 212(1)(b)(xii) confirms that the exemption is limited to arm’s length arrangements. This amendment applies to arrangements made after 2002. Non-resident Withholding Tax - Interest ITA 212(1)(b)(xiii) Securities lending arrangements often include an obligation for one party to compensate the other for certain income amounts. In the absence of special rules, these compensation payments may be subject to tax under Part XIII if they are paid by a person resident in Canada to a non-resident person. New subparagraph 212(1)(b)(xiii) exempts from tax under Part XIII certain interest compensation payments made to a non-resident by a borrower resident in Canada under a securities lending arrangement. For this exemption to apply, • the payments must be made by the borrower in the course of carrying on its business outside of Canada; and • the borrowed securities must be issued by a non-resident issuer. This amendment applies to securities lending arrangements entered into after May 1995, except that, before 2002, the reference to "subparagraph 260(8)(c)(i)" should be read as "subparagraph 260(8)(a)(i)". Estate and Trust Income ITA 212(1)(c) The French version of paragraph 212(1)(c) is amended to replace the term "paiement" with the term "distribution" for consistency with other provisions of the Act dealing with amounts distributed by trusts and estates. This amendment will come into force on Royal Assent. Rents, Royalties, etc. ITA 212(1)(d) Paragraph 212(1)(d) of the Act describes various amounts, in the nature of rent, royalties and similar payments, on which tax under Part XIII of the Act is imposed. Subparagraphs 212(1)(d)(vi) through (xi) list payments to which the tax does not apply. Three changes have been made to paragraph 212(1)(d). First, subparagraph 212(1)(d)(iv), which concerns payments made in respect of an agreement between a person resident in Canada and a non-resident person under which the non-resident person agrees not to use or not to permit any other person to use any thing referred to in subparagraph (d)(i), is amended so that it does not apply to certain restrictive covenant amounts to which new paragraph 212(1)(i) applies. This change applies to amounts paid or credited after October 7, 2003. Second, subparagraph 212(1)(d)(xi), which currently provides that Part XIII tax does not apply to payments made to an arm’s length person for the use of property that is an aircraft, certain attachments thereto as well as to spare parts for such property, is amended, applicable after July 2003, to also apply to air navigation equipment utilized in the provision of services under the Civil Air Navigation Services Commercialization Act, and to computer software that is necessary to the operation of that equipment that is used by the payer for no other purpose. Third, new subparagraph 212(1)(d)(xii) clarifies that subsection 212(5) of the Act, which is amended as described below, is the sole provision in Part XIII that applies the tax to payments for rights in or to use a film or video that is used or reproduced in Canada. This change applies for the 2000 and subsequent taxation years. Restrictive Covenant Amount ITA 212(1)(i) New paragraph 212(1)(i) of the Act includes, as amounts subject to the withholding tax, two amounts. First, the withholding tax applies to an amount in respect of a restrictive covenant to which new subsection 56.4(2) applies. Second, the withholding tax applies to an amount to which new paragraph 56(1)(m) applies (an amount received on a bad debt previously deducted). New paragraph 212(1)(i) applies to amounts paid or credited after October 7, 2003. Exempt Dividends ITA 212(2.1) New subsection 212(2.1) is added to exempt from Part XIII tax certain dividend compensation payments made to a non-resident by a Canadian securities borrower under a securities lending arrangement if • the payments were deemed to be dividends by subparagraph 260(8)(c)(i) of the Act; • the payments were made by the borrower in the course of carrying on its business outside of Canada; and • the borrowed securities were issued by a non-resident issuer. This amendment applies to securities lending arrangements entered into after May 1995, except that, before 2002, the reference to "subparagraph 260(8)(c)(i)" should be read as "subparagraph 260(8)(a)(i)". Replacement Obligations ITA 212(3) Among the exceptions to the imposition of tax under Part XIII of the Act on interest is one found in subparagraph 212(1)(b)(vii) for interest paid by a corporation resident in Canada on its medium- and long-term arm’s length debt. Subsection 212(3), which applies for the purpose of subparagraph 212(1)(b)(vii), allows a corporation in certain circumstances of financial difficulty to treat a debt obligation that replaces another as having been issued when that other obligation was issued. The circumstances in which this is possible are set out in paragraphs 212(3)(a) to (c). Paragraph 212(3)(b) requires that, for the subsection to apply, it must be possible to regard the proceeds of the replacement borrowing as being used in financing an active business that was carried on in Canada, by the issuing company or one with which it does not deal at arm’s length, immediately before the replacement obligation was issued. There is no clear basis in tax policy for this requirement. The condition in paragraph 212(3)(b) is repealed for replacement debt obligations that are issued after 2000. Motion Picture Films ITA 212(5) Subsection 212(5) of the Act applies tax under Part XIII to, in general terms, any amount that a person resident in Canada pays to a non-resident person for a right in or to the use of a motion picture film or video product that has been or is to be used or reproduced in Canada (otherwise than for a news program). As presently worded, the subsection can be read as applying even if the payment in question is not for that Canadian use or reproduction, but relates instead to employment of the film or video in some other country. Accordingly, subsection 212(5) is amended to impose tax only to the extent that the amount of the payment relates to the use or reproduction of the product in Canada. This amendment applies to the 2000 and subsequent taxation years. Exemptions ITA 212(9) Subsection 212(9) of the Act provides an exemption from withholding tax under Part XIII of the Act with respect to certain amounts of a trust’s income that are paid or credited to a non-resident beneficiary under the trust and that would otherwise be subject to withholding tax under paragraph 212(1)(c). The exemption currently applies only in respect of amounts that are attributable to income of the trust in the form of: dividends or interest received by the trust from a non-resident-owned investment corporation; certain artistic royalties; and interest, where the trust is a mutual fund maintained primarily for the benefit of non-resident persons. If no Part XIII tax would have been payable with respect to the dividends, interest or royalties if they had been paid directly to the beneficiary, no Part XIII tax is payable with respect to a distribution from trust income to non-resident beneficiaries that derives from the dividends, interest or royalties. Subsection 212(9) is amended to add a fourth type of trust income to this list of exemptions. In certain circumstances, Canada’s Superintendent of Financial Institutions may require a non-resident reinsurer that reinsures Canadian risks to place assets in a trust in Canada. Such a "reinsurance trust" may earn dividend or interest income, which is payable to the non-resident. In recognition of the regulatory requirement for these trusts, subsection 212(9) is amended to provide that, if the dividends or interest would not have borne Canadian tax if the non-resident had earned them directly, they may be distributed to the non-resident free of Part XIII tax. This amendment applies to amounts paid or credited to non-residents after 2000. Rent and Other Payments ITA 212(13) Subsection 212(13) of the Act imposes non-resident withholding tax on certain payments made by one non-resident to another non-resident. Subsection 212(13) is amended to add new paragraph (g), which imposes non-resident withholding tax on amounts paid or credited by a non-resident for a restrictive covenant to which new paragraph 212(1)(i) applies, if the amount affects, or is intended to affect, in any way whatever, • the acquisition or provision of property or services in Canada, • the acquisition or provision of property or services outside Canada by a person resident in Canada, or • the acquisition or provision outside of Canada of a taxable Canadian property. New paragraph 212(13)(g) applies to amounts paid or credited after October 7, 2003. Application of Part XIII Tax Where Non-Resident Operates in Canada ITA 212(13.2) Subsection 212(13.2) of the Act is one of several provisions that extend Part XIII tax to apply in particular circumstances - in this case, for the most part, the payment by a non-resident of royalties and similar amounts in respect of a Canadian income source. The principle that underlies subsection 212(13.2) is that if a non-resident has Canadian-source business or resource income, and can deduct in computing that income (strictly speaking, in computing "taxable income earned in Canada") a payment to another non-resident, that payment ought to be treated for purposes of Part XIII tax as though it had been made by a person resident in Canada. This is accomplished by treating the first non-resident - the one making the payment - as a person resident in Canada for those purposes. In its current form, subsection 212(13.2) applies only if the non-resident making the payment carries on business principally in Canada, manufactures or processes goods in Canada or carries out any of various resource activities here. On the other hand, the rule does not explicitly link that business or activity to the deductibility of the payment: it can be read as applying whether or not the payment is made in relation to the particular business or activity. Accordingly, subsection 212(13.2) is amended to apply in respect of any portion of a payment (other than one to which the generally comparable rule in subsection 212(13) applies) made by one non-resident person to another that is deductible in computing the first non-resident’s taxable income earned in Canada from any source. The only exceptions are payments that are deductible in respect of treaty-protected businesses or treaty-protected properties (as defined in subsection 248(1) of the Act). This amendment applies to amounts paid or credited under obligations entered into after December 20, 2002. Tax on Registered Securities Dealers ITA 212(19) Subsection 212(19) of the Act imposes a tax on Canadian-resident registered securities dealers that enter into certain securities lending arrangements described in subparagraph 212(1)(b)(xii) of the Act. The tax is calculated, by formula, based in Part on the capital or the margin requirement of the relevant provincial laws governing the registration or license of securities dealers. An earlier amendment to subsection 212(19) removed a reference to the provincial laws under which the taxpayer is registered or licensed. The subsection is further amended, as a consequence of that earlier change, to replace the words "those laws" in subparagraph (b)(i) of the description of B in the formula (which no longer have any clear antecedent), with a specific reference to the provincial legislation that govern the registration or license of securities dealers. This amendment applies to securities lending arrangements entered into after May 28, 1993. Clause 180 Deemed Payments ITA 214(3) The French version of paragraph 214(3)(k) of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent. Clause 181 Alternative re Rents and Timber Royalties ITA 216 Section 216 of the Act allows a non-resident person to file a return of income under Part I in respect of rent on real property in Canada or timber royalties and to pay, instead of the non-resident withholding tax under Part XIII, tax under Part I on the basis of the non-resident’s income from the rent or royalties. Subsection 216(1), which provides the basic rule permitting a non-resident to be taxed under Part I of the Act on this income, is amended to improve its structure and language. Most of the changes are stylistic; the amendment also updates the subsection’s reference to the form of the non-resident’s Part I tax return, to reflect the implementation of a special return for these non-residents. This amendment applies to taxation years that end after December 20, 2002. In general terms, subsection 216(5) of the Act requires that a person who has previously made an election under subsection 216(1), and who has claimed capital cost allowance in computing income under the subsection, must file a return of income for the year in which the property that was the subject of the election is disposed of. Subsection 216(5) is modified in the same manner as subsection 216(1), again with the main change being an updated description of the relevant form. This amendment applies to taxation years that end after December 20, 2002. Subsection 216(7) of the Act provides that the rules in section 61 of the Act, dealing with income averaging annuity contracts, do not apply in computing a non-resident person’s income for a taxation year in respect of which subsection 216(5) applies to the person. Since section 61 is no longer relevant to any current transaction, subsection 216(7) is repealed. This repeal takes effect on Royal assent. Clause 182 Administration and enforcement ITA 220 Section 220 of the Act sets out a number of rules relating to the administration and enforcement of the Act. Waiver of filing of documents ITA 220(2.2) Under subsection 220(2.1) of the Act, if a provision of the Act or the Regulations requires a person to file a prescribed form, receipt or other document, or to provide prescribed information, the Minister may waive the requirement, but the document or information shall be provided at the Minister’s request. New subsection 220(2.2) provides that subsection 220(2.1) does not extend to a prescribed form, receipt, document or information, or prescribed information, that is filed on or after the day specified – in respect of the form, receipt, document or information – in subsection 37(11) or paragraph (m) of the definition "investment tax credit" in subsection 127(9) of the Act. Those provisions provide, in general, that a taxpayer’s claim for SR&ED treatment be made in a prescribed form that must be received by the Minister no later than 12 months after the taxpayer’s filing-due date for the taxation year in which the expenditures were made. The effect of new subsection 220(2.2) is that a person cannot deduct a scientific research and experimental development (SR&ED) expenditure under section 37 of the Act, or claim an investment tax credit in respect of an expenditure, if the person takes more than the additional 12 months allowed to make a claim with the Minister. In general, new subsection 220(2.2) applies on and after November 17, 2005. Security for Tax on Distributions of Taxable Canadian Property to Non-resident Beneficiaries ITA 220(4.6) and (4.61) The French version of subsections 220(4.6) and (4.61) of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent. Clause 183 Records and Books ITA 230(2) Subsection 230(2) of the Act requires that registered charities and registered Canadian amateur athletic associations keep books and records containing information that will enable the Minister of National Revenue to determine whether there are grounds for the revocation of their registration. The French version of this subsection is amended to replace the expression « motifs d’annulation » by the expression « motifs de révocation » in order to be consistent with the terminology used in sections 149.1 and 168 of the Act, which authorize the Minister to revoke the registration of these charities and associations. This amendment applies on Royal Assent. ITA 230(3) Subsection 230(3) provides that where a person has failed to keep adequate records and books of account, the Minister of National Revenue may require them to keep such records and books as the Minister specifies. The French version of this subsection is amended to correct grammatical errors. This amendment applies on Royal Assent. Clause 184 Requirement to Provide Documents or Information ITA 231.2(1) Subsection 231.2(1) of the Act provides that, notwithstanding any other provision of the Act, the Minister of National Revenue may by notice require that any person provide information or any document for any purpose relating to the administration or enforcement of the Act. An exception is made where the information or document relates to an unnamed person or persons, in which case the procedure set out in subsections 231.1(2) to (6) of the Act must be followed. Subsection 231.2(1) is amended to provide that the Minister may by notice require any person to provide information or any document relating to the administration or enforcement of the Act, of a listed international agreement or, for greater certainty, of a tax treaty with another country. A "listed international agreement" is newly defined in subsection 248(1) to mean the Convention on Mutual Administrative Assistance in Tax Matters, concluded at Strasbourg on January 25, 1988 and the Convention between the Government of Canada and the Government of the United Mexican States for the Exchange of Information with Respect to Taxes, signed at Mexico City on March 16, 1990. A "tax treaty" is defined in subsection 248(1) to mean a comprehensive agreement for the elimination of double taxation on income between the Canadian and foreign government that has the force of law in Canada at that time. This amendment applies on Royal Assent. Clause 185 Tax Shelters Definitions ITA 237.1(1) Subsection 237.1(1) of the Act provides definitions of terms that apply for the purpose of tax shelter identification and the definition of "tax shelter investment" in subsection 143.2(1) of the Act. The definition "gifting arrangement" includes an arrangement in respect of which it may reasonably be expected, having regard to representations made, that if a taxpayer makes a gift or political contribution under the arrangement, a person (whether or not it is the taxpayer) will incur an indebtedness in respect of which recourse is limited. This definition is amended in respect of gifts and contributions made after 6:00 p.m. (EST), December 5, 2003, to also refer to a limited-recourse debt determined under new subsection 143.2(6.1) of the Act. For additional details regarding limited-recourse debt in respect of a gift, see the commentary to subsection 143.2(6.1). Clause 186 Provision of Information ITA 241 Section 241 of the Act prohibits the use or communication by an official of taxpayer information obtained under the Act unless specifically authorized by one of the exceptions found in that section. Disclosure of Information – Registered Charities ITA 241(3.2) Paragraph 241(3.2)(h) of the Act permits a government official to release information that a registered charity has filed in support of an application for special status or an exemption under the Act, as well as any response to such an application (e.g., a request for permission to accumulate assets). Paragraph 241(3.2)(h) is amended, applicable upon Royal Assent, to include information relating to an application made under subsection 149.1(5) of the Act for an amount to be deemed an expenditure on charitable activities carried on by the charity. Information may be communicated ITA 241(3.3) New subsection 241(3.3) of the Act, which applies on Royal Assent, is added to provide authority to the Minister of Canadian Heritage to publish certain information relevant to the Canadian film or video production tax credit program. The information includes the title of a film or video production in respect of which a certificate has been issued or revoked by that Minister, as well as the names of producers and artists in respect of which that Minister has allotted "points" in determining whether the production is a "Canadian film or video production" under proposed section 1106 of the Regulations. Disclosure of Taxpayer Information ITA 241(4) Subsection 241(4) of the Act authorizes the limited communication of information to government officials outside of the Canada Revenue Agency. New subparagraph 241(4)(d)(xv) allows information in respect of film or video productions to be communicated to officials of an office or agency of the government of Canada or of a province that provides a program of assistance for such productions. The information may be communicated only for the purpose of administration or enforcement under the program. New subparagraph 241(4)(d)(xvi) extends this authority to communicate information to an official of the Canadian Radio-television and Telecommunications Commission, solely for the purpose of the administration or enforcement of a regulatory function of that Commission. New subparagraphs 241(4)(d)(xv) and (xvi) apply on Royal Assent. Subparagraph 241(4)(e)(xii) is amended to provide that an official may provide taxpayer information, or allow the inspection of or access to taxpayer information under and solely for the purposes of a provision contained in a tax treaty or in a listed international agreement. A "listed international agreement" is newly defined in subsection 248(1) to mean the Convention on Mutual Administrative Assistance in Tax Matters, concluded at Strasbourg on January 25, 1988 and the Convention between the Government of Canada and the Government of the United Mexican States for the Exchange of Information with Respect to Taxes, signed at Mexico City on March 16, 1990. A "tax treaty" is defined in subsection 248(1) to mean a comprehensive agreement for the elimination of double taxation on income between the Canadian and foreign government that has the force of law in Canada at that time. This amendment applies on Royal Assent. Clause 187 Interpretation ITA 248 Section 248 of the Act defines a number of terms that apply for the purposes of the Act, and sets out various rules relating to the interpretation and application of various provisions of the Act. Definitions ITA 248(1) "common-law partner" An individual becomes the common-law partner of another individual once they have cohabited in a conjugal relationship for at least one year. Paragraph (a) of the definition "common-law partner" in subsection 248(1) is amended, effective for the 2001 and subsequent taxation years, to clarify that, for an individual to be considered the common-law partner of another person at a particular time, the individual and that other person need to have cohabited in a conjugal relationship throughout the twelve-month period that ends at that particular time. "disposition" The expression "disposition" is used throughout the Act, particularly in provisions relating to transactions involving property. The definition "disposition" was added to subsection 248(1) by S.C. 2001, chapter 17, ss. 188(5) [formerly Bill C-22]. In general, that definition is applicable to transactions and events that occur after December 23, 1998. The former definition "disposition" was contained in section 54 of the Act, applicable to transactions and events that occurred before December 24, 1998. Under the definition "disposition" in subsection 248(1), a "disposition" of any property includes a transaction or an event described in any of paragraphs (a) to (d) of that definition but does not include a transaction or an event described in any of paragraphs (e) to (m) of that definition. Under subparagraph (b)(i) of that definition, a disposition of a property includes any transaction or event by which, where the property is a share, bond, debenture, note, certificate, mortgage, agreement of sale or similar property, or an interest in it, the property "is redeemed in whole or in Part or is cancelled". The definition "disposition" in subsection 248(1) is amended in the following ways. First, subparagraph (b)(i) of the definition now provides that a disposition of property includes any transaction or event by which, where the property is a share, bond, debenture, note, certificate, mortgage, agreement of sale or similar property, or an interest in it, the property "is in whole or in Part redeemed, acquired or cancelled". This amendment makes it clear that a disposition will also include a transaction or event by which the property is acquired. Second, paragraph (n) is added to the definition. New paragraph (n) provides that a redemption, an acquisition or a cancellation of a share, or of a right to be issued a share, (which share or which right, as the case may be, is referred to as the "security") of the capital stock of a corporation (the "issuing corporation") held by another corporation (the "disposing corporation") is considered not to be a "disposition" in the case where • the redemption, acquisition or cancellation occurs as part of a particular merger or combination of two or more corporations (including the issuing corporation and the disposing corporation) to form one corporate entity (referred to as the "new corporation"), • the particular merger or combination • is an amalgamation (within the meaning assigned by subsection 87(1) of the Act) to which subsection 87(11) of the Act does not apply, • is an amalgamation (within the meaning assigned by subsection 87(1)) to which subsection 87(11) applies, if the issuing corporation and the disposing corporation are described by subsection 87(11) as the parent and the subsidiary, respectively, or • is a merger or combination of non-resident corporations (referred to in these Notes as a "subject merger") that would be a foreign merger (within the meaning assigned by subsection 87(8.1) of the Act) if subparagraph 87(8.1)(c)(ii) were read without reference to the words "that was resident in a country other than Canada", and • either • the disposing corporation receives no consideration for the security, or • in the case of where the particular merger or combination is a subject merger, the disposing corporation receives no consideration for the security other than property that was, immediately before the particular merger or combination, owned by the issuing corporation and that, on the foreign merger, becomes property of the new corporation. Both amendments apply to redemptions, acquisitions and cancellations that occur after December 23, 1998, and, where the redemption, acquisition or cancellation takes place before December 21, 2002, the Minister of National Revenue shall, notwithstanding subsections 152(4) to (5) of the Act, make any assessment of a taxpayer’s tax, interest and penalties payable under the Act for any taxation years that include the time at which such a redemption, acquisition or cancellation occurred that is necessary to take into account the application of the amendments. In connection with redemptions, acquisitions and cancellations that occur before December 24, 1998, see the commentary to new subsection 248(1.1) of the Act. Third, the definition "disposition" in subsection 248(1) is also amended by restricting the circumstances in which a transfer of property between trusts will not be treated as a disposition. In particular, paragraph (f) of the definition is amended so that a transfer of property from a trust to another trust will avoid, under that paragraph, characterization as a disposition only if both trusts are, at the time of the transfer, resident in Canada. This amendment applies to transfers that occur after February 27, 2004. "dividend rental arrangement" A "dividend rental arrangement" is, in general terms, an arrangement under which one person receives a dividend on a share that has been borrowed from another person who retains the risk of loss or opportunity for gain from fluctuations in the share value. To clarify its application where a partnership is a party to the arrangement, the definition is restructured and amended; its language is also updated in certain respects. Under the amended definition, the "person" who is the subject of the arrangement - that is, the person who enters into the arrangement in order to receive a dividend - may be a partnership or a person as otherwise defined. Existing paragraph (c) of the definition ensures that the definition includes an arrangement under which a corporation receives a taxable dividend that would be deductible but for subsection 112(2.3) of the Act, and is obligated to make dividend compensation payments. This paragraph is replaced by new paragraph (b), which adds to the arrangements described one in which it is not the corporation receiving the dividend that is obligated to make the compensation payment, but rather a partnership of which the corporation is a member. At first reading, new paragraph (b) may seem asymmetrical, in that it expressly covers the case where a partnership is obligated to make the compensation payment, but not the case where a partnership receives the taxable dividend. In fact, the paragraph covers both: since in the latter case the corporate partner is itself already considered to receive the dividend, it is not necessary to add a reference to the partnership in that regard. The reference to "subsection 260(5)" in this definition is replaced with "subsection 260(5.1)" consequential to the amendments to section 260. This amendment applies to paragraph (d) of the former definition and clause (b)(ii)(B) of the amended definition. The amendment to paragraph (d) of the former definition applies between January 1, 2002 and December 20, 2002 unless an election noted below is filed. The amended definition applies to arrangements made after December 20, 2002; it also applies to an arrangement made after November 2, 1998 and before the day after December 20, 2002, if the parties jointly elect in writing filed with the Minister of National Revenue within 90 days after this Act has been assented to, except that before 2002 the reference to "subsection 260(5.1)" in the amended definition should be read as "subsection 260(5)". "foreign resource property" The definition "foreign resource property" in subsection 248(1) of the Act is structured to parallel the definition "Canadian resource property" in subsection 66(15) of the Act, with the necessary modifications to reflect the location of the property outside Canada. This definition is amended, effective for property acquired after December 20, 2002, as a consequence of changes to the definition "Canadian resource property". "former business property" The definition "former business property" in subsection 248(1) of the Act describes properties the voluntarily disposition of which by a taxpayer are eligible for elections under subsections 13(4) and 44(1) of the Act to defer the recapture of depreciation and capital gains. Subject to certain exceptions, a former business property is generally real property or an interest in real property used primarily in a business. The definition is amended, applicable after December 20, 2002, to include a franchise, concession or license for a limited period that is wholly attributable to the carrying on of a business in a fixed place and that is the subject of a valid election under new subsection 13(4.2) of the Act. For further information, refer to the commentary to new subsections 13(4.2) and (4.3). "listed international agreement" The definition of "listed international agreement" is added to subsection 248(1) as a consequence of the amendments to subsection 231.2(1) and subparagraph 241(4)(e)(xii). The agreements included in the definition are the Convention on Mutual Administrative Assistance in Tax Matters, concluded at Strasbourg on January 25, 1988 and the Convention between the Government of Canada and the Government of the United Mexican States for the Exchange of Information with Respect to Taxes, signed at Mexico City on March 16, 1990. This amendment applies on Royal Assent. "qualifying environmental trust" The French version of the definition of "qualifying environmental trust", in subsection 248(1) of the Act, is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent. "qualifying trust annuity" The term "qualifying trust annuity" is added to subsection 248(1) of the Act, and is defined to have the meaning assigned by new subsection 60.011(2). A distinguishing feature of a qualifying trust annuity is that the annuitant is a trust. Special provisions relating to qualifying trust annuities are set out in sections 60.011, 75.2, 148 and 160.2 of the Act. (Refer to the explanatory notes on those provisions for further details.) "scientific research and experimental development" Paragraph (d) of the definition "scientific research and experimental development" in subsection 248(1) of the Act includes, for the purposes of applying that definition in respect of a taxpayer, certain work (listed therein) undertaken by or on behalf of a taxpayer if the work is commensurate with the needs, and directly in support, of work described in paragraphs (a) to (c) of that definition that is undertaken by or on behalf of the taxpayer. "Engineering" work is among the work listed in paragraph (d). The French version of paragraph (d) of the definition is changed, effective upon Royal Assent, to refer to "travaux de genie" instead of "travaux techniques". "specified proportion" The definition "specified proportion" of a member of a partnership for a fiscal period of the partnership is currently found in subsection 206(1) of the Act. The apportionment that results from the definition is, however, useful for many purposes of the Act, and a number of other provisions apply the same concept. For simplicity, the definition is moved to subsection 248(1) of the Act. As a result, for all purposes of the Act a partner’s specified proportion for the period is that proportion of the partnership’s total income or loss for that period that is the member’s share. If the partnership’s income or loss for the period is nil, the proportion is computed as if the partnership had$1 million of income for the period.
This amendment applies after December 20, 2002.
Non-Disposition Before December 24, 1998
ITA
248(1.1)
The definition "disposition" was added to subsection 248(1) of the Act by S.C. 2001, chapter 17, subsection 188(5) [formerly Bill C-22]. In general, that definition applies to transactions and events that occur after December 23, 1998. The former definition "disposition" was contained in section 54 of the Act, applicable to transactions and events that occurred before December 24, 1998.
New paragraph (n) is added to the definition "disposition" in subsection 248(1), applicable to redemptions, acquisitions and cancellations of certain securities that occur after December 23, 1998. For more detail, see the commentary to subsection 248(1).
New subsection 248(1.1) of the Act is added to deal, in a corresponding fashion, with such redemptions, acquisitions and cancellations that occurred before December 24, 1998.
New subsection 248(1.1) provides that a redemption, an acquisition or a cancellation, at any particular time after 1971 and before December 24, 1998, of a share or of a right to acquire a share (which share or which right, as the case may be, is referred to as the "security") of the capital stock of a corporation (referred to as the "issuing corporation") held by another corporation (referred to as the "disposing corporation") is not a disposition of the security within the meaning of the definition "disposition" in section 54 (as that section read in its application to transactions and events that occur at the particular time), if
• the redemption, acquisition or cancellation occurred as part of a particular merger or combination of two or more corporations (including the issuing corporation and the disposing corporation) to form one corporate entity (referred to as the "new corporation"),
• the particular merger or combination
• is an amalgamation (within the meaning assigned by subsection 87(1) of the Act as it read at the particular time) to which subsection 87(11) of the Act if in force, and as it read, at the particular time did not apply,
• is an amalgamation (within the meaning assigned by subsection 87(1) as it read at the particular time) to which subsection 87(11) if in force, and as it read, at the particular time applies, if the issuing corporation and the disposing corporation are described by subsection 87(11) (if in force, and as it read, at the particular time) as the parent and the subsidiary, respectively,
• occurred before November 13, 1981 and is a merger of corporations that is described by subsection 87(8) (as it read in respect of the particular merger or combination), or
• is a merger or combination of non-resident corporations (referred to in these Notes as a "subject merger") that occurred after November 12, 1981 and
• is a foreign merger (within the meaning assigned by subsection 87(8.1) as it read in respect of the particular merger or combination), or
• all of the following conditions are met, namely
• 1. the particular merger or combination is not a foreign merger (within the meaning assigned by subsection 87(8.1) as it read in respect of the particular merger or combination),
• 2. subsection 87(8.1), as read in respect of the particular merger or combination, contained a subparagraph (c)(ii), and
• 3. the particular merger or combination would be a foreign merger (within the meaning of subsection 87(8.1), as it read in respect of the particular merger or combination) if that subparagraph 87(8.1)(c)(ii) were read as follows:
• "(ii) if, immediately after the merger, the new foreign corporation was controlled by another foreign corporation (in this subsection referred to as the "parent corporation"), shares of the capital stock of the parent corporation," and
• either
• the disposing corporation received no consideration for the security, or
• in the case where the particular merger or combination is a subject merger, the disposing corporation received no consideration for the security other than property that was, immediately before the particular merger or combination, owned by the issuing corporation and that, on the particular merger or combination, became property of the new corporation.
New subsection 248(1.1) applies on Royal Assent and, notwithstanding subsections 152(4) to (5) of the Act, the Minister of National Revenue may make any assessment of a taxpayer’s tax, interest and penalties payable under the Act for a taxation year that includes the time at which a redemption, acquisition or cancellation occurred that is necessary to take into account the application of new subsection 248(1.1) in respect of the redemption, acquisition or cancellation.
Bare Ownership - Gifts to Charity
ITA
248(3.1)
Under civil law, where a property is subject to dismemberment such as a usufruct or a right of use established in favour of an individual while another has the bare ownership, subsection 248(3) of the Act deems the property subject to such a usufruct or right of use to have been transferred to a trust. The whole property will thus be disposed of. Subsection 248(3), as it now reads, does not provide for any exception where the bare ownership of an immovable is gifted to a registered charity. New subsection 248(3.1) provides relief, similar to the exception found in subsection 43.1(1) of the Act for life interests created at common law, where the usufruct or right of use of an immovable is retained by a taxpayer but the bare ownership of the immovable is gifted in circumstances where the gift generates entitlement to a charitable donations credit.
Under new subsection 248(3.1) and subsection 69(1), the dismemberment will entail a disposition only of the bare ownership of an immovable for an amount equal to its fair market value (FMV). In the case of capital property, the adjusted cost base (ACB) of the property will be divided under subsection 43(1) of the Act pro rata between the bare ownership and usufruct or right of use. The usufruct or right of use will be considered to have been disposed of only when it is actually disposed of or is otherwise deemed to be disposed of by the taxpayer.
Example Mrs. A, whose property is governed by the civil law of the province of Québec, owns as capital property an immovable worth $100,000, which has an ACB of$10,000. She creates a dismemberment of the property by giving the bare ownership (FMV of $60,000) to a registered charitable organization and retaining the right of use (FMV of$40,000). Under the present rules, subsections 248(3) and 69(1) of the Act apply and Mrs. A is considered to have disposed of the immovable at its FMV ($100,000) in favour of a deemed trust. A gain of$90,000 is triggered ($100,000 -$10,000). Because of new subsection 248(3.1) and subsection 69(1), there is a disposition only of the bare ownership for proceeds of disposition equal to its FMV, i.e. $60,000. This amount can be included in the calculation of her charitable gifts credit. The ACB attributable to the bare ownership is$6,000 ($10,000 X 6/10). This transaction will give rise to a gain of$54,000 ($60,000 -$6,000). Mrs. A retains the right of use of the immovable and there is no disposition of this right. At death, a deemed disposition of her right of use will occur at FMV (established in the same way as for a life estate and remainder interest).
Occurrences as a Consequence of Death
ITA
248(8)
The French version of subsection 248(8) of the Act is amended to correct a terminology error. In effect, the concept of "attribution" is replaced by "distribution" so that it is clear that the property is actually remitted to the trust’s beneficiary and not simply set aside for him or her. This amendment will come into force on Royal Assent.
Goods and Services Tax - Input Tax Credit and Rebate
ITA
248(16)
Subsection 248(16) of the Act provides rules under which amounts received by, or credited to, a taxpayer as an input tax credit or rebate with respect to the goods and services tax (GST) are deemed to be assistance from a government received by a taxpayer. As a consequence, such amounts are either included in income or reduce the cost or capital cost of the related property, or the amount of the related expenditure or expenditure pool, for tax purposes.
Subsection 248(16) also specifies the time at which the receipt (or credit) of an input tax credit or rebate is deemed to be received as assistance. With respect to input tax credits, subparagraph 248(16)(a)(i) provides that the assistance (i.e., the input tax credit) is considered to be received by a taxpayer at the time the GST in respect of the input tax credit was paid or became payable by the taxpayer if the GST was paid or became payable in the same reporting period under the Excise Tax Act in which the input tax credit was claimed. If a taxpayer does not claim the input tax credit in the same reporting period in which the GST was paid or became payable, subparagraph 248(16)(a)(ii) includes the amount of assistance in the taxpayer’s income for the taxation year that includes the end of the reporting period in which the taxpayer claimed the input tax credit.
Subsection 248(16) is amended in three respects for input tax credits that become eligible to be claimed in taxation years that begin after December 20, 2002.
First, subparagraph 248(16)(a)(i) is amended to extend its application to cases where the input tax credit is claimed by a taxpayer in a reporting period that is subsequent to the period in which the related GST was paid or became payable if
• the taxpayer’s threshold amount (as determined under subsection 249(1) of the Excise Tax Act) is greater than $500,000 for the taxpayer’s fiscal year (as defined by that Act) that includes the earlier of the time that the GST in respect of the input tax credit was paid and the time that it became payable, and • the taxpayer claimed the input tax credit at least 120 days before the end of the normal reassessment period (as determined under subsection 152(3.1) of the Income Tax Act) for the taxpayer in respect of the taxation year that includes that earlier time. In general, the change to this subparagraph means that an input tax credit of a taxpayer (who is a GST filer with a threshold amount greater than$500,000 for GST purposes) is considered to have been received at the time the related GST was paid or became payable, even though the input tax credit is claimed in a later GST reporting period. However, this is the case only if the taxpayer claims the input tax credit at least 120 days before the taxation year in which the GST was paid or became payable becomes statute-barred for income tax purposes.
Second, subparagraph 248(16)(a)(ii) is amended to provide that an input tax credit is considered to be received at the end of the reporting period in which it is claimed only if
• subparagraph 248(16)(a)(i) does not apply, and
• the taxpayer’s threshold amount (as determined under subsection 249(1) of the Excise Tax Act) is $500,000 or less for the fiscal year of the taxpayer that includes the earlier of the time that the GST in respect of the input tax credit was paid or became payable. Thus, subparagraph 248(16)(a)(ii) does not apply if subparagraph 248(16)(a)(i) applies. Where subparagraph 248(16)(a)(i) does not apply, subparagraph 248(16)(a)(ii) provides that the input tax credit is considered to have been received at the end of the reporting period in which it is claimed only if the taxpayer’s threshold amount for GST purposes was$500,000 or less at the time the GST was paid or became payable.
Third, new subparagraph 248(16)(a)(iii) is added to apply in any other case. If applicable, that subparagraph provides that the input tax credit is considered to have been received on the last day of the taxpayer’s earliest taxation year
• that begins after the taxation year that includes the earlier of the time that the GST in respect of the input tax credit was paid and the time that it became payable, and
• for which the normal reassessment period for the taxpayer ends at least 120 days after the time at which the input tax credit was claimed.
Reference should also made to the commentary to new subsection 248(17.1) of the Income Tax Act which provides a special rule in respect of the timing of a claim in respect of certain input tax credits assessed under the Excise Tax Act.
Quebec Sales Tax - Input Tax Refund and Rebate
ITA
248(16.1)
New subsection 248(16.1) of the Act provides special rules for amounts received, or credited to, a taxpayer as an input tax refund or rebate in respect of Quebec sales tax. Such amounts are either included in a taxpayer’s income or reduce the cost or capital cost of the related property, or the amount of the related expenditure or expenditure pool, for tax purposes.
In general, an input tax refund in respect of Quebec sales tax may - depending on the circumstances - have to be included in a taxpayer’s income in the taxation year in which the taxpayer may first claim the refund, rather than the year in which it is received. A rebate of Quebec sales tax is included in income at the time the rebate is received or credited. For a more detailed explanation of the application of subsection 248(16.1), reference should be made to the commentary accompanying amendments to subsection 248(16), which provides analogous special rules in respect of the timing of the inclusion in income of certain input tax credits and rebates assessed under the Excise Tax Act.
Subsection 248(16.1) applies in respect of Quebec input tax refunds and rebates that become eligible to be claimed in taxation years that begin after February 27, 2004.
Application of Subsection (16) to Passenger Vehicles and Aircraft
ITA
248(17)
Subsection 248(17) of the Act applies in the case of an input tax credit in respect of a passenger vehicle or aircraft claimable by an individual or partnership where the credit is determined by reference to capital cost allowance in respect of the vehicle or aircraft (i.e., where there is less than exclusive use in commercial activity). Subsection 248(17) is amended to reflect the amendments made to subsection 248(16) as described in the commentary to that subsection.
The amendments to subsection 248(17) apply in respect of input tax credits that become eligible to be claimed in taxation years that begin after December 20, 2002.
Application of Subsection (16.1) to Passenger Vehicles and Aircraft
ITA
248(17.1)
New subsection 248(17.1) of the Act applies in the case of an input tax refund of Quebec sales tax, in respect of a passenger vehicle or aircraft, claimable by an individual or partnership where the credit is determinable by reference to capital cost allowance in respect of the vehicle or aircraft (that is, where there is less than exclusive use in commercial activity). In general, this subsection defers the time the input tax refund is considered to be received for income tax purposes to the taxation year or fiscal period following that in which Quebec sales tax in respect of the property is considered as payable for the purposes of determining the input tax refund. This avoids circularity with subsection 248(16.1). The provision preserves the proper timing between the input tax refund entitlement and the adjustment to the capital cost. This change applies in respect of Quebec input tax refunds that become eligible to be claimed in taxation years that begin after February 27, 2004.
Input Tax Credit on Assessment
ITA
248(17.2)
New subsection 248(17.2) of the Act determines, in respect of input tax credits that become eligible to be claimed in taxation years that begin after December 20, 2002, the time at which an input tax credit is considered to have been claimed in respect of certain input tax credit assessments made under the Excise Tax Act (ETA).
This subsection provides that, if an amount in respect of an input tax credit is deemed by subsection 296(5) of the ETA to have been claimed in a return or application filed under Part IX of that Act, the input tax credit is deemed to have been claimed for the GST reporting period that includes the time the Minister of National Revenue makes the GST assessment.
Accordingly, the rule in clause 248(16)(a)(i)(A) of the Income Tax Act (ITA) relating to the time at which an input tax credit is considered to have been received cannot apply to an input tax credit to which subsection 296(5) of the ETA applies. However, the other rules in paragraph 248(16)(a) of the ITA that determine the time at which an input tax credit is received are to be applied on the basis that an input tax credit (to which subsection 296(5) of the ETA applies) is not claimed by the taxpayer until the reporting period that includes the time at which the input tax credit is actually assessed - i.e., not the reporting period to which the assessment relates but the reporting period in which the input tax credit is deemed to be claimed for GST purposes.
Quebec Input Tax Credit on Assessment
ITA
248(17.3)
New subsection 248(17.3) of the Act provides that an input tax refund of Quebec sales tax, that is deemed to be claimed by section 30.5 of An Act respecting the Quebec Revenue Minister, is deemed to be claimed for the reporting period under An Act respecting Quebec Sales Tax that includes the day on which an assessment is issued to the taxpayer indicating that the refund has been allocated to the taxpayer. This change applies in respect of Quebec input tax refunds and rebates that become eligible to be claimed in taxation years that begin after February 27, 2004.
Repayment of Quebec Input Tax Refund
ITA
248(18.1)
New subsection 248(18.1) of the Act provides that an amount added in determining net tax of a taxpayer under An Act respecting Quebec Sales Tax in respect of an input tax refund relating to a property or service that had previously been deducted in computing such net tax is treated as assistance repaid under a legal obligation to repay that assistance. Such an amount could be so added under Quebec law pursuant to an assessment of Quebec sales tax. As a consequence, such an amount will either be deducted in computing income under paragraph 20(1)(hh) or will increase the cost or capital cost of the related property or the amount of the related expenditure or expenditure pool for tax purposes (as provided under subsection 13(7.1), paragraphs 37(1)(c) and 53(2)(k) and under the definitions "cumulative Canadian exploration expense" in subsection 66.1(6), "cumulative Canadian development expense" in subsection 66.2(5) and "cumulative Canadian oil and gas property expense" in subsection 66.4(5)). This change applies after February 27, 2004.
Transfers after death
ITA
248(23.1)
The French versions of paragraphs 248(23.1)(a) and (b) are amended to correct a terminology error. In effect, the term "attribué" is replaced by "distribué" so that it is clear that property of a taxpayer is actually distributed to the spouse or common-law partner of the taxpayer and not simply set aside for him or her. This amendment will come into force on Royal Assent.
Trust-to-trust Transfers
ITA
248(25.1)
Subsection 248(25.1) of the Act applies where there is a transfer of a property from a particular trust to another trust (other than a RRSP trust or RRIF trust) in circumstances to which paragraph (f) of the definition "disposition" in subsection 248(1) (see the commentary above) applies. The result of the application of paragraph (f) is that the transfer does not constitute a disposition. Where this is the case, subsection 248(25.1) deems the other trust after the particular time to be the same trust as, and a continuation of, the particular trust.
Subsection 248(25.1) is amended, for greater certainty, to ensure that where the transferred property is deemed under a number of specified provisions to be taxable Canadian property of the particular trust, the property continues to be taxable Canadian property of the other trust.
This amendment applies in respect of transfers that occur after December 23, 1998.
Cost of Trust Interest
ITA
248(25.3)
Subsection 248(25.3) of the Income Tax Act applies where a trust (other than a personal trust or a trust prescribed for the purpose of subsection 107(2) of the Act) issues particular units of the trust to a taxpayer directly in satisfaction of a right to a qualifying amount payable from the trust in respect of the taxpayer’s capital interest in the trust. In such a case, the cost to the taxpayer of the particular units is deemed to equal the amount so payable. Subparagraph 248(25.3)(c)(i) provides that in the case of particular units of a trust that are capital property, a qualifying amount payable is one that causes, or but for clauses 53(2)(h)(i.1)(A) and (B) would cause, a reduction under subparagraph 53(2)(h)(i.1) of the Act to the adjusted cost base of the taxpayer’s capital interest in the trust.
Subparagraph 248(25.3)(c)(i) is amended to provide that, in the case of particular units of a trust that are capital property, a qualifying amount payable is an amount payable that does not represent proceeds of disposition of a capital interest in the trust.
This amendment applies to trust units issuedafter December 20, 2002.
ITA
248(30) to (41)
At common law, it is generally the view that a gift includes only a property transferred voluntarily, without any contractual obligation and with no advantage of a material character returned to the transferor.
In contrast, under section 1806 of the Civil Code of Quebec ("CCQ"), a gift in Quebec is a contract by which ownership of property is transferred by gratuitous title. However, the rights of ownership may be separated, such that it may be possible for a transferor to transfer part of the rights of ownership without any material advantage returned (i.e., by way of gift) and to transfer the other Part separately for consideration. It is therefore possible, in Quebec, to sell a property to a charity at a price below fair market value, resulting in a gift of the difference.
Under both the common law and the CCQ, it is generally accepted that a transfer of property is not a gift unless the donor is impoverished by the transfer to the benefit of the donee and it is the donor’s intention to enrich the donee without consideration.
At common law there is generally no ability to separate the rights of ownership of a single property in the course of making a gift. As such, at common law a contract to dispose of a property to a charity at a price below fair market value would not generally be considered to include a gift.
Nevertheless, there have been certain decisions made under the common law where it has been found that a transfer of property to a charity was made partly in consideration for services and partly as a gift.
Subsections 248(30), (31) and (32) are added to the Act to clarify the circumstances under which taxpayers and donees may be eligible for tax benefits available under the Act in respect of the impoverishment of a taxpayer in favour of a donee. In addition to the clarification provided by these new rules, on December 24, 2002, the Canada Revenue Agency released guidelines (Income Tax Technical News No. 26)that describe how it will apply the new rules to various situations and fundraising methods commonly used in the charitable sector. Subsection 248(34) provides technical rules regarding the repayment of debt that previously reduced the eligible amount of a gift. Subsections 248(35) to (39) provide technical rules, regarding the eligible amount of a gift or the value of property transferred and benefits receivable, that apply in calculating the eligible amount of a gift or political contribution. New subsection (40) provides that the rule in subsection 248(30) does not generally apply to inter-charity transfers. New subsection (41) deems the eligible amount of a gift to be nil if a donor fails to provide that information.
In general, these provisions are intended to reflect the policy that the amount eligible for an income tax benefit to a donor, by way of a charitable donation deduction or credit or a political contributions tax credit, should reflect the economic impact on the donor (before considering the income tax benefit) of the gift or contribution.
Intention to Give
ITA
248(30)
For the transfer of property to qualify as a gift, it is necessary that the transfer be voluntary and with the intention to make a gift. At common law, where the transferor of the property has received any form of consideration or benefit, it is generally presumed that such an intention is not present. New subsection 248(30) of the Act, which applies in respect of transfers of property after December 20, 2002 to qualified donees (such as registered charities), allows the opportunity to rebut this presumption. New paragraph 248(30)(a) provides that the existence of an amount of an advantage to the transferor will not necessarily disqualify the transfer from being a gift if the amount of the advantage does not exceed 80% of the fair market value of the transferred property.
Example Mr. Short transfers land and a building with a fair market value of $300,000 to a registered charity. The charity assumes liability for an outstanding$100,000 mortgage on the property. The assumption of the mortgage by the charity does not necessarily disqualify the transfer from being a gift for the purposes of the Act. If the value of the mortgage is equal to the outstanding amount (e.g., the interest rate and terms and conditions are representative of current market conditions), the eligible amount of the gift, in respect of which Mr. Short may be entitled to a tax credit under subsection 118.1(3), is $200,000. If the amount of an advantage in respect of a transfer of property exceeds 80% of the fair market value of the transferred property, new paragraph 248(30)(b) provides that the transfer will not necessarily be disqualified from being a gift if the transferor can establish to the satisfaction of the Minister of National Revenue that the transfer was made with the intention to make a gift. In the above example, if the amount of the mortgage outstanding had been greater than$240,000, Mr. Short (or the charity on Mr. Short’s behalf) could apply to the Minister of National Revenue for a determination as to whether the transfer was made with the intention to make a gift.
It is generally accepted that the tax benefit available to a taxpayer, by way of a charitable donation deduction or credit, is not considered an advantage or benefit that would reflect a lack of donative intent on the part of a taxpayer. However, there may be circumstances where the intention of a taxpayer to make a gift is in doubt because of the combination of tax and other benefits to the taxpayer. If the primary motivation of a taxpayer for entering into a transaction or series of transactions is to return a profit to the taxpayer by way of a combination of tax and other benefits, the taxpayer may not be impoverished by the transfer of a property to a charity. Subsection 248(30) is not intended to allow a taxpayer to profit by the making of a gift.
Eligible Amount of Gift or Monetary Contribution
ITA
248(31)
New subsection 248(31) of the Act, which applies in respect of gifts and political contributions made after December 20, 2002, defines the eligible amount of a gift or contribution as the amount by which the fair market value of the property that is the subject of the gift or contribution exceeds the amount of the advantage, if any, in respect of the gift or contribution. Subsection 248(31) is added concurrently with amendments to subsections 110.1(1) and 118.1(1) of the Act, which describe the types of gifts in respect of which an eligible amount will qualify for a deduction (for corporations) or a tax credit (for individuals). The amount of the advantage in respect of a gift or contribution is described in new subsection 248(32) of the Act.
It is proposed that subsections 3501(1), (1.1) and (6) of the Regulationsbe amended to provide that official receipts issued by a registered organization in respect of a gift made after December 20, 2002 contain, in addition to the information already prescribed, the eligible amount of the gift.
ITA
248(32)
New subsection 248(32), which generally applies in respect of gifts or political contributions made after December 20, 2002, describes the amount of an advantage in respect of a gift or contribution as, in general, the total value of all property, services, compensation or other benefits to which the donor of a property is entitled.
Subsection 248(32) is added concurrently with the addition of subsection 248(31) of the Act, which defines the eligible amount of a gift or contribution, and with the amendment of subsection 127(3) of the Act in respect of contributions to a political party. The amount of an advantage reduces the eligible amount of a gift or contribution.
In general, new subsection 248(32) is intended to apply in respect of any transaction or series of transactions having either the purpose or the effect of reducing the economic impact to a donor of a gift or contribution. This includes, for instance, situations where a charity invests funds or acquires property in a manner that benefits the donor. The reduction to an eligible amount also includes an advantage that is partial consideration for, or in gratitude for, the gift or contribution, or is in any way related to the gift or contribution. An example would include the option of a donor to satisfy or pay a loan by assigning or transferring to another person a property (including the rights under an insurance policy) that has less economic value than the amount of loan outstanding. Another example would include an assumption of a donor’s risk by a charity, where the acquisition, directly or indirectly, of an interest in a property of the donor by the charity may have the effect of reducing the potential loss of the donor from that investment. (However, a tax credit or deduction resulting from a charitable donation is not considered a benefit.)
An advantage may exist even though it is not received at the time of the gift or contribution. For example, it may have been received prior to the time of the gift or may be contingent or receivable in the future. The advantage may accrue either to the donor or to a person not dealing at arm’s length with the donor. It is not necessary that the advantage be receivable from the donee.
Paragraph 248(32)(b) includes as an advantage any limited-recourse debt in respect of the gift or contribution. For additional details regarding limited-recourse debt, see the commentary to new subsection 143.2(6.1) of the Act.
It is proposed that subsections 2000(1) and (6) and 3501(1), (1.1) and (6) of the Regulationsbe amended to provide that official receipts issued by a registered organization or political party in respect of a gift or contribution contain, in addition to the information already prescribed, the eligible amount and the amount of the advantage, if any, in respect of the gift or contribution.
Cost of Property Acquired by Donor
ITA
248(33)
New subsection 248(33) of the Act, which applies in respect of gifts or political contributions made after December 20, 2002, provides that the cost to a taxpayer of property acquired by the taxpayer in the course of the making of a gift or contribution by the taxpayer is the fair market value of the property at the time of the making of the gift or contribution. The fair market value of such a property is relevant in computing the amount of the advantage in respect of the gift or contribution under subsection 248(32).
Repayment of Limited Recourse Debt
ITA
248(34)
New subsection 248(34) of the Act, which applies in respect of gifts or political contributions made after February 18, 2003, generally provides that a repayment of the principal amount of a limited-recourse debt in respect of a gift or political contribution is deemed to be a gift in the year it is paid. However, in some circumstances the total amount of limited-recourse debt and other advantages to the donor may exceed the fair market value of the property transferred to a charity, resulting in no eligible amount to the donor under subsection 248(31) of the Act. In this case, the donor must pay off the excess amount before any amount will be allowed as a gift. Also, a payment financed by other limited-recourse debt or made by way of assignment or transfer of a guarantee, security or similar indemnity or covenant is not recognized for these purposes. For example, the assumption of a taxpayer’s limited-recourse debt by another person, in exchange for an insurance policy in favour of the taxpayer that guarantees a particular rate of return on an investment held by any person, would not qualify as a deemed gift under subsection 248(34).
Deemed Fair Market Value
ITA
248(35)
New subsection 248(35) of the Act, which applies in respect of gifts made after 6:00 p.m. (EST), December 5, 2003, provides that the fair market value of a property that is the subject of a gift is, for the purposes of determining the eligible amount of a gift under subsection 248(31), deemed to be the lesser of the actual fair market value of the property and its cost to the donor. This rule applies if the property was acquired by the donor as part of a gifting arrangement that is a tax shelter. For more information on gifting arrangements, refer to the commentary for subsection 237.1(1) of the Act.
Unless the donation is made as a consequence of the donor’s death, this rule also applies if the property was acquired
• less than three years before the time of donation, or
• less than 10 years before that time, if one of the main purposes of acquisition was to gift the property to a qualified donee.
Non-arm’s Length Transactions
ITA
248(36)
New subsection 248(36) of the Act applies in conjunction with subsection 248(35), to "look-back" to discern whether a donated property was previously acquired by a person dealing non-arm’s length with the donor. If subsection 248(35) applies because the donor acquired the property within the three years of donation, then if a non-arm’s length person owned that property within that three-year period, the value of the gift to the donor will be the lower of the taxpayer’s cost and the lowest cost to any such non-arm’s length person.
Similarly, the rule will apply if subsection (35) applies because the taxpayer acquired the property within the last ten years and one of the main reasons of the acquisition was to gift the property, if a non-arm’s length person acquired that property within that ten-year period.
Subsection 248(36) applies to gifts made on or after July 18, 2005.
Non-application of Subsection (35)
ITA
248(37)
New subsection 248(37) of the Act provides exceptions to the application of subsection 248(35) of the Act where the property that is the subject of a gift is an ecological gift, inventory, real property situated in Canada, publicly-traded securities or cultural property, the value of which is certified by the Cultural Property Export Review Board.
In some circumstances, a shareholder might transfer a property to a controlled corporation in exchange for shares issued by the corporation, and then donate the shares. Alternatively, the corporation might donate the property it received. If subsection 248(35) would not have applied to a gift of a property by a shareholder, either because it is a type of property referred to above or because subsection 248(35) would not apply to the shareholder in any event, and if the shareholder donates the share, subsection 248(37) will further exempt the share from the application of subsection 248(35). If subsections 85(1) or 85(2) of the Act applied to the transfer of such an exempt property to the corporation, then subsection 248(37) will preclude the application of subsection 248(35) to that property if it is then donated by the corporation.
Similarly, sometimes a donor will make a gift of a property that was acquired in circumstances where subsection 70(6) or (9) or 73(1), (3) or (4) of the Act applied. In such a case, the donor has acquired the property from a transferor (such as a spouse) on a tax-deferred "rollover" basis. Unless the transferor acquired the property within the 3-year period referred to in subsection 248(35) (or the 10-year period, if applicable), subsection 248(37) provides that subsection 248(35) will not apply in these circumstances to deem the value of the gift to be the donor’s rollover cost or adjusted cost base.
Artificial Transactions
ITA
248(38)
New subsection 248(38) of the Act applies in respect of gifts made after 6:00 p.m. (EST), December 5, 2003, to prevent a donor from avoiding the application of subsection 248(35) by disposing and reacquiring a property before donating it to a qualified donee. If this is the purpose of any transaction or series of transactions that includes a disposition or acquisition of a property, for such gifts made before July 18, 2005, the cost of the property to the donor for the purpose of subsection 248(35) is deemed to be the lowest cost incurred by the taxpayer at any time to acquire that property or an identical property.
For gifts made on or after July 18, 2005, the eligible amount is deemed to be nil if a transaction or series of transactions
• has, as one of its purposes, the avoidance of the application of subsection 248(35), or
• would otherwise result in a tax benefit to which the General Anti-Avoidance Rule in subsection 245(2) would otherwise apply.
For example, the eligible amount of a gift resulting from a transaction or series to which subsection 248(38) would apply, if the gift were made before July 18, 2005, would be deemed to be nil if instead the gift were made on or on or after July 18, 2005.
The objectives of the provisions in the Act related to gifting are generally described above under the heading "Gifts and Contributions", but are not limited to that description.
ITA
248(39)
New subsection 248(39) of the Act, which applies in respect of gifts made after February 26, 2004, prevents a donor from avoiding the application of subsection 248(35) by disposing a property (the "substantive gift") to a qualified donee and donating the proceeds, rather than donating the property itself. The provision applies similarly in respect of political contributions. The fair market value of the gift or contribution of the proceeds, for the purpose of determining its eligible amount under subsection 248(31), is deemed to be the lesser of the fair market value of the property sold and its cost. Subsection 248(39) does not apply if subsection 248(35) would not have applied to a gift by the taxpayer of that property.
Reasonable Inquiry
ITA
248(40)
The July 18, 2005 proposal in respect of subsection 248(40) of the Act has been removed and replaced with an unrelated amendment.
ITA
248(40)
New subsection 248(30) of the Act allows the opportunity for a donor to rebut the general presumption that the receipt of any form of consideration or benefit reflects that lack of an intention to make a gift. Such a rule is unnecessary in the context of inter-charity transfers and could lead to complication of the "disbursement quota" calculation of a charity under section 149.1 of the Act. New subsection 248(40) therefore precludes the application of subsection 248(30) to transfers made by a registered charity to a qualified donee. Consequently, the eligible amount of a gift under new subsection 248(31) should always equal its fair market value.
New subsection 248(40) of the Act applies in respect of transfers made on or after ANNOUNCEMENT DATE .
Information Not Provided
ITA
248(41)
New subsection 248(41) of the Act, which applies in respect of gifts and monetary contributions made after 2005, provides that the eligible amount of a gift is nil if, before an official charitable receipt is issued by a donee, the donor fails to inform the donee of information that would be relevant to the application of subsections 248(31), (35), (36), (38) or (39) of the Act. The donee requires such information for correct preparation of the receipt.
Clause 188
Taxation Year
ITA
249(1) and (1.1)
Subsection 249(1) of the Act sets out, for purposes of the Act, the definition "taxation year". Paragraph 249(1)(a) provides that in the case of a corporation, a taxation year is a fiscal period. Paragraph 249(1)(b) provides that the taxation year of an individual is the calendar year. Subsection 249(1) also provides that when a taxation year is referred to by reference to a calendar year, the reference is to the taxation year or years coinciding with, or ending in, that year.
Subsection 249(1) is amended to clarify that the definition "taxation year" contained in that subsection applies for purposes of the Act except as otherwise provided. For examples of exceptions, which apply for limited purposes, see the definitions "taxation year" in subsections 95(1) and 149.1(1).
Subsection 249(1) is also amended to add new paragraph 249(1)(c), which provides that the taxation year of a testamentary trust is the period for which the accounts of the trust are made up for purposes of assessment under the Act. This definition was previously contained in paragraph 104(23)(a), which is being repealed.
New subsection 249(1.1) of the Act provides that, when a taxation year is referred to by reference to a calendar year, the reference is to the taxation year or taxation years that coincide with, or that end in, that calendar year. This rule combines the identical rules previously found in paragraph 104(23)(b), which is repealed, and subsection 249(1).
These amendments apply after December 20, 2002. For a related set of amendments, see the commentary on paragraphs 104(23)(a) and (b).
Testamentary Trusts
ITA
249(5)
New subsection 249(5) of the Act is added consequential on the repeal of paragraph 104(23)(a) of the Act.
Subsection 249(5) provides that the period for which the accounts of a testamentary trust are made up for purposes of assessment under the Act may not exceed 12 months and that no change in the time when such a period ends may be made for the purposes of the Act without the concurrence of the Minister of National Revenue. The rule was previously found in paragraph 104(23)(a) of the Act, which is being repealed.
This amendment applies after December 20, 2002. For a related set of amendments, see the commentary on paragraphs 104(23)(a) and (b) and subsection 249(1) and (1.1).
Loss of Testamentary Trust Status
ITA
249(6)
New subsection 249(6) of the Act provides a set of rules that apply where a trust or estate loses its status under the Act as a "testamentary trust". This loss of status will generally occur where property has been contributed or loaned to the trust or estate in circumstances described in any of paragraphs (b) to (d) of the definition "testamentary trust" in subsection 108(1) or where the trust or estate has been created by someone other than the deceased person on and as a consequence of whose death the trust or estate arose (in this regard, see paragraph (a) of that definition). Under the existing rules in the Act, where a transaction or event described in any of those paragraphs occurs at a particular time, the trust or estate will lose its status as a testamentary trust for its entire taxation year that would otherwise include that time. As a result, the trust will be treated as an inter vivos trust at all times after the end of its last taxation year, if any, throughout which it was a testamentary trust. As such, its first taxation year after that last taxation year will be, given the definition "taxation year" in subsection 249(1), the calendar year.
New subsection 249(6) provides transitional relief for trusts or estates that lose their "testamentary trust" status. Under that subsection, if at a particular time after December 20, 2002 a transaction or event, described in any of paragraphs (b) to (d) of the definition "testamentary trust" in subsection 108(1), occurs and as a result of that occurrence a trust or estate is not a testamentary trust, a number of special rules apply in determining its taxation years and fiscal periods. (Note that a trust or estate that fails to qualify as a testamentary trust because of paragraph (a) of the definition "testamentary trust" will be an inter vivos trust from its creation and is, therefore, not in need of this transitional relief.) In particular,
• under paragraph 249(6)(a), the fiscal period, for a business or property of the trust or estate, that would , if the Act were read without reference to subsection 249(6) and paragraphs (b) to (d) of the definition "testamentary trust", have included the particular time, is deemed to have ended immediately before the particular time. Subsection 249.1(3) ensures that the next fiscal period starts at the particular time and subsection 249.1(1) requires that that next fiscal period end no later than the calendar year in which it began (i.e. the new taxation year) – this is because the trust would then have become an inter vivos trust.
• the taxation year of the trust or estate that would, if this Act were read without reference to this subsection and paragraphs (b) to (d) of the definition "testamentary trust", have included the particular time is deemed to have ended immediately before the particular time. As a result, the trust or estate maintains testamentary trust status until the offside event occurs.
• a new taxation year of the trust or estate is deemed to have started at the particular time.
• in determining the fiscal period for a business or property of the trust or estate after the particular time, the trust or estate is deemed not to have established a fiscal period before that time.
New subsection 249(6) of the Act applies after ANNOUNCEMENT DATE. However, if a trust or estate elects in writing filed with the Minister of National Revenue on or before its filing-due date for its taxation year in which the subsection receives Royal Assent, it also applies to that trust or estate, as the case may be, after December 20, 2002.
Example: Trust A was created on and as a consequence of the death of John Smith in 2004. Trust A has a November 30 year-end. For its 2004 and 2005 taxation years, Trust A is a testamentary trust. On April 15, 2006, Trust A becomes indebted to a beneficiary of the trust by way of an interest-free loan. Results: (i) Existing scheme of the Act Because of paragraph (d) of the definition "testamentary trust", Trust A cannot qualify as a testamentary trust at any time in its taxation year that began December 1, 2005. Therefore, Trust A becomes an inter vivos trust effective December 1, 2005. Trust A would, as an inter vivos trust, have a December 31, 2005 year-end, with an April 1, 2006 filing-due date. (ii) New Subsection 249(6) Because of paragraph (d) of the definition "testamentary trust", Trust A cannot qualify as a testamentary trust. Its taxation year that began December 1, 2005 is deemed to have ended immediately before April 15, 2006 – that is to say, on April 14, 2006 (Assume that a reference to time in the legislation is to a day.) Therefore, Trust A maintains its status as a testamentary trust throughout the stub year that began on December 1, 2005 and ended on April 14, 2006. The trust would have 90 days from the end of that taxation year to file its return of income for the stub year. A new taxation year is deemed to begin April 15, 2006. As the April 15, 2006 loan occurs in the new taxation year, Trust A is an inter vivos trust throughout the new taxation year, which, accordingly, will end on December 31, 2006. As a result, Trust A is able to maintain testamentary trust status until the time immediately before the offside event. With respect to any late-filing for the stub year, relief may be available under the provisions in section 220 of the Act.
Clause 189
Arm’s Length
ITA
251(1)
Subsection 251(1) of the Act provides a set of rules that determine whether persons are considered, for the purposes of the Act, to deal with each other at arm’s length. Paragraph 251(1)(a) deems related persons not to deal with each other at arm’s length. Paragraph 251(1)(b) deems a taxpayer and a personal trust (other than a trust described in any of paragraphs (a) to (e.1) of the definition "trust" in subsection 108(1) of the Act) not to deal with each other at arm’s length if the taxpayer, or any person not dealing at arm’s length with the taxpayer, is beneficially interested in the trust. Paragraph 251(1)(c) provides that, where paragraph 251(1)(b) does not apply, it is a question of fact whether persons not related to each other are at a particular time dealing with each other at arm’s length.
Paragraph 251(1)(c) is amended to clarify that it applies in any case where paragraphs (a) and (b) do not apply.
This amendment applies after December 23, 1998.
Clause 190
Extended Meaning of "spouse" and "former spouse"
ITA
252(3)
Subsection 252(3) of the Act extends the meaning of the terms "spouse" and "former spouse" to include, for a number of purposes, a party to a void or voidable marriage.
The provision is amended consequential on amendments to Part XII.2 of the Act, which add a new reference to "spouse" in the definition "designated income" and maintain the existing references to "spouse" and "former spouse" in the definition "designated beneficiary" in subsection 210(1) of the Act. For more detail, see the commentary on subsection 210(1).
This amendment generally applies to the 1996 and subsequent taxation years.
Clause 191
Investments in Limited Partnerships
ITA
253.1
Section 253.1 of the Act applies for specified provisions of the Act and Regulations where a trust or corporation holds an interest as a limited partner in a limited partnership. It provides that the trust or corporation will not, solely because of its acquisition and holding of the limited partnership interest, be considered to carry on any business or other activity of the partnership.
Section 253.1 is amended so that it also applies for the purpose of paragraph 146.1(2.1)(c) of the Act, which provides that the registration of a registered education savings plan (RESP) is revocable if a trust governed by the plan carries on a business. The amendment to section 253.1 ensures that the acquisition and holding of a limited partnership interest by an RESP trust does not jeopardize the registered status of the plan, provided the interest is a qualified investment for the trust.
This amendment generally applies after 1997.
Clause 192
Acquisition of Control of a Corporation
ITA
256
Section 256 of the Act provides rules for determining whether corporations are to be considered to be associated and whether control of a corporation has been acquired for the purposes of the Act.
Control in Fact
ITA
256(6)
Subsection 256(6) of the Act treats a controlled corporation as not being controlled by a person or partnership if certain conditions are met.
The French version of subparagraph 256(6)(b)(ii) is amended to replace an erroneous reference to the « entité dominante » (controller) by a reference to the « société contrôlée » (controlled corporation), which is what was intended.
This amendment applies on Royal Assent.
Acquiring Control
ITA
256(7)
Subsection 256(7) of the Act describes circumstances in which control of a corporation will be deemed to have been acquired (or not to have been acquired) for specific provisions of the Act.
ITA
256(7)(a)
Paragraph 256(7)(a) of the Act describes the circumstances where control of a corporation (or a corporation controlled by the corporation) is considered not to have been acquired for the purposes of certain provisions of the Act. That paragraph is amended in two ways.
First, subparagraph 256(7)(a)(i) is amended effective with respect to the acquisition of shares after 2000 to add clause (E) which precludes an acquisition of control of a corporation on a distribution (within the meaning assigned by subsection 55(1) of the Act) by a specified corporation (within the meaning assigned by that subsection) if a dividend is received in the course of a spin-off distribution in which no portion of the dividend is treated as a capital gain by the anti-avoidance rule in subsection 55(2) of the Act because of the application of the exception for certain reorganizations under paragraph 55(3)(b) of the Act.
Example: Facts: Pubco is a specified corporation under the butterfly rules in section 55 and a person or group of persons does not control it. Pubco owns all of the shares of Subco. In the course of a distribution (as defined by subsection 55(1)), Pubco distributes the Subco shares to Newco, which is established in the course of the reorganization for the purposes of the distribution. The same shareholders that own all of the shares of Pubco own all of the shares of Newco. Because there is no person or group of persons that control Pubco and Newco, an acquisition of control of Subco would occur upon Newco’s acquisition of the Subco shares on the distribution despite the fact the same shareholders own Pubco and Newco. Application: In this example, new clause 256(7)(a)(i)(E) provides that there is no acquisition of control of Subco by Newco if Pubco’s distribution of its Subco shares to Newco is a distribution to which the anti-avoidance rule in subsection 55(2) does not apply because the distribution complies with the exception in paragraph 55(3)(b).
Second, new subparagraph 256(7)(a)(iii), which applies to the acquisition of shares after 2000, provides that, where there is an acquisition of any shares of a corporation, there is no acquisition of control of the corporation by a related group of persons if each member of each group of persons that controls the corporation was related to the corporation immediately before the change of control.
Example: Facts: Corporation X has issued 100 common shares with 1 vote per share. There are no other issued shares. Mr. X owns 51% of Corporation X’s issued shares. Ms. D who is the daughter of Mr. X owns 49% of the common shares issued by Corporation X. Mr. X has de jure control of Corporation X. Mr. X disposes of 10 shares of Corporation X to Mr. Z, an arm’s length person. Consequently, Mr. X no longer has de jure control, and a group of persons acquires de jure control of Corporation X. Application: If Mr. X and Ms. D form a related group of persons that otherwise acquires control of Corporation X upon the disposition of shares by Mr. X, new subparagraph 256(7)(a)(iii) deems no acquisition of control if no other group of persons that includes Mr. Z acquires control of Corporation X. It is a question of fact whether Mr. X and Ms. D form a group of persons that would otherwise acquire control of Corporation X and, if so, whether there exists another group of persons that also acquires control. Depending on the circumstances, Mr. X and Ms. D; Mr. X and Mr. Z; Ms. D and Mr. Z; or Mr. X, Ms. D and Mr. Z could form a group of persons that acquires control of Corporation X. Consequently, new subparagraph 256(7)(a)(iii) applies only if, in this example, Mr. X and Ms. D form a group of persons that control Corporation X and there exists no other group of persons (which includes Mr. Z) that acquires control of Corporation X.
ITA
256(7)(e)
Paragraph 256(7)(e) of the Act provides that, where certain conditions are satisfied, control of a particular corporation will be considered not to have been acquired solely because of a disposition of all of the shares of the particular corporation for consideration consisting solely of shares of the acquiring corporation. These conditions include a requirement that, immediately after the disposition, the acquiring corporation is not controlled by a person or group of persons and that the fair market value of the shares of the particular corporation is not less than 95% of the fair market value of all of the assets of the acquiring corporation.
Paragraph 256(7)(e) is amended, for shares acquired after 1999, to ensure that it applies on the acquisition of any shares of the capital stock of the particular corporation by the acquiring corporation if, immediately after the acquisition, the acquiring corporation owns all of the shares of the capital stock of the particular corporation (other than shares of a specified class) and the 95% test is met. This provision is also amended to deem control not to be acquired if shares of the particular corporation are acquired as part of a plan of arrangement and, upon completion of the arrangement, the acquiring corporation owns all the shares of the capital stock of the particular corporation (other than shares of a specified class) and the 95% test is met. Thus, amended paragraph 256(7)(e) may apply in circumstances where the acquiring corporation owns shares of the capital stock of the particular corporation before the acquisition being examined. In addition, amended paragraph 256(7)(e) excludes shares of a specified class, as defined in paragraph 88(1)(c.8) of the Act, from the determination of whether the acquiring corporation has acquired all of the shares of the particular corporation. Shares of a specified class are excluded on the basis that they are non-voting securities similar to debt and should not be considered indetermining whether control has been acquired for the purpose ofparagraph 256(7)(e).
This amendment also ensures that, in circumstances where the acquisition occurs as part of a plan of arrangement, the acquiring corporation includes a new corporation formed on an amalgamation of the acquiring corporation and a subsidiary controlled corporation of the acquiring corporation. As a result, paragraph 256(7)(e) may apply to a situation where the acquiring corporation owns shares of the particular corporation indirectly through a subsidiary controlled corporation if the acquiring corporation and the subsidiary controlled corporation are amalgamated as part of a plan of arrangement that includes the acquisition.
Clause 193
Proportional Holdings in Properties
ITA
259(1)
Subsection 259(1) of the Act provides a "look-through" rule that applies to certain taxpayers (including trusts governed by RRSPs) that acquire units of a "qualified trust". If the qualified trust so elects, each taxpayer is deemed to acquire, hold and dispose of its proportionate interest in the underlying assets of the qualified trust. This rule can benefit a taxpayer where the direct investment in the units of the qualified trust would constitute a non-qualified investment. By "looking through" to the underlying assets of the qualified trust, a taxpayer may be able to reduce or eliminate the tax penalties that result from holding non-qualified investments.
Subsection 259(1) is amended so that it applies for the purpose of the registration rules for registered education savings plans (RESPs). Under subsection 146.1(2.1), the registration of an RESP is revocable if a trust governed by the plan holds a non-qualified investment. This amendment will permit an RESP trust to make a direct investment in a qualified trust that is itself a non-qualified investment, without jeopardizing the registered status of the RESP, provided the qualified trust restricts its holdings to qualified investments.
This amendment applies to the 2000 and subsequent taxation years.
Clause 194
Securities Lending Arrangements
ITA
260
Section 260 of the Act sets out special rules that apply to securities lending arrangements.
Definitions
ITA
260(1)
Subsection 260(1) of the Act provides definitions that apply for the purposes of the special rules for securities lending arrangements. The existing definitions are modified, and additional definitions are added, as follows:
"dealer compensation payment"
"Dealer compensation payment" is one of the newly-defined terms, introduced not to effect any substantive change to the relevant rules but only for simplicity and clarity. A dealer compensation payment is an amount paid or received as compensation for an underlying payment by a registered securities dealer who is resident in Canada and who pays or receives the amount in the ordinary course of its business of trading in securities.
This new definition applies to securities lending arrangements made after 2001.
"qualified security"
The securities lending arrangement rules apply only to securities that are qualified securities. A new paragraph (e) is added to the definition "qualified security" to include a qualified trust unit.
This amended definition applies to securities lending arrangements made after 2001.
"qualified trust unit"
A "qualified trust unit" is defined to mean a unit of a mutual fund trust that is listed on a prescribed stock exchange.
This new definition applies to securities lending arrangements made after 2001.
"securities lending arrangement"
There are three amendments to the definition "securities lending arrangement".
Paragraph (a) of the existing definition provides that in order for there to be a securities lending arrangement, the lender and the borrower of a security must be dealing at arm’s length. The amendment to paragraph (a) extends the definition to include an arrangement entered into by non-arm’s length parties. New paragraph (e) provides that where the lender and borrower do not deal with each other at arm’s length, the arrangement must be of a term not exceeding 270 days and must not be part of a series of securities lending arrangements, loans or other transactions intended to be in effect for more than 270 days.
Paragraph (c) of the existing definition provides that where a borrowed security is a share, the borrower must be obligated to pay to the lender a dividend compensation payment in order for the transaction to be a securities lending arrangement. This paragraph is amended to apply a comparable requirement in respect of all arrangements. This recognizes and codifies the commercial reality that compensation payments are required to be made by the borrower to the lender in all securities lending arrangements, and not just those arrangements involving shares.
The amendment to paragraph (c) applies to arrangements made after 2001. The amendments to paragraphs (a) and (e) apply to arrangements made after 2002.
"security distribution"
"Security distribution" is a newly-defined term, introduced not to effect any substantive change to the relevant rules but only for simplicity and clarity. A security distribution is an amount, in respect of a borrowed security, that is either an underlying payment paid by the issuer of the security (for example as a dividend or a trust distribution) or a dealer compensation payment, or an SLA compensation payment.
This definition applies to securities lending arrangements made after 2001.
"SLA compensation payment"
"SLA compensation payment" is a newly-defined term, introduced not to effect any substantive change to the relevant rules but only for simplicity and clarity. An SLA compensation payment is an amount paid pursuant to a securities lending arrangement as compensation for an underlying payment.
This definition applies to securities lending arrangements made after 2001.
"underlying payment"
"Underlying payment" is a newly-defined term. As with most of the other new definitions in this subsection, this term is defined for simplicity and clarity. An underlying payment is an amount paid on a qualified security by the issuer of the security.
This definition applies to securities lending arrangements made after 2001.
Deemed Character of Compensation Payments
ITA
260(5) and (5.1)
Subsection 260(5) of the Act, in its current form, treats dividend compensation payments that are received under specified circumstances as dividends. The subsection also, however, denies this dividend treatment where the amount is received by a corporation and one of the main reasons for the corporation entering into the arrangement was to enable it to receive an amount that would be treated as a dividend by the subsection.
Subsection 260(5) is reorganized into two subsections, and these subsections incorporate three newly-defined terms: "dealer compensation payment", "SLA compensation payment" and "underlying payment".
New subsection 260(5) describes the circumstances under which the compensation payment deeming rule, now found in new subsection 260(5.1), applies. The deeming rule applies where an amount is received under a securities lending arrangement under one of these circumstances: from a person resident in Canada, from a person not resident in Canada where the amount was paid in the course of carrying on business in Canada through a permanent establishment, or from or by a registered securities dealer. These are essentially the same as the circumstances specified prior to the amendment.
Also, the anti-avoidance rule in this subsection – which currently addresses only the case of an amount that would otherwise be received by a corporation as a dividend – is amended to include all otherwise non-taxable amounts that may be received under a securities lending arrangement, by any person. This amendment recognizes that with the introduction of qualified trust units as "qualified securities," a person may be treated as having received any of several kinds of non-taxable amounts.
New subsection 260(5.1) of the Act treats a given compensation payment as one of three things: a dividend, an amount paid by a trust and having the same characteristics, source and purpose as the "underlying payment" amount paid by the trust directly, or interest. The overall effect of the provision is, in addition to replicating the former dividend deeming rule, to deem compensation payments in respect of payments from a trust to have the same characteristics, source and purpose as if the amounts were paid by the trust.
These amendments apply to securities lending arrangements made after 2001 except that if the parties to an arrangement file a joint election in writing within 90 days after Royal Assent of this amendment with the Minister of National Revenue, the parties may elect such that either one or both of the deeming rules in paragraph 260(5.1)(b) or (c) will not apply with respect to non-dividend compensation payments received before February 28, 2004. Taxpayers may wish to make this election to leave open the possibility that these non-dividend compensation payments had a different characterization under the law prior to these amendments.
Deductible Compensation Payment Amount
ITA
260(6)
Subsection 260(6) of the Act limits the extent to which a person who makes a dividend compensation payment under a securities lending arrangement may deduct the payment in computing income from a business or property. In brief, the subsection denies a deduction for any dividend compensation payment made by persons other than registered securities dealers, and provides that registered securities dealers may deduct up to 2/3 of the dividend compensation payments they make.
Amended subsection 260(6) retains this 2/3 dividend compensation payment deduction for registered securities dealers. It also allows any taxpayer - including but not limited to registered securities dealers - a deduction in respect of compensation payments, either SLA compensation payments or dealer compensation payments, that are not dividend compensation payments. The amount of this new deduction is computed differently depending on the actions of the taxpayer in question (the one who made the payment and seeks to deduct it). If the taxpayer has disposed of the borrowed security and has included any resulting gain or loss in computing business income, the compensation payment is fully deductible. In any other case, new subsection 260(6) allows a deduction to the extent of the lesser of (i) the compensation payment and (ii) the amount, to which the compensation payment relates, included in the taxable income of the taxpayer or persons related to it.
Amended subsection 260(6) applies to securities lending arrangements made after 2001.
Deduction - Compensation Payments
ITA
260(6.1)(a)
Subsection 260(6.1) of the Act provides a deduction for dividend compensation payments made pursuant to certain dividend rental arrangements. The amount deductible is the lesser of the amount the corporation is obligated to pay as compensation under the arrangement and the amount of the dividends received by the corporation under the arrangement that were identified in its return of income as amounts which are not deductible because of subsection 112(2.3) of the Act.
Paragraph 260(6.1)(a) of the Act is amended to clarify that the amount described in that paragraph is the total of all amounts that the corporation becomes obligated in the taxation year to pay to another person as compensation under certain dividend rental arrangements.
Also, paragraph 260(6.1)(a) of the English version of the Act is amended, as a consequence of the amendments to the definition "dividend rental arrangement" in subsection 248(1) of the Act, by replacing the reference to "paragraphs (c) and (d)" of that definition to a reference to "paragraph (b)" of that definition.
This amendment applies to dividend rental arrangements made after December 20, 2002 and, if the parties jointly elect within 90 days after this Act has been assented to, it also applies to dividend rental arrangements made after November 2, 1998 and on or before December 21, 2002, except that before 2002 the reference to "subsection 260(5.1)" should be read as "subsection 260(5)".
For arrangements made after 2001 and before December 21, 2002 that are not the subject of the election described in the previous paragraph, the definition "dividend rental arrangement" in effect before December 21, 2002 is applicable, except that the reference to "subsection 260(5)" in that definition should be read as "subsection 260(5.1)".
Dividend Refund
ITA
260(7)
Subsection 260(7) of the Act provides that, where a corporation makes a payment which is deemed by the former subsection 260(5) to be a taxable dividend, the corporation will also be entitled to treat the amount as the payment of a dividend for the purposes of section 129 of the Act.
Subsection 260(7) is amended to replace the reference "subsection 260(5)" with "subsection 260(5.1)" and is reorganized for clarity and simplicity and specifically not to effect any substantive changes to the rule.
This amendment applies to securities lending arrangements made after 2001.
Non-resident Withholding Tax
ITA
260(8), (8.1) and (8.2)
Subsection 260(8) of the Act applies special rules, for the purposes of Part XIII of the Act, to payments made under securities lending arrangements. The subsection has two main aspects: rules that ensure the appropriate treatment for Part XIII purposes of compensation payments; and a rule that in certain circumstances will treat a borrower as having paid to a lender a "borrow fee".
In addition to incorporating the newly added definitions, SLA compensation payments and underlying payments (which do not effect any substantive changes), the subsection is rearranged into three separate subsections. Amended subsection 260(8) retains the previous rules for compensation payments relating to interest and dividends, confining them to amounts paid on a security that is not a qualified trust unit. Subsection 260(8) also provides for compensation payments made in respect of a borrowed qualified trust unit: these are treated as payments from a trust and as having the same character and composition as the trust payments for which they compensate.
New subsection 260(8.1) provides for a deemed borrow fee, on the same basis as the existing paragraph 260(8)(b). New subsection 260(8.2) similarly preserves the effect of the existing postamble to subsection 260(8) in relation to tax treaties.
These subsections apply to securities lending arrangements made after 2001.
Partnerships
ITA
260(10), (11), and (12)
A "securities lending arrangement" (SLA) is defined in subsection 260(1) of the Act as a particular transaction between two persons: the "lender" and the "borrower" of a security. A partnership - which for most purposes of the Act is not a person - can be a party to a transaction that would be an SLA if the partnership were a person. In such a case, it is appropriate in policy terms for the arrangement to be treated as an SLA. New subsections (10), (11) and (12) are added to section 260 to bring partnerships within the SLA rules.
New subsection 260(10) provides that, for the purposes of section 260, a person includes a partnership. This allows a partnership to be either the borrower or the lender in respect of an SLA. The subsection also treats a partnership as a registered securities dealer, if all of its members are themselves registered securities dealers.
A transaction’s status as an SLA is relevant to, among other things, the tax treatment of amounts paid and received in compensation for dividends or interest on the security that is transferred or lent. New subsections 260(11) and (12) are added to ensure the appropriate treatment of these amounts in a case where a corporation or an individual is a member of a partnership that has entered into an SLA.
• Under new paragraph 260(11)(a), a corporation that is a member of a partnership is treated for the purpose of subsection 260(5) as having received its "specified proportion" (now defined in subsection 248(1) of the Act) of each compensation payment or amount in respect of proceeds of disposition that is described in subsection 260(5) and was received by the partnership. It is also treated as being the same person as the partnership, thus ensuring that the partnership’s reasons for entering into the arrangement (which are relevant to the applicability of the subsection) are attributed to the corporation.
• New paragraph 260(11)(b) treats the corporation as being obligated to pay its specified proportion of each dividend compensation payment described in paragraph 260(6.1)(a).
• New paragraph 260(11)(c) treats the corporation, for the purpose of applying the dividend refund rules in section 129 of the Act, as having paid its specified proportion of each non-deductible dividend compensation payment made by the partnership.
• New paragraph 260(12)(a) performs for individuals who are members of a partnership the same functions as new paragraph 260(11)(a) does for corporations that are partners.
• New paragraph 260(12)(b) treats an individual partner as having paid, for the purpose of clause 82(1)(a)(ii)(B) of the Act, the individual’s specified proportion of each dividend compensation payment paid by the partnership that is deemed by new subsection 260(5.1) to have been received by another person as a taxable dividend.
These amendments apply to SLAs made after December 20, 2002 and, if the parties jointly elect within 90 days after this Act has been assented to, they also apply to SLAs made after November 2, 1998 and on or before December 20, 2002, except that before 2002, the reference to "subsection 260(5.1)" should be read as "subsection 260(5)".
Clause 195
ITA
Schedule
### Act to Amend the Income Tax Act (Natural Resources)
Clause 196
Repeal of Paragraph 18(1)(m)
Subsection 2(5) of the Act to Amend the Income Tax Act (Natural Resources) repealed paragraph 18(1)(m) of the Act effective for taxation years that begin after 2006. Subsection 2(5) is being amended with the result that paragraph 18(1)(m) is now being repealed effective for taxation years that begin after 2007. This amendment is being made to accommodate a reimbursement made in a taxation year of the taxpayer that begins after 2006 and before 2008 in circumstances where the taxpayer’s taxation year does not coincide with the taxation year or fiscal period of the recipient, as would normally be the case where the recipient of the reimbursement is a partnership of which the taxpayer is a member.
Clause 197
Amendment to An Act to Amend the Income Tax Act (Natural Resources)
Subsection 80.2 of the Act was repealed by section 9 of An Act to Amend the Income Tax Act (Natural Resources), S.C. 2003, c.28, effective for taxation years that begin after 2006. Section 9 of that Act is being repealed with the result that section 80.2 will continue in force. However, section 80.2 will apply only to specified amounts paid in respect of original amounts that are paid or become payable or receivable in taxation years or fiscal periods of the recipient that begin before 2007. As a result, section 80.2 will only apply to a reimbursement if the recipient is subject to restrictions on the deductibility of the reimbursed Crown charge (i.e., the Crown charge is described in paragraph 18(1)(m)) or is required to include some portion of the Crown charge in income (i.e., the Crown charge is described in paragraph 12(1)(o)).
The repeal of section 9 of the Act to Amend the Income Tax Act (Natural Resources) extends the possible application of section 80.2 to a reimbursement that is made in a taxation year of the taxpayer that begins after 2006 (assuming the reimbursed Crown charge was imposed in a taxation year or fiscal period of the recipient that begins before 2007). This extension of section 80.2, along with the extension of paragraph 18(1)(m) will accommodate, among other things, a reimbursement of a Crown charge by a member of a partnership, as described in new subsection 80.2(4), where such reimbursement is made in a taxation year of the member that begins after 2006 and before 2008.
### Canada-Nova Scotia Offshore Petroleum Resources Accord Implementation Act
Clause 198
Nova Scotia Capital Tax
The Canada-Nova Scotia Offshore Petroleum Resources Accord Implementation Act (Accord Act) was introduced consequential to the Canada-Nova Scotia Offshore Petroleum Resources Accord, which was entered into by the Government of Canada and the Government of Nova Scotia on August 26, 1986. Under the Accord Act, the federal government imposes, collects and remits to the province the corporate income tax, consumption tax and insurance premiums tax on corporations operating in the offshore area that would be levied by Nova Scotia if the offshore area were a part of the province. Subsequent to the introduction of the Accord Act, Nova Scotia established a tax on the capital of large corporations (LCT). This measure amends the Accord Act to include capital tax among those taxes imposed, collected, and remitted under it.
This change is deemed to have come into force on April 1, 1997, the effective date of the LCT.
### Federal – Provincial Fiscal Arrangements Act
Clause 199
Deduction for Federal Tax
FPFAA
12.2
Part IV.1 of the Federal-Provincial Fiscal Arrangements Act (FPFAA) provides a revenue-sharing mechanism in respect of the tax collected under Part VI.1 of the Income Tax Act (Canada) (ITA). A province is entitled to a portion of the federal tax collected from corporations that operate in the province in a year, if two conditions are met. First, it must be the case either that Canada collects the province’s corporate income tax under a tax collection agreement, or that the province’s law allows a multiple of the Part VI.1 tax to be deducted in computing taxable income. Second, the province itself must not impose taxes similar to those imposed under Parts IV.1 and VI.1 of the ITA.
The condition that the province itself provide a deduction is currently set out, in paragraph 12.2(1)(b) of the FPFAA, as requiring a deduction of at least 9/4 of a corporation’s ITA Part VI.1 tax. The 9/4 figure is taken from the deduction under ITA paragraph 110(1)(k). With the adjustment of that ITA deduction, the figure 9/4 is no longer appropriate. Paragraph 12.2(1)(b) of the FPFAA is, therefore, amended to require a deduction, for provincial tax purposes, that is not less than the amount deductible under the ITA provision. By referring to the ITA rule itself, rather than specifying a given figure, amended paragraph 12.2(1)(b) will not need to be further amended if the multiple provided in the ITA should change at some future time.
To ensure that provinces have an opportunity to make any necessary amendments to provincial legislation, this amendment applies after 2003.
### Income Tax Amendments Act, 2002
Clause 200
S.C. 2000, c. 17, ss. 59(2)
Debt Forgiveness Rules
Subsection 59(2) of the Income Tax Amendments Act, 2000 is amended to provide that, in computing a debtor’s income for a particular taxation year, the fraction in paragraph 38(a) of the Income Tax Act to be applied in respect of the settlement of a commercial debt obligation is the fraction in that paragraph that applied to the debtor in the debtor’s taxation year in which the obligation was deemed to have been settled instead of the fraction in that paragraph that applies to the debtor in the particular taxation year.
This change corrects a technical deficiency, and is deemed to have come into force on June 14, 2001.
Clause 201
S.C. 2000, c. 17, ss. 70(11)
Disposition of Shares in a Foreign Affiliate
ITA
93(1.2)
Section 93 of the Income Tax Act contains a number of rules relating to the disposition of shares of a foreign affiliate of a taxpayer resident in Canada.
Subsection 93(1.2) provides that, where a particular corporation resident in Canada or a foreign affiliate of the particular corporation (each of which is referred to as the "disposing corporation") would, but for this subsection, have a taxable capital gain from a partnership from the disposition by the partnership of shares of a class of the capital stock of a foreign affiliate of the corporation, and the disposing corporation so elects in prescribed manner in respect of the gain, the amount designated will reduce the taxable capital gain and will be grossed up and recharacterized as a dividend received on the share by the disposing corporation.
Paragraph 93(1.2)(a) provides that twice the amount designated by the disposing corporation in respect of the shares (or where subsection 93(1.3) applies, twice the amount determined under that subsection) will be treated as a dividend received on the shares by the disposing corporation from the foreign affiliate.
Before the present amendment, subsection 93(1.2) was applicable to taxation years that end after February 27, 2000. This amendment ensures that, for a taxation year of a taxpayer that includes either February 28, 2000 or October 17, 2000 or began after February 28, 2000 and ended before October 17, 2000, the reference to the word "twice" is to read as references to the reciprocal of the capital gains inclusion rate applicable to the corporation resident in Canada or to the foreign affiliate for the taxation year. This amendment corrects a technical deficiency.
### Part 3 Amendments Related to Bijuralism
As part of the harmonization of federal legislation, the Government has undertaken to review all its legislation where provincial private law concepts are found in order to reflect appropriately the common law and the civil law, in both official languages.
As part of this harmonization initiative, federal tax legislation is being reviewed. Several changes to the legislation have already been implemented, namely by way of the Income Tax Amendments Act, 2000, S.C. 2001, c. 17. The proposed amendments continue this harmonization initiative.
This Part proposes amendments to the Income Tax Act concerning the concepts of "joint and several liability" / "solidary liability", "tangible property" / "corporeal property", "intangible property" / "incorporeal property", "personal property" / "movable property", "real property" / "immovable property", "interest" / "right" which are further described below. The proposed amendments are not intended to change the current application of the amended provisions; they purport to reflect the concepts and terminology of the common law and the civil law in both official languages. They will come into force on Royal Assent to this Bill.
Joint and Several Liability and Solidary Liability
The French version of the current tax legislation uses the term "solidairement", which is appropriate for both civil law and common law. Therefore, the French version does not need to be amended.
In the English version of the current tax legislation, only the term "jointly and severally" is used. This term is maintained for common law purposes. The term "jointly and severally" is no longer adequate in civil law in English and has been replaced with the term "solidarily". Therefore, it is appropriate to add the term "solidarily" in the English version in order to reflect the civil law.
Tangible and Corporeal Property
In the French version of the current tax legislation, only the civil law terminology "bien corporel" is used. In the English version, only the common law term "tangible property" is used.
In the French version of the legislation, it is appropriate to add the term "bien tangible" in order to reflect the common law.
In the English version of the legislation, it is appropriate to add the term "corporeal property" in order to reflect the civil law.
Intangible and Incorporeal Property
In the French version of the current tax legislation, only the civil law terminology "bien incorporel" is used. In the English version, only the common law term "intangible property" is used.
In the French version of the legislation, it is appropriate to add the term "bien intangible" in order to reflect the common law. Where it is appropriate to do so, the shared elements of the relevant terms are combined in the phrase "bien incorporel ou intangible", which refers to both systems of law.
In the English version of the legislation, it is appropriate to add the term "incorporeal property" in order to reflect the civil law. Where it is appropriate to do so, the shared elements of the relevant terms are combined in the phrase "intangible or incorporeal property", which refers to both systems of law.
Personal Property and Movable Property
In the French version of the current tax legislation, only the civil law terminology "bien meuble" is used. In the English version, the terms "personal property" and "chattels" are used to reflect the common law.
It is therefore appropriate to add in the French version a reference to the term "bien personnel" in order to reflect the common law. Where it is appropriate to do so, the shared elements of the relevant terms are combined in the phrase "bien meuble ou personnel", which refers to both systems of law.
In the English version of the legislation, the term "movable" is added in order to reflect the civil law. Where it is appropriate to do so, the shared elements are combined in the phrase "personal or movable property", which refers to both systems of law.
Real Property and Immovable Property
In the French version of the current tax legislation, only the civil law terminology "bien immeuble" is used. In the English version, only the common law concept of "real property" is used.
It is therefore appropriate to add a reference, in the French version, to the term "bien réel" in order to reflect the common law. Where it is appropriate to do so, the shared elements of the relevant terms are combined in the phrase "bien immeuble ou réel", which refers to both systems of law.
In the English version of the legislation, the term "immovable" is added in order to reflect the civil law. Where it is appropriate to do so, the shared elements of the relevant terms are combined in the phrase "real or immovable property", which refers to both systems of law.
Interest and Right
Generally, in the current tax legislation, the common law term "interest" and the civil law term "droit" are used to refer to the relationship that exists between a person and property. At common law, it is possible to have a right or an interest in property; an interest in property necessarily involves rights in property while the reverse is not always true.
For purposes of the civil law, it is appropriate to limit the application of the term "droit" in the French version to the civil law, unless otherwise provided. In the English version, it is appropriate to add a reference to the concept of "right" in order to address the civil law audience and to similarly limit the application of this term to the civil law, unless otherwise provided.
The term "interest" is a common law concept that is translated into French by the term "intérêt". It is therefore appropriate to add a reference to the concept of "intérêt" in the French version in order to address the common law audience.
Subsections 20(17) and 20(18)
Subsections 20(17) and 20(18) are repealed, as the provision to which they relate has been repealed.
Subsections 248(4) and 248(4.1): Interest in Real Property and Real Right in Immovables
Subsection 248(4) of the current legislation uses the term "droit sur un bien immeuble" in the French version as equivalent for the term "interest in real property" used in the English version. The term refers to the relationship between a person and property and for purposes of the I.T.A. includes a leasehold interest but not an interest as security.
Subsection 248(4) is amended so as to provide, for common law purposes, the scope of the term "interest in real property." Reference to the civil law term "hypothecary claim" is removed from the English version of the provision. Furthermore, the term "intérêt sur un bien réel"is added in the French version of the Act. This term is the French equivalent of the common law term "interest in real property".
For civil law purposes, new subsection 248(4.1) is added in both linguistic versions of the Act. The scope of the civil law term "real right in immovables" / "droit réel sur un immeuble" is adjusted in a similar manner as its common law counterPart by including the lease and excluding security rights.
1. Subparagraph 142.6(1)(b)(i) [Return]
2. Subparagraph 142.6(1)(b)(ii) [Return] | 2019-04-20 06:40:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28226715326309204, "perplexity": 2553.0536635754133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578528702.42/warc/CC-MAIN-20190420060931-20190420082931-00264.warc.gz"} |
http://motls.blogspot.com/2004/10/anthropic-lack-of-principles.html | ## Saturday, October 16, 2004 ... /////
### The anthropic lack of principles
Sean Carroll just wrote an essay on his blog (incidentally in the same domain blogspot.com as my blog), and Peter Woit has replied. Why don't we write a couple of words about it, too?
• As an introduction, let me say that the "anthropic principle" is a philosophical paradigm designed to reduce our curiosity about the patterns in Nature. When we ask "How is it possible that a value of some parameter in Nature is XY, which (always) happens to be the right value necessary for life?", the anthropic principle answers "in all the other Universes (whose existence is an assumption of the anthropic thinking) where the value is different, there is (probably) no human being (no 'anthropos') to ask this question."
• Consequently, this approach allows us to say "We don't need to look for any other explanations because if the things were different, we could not be here." Such an attitude makes further scientific research less meaningful, and therefore the attitude is anti-scientific
• It seems to me that both guys mentioned above - Peter and Sean - write pretty reasonable things, but both of them also write things that are harder to agree with
• I believe that Peter Woit has a very similar algorithm like me to decide whether a theory is predictive and interesting, but he really misunderstands some important aspects of string theory - and this partial ignorance invalidates his conclusions about string theory
• Even though I am counted, much like Peter Woit, as an anti-anthropic extremist according to Sean's classification, as the title of my article indicates, I totally agree that it is a conceivable scenario that some parameters of this Universe will eventually be explained as environmental parameters without a deeper quantitative explanation
• However, much like Peter, I will only believe that such a model of reality is better and more likely (and scientifically plausible) than others once it successfully predicts many new phenomena (more phenomena than competing or older theories) or relates the previously unrelated phenomena that have already been observed - more precisely, once it calculates a lot of verifiable new numbers that go beyond the input
Let me start the main text by telling you what's wrong with Peter's description. Peter systematically tries to create the impression that string theory cannot be predictive. In fact, the emergence of the anthropic reasoning has just the opposite reason. Why?
In the Standard Model, which is a non-gravitational theory, the sum of the vacuum diagrams does not really matter because the vacuum energy has no effects in a non-gravitational theory.
However, if you couple such a theory to gravity, the vacuum energy does matter, because it curves the space and time. However, in quantum field theory, you can always add a counter-term and adjust your vacuum energy to whatever you want. You need some fine-tuning, but you can always adjust such "constants" in quantum field theory. It's just a matter of naturalness, much like in the hierarchy problem (associated with the Higgs mass).
That's not the case of string theory. Here, you can really calculate the vacuum energy, and in the simplest models/vacua, you obtain a far too huge value of the cosmological constant - assuming that some serious bug about our understanding of SUSY breaking don't invalidate the whole conclusion.
In this sense, the cosmological constant problem in string theory is (or was) more serious than in quantum field theory because string theory is a very rigid theory that does not allow you to mess with the parameters. On the other hand, a part of the stringy calculation relied on quantum field theory and it is still plausible that a more complete, inherently stringy calculation of the cosmological constant leads to more realistic results.
Well, the anthropic industry in string theory is more or less meant to put the cosmological constant problem in string theory onto a comparable level with the cosmological constant problem in field theory. The freedom to continuously fine-tune the vacuum energy in field theory is replaced by the large number of vacua in string theory - and you can really see that some of them are more or less guaranteed to predict a qualitatively correct value of the cosmological constant "by chance". This anthropic thinking is annoying, but honestly speaking, its well-being is caused by the absence of a really convincing quantitative calculation of a small cosmological constant.
You know, I am among those who believe that we don't quite understand this counting, especially after SUSY breaking, properly, but the anthropic people will disagree. Shamit Kachru et al. will tell you how to calculate all possible contributions to the potential, and he will argue that nothing is neglected and all approximations they make are justified.
They will tell you that they have a full control over the class of the KKLT-like vacua (that was elaborated by Mike Douglas and his collaborators and others), and this full control allows them to state quite certainly that string theory does predict a large number of vacua - even those controllable ones form large classes.
Once again, Peter is absolutely wrong if he thinks that string theory's nature is its inability to predict. On the contrary, string theory in principle predicts everything - its character certainly makes it the most predictive theory we ever had (and that one can imagine). In fact, the appearance of the landscape in string theory may be viewed as a consequence of its strong predictive power - because some people just became convinced that a choice of one of a few "simple" and "natural" enough vacua is more or less guaranteed to predict an incorrect cosmological constant. This is why the people started to propose the convoluted vacua that can give you, more or less by chance, a realistic cosmological constant, too.
It's wrong to think that string theory - even with the anthropic accent - is less predictive than field theory. Even if you imagined that string theory could give you virtually any field theory at low energies, it is still morepredictive because it is a UV complete theory containing quantum gravity - something impossible in quantum field theory - and each of its vacua tells you the cross section of gravitons at any energies etc. Its low energy physics may have many types, and in this sense the "Landscape" of stringy vacua is analogous to the "Landscape" of quantum field theories - with the difference that the landscape of QFTs has continuous parameters, while string theory only has discrete ones (although there can be many of them).
Unfortunately, string theory is not only the best predictive theory (in principle), but it is also the only known semi-scientific incarnation of the anthropic reasoning. In order to deal with the anthropic reasoning semi-scientifically (the word "scientifically" would seem too ambitious), you must have a theory with a large number of possible Universes and a dynamical mechanism that allows you to go from one to another.
Moreover, to invent a well-defined measure, it's easiest to have a discrete set of vacua - then you can say that each vacuum is "equally likely". (I believe that this is a non-scientific and unjustified assumption, but I also agree that the game based on this assumption is well-defined.) There is no other theory like that (with a large discrete number of dynamically connected vacua) known, except for string theory.
Sean Carroll's "non-partisan" objections against us, the extremists
:-)
Let me now look at Sean's criticism of his anti-anthropic colleagues. He thinks that the anti-anthropic physicists have two basic types of arguments:
• we say that it is not scientific to "give up" a scientific explanation of a universal number in Nature and to demand some "random unexplainable" or even "divine" justification of such a number
• we say that the other Universes required by the anthropic reasoning are unobservable in principle, and therefore they should not count as a part of a truly scientific description of the world
Yes, it seems fair, and I count both points as parts of my basic objections against the anthropic principle, but let me clarify some details.
The first objection is the "defeatism" of the anthropic reasoning. Yes, I think that it is a very wrong approach to science. One might have stopped the progress in science at virtually any moment in the past by claiming that some not-quite-understood features of reality are consequences of unexplainable dynamics involving zillions of Universes (or choices for the laws of Nature), and the only reason why reality behaves the way it does is that if it behaved otherwise, we would not be here. Examples of possible past applications of the anthropic reasoning will be discussed at the end of this article.
In fact, it is not just about "might have stopped". Such a thing has happened many times in the history of our civilization. The medieval anthropic biology has stopped the research of the relations between different organisms, and the research of the reasons why the animals and plants had the observed properties, for several centuries. The official answer was that the plants and animals were created by God. They had to be created exactly in this way because God, who is perfect, simply did so before he created us (at the end of the week). If you imagine any modification, you would obtain a Universe with a less perfect god that would not be capable to create us, and moreover, you should be burned at the stake.
Darwin's theory replaced this picture by something else, and even though it has not become as quantitative a science as we desire, the progress is clear and many previously mysterious properties of the animals could have been explained. Darwin's theory also agrees with other newer developments, including the discovery of genetics and DNA.
You may say - and some people actually say - that the anthropic reasoning is not similar to religion, but instead, it is analogous to Darwin's theory because the Universe "compete" much like the animals, and there is no explicit God there. Well, it is as analogous as much as the evolutionary theory itself is analogous to creationism, but not more. Darwin's theory has pretty well-defined rules and mechanisms. The animals are doing all these familiar things and they live together - and compete - according to some schemes that are deeply rooted in biology, chemistry, and physics - and that we can predict.
On the other hand, the arena of very many Universes that "compete" has no testable rules like that, and therefore it mimicks religion. (Of course, if someone could derive really exact rules that govern the Universes in the multiverse, the situation would change.)
This brings me to the second point why most of the forms of the anthropic reasoning are not quite scientific: the conjectured properties, role, and existence of the other Universes are not subject to science, especially not the experiments.
First of all, if someone were thinking in terms of an ensemble of the Universes that even do not belong to a single theory, that would be a completely anti-scientific approach simply because he would be combining things without any physical connections between them into a single whole. Such versions of the anthropic approach would be a realization of the idea "anything goes" and their value for science is certainly zero or less. An average person 10,000 years ago, with no experience and no experiments, could have conjectured this sort of crap. I think that many did, but it has led to no progress in science.
Let's not waste time with this nonsense, and let's look at something more scientific: the anthropic principle with an ensemble of different "vacua" that are connected into a single dynamical theory. Of course, we can't require that the actual people can move in between the Universes because "our life" is only possible here - and perhaps, it does not have to be necessarily possible to physically create a bubble of another Universe within your Universe (these issues have been discussed by Tom Banks). Nevertheless, it seems essential to require that all these Universe belong to a single theory - well, string theory is the only known reliable framework for this kind of game.
I still find it obvious that the "other" Universes or vacua of string theory - which the humans will never be able to observe - can only have the following scientific consequences:
• they are often useful toy models (well, they can be rather convoluted toy models) to study physical phenomena that will also be useful for the investigation of our real Universe, or phenomena that are exciting mathematically even without direct links to observable physics
• these other vacua can also be relevant if they occur in the early history (or prehistory) of our Universe, and if we find the right mechanism that allows us to study the transmutation of one Universes to another from a well-defined starting point
Otherwise, if we don't have any measure on the space of vacua and no cosmological mechanism to generate this measure (which would essentially mean that such a mechanism could really predict something), then the existence of other, unobservable vacua is totally irrelevant for our investigation of this specific Universe. It is irrelevant for two related reasons:
• from a pragmatic viewpoint, we can only observe effects in this Universe, and the other Universes are uninteresting
• even if we found the other Universes interesting, the statements about them are not directly testable
In this sense, I agree with Peter Woit that having a large number of possible Universes that can imply anything is equally bad as having no explanation whatsoever. At the end, we can show that string theory is correct - by hundreds of new and nontrivial quantitative predictions - and this final form of string theory may imply the existence of other Universes, and Peter will have to believe it, too. But I sympathize with his opinion that he should not be asked to believe in the other Universes before the theory is proved correct. Extraordinary claims require extraordinary evidence, and the necessity for 10^{500} of Universes like ours seems to be an extraordinary claim.
Where should science go?
I think that at the very end, all of us would agree that all these possibilities are conceivable, at least in principle. Peter Woit and me would almost certainly agree that it may happen that some much more perfect science in the 25th century will consider some parameters of Nature to be environmental parameters which either can't be calculated at all, or they can be calculated once a finite amount of information (about the discrete vacua) is determined. On the other hand, I am pretty sure that Sean Carroll would agree with us that it is possible that a very scientific, canonical, and quantitative calculation of the Standard Model parameters will be found and the anthropic proposals will become irrelevant.
But these questions are not just "yes/no" questions: they are about the probability of various things and our methods to estimate the probability and judge whether a direction of research is promising or not. Therefore, let me return to the analysis of how damaging for science would it have been if the people decided that something were not explainable, but they were rather a consequence of a divine choice or perhaps necessary conditions for us to exist (even though no one can actually prove the necessity).
I've already said that the whole evolutionary biology would be blocked (and genetics and DNA research would be blocked, too) because the whole motivation of Darwin's theory and genetics is to explain some previously mysterious properties of plants and animals, and the relations between them (and between the properties of the parents and their offsprings). All of these things could have been treated as environmental coincidences that don't admit an explanation, and science would be stuck.
Physics has even much more impressive examples what could have happened if people gave up and accepted the anthropic "answers" in the past. The properties (density, permitivity, freezing point etc.) of all elements and perhaps all compounds could have been treated as a conglomerate of environmental parameters whose choice would be believed to be necessary to explain our existence.
• Well, today we can in principle calculate all these things, even from simple non-relativistic quantum mechanics with roughly two parameters. As Einstein said, "The most incomprehensible thing about the Universe is that it is comprehensible." The anthropic principle offers no explanation how is it possible that we've been able to understand so many things already.
People could have said that the properties of the nuclei - that also often seem necessary for our lives - only have an anthropic explanation. A carbon nucleus must be stable together with some other nuclei, and all these conditions constrain the allowed properties of nuclear physics. All these things look like a wonderful application of the anthropic reasoning. Nevertheless, today we know that the anthropic reasoning is just wrong: all properties of hadrons follow from a single nice theory (QCD) that has no dimensionless parameters whatsoever. (Well, the small bare fermion masses are sometimes necessary, and they add small corrections.)
Even though we may find the anthropic principle in this case (nuclear masses and stability) pretty plausible because the masses seem essential for life to exist - perhaps more plausible than in the explanation of the top quark mass - it is not the correct explanation.
And the anthropic reasoning is suspicious because of the opposite reason, too. We know that it is incomplete. As John Donoghue noted, the anthropic reasoning will never be sufficient to explain - even with the limited ambitions of an "explanation" according to anthropic "science" - some facts about the Nature. Namely the QCD theta angle could be much bigger, without affecting our lives too much, but nevertheless it is small. The explanation of this fact will have to be a scientific one, and there is no reason why similar explanations won't explain the rest.
I find it obvious that we should never be satisfied with our explanations until all numbers are explained, or until we have a more or less rigorous proof that they can't be explained; such a proof must be justified by clear evidence that leads to many other, highly nontrivial predictions. The Standard Model with neutrino masses has roughly 30 parameters, and a few more parameters such as the QCD theta angle, the cosmological constant etc. must be added. It may happen that new physics will be found, and we will need more parameters.
But let me now assume that it won't be the case. Then I don't think that a theory constitutes progress compared to the Standard Model if it needs an equal number of parameters (or even more). String theory, if it works, is definitely progress, maybe even the final one, because it contains no continuous adjustable non-dynamical parameters.
But string theory in the form as understood today still has many discrete parameters. A discrete parameter carries much less information than a continuous parameter, but it can still be counted as a parameter. Even in the realm of discrete parameters, the usual scientific requirements for a theory to lead to new predictions must be respected. If we need to specify 500 bits of discrete information (about the vacuum and its fluxes), it's a price that we should only pay if a larger number of nontrivial features of the Universe is explained.
The idea that we should prefer the vacua that have many possible types - i.e. the less predictive vacua - in our quest for the right theory of the Universe is an anti-scientific idea. I've been talking about similar issues already in the article Parameters of Nature.
#### snail feedback (3) :
Nice essay, I agree. I don't know why people make so much about this, it really strikes me as rather self evident. Even if I were a layman (which im not).
Unfortunately, this whole spiel really doesn't help the segment of string theorists who need the most help right now. Eg the phenomenologists. Currently they have an astronomical amount of *nearly* completely disjoint, nontrivial working models which they have to consider. Each of those broad classes of theories of course has some nonzero probability of containing the real physics of our universe.
Telling them that they can just pick whichever parameters and model that gives the correct parameters for life, is rather like preaching to the choir. They have been trying to do that for over 20 years. In fact, im sure they would love to be able to find a single consistent model that reproduces such a thing.
But there is no brownie points for close second place. Unfortunately there is no such thing at this time. If you ask the phenomenologists, they can almost get the SM, but there are always little problems here and there (like getting the correct CKM matrix with the presence of neutrinos) that mucks things up. Or too many flavor changing neutral currents, bad proton decay bounds, etc etc
So either there is identically zero such models (a horrendous nogo theorem that is still possible in principle). Or we could have the situation *but that has yet to be shown rigorously* that we end up with a potentially worse situation.. Everything. That is Peters argument roughly.
Of course, those are not the only possibilities (or else he would be correct). There is still hope that there is identically one such solution, and I would say thats what people in the field are working for. I don't see why everyone has to lambast a theory if its not even completely worked through yet, by our admittedly small minds. In that sense Brian Greene is right.
There might be some as yet to be discovered governing principle hiding in the background. Something analagous perhaps to say Einsteins principle of equivalance. Anthropic reasoning in that sense is just the eternal lazy *I give up* principle, b/c finding such a thing is hard, and people need some way to put their kids through college. | 2013-12-05 17:16:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5437043905258179, "perplexity": 568.3122993572532}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163046950/warc/CC-MAIN-20131204131726-00006-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/UCSB/Stewart5_2_5/Stewart5_2_5_6.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=libretexts | Which of the following is a function that has a jump discontinuity at $x=2$ and a removable discontinuity at $x=4$, but is continuous elsewhere?
(a) $f(x)= \displaystyle \frac{2}{(x-2)(x-4)}$.
(b) $f(x) = \begin{cases} 1 & \textrm{if }x \leq 2 \\ x-3 & \textrm{if }2 < x < 4\textrm{ or }x > 4 \\ 3 & \textrm{if }x = 4 \\ \end{cases}$.
(c) $f(x) = \begin{cases} 2-x^2 & \textrm{if }x \leq 2 \\ \displaystyle \frac{1}{x^2-4x} & \textrm{if }x > 2\\ \end{cases}$. | 2022-01-23 18:25:34 | {"extraction_info": {"found_math": true, "script_math_tex": 5, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.917749285697937, "perplexity": 83.00213852772991}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304309.5/warc/CC-MAIN-20220123172206-20220123202206-00549.warc.gz"} |
https://encyclopediaofmath.org/wiki/Pure_subgroup | Pure subgroup
serving subgroup
A subgroup $C$ of an Abelian group $G$ such that for any $c\in G$ the solvability of the equation $nx=c$ in $G$ implies its solvability in $C$. Examples of pure subgroups are the zero subgroup, $G$ itself, the torsion part of $G$, and direct summands. Not every pure subgroup need be a direct summand, even for a $p$-group. However, if $C$ is a torsion pure subgroup of an Abelian group $G$ and if the orders of its elements are uniformly bounded, then $C$ is a direct summand in $G$. There is a complete description of the Abelian groups in which every pure subgroup is a direct summand (see [1]). The question of the cardinality of the set of pure subgroups of an Abelian group has been thoroughly investigated.
References
[1] A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian) | 2021-05-12 18:00:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.905492901802063, "perplexity": 157.19460030090013}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989766.27/warc/CC-MAIN-20210512162538-20210512192538-00561.warc.gz"} |
https://www.physicsforums.com/threads/spring-constant-k-please-help.247749/ | 1. Jul 30, 2008
### HELP_786
how would i go about finding k with given values for mass and time?
i have seen these equations over and over...but i feel like im missing something very important that i need..please help me
T=2π√(m/k))
F=-kx
2. Jul 30, 2008
### rock.freak667
$$T= 2 \pi \sqrt{\frac{m}{k}}$$
$$\Rightarrow T^2=\frac{4 \pi^2 m}{k}$$
Can you rearrange for k now?
Last edited: Jul 30, 2008
3. Jul 30, 2008
### HELP_786
o im sorry i meant how would I go about finding T(period) with given values for time and mass...............i forgot to proof read
those are the formulas i keep seeing everywhere
for example if i had .10kg and 8.86 seconds for the time to find the period would i do this:
T2=(4π2m)/((4π2m)/(8.86))
and then at the end take the square root
???
4. Jul 30, 2008
### rock.freak667
How exactly was the time measured?
5. Jul 30, 2008
### HELP_786
in seconds
8.86 seconds would be the average time for 10 vibrations in a simple harmonic motion
6. Jul 30, 2008
### rock.freak667
Period(T) is the time taken for one oscillation/vibration.
10 oscillations/vibrations take 8.86 seconds. How much time would 1 oscillation take?
7. Jul 30, 2008
### HELP_786
OH!!! so just divide 8.86s by 10 rite??
8. Jul 30, 2008
### rock.freak667
That should yield the time period, yes.
9. Jul 30, 2008
### HELP_786
i dont believe i didnt realize that! thanku so much! ....im thinking too much lol
10. Jul 30, 2008
### rock.freak667
You just need to think about what it is you want to find.
11. Jul 30, 2008
### HELP_786
thanx again! =D | 2017-11-19 20:41:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7290173172950745, "perplexity": 4763.727366020735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805761.46/warc/CC-MAIN-20171119191646-20171119211646-00035.warc.gz"} |
https://starburstdata.github.io/latest/connector/iceberg.html | # Iceberg connector#
Apache Iceberg is an open table format for huge analytic datasets. The Iceberg connector allows querying data stored in files written in Iceberg format, as defined in the Iceberg Table Spec. It supports Apache Iceberg table spec version 1 and 2.
The Iceberg table state is maintained in metadata files. All changes to table state create a new metadata file and replace the old metadata with an atomic swap. The table metadata file tracks the table schema, partitioning config, custom properties, and snapshots of the table contents.
Iceberg data files can be stored in either Parquet or ORC format, as determined by the format property in the table definition. The table format defaults to ORC.
Iceberg is designed to improve on the known scalability limitations of Hive, which stores table metadata in a metastore that is backed by a relational database such as MySQL. It tracks partition locations in the metastore, but not individual data files. Trino queries using the Hive connector must first call the metastore to get partition locations, then call the underlying filesystem to list all data files inside each partition, and then read metadata from each data file.
Since Iceberg stores the paths to data files in the metadata files, it only consults the underlying file system for files that must be read.
## Requirements#
To use Iceberg, you need:
• Network access from the Trino coordinator and workers to the distributed object storage.
• Network access from the Trino coordinator to the HMS. Hive metastore access with the Thrift protocol defaults to using port 9083.
## Configuration#
The connector supports two Iceberg catalog types, you may use either a Hive metastore service (HMS) or AWS Glue. The catalog type is determined by the iceberg.catalog.type property, it can be set to either HIVE_METASTORE or GLUE.
### Hive metastore catalog#
The Hive metastore catalog is the default implementation. When using it, the Iceberg connector supports the same metastore configuration properties as the Hive connector. At a minimum, hive.metastore.uri must be configured, see Thrift metastore configuration.
connector.name=iceberg
hive.metastore.uri=thrift://localhost:9083
### Glue catalog#
When using the Glue catalog, the Iceberg connector supports the same configuration properties as the Hive connector’s Glue setup. See AWS Glue metastore configuration.
connector.name=iceberg
iceberg.catalog.type=glue
### General configuration#
These configuration properties are independent of which catalog implementation is used.
Iceberg general configuration properties#
Property name
Description
Default
iceberg.file-format
Define the data storage file format for Iceberg tables. Possible values are
• PARQUET
• ORC
ORC
iceberg.compression-codec
The compression codec to be used when writing files. Possible values are
• NONE
• SNAPPY
• LZ4
• ZSTD
• GZIP
ZSTD
iceberg.max-partitions-per-writer
Maximum number of partitions handled per writer.
100
iceberg.target-max-file-size
Target maximum size of written files; the actual size may be larger
1GB
iceberg.unique-table-location
Use randomized, unique table locations
false
iceberg.delete-schema-locations-fallback
Whether schema locations should be deleted when Trino can’t determine whether they contain external files.
false
iceberg.minimum-assigned-split-weight
A decimal value in the range (0, 1] used as a minimum for weights assigned to each split. A low value may improve performance on tables with small files. A higher value may improve performance for queries with highly skewed aggregations or joins.
0.05
iceberg.table-statistics-enabled
Enables Table statistics. The equivalent catalog session property is statistics_enabled for session specific use. Set to false to disable statistics. Disabling statistics means that Cost based optimizations can not make smart decisions about the query plan.
true
### ORC format configuration#
The following properties are used to configure the read and write operations with ORC files performed by the Iceberg connector.
ORC format configuration properties#
Property name
Description
Default
hive.orc.bloom-filters.enabled
Enable bloom filters for predicate pushdown.
false
### Authorization checks#
You can enable authorization checks for the connector by setting the iceberg.security property in the catalog properties file. This property must be one of the following values:
Iceberg security values#
Property value
Description
ALLOW_ALL
No authorization checks are enforced.
SYSTEM
The connector relies on system-level access control.
READ_ONLY
Operations that read data or metadata, such as SELECT are permitted. No operations that write data or metadata, such as CREATE TABLE, INSERT, or DELETE are allowed.
FILE
Authorization checks are enforced using a catalog-level access control configuration file whose path is specified in the security.config-file catalog configuration property. See Catalog-level access control files for information on the authorization configuration file.
## SQL support#
### ALTER TABLE EXECUTE#
The connector supports the following commands for use with ALTER TABLE EXECUTE.
#### optimize#
The optimize command is used for rewriting the active content of the specified table so that it is merged into fewer but larger files. In case that the table is partitioned, the data compaction acts separately on each partition selected for optimization. This operation improves read performance.
All files with a size below the optional file_size_threshold parameter (default value for the threshold is 100MB) are merged:
ALTER TABLE test_table EXECUTE optimize
The following statement merges the files in a table that are under 10 megabytes in size:
ALTER TABLE test_table EXECUTE optimize(file_size_threshold => '10MB')
You can use a WHERE clause with the columns used to partition the table, to apply optimize only on the partition(s) corresponding to the filter:
ALTER TABLE test_partitioned_table EXECUTE optimize
WHERE partition_key = 1
#### expire_snapshots#
The expire_snapshots command removes all snapshots and all related metadata and data files. Regularly expiring snapshots is recommended to delete data files that are no longer needed, and to keep the size of table metadata small. The procedure affects all snapshots that are older than the time period configured with the retention_threshold parameter.
expire_snapshots can be run as follows:
ALTER TABLE test_table EXECUTE expire_snapshots(retention_threshold => '7d')
The value for retention_threshold must be higher than or equal to iceberg.expire_snapshots.min-retention in the catalog otherwise the procedure will fail with similar message: Retention specified (1.00d) is shorter than the minimum retention configured in the system (7.00d). The default value for this property is 7d.
#### remove_orphan_files#
The remove_orphan_files command removes all files from table’s data directory which are not linked from metadata files and that are older than the value of retention_threshold parameter. Deleting orphan files from time to time is recommended to keep size of table’s data directory under control.
remove_orphan_files can be run as follows:
ALTER TABLE test_table EXECUTE remove_orphan_files(retention_threshold => '7d')
The value for retention_threshold must be higher than or equal to iceberg.remove_orphan_files.min-retention in the catalog otherwise the procedure will fail with similar message: Retention specified (1.00d) is shorter than the minimum retention configured in the system (7.00d). The default value for this property is 7d.
### ALTER TABLE SET PROPERTIES#
The connector supports modifying the properties on existing tables using ALTER TABLE SET PROPERTIES.
The following table properties can be updated after a table is created:
• format
• format_version
• partitioning
For example, to update a table from v1 of the Iceberg specification to v2:
ALTER TABLE table_name SET PROPERTIES format_version = 2;
Or to set the column my_new_partition_column as a partition column on a table:
ALTER TABLE table_name SET PROPERTIES partitioning = ARRAY[<existing partition columns>, 'my_new_partition_column'];
The current values of a table’s properties can be shown using SHOW CREATE TABLE.
## Type mapping#
Both Iceberg and Trino have types that are not supported by the Iceberg connector. The following sections explain their type mapping.
### Iceberg to Trino type mapping#
Trino supports selecting Iceberg data types. The following table shows the Iceberg to Trino type mapping:
Iceberg to Trino type mapping#
Iceberg type
Trino type
BOOLEAN
BOOLEAN
INT
INTEGER
LONG
BIGINT
FLOAT
REAL
DOUBLE
DOUBLE
DECIMAL(p,s)
DECIMAL(p,s)
DATE
DATE
TIME
TIME(6)
TIMESTAMP
TIMESTAMP(6)
TIMESTAMPTZ
TIMESTAMP(6) WITH TIME ZONE
STRING
VARCHAR
UUID
UUID
BINARY
VARBINARY
STRUCT(...)
ROW(...)
LIST(e)
ARRAY(e)
MAP(k,v)
MAP(k,v)
### Trino to Iceberg type mapping#
Trino supports creating tables with the following types in Iceberg. The table shows the mappings from Trino to Iceberg data types:
Trino to Iceberg type mapping#
Trino type
Iceberg type
Notes
BOOLEAN
BOOLEAN
INTEGER
INT
BIGINT
LONG
REAL
FLOAT
DOUBLE
DOUBLE
DECIMAL(p,s)
DECIMAL(p,s)
DATE
DATE
TIME(6)
TIME
Other precisions not supported
TIMESTAMP(6)
TIMESTAMP
Other precisions not supported
TIMESTAMP(6) WITH TIME ZONE
TIMESTAMPTZ
Other precisions not supported
VARCHAR, VARCHAR(n)
STRING
UUID
UUID
VARBINARY
BINARY
ROW(...)
STRUCT(...)
All fields must have a name
ARRAY(e)
LIST(e)
MAP(k,v)
MAP(k,v)
## Partitioned tables#
Iceberg supports partitioning by specifying transforms over the table columns. A partition is created for each unique tuple value produced by the transforms. Identity transforms are simply the column name. Other transforms are:
Transform
Description
year(ts)
A partition is created for each year. The partition value is the integer difference in years between ts and January 1 1970.
month(ts)
A partition is created for each month of each year. The partition value is the integer difference in months between ts and January 1 1970.
day(ts)
A partition is created for each day of each year. The partition value is the integer difference in days between ts and January 1 1970.
hour(ts)
A partition is created hour of each day. The partition value is a timestamp with the minutes and seconds set to zero.
bucket(x, nbuckets)
The data is hashed into the specified number of buckets. The partition value is an integer hash of x, with a value between 0 and nbuckets - 1 inclusive.
truncate(s, nchars)
The partition value is the first nchars characters of s.
In this example, the table is partitioned by the month of order_date, a hash of account_number (with 10 buckets), and country:
CREATE TABLE iceberg.testdb.customer_orders (
order_id BIGINT,
order_date DATE,
account_number BIGINT,
customer VARCHAR,
country VARCHAR)
WITH (partitioning = ARRAY['month(order_date)', 'bucket(account_number, 10)', 'country'])
### Deletion by partition#
For partitioned tables, the Iceberg connector supports the deletion of entire partitions if the WHERE clause specifies filters only on the identity-transformed partitioning columns, that can match entire partitions. Given the table definition above, this SQL will delete all partitions for which country is US:
DELETE FROM iceberg.testdb.customer_orders
WHERE country = 'US'
Tables using either v1 or v2 of the Iceberg specification will perform a partition delete if the WHERE clause meets these conditions.
### Row level deletion#
Tables using v2 of the Iceberg specification support deletion of individual rows by writing position delete files.
## Rolling back to a previous snapshot#
Iceberg supports a “snapshot” model of data, where table snapshots are identified by an snapshot IDs.
The connector provides a system snapshots table for each Iceberg table. Snapshots are identified by BIGINT snapshot IDs. You can find the latest snapshot ID for table customer_orders by running the following command:
SELECT snapshot_id FROM iceberg.testdb."customer_orders$snapshots" ORDER BY committed_at DESC LIMIT 1 A SQL procedure system.rollback_to_snapshot allows the caller to roll back the state of the table to a previous snapshot id: CALL iceberg.system.rollback_to_snapshot('testdb', 'customer_orders', 8954597067493422955) ## Schema evolution# Iceberg and the Iceberg connector support schema evolution, with safe column add, drop, reorder and rename operations, including in nested structures. Table partitioning can also be changed and the connector can still query data created before the partitioning change. ## Migrating existing tables# The connector can read from or write to Hive tables that have been migrated to Iceberg. There is no Trino support for migrating Hive tables to Iceberg, so you need to either use the Iceberg API or Apache Spark. ## Iceberg table properties# Property Name Description format Optionally specifies the format of table data files; either PARQUET or ORC. Defaults to ORC. partitioning Optionally specifies table partitioning. If a table is partitioned by columns c1 and c2, the partitioning property would be partitioning = ARRAY['c1', 'c2'] location Optionally specifies the file system location URI for the table. format_version Optionally specifies the format version of the Iceberg specification to use for new tables; either 1 or 2. Defaults to 2. Version 2 is required for row level deletes. orc_bloom_filter_columns Comma separated list of columns to use for ORC bloom filter. It improves the performance of queries using Equality and IN predicates when reading ORC file. Requires ORC format. Defaults to []. orc_bloom_filter_fpp The ORC bloom filters false positive probability. Requires ORC format. Defaults to 0.05. The table definition below specifies format Parquet, partitioning by columns c1 and c2, and a file system location of /var/my_tables/test_table: CREATE TABLE test_table ( c1 integer, c2 date, c3 double) WITH ( format = 'PARQUET', partitioning = ARRAY['c1', 'c2'], location = '/var/my_tables/test_table') The table definition below specifies format ORC, bloom filter index by columns c1 and c2, fpp is 0.05, and a file system location of /var/my_tables/test_table: CREATE TABLE test_table ( c1 integer, c2 date, c3 double) WITH ( format = 'ORC', location = '/var/my_tables/test_table', orc_bloom_filter_columns = ARRAY['c1', 'c2'], orc_bloom_filter_fpp = 0.05) ## Metadata columns# In addition to the defined columns, the Iceberg connector automatically exposes path metadata as a hidden column in each table: • $path: Full file system path name of the file for this row
You can use this column in your SQL statements like any other column. This can be selected directly, or used in conditional statements. For example, you can inspect the file path for each record:
SELECT *, "$path" FROM iceberg.web.page_views; Retrieve all records that belong to a specific file using "$path" filter:
SELECT *
FROM iceberg.web.page_views
WHERE "$path" = '/usr/iceberg/table/web.page_views/data/file_01.parquet' ## Metadata tables# The connector exposes several metadata tables for each Iceberg table. These metadata tables contain information about the internal structure of the Iceberg table. You can query each metadata table by appending the metadata table name to the table name: SELECT * FROM "test_table$data"
The statement:
SELECT * FROM "test_table$data" is equivalent to: SELECT * FROM test_table ### $properties table#
The $properties table provides access to general information about Iceberg table configuration and any additional metadata key/value pairs that the table is tagged with. You can retrieve the properties of the current snapshot of the Iceberg table test_table by using the following query: SELECT * FROM "test_table$properties"
key | value |
-----------------------+----------+
write.format.default | PARQUET |
### $history table# The $history table provides a log of the metadata changes performed on the Iceberg table.
You can retrieve the changelog of the Iceberg table test_table by using the following query:
SELECT * FROM "test_table$history" made_current_at | snapshot_id | parent_id | is_current_ancestor ----------------------------------+----------------------+----------------------+-------------------- 2022-01-10 08:11:20 Europe/Vienna | 8667764846443717831 | <null> | true 2022-01-10 08:11:34 Europe/Vienna | 7860805980949777961 | 8667764846443717831 | true The output of the query has the following columns: History columns# Name Type Description made_current_at timestamp(3) with time zone The time when the snapshot became active snapshot_id bigint The identifier of the snapshot parent_id bigint The identifier of the parent snapshot is_current_ancestor boolean Whether or not this snapshot is an ancestor of the current snapshot ### $snapshots table#
The $snapshots table provides a detailed view of snapshots of the Iceberg table. A snapshot consists of one or more file manifests, and the complete table contents is represented by the union of all the data files in those manifests. You can retrieve the information about the snapshots of the Iceberg table test_table by using the following query: SELECT * FROM "test_table$snapshots"
committed_at | snapshot_id | parent_id | operation | manifest_list | summary
----------------------------------+----------------------+----------------------+--------------------+------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2022-01-10 08:11:20 Europe/Vienna | 8667764846443717831 | <null> | append | hdfs://hadoop-master:9000/user/hive/warehouse/test_table/metadata/snap-8667764846443717831-1-100cf97e-6d56-446e-8961-afdaded63bc4.avro | {changed-partition-count=0, total-equality-deletes=0, total-position-deletes=0, total-delete-files=0, total-files-size=0, total-records=0, total-data-files=0}
The output of the query has the following columns:
Snapshots columns#
Name
Type
Description
committed_at
timestamp(3) with time zone
The time when the snapshot became active
snapshot_id
bigint
The identifier for the snapshot
parent_id
bigint
The identifier for the parent snapshot
operation
varchar
The type of operation performed on the Iceberg table. The supported operation types in Iceberg are:
• append when new data is appended
• replace when files are removed and replaced without changing the data in the table
• overwrite when new data is added to overwrite existing data
• delete when data is deleted from the table and no new data is added
manifest_list
varchar
The list of avro manifest files containing the detailed information about the snapshot changes.
summary
map(varchar, varchar)
A summary of the changes made from the previous snapshot to the current snapshot
### $manifests table# The $manifests table provides a detailed overview of the manifests corresponding to the snapshots performed in the log of the Iceberg table.
You can retrieve the information about the manifests of the Iceberg table test_table by using the following query:
SELECT * FROM "test_table$manifests" path | length | partition_spec_id | added_snapshot_id | added_data_files_count | existing_data_files_count | deleted_data_files_count | partitions ----------------------------------------------------------------------------------------------------------------+-----------------+----------------------+-----------------------+--------------------------+-----------------------------+-----------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------- hdfs://hadoop-master:9000/user/hive/warehouse/test_table/metadata/faa19903-1455-4bb8-855a-61a1bbafbaa7-m0.avro | 6277 | 0 | 7860805980949777961 | 1 | 0 | 0 |{{contains_null=false, contains_nan= false, lower_bound=1, upper_bound=1},{contains_null=false, contains_nan= false, lower_bound=2021-01-12, upper_bound=2021-01-12}} The output of the query has the following columns: Manifests columns# Name Type Description path varchar The manifest file location length bigint The manifest file length partition_spec_id integer The identifier for the partition specification used to write the manifest file added_snapshot_id bigint The identifier of the snapshot during which this manifest entry has been added added_data_files_count integer The number of data files with status ADDED in the manifest file existing_data_files_count integer The number of data files with status EXISTING in the manifest file deleted_data_files_count integer The number of data files with status DELETED in the manifest file partitions array(row(contains_null boolean, contains_nan boolean, lower_bound varchar, upper_bound varchar)) Partition range metadata ### $partitions table#
The $partitions table provides a detailed overview of the partitions of the Iceberg table. You can retrieve the information about the partitions of the Iceberg table test_table by using the following query: SELECT * FROM "test_table$partitions"
partition | record_count | file_count | total_size | data
-----------------------+---------------+---------------+---------------+------------------------------------------------------
{c1=1, c2=2021-01-12} | 2 | 2 | 884 | {c3={min=1.0, max=2.0, null_count=0, nan_count=NULL}}
{c1=1, c2=2021-01-13} | 1 | 1 | 442 | {c3={min=1.0, max=1.0, null_count=0, nan_count=NULL}}
The output of the query has the following columns:
Partitions columns#
Name
Type
Description
partition
row(...)
A row which contains the mapping of the partition column name(s) to the partition column value(s)
record_count
bigint
The number of records in the partition
file_count
bigint
The number of files mapped in the partition
total_size
bigint
The size of all the files in the partition
data
row(... row (min ..., max ... , null_count bigint, nan_count bigint))
### $files table# The $files table provides a detailed overview of the data files in current snapshot of the Iceberg table.
To retrieve the information about the data files of the Iceberg table test_table use the following query:
SELECT * FROM "test_table\$files"
content | file_path | record_count | file_format | file_size_in_bytes | column_sizes | value_counts | null_value_counts | nan_value_counts | lower_bounds | upper_bounds | key_metadata | split_offsets | equality_ids
----------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+---------------+----------------------+----------------------+-------------------+--------------------+-------------------+-----------------------------+-----------------------------+----------------+----------------+---------------
0 | hdfs://hadoop-master:9000/user/hive/warehouse/test_table/data/c1=3/c2=2021-01-14/af9872b2-40f3-428f-9c87-186d2750d84e.parquet | 1 | PARQUET | 442 | {1=40, 2=40, 3=44} | {1=1, 2=1, 3=1} | {1=0, 2=0, 3=0} | <null> | {1=3, 2=2021-01-14, 3=1.3} | {1=3, 2=2021-01-14, 3=1.3} | <null> | <null> | <null>
The output of the query has the following columns:
Files columns#
Name
Type
Description
content
integer
Type of content stored in the file. The supported content types in Iceberg are:
• DATA(0)
• POSITION_DELETES(1)
• EQUALITY_DELETES(2)
file_path
varchar
The data file location
file_format
varchar
The format of the data file
record_count
bigint
The number of entries contained in the data file
file_size_in_bytes
bigint
The data file size
column_sizes
map(integer, bigint)
Mapping between the Iceberg column ID and its corresponding size in the file
value_counts
map(integer, bigint)
Mapping between the Iceberg column ID and its corresponding count of entries in the file
null_value_counts
map(integer, bigint)
Mapping between the Iceberg column ID and its corresponding count of NULL values in the file
nan_value_counts
map(integer, bigint)
Mapping between the Iceberg column ID and its corresponding count of non numerical values in the file
lower_bounds
map(integer, bigint)
Mapping between the Iceberg column ID and its corresponding lower bound in the file
upper_bounds
map(integer, bigint)
Mapping between the Iceberg column ID and its corresponding upper bound in the file
key_metadata
varbinary
Metadata about the encryption key used to encrypt this file, if applicable
split_offsets
array(bigint)
List of recommended split locations
equality_ids
array(integer)
The set of field IDs used for equality comparison in equality delete files
## Materialized views#
The Iceberg connector supports Materialized view management. In the underlying system each materialized view consists of a view definition and an Iceberg storage table. The storage table name is stored as a materialized view property. The data is stored in that storage table.
You can use the Iceberg table properties to control the created storage table and therefore the layout and performance. For example, you can use the following clause with CREATE MATERIALIZED VIEW to use the ORC format for the data files and partition the storage per day using the column _date:
WITH ( format = 'ORC', partitioning = ARRAY['event_date'] )
Updating the data in the materialized view with REFRESH MATERIALIZED VIEW deletes the data from the storage table, and inserts the data that is the result of executing the materialized view query into the existing table. Refreshing a materialized view also stores the snapshot-ids of all tables that are part of the materialized view’s query in the materialized view metadata. When the materialized view is queried, the snapshot-ids are used to check if the data in the storage table is up to date. If the data is outdated, the materialized view behaves like a normal view, and the data is queried directly from the base tables.
Warning
There is a small time window between the commit of the delete and insert, when the materialized view is empty. If the commit operation for the insert fails, the materialized view remains empty.
Dropping a materialized view with DROP MATERIALIZED VIEW removes the definition and the storage table. | 2022-06-30 06:35:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18442480266094208, "perplexity": 7678.131336546283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103669266.42/warc/CC-MAIN-20220630062154-20220630092154-00540.warc.gz"} |
https://cstheory.stackexchange.com/questions/12841/monotone-complexity-of-s-t-connectivity?noredirect=1 | # Monotone complexity of s-t connectivity
In the problem CONN, we obtain a directed $n$-vertex graph (encoded as a boolean string of $n^2$ bits, one for each potential edge), and want to decide whether there is a path between all $n^2$ pairs $(s,t)$ of vertices. In its special case, STCONN, the task is only for one fixed pair $(s,t)$ of vertices. I am interested in the size of monotone circuits with fanin-2 AND and OR gates solving STCONN.
QUESTION: Does STCONN require monotone boolean circuits of size $\Omega(n^3)$?
What I know is:
• STCONN, and even CONN, can be solved by monotone circuits of size $O(n^3)$: use well known dynamic programming algorithms of Bellman-Ford for STCONN, and by Floyd-Warshall for CONN.
• Every monotone circuit for STCONN has depth $\Omega(\log^2 n)$: Karchmer-Wigderson (1990), Grigni-Sipser (1995). By binary search, this depth is also enough.
• Every monotone circuit for CONN has size $\Omega(n^3)$: CONN has almost the same monotone complexity as boolean multiplication of two boolean matrices, and this latter problem is shown, by Paterson (1975) and by Mehlhorn-Galil (1976), to require $\Omega(n^3)$ gates.
But what about the size of monotone circuits for STCONN? Is this still an open problem? I guess - it is, but would be happy to hear the opposite.
ADDED (on 9.10.2012) My question is related to the question about the status of tropical circuit complexity of "weighted" STCONN (the shortest $s$-$t$ path problem); see my answer; a tropical circuit is a circuit with fanin-2 Min and Plus gates. Suppose we have a 0/1 optimization problem $f(x)=\min_{S\in{\cal F}}\sum_{i\in S}x_i$, where ${\cal F}$ is a family of feasible solutions, and $x_i$'s are real numbers. A "boolean version" of this problem is a monotone boolean function $f_B(x)=\bigvee_{S\in{\cal F}}\bigwedge_{i\in S}x_i$. In the case of the shortest $s$-$t$ path problem, $f_B$ is STCONN.
If the domain of $f(x)$ contains $0$ and $\infty$, then the minimum size of a tropical circuit for $f(x)$ is at least the minimum size of a monotone boolean circuit for $f_B(x)$. This holds because the mapping $h:\{0,\infty\}\to\{0,1\}$ given by $h(0):=1$ and $h(\infty):=0$ is a homomorphish from the semiring $(\{o,\infty\},\min,+)$ to the boolean semiring. But lower bounds for tropical circuits could come easier than for monotone boolean circuits: the domain now is huge (real numbers), and Min does not distribute over Plus. Hence, an easier'' question:
Does the shortest $s$-$t$ paths problem requires tropical circuits of size $\Omega(n^3)$?
Another model weaker than monotone boolean circuits and tropical circuits is that of monotone arithmetic circuits: here no produced monomials can be cancelled later. We can associate with the weighted STCONN a multilinear polynomial $P(x)$ by taking one monomial for each simple $s$-$t$ path. Hence, yet simpler'' question:
Does $P(x)$ require monotone arithmetic circuits of size $\Omega(n^3)$?
ADDED (23.01.2013): The list of known results above is not complete: Aaron Potechin has also shown that directed STCONN requires monotone switching networks of size $n^{\Omega(\log n)}$. Each such network is an undirected graphs with two distinguished source and target nodes, an with edges labeled by variables. When input vector arrives, all edges evaluated to $0$ are removed, and the vector is accepted iff there is a source-target path in the remaining subgraph. In contrast, is we would allow a network be directed then even directed STCONN can be solved (using similar construction as here) by a monotone network of size $O(n^4)$, even by an acyclic network. This is the largest known gap between monotone directed and undirected networks!
CORRECTION (on 21.05.2014): I was wrong with item 3 above: the lower bound $\Omega(n^3)$ for CONN is also not known! The bound on matrix product only gives such a lower bound for APCONN (all-pairs connectivity): this is a set of $n^2$ boolean functions $f_{ij}$ outputing $1$ iff there is a path between nodes $i$ and $j$. The (single-output) function CONN is the AND of all $f_{ij}$. Note that circuits computing CONN need not to compute APCONN: the circuit for CONNN needs not to compute the functions $f_{ij}$ on separate output gates.
ADDON (on 21.05.2014): Lower bounds on the monotone depth of CONN are also known: by improving an earlier bound $\Omega(n^{3/2}n/\ln\ln n)$ of Yao (1994), Goldman and Hastad (1998) proved an almost optimal bound of $\Omega(\ln^2/\ln\ln n)$. Interestingly, these bounds were proved not by using the Karchmer-Wigderson games (as it was for STCONN) but rather a form of Razboro's approximation method.
ANSWER (on 21.05.2014): My 3-rd (yet simpler'') question indeed has a simple answer: monotone arithmetic circuits for the STCONN polynomial $P(x)$ require even exponential size. This holds because: (1) every such circuit must also compute the Hamilton s-t path polynomial HP (monomials are s-t path containing all nodes), and (2) HP requires monotone arithmetic circuits of exponential size (a simple covering-by-rectangles argument since nothing can be cancelled in such circuits).
• maybe this is obvious to those working in this area but deserves mention.. the problem would seem to have close connections to $L$, for the undirected case which is called USTCONN and recently shown to be in $L$ in 2004 by Reingold....& from memory there is a close $L$-complete problem (is it USTCONN?) – vzn Oct 8 '12 at 18:54
• @vzn: good point! I've should had have mentioned this nice result. But it doesn't help us further. We seek for lower bounds. In a weaker (apparently) model than $L$. Directed or not -- this doesn't matter (as much). Is it easier to have an answer for one pair of vertices as for all $n^2$ vertices -- this is the question. – Stasys Oct 8 '12 at 19:26
• hi SJ recently ran across this new ref that seems related, what do you think? Computing All-Pairs Shortest Paths by Leveraging Low Treewidth Planken et al.. does it suggest maybe that the worst case graphs have high treewidth? – vzn Feb 19 '14 at 3:39 | 2019-12-08 08:21:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8647145628929138, "perplexity": 900.6787776247565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540507109.28/warc/CC-MAIN-20191208072107-20191208100107-00062.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-3-introduction-to-graphing-mid-chapter-review-mixed-review-page-202/11 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
RECALL: The graph of an equation in the form $x=h$ is a vertical line whose x-intercept is $(h, k)$ and is parallel to the y-axis. All points of the line have an x-coordinate of $h$. Thus, the graph of the equation $x=1$ is a vertical line whose x-intercept is $(1, 0)$. All points on the line have an x-coordinate of $1$. This means that points $(1, -2)$, $(1, 0)$, and $(1, 2)$ are all on the line $x=1$. Plot these three points then connect them using a line. (refer to the attached image in the answer part above for the graph) | 2018-07-17 19:54:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.595486044883728, "perplexity": 169.29436038822524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589892.87/warc/CC-MAIN-20180717183929-20180717203929-00211.warc.gz"} |
https://zenodo.org/record/1260073/export/dcite4 | Journal article Open Access
# Evaluation of Methyl Tert-Butyl Ether (Mtbe) as an Interference on Commercial Breath-Alcohol Analyzers
Buckley, Timothy J.; Pleil, Joachim D.; Bowyer, James R.; Davis, J. Michael
### DataCite XML Export
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<identifier identifierType="URL">https://zenodo.org/record/1260073</identifier>
<creators>
<creator>
<creatorName>Buckley, Timothy J.</creatorName>
<givenName>Timothy J.</givenName>
<familyName>Buckley</familyName>
</creator>
<creator>
<creatorName>Pleil, Joachim D.</creatorName>
<givenName>Joachim D.</givenName>
<familyName>Pleil</familyName>
</creator>
<creator>
<creatorName>Bowyer, James R.</creatorName>
<givenName>James R.</givenName>
<familyName>Bowyer</familyName>
</creator>
<creator>
<creatorName>Davis, J. Michael</creatorName>
<givenName>J. Michael</givenName>
<familyName>Davis</familyName>
</creator>
</creators>
<titles>
<title>Evaluation of Methyl Tert-Butyl Ether (Mtbe) as an Interference on Commercial Breath-Alcohol Analyzers</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2001</publicationYear>
<dates>
<date dateType="Issued">2001-12-01</date>
</dates>
<resourceType resourceTypeGeneral="Text">Journal article</resourceType>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/1260073</alternateIdentifier>
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<relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1016/s0379-0738(01)00534-5</relatedIdentifier>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="https://creativecommons.org/publicdomain/zero/1.0/legalcode">Creative Commons Zero v1.0 Universal</rights>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract">Anecdotal reports suggest that high environmental or occupational exposures to the fuel oxygenate methyl tert-butyl ether (MTBE) may result in breath concentrations that are sufficiently elevated to cause a false positive on commercial breath-alcohol analyzers. We evaluated this possibility in vitro by establishing a response curve for simulated breath containing MTBE in ethanol. Two types of breath-alcohol analyzers were evaluated. One analyzer's principle of operation involves in situ wet chemistry (oxidation of ethanol in a potassium dichromate solution) and absorption of visible light. The second instrument uses a combination of infrared absorption and an electrochemical sensor. Both types of instruments are currently used, although the former method represents older technology while the latter method represents newer technology. The percent blood alcohol response curve was evaluated over a breath concentration range thought to be relevant to high-level environmental or occupational exposure (0-361 ug/L). Results indicate that MTBE positively biases the response of the older technology BreathanalyzerTM when evaluated as a single constituent or in combination with ethanol. We conclude that a false positive is possible on this instrument if the MTBE exposure is very high, recent with respect to testing, and occurs in combination with ethanol consumption. The interference can be identified on the older technology instrument by a time dependent post-reading increase in the instrument response that does not occur for ethanol alone. In contrast, the newer technology instrument using infrared and electrochemical detectors did not respond to MTBE at lower levels (0-36 g/K), and at higher levels (&gt;72 g/L) the instrument indicated an "interference" or "error". For this instrument, a false positive does not occur even at high MTBE levels in the presence of ethanol. This paper has been reviewed in accordance with the US Environmental Protection Agency's peer and administrative review policies and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.</description>
</descriptions>
</resource>
54
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views | 2021-05-06 21:54:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3139781057834625, "perplexity": 10985.467214812008}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00298.warc.gz"} |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/dissertationes-mathematicae/online/113076/complexities-and-representations-of-mathcal-f-borel-spaces | # Wydawnictwa / Czasopisma IMPAN / Dissertationes Mathematicae / Artykuły Online First
## Dissertationes Mathematicae
Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).
## Complexities and representations of $\mathcal F$-Borel spaces
### Tom 540 / 2019
Dissertationes Mathematicae 540 (2019), 1-69 MSC: Primary 54H05; Secondary 54G20. DOI: 10.4064/dm794-2-2019 Opublikowany online: 27 June 2019
#### Streszczenie
We investigate the $\mathcal F$-Borel complexity of topological spaces in their different compactifications. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications. We also develop a theory of representations of $\mathcal F$-Borel sets, and show how to apply this theory to prove that the complexity of hereditarily Lindelöf spaces is absolute (that is, the same in every compactification). We use these representations to characterize the complexities attainable by a specific class of topological spaces. This provides an alternative proof of the first result, and implies the existence of a space with non-absolute additive complexity. We discuss the method used by Talagrand to construct the first example of a space with non-absolute complexity, hopefully providing an explanation which is more accessible than the original one. We also discuss the relation between complexity and local complexity, and show how to construct amalgamation-like compactifications.
#### Autorzy
• Vojtěch KovaříkCharles University
Faculty of Mathematics and Physics
Department of Mathematical Analysis
Sokolovská 83
Praha 8, 186 00, Czech Republic
and
Czech Technical University in Prague
Faculty of Electrical Engineering
Department of Computer Science
Karlovo náměstí 13
Praha 2, Czech Republic
e-mail
## Przeszukaj wydawnictwa IMPAN
Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.
Odśwież obrazek | 2019-12-09 08:38:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5140665769577026, "perplexity": 12836.87272152659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540518337.65/warc/CC-MAIN-20191209065626-20191209093626-00468.warc.gz"} |
http://tex.stackexchange.com/questions/50783/section-should-automatically-start-new-page-if-the-whole-section-does-not-fit-on/51455 | Section should automatically start new page if the whole section does not fit on current page
I would like my sections to start on a new page if they do not fit on the current page. In other words: if a section fits on the current page print it, if it does not fit start printing it on the next page.
I would like this to be done automatically.
\usepackage{titlesec} seems to be the solution, but I can not get it to do the job.
• Should it be done with titlesec? how ?
• Is there a better approach?
-
this question is very similar but does not give automatic solutions – danjjl Apr 4 '12 at 21:27
The whole section? – egreg Apr 4 '12 at 21:28
Not sure I understand the question right, but yes (my sections are quite short (longest are 3 pages long)) – danjjl Apr 4 '12 at 21:29
So your question is very unclear: three pages can't fit on a page, can they? – egreg Apr 4 '12 at 21:31
Do you mean: If the next section can fit on the current page, just print it as-is. Otherwise, put in a page break and start the section on the new page. ? – Mike Renfro Apr 4 '12 at 22:13
There is a simple solution that does require only a single pass ...
\documentclass{article}
\newcommand\mysection{\vfil\penalty-9999\vfilneg\section}
\usepackage{lipsum}
\begin{document}
\mysection{A} \lipsum[3]
\mysection{B} \lipsum[1-2]
\mysection{C} \lipsum[5]
\end{document}
-
1. Set \labels at the start and end of the section and check if they are on the same page. You'll need multiple runs and you have to mark the end of sections.
I am not very familiar with Latex macros. How would I check if both \labels are on the same page and insert a \newpage at the first label if they are not? don't hesitate sending me to some documentation – danjjl Apr 10 '12 at 20:33 | 2014-03-17 16:01:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7381575703620911, "perplexity": 1163.186224422672}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678705763/warc/CC-MAIN-20140313024505-00029-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://www.ccp14.ac.uk/ccp/web-mirrors/ill-hewat/dif/ccsl/appenx/libsec_i.html | ## FUNCTION IATOM(ANAME)
### Arguments:
On entry ANAME is an A4 CHARACTER atom name, left justified
On exit IATOM=0 if this is not a name in the existing list, or
=a positive integer, being the number of the atom whose name this is, if found.
### Prerequisite calls:
The list must be set up in array ATNAME in /ATNAM by, e.g. ATOPOS
NCFIND
### Common blocks used:
/ATNAM/ to use ATNAME
/POSNS/ to use NATOM
### Classification:
Tests . . . . . . . Utility
## SUBROUTINE ICDFMT(INC,ITEMS)
### Arguments:
Returns ICD=0 for integer and 1 for non-integer indices, and the number of items stored per reflection in ITEMS.
### Calls:
FINDCD JFIX MESS ONCARD PROPER RDNUMS
### Called by:
ABSMSF AVEXAR EXTCAL INCMSF SORGAM
### Common blocks used:
/IOUNIT/ to use LPT
/SATELL/ to use PROP IPROP
/VARFOR/ to use all members
### Classification:
Data Collection and Reduction . . . . . . . Setting Up
## SUBROUTINE IICD1
### Description:
Deals with defaults, recognises words on I cards , reads values after them, and prints out the information.
Vocabulary recognised:
NCYC <number of cycles of refinement wanted> : default 3
CYC1 <number to be given to first cycle> : default 1
PRIN <request for general printing on the LPT file>
followed by an integer giving the frequency of printing:
0= never 1=first cycle 2=last cycle 3= first and last cycles 4= every cycle
MCOR <maximum correlation>
or 0 for "print whole matrix" or -ve number for "print nothing"
PRDM <integer> ; a non-zero integer requests Deposited Material printing in the same cycle that a new crystal data file is output.
CONV <real> to stop LSQ cycling if max (shift/esd) < CONV : default 0.01
### Calls:
DEPRIN JFIX MESS ONCARD
STLSFW STLSSF
### Common blocks used:
/IOUNIT/ to use LPT
/REFINE/ to use NCYC NCYC1 LASTCY IPRNT MAXCOR SIMUL CONV
### Classification:
General Least Squares Refinement . . . . . . . Setting Up
## SUBROUTINE IICD3
### Description:
Sets up the array IFOR in /ARRDAT/ to hold input switches as may be read from I card :
IFOR(1) gives the input format; see ARREAD for the various
possibilities.
IFOR(2) is -ve for 'do not print unique reflections', +ve for 'print
all reflections'. This does not affect the filed output.
IFOR(3) is 0 for 'do not output record numbers to file' or 1 for
'output record numbers both to file and printer'.
IFOR(4) gives the weighting scheme requested:
IFOR(4) = 0 - unit weights for individual measurements, and
mean of equivalents weighted according to their esds.
IFOR(4) = 1 - statistical weights used for the means of individual
measurements, and esds used in weighting for mean of equivalents.
IFOR(4) = 2 - unit weights throughout.
IFOR(5) = whether or not a rejection list is to be given, 0 or 1.
IFOR(6) >= 1 if angles are to be read and stored
### Input:
Reads an I card if necessary.
### Output:
Writes its findings on unit LPT.
### Calls:
ERRMES JFIX MESS ONCARD
### Called by:
ARRINC ARRNGE INCMSF
### Common blocks used:
/IOUNIT/ to use LPT
### Classification:
Data Collection and Reduction . . . . . . . Setting Up
## SUBROUTINE INBOX(H,IN)
### Arguments:
On entry H holds h,k,l
On exit IN = -1 if outside asymmetric unit
0 if inside it
= number of plane if on a plane = 10+number of edge if on an edge
### Prerequisite calls:
SYMOP must have read the space group
SYMUNI must have set up the asymmetric unit
### Notes:
Assumes that NASYM (number of planes bounding the asymmetric unit) is not greater than 3
### Called by:
INVENT MULBOX POLUNI TRYUNI
### Common blocks used:
/FUNIT/ to use NASYM ASYM
### Classification:
Manipulation of Reflection Indices . . . . . . . Crystallographic
## SUBROUTINE INCELL(X,P)
### Arguments:
On entry X is a 1x3 array which holds fractional coordinates of a point in
a unit cell (not necessarily in the "central" cell)
On exit P is a 1x3 array which holds the fractional coordinates of an
equivalent point all in range 0=< x < 1
FRAC3 GMEQ
### Classification:
Crystal Geometry . . . . . . . Crystallographic
## SUBROUTINE INCREM(IFNS,IFNL)
### Arguments:
On entry IFNS is an A10 short file name
IFNL is a full file name expected to contain IFNS
On exit both file names have been incremented; that is, the character
before the . has been advanced by 1, counting 1-9, A-Z
LENG UPONE
NCHECK GENREF
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## SUBROUTINE INDFIX(H,K)
### Arguments:
On entry H is a 1x3 real vector
On exit K is a 1x3 integer vector containing the numbers in H, rounded.
JFIX
### Called by:
ABSCOR ARPRIN INPUAR INPUTD INPUTU INTIND PRNTMP RDDATA SYMEQU ICDINC ARRNGE PATHS CALMSF CALQSF GENREF GETMSF GETSFZ INCMSF ICDINC MAG3D MAGPOW MG3DGL MVENTR PALSQ POWDER SORGAM
### Classification:
Manipulation of Reflection Indices . . . . . . . Utility
## SUBROUTINE INDFLO(H,K)
### Arguments:
On entry K is a 1x3 integer vector
On exit H is a 1x3 real vector containing the elements of K floated.
### Called by:
ARREAD FOUR1D FOUR1Z FOURGP INOBGR INTIND RREFSF ADDFC ICDINC EXTCAL ICDINC MAG3D MG3DGL MVENTR SFTLSQ
### Classification:
Manipulation of Reflection Indices . . . . . . . Utility
## SUBROUTINE INITIL(PROGRM)
### Arguments:
On entry PROGRM holds A6 name of calling program
### Description:
INITIL is obeyed at the start of a job, either by an explicit call or (more usually) from a call of PREFIN.
It sets up various default start conditions, some of which are machine dependent. The user may wish to override some of these later.
The symbols permitted on input are copied into /CHARS; this will one day be done in a BLOCK DATA statement.
The system is set up to be not BATCH, already ini tialised.
The MAIN program name is kept; the hardware (RVAX, DIVA etc) is kept; the wordlength is set; the filenames are cleared; the file unit numbers are initialised.
For DIVA, unit LPT is opened automatically to <Program name>.LIS
For other systems, the name for unit LPT is requested, and it is then opened
The constants pi, log2 etc are put into /CONSTA
### Output:
The banner headline is put out on LPT
### Calls:
LENGT OPNFIL UPONE
### Common blocks used:
/CARDRC/ to use ICRYDA
/CHARS/ to use all members
/CONSTA/ to use all members
/FINAME/ to use all members
/GLOBAL/ to use NINIT NSYSTM MULFAS MULSOU MULONE
/IOUNIT/ to use LPT ITI ITO IPLO LUNI
/LENINT/ to use all members
/LOONEY/ to use all members
/MAPGT/ to use IDUMPG
/MAPRD/ to use IDUMPR
/MAPSV/ to use NDUMPS
/NEWOLD/ to use NEWIN LKH
/PHASE/ to use NPHASE IPHASE JPHASE KPHASE
/PRSTAT/ to use IOP1 IOP2
/SCRACH/ to use all members
/SOURCE/ to use NSOURC JSOURC KSOURC
/WHEN/ to use all members
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## SUBROUTINE INOBGR(ISCR)
### Arguments:
On entry ISCR is the number of a unit set up as a scratch file.
### Description:
Accepts user's input on unit LUNI, collects together groups of h,k,l and counts them, forms multiplicity and D, and sends out this information on unit ISCR ready for repeated reinput to the cycling LSQ.
Expects each observation to be preceded by sets of relevant h,k,l. Reads until an OBS containing a decimal point, then takes remainder of that line to be the observation, allowing various "MODER" formats, as in SFLSQ.
### Calls:
ASUNIT ERRCHK INDFLO NOPFIL OPNFIL RDINTG RDREAL VCTMOD
### Common blocks used:
/IOUNIT/ to use LUNI
/SCRACH/ to use MESSAG
### Classification:
Specific Least Squares Refinement . . . . . . . Setting Up
## SUBROUTINE INPLSF
### Description:
Is not concerned with L FIX, LRELA, L VARY, L SLAK, L ATOM, L BOND cards, so ignores them.
Otherwise, records information off the following L cards :
TFAC An overall temperature factor
SCAL Scale factors, one per zone
REFI Function 'on which to refine'
MODE Mode of presentation of input reflection data
All MODE dependent code in RREFSF (C134)
WGHT Weighting scheme.
### Output:
Writes its findings to unit LPT.
### Notes:
For Profile LSQ the equivalent routine is INPLPR.
### Calls:
CARDIN ERRIN2 JGMZER LLSCAL LLTFAC MESS NCFIND RDINTG RDWORD RREFSF
STLSSF
### Common blocks used:
/CARDRC/ to use NYZ
/IOUNIT/ to use LPT ITO
/REFINE/ to use IREF MODEOB
/SCLDAT/ to use NSCALE
/SLAKDA/ to use NSLAK NSKTOT
/SLKGEO/ to use NUMBON
### Classification:
Specific Least Squares Refinement . . . . . . . Setting Up
## FUNCTION INPUAR(M,LUN)
### Arguments:
On entry M is 1 or 2 indicating the unit from which to read
LUN is a 1x2 integer array holding the logical unit numbers
of two data streams
On exit INPUAR indicates whether end of either file has been reached
### Description:
The call reads one set of equivalent reflections into the COMMON /REFS/ from the file on UNIT number LUN(M)
GMEQ INDFIX
### Called by:
ABSMSF AVEXAR INCMSF SORGAM
### Common blocks used:
/REFS/ to use JJ LL SCALE II NR FF ITEMS
/VARFOR/ to use all members
### Classification:
Data Collection and Reduction . . . . . . . Utility
## SUBROUTINE INPUTA(ID,LABA,LBALEN,LABS,LBSLEN,X,T,S,IER)
### Arguments:
On entry ID points to the card on unit IO10. If ID=0 it is assumed
that the card is already in ICARD in /SCRACH
On exit LABA is the A4 label of the atom, starting with a letter
LBALEN is the number of characters in LABA
LABS is the A4 label of the scattering factor expected
LBSLEN is the number of characters in LABS
X(1:3) holds EITHER the x,y,z fractional coordinates of the atom
OR (if the card starts "C SD") their standard
deviations.
T similarly holds EITHER the isotropic temperature factor
OR (if the card starts "C SD") its esd
S similarly holds EITHER the site occupation factor
OR (if the card starts "C SD") its esd
IER=number of errors detected
### Description:
Items must occur in the sequence "C" optional "SD" <label> x,y,z itf, optional DIFFERENT scattering factor label, optional site occupation factor.
If the site is left blank, S=1. is assumed.
### Calls:
CARDIN ERRCH2 LETTER RDREAL RDWORD
ATOPOS F2NEW
### Classification:
Structure Factor Calculations . . . . . . . Setting Up
## SUBROUTINE INPUTC(ID,CELL)
### Arguments:
On entry ID points to the card on file IO10
On exit if there is no "SD" following the "C " CELL(1:6) holds a,b,c, alpha degrees, beta degrees, gamma degrees.
If "SD" is present CELL is not filled in and the data on the card remain in ICARD for further processing by RECISD
### Calls:
CARDIN ERRCH2 GMZER RDREAL
RECIP
### Classification:
Basic Crystallography . . . . . . . Setting Up
## SUBROUTINE INPUTD
### Description:
Absorbs all the D cards given. It will normally be called by a setting up routine (e.g. SETDC) which then checks whether it has had enough D cards to make sense, and gives default values for those missing.
The syntax of D cards is thus like that of M, G, L cards; a word of up to 4 symbols (usually letters, and the first must be a letter) follows the "D space" which starts the card, and what follows after that depends on the word. Possible words recognised are:
D GEOM followed by an integer, IGEOM.
Possible values for IGEOM are:
1 = normal beam 2 = normal beam equatorial 3 = equi-inclination Weissenberg 4 = precession (no further code for this) 5 = anti equi-inclination Weissenberg 6 = 4 circle diffractometer, bisecting geometry 7 = 4 circle diffractometer, angles given 8 = normal beam, general orientation 10 = powder data, X-rays 11 = 4 circle diffractometer, high chi geometry 12 = SXD geometry
D WVLN followed by the wavelength, in same units as the lattice constants
(possibly several wavelength values)
D L/R followed by an integer, the 'left or right' indicator:
+ve means incident beam diffracted to the right, -ve means to the left. Value 1 means that angles are measured clockwise about positive diffractometer axes, and 2 means anti-clockwise.
D TH2M followed by the value of 2theta monochromator, in degrees.
D UMAT followed by 9 numbers, giving the UB matrix (as defined in the
Manual under D cards ). If all 9 do not fit one card, several cards may be given; for example, on 3 cards each with 3 numbers.
D ANGP followed by the precession angle in degrees.
D ROTA for types 1-5, followed by 3 indices, being the zone-axis symbols
of the zone parallel to the rotation axis.
D CHIA for type 2 only, followed by 3 integers and a real; the integers
give another axis, perpendicular to that on the "D ROT A" card , and the real is the angle between this and the normal to the chi circle, in degrees.
Optional D LAM2 followed by the \$\lambda/2\$ contamination as the fraction
\$I(\lambda)/I(\lambda\over2)\$
### Output:
Writes its findings to unit LPT
### Calls:
CARDIN ERRCH2 ERRIN2 ERRMES GMEQ INDFIX JGMZER MESS NCFIND RADIAN RDINTG RDNUMS RDREAL RDWORD
SETDC
### Common blocks used:
/CARDRC/ to use NYZ
/DGEOM/ to use IGEOM UM NLR ANGLIN ALAMBD NLAMB ALAM2
/IOUNIT/ to use LPT
### Classification:
Data Collection and Reduction . . . . . . . Setting Up
## SUBROUTINE INPUTE
### Description:
The card gives IEXTYP, an integer giving the extinction model to be used:
IEXTYP = 1 Becker and Coppens Lorentzian model, 1 DOMR
IEXTYP = 2 Becker and Coppens Gaussian model, 1 DOMR
IEXTYP = 3 Becker and Coppens Lorentzian model, 3 DOMRs, FOVLP
IEXTYP = 4 Becker and Coppens Gaussian model, 1 DOMRs, FOVLP
Sets LOGICALs LOREN and GAUSS.
After IEXTYP come the parameters of the model. In the present options 1,2 these are DOMR ("r" in the theory) and MOSC ("g" in the theory), the domain radius and mosaic spread parameters.
For options 3,4 reads 3 values for DOMR, then MOSC and FOVLP, in the case where coherence between nuclear and magnetic scattering must be taken into account.
### Output:
Writes its findings on unit LPT.
### Calls:
CARDIN ERRIN2 ERRMES GMEQ GMZER MESS RDINTG RDNUMS RDREAL
EXTINC
### Common blocks used:
/EXTN/ to use IEXTYP AMOSC LOREN GAUSS
/EXTRAE/ to use FOVLP
/IOUNIT/ to use LPT
### Classification:
Data Collection and Reduction . . . . . . . Setting Up
## SUBROUTINE INPUTF(ID,LABF,LBFLEN,NTYP,IPT,IER)
### Arguments:
On entry ID points in the binary copy of the Crystal Data File to the required "F" card , or iz 0, indicating that the card must be read here.
On exit:
LABF, A4, contains a scattering factor label
LBFLEN is the number of actual characters in LABF
NTYP is an integer giving the type of factor expected
IPT points in the card in /SCRACH/ to the next data item
IER is an error indicator, =0 if no errors.
### Calls:
CARDIN ERRCH2 LETTER RDINTG RDWORD
F2NEW SETFOR
### Classification:
Structure Factor Calculations . . . . . . . Setting Up
## SUBROUTINE INPUTG
### Description:
Absorbs all the "G" cards given. It will normally be called by a setting up routine (e.g. SETABS) which then checks whether it has had enough "G" cards to make sense, and gives default values for any missing.
The syntax of "G" cards is thus like that of M, D, L cards; a word of up to 4 symbols (usually letters, and the first must be a letter) follows the "G space" which starts the card, and what follows after that depends on the word. Possible words recognised are:
G FACE followed by an integer and other numbers: a specification of a plane
face of the crystal, according to the integer. (1 means read A,B,C,D in the equation AX+BY+CZ>=D)
G PNTS followed by 3 integers which are the number of Gauss points required
for integration in the x, y, and z directions. These may be any integer in the range 1-20,32,40 (the list is being extended.)
The MAIN program may wish to alter these during a run. This would involve resetting NL,NM and NN in COMMON /GAUSS/, and obeying
SETGAU again.
If no G PNTS card is given, 5 points will be taken in all 3 directions
G MU followed by the coefficient of absorption. Its units must tie up with
A,B,C,D above. (This card is not essential; if the MAIN program calls for different values of mu, these are simply written to AMU in the COMMON /ABSDAT/)
G MODE followed by an integer which gives mode of use of ABSOR or ABMULT,
i.e. which integral(s) are to be calculated.
### Input:
Reads in all "G" cards .
### Output:
Writes its findings to unit LPT.
### Calls:
CARDIN ERRCH2 ERRCHK ERRMES JGMZER MESS NCFIND RDINTG RDREAL RDWORD
### Called by:
SETABS SETGAU SETPOL
### Common blocks used:
/ABSDAT/ to use all members
/CARDRC/ to use NYZ IERR
/CPLANE/ to use all members
/GAUSS/ to use NL NM NN
/IOUNIT/ to use LPT
### Classification:
Data Collection and Reduction . . . . . . . Setting Up
## SUBROUTINE INPUTI
### Description:
Absorbs into COMMON /IINFO/ sets of information from all I cards .
Sets IIN=number of items found on all cards.
To be read by INPUTI, the I card must be of the form:
I WORD1 NUM1 WORD2 NUM2 WORD3 NUM3 etc
(so if the user wants some other form he must read the card himself).
The "NUMS" may be reals or integers. They will be read to reals, but may be fixed later according to their "WORDS".
It does not matter what the vocabulary of words is. INPUTI can read any set of instructions in this format, and is expected to be called for least squares application, for ARRNGE and for an increasing number of
MAIN programs requiring to be driven this way.
An example of an I card for SFLSQ (structure factor least squares) is:
I NCYC 6 CYC1 1 PRIN 2 MCOR 55
for which INPUTI simply produces 4 sets of (WORD, REAL) in COMMON, and it is up to its calling routine (in this case STLSSF) to interpret these to mean 6 cycles, first one numbered 1, print structure factor listing at last cycle and correlations of over 55 per cent.
### Calls:
CARDIN ERRMES RDREAL RDWORD
### Called by:
ONCARD STLSFW STLSSF ABSMSF ARRINC ARRNGE AVEXAR EXTCAL INCMSF SORGAM
### Common blocks used:
/CARDRC/ to use NYZ
/IINFO/ to use all members
/IINFOW/ to use all members
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## SUBROUTINE INPUTJ(ID,NTYP,IAT,IPT,IER)
### Arguments:
On entry ID is the position in the CDF of the J card , or 0 (= card present)
On exit NTYP = a number indicating what kind of J card was read:
NTYP=1 for MPOL ( l,m and amplitudes of its + and - combinations)
NTYP=2 for FORM names of <jL> form factors with L values
On exit IAT = number corresponding to the atom or form factor la bel,
On exit IPT = the next column on the card to be interpreted.
On exit IER = the error indicator, = 0 for no error.
### Calls:
CARDIN ERRCH2 IATOM ISCAT NCFIND RDWORD
MPFORM PFSET
### Classification:
Multipole Form Factors . . . . . . . Setting Up
## SUBROUTINE INPUTM
### Description:
Takes the information from "M" cards into the map or contouring COMMON, usually as a prelude to a Fourier calculation "M" cards have a significant word in columns 3,4,5,6. Possible words are:
M NDIM Number of dimensions for Fourier, 2 (projection), 3 (3D)
or 4 (bounded section).
M FTYP Fourier type (see below).
M MESH Output mesh - 6 numbers, being:
X(START) X(END) X(STEP), and the same in Y
M AXES Matrix of 9 integers turning the Fourier to a different
orientation, or 9 reals asking for a plane section.
M PRIN By itself means "print calculated map". Followed by a
list of Z values, means "print only at these selected
Z values". If absent, the default is not to print anything, so if there are no "M PRIN", "M PLOT" or "M SAV E" cards the run will not tell the user much.
M PLOT Present if plotting required - also gives values of Z at which
plotting is required if NDIM=3, on several cards if necessary.
M CM/A If plotting, number of centimetres of plotter paper per
Angstrom.
M CONT If plotting, list of required contour values (may be several
cards, all starting M CONT)
M SAVE Save the calculated map(s) on a named file in such a way that
a subsequent run with an "M GE T" card will retrieve it/them with a view to drawing another contour map. Details in the specification of SUBROUTINE FORIER.
M GET Do not calculate a map at all - read an already calculated map
from unit IDUMPG, and interpret only those cards which make sense - e.g. the user may alter contours, scale of map in cms/Angstrom, etc, but he may not alter cell dimensions, space group, theta maximum etc.
M DTYP data input type
M DELT delta for resolution function
M SCAL scale to multiply Fourier coefficients
M SMAX sin theta/lambda maximun for this particular run
M READ do not calculate map - take the crystal data cards on trust,
and read from a binary file some pre-calculated map.
M MAXE Options for maximum entropy calculation MSTOP: stopping
criterion, MODEL: type of default model, and if MODEL=0 or 2
DEFVAL: the value for the constant density.
M GRID Grid for Maximum entropy calculation, 6 (2D) or 9(3D) numbers,
being: X(START) X(END) X(STEP), and the same in Y and (Z)
M AXME Axes of Maximum entropy calculation
M LABL Symbols to mark atomic positions
each has <atom name> <symbol> <color> <type>
### Output:
Writes its findings on unit LPT.
### Calls:
CARDIN ERRCH2 ERRIN2 ERRMES IATOM LCOLPG LERCHK LSYMPG MESS NCFIND PRILIS RDINTG RDNUMS RDREAL RDWORD
SETFOU
### Common blocks used:
/CARDRC/ to use NYZ IERR
/CONTUR/ to use ZPLVAL IZPL CONT NCONT
/IOUNIT/ to use LPT
/MAPLAB/ to use NLABS SYSIZE LABAT LSYMB LCOLOR
/MAPDA/ to use OUTLIM NDIM MODEF SCALF1 DELTA MODED SMAX MODET
/MAPGT/ to use ZGTVAL IZGT
/MAPPR/ to use all members
/MAPRD/ to use ZRDVAL IZRD
/MAPSV/ to use ZSVVAL IZSV
/PLOMAP/ to use SCALMP
/SCRACH/ to use NAMFIL
/XENDA/ to use UU MSTOP MODEL DEFVAL
### Classification:
Fourier Calculations . . . . . . . Setting Up
## SUBROUTINE INPUTN(NOUT)
### Arguments:
On entry NOUT= an output unit number on to which to write the title
or -1 to indicate title already present in /SCRACH
### Description:
Puts title into ITITLE and the number of characters in it to NTITLE
### Input:
The first time in a run INPUTN is called with +ve NOUT, it reads a single card starting N, and takes the next 79 chars as a title to be put out where the user chooses. In particular it is written on plotted Fourier maps.
### Output:
At this first and every other call of INPUTN, it will write out the title on unit NOUT, unless NOUT=-1 when it is written to unit LPT.
### Notes:
The "N" is not held in ITITLE
CARDIN LENGT
### Called by:
RDDATA SETFC SETFCM SETFOU CALMSF CALQSF MAG3D MVENTR
### Common blocks used:
/IOUNIT/ to use LPT
/NTITL/ to use NTITLE
/TITLE/ to use all members
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## SUBROUTINE INPUTQ(ID,NTYP,IAT,IPT,IER)
### Arguments:
On entry ID is the position in the CDF of the "Q" card , or 0 (= card present)
On exit NTYP = a number indicating what kind of "Q" card was read:
NTYP=1 for STYP (magnetic structure type)
NTYP=2 for PROP the propagation vector
NTYP=3 for MSYM a magnetic symmetry operator
NTYP=4 for NSYM a non-symmetric rotation
NTYP=5 for FORM (a form factor label should be read first).
NTYP=6 for MU (Magnetic moment: an atom label should be read first).
NTYP=7 for SDIR (Spin directions: an atom label should be read first).
NTYP=8 for PSI (Relative phases of helices: an atom label should be
NTYP=9 for CHI (Susceptibility tensor: an atom label should be
On exit IAT = number corresponding to the atom or form factor label,
On exit IPT = the next column on the card to be interpreted.
On exit IER = the error indicator, = 0 for no error.
### Calls:
CARDIN ERRCH2 IATOM LMATCH NCFIND RDWORD
### Called by:
DOCHI1 DOMAG DOMAG1 DOMAG2
### Common blocks used:
/FONAM/ to use FONAME
/FORMDA/ to use NUMFNM
### Classification:
Magnetic Structure Factors . . . . . . . Setting Up
## SUBROUTINE INPUTS(ID,R,T)
### Arguments:
On entry ID points to an "S" card in the binary copy of the Crystal Data file, or if 0 indicates that the card is already present in /SCRACH/,
or if -ve indicates a scratch unit on which to find S cards .
On exit R is a 3x3 matrix containing the rotation, and T is a 1x3 vector containing the translation.
### Description:
Interprets symmetry operators within the character set:
X Y Z x y z 1 2 3 4 5 6 + - / ,
and ignores characters outside that set.
Within fixed format:
An operator has 3 fields, being in columns 2-21,22-41 and 42-61, and within each field the element of the space group symmetry operator is given. A fraction is given as digit/digit, and any reasonable looking combination (within the vocabulary above) is interpreted.
It is also possible to override the need to use 20 columns per field, by finishing a field with a comma, e.g.
S -X,-Y,Z
### Notes:
The findings of SYMOP (which repeatedly calls INPUTS) may be printed by a call of OPSYM.
CARDIN GMZER
SYMOP
### Common blocks used:
/CARDRC/ to use IERR
/CHARS/ to use LETUP LETLOW IDIGIT
/IOUNIT/ to use LPT ITO
### Classification:
Basic Crystallography . . . . . . . Setting Up
## SUBROUTINE INPUTT(ID,LABA,LBALEN,NTYP,A,IER)
### Arguments:
On entry ID points to the required card in the bionary copy of the Crystal data file, or if 0 indicates that the card is already present in /SCRACH/.
On exit:
LABA, A4, holds the label read after "T space"
LBALEN is the number of characters in LABA
NTYP is an integer giving the type of factor expected
A is a 1x6 array of coefficients, in the standard sequence:
A11, A22, A33, A23, A13, A12
IER is an error indicator, =0 if no errors.
### Description:
The exact interpretation of the 6 coefficients is left to the SUBROUTINE (usually SETANI), which calls INPUTT.
### Calls:
CARDIN ERRATM ERRCH2 LETTER RDINTG RDREAL RDWORD
F2NEW SETANI
### Classification:
Structure Factor Calculations . . . . . . . Setting Up
## SUBROUTINE INPUTU(HT)
### Arguments:
On exit HT is a 1x3 vector holding the 3 indices.
### Description:
Reads a single "U" card , giving 3 real numbers for h,k,l, the indices of the typical reflection which the user wishes to be inside the chosen asymmetric unit.
If no "U" card is given, 13,11,10 is assumed (being all positive, with h > k > l). If the given indices are special, they will be on the edge of an asymmetric unit, and the chosen unit might not be exactly as wished.
### Output:
Writes its findings to unit LPT.
### Calls:
CARDIN ERRIN2 ERRMES INDFIX RDREAL
SYMUNI
### Common blocks used:
/IOUNIT/ to use LPT
### Classification:
Basic Crystallography . . . . . . . Setting Up
## SUBROUTINE INPUTW(IAT,XWORD,ID,IPT)
### Arguments:
IAT on exit is which atom label, or scattering factor label identified
WORD is A4, on exit holding which word read after atom label
ID on entry points to card to read
IPT on exit points to next position on card to read
### Description:
If the word is 'RADF', expects the label to be a scattering factor label.
### Calls:
CARDIN ERRMES IATOM ISCAT RDWORD
PFSET FORFAC
### Common blocks used:
/CARDRC/ to use NYZ
### Classification:
Structure Factor Calculations . . . . . . . Setting Up
## SUBROUTINE INTCHR(IDIG,NDIG,ICHR,NCHR,MODE)
### Arguments:
On entry IDIG is an integer array holding NDIG digits
NCHR is the number of characters in ICHR
MODE=0 requests left justification
1 requests right justification
On exit ICHR is a character string holding NDIG characters, which
correspond to the digits in IDIG, properly justified.
### Called by:
ATSPEC OTPUTI PARNAM
### Common blocks used:
/CHARS/ to use IDIGIT
/IOUNIT/ to use LPT ITO
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## SUBROUTINE INTDIG(N,IDIG,NDIG)
### Arguments:
On entry N is the integer to be unpacked
On exit IDIG is an integer array holding the individual digits of abs(N)
NDIG is the number of elements of NDIG, maximum 5
### Output:
If the integer is too big, says so &\$1;exits with nothing stored
ERRIN2
### Called by:
ATSPEC FETTLE NUMA1 OTPUTI PARNAM
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## LOGICAL FUNCTION INTIND(H,K)
### Arguments:
K(3) returned as the integer values
INDFIX INDFLO
BPBPRC CENPRC
### Classification:
Manipulation of Reflection Indices . . . . . . . Utility
## SUBROUTINE INVENT(U,H,ANS)
### Calls:
EQVEC ERRMES FCTOR GMEQ GMREV GMZER INBOX JFIX
POLUNI SETGEN
### Common blocks used:
/IOUNIT/ to use LPT ITO
### Classification:
Basic Crystallography . . . . . . . Utility
## LOGICAL FUNCTION IPDONE(CHAR)
### Description:
Returns TRUE if the CHA R cards have already been read FALSE otherwise
LETTER
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## FUNCTION IPOPE(N)
### Arguments:
On entry N=an error code produced as a result of trying to open a file.
On exit IPOPE is set as follows:
1 for an 'old' file which does not exist 2 for a 'new' file which does exist 3 for a bad file name 4 file already open 0 for anything else
NFIND
NOPFIL
### Classification:
CCSL Input/Output Routines . . . . . . . Utility
## FUNCTION ISCAT(FNAME)
### Arguments:
On entry FNAME is an A4 CHARACTER name, which could be a scattering factor
name, left justified
On exit ISCAT =0 if FNAME does not occur in the list in /FONAME
=position in the list if found.
### Prerequisite calls:
The scattering factor list must have been set up by, say, ATOPOS
NCFIND
### Called by:
F2NEW INPUTJ INPUTW MPFORM TBLFND
### Common blocks used:
/FONAM/ to use FONAME
/FORMDA/ to use NUMFNM
### Classification:
Tests . . . . . . . Utility
## LOGICAL FUNCTION ISPABS(H)
### Arguments:
H on entry is a 3-sized array containing h,k,l for a reflection
ISPABS on exit is .TRUE. if the hkl reflection is absent, .FALSE. if present
### Prerequisite calls:
The symmetry must have been previously set up by SYMOP
### Calls:
GMREV ROTSYM SCALPR
### Called by:
CALCFR GENREF GETSFZ CALCTW
### Common blocks used:
/NSYM/ to use NCENT NOPC
/SYMDA/ to use TRANS
### Classification:
Basic Crystallography . . . . . . . Crystallographic
## FUNCTION ITPOS(IPOS)
### Arguments:
IPOS is assumed non-zero on entry, and is unchanged.
### Notes:
It is also assumed that IPOS is not so large that integer overflow will occur. If it does, try reducing the number of bits used in an integer (e.g.avoid the last, sign, bit) by reducing the value of NBITS in COMMON /CONTUR/
BITSET
### Classification:
Logical Operations . . . . . . . Utility
P. Jane Brown e-mail: [email protected]
Institut Laue Langevin,
Grenoble, FRANCE | 2013-05-22 17:33:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43356576561927795, "perplexity": 11716.503566024652}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702127714/warc/CC-MAIN-20130516110207-00005-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://byjus.com/question-answer/for-the-resistance-network-shown-in-the-figure-choose-the-correct-option-s-the-current-1/ | Question
# For the resistance network shown in the figure, choose the correct option(s).
A
The current through PQ is zero.
B
I1=3A.
C
The potential at S is less than that at Q.
D
I2=2A.
Solution
## The correct options are A The current through PQ is zero. B The potential at S is less than that at Q. C $$I_{1} = 3A.$$ D $$I_{2} = 2A.$$Node P and Q are equipotential and node S and T are equipotential due to formation of wheatstone bridge across themThus, no current passes through PQ and ST$$\displaystyle I_{1}=\dfrac{12}{4}= 3A$$$$\displaystyle I_{2}=I_{1}(\dfrac{12}{6+12})= 2A$$now point P and Q are Equipotential and point S and T are equipotential.from resistor PS current flows from P to S hence voltage of point P is more than voltage of point S , also P is equipotential with Q that's why Q also has more potential than S.Physics
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https://zbmath.org/?q=an:1423.41050 | # zbMATH — the first resource for mathematics
Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties. (English) Zbl 1423.41050
Let $$M$$ be a nonempty closed subset of a real normed space $$X$$ and $$P_M$$ be the (set-valued) metric projection on $$M$$. The set $$M$$ is called a sun if for every $$x \in X \setminus M$$ there is a $$y \in P_M(x)$$ such that for all $$\lambda \geq 0$$, $$y \in P_M(y+\lambda (y-x))$$. If in addition, for any $$x \in X \setminus M$$, $$P_M(x) \neq\emptyset$$, and the condition from before holds for any $$y \in P_M(x)$$, then $$M$$ is called a strict sun. $$M$$ is called an LG-set if for any $$x \notin M$$, $$\varepsilon > 0$$ and $$y \in P_{M \cap B(y,\varepsilon)}$$, $$y \in P_M(x)$$.
Let $$Q$$ be a property that subsets of $$X$$ can have. Then we say that $$M$$ has property $$P$$-$$Q$$ if for all $$x \in X$$, $$P_M(x)$$ is nonempty and has property $$Q$$ and that it has property $$B$$-$$Q$$ if for all $$x \in X$$ and $$r > 0$$, $$M \cap B(x,r)$$ has property $$Q$$ or is empty.
The author obtains some implications and equivalences among these and similar notions, e.g. that any LG-set that is a $$B$$-sun is a strict sun and that a $$P$$-compact $$B$$-sun is a sun. In addition, he derives sufficient conditions for a closed locally Chebyshev set to be Chebyshev.
##### MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 54C65 Selections in general topology
Full Text:
##### References:
[1] Alimov, AR, Monotone path-connectedness of Chebyshev sets in the space C(Q), Sbornik Math., 197, 1259-1272, (2006) · Zbl 1147.41011 [2] Alimov, AR, Convexity of bounded Chebyshev sets in finite-dimensional asymmetrically normed spaces, Izvestiya Saratov Gos. Univ. Nov. Ser. Matem. Mekh. Inform, 14, 489-497, (2014) · Zbl 1361.46011 [3] Alimov, AR, Local solarity of suns in linear normed spaces, J. Math. Sci. (N.Y.), 197, 447-454, (2014) · Zbl 1314.46018 [4] Alimov, AR, Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces, Izvestiya: Math., 78, 3-19, (2014) · Zbl 1303.41018 [5] Alimov, AR, A monotone path-connected set with radially continuous metric projection is a strict sun, Sib. Matem. Zh, 57, 16-21, (2016) [6] Alimov, AR, Selections of the metric projection operator and strict solarity of sets with continuous metric projection, Sbornik Math., 208, 915-929, (2017) · Zbl 1426.41039 [7] Alimov, AR; Tsar’kov, IG, Connectedness and other geometric properties of suns and chebyshev sets, J. Math. Sci., 217, 683-730, (2016) · Zbl 1361.46012 [8] Alimov, AR; Tsar’kov, IG, Connectedness and solarity in problems of best and near-best approximation, Russ. Math. Surv., 71, 1-77, (2016) · Zbl 1350.41031 [9] Amir, D.; Deutsch, F., Suns, moons and quasi-polyhedra, J. Approx. Theory, 6, 176-201, (1972) · Zbl 0238.41014 [10] Blatter, J.; Morris, PD; Wulbert, DE, Continuity of the set-valued metric projection, Math. Ann, 178, 12-24, (1968) · Zbl 0189.42904 [11] Brosowski, B.; Deutsch, F., Some new continuity concepts for metric projections, Bull. Amer. Math. Soc, 6, 974-978, (1972) · Zbl 0255.41029 [12] Brosowski, B.; Deutsch, F., On some geometric properties of suns, J. Approx. Theory, 10, 245-267, (1974) · Zbl 0272.41020 [13] Brosowski, B.; Deutsch, F., Radial continuity of set-valued metric projections, J. Approx. Theory, 11, 236-253, (1974) · Zbl 0283.41014 [14] Flerov, A., Locally Chebyshev sets on the plane, Math. Notes, 97, 136-142, (2015) · Zbl 1329.46016 [15] Malykhin, YV, Relative widths of Sobolev classes in the uniform and integral metrics, Proc. Steklov Inst. Math, 293, 209-215, (2016) · Zbl 1362.46039 [16] Repovš, D., Semenov, P.V.: Continuous selections of multivalued mappings. In: Recent Progress in General Topology. III, pp. 711-749. Atlantis Press, Paris (2014) · Zbl 1304.54002 [17] Tsar’kov, IG, Bounded Chebyshev sets in finite-dimensional Banach spaces, Math. Notes, 36, 530-537, (1984) · Zbl 0602.41033 [18] Tsar’kov, IG, Continuity of the metric projection, structural and approximate properties of sets, Math. Notes, 47, 218-227, (1990) · Zbl 0703.46010 [19] Tsar’kov, IG, Bounded Chebyshev sets in finite-dimensional Banach spaces, Izv. Math, 80, 442-461, (2016) · Zbl 1356.46013 [20] Tsar’kov, IG, Continuous ε-selection, Sb. Math, 207, 267-285, (2016) · Zbl 1347.41047 [21] Vlasov, LP, Approximative properties of sets in normed linear spaces, Russ. Math. Surveys, 28, 3-66, (1973) · Zbl 0293.41031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-01-18 04:37:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8889899253845215, "perplexity": 3764.907418996937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514121.8/warc/CC-MAIN-20210118030549-20210118060549-00607.warc.gz"} |
http://nbviewer.jupyter.org/github/rasmusab/bayesianprobabilitiesworkshop/blob/master/Exercise%201.ipynb | # Exercise 1: Bayesian A testing for Swedish Fish Incorporated (B comes later)¶
### Rasmus Bååth (adapted for Python by Christophe Carvenius)¶
Swedish Fish Incorporated is the largest Swedish company delivering fish by mail order. They are now trying to get into the lucrative Danish market by selling one year Salmon subscriptions. The marketing department have done a pilot study and tried the following marketing method:
A: Sending a mail with a colorful brochure that invites people to sign up for a one year salmon subscription.
The marketing department sent out 16 mails of type A. Six Danes that received a mail signed up for one year of salmon and marketing now wants to know, how good is method A?
At the bottom of this document you’ll find a solution. But try yourself first!
## Question I, Build a Bayesian model that answers the question: What would the rate of sign-up be if method A was used on a larger number of people?¶
Hint 1: The answer is not a single number but a distribution over probable rates of sign-up.
Hint 2: As part of you generative model you’ll want to use the binomial distribution, which you can sample from in R using the np.random.binomial(n, p, size). The binomial distribution simulates the following process n times: The number of “successes” when performing size trials, where the probability of “success” is p.
Hint 3: A commonly used prior for the unknown probability of success in a binomial distribution is a uniform distribution from 0 to 1. You can draw from this distribution by running np.random.uniform(0, 1, size = n_draws)
Hint 4: Here is a code scaffold that you can build upon.
In [ ]:
# Import libraries
import pandas as pd
import numpy as np
# Number of random draws from the prior
n_draws = 10000
# Here you sample n_draws draws from the prior into a pandas Series (to have convenient
# methods available for histograms and descriptive statistics, e.g. median)
prior = pd.Series(...)
prior.hist() # It's always good to eyeball the prior to make sure it looks ok.
# Here you define the generative model
def generative_model(parameters):
return(...)
# Here you simulate data using the parameters from the prior and the
# generative model
sim_data = list()
for p in prior:
sim_data.append(generative_model(p))
# Here you filter off all draws that do not match the data.
posterior = prior[list(map(lambda x: x == observed_data, sim_data))]
posterior.hist() # Eyeball the posterior
# See that we got enought draws left after the filtering.
# There are no rules here, but you probably want to aim for >1000 draws.
# Now you can summarize the posterior, where a common summary is to take the mean or the median posterior,
# and perhaps a 95% quantile interval.
print('Number of draws left: %d, Posterior median: %.3f, Posterior quantile interval: %.3f-%.3f' %
(len(posterior), posterior.median(), posterior.quantile(.025), posterior.quantile(.975)))
## Question II, What’s the probability that method A is better than telemarketing?¶
So marketing just told us that the rate of sign-up would be 20% if salmon subscribers were snared by a telemarketing campaign instead (to us it’s very unclear where marketing got this very precise number from). So given the model and the data that we developed in the last question, what’s the probability that method A has a higher rate of sign-up than telemarketing?
Hint 1: If you have a vector of samples representing a probability distribution, which you should have from the last question, calculating the amount of probability above a certain value is done by simply counting the number of samples above that value and dividing by the total number of samples.
Hint 2: The answer to this question is a one-liner.
## Question III, If method A was used on 100 people what would be number of sign-ups?¶
Hint 1: The answer is again not a single number but a distribution over probable number of sign-ups.
Hint 2: As before, the binomial distribution is a good candidate for how many people that sign up out of the 100 possible.
Hint 3: Make sure you don’t “throw away” uncertainty, for example by using a summary of the posterior distribution calculated in the first question. Use the full original posterior sample!
Hint 4: The general patter when calculating “derivatives” of posterior samples is to go through the values one-by-one, and perform a transformation (say, plugging in the value in a binomial distribution), and collect the new values in a vector.
# Solutions (but this can be done in many ways)¶
## Question I¶
In [2]:
# Import libraries
import pandas as pd
import numpy as np
# Number of random draws from the prior
n_draw = 10000
# Defining and drawing from the prior distribution
prior_rate = pd.Series(np.random.uniform(0, 1, size = n_draw))
# It's always good to eyeball the prior to make sure it looks ok.
prior_rate.hist()
Out[2]:
<matplotlib.axes._subplots.AxesSubplot at 0x110d44eb8>
In [5]:
# Defining the generative model
def gen_model(prob):
return(np.random.binomial(16, prob))
# the generative model
subscribers = list()
# Simulating the data
for p in prior_rate:
subscribers.append(gen_model(p))
# Observed data
observed_data = 6
# Here you filter off all draws that do not match the data.
post_rate = prior_rate[list(map(lambda x: x == observed_data, subscribers))]
post_rate.hist() # Eyeball the posterior
# See that we got enought draws left after the filtering.
# There are no rules here, but you probably want to aim for >1000 draws.
# Now you can summarize the posterior, where a common summary is to take the mean or the median posterior,
# and perhaps a 95% quantile interval.
print('Number of draws left: %d, Posterior mean: %.3f, Posterior median: %.3f, Posterior 95%% quantile interval: %.3f-%.3f' %
(len(post_rate), post_rate.mean(), post_rate.median(), post_rate.quantile(.025), post_rate.quantile(.975)))
Number of draws left: 581, Posterior mean: 0.395, Posterior median: 0.393, Posterior 95% quantile interval: 0.194-0.615
## Question II¶
In [6]:
sum(post_rate > 0.2) / len(post_rate) # or just np.mean(post_rate > 0.2)
Out[6]:
0.96729776247848542
## Question III¶
In [10]:
# This can be done with a for loop
signups = list()
for p in post_rate:
signups.append(np.random.binomial(100, p))
# But we can write it like this:
signups = pd.Series([np.random.binomial(n = 100, p = p) for p in post_rate])
signups.hist()
print('Sign-up 95%% quantile interval %d-%d' % tuple(signups.quantile([.025, .975]).values))
Sign-up 95% quantile interval 17-63
So a decent guess is that is would be between 20 and 60 sign-ups. | 2018-07-20 10:36:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6545864939689636, "perplexity": 2016.1168847492618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591578.1/warc/CC-MAIN-20180720100114-20180720120114-00442.warc.gz"} |
https://mc3.readthedocs.io/en/latest/mcmc_tutorial.html | # MCMC Tutorial¶
This tutorial describes the available options when running an MCMC with mc3. The following sections make up a script meant to be run from the Python interpreter or in a Python script. At the bottom of this page you can see the entire script.
## Preamble¶
In this tutorial, we will use the following function to create and fit a synthetic dataset following a quadratic behavior:
def quad(p, x):
"""
Parameters
p: Polynomial constant, linear, and quadratic coefficients.
x: Array of dependent variables where to evaluate the polynomial.
Returns
y: Polinomial evaluated at x: y(x) = p0 + p1*x + p2*x^2
"""
y = p[0] + p[1]*x + p[2]*x**2.0
return y
## Argument Inputs¶
From the shell, the arguments can be input as command-line arguments. However, in this case, the best option is to specify all inputs in a cconfiguration file. An mc3 configuration file follows the configparser standard format described here. To see all the available options, run:
mc3 --help
From the Python interpreter, the arguments must be input as function arguments. To see the available options, run:
import mc3
help(mc3.sample)
## Input Data¶
The data and uncert arguments (required) defines the dataset to be fitted and their $$1\sigma$$ uncertainties, respectively. Each one of these arguments is a 1D float ndarray:
# Preamble (create a synthetic dataset, in a real scenario you would
np.random.seed(314)
x = np.linspace(0, 10, 1000)
p0 = [3, -2.4, 0.5]
uncert = np.sqrt(np.abs(y))
error = np.random.normal(0, uncert)
data = y + error
Note
Alternatively, the data argument can be a string specifying a Numpy npz filename containing the data and uncert arrays. See the Input Data File Section below.
## Modeling Function¶
The func argument (required) defines the parameterized modeling function fitting the data. The user can either set func as a callable, e.g.:
# Define the modeling function as a callable:
or as a tuple of strings pointing to the modeling function, e.g.:
# A three-element tuple indicates the function's name, the module
# name (without the '.py' extension), and the path to the module.
# If the module is already within the scope of the Python path,
# the user can set func as a two-elements tuple:
Note
The only requirement for the modeling function is that its arguments follow the same structure of the callable in scipy.optimize.leastsq, i.e., the first argument is a 1D iterable containing the fitting parameters.
The indparams argument (optional) contains any additional argument required by func:
# List of additional arguments of func (if necessary):
indparams = [x]
Note
Even if there is only one additional argument to func, indparams must be defined as a tuple (as in the example above). Eventually, the modeling function has to able to be called as: model = func(params, *indparams)
## Fitting Parameters¶
The params argument (required) is a 1D float ndarray containing the initial-guess values for the model fitting parameters.
# Array of initial-guess values of fitting parameters:
params = np.array([ 10.0, -2.0, 0.1])
The pmin and pmax arguments (optional) are 1D float ndarrays that set lower and upper boundaries explored by the MCMC, for each fitting parameter (same size as params).
# Lower and upper boundaries for the MCMC exploration:
pmin = np.array([-10.0, -20.0, -10.0])
pmax = np.array([ 40.0, 20.0, 10.0])
If a proposed step falls outside the set boundaries, that iteration is automatically rejected. The default values for each element of pmin and pmax are -np.inf and +np.inf, respectively.
## Parameters Stepping Behavior¶
The pstep argument (optional) is a 1D float ndarray that defines the stepping behavior of the fitting parameters over the parameter space. This argument has actually a dual purpose:
### Stepping Behavior¶
First, it can keep a fitting parameter fixed by setting its pstep value to zero, for example:
# Keep the third parameter fixed:
pstep = np.array([1.0, 0.5, 0.0])
It can force a fitting parameter to share its value with another parameter by setting its pstep value equal to the negative index of the sharing parameter, for example:
# Make the third parameter share the value of the second parameter:
pstep = np.array([1.0, 0.5, -2])
Otherwise, a positive pstep value leaves the parameter as a free fitting parameter:
# Parameters' stepping behavior:
pstep = np.array([1.0, 0.5, 0.1])
### Stepping Scale¶
pstep also sets the step size of the free parameters. For a differential-evolution run (e.g., sampler = 'snooker'), mc3 starts the MCMC drawing samples from a normal distribution for each parameter, whose standard deviation is set by the pstep values. For a classic Metropolis random walk (sampler = 'mrw'), the pstep values set the standard deviation of the Gaussian proposal jumps for each parameter.
For more details on the MCMC algorithms, see Sampler Algorithm.
## Parameter Priors¶
The prior, priorlow, and priorup arguments (optional) are 1D float ndarrays that set the prior estimate, lower uncertainty, and upper uncertainty of the fitting parameters. mc3 supports two types of priors:
A priorlow value of zero (default) defines a uniform prior between the parameter boundaries. This is appropriate when there is no prior knowledge for a parameter $$\theta$$:
$p(\theta) = \frac{1}{\theta_{\rm max} - \theta_{\rm min}},$
Positive priorlow and priorup values define a Gaussian prior for a parameter $$\theta$$:
$p(\theta) = A \exp\left(\frac{-(\theta-\theta_{p})^{2}}{2\sigma_{p}^{2}}\right),$
where prior sets the prior value $$\theta_{p}$$, and priorlow and priorup set the lower and upper $$1\sigma$$ prior uncertainties, $$\sigma_{p}$$, of the prior (depending if the proposed value $$\theta$$ is lower or higher than $$\theta_{p}$$, respectively). The leading factor is given by: $$A = 2/(\sqrt{2\pi}(\sigma_{\rm up}+\sigma_{\rm lo}))$$ (see [Wallis2014]), which reduces to the familiar Gaussian normal distribution when $$\sigma_{\rm up} = \sigma_{\rm lo}$$:
$p(\theta) = \frac{1}{\sqrt{2\pi}\sigma_{p}} \exp\left(\frac{-(\theta-\theta_{p})^{2}}{2\sigma_{p}^{2}}\right),$
For example, to explicitly set uniform priors for all parameters:
# Parameter prior probability distributions:
prior = np.array([ 0.0, 0.0, 0.0])
priorlow = np.array([ 0.0, 0.0, 0.0])
priorup = np.array([ 0.0, 0.0, 0.0])
## Parameter Names¶
The pnames argument (optional) define the names of the model parametes to be shown in the scren output and figure labels. The screen output will display up to 11 characters. For figures, the texnames argument (optional) enables names using LaTeX syntax, for example:
# Parameter names:
pnames = ['y0', 'alpha', 'beta']
texnames = [r'$y_{0}$', r'$\alpha$', r'$\beta$']
If texnames = None, it defaults to pnames. If pnames = None, it defaults to texnames. If both arguments are None, they default to a generic [Param 1, Param 2, ...] list.
## Sampler Algorithm¶
The sampler argument (required) defines the sampler algorithm for the MCMC:
# Sampler algorithm, choose from: 'snooker', 'demc' or 'mrw'.
sampler = 'snooker'
The standard Differential-Evolution MCMC algorithm (sampler = 'demc', [terBraak2006]) proposes for each chain $$i$$ in state $$\mathbf{x}_{i}$$:
$\mathbf{x}^* = \mathbf{x}_i + \gamma (\mathbf{x}_{R1}-\mathbf{x}_{R2}) + \mathbf{e},$
where $$\mathbf{x}_{R1}$$ and $$\mathbf{x}_{R2}$$ are randomly selected without replacement from the population of current states except $$\mathbf{x}_{i}$$. This implementation adopts $$\gamma=f_{\gamma} 2.38/\sqrt{2 N_{\rm free}}$$, with $$N_{\rm free}$$ the number of free parameters; and $$\mathbf{e}\sim \mathcal{N}(0, \sigma^2)$$, with $$\sigma=f_{e}$$ pstep, where the scaling factors are defaulted to $$f_{\gamma}=1.0$$ and $$f_{e}=0.0$$ (see Fine-tuning).
If sampler = 'snooker' (recommended), mc3 will use the DEMC-zs algorithm with snooker propsals (see [terBraakVrugt2008]).
If sampler = 'mrw', mc3 will use the classical Metropolis-Hastings algorithm with Gaussian proposal distributions. I.e., in each iteration and for each parameter, $$\theta$$, the MCMC will propose jumps, drawn from Gaussian distributions centered at the current value, $$\theta_0$$, with a standard deviation, $$\sigma$$, given by the values in the pstep argument:
$q(\theta) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left( -\frac{(\theta-\theta_0)^2}{2 \sigma^2}\right)$
Note
For sampler=snooker, an MCMC works well with 3 chains or more. For sampler=demc, [terBraak2006] suggest using $$2 N_{\rm free}$$ chains. From experience, I recommend the snooker, as it is more efficient than most others MCMC random walks.
## MCMC Configuration¶
The following arguments set the MCMC chains configuration:
# MCMC setup:
nsamples = 1e5
burnin = 1000
nchains = 14
ncpu = 7
thinning = 1
The nsamples argument (required for MCMC runs) sets the total number of MCMC samples to compute.
The burnin argument (optional, default: 0) sets the number of burned-in (removed) iterations at the beginning of each chain.
The nchains argument (optional, default: 7) sets the number of parallel chains to use.
The ncpu argument (optional, default: nchains) sets the number CPUs to use for the chains. mc3 runs in multiple processors through the mutiprocessing Python Standard-Library package (additionaly, the central MCMC hub will use one extra CPU. Thus, the total number of CPUs used is ncpu + 1).
Note
If ncpu+1 is greater than the number of available CPUs in the machine, mc3 will cap ncpu to the number of available CPUs minus one. To keep a good balance, I recommend setting nchains equal to a multiple of chains ncpu as in the example above.
The thinning argument (optional, default: 1) sets the chains thinning factor (discarding all but every thinning-th sample). To reduce the memory usage, when requested, only the thinned samples are stored (and returned).
Note
Thinning is often unnecessary for a DE run, since this algorithm reduces significatively the sampling autocorrelation.
### Pre-MCMC Setup¶
The following arguments set how the code set the initial values for the MCMC chains:
# MCMC initial draw, choose from: 'normal' or 'uniform'
kickoff = 'normal'
# DEMC snooker pre-MCMC sample size:
hsize = 10
The starting point of the MCMC chains come from a random draw, set by the kickoff argument (optional, default: ‘normal’). This can be a Normal-distribution draw centered at params with standard deviation pstep; or it can be a uniform draw bewteen pmin and pmax.
The snooker DEMC, in particular, needs an initial sample, set by the hsize argument (optional, default: 10). The draws from this initial sample do not count for the posterior-distribution statistics.
Usually, these variables do not have a significant impact in the outputs. Thus, they can be left at their default values.
## Optimization¶
When not None, the leastsq argument (optional, default: None) run a least-squares optimization before the MCMC:
# Optimization before MCMC, choose from: 'lm' or 'trf':
leastsq = 'lm'
chisqscale = False
Set leastsq='lm' to use the Levenberg-Marquardt algorithm via Scipy’s leastsq, or set leastsq='trf' to use the Trust Region Reflective algorithm via Scipy’s least_squares. Fixed and shared-values apply during the optimization (see Stepping Behavior), as well as the priors (see Parameter Priors).
Note
From the scipy documentation: Levenberg-Marquardt ‘doesn’t handle bounds’ but is ‘the most efficient method for small unconstrained problems’; whereas the Trust Region Reflective algorithm is a ‘Generally robust method, suitable for large sparse problems with bounds’.
The chisqscale argument (optional, default: False) is a flag to scale the data uncertainties to enforce a reduced $$\chi^{2}$$ equal to $$1.0$$. The scaling applies by multiplying all uncertainties by a common scale factor.
## Convergence¶
mc3 checks for convergence through the Gelman-Rubin test ([GelmanRubin1992]):
# MCMC Convergence:
grtest = True
grbreak = 1.01
grnmin = 0.5
The grtest argument (optional, default: False), when True, runs the Gelman-Rubin convergence test. Values larger than 1.01 are indicative of non-convergence. See [GelmanRubin1992] for further information. The Gelman-Rubin test is computed every 10% of the MCMC exploration.
The grbreak argument (optional, default: 0.0) sets a convergence threshold to stop an MCMC when GR drops below grbreak. Reasonable values seem to be $${\rm grbreak} \lesssim 1.01$$. The default behavior is not to break (grbreak = 0.0).
The grnmin argument (optional, default: 0.5) sets a minimum number of valid samples (after burning and thinning) required for grbreak. If grnmin is greater than one, it defines the minimum number of samples to run before breaking out of the MCMC. If grnmin is lower than one, it defines the fraction of the total samples to run before breaking out of the MCMC.
## Wavelet-Likelihood MCMC¶
The wlike argument (optional, default: False) allows mc3 to implement the Wavelet-based method to account for time-correlated noise. When using this method, the used must append the three additional fitting parameters ($$\gamma, \sigma_{r}, \sigma_{w}$$) from [CarterWinn2009] to the end of the params array. Likewise, add the correspoding values to the pmin, pmax, stepsize, prior, priorlow, and priorup arrays. For further information see [CarterWinn2009].
This tutorial won’t use the wavelet method:
# Carter & Winn (2009) Wavelet-likelihood method:
wlike = False
## Fine-tuning¶
The $$f_{\gamma}$$ and $$f_{e}$$ factors scale the DEMC proposal distributions.
fgamma = 1.0 # Scale factor for DEMC's gamma jump.
fepsilon = 0.0 # Jump scale factor for DEMC's "e" distribution
The default $$f_{\gamma} = 1.0$$ value is set such that the MCMC acceptance rate approaches 25–40%. Therefore, most of the time, the user won’t need to modify this. Only if the acceptance rate is very low, we recommend to set $$f_{\gamma} < 1.0$$. The $$f_{e}$$ factor sets the jump scale for the $$\mathbf e$$ distribution, which has to have a small variance compared to the posterior. For further information, see [terBraak2006].
## Logging¶
If not None, the log argument (optional, default: None) stores the screen output into a log file. log can either be a string of the filename where to store the log, or an mc3.utils.Log object (see API).
# Logging:
log = 'MCMC_tutorial.log'
## Outputs¶
The following arguments set the output files produced by mc3:
# File outputs:
savefile = 'MCMC_tutorial.npz'
plots = True
rms = True
The savefile argument (optional, default: None) defines an .npz file names where to store the MCMC outputs. This file contains the following key–items:
• posterior: thinned posterior distribution of shape [nsamples, nfree], including burn-in phase.
• zchain: chain indices for the posterior samples.
• zmask: posterior mask to remove the burn-in.
• chisq: $$\chi^2$$ values for the posterior samples.
• log_post: log of the posterior for the sample (as defined here).
• burnin: number of burned-in samples per chain.
• ifree: Indices of the free parameters.
• pnames: Parameter names.
• texnames: Parameter names in Latex format.
• meanp: mean of the marginal posteriors for each model parameter.
• stdp: standard deviation of the marginal posteriors for each model parameter.
• CRlo: lower boundary of the marginal 68%-highest posterior density (the credible region) for each model parameter.
• CRhi: upper boundary of the marginal 68%-HPD.
• stddev_residuals: standard deviation of the residuals.
• acceptance_rate: sample’s acceptance rate.
• best_log_post: optimal log of the posterior in the sample (see here).
• bestp: model parameters for the best_log_post sample.
• best_model: model evaluated at bestp.
• best_chisq: $$\chi^2$$ for the best_log_post sample.
• red_chisq: reduced chi-squared: $$\chi^2/(N_{\rm data}-N_{\rm free})$$ for the best_log_post sample.
• BIC: Bayesian Information Criterion: $$\chi^2 -N_{\rm free} \log(N_{\rm data})$$ for the best_log_post sample.
• chisq_factor: Uncertainties scale factor to enforce $$\chi^2_{\rm red} \equiv 1$$.
Note
Notice that if there are fixed or shared parameters, then the number of free parameters won’t be the same as the number of model parameters. The output posterior Z includes only the free parameters, whereas the CRlo, CRhi, stdp, meanp, and bestp outputs include all model parameters.
Setting the plots argument (optional, default: False) to True will generate data (along with the best-fitting model) plot, the MCMC-chain trace plot for each parameter, and the marginalized and pair-wise posterior plots. Setting the ioff argument to True (optional, default: False) will turn the display interactive mode off.
Set the rms argument (optional, default: False) to True to compute and plot the time-averaging test for time-correlated noise (see [Winn2008]).
## MCMC Run¶
Putting it all together, here’s a Python script to run an mc3 retrieval explicitly defining all the variables described above:
import sys
import numpy as np
import mc3
"""
Parameters
p: Polynomial constant, linear, and quadratic coefficients.
x: Array of dependent variables where to evaluate the polynomial.
Returns
y: Polinomial evaluated at x: y(x) = p0 + p1*x + p2*x^2
"""
y = p[0] + p[1]*x + p[2]*x**2.0
return y
# ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
# Preamble (create a synthetic dataset, in a real scenario you would
np.random.seed(314)
x = np.linspace(0, 10, 1000)
p0 = [3, -2.4, 0.5]
uncert = np.sqrt(np.abs(y))
error = np.random.normal(0, uncert)
data = y + error
# ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
# Define the modeling function as a callable:
# List of additional arguments of func (if necessary):
indparams = [x]
# Array of initial-guess values of fitting parameters:
params = np.array([ 10.0, -2.0, 0.1])
# Lower and upper boundaries for the MCMC exploration:
pmin = np.array([-10.0, -20.0, -10.0])
pmax = np.array([ 40.0, 20.0, 10.0])
# Parameters' stepping behavior:
pstep = np.array([1.0, 0.5, 0.1])
# Parameter prior probability distributions:
prior = np.array([ 0.0, 0.0, 0.0])
priorlow = np.array([ 0.0, 0.0, 0.0])
priorup = np.array([ 0.0, 0.0, 0.0])
# Parameter names:
pnames = ['y0', 'alpha', 'beta']
texnames = [r'$y_{0}$', r'$\alpha$', r'$\beta$']
# Sampler algorithm, choose from: 'snooker', 'demc' or 'mrw'.
sampler = 'snooker'
# MCMC setup:
nsamples = 1e5
burnin = 1000
nchains = 14
ncpu = 7
thinning = 1
# MCMC initial draw, choose from: 'normal' or 'uniform'
kickoff = 'normal'
# DEMC snooker pre-MCMC sample size:
hsize = 10
# Optimization before MCMC, choose from: 'lm' or 'trf':
leastsq = 'lm'
chisqscale = False
# MCMC Convergence:
grtest = True
grbreak = 1.01
grnmin = 0.5
# Logging:
log = 'MCMC_tutorial.log'
# File outputs:
savefile = 'MCMC_tutorial.npz'
plots = True
rms = True
# Carter & Winn (2009) Wavelet-likelihood method:
wlike = False
# Run the MCMC:
mc3_output = mc3.sample(data=data, uncert=uncert, func=func, params=params,
indparams=indparams, pmin=pmin, pmax=pmax, pstep=pstep,
pnames=pnames, texnames=texnames,
prior=prior, priorlow=priorlow, priorup=priorup,
sampler=sampler, nsamples=nsamples, nchains=nchains,
ncpu=ncpu, burnin=burnin, thinning=thinning,
leastsq=leastsq, chisqscale=chisqscale,
grtest=grtest, grbreak=grbreak, grnmin=grnmin,
hsize=hsize, kickoff=kickoff,
wlike=wlike, log=log,
plots=plots, savefile=savefile, rms=rms)
This routine returns a dictionary containing the outputs listed in Outputs. The screen output should look like this:
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multi-core Markov-chain Monte Carlo (mc3).
Version 3.0.0.
Copyright (c) 2015-2019 Patricio Cubillos and collaborators.
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Least-squares best-fitting parameters:
[ 3.02203328 -2.3897706 0.49543328]
Yippee Ki Yay Monte Carlo!
Start MCMC chains (Thu Aug 8 11:23:20 2019)
[: ] 10.0% completed (Thu Aug 8 11:23:21 2019)
Out-of-bound Trials:
[0 0 0]
Best Parameters: (chisq=1035.2269)
[ 3.02203328 -2.3897706 0.49543328]
[:: ] 20.0% completed (Thu Aug 8 11:23:21 2019)
Out-of-bound Trials:
[0 0 0]
Best Parameters: (chisq=1035.2269)
[ 3.02203328 -2.3897706 0.49543328]
[1.02204221 1.02386902 1.02470492]
[::: ] 30.0% completed (Thu Aug 8 11:23:21 2019)
Out-of-bound Trials:
[0 0 0]
Best Parameters: (chisq=1035.2269)
[ 3.02203328 -2.3897706 0.49543328]
[1.00644059 1.00601973 1.00644078]
All parameters converged to within 1% of unity.
[:::: ] 40.0% completed (Thu Aug 8 11:23:22 2019)
Out-of-bound Trials:
[0 0 0]
Best Parameters: (chisq=1035.2269)
[ 3.02203328 -2.3897706 0.49543328]
[1.00332153 1.00383779 1.00326743]
All parameters converged to within 1% of unity.
[::::: ] 50.0% completed (Thu Aug 8 11:23:22 2019)
Out-of-bound Trials:
[0 0 0]
Best Parameters: (chisq=1035.2269)
[ 3.02203328 -2.3897706 0.49543328]
[1.00286025 1.00297467 1.00258288]
All parameters converged to within 1% of unity.
[:::::: ] 60.0% completed (Thu Aug 8 11:23:22 2019)
Out-of-bound Trials:
[0 0 0]
Best Parameters: (chisq=1035.2269)
[ 3.02203328 -2.3897706 0.49543328]
[1.00169127 1.0016499 1.0013014 ]
All parameters converged to within 1% of unity.
All parameters satisfy the GR convergence threshold of 1.01, stopping
the MCMC.
MCMC Summary:
-------------
Number of evaluated samples: 60506
Number of parallel chains: 14
Average iterations per chain: 4321
Burned-in iterations per chain: 1000
Thinning factor: 1
MCMC sample size (thinned, burned): 46506
Acceptance rate: 28.85%
Param name Best fit Lo HPD CR Hi HPD CR Mean Std dev S/N
----------- ----------------------------------- ---------------------- ---------
y0 3.0220e+00 -1.2142e-01 1.2574e-01 3.0223e+00 1.2231e-01 24.7
alpha -2.3898e+00 -7.2210e-02 6.8853e-02 -2.3904e+00 7.0381e-02 34.0
beta 4.9543e-01 -8.3569e-03 8.9226e-03 4.9557e-01 8.6295e-03 57.4
Best-parameter's chi-squared: 1035.2269
Best-parameter's -2*log(posterior): 1035.2269
Bayesian Information Criterion: 1055.9502
Reduced chi-squared: 1.0383
Standard deviation of residuals: 2.77253
Output MCMC files:
'MCMC_tutorial.npz'
'MCMC_tutorial_trace.png'
'MCMC_tutorial_pairwise.png'
'MCMC_tutorial_posterior.png'
'MCMC_tutorial_RMS.png'
'MCMC_tutorial_model.png'
'MCMC_tutorial.log'
## Resume a Previous Run¶
It is also possible to add more samples to a previous run (identified by the .npz output file name). To do this, set the resume = True. Ideally, keep the same number of MCMC chains from the previous run to avoid any conflict with the shape of the posterior. This resumed run will append nsamples samples into the posterior output from the previous run (overwritting all output files).
## Inputs from Files¶
The data, uncert, indparams, params, pmin, pmax, stepsize, prior, priorlow, and priorup input arrays can be optionally be given as input file. Furthermore, multiple input arguments can be combined into a single file.
### Input Data File¶
The data, uncert, and indparams inputs can be provided as binary numpy .npz files. data and uncert can be stored together into a single file. An indparams input file contain the list of independent variables (must be a list, even if there is a single independent variable).
The utils sub-package of mc3 provide utility functions to save and load these files. This script shows how to create data and indparams input files:
import numpy as np
import mc3
# Create a synthetic dataset using a quadratic polynomial curve:
x = np.linspace(0.0, 10, 1000)
p0 = [3, -2.4, 0.5]
error = np.random.normal(0, uncert)
data = y + error
uncert = np.sqrt(np.abs(y))
# data.npz contains the data and uncertainty arrays:
mc3.utils.savebin([data, uncert], 'data.npz')
# indp.npz contains a list of variables:
mc3.utils.savebin([x], 'indp.npz')
### Model Parameters¶
The params, pmin, pmax, stepsize, prior, priorlow, and priorup inputs can be provided as plain ASCII files. For simplycity all of these input arguments can be combined into a single file.
In the params file, each line correspond to one model parameter, whereas each column correspond to one of the input array arguments. This input file can hold as few or as many of these argument arrays, as long as they are provided in that exact order. Empty or comment lines are allowed (and ignored by the reader). A valid params file look like this:
# params pmin pmax stepsize
10 -10 40 1.0
-2.0 -20 20 0.5
0.1 -10 10 0.1
Alternatively, the utils sub-package of mc3 provide utility functions to save and load these files:
params = [ 10, -2.0, 0.1]
pmin = [-10, -20, -10]
pmax = [ 40, 20, 10]
stepsize = [ 1, 0.5, 0.1]
# Store ASCII arrays:
mc3.utils.saveascii([params, pmin, pmax, stepsize], 'params.txt')
Then, to run the MCMC simply provide the input file names to the mc3 routine:
# Set arguments as the file names:
data = 'data.npz'
indparams = 'indp.npz'
params = 'params.txt'
# Run the MCMC:
mc3_output = mc3.sample(data=data, func=func, params=params,
indparams=indparams, sampler=sampler, nsamples=nsamples, nchains=nchains,
ncpu=ncpu, burnin=burnin, leastsq=leastsq, chisqscale=chisqscale,
grtest=grtest, grbreak=grbreak, grnmin=grnmin,
log=log, plots=plots, savefile=savefile, rms=rms) | 2021-12-03 09:51:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6194760799407959, "perplexity": 8738.16280322584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362619.23/warc/CC-MAIN-20211203091120-20211203121120-00346.warc.gz"} |
https://www.proofwiki.org/wiki/Definition:Two-Row_Notation | # Definition:Permutation on n Letters/Two-Row Notation
(Redirected from Definition:Two-Row Notation)
## Definition
Let $\pi$ be a permutation on $n$ letters.
The two-row notation for $\pi$ is written as two rows of elements of $\N_n$, as follows:
$\pi = \begin{pmatrix} 1 & 2 & 3 & \ldots & n \\ \map \pi 1 & \map \pi 2 & \map \pi 3 & \ldots & \map \pi n \end{pmatrix}$
The bottom row contains the effect of $\pi$ on the corresponding entries in the top row.
## Also defined as
Some sources use two-row notation to define mappings which are not necessarily permutations. However, this is rarely done because of its general unwieldiness.
## Also known as
Some sources refer to a presentation in two-row notation as a tableau.
Some sources use square brackets for the two-row notation:
$\pi = \begin{bmatrix} 1 & 2 & 3 & \ldots & n \\ \map \pi 1 & \map \pi 2 & \map \pi 3 & \ldots & \map \pi n \end{bmatrix}$
## Examples
### Permutations in $S_3$
The permutations on the symmetric group on $3$ letters $S_3$ can be depicted in two-row notation as:
$\begin{pmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 2 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \end{pmatrix}$
$\begin{pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{pmatrix}$
### Permutation in $S_4$
The permutation on the symmetric group on $4$ letters $S_4$ defined as:
$1 \mapsto 3, 2 \mapsto 2, 3 \mapsto 4, 4 \mapsto 1$
can be depicted in two-row notation as:
$\begin{pmatrix} 1 & 2 & 3 & 4 \\ 3 & 2 & 4 & 1 \end{pmatrix}$
## Technical Note
The $\LaTeX$ code for $\begin{pmatrix} a & b & c & d \\ d & b & c & a \end{pmatrix}$ is \begin{pmatrix} a & b & c & d \\ d & b & c & a \end{pmatrix} .
For a more compact presentation, the code:
\dbinom {a \ b \ c \ d} {d \ b \ c \ a}
can be used, which gives:
$\dbinom {a \ b \ c \ d} {d \ b \ c \ a}$
However, this technique does not work well when the width of the fields is non-uniform:
$\dbinom {m \ l \ l \ m} {m \ m \ l \ l}$ | 2022-12-08 12:04:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.989112138748169, "perplexity": 854.5740142821403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00044.warc.gz"} |
https://labs.tib.eu/arxiv/?author=Y.%20Penichot | • ### The STEREO Experiment(1804.09052)
April 24, 2018 hep-ex, physics.ins-det
The STEREO experiment is a very short baseline reactor antineutrino experiment aiming at testing the hypothesis of light sterile neutrinos as an explanation of the deficit of the observed neutrino interaction rate with respect to the predicted rate, known as the Reactor Antineutrino Anomaly. The detector center is located 10 m away from the compact, highly $^{235}$U enriched core of the research nuclear reactor of the Institut Laue Langevin in Grenoble, France. This paper describes the STEREO site, the detector components and associated shielding designed to suppress the external sources of background which were characterized on site. It reports the performances in terms of detector response and energy reconstruction.
• ### Development of $^{100}$Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search(1704.01758)
Oct. 4, 2017 nucl-ex, physics.ins-det
This paper reports on the development of a technology involving $^{100}$Mo-enriched scintillating bolometers, compatible with the goals of CUPID, a proposed next-generation bolometric experiment to search for neutrinoless double-beta decay. Large mass ($\sim$1~kg), high optical quality, radiopure $^{100}$Mo-containing zinc and lithium molybdate crystals have been produced and used to develop high performance single detector modules based on 0.2--0.4~kg scintillating bolometers. In particular, the energy resolution of the lithium molybdate detectors near the $Q$-value of the double-beta transition of $^{100}$Mo (3034~keV) is 4--6~keV FWHM. The rejection of the $\alpha$-induced dominant background above 2.6~MeV is better than 8$\sigma$. Less than 10~$\mu$Bq/kg activity of $^{232}$Th ($^{228}$Th) and $^{226}$Ra in the crystals is ensured by boule recrystallization. The potential of $^{100}$Mo-enriched scintillating bolometers to perform high sensitivity double-beta decay searches has been demonstrated with only 10~kg$\times$d exposure: the two neutrino double-beta decay half-life of $^{100}$Mo has been measured with the up-to-date highest accuracy as $T_{1/2}$ = [6.90 $\pm$ 0.15(stat.) $\pm$ 0.37(syst.)] $\times$ 10$^{18}$~yr. Both crystallization and detector technologies favor lithium molybdate, which has been selected for the ongoing construction of the CUPID-0/Mo demonstrator, containing several kg of $^{100}$Mo.
• ### Proceedings of the third French-Ukrainian workshop on the instrumentation developments for HEP(1512.07393)
Dec. 23, 2015 hep-ex, nucl-ex, physics.ins-det
The reports collected in these proceedings have been presented in the third French-Ukrainian workshop on the instrumentation developments for high-energy physics held at LAL, Orsay on October 15-16. The workshop was conducted in the scope of the IDEATE International Associated Laboratory (LIA). Joint developments between French and Ukrainian laboratories and universities as well as new proposals have been discussed. The main topics of the papers presented in the Proceedings are developments for accelerator and beam monitoring, detector developments, joint developments for large-scale high-energy and astroparticle physics projects, medical applications.
• This work is on the Physics of the B Factories. Part A of this book contains a brief description of the SLAC and KEK B Factories as well as their detectors, BaBar and Belle, and data taking related issues. Part B discusses tools and methods used by the experiments in order to obtain results. The results themselves can be found in Part C. Please note that version 3 on the archive is the auxiliary version of the Physics of the B Factories book. This uses the notation alpha, beta, gamma for the angles of the Unitarity Triangle. The nominal version uses the notation phi_1, phi_2 and phi_3. Please cite this work as Eur. Phys. J. C74 (2014) 3026.
• ### Scintillating bolometers based on ZnMoO$_4$ and Zn$^{100}$MoO$_4$ crystals to search for 0$\nu$2$\beta$ decay of $^{100}$Mo (LUMINEU project): first tests at the Modane Underground Laboratory(1502.01161)
Feb. 4, 2015 nucl-ex, physics.ins-det
The technology of scintillating bolometers based on zinc molybdate (ZnMoO$_4$) crystals is under development within the LUMINEU project to search for 0$\nu$2$\beta$ decay of $^{100}$Mo with the goal to set the basis for large scale experiments capable to explore the inverted hierarchy region of the neutrino mass pattern. Advanced ZnMoO$_4$ crystal scintillators with mass of $\sim$~0.3 kg were developed and Zn$^{100}$MoO$_4$ crystal from enriched $^{100}$Mo was produced for the first time by using the low-thermal-gradient Czochralski technique. One ZnMoO$_4$ scintillator and two samples (59 g and 63 g) cut from the enriched boule were tested aboveground at milli-Kelvin temperature as scintillating bolometers showing a high detection performance. The first results of the low background measurements with three ZnMoO$_4$ and two enriched detectors installed in the EDELWEISS set-up at the Modane Underground Laboratory (France) are presented.
• ### Purification of molybdenum oxide, growth and characterization of medium size zinc molybdate crystals for the LUMINEU program(1312.3515)
Dec. 12, 2013 nucl-ex, physics.ins-det
The LUMINEU program aims at performing a pilot experiment on neutrinoless double beta decay of 100Mo using radiopure ZnMoO4 crystals operated as scintillating bolometers. Growth of high quality radiopure crystals is a complex task, since there are no commercially available molybdenum compounds with the required levels of purity and radioactive contamination. This paper discusses approaches to purify molybdenum and synthesize compound for high quality radiopure ZnMoO4 crystal growth. A combination of a double sublimation (with addition of zinc molybdate) with subsequent recrystallization in aqueous solutions (using zinc molybdate as a collector) was used. Zinc molybdate crystals up to 1.5 kg were grown by the low-thermal-gradient Czochralski technique, their optical, luminescent, diamagnetic, thermal and bolometric properties were tested. | 2020-12-04 18:22:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5295071005821228, "perplexity": 5830.139297114286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141740670.93/warc/CC-MAIN-20201204162500-20201204192500-00596.warc.gz"} |
https://blog.nathantsoi.com/article/java-reversing-tips/ | Perhaps this post should be titled "Java un-reversing tips" since I'll start by assuming you've decompiled your .class files, modified the sources and are ready to get the modified jar running again.
A few things have to happen. First, you probably should have only de-compiled the single .java file you were interested in modifying. In my experience decompilers are far from perfect, so each file takes a bit of coercing before it will compile again.
The command you'll want to use to recompile that single file is something like:
javac -cp ../original.jar com/whatever/DecompiledAndModified.java
This will let DecompiledAndModified.java's dependencies resolve against the original.jar so you don't have to mess with more sources.
Assuming you've unzipped the jar somewhere (mkdir -p /tmp/original && cd /tmp/original && unzip original.jar), you'll want to remove any security checksums in the META-INF folder. There might be more than this, but here's a start:
rm META-INF/*.SF META-INF/*.RSA
echo 'Manifest-Version: 1.0' > META-INF/MANIFEST.MF
Copy the .class file output from the javac command above into the folder of unzipped sources, overwriting the original, and zip it all back up:
zip -r ../modified.jar *
Run it! | 2023-01-28 19:55:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6241168975830078, "perplexity": 9295.790788124767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499654.54/warc/CC-MAIN-20230128184907-20230128214907-00650.warc.gz"} |
https://en.wikibooks.org/wiki/Trigonometry/Law_of_Cosines | # Trigonometry/Law of Cosines
## Law of Cosines
The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines:[1]
$a^2+b^2-2ab\cos{\theta}=c^2, \,$
where θ is the angle between sides a and b.
### Does the formula make sense?
This formula had better agree with the Pythagorean Theorem when $\displaystyle \theta=90^\circ$.
So try it...
When $\displaystyle \theta=90^\circ$, $\displaystyle \cos\theta=\cos 90^\circ=0$
The $\displaystyle -2ab\cos\theta=0$ and the formula reduces to the usual Pythagorean theorem.
## Permutations
For any triangle with angles A, B, and C and corresponding opposite side lengths a, b, and c, the Law of Cosines states that
$a^2=b^2 + c^2 - 2bc \cdot\cos A,$
$b^2=a^2 + c^2 - 2ac \cdot\cos B,$
$c^2=a^2 + b^2 - 2ab \cdot\cos C.$
### Proof
Dropping a perpendicular OC from vertex C to intersect AB (or AB extended) at O splits this triangle into two right-angled triangles AOC and BOC, with altitude h from side c.
First we will find the lengths of the other two sides of triangle AOC in terms of known quantities, using triangle BOC.
h=a sin B
Side c is split into two segments, with total length c.
OB has length a cos B
AO has length c - a cos B
Now we can use the Pythagorean Theorem to find b, since b2 = AO2 + h2.
$\begin{matrix}b^2 & = & (c-a\cos B)^2+a^2\sin^2 B \\ \ &=& c^2-2ac\cos B +a^2\cos^2 B+a^2\sin^2 B\\ \ &=& a^2+c^2-2ac\cos B\end{matrix}$
The corresponding expressions for a and c can be proved similarly.
The formula can be rearranged:
$cos(C) = \frac{a^2+b^2-c^2}{2ab}$
and similarly for cos(A) and cos(B).
## Applications
This formula can be used to find the third side of a triangle if the other two sides and the angle between them are known. The rearranged formula can be used to find the angles of a triangle if all three sides are known. See Solving Triangles Given SAS.
## Notes
1. Lawrence S. Leff (2005-05-01). cited work. Barron's Educational Series. p. 326. ISBN 0764128922. | 2014-04-16 05:18:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8867365121841431, "perplexity": 731.5270742591179}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00356-ip-10-147-4-33.ec2.internal.warc.gz"} |
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# In the figure above, if AC = 18, what is the area of ∆ BCD?
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In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]
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In the figure above, if AC = 18, what is the area of ∆ BCD?
(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined
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Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]
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24 Aug 2017, 02:51
Bunuel wrote:
In the figure above, if AC = 18, what is the area of ∆ BCD?
(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined
Attachment:
2017-08-24_1249.png
$$AB = \sqrt{100-64} = \sqrt{36} = 6$$
Area of ABC = 1/2 * 6 * 18 = 54
Area of ABD = 1/2 * 6 * 8 = 24
Area of BCD = 54-24 = 30
B
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Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]
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24 Aug 2017, 05:00
AB^2 + 8^2 = 100
We get AB = 6
Area of triangle ABC - Area of triangle ABD = Area of triangle DBC
We get area = 30
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Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]
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24 Aug 2017, 05:10
In right angled ∆BAD, AB $$= \sqrt{100 - 64} = \sqrt{36} = 6$$
The area of the ∆BAC = $$\frac{1}{2} * AB * AC = \frac{1}{2} * 6 * 18 = 54$$
The triangles have the same height, but their bases are in the ratio $$9:4(18:8)$$
Hence, the areas of the two triangles also have to be in the same ratio.
So the area of the ∆BCD must be $$\frac{9-4}{9}*54 = 30$$(Option B)
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Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]
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24 Aug 2017, 13:09
Bunuel wrote:
In the figure above, if AC = 18, what is the area of ∆ BCD?
(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined
Attachment:
2017-08-24_1249.png
$$Area = \frac{b*h}{2}$$
The height AB of ∆ BCD is the short leg of a 3-4-5 triangle, ∆ ABD.
Sides here have ratio of 6: 8: 10 (multiplier is x = 2, so 3x is 3*2 = 6)
If you are given a right triangle, and two of the three sides correspond with the 3x: 4x: 5x ratio, by definition the third side also corresponds.
Base CD of ∆ BCD is 10
(18 - 8) = 10
$$\frac{(6 * 10)}{2}$$ = 30
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Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink]
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29 Aug 2017, 16:18
Bunuel wrote:
In the figure above, if AC = 18, what is the area of ∆ BCD?
(A) 15
(B) 30
(C) 54
(D) 60
(E) It cannot be determined
Since triangle ABD is a right triangle, we see that it’s a 6-8-10 right triangle with a height of 6. Thus, the area of triangle ABD is (8 x 6)/2 = 24.
Since triangle ABC is also a right triangle, the area of triangle ABC is [18 x 6]/2 = 54.
Since the area of triangle BCD is the difference between the areas of triangle ABC and triangle ABD, the area of triangle BCD is 54 - 24 = 30.
Alternate Solution:
We see that |DC| = |AC| - |AD| = 18 - 8 = 10. We also note that the height belonging to this base is the side AB, which is found to have a length of 6 from the ABD right triangle. Thus, the area of BCD is (10 x 6)/2 = 30.
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Re: In the figure above, if AC = 18, what is the area of ∆ BCD? [#permalink] 29 Aug 2017, 16:18
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# In the figure above, if AC = 18, what is the area of ∆ BCD?
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2019-05-23 07:29:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8326327204704285, "perplexity": 2575.09175953591}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257156.50/warc/CC-MAIN-20190523063645-20190523085645-00466.warc.gz"} |
http://math.stackexchange.com/questions/122033/is-this-a-subspace-of-mathbbr3?answertab=active | # Is this a subspace of $\mathbb{R}^3$?
$$\{(x,y,z)|2x+9y=0, 8x-5z=0\}$$
I solved these as simultaneous equations giving me the equation $36y + 5z = 0$ or $y=-\frac{5}{36}z$, which I can write as
$$\begin{bmatrix} -\frac{5}{36}z \\ z \\ \end{bmatrix} = 0.$$
Substituting $0$ for $z$ satisfies this equation. And it is closed multiplication and addition so this the original set is a subspace of $\mathbb{R}^3$. Is that method correct or am I completely off with this?
-
You forgot to write $x$ in terms of $z$. – lhf Mar 19 '12 at 11:29
After you solve $y = -\frac{5}{36}z$, you should substitute into the first equation to find a relationship with $x$:
\begin{align*} 2x + 9\left(-\frac{5}{36}z\right) &= 0 \\ 2x - \frac{5}{4}z &= 0 \\ x &= \frac{5}{8}z \end{align*}
This implies all vectors in the set can be written in the form: $$\left[\begin{array}{c} x \\ y \\ z \\ \end{array}\right] = \left[\begin{array}{c} \frac{5}{8}z \\ -\frac{5}{36}z \\ z \\ \end{array}\right] = \left[\begin{array}{c} \frac{5}{8} \\ -\frac{5}{36} \\ 1 \\ \end{array}\right]z$$
And this implies the set is a vector subspace of $\mathbb{R}^3$, since it can be written as the span of some number of vectors of $\mathbb{R}^3$.
There are other ways to analyze the set, but hopefully this method is closest to what you have already tried.
-
Let $V=\{(x,y,z)|2x+9y=0, 8x-5z=0\}$. To check that $V$ is a linear subspace of $\mathbb{R}^3$ we need to check $3$ things:
• $0=(0,0,0)\in V$,
• If $v\in V$ and $\lambda\in\mathbb{R}$, then $\lambda\cdot v \in V$, and
• If $v,w\in V$, then $v+w\in V$.
Let's show that these three conditions are satisfied:
• $0=(0,0,0)\in V$: Indeed $2\cdot 0 +9\cdot 0 = 0$ and $8\cdot 0 - 5\cdot 0 =0$, so $(0,0,0)\in V$.
• If $v\in V$ and $\lambda\in\mathbb{R}$, then $\lambda\cdot v \in V$: suppose $v=(x_0,y_0,z_0)$ and $v\in V$. Then, $2x_0+9y_0=0$ and $8x_0-5z_0=0$. Thus, $$2(\lambda x_0)+9(\lambda y_0) = \lambda (2x_0+9y_0)=\lambda(0)=0$$ and $$8(\lambda x_0)-5(\lambda z_0)= \lambda(8x_0-5z_0)=\lambda (0)=0.$$ Hence, $\lambda v = (\lambda x_0, \lambda y_0, \lambda z_0) \in V$ as well.
• If $v,w\in V$, then $v+w\in V$: let $v=(x_0,y_0,z_0)$ and $w=(x_1,y_1,z_1)$, and suppose $v,w\in V$. Then, $2x_0+9y_0=0$ and $8x_0-5z_0=0$, and $2x_1+9y_1=0$ and $8x_1-5z_1=0$. Hence: $$2(x_0+x_1)+9(y_0+y_1)= (2x_0+9y_0)+(2x_1+9y_1)=0+0=0$$ and $$8(x_0+y_0)-5(z_0+z_1)=(8x_0-5z_0)+(8x_1-5z_1)=0+0=0.$$ Hence $v+w\in V$ as well.
All three conditions are verified and therefore $V$ is a linear subspace of $\mathbb{R}^3$.
- | 2014-07-26 19:45:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995063543319702, "perplexity": 113.06139073407473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997904391.23/warc/CC-MAIN-20140722025824-00195-ip-10-33-131-23.ec2.internal.warc.gz"} |
http://tahirhassan.blogspot.com/2016/03/elisp-writing-and-evaluating-code.html | # Tahir Hassan's Blog
My Technical Notes
## Thursday, 17 March 2016
### ELisp: Writing and Evaluating Code
#### Using ielm Repl
You can start it by M-x ielm This will switch the current window to a new ielm buffer. This is a simple repl in which you can write statements and press enter.
#### Using a buffer (not ielm)
Within for example, the *scratch* buffer (or any other lisp buffer for that matter), we can write our code and evaluate it; evaluations are printed in the *Messages* buffer. If we have *scratch* and *Messages* buffers open in two separate windows, and we can evaluate the code in *scratch* and see the results immediately in *Messages*.
##### Keybindings for Evaluation
The following keybindings hold when we are in Lisp Interaction mode:
• C-x C-e our cursor must be after the close-paren of the expression we want to evaluate. The result populates the minibuffer and the *Messages* buffer.
• C-M-x will execute the "root" expression that we are currently in. Just like C-x C-e, it will populate the minibuffer and the *Messages* buffer.
• C-j our cursor must be after the close-paren. This will execute the expression and populate the *scratch* buffer. | 2018-01-23 09:31:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26908573508262634, "perplexity": 7567.387465533841}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891886.70/warc/CC-MAIN-20180123091931-20180123111931-00365.warc.gz"} |
https://tex.stackexchange.com/questions/116296/o-does-not-fit-standalone-class | # O does not fit standalone class [duplicate]
This question already has an answer here:
Why are the top and bottom of the O cut off when I use the standalone class without any larger symbols?
\documentclass{standalone}%
\begin{document}%
O%
\end{document}%
## marked as duplicate by Werner, Tim N, John Wickerson, Thorsten, Stefan Kottwitz♦May 27 '13 at 6:25
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
## 2 Answers
You can use the option [border=<size>] to change the margin.
\documentclass[border=2pt]{standalone}
\begin{document}
O
\end{document}
Aren't. Without 12pt and \Huge is also OK, but less visible.
\documentclass[12pt]{standalone}% \begin{document}% \Huge
O% \end{document}%
(Sorry that not as a comment, but i don't know, how to add a picture there). | 2019-05-25 21:27:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7444837689399719, "perplexity": 1808.3809367936506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232258451.88/warc/CC-MAIN-20190525204936-20190525230936-00480.warc.gz"} |
https://electronics.stackexchange.com/tags/bluetooth-low-energy/hot | # Tag Info
14
Here are most of the BLE chips I know: TI CC254x: old, well known, power efficiency is not great, extremely widely used. power: 27mA@any supply voltage, size: 6x6mm, price: $1.95. NOTE: no DC-DC converter on board. nRF51822: newer, excellent, good if a non-realtime MCU is needed, power: 8.0mA@3V, size: 3.5x3.8mm (more commonly 6x6mm), price:$1.92. nRF8001:...
12
BLE is very unsuitable for even medium bandwidth streaming (audio or video), because it is designed for transfer of few and small data packets with lots of sleeping time in between. This is why it is called 'low energy' and not 'low power' - it reduces the amount of picojoules per bit for small packets with respect to competing standards. Other standards ...
11
This smacks of a grounds-not-tied-together issue. It looks like the USB-to-UART device has only 2 lines going to the Pictail board. I would presume those are just the UART Tx and Rx lines, and not ground. If the grounds of all three boards are not tied together, digital signals between the boards will be interpreted incorrectly and will lead to undefined ...
10
There is another aspect to this that is being missed in the other answers. As per the Core BLE specification, only one advertising channel is being looked at during each scanInterval and is rotated to the next of 3 channels with each interval. So if there is RF interference on that channel you might not see the device even if you have the scanWindow equal ...
10
Bluetooth Basic Rate/Enhanced Data Rate (BR/EDR) is typically used for relatively short-range, continuous wireless connection such as streaming audio to headsets. Bluetooth low energy (LE) is designed to use short bursts of longer-range radio connection, making it ideal for Internet of Things (IoT) applications that don’t require continuous connection. ...
10
The goal of this rather long analysis is to ensure you look like the sharpest RF dude your company has ever hired :) The free space path loss range of a an RF system can be calculated. For a typical class 2 Bluetooth system, assuming +4dBm of transmit power, -70dBm receiver, & unity gain antennas, you will find that the range that gives you 74 dB of ...
10
Use a second DIO to control the pull-up voltage. The output is normally low. Set it high momentarily, read the DIO input, set the output low. simulate this circuit – Schematic created using CircuitLab
8
Well, with 100kbps, you may be able to stream a low quality video the size of a post stamp :-) Without any precision, I will imagine you want HD (not even full HD) @30fps in H264, with average motion (factor 2), an approximate bitrate estimation could be : (1280px*720px)*30fps*2*0.07 ~= 3800kbps So you have to reduce this by a factor 38 (at least !). Say ...
8
They're not the same thing From the Wikipedia article on the Bluetooth specifications: [Bluetooth Core Specification version 4.0] includes Classic Bluetooth, Bluetooth high speed and Bluetooth low energy protocols. Getting a Bluetooth LE device or chip does not mean it will work with Bluetooth Classic. From the Bluetooth LE Wikipedia page: The ...
8
The question has been studied extensively. According to this lecture, at 2.4GHz (microwave frequency as well) the 1/e (63% loss) occurs in 1.4cm. You probably can do better with 9600 baud UART. :-(
7
Consumer Devices Android Samsung phones[specify] HTC phones[specify] Android 4.3 (API level 18) comes with an official Bluetooth Low Energy API. In older versions, BLE was not integrated into the Android API so each manufacturer had/has their own API. Apple iOS iPhone 4S, 5+ iPad 3g, 4g, mini iPod Touch 5g, Nano 7g OS X MacBook Air (Mid 2011/Model 4,x+)...
7
TL;DR version -- if you are trying to do this for just one chip and just yourself (i.e. not a product), it's probably not worth it since you'll need to spend at least \$50 for a programmer. The CC2541 is a combination of a BLE radio and 8051 with either 256K or 128K flash, and 8K of RAM. It has 23 GPIO pins, some of which can be re-purposed as I²C, SPI, ...
6
I assume you have a small beacon PCB that you haven't designed yourself, so you need to work with it as-is. if you're laying out the board, you have more options... 1. Restricting the area covered by a beacon You're onto the right track here - mounting it above the supermarket aisle, or what have you, is probably best, then you can focus the signal into a ...
6
Since this is RF IC, following schematic won't be enough. When building circuits the first time, it's always recommended to follow design guide/ reference schematic as much as you can. That will be a huge step forward to making your circuit work. Since this is RF stuff, you need to go a step further. Being familiar how to interface antenna and which ...
6
Obviously nobody can answer this since we have no idea what your soldering capabilities are, and what equipment is available. Actually think about it. As for whether it is generally possible or advisable, no, not in the general case. Some "modules" are specifically designed to be mounted on another PCB. In that case, yes, it's obviously possible for ...
5
I propose you use a nordic nRF51822 chip that includes the temperature information in advertisement data with an advertisement period of 1 to 2 seconds. Use connectable undirected advertisements. If something wishes to connect to the temperature monitor, implement an appropriate temperature characteristic. Bluetooth SIG Temperature measurement ...
5
Because that is the FCC limit for Class II Bluetooth (10 meter range) transmitters. The FCC determined that 4 dBm was adequate to support the range, and more would increase interference with other stations.
5
Beacon and sensor are terms used in short range networks used for position or presence location systems. BLE - Blue Tooth Low Power - systems are frequently used for this purpose as they interface with Bluetooth systems present in most "smart phones" and the low power consumption of BLE allows long battery life as nodes. The following is BLE focused as this ...
5
The module already includes a microcontroller. The website you linked to says: The on-chip processor has sufficient space for many applications, so a carrier board may only include sensors and a battery. The module is based on a Nordic nRF52832 chip that has an ARM Cortex-M4F, which includes 512Kbytes of flash memory and 64Kbytes of RAM. You'll need to ...
5
I just want to know on what the BLE range depends on other than the following : just from the top of my head (and assuming BLE doesn't use MIMO): Antennas (not all antennas are equally efficient at converting current to radio waves or vice versa. Also, antennas work better in one spatial direction than into others) transmission losses and mismatch losses ...
5
Use 2 GPIOs (we'll call them GPIO 1 and 2) to monitor the switch, and test for switch closure by checking for continuity. This works as follows: Wake up the CPU set GPIO 1 high, check GPIO 2 state set GPIO 1 low, check GPIO 2 state If GPIO2 followed GPIO1, then the switch was closed. If not, no. This improves on pull-up or pull-down since there's no ...
4
The advertisement packet your beacons send can contain custom data. However the space is very limited, around 31 bytes. About 16bytes of it goes to the 128bit "service UUID" of your beacon. The structure of the packet is defined by the bluetooth spec and it does have some overhead, so I'm not sure how much is actually available for the custom data. The ...
4
Take a look at my answer here about low power radios: Low-power wireless module strategy The core problem is that BOTH receive and transmit typically take on the order of 10mA to 30mA for integrated radios. Therefore to get average power down you must use some kind of radio duty ratioing technique (there are many). As an example, ContikiMAC can route ...
4
Your main concern with any wireless module on a low-performance power supply is to design in very heavy decoupling. Coin cells in particular - excluding recheargable lithium ion type (which are very rare) - have internal resistance up to about 100 ohms, so you will not be able to draw more than a couple of milliamps from them. As your BLE113 module is ...
4
If you look at the block diagram on page 20 of your linked datasheet, you'll see that all of the I/O, including the USARTs, go to the 8051 controller. The 8051, in turn, is the only path to the Bluetooth radio section. Therefore, I'd say that the internal microcontroller is required for the module to function.
4
It looks very feasible although you will need to mount the chip onto a breakout board yourself and considering it is only offered in a QFN or BGA package, you will probably need hot air rework or some sort of reflow oven. QFN to DIP breakout boards are very simple and can readily available on eBay or some electronics store like Sparkfun. You will need a ...
4
I don't want to sound negative, but this is a bare chip, that must be interfaced to a (possible on-PCB) antenna. This is highly specialized work, I would not touch it myself. Since you ask here about the much much easier task of connecting the uC part of that chip, I think this is way over your head. If you want to make large quantities of your product, ...
4
This falls under the topic of "permissive changes". The FCC has a document called PERMISSIVE CHANGE POLICY which outlines what can or cannot be changed without requiring a new FCC ID. Under section 2 c). it says, "Part substitution – electrically identical parts may be substituted." I would assume that the two batteries are the same voltage, but perhaps ...
4
It's a bandpass filter. The crossed out waves tell you that frequencies above and below the passband are rejected. The legend says the passband is centred on 2.45GHz. It's not part of the chip, but an external component. The schematic tells you nothing more about it, such as bandwidth, insertion loss, stopband attenuation, etc. Hopefully the text has more ...
4
First, referring to your existing design, the important thing about a PCB antenna is to have no ground plane under the entire antenna, and to follow the layout shown in TI's application note exactly. It's not a bad idea to include the Pi network, it may be useful for during RF testing. You should be able to continue the 50 ohm feed for a little ways, as ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2020-10-30 11:18:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2987581789493561, "perplexity": 2140.305233418072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107910204.90/warc/CC-MAIN-20201030093118-20201030123118-00524.warc.gz"} |
http://libros.duhnnae.com/2017/sep3/150540828780-Hydrodynamical-simulations-of-galaxy-clusters-in-dark-energy-cosmologies-I-general-properties-Astrophysics-Cosmology-and-Nongalactic-Astrophysic.php | # Hydrodynamical simulations of galaxy clusters in dark energy cosmologies: I. general properties - Astrophysics > Cosmology and Nongalactic Astrophysics
Hydrodynamical simulations of galaxy clusters in dark energy cosmologies: I. general properties - Astrophysics > Cosmology and Nongalactic Astrophysics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Abstract: We investigate the influence of dark energy on structure formation, withinfive different cosmological models, namely a concordance $\Lambda$CDM model,two models with dynamical dark energy, viewed as a quintessence scalar fieldusing a RP and a SUGRA potential form and two extended quintessence modelsEQp and EQn where the quintessence scalar field interacts non-minimally withgravity scalar-tensor theories. We adopted for all models the normalizationof the matter power spectrum $\sigma {8}$ to match the CMB data. In the modelswith dynamical dark energy and quintessence, we describe the equation of statewith $w 0\approx-0.9$, still within the range allowed by observations. For eachmodel, we have performed hydrodynamical simulations in a cosmological box of$300 \ { m{Mpc}} \ h^{-1}^{3}$ including baryons and allowing for coolingand star formation. The contemporary presence of evolving dark energy andbaryon physics allows us to investigate the interplay between the differentbackground cosmology and the evolution of the luminous matter. Since clusterbaryon fraction can be used to constrain other cosmological parameters such as$\Omega {m}$, we also analyse how dark energy influences the baryon content ofgalaxy clusters. We find that, in models with dynamical dark energy, theevolving cosmological background leads to different star formation rates anddifferent formation histories of galaxy clusters, but the baryon physics is notaffected in a relevant way. We investigate several proxies of the cluster massfunction based on X-ray observables like temperature, luminosity, $M {gas}$,and $Y {gas}$. We conclude that the X-ray temperature and $M {gas}$ functionsare better diagnostic to disentangle the growth of structures among differentdark energy models. Abridged
Autor: Cristiano De Boni, Klaus Dolag, Stefano Ettori, Lauro Moscardini, Valeria Pettorino, Carlo Baccigalupi
Fuente: https://arxiv.org/ | 2018-01-19 07:38:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5392682552337646, "perplexity": 6598.6336679392425}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00611.warc.gz"} |
https://evolution-resources.com/cfs-charges-nkjro/area-of-quadrilateral-a6e254 | Depending on the length of the sides and measure of the angle there are seven types of quadrilaterals: Square⦠1. Example: Find the a cm . Consider a quadrilateral whose sides are given by the vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$, such that $\vec{a}+\vec{b}+\vec{c}+\vec{d}=0$.. Scoring a Q50-51 on the GMAT helps you get a 700+ GMAT score. And then finally, this is a 3 by 4 rectangle. Represent the sides of the quadrilateral by the vectors , , , and arranged such that and the diagonals by the vectors and arranged so that and . Rectangle. Square: A quadrilateral with four congruent sides and four right angles; a square is both a rhombus and a rectangle. Area of B = ½b × h = ½ × 20m × 14m = 140m 2. A worksheet, 2 pages, covering the area of parallelograms, then the area of trapezia. In the figure above, if you drag a point past its neighbor the quadrilateral ⦠The area of quadrilaterals worksheets with answers is a complete practice package for 6th grade, 7th grade, and 8th grade children. Read it or download it for free. Note how the semi-perimeter (p) and the area are calculated. Calculating area (in square units) for a square and rectangle is easy: A = Width x Length (W x L), which for a square means the same thing as W^2. Area of Quadrilaterals Worksheets. The general formula of the area of a quadrilateral is base * height, also written as b*h and the unit of measurement is m 2.There are two types of quadrilaterals - regular and irregular. Area of a Quadrilateral. The sum of interior angles in a quadrilateral is 360°. Choose the number of decimal ⦠So it has a total area of 27. A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides. Solving Area of irregular quadrilateral. This is a particular case of Bretschneider's formula (we know that sum of two opposite angles are 180), known as Brahmagupta's formula, where s - semiperimeter. Side of polygon given area. Area of a quadrilateral. Types of Quadrilateral The following types of quadrilateral are (1) Square ⦠1/2 ab sin(θ) = (1/2)(3)(12)sin(120) â 15.6 Great! Area of a cyclic quadrilateral. Thus, if the diagonals of a quadrilateral are perpendicular, its area is given by half of the product of its diagonal lengths. Area of a parallelogram given sides and angle. Area ⦠The sum of the internal angles of the quadrilateral is 360 degree. The standard unit of area in the International System of Units (SI) is the square meter, or m 2. A quadrilateral has: four sides (edges) four vertices (corners) interior angles that add to 360 degrees: Try drawing a quadrilateral, ⦠Use our sample 'Area of a Trapezoid Diagram.' Then (3) (4) where is the determinant and is a two-dimensional cross product. Again, try to prove this in both an algebraic and a geometric way. Can you prove that the areas of these two red quadrilaterals sum to the area of the yellow square? There is an arithmetic starter included as well as a number of questions to work through (including pink and green bubbles for support and challenge) where answers can then be discussed. We are providing you with the quadrilateral area, formula, types and its properties along with the solved questions. 4. If you have a square with sides 17 cm long, the area is 289 square cm. Notice that in our irregular quadrilateral, we can find the area of triangle ABC using the SAS method with a = 3, b = 12, and θ = 120 degrees. Square formula â Area and perimeter of a square. Practice Questions. For this, you can use the calculator above by entering arbitrary angles whose sum ⦠If you have a rectangle with two sides 17 cm and two sides 34 cm, the area is 17 x ⦠Area of a parallelogram given base and height. But it has 12 of those unit square, so it has an area of 12. 'Crossed' polygons. Area of a regular polygon. Featured here are exercises to identify the type and use appropriate formulas to find the area of quadrilaterals like rectangles, rhombus, trapezoids, parallelograms and kites, with dimensions ⦠Area of a quadrilateral given four sides and the fact that it is a cyclic quadrilateral. I'm told that the area of the quadrilateral can be calculated by half of the determinant of the matrix with columns given by the diagonals of the quadrilateral. Area of the quadrilateral is the region enclosed by the four sides of this polygon. Let's break the area into two parts: Part A is a square: Area of A = a 2 = 20m × 20m = 400m 2. Prove that the areas of these two red quadrilaterals sum to the area of quadrilaterals: Square⦠quadrilateral Calculator agree. Diagram. the area of any irregular quadrilateral area of quadrilateral quadrangle, you can find three formulas... A base of 20m and a geometric way between them, β and γ of quadrilaterals: Square⦠quadrilateral.! Number of decimal ⦠Use our sample 'Area of a quadrilateral is 360°, rectangle parallelogram... The properties of quadrilaterals Worksheets calculation is done by fragmenting the quadrilateral ABCD into two triangles just all... ¦ a quadrilateral as a quadrilateral is 360 degree so 2.5 plus 2.5 5! Helps you get the area of quadrilaterals, the opposite corners is called its diagonal θ =... ) sin ( θ ) = ( 1/2 ) ( 12 ) sin ( θ ) (! Need to know two of the quadrilateral in to two triangles ABC and ACD helps you get a GMAT! A complete practice package for 6th grade, and four angles them square... That has four sides in it a ⦠square area of quadrilateral â area and perimeter a! Quadrilateral area by own diagonal AC, we just add all of these two red quadrilaterals sum to area... Know two of the most common simple shapes, and 8th grade.! Perimeter of a square is pressed from two opposite corners is called diagonal! A negative value, take it as positive two red quadrilaterals sum to area! 289 square cm irregular quadrilateral or quadrangle, then considering the diagonal AC, we always the. Is done by fragmenting the quadrilateral is never negative area formulae rectangle is a quadrilateral never. All four sides of this problem be inscribed in it touching all four sides is known as a.! This is a closed figure that has four sides, then a+c=b+d area of quadrilateral 80 x 70 x Sin60 sides..., convex quadrilateral or irregular rectangle is shown instantly by clicking calculate button Latest... Bc sin = 80 x 70 x Sin60 1 ) square ⦠area of.! Our Cookie Policy h = ½ × 20m × 14m = area of quadrilateral 2 and is quadrilateral! The yellow square the yellow square that it is a complete practice for! Using the formula below, you can find three different formulas to calculate is. Be classified into different types some of them are square, so it has area..., how to calculate the area of a + area of quadrilaterals Worksheets with answers is cyclic! Ab sin ( 120 ) â 15.6 Great are equations for some quadrilaterals, we to! Sides equal with unequal diagonal, which can be of different types some of the angle are... = ( 1/2 ) ( 3 ) ( 12 ) sin ( θ ) = 4849 sq the. Known as a negative value, take it as positive four sides, four,. We want to find the total area is: area = bc sin 80. Of different types some of them are square, rectangle, parallelogram, rhombus and trapezoid 2. Clicking calculate button area of a quadrilateral is circumcyclic, i.e diagonal AC, just! Opposite corners is called its diagonal in it sideways it has an of! By four sides and measure of the basic area formulae then considering the diagonal AC, we need know! The opposite corners the rhombus is a closed figure that has four sides and measure of quadrilateral! The first three lengths a, B and c and the area of the two from... Four sides, then considering the diagonal divides the quadrilateral in to two triangles ABC and ACD 3! Quadrilateral with four right angles take it as positive you have a square is pressed two. Calculate button then considering the diagonal divides the quadrilateral ABCD into two triangles and... Considering the diagonal divides the quadrilateral ABCD into two triangles ABC and.! B and c and the fact that it is a two-dimensional cross product area is: =. Is shown instantly by clicking calculate button by noting that the areas of together... Two opposite corners is called its diagonal for SSC CGL Tier 2 Study material ) ( 4 where... General, convex quadrilateral or quadrangle to our Cookie Policy = ½ 20m... The sum of the quadrilateral for 6th grade, 7th grade, and four angles never negative of Maths here! The diagonal AC, we just add all of these together area of quadrilateral are for! Closed figure that has four sides is known as a quadrilateral with four right.! Angle there are a ⦠square formula â area and perimeter of a square with sides cm., and four angles be of different types some of them are square, rectangle, parallelogram rhombus... 1/2 ab sin ( 120 ) â 15.6 Great is 360° 3 by rectangle... That is, we just add all of these two red quadrilaterals sum to the of! Region enclosed by the four sides, then considering the diagonal AC we. Properties of area of quadrilateral to calculate the area of B = ½b × h = ½ × 20m × 14m 140m. Again, try to prove this in both an algebraic and a geometric way to know two of the area! For 6th grade, and 8th grade children closed figure that has sides., area of quadrilateral can calculate the area of any irregular quadrilateral or quadrangle AC, always! Tier 2 Study material this polygon 2 Study material our Cookie Policy finally, this easily... Following types of quadrilateral 11.1 quadrilateral a plane figure bounded by four sides of this polygon Free Latest Pattern of! Formula â area and perimeter area of quadrilateral a quadrilateral with four right angles ) properties region... Is circumcyclic, i.e the areas of these two red quadrilaterals sum to the area are.! Corners the rhombus is a complete practice package for 6th grade, and 8th grade.. ) properties in both an algebraic and a geometric way both an algebraic and a height of.! This polygon × 14m = 140m 2 p ) and the two angles between them, and! Don Steward, whose ideas formed the basis of this problem number of decimal Use! And 8th grade children ( also see this on Interactive quadrilaterals ) properties rectangle, parallelogram, and... And perimeter of a trapezoid Diagram. the unit squares in here degree!, which bisect each other quadrilaterals ) properties of this problem to prove in! 5, plus 4 is 9, plus 4 is 9, 4! Of 20m and a geometric way ideas formed the basis of this problem tangents a! ( 1 ) square ⦠area of B = 400m 2 + 140m 2 = 540m 2 equal unequal. And you could even count the unit squares in here a, B c! This in both an algebraic and a height of 14m fact and the properties of quadrilaterals to the. Area ⦠a quadrilateral given four sides of this problem to calculate area is area... Q50-51 on the length of the quadrilateral ABCD into two triangles ABC and ACD 4.. Properties of quadrilaterals Worksheets area and perimeter of a quadrilateral as positive in here angles in a quadrilateral given sides... Free notes of Maths click here for Free Latest Pattern Questions of Maths... Corners is called its diagonal by 4 rectangle website, you can find three formulas... Know two of the quadrilateral is 360 degree = bc sin = x... Are ( 1 ) square ⦠area of a square is pressed from opposite! Unit squares in here is: area = bc sin = 80 x 70 x Sin60 convex... Get a 700+ GMAT score could even count the unit squares in here is known as a.... Is 27 types some of the two tangents from a point to a circle are equal in length to. And measure of the yellow square every input combination of irregular quadrilateral can be classified into different some. Also see this on Interactive quadrilaterals ) properties are parallel and opposite angles are equal 2! Of Arithmetic Maths get Free notes of Maths click here for SSC CGL 2! Steward, whose ideas formed the basis of this polygon region enclosed by the four sides then! Types some of the angle there are seven types of quadrilateral 11.1 quadrilateral a plane figure by! Want to find the total area, we just add all of these.... Area, we always take the area of 12 of B = ½b × h ½. Area and perimeter of a quadrilateral as a negative value, take as... Of decimal ⦠Use our sample 'Area of a trapezoid Diagram. quadrilaterals, we always take the are. Fact that it is a 3 by 4 rectangle this problem length of the two between... Opposite corners the rhombus is a complete practice package for 6th grade, 7th grade, grade... The formula below, you can calculate the area of each is calculated Great... 289 square cm four vertices, and four angles each other with unequal diagonal, which can be used calculate! It as positive, B and c and the two angles between them, β and γ degree., take it as positive thanks to Don Steward, whose ideas formed basis! Different formulas to calculate area is 289 square cm with thanks to Don Steward, whose formed. Free area of quadrilateral of Maths click here for SSC CGL Tier 2 Study material to find the total area is.... | 2022-10-05 03:00:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6766583323478699, "perplexity": 958.951053903145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337531.3/warc/CC-MAIN-20221005011205-20221005041205-00308.warc.gz"} |
https://vincentarelbundock.github.io/modelsummary/reference/datasummary_balance.html | Balance table: Summary statistics for different subsets of the data (e.g., control and treatment groups)
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)
## Arguments
formula a one-sided formula with the "condition" or "column" variable on the right-hand side. A data.frame (or tibble). If this data includes columns called "blocks", "clusters", and/or "weights", the "estimatr" package will consider them when calculating the difference in means. If there is a weights column, the reported mean and standard errors will also be weighted. filename or object type (character string) Supported filename extensions: .html, .tex, .md, .txt, .png, .jpg. Supported object types: "default", "html", "markdown", "latex", "latex_tabular", "data.frame", "modelsummary_list", "gt", "kableExtra", "huxtable", "flextable", "jupyter". Warning: Users should not supply a file name to the output argument if they intend to customize the table with external packages. See the 'Details' section. LaTeX compilation requires the booktabs and siunitx packages, but siunitx can be disabled or replaced with global options. See the 'Details' section. The default output formats and table-making packages can be modified with global options. See the 'Details' section. determines how to format numeric values integer: the number of digits to keep after the period format(round(x, fmt), nsmall=fmt) character: passed to the sprintf function (e.g., '%.3f' keeps 3 digits with trailing zero). See ?sprintf function: returns a formatted character string. Note on LaTeX formatting: To ensure proper typography, all numeric entries are enclosed in the \num{} command from the siunitx LaTeX package by default. This behavior can be altered with global options. See the 'Details' section. string list or vector of notes to append to the bottom of the table. A string with a number of characters equal to the number of columns in the table (e.g., align = "lcc"). Valid characters: l, c, r, S. "l": left-aligned column "c": centered column "r": right-aligned column "d": dot-aligned column. Only supported for LaTeX/PDF tables produced by kableExtra. These commands must appear in the LaTeX preamble (they are added automatically when compiling Rmarkdown documents to PDF): \usepackage{booktabs} \usepackage{siunitx} \newcolumntype{d}{S[input-symbols = ()]} a data.frame (or tibble) with the same number of rows as your main table. a data.frame (or tibble) with the same number of columns as your main table. By default, rows are appended to the bottom of the table. You can define a "position" attribute of integers to set the row positions. See Examples section below. TRUE calculates a difference in means with uncertainty estimates. This option is only available if the estimatr package is installed. If data includes columns named "blocks", "clusters", or "weights", this information will be taken into account automatically by estimatr::difference_in_means. string: "std.error" or "p.value" boolean TRUE escapes or substitutes LaTeX/HTML characters which could prevent the file from compiling/displaying. This setting does not affect captions or notes. all other arguments are passed through to the extractor and table-making functions. This allows users to pass arguments directly to modelsummary in order to affect the behavior of other functions behind the scenes. Examples include: broom::tidy(exponentiate=TRUE) to exponentiate logistic regression. Please see the modelsummary vignette on the package website for important technical notes on this topic. performance::model_performance(metrics="RMSE") to select goodness-of-fit statistics to extract using the performance package (must have set options(modelsummary_get="easystats") first).
## Global Options
The behavior of modelsummary can be affected by setting global options:
• modelsummary_factory_default
• modelsummary_factory_latex
• modelsummary_factory_html
• modelsummary_factory_png
• modelsummary_get
• modelsummary_format_numeric_latex
• modelsummary_format_numeric_html
### Table-making packages
modelsummary supports 4 table-making packages: kableExtra, gt, flextable, and huxtable. Some of these packages have overlapping functionalities. For example, 3 of those packages can export to LaTeX. To change the default backend used for a specific file format, you can use the options function:
options(modelsummary_factory_html = 'kableExtra') options(modelsummary_factory_latex = 'gt') options(modelsummary_factory_word = 'huxtable') options(modelsummary_factory_png = 'gt')
### Model extraction functions
modelsummary can use two sets of packages to extract information from statistical models: broom and the easystats family (performance and parameters). By default, it uses broom first and easystats as a fallback if broom fails. You can change the order of priorities or include goodness-of-fit extracted by both packages by setting:
options(modelsummary_get = "broom") options(modelsummary_get = "easystats") options(modelsummary_get = "all")
### Formatting numeric entries
By default, LaTeX tables enclose all numeric entries in the \num{} command from the siunitx package. To prevent this behavior, or to enclose numbers in dollar signs (for LaTeX math mode), users can call:
options(modelsummary_format_numeric_latex = "plain") options(modelsummary_format_numeric_latex = "mathmode")
A similar option can be used to display numerical entries using MathJax in HTML tables:
options(modelsummary_format_numeric_html = "mathjax")
## Examples
if (FALSE) {
datasummary_balance(~am, mtcars)
} | 2021-10-18 12:49:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5277428030967712, "perplexity": 8365.855635849935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585203.61/warc/CC-MAIN-20211018124412-20211018154412-00205.warc.gz"} |
https://deepai.org/publication/multi-resolution-approximations-of-gaussian-processes-for-large-spatial-datasets | # Multi-resolution approximations of Gaussian processes for large spatial datasets
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple resolutions to achieve fast inference and that can (approximately) represent any covariance structure. We consider two special cases of this multi-resolution-approximation framework, a taper version and a domain-partitioning (block) version. We describe theoretical properties and inference procedures, and study the computational complexity of the methods. Numerical comparisons and an application to satellite data are also provided.
## Authors
• 15 publications
• 3 publications
08/21/2017
### A general framework for Vecchia approximations of Gaussian processes
Gaussian processes (GPs) are commonly used as models for functions, time...
06/15/2016
### Understanding Probabilistic Sparse Gaussian Process Approximations
Good sparse approximations are essential for practical inference in Gaus...
01/29/2020
### Convergence Guarantees for Gaussian Process Approximations Under Several Observation Models
Gaussian processes are ubiquitous in statistical analysis, machine learn...
05/20/2019
### Gaussian Process Learning via Fisher Scoring of Vecchia's Approximation
We derive a single pass algorithm for computing the gradient and Fisher ...
07/03/2020
### Karhunen-Loève Expansions for Axially Symmetric Gaussian Processes: Modeling Strategies and L^2 Approximations
Axially symmetric processes on spheres, for which the second-order depen...
06/30/2020
### Spatiotemporal Multi-Resolution Approximations for Analyzing Global Environmental Data
Technological developments and open data policies have made large, globa...
04/03/2020
### Faster Gaussian Processes via Deep Embeddings
Gaussian processes provide a probabilistic framework for quantifying unc...
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## 1 Introduction
Gaussian processes (GPs) are highly popular models for spatial data, time series, and functions. They are flexible and allow natural uncertainty quantification, but their computational complexity is cubic in the data size. This prohibits GPs from being used directly for the analysis of many modern datasets consisting of a large number of observations, such as satellite remote-sensing data.
Consequently, many approximations or assumptions have been proposed that allow the application of GPs to large spatial datasets. Some of these approaches are most appropriate for capturing fine-scale structure (e.g., Furrer et al., 2006; Kaufman et al., 2008), while others are more capable at capturing large-scale structure (e.g., Higdon, 1998; Mardia et al., 1998; Wikle and Cressie, 1999; Cressie and Johannesson, 2008; Katzfuss and Cressie, 2009, 2011, 2012). Lindgren et al. (2011)
proposed an approximation based on viewing a GP with Matérn covariance as the solution to the corresponding stochastic partial differential equation. Vecchia’s method and its extensions
(e.g., Vecchia, 1988; Stein et al., 2004; Datta et al., 2016; Katzfuss and Guinness, 2017) are discontinuous and assume the so-called screening effect to hold, meaning that any given observation is conditionally independent from other observations given a small subset of (typically, nearby) observations.
We propose here a class of multi-resolution-approximation (-RA) of GPs, which allows capturing spatial structure at all scales. The -RA framework is based on an orthogonal decomposition of the GP of interest into processes at multiple resolutions by iteratively applying the predictive process (Quiñonero-Candela and Rasmussen, 2005; Banerjee et al., 2008). The process at each resolution has an equivalent representation as a weighted sum of spatial basis functions. For increasing resolution, the number of functions increases while their scale decreases. Unlike other multi-resolution models or wavelets (e.g. Chui, 1992; Johannesson et al., 2007; Cressie and Johannesson, 2008; Nychka et al., 2015), our -RA automatically specifies the basis functions and the prior distributions of their weights to adapt to the given covariance function of interest, without requiring any restrictions on this covariance function. Thus, in contrast to other approaches, it is clear which covariance structure is approximated by the sum of basis functions in the -RA.
To achieve computational feasibility within the -RA framework, an approximation of the “remainder process” at each resolution using so-called modulating functions is necessary. We consider two special cases: For the -RA taper, the modulating functions are taken to be tapering functions (i.e., compactly supported correlation functions). For increasing resolution, the remainder process is approximated with increasingly restrictive tapering functions, leading to increasingly sparse matrices. In contrast, the -RA-block iteratively splits each region at each resolution into a set of subregions, with the remainder process assumed to be independent between these subregions. This can lead to discontinuities at the region boundaries. A special case of the -RA-block (Katzfuss, 2017) performed very well in a recent comparison of different methods for large spatial data (Heaton et al., 2017). A further special case of the -RA with only one resolution is given by the full-scale approximation (Snelson and Ghahramani, 2007; Sang et al., 2011; Sang and Huang, 2012).
The -RA is suitable for inference based on large numbers of observations from a GP, which may be irregularly spaced. We will describe inference procedures that rely on operations on sparse matrices for computational feasibility. The -RA-block can deal with massive datasets with tens of millions of observations or more, as it amenable to parallel computations on modern distributed computing systems. It can be viewed as a Vecchia-type approximation (Katzfuss and Guinness, 2017), and the approximated covariance matrix is a so-called hierarchical off-diagonal low-rank matrix (e.g., Ambikasaran et al., 2016). The -RA-taper leads to more general sparse matrices, and thus requires more careful algorithms to fully exploit the sparsity structure, but it has the advantage of not introducing artificial discontinuities.
Relative to the -RA-block in Katzfuss (2017), the contributions of our paper are the following: We introduce a general framework for -RAs that provides a new, intuitive perspective on this approach. This allows an extension of the -RA-block of Katzfuss (2017) that removes the requirement that knots at the finest resolution correspond to the observed locations, and it enables us to introduce a novel -RA-taper approach that extends the ideas of Sang and Huang (2012) to more than one resolution. We provide more insights about the theoretical and computational properties of both versions of the -RA. We also include further implementation details and numerical comparisons.
This article is organized as follows. In Section 2, we first describe an exact orthogonal multi-resolution decomposition of a GP, which then leads to the -RA framework and the two special cases described above by applying the appropriate modulating functions. We also study their theoretical properties. In Section 3, we discuss the algorithms necessary for statistical inference using the -RA and provide details of the computational complexity. Numerical comparisons on simulated and real data are given in Sections 4 and 5, respectively. We conclude in Section 6. All proofs can be found in Appendix A. Additional simulation results can be found in a separate Supplementary Material document. All code will be provided upon publication.
## 2 Multi-resolution approximations
### 2.1 The true Gaussian process
Let , or , be the true spatial field or process of interest on a continuous (non-gridded) domain , . We assume that is a zero-mean Gaussian process with covariance function . We place no restrictions on
, other than assuming that it is a positive-definite function that is known up to a vector of parameters,
. In real applications,
will often not have mean zero, but estimating and subtracting the mean is usually not a computational problem. Once
has been observed at a set of spatial locations , the basic goal of spatial statistics is to make (likelihood-based) inference on the parameters and to obtain spatial predictions of at a set of locations (i.e., to obtain the posterior distribution of ). Direct computation based on the Cholesky decomposition of the resulting covariance matrix requires time and memory complexity, which is computationally infeasible when .
### 2.2 Preliminaries
A multi-resolution approximation with resolutions (-RA) requires two main “ingredients”: knots and modulating functions. The multi-resolutional set of knots, , is chosen such that, for all , , is a set of knots, with . We assume that the number of knots increases with resolution (i.e., ). An illustration of such a set of knots in a simple toy example is given in Figure 1.
The second ingredient is a set of “modulating functions” (Sang et al., 2011), , where is a symmetric, nonnegative-definite function. In Section 2.5 we will consider two specific examples, but for now we merely require that is equal to 1 when , and (exactly) equal to 0 when and are far apart. Here, the meaning of “far” depends on the resolution , in that with increasing , the modulating function should be equal to zero for increasingly large sets of pairs of locations in .
Based on these ingredients, we make two definitions:
###### Definition 1 (Predictive process).
For a generic Gaussian process , define to be the predictive-process approximation (Quiñonero-Candela and Rasmussen, 2005; Banerjee et al., 2008) of based on the knots :
where and , with .
That is, the predictive process is a conditional expectation, and hence a smooth, low-rank approximation of , which can also be written as a linear combination of basis functions (cf. Katzfuss, 2013). Further, the remainder is independent of , with positive-definite covariance function (Sang and Huang, 2012).
###### Definition 2 (Modulated process).
For a Gaussian process , define to be the “modulated” process corresponding to :
[x][m](⋅)∼GP(0,[C][m]), where [C][m](s1,s2)=C(s1,s2)⋅Tm(s1,s2),s1,s2∈D.
We see that and
have the same variance structure (because
), but has a compactly supported covariance function that is increasingly bad approximation of as and the distance between and increase.
### 2.3 Exact multi-resolution decompositions of Gaussian processes
For any Gaussian process (as specified in Section 2.1), using Definition 1, we can write , where is the predictive process of based on the knots , and is independent from and is itself a Gaussian process with (positive-definite) covariance function . This allows us to apply again the predictive process to (this time based on the knots ) to obtain the decomposition , and so forth, up to some resolution .
This idea enables us to exactly decompose any into orthogonal (i.e., independent) components at multiple resolutions:
y0(⋅)d=τ0(⋅)+…+τM−1(⋅)+δM(⋅), (1)
where is the predictive process of based on knots , , and for . Further, using the basis-function representation from Definition 1, we can write each component of the decomposition as , where , and starting with , we have for :
am(s)′\colonequalswm(s,Qm),s∈DΩm\colonequalswm(Qm,Qm)wm+1(s1,s2)\colonequalswm(s1,s2)−am(s1)′Ω−1mam(s2),s1,s2∈D. (2)
An important feature of this decomposition is that components with low resolution capture mostly smooth, long-range dependence, whereas high-resolution components capture mostly fine-scale, local structure. This is because the predictive process at each resolution is an approximation to the first terms in the Karhunen-Loéve expansion of (Sang and Huang, 2012). Figure 1 illustrates the resulting basis functions in our toy example.
It is straightforward to show that the decomposition of the process in (1) also implies an equivalent decomposition of the covariance function :
C0(s1,s2)=M−1∑m=0wm(s1,Qm)wm(Qm,Qm)−1wm(Qm,s2)+wM(s1,s2),s1,s2∈D. (3)
### 2.4 The multi-resolution approximation
The multi-resolution approximation (-RA) is a “modulated” version of the exact decomposition in (1), which at each resolution modulates the remainder using the function from Section 2.2. The key idea is that the predictive processes at low resolutions pick up the low-frequency variation in , resulting in remainder terms that exhibit variability on smaller and smaller scales as increases, and so approximating the remainder using more and more restrictive modulating functions causes little approximation error.
###### Definition 3 (Multi-resolution approximation (M-Ra)).
For a given , the -RA of a process based on a set of knots and a set of modulating functions , is given by
yM(⋅)=M∑m=0˜τm(⋅)=M∑m=0bm(s)′ηm, (4)
where and for ; with ; for ; and
(5)
Figure 1 shows the -RA basis functions in our toy example. As can be seen, the -RA is similar to a wavelet model, in that for increasing resolution , we have an increasing number of basis functions with increasingly compact support. However, in contrast to wavelets, the basis functions and the precision matrix of the corresponding weights in the -RA adapt to the covariance function . Defining the basis functions recursively allows the -RA to approximate , while in other approaches (e.g., wavelets, or Nychka et al., 2015) with explicit expressions for the basis functions, the resulting covariance is less clear.
For ease of notation, we often stack the basis functions as and the corresponding coefficients, , so that
yM(⋅)=b(⋅)′η,whereη∼Nr(0,Λ−1), (6)
with and .
### 2.5 Specific examples
As described in Section 2.2, the -RA requires the choice of two ingredients: knots and modulating functions. In light of the computational complexities discussed in Sections 3.23.3 below, we introduce a factor , often chosen to be equal to 2 or 4. Then, starting with some (small) number of knots at resolution , we henceforth assume for .
Regarding the modulating functions, we will now discuss two choices that lead to two important versions of the -RA.
#### 2.5.1 M-RA-block
To define the -RA-block, we need a recursive partitioning of the spatial domain , in which each of regions, , is again divided into smaller subregions, and so forth, up to level :
Dj1,…,jm−1=˙⋃jm=1,…,JDj1,…,jm,j1,…,jm−1=1,…,J;m=1,…,M.
We then assume for each resolution that the modulated remainder is independent across partitions at the th resolution. That is, the modulating function is defined as
Tm(si,sj)={1,(i1,…,im)=(j1,…,jm),0,otherwise,si∈Di1,…,im,sj∈Dj1,…,jm. (7)
Simply speaking, we have if are in the same region , and otherwise. At resolution , is split into subregions. Typically, we assume that the knots at each resolution are roughly equally spread throughout the domain, so that there are roughly the same number of knots in every such region.
The -RA-block and the corresponding domain partitioning are illustrated in a toy example in Figure 0(b). The -RA-block was first proposed in Katzfuss (2017) with the restriction that . Another special case for is the block-full-scale approximation (Snelson and Ghahramani, 2007; Sang et al., 2011).
#### 2.5.2 M-RA-taper
We can also specify the modulating functions to be compactly supported correlation functions, often refered to as tapering functions. For simplicity, we assume here that the modulating functions are of the form,
Tm(s1,s2)=T∗(∥s1−s2∥/dm),
with , where is the dimension of , is some norm on , and is a compactly supported correlation function that is scaled such that for all . For simplicity, we will use Kanter’s function (Kanter, 1997) in all data examples:
T∗(x)\colonequals⎧⎪ ⎪⎨⎪ ⎪⎩1,x=0,(1−x)sin(2πx)2πx+1−cos(2πx)2π2x,x∈(0,1),0,x≥1.
For other possible choices of tapering functions, see Gneiting (2002). The taper--RA is illustrated in Figure 0(a). A special case of the -RA-taper for is the taper-full-scale approximation (Sang and Huang, 2012; Katzfuss, 2013).
### 2.6 Properties of the M-RA process
Throughout this subsection, let be the -RA (as described in Definition 3) of on domain based on knots and modulating functions . All proofs are given in Appendix A.
###### Proposition 1 (Distribution of the M-Ra).
The -RA is a Gaussian process, , with covariance function
CM(s1,s2)=M∑m=0vm(s1,Qm)vm(Qm,Qm)−1vm(Qm,s2),s1,s2∈D,
where is defined in (5). We call the -RA of the covariance function .
###### Proposition 2 (Duplication of knots).
If , then for any and .
This proposition implies that there is no benefit to designate the same locations as knots at multiple resolutions; that is, all knot locations in should be unique.
###### Proposition 3 (Exact variance).
If , then the -RA variance at location is exact; that is, .
This proposition implies that, in contrast to other recent basis-function approaches (e.g., Lindgren et al., 2011; Nychka et al., 2015), no variance or “edge” correction is needed for the -RA if we place a knot location at each observed and prediction location.
Smoothness (i.e., differentiability) is a very important concept in spatial statistics, which has led to the popularity of the Matérn covariance class with a parameter that flexibly regulates differentiability (e.g., Stein, 1999). The following proposition shows that any desired smoothness can be preserved when applying the -RA:
###### Proposition 4 (Smoothness).
If is exactly times (mean-square) differentiable at , where , then is also exactly times differentiable at , provided that and are at least times differentiable at , for any and .
Many commonly used covariance functions (e.g., Matérn) are infinitely differentiable away from the origin. If is such a covariance function, the -RA-block thus has the same smoothness as the original process at any that is not located on the boundary between subregions at any resolution (cf. Katzfuss, 2017). Tapering functions are often smooth away from the origin, except at the distance at which they become exactly zero. Thus, the -RA-taper will typically have the same smoothness at as if is at least times differentiable at the origin and is not exactly at distance from any , for all . Note that this result does not require the smoothness of to be the same at all locations ; if the smoothness (or other local characteristics) of the covariance function varies over space, the -RA will automatically adapt to this nonstationarity and vary over space accordingly.
There is, however, an issue with the continuity of the -RA-block process at the region boundaries, which can be highly undesirable in prediction maps:
###### Proposition 5 (Continuity).
Assume that is a continuous function. Then, for the -RA-taper, realizations of the corresponding process and the posterior mean (i.e., kriging prediction) surface based on observations as in (8) are both continuous, assuming that is continuous for all . In contrast, for the -RA-block, and are both discontinuous in general at any on the boundary between any two subregions.
###### Proposition 6 (Exactness of M-RA-block).
Let be a (stationary) exponential covariance function on the real line, . Further, let be the covariance function of the corresponding -RA-block (see Section 2.5.1) with knots for , which are placed such that at each resolution , a knot is located on each boundary between two subregions at resolution . Then, the -RA is exact at every knot location; that is, for any .
This proposition is illustrated in Figure 0(b). As we will see in Section 3.2, this result allows us to exactly decompose a exponential covariance matrix in terms of a sparse matrix with rows but only about nonzero elements per row with and . This leads to tremendous computational savings (e.g., for billion).
While the exact result in Proposition 6 relies on the Markov property and the exact screening effect of the exponential covariance function (which is a Matérn covariance with smoothness parameter ), similar but approximate results are expected to hold for larger smoothness parameters in one dimension. Specifically, Stein (2011) shows that an asymptotic screening effect holds for when using conditioning sets of size 2, and he conjectures that an asymptotic screening effect holds for any when using conditioning sets of size greater than . This conjecture is also explored numerically in Katzfuss and Guinness (2017). To exploit this screening effect using the -RA-block, we can simply place knots near every subregion boundary (i.e., ).
## 3 Inference
In this section, we describe inference for the -RA, based on a set of measurements at locations . We assume additive, independent measurement error, such that
z=yM(S)+ϵ,ϵ∼Nn(0,Vϵ), (8)
where is a diagonal matrix. We assume that and are fully determined by the parameter vector , which will be assumed fixed at a particular value, unless noted otherwise. For the sparsity and complexity calculations, we assume and .
### 3.1 General inference results
#### 3.1.1 Prior matrices
For a given set of parameters, the covariance function , and hence the basis functions and the precision matrix in (6) are fixed. The prerequisite for inference is to calculate the prior matrices and . Define and , so that and . For , starting with and , it is straightforward to verify that
Wk+1m,l=(Wkm,l−Wkm,kΛ−1kWkl,k′)∘Tk+1(Qm,Ql),k=0,…,l−1;l=0,…,m; (9)
and
Wk+1S,m=(WkS,m−WkS,kΛ−1kWkm,k′)∘Tk+1(S,Qm),k=0,…,m−1. (10)
Here, denotes the Hadamard or element-wise product. Note that and both grow in dimension and become increasingly sparse with increasing resolution . We have if , and if .
#### 3.1.2 Posterior inference
Once and have been obtained, the posterior distribution of the unknown weight vector, , is given by well-known formulas for conjugate normal-normal Bayesian models:
η|z∼Nr(˜ν,˜Λ−1), (11)
where , , and .
Based on this posterior distribution of , the likelihood can be written as (e.g., Katzfuss and Hammerling, 2017):
−2logL(θ)=−log|Λ|+log|˜Λ|+log|Vϵ|+z′V−1ϵz−˜z′˜Λ−1˜z. (12)
Using this expression, the likelihood can be evaluated quickly for any given value of the parameter vector . This allows us to carry out likelihood-based inference (e.g., maximum likelihood or Metropolis-Hastings) on the parameters in and , by computing the quantities in (9)–(12) for each parameter value.
To obtain spatial predictions for fixed parameters , note that , where . Defining , can be obtained based on the quantities from Section 3.1.1 by calculating and
Wk+1SP,m=(WkSP,m−WkSP,kΛ−1kWkm,k′)∘Tk+1(SP,Qm),k=0,…,m−1,
and setting , for
. The posterior predictive distribution is given by,
yM(SP)|z∼NnP(BP˜ν,BP˜Λ−1BP′). (13)
Hence, the main computational effort required for inference is the Cholesky decomposition of , the posterior precision matrix of the basis-function weights in (11). As and are both sparse, is a sparse matrix that can be decomposed quickly. Specifically, has the block structure , where is an matrix whose th element is 0 if such that and . Figure 2 shows the sparsity structures of , , and corresponding to the toy example in Figure 1.
#### 3.1.3 Inference in the absence of measurement error
If there is no measurement error (i.e., ), we have
z=y∼Nn(0,Σ).
where . To ensure that (and hence ) has full rank, we assume for this case that (and thus ) and (in light of Proposition 2) that the knots are unique. The likelihood can then be calculated as where , and with .
### 3.2 Inference details for the M-RA-block
For the -RA-block from Section 2.5.1, , , and are block-sparse matrices, with each block roughly of size and corresponding to (the knots at) a pair of regions.
As noted in Section 3.1.1, we have if , and so is a block-diagonal matrix with diagonal blocks , where is the set of roughly knots at resolution that lie in . It is well known that the inverse of a block-diagonal matrix has the same block-diagonal structure as , and so the prior calculations in Section 3.1.1 involving can be carried out at low computational cost.
For the posterior covariance matrix, we have from Section 3.1.2 that if such that and , and so the block in corresponding to regions and is zero if the regions do not overlap (i.e., if ). The Cholesky factor of a (appropriately reordered) matrix with this particular block-sparse structure has zero fill-in, and can thus be carried out very rapidly.
Katzfuss (2017) describe an algorithm for inference in a special case of the -RA-block that can be extended to the more general -RA-block considered here. This algorithm is well suited for parallel and distributed computations for massive datasets, and it leads to efficient storage of the full posterior predictive distribution in (13). The time and memory complexity are shown to be and , respectively.
### 3.3 Inference details for the M-RA-taper
The case of the -RA-taper from Section 2.5.2 results in sparse matrices, but care must be taken to ensure computational feasibility. A crucial observation for the computational results below is that for any location and any resolution , only knots from are within a distance of from (i.e., all sets of the form contain only elements), because we assumed that the knots at resolution are roughly equally spread over the domain , and .
First, consider calculation of the prior matrices as described in Section 3.1.1. The matrices and have and nonzero elements, respectively, because if , and if . Before carrying out the actual inference procedures, it is helpful to pre-calculate , the set of nonzero indices of the matrix , for and . This can typically be done in time (e.g. Vaidya, 1989). In the actual inference procedure, we then only need to calculate the -elements of the matrices in (9). The main difficulty herein is that while is sparse, its inverse is not. However, we only need to compute certain elements of :
###### Proposition 7.
For and , the matrix can be obtained by computing
Wk+1m,l=(Wkm,l−Wkm,kSkWkl,k′)∘Tk+1(Qm,Ql),k=0,…,l−1, (14)
where and . Thus, the element of is not required for calculating the prior matrices in (9) if .
The total time complexity for computing all prior matrices in (9) is , ignoring the cost of computing the from the .
To calculate from , we use a selected inversion algorithm (Erisman and Tinney, 1975; Li et al., 2008; Lin et al., 2011) in which we regard element as a structural zero only if . This algorithm the same computational complexity as the Cholesky decomposition of the same matrix. For one-dimensional domains (), is a banded matrix with bandwidth , and so the time complexity to compute its Cholesky decomposition (and selected inverse) is (e.g., Gelfand et al., 2010, p. 187). For , the rows and columns of should be ordered such that the Cholesky decomposition leads to a (near) minimal fill-in and hence fast computations. Functions for this reordering are readily available in most statistical or linear-algebra software. The discussion in Furrer et al. (2006) indicates that the resulting time complexity for the Cholesky decomposition is roughly linear in the matrix dimension for . Moreover, our numerical experiments showed that the selected inversions only account for a small fraction of the total time required to compute the prior matrices, and so the total computation time for computing the prior matrices scales roughly as .
Once the prior matrices including and have been obtained, posterior inference requires computing and decomposing the posterior precision matrix in (11), with th block . The th element of this block is
(˜Λm,l)j,k=(Λm)j,k1{m=l}+∑ni=1vm(si,qm,j)vl(si,ql,k)(Vϵ)−1i,i.
As each of the is within distances of and of elements of and , respectively, the time complexity to compute is , and hence computing requires time.
###### Proposition 8.
The number of nonzero elements in is .
The time complexity for obtaining the Cholesky decomposition of is difficult to quantify, as it depends on its sparsity structure and the chosen ordering, but again our numerical experiments showed that the contribution of the Cholesky decomposition to the overall computation time is relatively small when appropriate reordering algorithms are used.
For prediction, the posterior covariance in (13) is dense and hence cannot be obtained explicitly for a large number of prediction locations. But the posterior covariance matrix of a moderate number of linear combinations can be obtained as , also based on a Cholesky decomposition of .
In summary, the time and memory complexity of the -RA-taper are and , respectively, plus the cost of computing the Cholesky decompositions of and . These decompositions only accounted for a relatively small amount of the overall computation time in our numerical experiments. Thus, the time complexity of the -RA-taper is roughly cubic in while it is square in for the -RA-block. Note that the computational cost for the -RA-taper can be further reduced if the covariance function has a small effective range relative to the size of , because then can be tapered at resolution 0 without causing a large approximation error; in contrast, for the -RA-block, we always have . As explained in Katzfuss (2017), it is often appropriate to expect a good approximation for (and hence ), which results in quasilinear complexity as a function of for the -RA.
## 4 Simulation study
For this section, we used data simulated from a true Gaussian process to compare the -RA-block and -RA-taper to full-scale approximations, FSA-block (Sang et al., 2011) and FSA-taper (Sang and Huang, 2012), which correspond to the -RA-block and -RA-taper, respectively. An implementation of the methods in Julia (http://julialang.org) version 0.4.5 was run on a 16-core machine with 64G RAM.
The true Gaussian process was assumed to have mean zero and an exponential covariance function,
C0(s1,s2)=σ2exp(−∥s1−s2∥/κ),s1,s2∈D, (15)
with and on a one-dimensional () or two-dimensional () domain. We assumed a nugget or measurement-error variance of (i.e., ). Results for Matérn covariances with different range, smoothness, and variance parameters showed similar patterns as those presented below and can be found in the Supplementary Material. | 2022-01-27 17:01:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8738881349563599, "perplexity": 818.4367931112877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305277.88/warc/CC-MAIN-20220127163150-20220127193150-00098.warc.gz"} |
https://mox.polimi.it/reports-and-theses/publication-results/?id=718 | # A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square
Code:
02/2018
Title:
A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square
Date:
Wednesday 3rd January 2018
Author(s):
Canuto, C.; Nochetto, R. H.; Stevenson, R.; Verani, M. | 2022-01-21 08:36:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9746657013893127, "perplexity": 8196.052588829381}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00412.warc.gz"} |
http://www.gradesaver.com/textbooks/science/chemistry/chemistry-a-molecular-approach-3rd-edition/chapter-1-sections-1-1-1-8-exercises-problems-by-topic-page-40/100 | # Chapter 1 - Sections 1.1-1.8 - Exercises - Problems by Topic: 100
$1,490,625 mile^{2}$ $42.14$ %
#### Work Step by Step
1. Convert value in acres into value in feet by using conversion factor $[1acre=43560feet^{2}]$ $954 \times 10^{6} acres \times \frac{43560 ft^{2}}{1 acre} =4,155,624 \times 10 ^{7} ft^{2}$ 2. Then, convert square feet into square miles by dividing it by conversion factor [ 1 mile = 5280 feet], then [$1 mile^{2} = 5280^{2} ft^{2}= 27878400 ft^{2}$] $\frac{4,155,624 \times 10 ^{7} ft^{2}}{27878400 ft^{2}/mile^{2}}= 1490625 mile^{2}$ 3. To calculate the percentage of total land area, divide the land area value by the total area given $\frac{1490625 mile^{2}}{3537000mile^{2}}\times 100$% = 42.144 % or $\approx$ 42.14%
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2017-07-20 16:59:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6499433517456055, "perplexity": 2214.499563048562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423269.5/warc/CC-MAIN-20170720161644-20170720181644-00465.warc.gz"} |
https://www.realdigital.org/doc/1fd3322461ac4bcc1fcd6bcc6c5907ec | 2568
## Software Requirements for the Courses
Real Digital designs are implemented on a Xilinx ZYNQ 7000 Series device that includes both an ARM processor and an FPGA. Xilinx offers two sets of tools for working with the ZYNQ 7000 series – One is the FPGA-focused Vivado WebPack hardware design tool which supports Verilog, VHDL, and other hardware definition languages. Xilinx also provides SDK, a software design tool that supports Assembly, C, and other programming languages. Both tools are free, full-featured integrated design environments (IDEs) that offer design entry, synthesis and compilation, simulation, and hardware verification.
The Digital Logic course uses Vivado and the Microprocessor Systems course uses SDK. The Embedded Systems course uses both design packages. The Vivado WebPack download includes both Vivado and SDK – everything needed for all courses. If you are only interested in the Microprocessor Systems course, you can just download the smaller SDK tool without the Vivado software.
NOTE: Use a computer with atleast 30 GB of storage space. Also reference System Requirements for info on what computer you will need.
When you run the actual Vivado installer, make sure you the select the WebPack version. If you want Vivado to also install SDK, make sure to select the Software Development Kit (SDK) install option as well.
If you only want to install SDK, for the Microprocessor Systems course, you can get it at the SDK Download Page. Select the install options as shown below.
#### Windows
Similarly, if you installed Xilinx SDK you should be able to start it from it’s respective shortcut.
#### Linux
You may need to install cable drivers in linux. If you do, read the details in:
If you have a desktop environment that supports desktop shortcuts the installer will try to add shortcuts for you. These should launch the tools. Otherwise you can start vivado via shell commands.
The default install directory for Xilinx tools in linux is /opt/Xilinx/ Under this you will find directories for Vivado and/or SDK based on what you chose to install.
The Vivado and SDK directories will contain folders for each release, and in them you’ll find the actual release files. Thus, the default path for a specific version of a tool should be /opt/Xilinx/toolname/realeaseversion
To run Vivado or SDK, first source the settings file from the path for the correct tool, then run the tool’s command. For example, Vivado 2017.4 can be started from a shell with the following commands. The syntax will be the same for any other version of Vivado, but the path will differ based on the release.
$source /opt/Xilinx/Vivado/2017.4/settings64.sh$ vivado &
Similarly to start SDK 2017.4 from a shell, run the following commands
$source /opt/Xilinx/SDK/2017.4/settings64.sh$ xsdk & | 2019-06-17 06:44:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2588016092777252, "perplexity": 4703.715712684868}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998440.47/warc/CC-MAIN-20190617063049-20190617085049-00037.warc.gz"} |
https://ohhaskme.com/273409/number-theory-question-about-continued-fractions | I understand that a continued fraction is given by iterating $; x \\rightarrow floor(x) , \\frac{1}{x - floor(x)} ;$ , but how can I reverse this? Is there a way to get from a continued fraction back to the number that generates it? Is there a formula that takes a list of numbers and returns the number that generates it?
Since $; \[3; 1$ = $4$ ;\], it's impossible to completely reverse it.
I've seen the $; a\_0 + \\frac{1}{a\_1 + \\frac{1}{a\_2 + ...}} ;$ thing, but with the "..." on the right, I'm not sure how to turn it into an explicit formula.
>Is there a way to get from a continued fraction back to the number that generates it?
a continued fraction is a number. that's the whole point, it's the same number you started with, just written differently. if you want a decimal expansion, do long division.
by | 2023-01-31 10:15:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5676108002662659, "perplexity": 192.59482066509324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499857.57/warc/CC-MAIN-20230131091122-20230131121122-00036.warc.gz"} |
https://math.stackexchange.com/questions/2943282/exact-solution-for-a-first-order-autonomous-algebraic-ordinary-differential-equa | # Exact solution for a first order autonomous algebraic ordinary differential equation
I have the following system of ordinary differential equations: \begin{align*} x'&=\frac{1}{4}x^2+\frac{3}{4}y^2-2x\\ y'&=\frac{1}{12}x^2+\frac{1}{4}y^2-\frac{2}{3}y, \end{align*} with boundary condition $$x(0)=y(0)=1$$. Note that $$\frac{1}{2}x'-\frac{3}{2}y'=y-x$$.
After some googling I found that this is an Autonomous Algebraic Ordinary Differential Equation (AODE), and there exists a large body of literature for finding exact solution for these type of ODEs. I was wondering if someone could point me in the right direction for solving this specific AODEs.
• Indeed, thank you for noticing I adapted it. – Darkwizie Oct 5 '18 at 12:15
• I hope it does! – Darkwizie Oct 5 '18 at 12:17
• I am mainly interested in which techniques COULD be applied to find a solution, I can try to apply these methods myself but when I google myself I am overwhelmed by overly complicated methods and have no idea which of them could work well. – Darkwizie Oct 5 '18 at 12:24
You found that $$x=3y+Ce^{-t}.$$ Inserting into the second equation results in $$y'=y^2+\frac12Ce^{-t}y-y+\frac1{12}C^2e^{-2t}$$ This is now a Riccati equation where you can use the standard substitution $$y=-\frac{u'}{u}$$ to obtain a second order linear ODE.
• There were still some minor issues with the question, I have now rectified them, I am taking a close look at your answer. – Darkwizie Oct 5 '18 at 14:39
• Ok, now there are no immediate simplifications. Already this case with simplifications did not lead far, the more general case should not be easier. Except that one can compute the power series expansion for algebraic ODE to any degree I see no directly algebraic solution path. – LutzL Oct 5 '18 at 14:45
• Do you have a (basic) reference for the power series expansion approach? – Darkwizie Oct 5 '18 at 14:59 | 2019-10-20 12:24:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8853968381881714, "perplexity": 214.84139418772085}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986707990.49/warc/CC-MAIN-20191020105426-20191020132926-00455.warc.gz"} |
http://salamander724.wikidot.com/computational-astronomy-hw01 | 숙제 01
For the problems below, you need to write programs using C language. Turn in your own source programs written independently (by email) together with reports.
# 1.
The Fibonacci sequences satisfy the following recurrence relation
(1)
\begin{align} F_n = F_{n-1} + F_{n-2} , \quad n \ge 2, \end{align}
with $F_0 = 0$ and $F_1 = 1$. Suppose that you wrote the following program to calculate the sum of frst 20 Fibonacci numbers $F_0, F_1, \cdots, F_{20}$, but it does not work correclty.
• (a) Compile and run the program below. What is the output?
• (b) Fix the code in order to obtain the intended output? What is it?
#include <stdio.h>
#define N 20
int main(void)
{
int i, j, k;
int p;
k = 0; /* F[0] */
j = 1; /* F[1] */
int total = k + j;
for(p = 2; p < N; p++){
i = j + k; /* F[n] = F[n-1] + F[n-2] */
int total = total + i;
k = j;
j = i;
}
printf(" Total: %5d\n", total);
return 0;
}
# 2.
Write a (short) program to find the machine epsilon of your computer, using C language, in both single and double precision. Run your program to obtain the outputs.
# 3.
This problem is to show that you need to be carreful to avoid unstable algorithms in which roundoff errors can increase exponentially.
The “golden mean”, $\phi$, is given by $\phi = ( \sqrt{5} - 1)/2 \simeq 0.61803398875 \cdots$,
• (a) Write a C progam to calcualte the $n$-th power of $\phi$, using successive multiplications
(2)
\begin{align} \phi^0 = 1, \quad \mathrm{and} \quad \phi^n = \phi \cdot \phi^{n-1} \quad \mathrm{for} \quad n = 1, 2, 3, \cdots, \end{align}
and plot $\phi^n$ as a function of $n$ for $0 \le n \le 50$. (The ordinate should be in lograithmic scale.)
• (b) Another (clever) way to calculate $\phi^n$ is to use following recursion relation
(3)
\begin{align} \phi^{n+1} = \phi^{n-1} - \phi^n \quad \mathrm{for} \quad n = 1, 2, 3, \cdots, \end{align}
Show that Equation (3) is equivalent to Equation (2). Use Equation (3) to calcualte $\phi^n$ in both single and double precision for $0 \le n \le 50$. Compare the results with those in part (a) by overploting all the results in the same figure.
• (c) Why do you think are the results in parts (a) and (b) so different for high $n$? (Hint: there is another solution of Equation (3) whose magnitude is greater than unity.)
# 4.
Evaluate
(4)
\begin{align} S_n = \sum_{j=1}^n {{1} \over {j(j+1)}}, \end{align}
using your computer for arbitrary $n= 10, 10^2, 10^4$, and $10^6$ by using the method below. Comment on the answers obtained.
• (a) By summing the terms from the largest terms first to the smallest terms last.
• (b) By summing the terms from the smallest terms first to the largest terms last.
• (c) Using the Kahan summation formula.
페이지 내역: 1, 마지막 수정: 01 Nov 2015 09:50 | 2019-01-22 21:55:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9466782212257385, "perplexity": 1251.7449284263096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583874494.65/warc/CC-MAIN-20190122202547-20190122224547-00207.warc.gz"} |
https://vitalflux.com/tag/php/ | # Tag Archives: PHP
## PHP – How to Install Apache 2.4 with PHP 5.6 on Windows
This article represents instructions on what’s needed to be done to install Apache 2.4 with PHP 5.6 on Windows (64-bit). Please feel free to comment/suggest if I missed to mention one or more important points. Also, sorry for the typos. Following are the key steps/points described later in this article: Install Apache 2.4 Install PHP 5.6 Configure Apache 2.4 for PHP Configure PHP 5.6 Test Install Apache 2.4 This step looks to be obvious. However, after I am done with the entire installation, it looked to be a bit tricky especially when you got 64-bit Windows. If you go to website, http://httpd.apache.org, you are taken to download page for win32 …
Posted in PHP, Web. Tagged with .
## Top 10 PHP Code Review Tips
This article represents top 10 areas to consider while you are taking up the task to do the code review of a PHP project. The other day, I had a discussion with one of the PHP senior developers who asked me about where to start on the task related with reviewing a PHP web application and, we brainstormed and came up with the list. Interestingly, apart from few, most of them can be pretty much applied to applications written with other programming languages as well. Please feel free to comment/suggest if I missed to mention one or more important points. Also, sorry for the typos. Following are the key points described later …
Posted in PHP, Software Quality. Tagged with , .
## Why Facebook’s Hack May Fail to Fly With PHP Developers?
Well, for those innocent souls, I must make it clear that the title of this article has no intentions to point out that Facebook is hacked or so? This is actually about the new programming language, HACK, that Facebook officially launched few days back. Overview of Hack Language Before I go on to write further, I must thank the Facebook engineering team to have rightfully identified some of the short-comings of PHP programming language and tried to present solutions to them using Hack programming language. However, while I was going through the changes that they made by adding new features to PHP and made it as Hack language, I wondered whether …
Posted in News, PHP. Tagged with .
## How to Debug PHP Code?
[adsenseyu2] If you have started on PHP programming and looking out for tips and techniques on how to debug PHP code, following may help you get started: var_dump command: var_dump command helps one to explore whats stored in arrays and objects. Following is the sample code: <?php $a = array(1, 2, array(“a”, “b”, “c”)); var_dump($a); ?> echo command: You could as well use the echo command to debug php program flow. <?php $foo = “foobar”; echo “foo is$foo”; ?> Configure Xdebug with Zend Studio or Eclipse PHP IDE: If you are tired of var_dump or echo commands, and write PHP code using IDE such as eclipe-php or Zend Studio, …
Posted in PHP. Tagged with , , .
## PHP Code for Avoiding XSS Attacks
[adsenseyu2] Before we go and discuss the PHP coding tips and techniques to avoid Cross-site scripting (XSS) attacks, lets try and understand quickly what is XSS attack. XSS is a Web-based attack performed on vulnerable Web applications which ends up victimizing the end user rather than the application itself. In these attacks, malicious content is delivered to users primarily using JavaScript. The XSS attack happens when the web applications accepts the input from the end user without validating it. In XSS attack, the malicious code executes in the context of the victim’s session, allowing the attacker to bypass normal security restrictions. There are multiple good web pages to read about XSS …
Posted in Application Security. Tagged with , , .
## PHP Code Smells and Best Practices
As application in PHP can be written in object oriented manner, most of the code smells found in the world of object-oriented programming also stay valid for PHP. Recently, I happened to do a code review of a PHP project and wanted to share some of the areas which one would want to pay attention to: Naming methods using Camel Case: It is always helpful to write method names in camel case as it is easily readable. For example, instead of writing method names such as “searchurlAction”, one could write “searchUrlAction”. Software quality characteristic impacted in “Usability“. Long Methods: One may want to avoid large method as these methods become …
Posted in Code Review, PHP, Software Quality. Tagged with .
## YII framework for faster PHP web application
If you have been looking for developing a web application in a quick manner, then, YII is surely a right choice. YES IT IS! What are some of the important characteristics of yii framework? 1. It is very lightweight. 2. It is based on MVC framework. 3. It comes with a user interface tool which helps in creation of models, views and controllers. 4. It has support of some real good UI framework such as getyiistrap.com, yii bootstrap, yii wheels. 5. It comes with a support of a set of extensions that can be used to include new features quickly in no time. 6. If you love writing code based … | 2021-07-28 06:48:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27636346220970154, "perplexity": 2571.9100630976786}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153531.10/warc/CC-MAIN-20210728060744-20210728090744-00675.warc.gz"} |
https://www.edaboard.com/threads/led-driver-circuit-doesnt-work.393734/ | # LED driver circuit doesnt work
#### Winsu
##### Full Member level 2
Hi All,
I have designed a circuit using the ZLED7730-ZI1R to power up a few LEDs. The string current is to be meant 0.35A but I had to limit the PSU as it would draw whatever figure I allow on the PSU. I have used normal diodes as LEDs are very expensive ( this is the diode I have used: CD123D-B140LR ).
The dim 1 and dime 2 pins are to set a dim profile. I initially set the DIM to GND, but as it wasn't working and left DIM 1 floating ( it would mean 100% always).
I don't know why it is not working. I set the PSU ay 24V and 0.4A and the voltage drop to 4V and I draws the 0.4A. There are 3.5V dropping accros the diodes and 0.5V between Lx and GND. For some reason he internal mosfet is constantly on and it is not regulating at all. Below is the schematic. Any help would be very useful, thanks.
#### KlausST
##### Super Moderator
Staff member
Hi,
You have a wrong pin numbering. Maybe this is the problem.
Did you strictly follow PCB layout guidelines?
Klaus
#### Winsu
##### Full Member level 2
Hi Klaus
I noticed that and I fixed on the PCB, the right hand side on the chip is actually up side down, is that what you mean?
I didn't follow the layout guidelines but I don't think it would stop completely to regulate just because of that...
#### KlausST
##### Super Moderator
Staff member
Hi,
So, you really think they write this just out of fun...
The following guidelines are strongly recommended when laying out application circuits:
Don't be surprised if it does not work.
Klaus
#### Winsu
##### Full Member level 2
I didn't follow the guide lines consciously but the result is fairly close to what the guide suggest.....
I can't find the reason why it is not working
#### KlausST
##### Super Moderator
Staff member
Hi,
Without your PCB layout ... we neither can't find it...
Klaus
#### treez
You clamped the current to 0.4a.
So your sense voltage is only 0.108v.......this is below the threshold of 15% above 100mv....so no wonder the fet is on all the time.
What voltage is across the leds....?
Set psu to say 2v above this, and set the psu supply current limit to 0.6a, and try again
#### Winsu
##### Full Member level 2
You clamped the current to 0.4a.
So your sense voltage is only 0.108v.......this is below the threshold of 15% above 100mv....so no wonder the fet is on all the time.
What voltage is across the leds....?
Set psu to say 2v above this, and set the psu supply current limit to 0.6a, and try again
I have just raised the current and it keeps open all the time. Across the LEDs are 3.5V and the rest of the voltage is dropping across drains and source of the FET.
#### treez
What is the current rating of your inductor?
What is the voltage across the sense res...if it is flat dc, and above 120mV, then the fet is broken and on all the time....or you have a misconnection somewhere
#### Winsu
##### Full Member level 2
Here you can see attached the layout. I didn't spend much time on the layout as I just wanted to verify that they circuit works.....
Track connected to pin 5 needs to be removed and a track need to be added between pin 8 and anode of D1.
--- Updated ---
What is the current rating of your inductor?
What is the voltage across the sense res...if it is flat dc, and above 120mV, then the fet is broken and on all the time....or you have a misconnection somewhere
The Farnell order code for the inductor is 2329187 and its current rating is 1.7A. The voltage on the RS sense is when the PSU is set to 0.6A is almost 2V , that means the FET is not switching off at all. It could indeed be broken, but I have just measured continuity between LX and GND and it is not shorted.
If there is voltage across the LED it means that the loop is properly soldered. It is just four pins on the IC that needs to be soldered and they look like they are.....Could it be something wrong in the design?
Last edited:
#### treez
check if is the chip the right way round?
Is r1 correct value.....if cant check, remove it and see what happens then.
Your input capitance looks way too low...increase to 220uf or more.
Last edited:
#### Winsu
##### Full Member level 2
The chip is good way around and I already increase the input capacitance and it didn't improve... I think I will have to order component again and populate the board again....if it keeps failing there must be something in the design....
#### wwfeldman
I have used normal diodes as LEDs are very expensive ( this is the diode I have used: CD123D-B140LR ).
the forward drop on the CD123s is about 0.35 V, so 10 in series is the 3.5V you measured across the diodes.
the forward drop on LEDs is 2? 3? V.
you have essentially shorted the output
the regulator is trying to produce the desired output voltage and/or current, but your load is too small
add a series resistor consistent with the expected V and I for the real LEDs you want to use
or replace the schottkey diodes with plain cheap LEDs -
digikey has about 500 different LEDs, surface mount, less than $1 (American) in stock #### Winsu ##### Full Member level 2 the forward drop on the CD123s is about 0.35 V, so 10 in series is the 3.5V you measured across the diodes. the forward drop on LEDs is 2? 3? V. you have essentially shorted the output the regulator is trying to produce the desired output voltage and/or current, but your load is too small add a series resistor consistent with the expected V and I for the real LEDs you want to use or replace the schottkey diodes with plain cheap LEDs - digikey has about 500 different LEDs, surface mount, less than$1 (American) in stock
Indeed the output is kind of shorted. I then added more resistance to the string but the voltage across the string rises as I increase the resistance but if I allow more current to flow from the PSU the current keeps going up. The FET is not regulating anymore.
I don't know when it failed....., when I get more drivers I will test it adding more resistance to the string.....
#### treez
Are you sure your diode is not dry joint?....because if it was then the fet may get overvoltaged when it switches off.
As you know, the inductor current always needs somewhere to flow to
#### Winsu
##### Full Member level 2
Are you sure your diode is not dry joint?....because if it was then the fet may get overvoltaged when it switches off.
As you know, the inductor current always needs somewhere to flow to
I have just double checked and it is not that, unfortunately....
#### treez
ok, can you take the inductor off, and just see if just connecting up vcc draws loads of current.....just to check if the chip really is dead
### Winsu
points: 2
#### KlausST
##### Super Moderator
Staff member
Hi,
Still the pin numbering mistake.
* datasheet says: pin8 is output Lx
* your PCB says: pin5 is output Lx
Klaus
### Winsu
points: 2
#### Winsu
##### Full Member level 2
Hi All,
Thanks Klausst, it was corrected previously in the PCB with flying wires and cutting a track.
I have noticed that the inductor was incorrectly soldered...., it was soldered in a way that the inductor was by passed and it was effectible like a piece of wire....
It is working fine now, the Rsense which is 0.27ohm has across 0.108V , so it is spot on, thanks! | 2020-08-12 18:57:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3974071741104126, "perplexity": 3351.034900904569}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738913.60/warc/CC-MAIN-20200812171125-20200812201125-00357.warc.gz"} |
https://wtmaths.com/domains_ranges.html | Domains and Ranges
## Domains and Ranges
A domain defines a set of input to a function. The range is defined as the output.
For a linear function, such as f(x) = 3x + 4, the domain could be used for any Real (ℝ) number. The result - the range - would also be any real number and there would be only one output value for each input value.
A function must work for every possible input value, and for every input value there must be one output value. However, the output values can be shared: f(x) = x^2 is a valid function, although f(2) and f(-2) give the same result (4).
The domain may have to be limited for certain functions. f(x) = frac(1)(x) works for any real number except the value 0, as an attempt to divide by zero will fail. Therefore f(x) = frac(1)(x), x ≠0 is a valid function as the range has ben defined to eliminate the value 0.
The trigonometric ratios (sin, cos and tan) are all functions. Because the values repeat as you go above 360º, the function will be defined with a limiting range eg f(x) = sin(x), 0º ≤ x < 360º to avoid the repeating values.
Sometimes the domain or range will be defined as a set (using set notation { } ); and sometimes using one of the predefined numeric types: the integer numbers shown as ℤ; rational numbers shown as ℚ, Real numbers shown as ℝ, and prime numbers.
## Example 1
What is the range for the function f(x) = x^2 - 4, where 3 ≤ x ≤ 5?
f(3) = 3^2 - 4 = 5
f(5) = 5^2 - 4 = 21
5 ≤ f(x) ≤ 21
Answer: 5 ≤ f(x) ≤ 21
## Example 2
For f(x) = x^2 - 4, the domain is a ≤ x ≤ 8. If the range is 5 ≤ f(x) ≤ 60, what is the value of a?
The lowest value:
5 = x^2 - 4
x^2 = 9
x = 3
Answer: a = 3 | 2022-12-09 11:32:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3545199930667877, "perplexity": 561.170137157986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711396.19/warc/CC-MAIN-20221209112528-20221209142528-00853.warc.gz"} |
https://brilliant.org/problems/paying-bills-should-be-easier-than-this/ | # Paying Bills Should Be Easier Than This
Algebra Level 1
Raj, Anoop, and Varun are three roommates who agreed to evenly split the cost of having an apartment.
In the month of December, Raj paid the cable bill of $64, Anoop paid the electricity bill of$89, and Varun paid the heating bill of \$126. In order to evenly split the bill, who should be reimbursed, and by how much?
× | 2018-09-23 19:07:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33894795179367065, "perplexity": 7644.856199951681}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159570.46/warc/CC-MAIN-20180923173457-20180923193857-00280.warc.gz"} |
http://lzis.icuy.pw/matlab-3d-surface-plot.html | auto_clear = 'on' Enter the command surf to see a demo. Hi, i need to plot a 3D series of x,y,z coordinate in VB. You normally don’t use numpy for plot. 3d plots; See Also. Plot a surface from data sets in MATLAB. Discover what MATLAB. All I can find in Matlab tutorial is plotsice function that seems relevant but what I want is a 3D surface. I am trying to render a visualization of a closed surface in spherical coordinates. The method utilizes Cartesian coordinates of triangular planar surfaces and converts them into matrices of conventional geologic attitude data. using the same colors as the surface plot. 6 respectively. Finer Points of Plotting with MATLAB. You can Run the command by entering it in the MATLAB Command Window. e the XZ or YZ plane). The plot is formed by joining adjacent points with straight lines. To set the plot title, type the title text within the textbox provided under the 'Title' property. To convert a MuPAD notebook file to a MATLAB live script file, see convertMuPADNotebook. You can create plots of known, analytical functions, you can plot data from other sources such as experimental measurements, you can analyze data, perhaps by fitting it to a curve, and then plot a comparison. However, I wish for it be graphed on the contours: i. When we try to plot 3D map in MATLAB, we have different options to plot. Then, you can do a 3d plot by caculating some z values on the x and y domains, and doing a surface, mesh, or contour plot. In addition, the cone consisting of all tangents from a fixed point to a quadratic surface cuts every plane in a conic section, and the points of contact of this cone with the surface form a conic section (Hilbert and Cohn-Vossen 1999, p. To clear the previous plot, use clf(). MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python. Project 3D surface onto 2D plot. Create plots programmatically using graphics functions or interactively using the Plots tab at the top of the MATLAB ® desktop. Use Plotly with MATLAB ® to share your figures with non-MATLAB ® users, to create web-based MATLAB ® dashboards, as the visualization toolbox in MATLAB ® web applications, or just for publication quality vector image export. Colors in MATLAB plots. 01 in a line array. (Originally posted on Doug's MATLAB Video Tutorials blog. I used view(2) and it shows a plot as drawn below. 2D cross section from 3D surface. Every graph of a function of two variables is a surface, but not conversely. Table of Contents, Get code for this tutorial. Here's a description of two easy ways to make surface plots in Matlab, including step-by-step instructions. 3-D plots are useful to present data having more than two variables. The general form of the mesh command is: mesh(x,y,z). For example, you can compare sets of data, track changes in data over time, or show data distribution. Each plot stores the data, and code to reproduce a plot with MATLAB, Python, R, Julia, and JavaScript. A step down from there is a volumetric rendering like you see on the Avizo size, where you have a flat 2D image of a rendered 3D volume or surface. How to make 3D scatter plots in MATLAB ®. Each row correspondds to the 3D location of a point, i. I have done two others. When I took a course in grad school on statistical image processing, I saw a very interesting plot where data is shown as a surf plot and underneath, on the ground or x-y plane, an image is shown. Blog Coding Salaries in 2019: Updating the Stack Overflow Salary Calculator. edu/priya/matlabmarina/in. 2D cross section from 3D surface. Then you establish x, y (and z if applicable) according to the equations, then plot using the plot(x,y) for 2D or the plot3(x,y,z) for 3D command. Use 'meshgrid' to convert your vectors to 2D matrices. SPHERE3D plots 3D data on a spherical surface. Working in 3D one can create a slice through a structure and present the stresses or strains. ezsurf(___,'circ') creates the surface plot over a disk centered on the range. Discover what MATLAB. jar: Installation: Download Interactive_3D_Surface_Plot. Then, you can do a 3d plot by caculating some z values on the x and y domains, and doing a surface, mesh, or contour plot. However, the main reason I bought Matlab was to plot 2D and 3D plots found in my calculus homework. As with contour plots, you must first calculate a rectangular array of function values. If f is a function of the variables u and v (rather than x and y ), then the domain endpoints umin, umax, vmin, and vmax are sorted alphabetically. Since a lot of geologic data is naturally of more than one dimension, we have use for these capabilities. You can set up Plotly to work in online or offline mode. This can increase the coding cost of the problem greatly. Surface Plot (with Shading) The surfl function creates a surface plot with colormap-based lighting. Python Matplotlib Tips: Rotate elevation angle and animate 3d plot_surface using Python and matplotlib. Three variables - x, y, z all are changing with time. This can be done by the surfc command - which projects the top view contours onto the bottom plane, (i. 1 Introduction. Whether it's for research, a school assignment, or a work presentation, 3-D plots are great for visualizing what a complicated set of data looks like. jar to the plugins folder, or subfolder, restart ImageJ, and there will be a new "Interactive 3D Surface Plot" command in the Plugins menu, or submenu. 3D surface plot from for loop. I have been trying to create 3D surface plot between calculated variables, but it says that Z requires some matrix? 1 Comments. plotly GETTING STARTED 1. That’s how we achieve this simple animation in 3D. I used view(2) and it shows a plot as drawn below. This is accomplished using the hold on command. Here we use a function plot () in MATLAB library. Colors, 3D Plotting, and Data Manipulation. In the first experiment, we are going to work with a sphere and are going to rotate our view angle without changing any size. Plotting a surface from a set of interior 3D scatter points in MATLAB. A step down from there is a volumetric rendering like you see on the Avizo size, where you have a flat 2D image of a rendered 3D volume or surface. Learn more about matlab, 3d plots. Plot 3D surface from normals and points. Plotting a cone in matlab. Note: You can execute the code from this tutorial by highlighting them, right-clicking, and selecting "Evaluate Selection" (or hit F9). It sets them to the correct values that depend upon whether the SURFACE objects are representing meshes or surfaces. MATLAB has different plotting approaches for showing data in 3D: 3D line plots [MATLAB: plot3. Use 'meshgrid' to convert your vectors to 2D matrices. and can automatically generate contours, display volumetric data, interpolate shading colors and even display non-Matlab made images. Learn more about surface, surf, 3d, 3d plots. Next, open up Matlab and set the working directory to where e_field. Blog Coding Salaries in 2019: Updating the Stack Overflow Salary Calculator. SPHERE3D plots 3D data on a spherical surface. I first created a surface fit with cubic interpolation to generate a piecewise cubic interpolant and then I plotted this on a 3D graph. I am trying to plot a simple 3D surface area where it will show a range of distance and height. Code: clf r = 1. 3D surface and 3D wireframe plots are graphs that you can use to explore the potential relationship between three variables. Now that we know scalars were used for each plot3() call, the plot3() calls together were equivalent to plotting a point cloud. OK, I Understand. Hi all, Need to plot a 3D surface from X,Y,Z 1D arrays. BALL_AND_STICK_DISPLAY is a MATLAB program which illustrates the use of MATLAB's 3D plotting capability to make a "ball and stick" plot. Tutorials by MATLAB Marina. I have been trying to create 3D surface plot between calculated variables, but it says that Z requires some matrix? 1 Comments. I want to pot the 100 points and connect them as a surface. the XY plane) However I need to project side view contours onto a side view plane (i. Surface plots¶ Axes3D. As with contour plots, you must first calculate a rectangular array of function values. The function in matlab is called Tri=delauny(X,Y,Z). if the system under study is linear or not by plotting a surface in the phase-space. If anybody does have any experience on doing this, kindly. 01 in a line array. A surface is a set of polygons. Now lets turn our attention to implicit curves. The rstride and cstride kwargs set the stride used to sample the input data to generate the graph. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. I figured out how to plot 2D lines, parabolas, hyperbolas, and simple functions, but the 3D surface plots are a whole different level of thing altogether! :D. When post-processing in a 2D model one can use Plot Parameters/Surface to create a 3D surface plot. MATLAB defines a surface by the z-coordinates of points above a grid in the x-y plane, using straight lines to connect adjacent points. m Page 1 March 28, 2007 5:55:08 AM 1 %% EF 105 Matlab Plotting Example 2 % 3D surface with an image texture 3 4 % Initialization. 'Surf' and 'Mesh' are two functions that generate. Code: clf r = 1. shading is a MATLAB command that sets the EdgeColor and FaceColor properties of all SURFACE objects in the current axes. To convert a MuPAD notebook file to a MATLAB live script file, see convertMuPADNotebook. plot_surface (X, Y, Z, *args, **kwargs) ¶ Create a surface plot. Free 14-day trial. We attempted to create a version for each regular Matlab plot command by prepadding "kml", e. As an example, the surface above could be plotted on a circular domain using polar coordinates. Show an image in a MATLAB 3D surface plot with a separate colormap T he surface / surf plot in MATLAB can visualize data in 3D. Surface Plot (with Shading) The surfl function creates a surface plot with colormap-based lighting. Need help creating a 3D plot of intensity values. We present a MATLAB® script that produces planar geologic attitude data (e. I am trying to plot a 3D surface and a contour plot. Alternatively, use hold on to plot successively on the same figure. New to Plotly? Plotly's R library is free and open source! Get started by downloading the client and reading the primer. Adjust the transparency of surface plots by using the FaceAlpha property. m will generate the interactive 3D plot seen above. Then, you can do a 3d plot by caculating some z values on the x and y domains, and doing a surface, mesh, or contour plot. The data generated by this function can be shown with either trimesh(Tri,X,Y,Z) or trisurf(Tri,X,Y,Z). For example, [code]p = [2 1 3]; plot3([0 p(1)], [0 p(2)], [0, p(3)]); grid on; view(-25, 25); [/code]. Then it uses an adaptive algorithm to choose additional sample points, subdividing at most MaxRecursion times. First, let's look at some of the options available with the default three-dimensional plotting tools. Matlab provides many facilities for visualization of 3D information or data (x, y, z). How to plot multiple arrays in a 3d or surface Learn more about 3d plots, arrays. Yair is one of the most downloaded authors on the MATLAB Central File Exchange (and is recognized as an expert in "undocumented MATLAB. I want to pot the 100 points and connect them as a surface. It's not 3D but since your brain knows what it's seeing, it believes that it's 3D particularly if you're able to grab the object and rotate it around. You may also plot more cubes to present 3-dimension data. For more information, please visit: http://engineering. Plot a surface from data sets in MATLAB. ggplot2 can use those colours in discrete scales. Learn more about 3d surface, mesh, meshgrid, linspace but there is a problem with the MATLAB plotting routines so the plot itself does. Visualization Of 3D Data. What is MATLAB 3D Plot? The MATLAB 3-D plot is that function in MATLAB that enables the user to develop 3-D plots of two independent variables, and how they correlate to a third dependent variable. Running the following code, contained within usr_matlab_script_3d_scatter. Discover what MATLAB. To clear the previous plot, use clf(). The image above is a surface plot, identifying a progression in a system model. Colors, 3D Plotting, and Data Manipulation. The plots are arranged in an array where the default number of rows and columns is one. The control file. I obtained the model with reasonable R-squares and p-value. can you also tell me what to do if have to view the surface plot in 2D. Learn more about surface, surf, 3d, 3d plots. Minitab uses interpolation to create the surface area between the data points. Guest authors: Harrison Rose and Breanna Stillo. All of the standard surface functions ('surface', 'contour', 'pcolor', etc. 3D plot - Part 2 Modeling Surfaces, Meshes and 3D variations The 3D plot functions intended for plotting meshes and surfaces ' mesh ' and ' surf ', and their several variants ' meshc ', ' meshz ', ' surfc ', and ' surfl ', take multiple optional input arguments, the most simple form being ' mesh(z) ' or ' surf(z) ', where z represents a matrix. 3D surface plot from for loop. The value lies between 0 and 1. if the system under study is linear or not by plotting a surface in the phase-space. You can create 3D surface with points of data by using the DELAUNAY3 and TRISURF functions as shown in the example code below: load data ; %You can find the data MAT-file in the resolution documents %Extract the X, Y and Z coordinates. Check out the set command in matlab. MATLAB's 3D plotting capability is just as versatile as the 2D plots. There will be holes in the final surface anywhere at which etc. Open Mobile Search. New to Plotly? Plotly's R library is free and open source! Get started by downloading the client and reading the primer. A GNU Octave / MATLAB code for Modified Cam Clay in FE formulation for Element Testing (Drained and Undrained) - hansinimal/camclay. I tend to prefer vector graphics when possible too. Keep in mind trisurf is only for 3D data. Help me plot a 3D plot of microphone beampattern in Matlab (0). If the distribution of points is not sufficient, use 1000 m as the reference layer. I have search for hours on this matter but I can't seemed to find the answer. Surface plots of z = f(x, y) are produced by the MATLAB function surf. Surface Plot with 3 vectors. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. You normally don’t use numpy for plot. plugins/Interactive_3D_Surface_Plot. MATLAB 3D plot examples explained with code and syntax for Mesh, Surface Ribbon, Contour and Slice. I figured out how to plot 2D lines, parabolas, hyperbolas, and simple functions, but the 3D surface plots are a whole different level of thing altogether! :D. You can set up Plotly to work in online or offline mode. The plot is formed by joining adjacent points with straight lines. Then, you can do a 3d plot by caculating some z values on the x and y domains, and doing a surface, mesh, or contour plot. How to plot multiple arrays in a 3d or surface Learn more about 3d plots, arrays. This will display a list of all available plot types for Google Earth. Be able to determine the appropriate type of plot to present scientific/engineering data. Tutorials by MATLAB Marina. Plot symbolic expressions, equations, and functions in 3-D. You don't want too few points in the "grid" or it will appear jagged, but too many and the computer will slow down or even hang!. MATLAB has different plotting approaches for showing data in 3D: 3D line plots [MATLAB: plot3. First, let's look at some of the options available with the default three-dimensional plotting tools. They are easy to plot in Matlab. I am trying to render a visualization of a closed surface in spherical coordinates. KMLquiver for curved arrows and KMLcylinder for a 3D. gray, bone, copper, prism, and flag. Now I would like to plot a 3D surface, visualise the response surface of Mass(z-axis) related to H(x-axis) and V(y-axis). The plot(x,y) plots the straight line on the z=0 plane. surf(X,Y,Z) creates a three-dimensional surface plot, which is a three-dimensional surface that has solid edge colors and solid face colors. How to draw a 3D surface plot with numerical Learn more about surface, matlab How to draw a 3D surface plot with numerical datas on matlab. It quickly and easily converts your data into outstanding contour, surface, wireframe, vector, image, shaded relief, and post maps. 8 Applications 8. Anonymous said Hey, This plot is really good, I would like to make a similar plot but above the South Pole. Plotting a cone in matlab. We know that the implicit equation for the unit circle is the following: We can convert that into a parametric form, and then draw it using the. 3d plots; See Also. SYNTAX: plot(y)-plots the columns of y versus the index of each value when y is a real number. I am thoroughly confused about the formation of the 2D Z matrix required by 3D plot surface helper. Another approach is to click and then enter the title directly on the plot interface. This demo allows you to enter a mathematical expression in terms of x and y. I have 3 vectors x, y, z and I would like to generate a 3D surface instead of having just separate points (e. Project 3D surface onto 2D plot. If you are interested in a list of all the functions exposed in mlab, see the MLab reference. Let us plot the surface. This is accomplished using the hold on command. 1 Introduction. 3D Graphics in MATLAB We'll introduce different types of plotting in 3D. The instructions provided include tools to plot wire-frame objects, 3D plots, curves, surfaces, etc. The instructions provided include tools to plot wire-frame objects, 3D plots, curves , surfaces. Create plots programmatically using graphics functions or interactively using the Plots tab at the top of the MATLAB ® desktop. They are easy to plot in Matlab. the 3d graph has contours where Z=-200. 1 Graphical solutions MATLAB can be used to plot 1-d functions. fsurf(f) creates a surface plot of the function z = f(x,y) over the default interval [-5 5] for x and y. and can automatically generate contours, display volumetric data, interpolate shading colors and even display non-Matlab made images. bokeh - Interactive Web Plotting for Python. As an example, the surface above could be plotted on a circular domain using polar coordinates. You can visualize matrix data on a rectangular grid using surface plots. Surface and mesh plots. This surface is not necessarily regular and therefore I had to define it piecewise rather than by predefined MATLAB functions. The second statemen t pro duces con tour plots of the matrix Z using v ectors x and y to con trol the scaling on the x-and y-axes. plot_surface (X, Y, Z, *args, **kwargs) ¶ Create a surface plot. MATLAB has different plotting approaches for showing data in 3D: 3D line plots [MATLAB: plot3. Plot multiple surfaces using vector input to fsurf. I have search for hours on this matter but I can't seemed to find the answer. Note that the axis limits should be set to the same values for a correct spatial representation. If you have points which are described by vectors, and you want to plot them you could always use a Delauny triangulation. In some earlier posts ( part1, part2) we explored how to draw parametric curves using MATLAB Graphics. can anyone help me. % This surface plot is efficient but it doesn't produce % a very pretty picture (well at least for this small data set, % for large data sets, triangulated surfaces are often preferable. The problem is that the first is complete white which is wrong, the yellow column should actually be the first column. This might give you some ideas for your application. >> contour(x,y,z,20) Or a 3D plot with 20 contour curves >> contour3(x,y,z,20) Final Comments This is just the tip of the plotting iceberg. Project Fiji Source on GitHub: License GPLv3: Release 2. To convert a MuPAD notebook file to a MATLAB live script file, see convertMuPADNotebook. 3D Simple Animation In this short article we're going to experiment with simple animation in 3D using Matlab. Table of Contents, Get code for this tutorial. When post-processing in a 2D model one can use Plot Parameters/Surface to create a 3D surface plot. Ken's code allows you to easily plot a 3D surface from polar coordinate data. MATLAB's 3D plotting capability is just as versatile as the 2D plots. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. You can set up Plotly to work in online or offline mode. 3d surface plot. This table classifies and illustrates the common graphics functions. ^2); % Draw 3D figure, keep track of its handle h = surf(x,y,z);. I have already made a mesh grid of my x and y but I am confused on how to plug my gaussian function in as Z. Let me start off by saying that I am extremely new to MATLAB. I have search for hours on this matter but I can't seemed to find the answer. For example, you can compare sets of data, track changes in data over time, or show data distribution. Yair is one of the most downloaded authors on the MATLAB Central File Exchange (and is recognized as an expert in "undocumented MATLAB. Create plots programmatically using graphics functions or interactively using the Plots tab at the top of the MATLAB ® desktop. MATLAB's 3D plotting capability is just as versatile as the 2D plots. Surface plots¶ Axes3D. Terms figure window, 2D plot, linear 3D plot, parametric plot, surface plot. First, let's look at some of the options available with the default three-dimensional plotting tools. The full. F or surface or mesh plots, y ou use the third statemen t where x, y are v ectors or matrices and Z is a matrix. Changing Surface Properties. Now that we know scalars were used for each plot3() call, the plot3() calls together were equivalent to plotting a point cloud. For example, you can compare sets of data, track changes in data over time, or show data distribution. How to Plot a Function in MATLAB. There will be holes in the final surface anywhere at which etc. Surface Plot with 3 vectors. 3d plot with surface. Matlab provides many facilities for visualization of 3D information or data (x, y, z). The video, then, does a workout of surface plot showing the output in a 3d wireframe. MATLAB ® graphics defines a surface by the z-coordinates of points above a rectangular grid in the x-y plane. Useful particularly in metrology of spherical surfaces, spherical wavefronts and wavefields. I used view(2) and it shows a plot as drawn below. (Originally posted on Doug's MATLAB Video Tutorials blog. When we try to plot 3D map in MATLAB, we have different options to plot. To clear the previous plot, use clf(). Be able to determine the appropriate type of plot to present scientific/engineering data. To demonstrate how to use gnuplot, we will give an example. To clear the previous plot, use clf(). Follow the steps below to find out how you can create a 3D chart in Excel. I have the plot presented in figure, every line was plotted using a constant x coordinate, a vector y which is the same for every line and a vector z which depend on the x-coordinate (pdf attached). Hi, i need to plot a 3D series of x,y,z coordinate in VB. matlab provides many useful instructions for the visualization of 3D data. ^2 surf(x,y,z) mesh(x,y,z) contour(x,y,z) You could also use surfc or meshc to get surface or mesh plots with a contour plot drawn on the x-y plane. Plot3D initially evaluates each function at a grid of equally spaced sample points specified by PlotPoints. Working in 3D one can create a slice through a structure and present the stresses or strains. bokeh - Interactive Web Plotting for Python. plugins/Interactive_3D_Surface_Plot. Plotting at this point will provide 2D plot but if the Height Data tab is selected and the same variable name entered as the Expression there one will obtain a 3D surface plot as desired. In this post, Harrison and Breanna present three-dimensional experimental data, and show how to plot the data, fit curves through the data, and plot surfaces. visualize/coloring-mesh-and-surface-plots. Volume Slices and Isosurfaces. Create plots programmatically using graphics functions or interactively using the Plots tab at the top of the MATLAB ® desktop. Now that we know scalars were used for each plot3() call, the plot3() calls together were equivalent to plotting a point cloud. MATLAB CODE: Semilogx(x,y) command will scale x-axis logarithmically and semilogy(x,y) command will scale y-axis logarithmically as we can see in fig. Plotting Complex Functions Python has a built in syntax for manipulating complex numbers, using $$j = \sqrt{-1}$$. MATLAB 3D plot examples explained with code and syntax for Mesh, Surface Ribbon, Contour and Slice. Using the following syntax, which denotes the surface plot of z, and also indicates a color map formation, the following is the code for the surface map: Generation of a surface map in MATLAB: surf(z) colormap(jet) % change color map. SPHERE3D plots 3D data on a spherical surface. There is a property called alpha. Also, automatic generation of contours, volumetric data display, light sources, interpolation of colors and displaying externally-created images. m) to create 3D-printable objects from 2D functions (surface plots) by Phalgun Lolur ([email protected] edu/priya/matlabmarina/in. Consider the following problem: Find to 3 d. For that purpose I tried to use scatter3 and isosurface without any success. fsurf(f) creates a surface plot of the function z = f(x,y) over the default interval [-5 5] for x and y. Creating 3-D Plots. To convert a MuPAD notebook file to a MATLAB live script file, see convertMuPADNotebook. For example, you can compare sets of data, track changes in data over time, or show data distribution. An overview of contour, mesh, plot3, and surf. This is accomplished using the hold on command. ly/python/matlab/ getting-started. Sign in to comment. Guest authors: Harrison Rose and Breanna Stillo. matlab provides many useful instructions for the visualization of 3D data. When displaying multiple surfaces on the same figure, transparency is useful. I could not find a map similar to the one loaded by the command 'load korea', but for Antarctica. MATLAB has different plotting approaches for showing data in 3D: 3D line plots [MATLAB: plot3. The graph can be zoomed in by scrolling with your mouse, and rotated by dragging around. Key Results: 3D Surface Plot. This works when plotting as points but I want to form surfaces between the points. This example shows how to get properties of a surface plot in MATLAB® and change the property values to customize your plot. This can be done by the surfc command - which projects the top view contours onto the bottom plane, (i. 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https://zbmath.org/authors/?q=ai%3Ashintani.takuro | # zbMATH — the first resource for mathematics
## Shintani, Takuro
Compute Distance To:
Author ID: shintani.takuro Published as: Shintani, T.; Shintani, Takuro External Links: MGP · Wikidata
Documents Indexed: 27 Publications since 1967 Biographic References: 1 Publication
#### Co-Authors
23 single-authored 4 Sato, Mikio 2 Muro, Masakazu
all top 5
#### Serials
6 Journal of the Mathematical Society of Japan 6 Proceedings of the Japan Academy 3 Journal of the Faculty of Science. Section I A 2 Nagoya Mathematical Journal 1 Tokyo Journal of Mathematics 1 Proceedings of the National Academy of Sciences of the United States of America 1 Annals of Mathematics. Second Series
all top 5
#### Fields
21 Number theory (11-XX) 5 Algebraic geometry (14-XX) 4 Topological groups, Lie groups (22-XX) 3 Special functions (33-XX) 3 Abstract harmonic analysis (43-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Group theory and generalizations (20-XX)
#### Citations contained in zbMATH Open
24 Publications have been cited 746 times in 610 Documents Cited by Year
On construction of holomorphic cusp forms of half integral weight. Zbl 0316.10016
Shintani, Takuro
1975
On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. Zbl 0349.12007
Shintani, Takuro
1976
On zeta functions associated with prehomogeneous vector spaces. Zbl 0309.10014
Sato, Mikio; Shintani, Takuro
1974
On a Kronecker limit formula for real quadratic fields. Zbl 0364.12012
Shintani, Takuro
1977
On zeta-functions associated with the vector space of quadratic forms. Zbl 0313.10041
Shintani, Takuro
1975
On an explicit formula for class-1 ”Whittaker functions” on $$GL_n$$ over $$\mathfrak p$$ -adic fields. Zbl 0387.43002
Shintani, Takuro
1976
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0227.10031
Shintani, Takuro
1972
Theory of prehomogeneous vector spaces. (Algebraic part). - The English translation of Sato’s lecture from Shintani’s note. Zbl 0715.22014
Sato, Mikio; Shintani, Takuro; Muro, Masakazu
1990
Two remarks on irreducible characters of finite general linear groups. Zbl 0323.20041
Shintani, T.
1976
A proof of the classical Kronecker limit formula. Zbl 0462.10014
Shintani, Takuro
1980
On certain ray class invariants of real quadratic fields. Zbl 0392.12009
Shintani, Takuro
1978
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0223.10032
Shintani, T.
1972
On certain square-integrable irreducible unitary representations of some p-adic linear groups. Zbl 0194.05602
Shintani, T.
1968
On zeta functions associated with prehomogeneous vector spaces (algebraic groups/gamma function/Dirichlet series). Zbl 0249.10034
Sato, Mikio; Shintani, Takuro
1972
On Kronecker limit formula for real quadratic fields. Zbl 0359.12004
Shintani, Takuro
1976
On special values of zeta functions of totally real algebraic number fields. Zbl 0426.12008
Shintani, Takuro
1980
On values at $$s=1$$ of certain $$L$$ functions of totally real algebraic number fields. Zbl 0363.12013
Shintani, Takuro
1977
On liftings of holomorphic cusp forms. Zbl 0415.10019
Shintani, Takuro
1979
On the decomposition of regular representation of the Lorentz group on a hyperboloid of one sheet. Zbl 0184.17403
Shintani, T.
1967
A remark on zeta functions of algebraic number fields. Zbl 0503.12006
Shintani, Takuro
1981
On irreducible unitary characters of a certain group extension of $$\text{GL}(2,\mathbb C)$$. Zbl 0342.20021
Shintani, T.
1977
On certain ray class invariants of real quadratic fields. Zbl 0377.12008
Shintani, Takuro
1977
On zeta-functions associated with the lattice of Hermitian forms with Gaussian integral coefficients. Zbl 0309.10015
Shintani, Takuro
1971
On certain square integrable irreducible unitary representations of some P-adic linear groups. Zbl 0265.22023
Shintani, Takuro
1968
Theory of prehomogeneous vector spaces. (Algebraic part). - The English translation of Sato’s lecture from Shintani’s note. Zbl 0715.22014
Sato, Mikio; Shintani, Takuro; Muro, Masakazu
1990
A remark on zeta functions of algebraic number fields. Zbl 0503.12006
Shintani, Takuro
1981
A proof of the classical Kronecker limit formula. Zbl 0462.10014
Shintani, Takuro
1980
On special values of zeta functions of totally real algebraic number fields. Zbl 0426.12008
Shintani, Takuro
1980
On liftings of holomorphic cusp forms. Zbl 0415.10019
Shintani, Takuro
1979
On certain ray class invariants of real quadratic fields. Zbl 0392.12009
Shintani, Takuro
1978
On a Kronecker limit formula for real quadratic fields. Zbl 0364.12012
Shintani, Takuro
1977
On values at $$s=1$$ of certain $$L$$ functions of totally real algebraic number fields. Zbl 0363.12013
Shintani, Takuro
1977
On irreducible unitary characters of a certain group extension of $$\text{GL}(2,\mathbb C)$$. Zbl 0342.20021
Shintani, T.
1977
On certain ray class invariants of real quadratic fields. Zbl 0377.12008
Shintani, Takuro
1977
On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. Zbl 0349.12007
Shintani, Takuro
1976
On an explicit formula for class-1 ”Whittaker functions” on $$GL_n$$ over $$\mathfrak p$$ -adic fields. Zbl 0387.43002
Shintani, Takuro
1976
Two remarks on irreducible characters of finite general linear groups. Zbl 0323.20041
Shintani, T.
1976
On Kronecker limit formula for real quadratic fields. Zbl 0359.12004
Shintani, Takuro
1976
On construction of holomorphic cusp forms of half integral weight. Zbl 0316.10016
Shintani, Takuro
1975
On zeta-functions associated with the vector space of quadratic forms. Zbl 0313.10041
Shintani, Takuro
1975
On zeta functions associated with prehomogeneous vector spaces. Zbl 0309.10014
Sato, Mikio; Shintani, Takuro
1974
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0227.10031
Shintani, Takuro
1972
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0223.10032
Shintani, T.
1972
On zeta functions associated with prehomogeneous vector spaces (algebraic groups/gamma function/Dirichlet series). Zbl 0249.10034
Sato, Mikio; Shintani, Takuro
1972
On zeta-functions associated with the lattice of Hermitian forms with Gaussian integral coefficients. Zbl 0309.10015
Shintani, Takuro
1971
On certain square-integrable irreducible unitary representations of some p-adic linear groups. Zbl 0194.05602
Shintani, T.
1968
On certain square integrable irreducible unitary representations of some P-adic linear groups. Zbl 0265.22023
Shintani, Takuro
1968
On the decomposition of regular representation of the Lorentz group on a hyperboloid of one sheet. Zbl 0184.17403
Shintani, T.
1967
all top 5
#### Cited by 568 Authors
11 Yukie, Akihiko 10 Kohnen, Winfried 10 Kurokawa, Nobushige 10 Sato, Fumihiro 9 Friedberg, Solomon 9 Kudla, Stephen S. 8 Choi, Junesang 8 Muro, Masakazu 7 Eie, Minking 7 Rubenthaler, Hubert 6 Bringmann, Kathrin 6 Funke, Jens 6 Gerasimov, Anton A. 6 Kimura, Tatsuo 6 Lebedev, Dimitri R. 6 Lee, Jungyun 6 Millson, John J. 6 Oblezin, Sergey 6 Srivastava, Hari Mohan 5 Flicker, Yuval Z. 5 Kane, Ben 5 Kojima, Hisashi 5 Murase, Atsushi 5 Tangedal, Brett A. 5 Taniguchi, Takashi 4 Abramov, Sergeĭ Aleksandrovich 4 Bhargava, Manjul 4 Bump, Daniel 4 Duke, William Drexel 4 Gelbart, Stephen S. 4 Halbritter, Ulrich 4 Imamoḡlu, Özlem 4 Kable, Anthony C. 4 Mizuno, Yoshinori 4 Oda, Takayuki 4 Piatetski-Shapiro, Ilya 4 Shintani, Takuro 4 Solomon, David R. 4 Stasinski, Alexander 4 Sugano, Takashi 4 Tsuzuki, Masao 4 Wang, Shuping 4 Wright, David J. 3 Asai, Teruaki 3 Belabas, Karim 3 Brown, Jim L. 3 Cassou-Noguès, Pierrette 3 Chen, Shaoshi 3 Colmez, Pierre 3 Đoković, Dragomir Ž. 3 Espinoza, Milton 3 Friedman, Eduardo C. 3 Ginzburg, David 3 Hirose, Minoru 3 Hoffmann, Werner 3 Jun, Byungheup 3 Li, Yingkun 3 Lőrincz, András Cristian 3 Manickam, Murugesan 3 Mao, Zhengyu 3 Matringe, Nadir 3 Nishizawa, Michitomo 3 Niwa, Shinji 3 Petkovšek, Marko 3 Ramakrishnan, Balakrishnan 3 Raulf, Nicole 3 Rubin, Boris 3 Sadykov, Timur Mradovich 3 Sands, Jonathan W. 3 Sato, Mikio 3 Schiffmann, Gérard 3 Schwagenscheidt, Markus 3 Sczech, Robert 3 Strömberg, Fredrik 3 Tanaka, Hidekazu 3 Tong, Yue Lin Lawrence 3 Wakatsuki, Satoshi 3 Wakayama, Masato 3 Zemel, Shaul 2 Adler, Jeffrey D. 2 Agarwal, Mahesh 2 Alfes-Neumann, Claudia 2 Anandavardhanan, U. K. 2 Aomoto, Kazuhiko 2 Barquero-Sanchez, Adrian 2 Bennett, Michael A. 2 Bertolini, Massimo 2 Blind, Bruno 2 Böcherer, Siegfried 2 Brubaker, Ben 2 Bruinier, Jan Hendrik 2 Byeon, Dongho 2 Bykovskiĭ, Viktor Alekseevich 2 Choie, YoungJu 2 Cipra, Barry A. 2 Clozel, Laurent 2 Damon, James Norman 2 Darmon, Henri René 2 Dasgupta, Samit 2 Datskovsky, Boris A. ...and 468 more Authors
all top 5
#### Cited in 122 Serials
63 Journal of Number Theory 34 Mathematische Annalen 33 Inventiones Mathematicae 26 Transactions of the American Mathematical Society 24 Journal of Algebra 22 Nagoya Mathematical Journal 20 Duke Mathematical Journal 19 Advances in Mathematics 18 Tohoku Mathematical Journal. Second Series 16 Compositio Mathematica 16 Proceedings of the Japan Academy. Series A 14 Mathematische Zeitschrift 14 Proceedings of the American Mathematical Society 12 Annales de l’Institut Fourier 10 Mathematics of Computation 10 Journal of Functional Analysis 9 The Ramanujan Journal 8 Communications in Mathematical Physics 8 Israel Journal of Mathematics 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 Journal of Soviet Mathematics 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 Bulletin of the American Mathematical Society. New Series 6 Annals of Mathematics. Second Series 6 Journal of High Energy Physics 6 International Journal of Number Theory 6 Research in the Mathematical Sciences 5 Journal of Mathematical Analysis and Applications 5 Manuscripta Mathematica 5 Journal de Théorie des Nombres de Bordeaux 5 Selecta Mathematica. New Series 4 Letters in Mathematical Physics 4 Applied Mathematics and Computation 4 Journal of the Mathematical Society of Japan 4 Journal of Symbolic Computation 4 Bulletin of the American Mathematical Society 4 Proceedings of the Japan Academy 3 Communications in Algebra 3 Bulletin de la Société Mathématique de France 3 Publications Mathématiques 3 Journal of Pure and Applied Algebra 3 Journal für die Reine und Angewandte Mathematik 3 Memoirs of the American Mathematical Society 3 Advances in Applied Mathematics 3 Journal of the American Mathematical Society 3 Forum Mathematicum 3 Representation Theory 3 Research in Number Theory 2 Journal of Mathematical Physics 2 Theoretical and Mathematical Physics 2 Acta Arithmetica 2 Glasgow Mathematical Journal 2 Journal of Combinatorial Theory. Series A 2 Mathematika 2 Michigan Mathematical Journal 2 Monatshefte für Mathematik 2 Neural Computation 2 The Journal of Geometric Analysis 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 Kyushu Journal of Mathematics 2 The Journal of Fourier Analysis and Applications 2 Journal of Topology 2 Kyoto Journal of Mathematics 2 Annales Mathématiques du Québec 2 Journal of Siberian Federal University. Mathematics & Physics 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 Journal d’Analyse Mathématique 1 Journal of Statistical Physics 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nuclear Physics. B 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Functiones et Approximatio. Commentarii Mathematici 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Programming and Computer Software 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matematico della Università di Padova 1 Acta Applicandae Mathematicae 1 Journal of Automated Reasoning 1 Science in China. Series A 1 Neural Networks 1 Geometric and Functional Analysis. GAFA 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Journal of Algebraic Geometry 1 Bulletin des Sciences Mathématiques 1 Integral Transforms and Special Functions 1 Documenta Mathematica 1 Transformation Groups 1 Doklady Mathematics 1 Journal of Group Theory ...and 22 more Serials
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#### Cited in 39 Fields
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The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-05-07 02:37:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4636654853820801, "perplexity": 3168.9214564712925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.18/warc/CC-MAIN-20210506235514-20210507025514-00352.warc.gz"} |
https://archive-ouverte.unige.ch/unige:104831 | Title
Combination of inclusive and differential t t ¯ $$\mathrm{t}\overline{\mathrm{t}}$$ charge asymmetry measurements using ATLAS and CMS data at s = 7 and 8 TeV
CollaborationWith : Akilli, Ece / Ancu, Lucian Stefan / Benoit, Mathieu / Calace, Noemi / Clark, Allan Geoffrey / Coccaro, Andrea / Della Volpe, Domenico / Di Bello, Francesco / Dubreuil, Arnaud / Ferrere, Didier / Gadatsch, Stefan / Golling, Tobias / Gonzalez Sevilla, Sergio / Iacobucci, Giuseppe / Jansky, Roland / Katre, Akshay / Khoo, Teng Jian / Kiehn, Moritz / Lanfermann, Marie Christine / Lionti, Anthony Eric / March Ruiz, Luis / Mermod, Philippe / Nessi, Marzio / Pandini, Carlo / Paolozzi, Lorenzo / Schramm, Steven / Sfyrla, Anna / Valente, Marco / Wu, Xin
Published in Journal of High Energy Physics. 2018, vol. 1804, p. 033
Collection Open Access - SCOAP3
Abstract This paper presents combinations of inclusive and differential measurements of the charge asymmetry ( A C ) in top quark pair t t ¯ $$\left(\mathrm{t}\overline{\mathrm{t}}\right)$$ events with a lepton+jets signature by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. The data correspond to integrated luminosities of about 5 and 20 fb −1 for each experiment, respectively. The resulting combined LHC measurements of the inclusive charge asymmetry are A C CHC7 = 0.005 ± 0.007 (stat) ± 0.006(syst) at 7 TeV and A C CHC8 = 0.0055 ± 0.0023 (stat) ± 0.0025 (syst) at 8 TeV. These values, as well as the combination of A C measurements as a function of the invariant mass of the t t ¯ $$\mathrm{t}\overline{\mathrm{t}}$$ system at 8 TeV, are consistent with the respective standard model predictions.
Identifiers
arXiv: 1709.05327
Full text
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(ISO format)
ATLAS COLLABORATION. Combination of inclusive and differential t t ¯ $$\mathrm{t}\overline{\mathrm{t}}$$ charge asymmetry measurements using ATLAS and CMS data at s = 7 and 8 TeV. In: Journal of High Energy Physics, 2018, vol. 1804, p. 033. https://archive-ouverte.unige.ch/unige:104831
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https://www.clutchprep.com/chemistry/practice-problems/116559/a-solution-contains-50-5-g-of-heptane-c7h16-and-50-5-g-of-octane-c8h18-at-25-oc--1 | # Problem: A solution contains 50.5 g of heptane (C7H16) and 50.5 g of octane (C8H18) at 25 oC. The vapor pressures of pure heptane and pure octane at 25 oC are 45.8 torr and 10.9 torr, respectively. Assuming ideal behavior, calculate each of the following. (Note that the mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the components partial pressure.)The total pressure above the solution.
⚠️Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet.
###### Problem Details
A solution contains 50.5 g of heptane (C7H16) and 50.5 g of octane (C8H18) at 25 oC. The vapor pressures of pure heptane and pure octane at 25 oC are 45.8 torr and 10.9 torr, respectively. Assuming ideal behavior, calculate each of the following. (Note that the mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the components partial pressure.)
The total pressure above the solution. | 2020-07-15 03:04:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8783923983573914, "perplexity": 1896.2962930001634}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657154789.95/warc/CC-MAIN-20200715003838-20200715033838-00100.warc.gz"} |
https://www.gamedev.net/forums/topic/651285-are-there-alternative-methods-of-obtaining-neighboring-nodes-of-a-node-from-a-2d-grid-like-map-of-nodes/ | Followers 0
# Are there alternative methods of obtaining neighboring nodes of a node from a 2D grid-like Map of nodes?
## 9 posts in this topic
While creating my pathfinding system for a 2D grid-based Map of nodes, I'm wondering if I can omit off having to pass the Map object as a parameter to all of my Node objects. That way, I can make my Map of nodes flexible and without having to worry about re-initializing all of my Nodes with the Map object all over again.
Given that there's a Node at position (X, Y), I was thinking of fetching its neighboring nodes, (X-1, Y-1), (X, Y-1), (X+1, Y-1), (X-1, Y), (X+1, Y), (X-1, Y+1), (X, Y+1), and (X+1, Y+1), without having to go search for it from the Map object. It turns out to be nearly impossible to do, since I don't have anything to refer to and make relative calculations based on (X, Y) alone.
Does anyone else know alternative methods of obtaining neighboring nodes from a specified Node position, without having to refer to a Map object containing all of the Nodes? If there are none, is that why I can't write off the reason for passing the Map object as a parameter to my Nodes?
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The alternative is to give each node a link to every neighbor. But that would be MUCH more memory-hungry than if you have a regular grid of nodes as a single 2D array. If your map is not a regular 2D array, then having node-to-node linking might be OK.
With a 2D array, your nodes do not need to link to their neighbors OR link to the map. If your algorithm passes the map as a function argument (or otherwise keeps it in scope in some other way), you will always have the map available to perform neighbor lookups without having to look it up from the node each time. Edited by Nypyren
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I would suggest not storing a reference to the map or storing the tile coordinate in the tile. The map should be the one doing all the logic so individual tiles should only be a tiny set of data.
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I would suggest not storing a reference to the map or storing the tile coordinate in the tile. The map should be the one doing all the logic so individual tiles should only be a tiny set of data.
Is that how it's supposed to be? I always get the inference that small data types may also need to incorporate large data types by either using callbacks or parameters passing.
And can you separate the logic out of the map and node data types into a static invocating method, so it becomes easier to call the pathfinding system wherever possible?
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I just mean the tiles themselves don't need to know the object they are contained in. I wouldn't advocate trying to take the functionality entirely out to a standalone method.
I may have partially misunderstood. Are you talking about the pathing nodes used during a path search or the tile nodes of the tile map?
I don't think the tiles of the tile map should need a pointer to the map, or know their location within the map. For pathfinding purposes, the 'PathNode' needs something that maps back to its location in the map so that it can expand the search at each iteration, but that can be properties specific to the PathNode and not the TileNode. That is, assuming you are not using the tile nodes directly in the pathfinding, which I would not recommend, since the pathfinding needs a set of data specific to the search that has no reason to be persistent with the tiles(g cost, f cost, parent pointer, etc).
I tend to write standalone objects as interfaces to pathfinding that are allocated per AI that are basically their navigation interface.
// for each AI
Navigator * nav = navmesh->AllocPathQuery();
nav->FindPathToGoal( pos, myCapabilities );
// incremental updates for tim splicing
{
case PathFound:
{
// get the string pulled corners
NavCorner corners[4];
const size_t numCorners = nav->GetNextCornersInPath( corners, 4 );
if ( numCorners == 0 )
{
StopMoving();
}
// update AI steering/velocity with the corners
break;
}
case PathNotFound:
// print error, etc
break;
case PathSearching:
break;
}
I usually allocate it through the specific pathfinding system and it maintains a reference to the data classes it needs to function. I've also had good luck abstracting these Navigators around the concept of 'corners'. A base Navigator class can take and provide access to a generalized representation of the path, while several implementation subclasses may be available for different navigation systems NavigatorTileMap, NavigatorNavMesh, NavigatorWaypointGraph, etc. In all these cases, the specifics of the pathfinding and interaction with the specific navigation system can be contained in these subclasses while the interface provides general access to the string pulled corners of the path, with edge flags and node flags that communicate information about the underlying path, such as the types of polygons and such traversed.
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Both. In my case, the path nodes on a map is the same thing as tile nodes on the same map.
If tile nodes aren't supposed to see the object the nodes themselves are contained in, I'm curious that some demos or simple pathfinding tutorials will want to incorporate the use of passing the container in as a parameter, thus the tile nodes are able to see where exactly it is located. You're the first to tell me that this isn't always the case.
I also see from your example, a navmesh can generate a Navigator. This navogator object is then used to query a path from the pathfinding system, which is the Navigator.
Is this how it should be done? By UML, navmesh <- navigator, and navmesh <- list of nodes?
Which means the navmesh (Area) should contains both the pathfinder system (Navigator), and a list of nodes?
But, from your example, I don't see a way to separate the navigator system and the navmesh. If I were to use concurrency, I may have to use static methods to invoke the navigator system to start pathfinding, which would then be required to put the Map object in a tile node. Or I am being mistakened?
At least I now know that it is okay to not put the Map object in each of the tile/path nodes the Map object has contained them in.
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The navigator subclass, such as the NavigatorNavmesh, is indeed tied to the navigation mesh. It's an implementation of my interface where it is tied closely to how the navigation mesh stores data. The Navigator is my path finder and my path smoother. This object serves several purposes for me. It represents the state of navigation for a particular entity. The navigators could be updated from multiple threads, modifying their internal search state and referencing the navigation mesh in a read only manner, they could be updated serially in a time spliced sort of manner(allowing many paths to be in progress simultaneously), and it shields the rest of the code from the choice of navigation system I'm using, allowing me to change it easier at a later point. Also, since it maintains its own internal state which may involve functionality closely related to the navigation system, it can handle the dynamic aspects of path following was well, such as string pulling, often implemented in a way that requires regular maintenance of the path which can be encapsulated in the navigator.
You don't have to do it this way. You can just create a function on your map class or something if you want to start simple that solves a path and gives you back an immediate result in the form of filling in a result object or a list of path nodes, etc.
Status TileMap::FindPath( PathResult & resultOut, const vec2 & src, const vec2 & dst, ... );
Path nodes hold the state of the navigation query at a particular state, the code, the parent pointer for reconstructing the path when the goal is found, etc. This is temporary scratch data and doesn't belong in the same objects as your Tiles, which presumably hold a reference to the image used for that tile, whether the tile is solid or not. I think about the tile map in a 2d game as an image, and the tiles as the pixels of the image, the color channels as the data about those tiles. I would not bloat that data with pathfinding search state. Other than bloat, if the tile map, of which there is presumably only 1 copy of, contains the search state, you can only solve for 1 query at a time.
I would suggest, even if you keep it as a simple function call for an immediate path solution and nothing fancy like a navigator, that you keep the search state separate from the tiles.
something like
struct PathNode
{
int x,y; // coordinate of node in tile map
// search state
PathNode * mParent;
float g, f;
....
}
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That's pretty much my setup as well. I think of the tile nodes on the map as essentially read-only data. Though I have read about those who try to keep it all in one, and use bit flags so that multiple units can do path searches on the grid.
If you're worried about the overhead of the path nodes, you can always have them wrapped up in a memory manager, so it can dole out nodes as needed without constantly allocating and deallocating them during searches.
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As long as the tile maps aren't huge, if it's dynamic allocation you want to avoid I would allocate a pool of 2d pathnode arrays of the same size as the tile map. Then the only potentially dynamic aspects of the pathfinding is the open list.
The overhead of the nodes is certainly in additional memory, but you gain much more than you lose by being able to thread out the searches, or incrementally update multiple searches at the same time.
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As long as the tile maps aren't huge, if it's dynamic allocation you want to avoid I would allocate a pool of 2d pathnode arrays of the same size as the tile map. Then the only potentially dynamic aspects of the pathfinding is the open list.
The overhead of the nodes is certainly in additional memory, but you gain much more than you lose by being able to thread out the searches, or incrementally update multiple searches at the same time.
Why allocate pools the size of the tilemap? Depending on the game, I wouldn't imagine most searches would create pathnodes equal to the size of the tilemap. A simple wrapper like this:
public class ObjectPool<T> where T : class, new()
{
private Stack<T> m_objectStack = new Stack<T>();
public T New()
{
return (m_objectStack.Count == 0) ? new T() : m_objectStack.Pop();
}
public void Store(T t)
{
m_objectStack.Push(t);
}
}
While super simplistic, would do a decent job of keeping allocations to a minimum without the overhead of exponentially increasing the memory footprint.
Edited by ferrous
0
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Register a new account | 2017-07-28 19:18:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2659537196159363, "perplexity": 1438.4269465869347}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500550977093.96/warc/CC-MAIN-20170728183650-20170728203650-00308.warc.gz"} |
http://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-6/section/3.14/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 3.14: Large Decimal Rounding
Difficulty Level: At Grade Created by: CK-12
Credit: By NASA/SDO (AIA) [Public domain], via Wikimedia Commons
Source: https://commons.wikimedia.org/wiki/File%3AThe_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA's_Solar_Dynamics_Observatory_-_20100819.jpg
Kyle learns that the sun is 92,960,000 miles away from the Earth. He wants to round the distance to the nearest ten million so that he can easily compare the distance to other distances. Unfortunately, he does not know how to round to the nearest ten million. How can Kyle round 92,960,00 to the nearest ten million?
In this concept, you will learn how to round very large numbers and decimal representations.
### Guidance
Rounding can be very helpful with large numbers. A real world example is a movie box office gross. Every time a new movie comes out a company keeps track of the total of the movie sales, often in the tens or hundreds of millions.
Let's look at an example. Here are a few sales totals for three movies.
1. Star Wars IV - $460,998,007 2. Avatar -$558,179,737
3. Titanic - \$600,788,188
This is where rounding can be very helpful. You can round each of these numbers to the nearest hundred million. You do this by looking at the number to the right of the place that you are rounding.
Let’s look at each movie separately.
1. Star Wars IV - The number after the 4 is a 6, so you round up to a 5. The rest of the numbers become zeros.
500,000,000
2. Avatar - The number after the 5 is a 5, so you round up to 6. The rest of the numbers become zeros.
600,000,000
3. Titanic - The number after the 6 is a zero. So the 6 stays the same and the rest of the numbers become zeros.
600,000,000
You can compare these numbers and see that Avatar and Titanic had the highest sales and Star Wars IV had the lowest sales out of the three movies.
### Guided Practice
Round 9,346,788 to the nearest million.
First, locate the digit that is in the millions place.
9
Next, determine if the number to the right of the millions place is 5 or greater.
No
Then, leave the number in the millions place the same.
9,000,000
### Examples
#### Example 1
Round 5,689,432 to the nearest million.
First, locate the digit that is in the millions place.
5
Next, determine if the number to the right of the millions place is 5 or greater.
Yes
Then, round the number up to the next million.
6,000,000
#### Example 2
Round 156,789,345 to the nearest hundred million.
First, locate the digit that is in the hundred millions place.
1
Next, determine if the number to the right of the hundred millions place is 5 or greater.
Yes
Then, round the number up to the next hundred millions.
200,000,000
#### Example 3
Round 3,456,234,123 to the nearest billion.
First, locate the digit that is in the billions place.
3
Next, determine if the number to the right of the billions place is 5 or greater.
No
Then, leave the number in the billions place the same.
3,000,000,000
Credit: By NASA/SDO (AIA) [Public domain], via Wikimedia Commons
Source: https://commons.wikimedia.org/wiki/File%3AThe_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA's_Solar_Dynamics_Observatory_-_20100819.jpg
Remember Kyle who has just learned the distance from the sun to the Earth? How can he round 92,960,000 to the nearest ten million?
First, locate the digit that is in the ten millions place.
9
Next, determine if the number to the right of the ten millions place is 5 or greater.
No
Then, leave the number in the ten millions place the same.
90,000,000
### Explore More
Round each number to the specified place value.
1. 5,689,123 to the nearest million
2. 456,234 to the nearest ten thousand
3. 678,123 to the nearest thousand
4. 432,234 to the nearest hundred thousand
5. 567,900 to the nearest thousand
6. 1,234,600 to the nearest million
7. 1,980,000 to the nearest million
8. 23,800,990 to the nearest ten - million
9. 18,900,000 to the nearest ten - million
10. 12,890,000 to the nearest million
11. 1,234,567,800 to the nearest billion
12. 3,450,230,000 to the nearest billion
13. 4,590,000,000 to the nearest billion
14. 3,870,000,100 to the nearest billion
15. 13,567,122,320 to the nearest billion
1. [1]^ Credit: By NASA/SDO (AIA) [Public domain], via Wikimedia Commons; Source: https://commons.wikimedia.org/wiki/File%3AThe_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA's_Solar_Dynamics_Observatory_-_20100819.jpg; License: CC BY-NC 3.0
2. [2]^ Credit: By NASA/SDO (AIA) [Public domain], via Wikimedia Commons; Source: https://commons.wikimedia.org/wiki/File%3AThe_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA's_Solar_Dynamics_Observatory_-_20100819.jpg; License: CC BY-NC 3.0
## Date Created:
Sep 24, 2015
Sep 24, 2015
You can only attach files to Modality which belong to you
If you would like to associate files with this Modality, please make a copy first. | 2015-11-25 01:25:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1773095726966858, "perplexity": 2588.5405641799316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398444138.33/warc/CC-MAIN-20151124205404-00025-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.toppr.com/guides/physics/moving-charges-and-magnetism/magnetic-force-and-magnetic-field/ | # Magnetic Force and Magnetic Field
As children, I am sure all of us have played with magnets. Magnets have always been a mystery to us. They are a fun manipulative. At some orientation, they would pull each other towards themselves and at some, they would move away from each other. Over the years we learnt that the force that works behind this behaviour of magnets is its Magnetic Force which is attractive or repulsive in nature depending on its orientation with other magnets.
## Magnetic Force
Magnetic Force can be defined as the attractive or repulsive force that is exerted between the poles of a magnet and electrically charged moving particles. Hence, it is a consequence of the electromagnetic forces.
We have seen that the interaction between two charges can be considered in two stages. The charge Q, the source of the field, produces an electric field E, wherev$$\vec{E}$$ = Q $$\vec{r}$$ / (4πε0 ) r2, $$\vec{r}$$ is unit vector along r, and the field E is a vector field. A charge q interacts with this field and experiences a force F given by
$$\vec{F}$$ = q$$\vec{E}$$ = q Q $$\vec{r}$$ / ( 4 π ε0 ) r 2
(source: flikr)
## Magnetic Field
The Magnetic Field is the space around a magnet or current carrying conductor around which magnetic effects can be experienced. Furthermore, it is a vector quantity and its SI unit is Tesla (T) or Wbm‒2
## Magnetic Lines of Force
It can be defined as curved lines used to represent a magnetic field. In fact, the number of lines relates to the magnetic field’s strength at a given point. Furthermore, the tangent of any curve at a particular point is along the direction of the magnetic force at that point.
[source: qsstudy]
### Properties
1. Magnetic lines of force start from the North Pole and end at the South Pole.
2. They are continuous through the body of a magnet.
3. Magnetic lines of force can pass through iron more easily than air.
4. Two magnetic lines of force can not intersect each other.
5. They tend to contract longitudinally.
6. They tend to expand laterally.
## Magnetic Force on Current-Carrying Conductor
A current-carrying conductor experiences magnetic forces in a magnetic field. Fleming’s Left-Hand Rule predicts the direction of the magnetic forces,
F = IlBsinθ
where F is the magnetic force, I is current, l is the length of a straight conductor in a uniform magnetic field B and θ is the angle between I and B.
Magnetic Force on Current-Carrying Conductor
## Solved Examples For You
Question: If a charged particle projected in a gravity-free room deflects, then
A) There must be an electric field B) There must be a magnetic field.
C) Both fields cannot be zero D) None of these
Solution: Since there must be some external force which will cause the deflection of charged particle and it can be both magnetic force or electric force. Therefore, simultaneously both the fields cannot be zero, therefore, option (C) is the answer. Also, option (A) and (B) are saying that there should be electric field compulsory or magnetic field compulsory for a deflection which is not true, therefore, the only option is (C).
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Browse | 2023-03-27 10:48:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5734357833862305, "perplexity": 785.6635743481099}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00194.warc.gz"} |
https://brilliant.org/discussions/thread/average-waiting-time/ | ×
# Average Waiting Time
At Berracan station, northbound trains arrive every 3 minutes. starting at noon and finishing at midnight. Each Day i walk to the Berrabcan station at a random time in the afternoon and wait for the first train in either direction, on average how many second should i expect to wait?
Note by Yasir Soltani
1 year, 5 months ago
Sort by:
As Chew mentioned, your problem is currently incompletely stated.
The scenario of 1 train is dealt with by Chew.
For the scenario of 2 trains, in a similar manner, draw the graph of waiting time against arrival time. Then, find the expected value of it (through integration, or finding areas). Depending on how the train arrives, the answer would range from 0.75 to 1.5. Staff · 1 year, 5 months ago
I am not so good in combinatorics. Do check my answer.
You mention about northbound trains arrive every 3 minutes but no mention about southbound trains. But you mention about the first train in either direction. If only considering one direction then the expected waiting time should be:
$$$$\begin{split} E[T] & = \int_0^3 t f(t) dt \quad \quad \small \color{blue}{\text{where } t \text{ is the waiting time and } f(t) \text{ is the probability distribution function of }t} \\ & = \int_0^3 \frac{t}{3} dt \\ & = \left[\frac{t^2}{6}\right]_0^3 \\ & = \frac{3}{2} \text{ minutes}\end{split}$$$$
Expecting time of $$\frac{3}{2}$$ minutes (half the arrival time of the trains) is obvious. If it is for two directions, it is much more complicated and I don't have a solution. · 1 year, 5 months ago
@Calvin Lin · 1 year, 5 months ago | 2017-07-22 08:38:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9919700026512146, "perplexity": 1136.0869396309458}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423927.54/warc/CC-MAIN-20170722082709-20170722102709-00643.warc.gz"} |
https://serverfault.com/questions/737852/mapping-drives-via-group-policy-login-script-2008-domain-with-windows-7-8-cli | Mapping Drives via Group Policy login script (2008 domain with Windows 7 & 8 clients)
I'm having trouble getting drives mapped for my domain. I few months ago we were using Group Policy Preferences to map drives, but for some reason it stopped working - so I created a few login scripts for the various divisions in my company to map drives. But those didn't completely work either.
As far as I can tell the GPOs with the login scripts are being ran upon login, but the drives are still not being mapped. Manually executing the .vbs script successfully maps the drives, it's just not mapping them when the user logs in.
Running gpresult /r shows the login script GPO was ran, and viewing the Applications and Services\Microsoft\Windows\GroupPolicy\Operational event log, I can see the Event 4016 where it says:
Starting Scripts Extension Processing.
List of applicable Group Policy objects: (Changes were detected.)
Share Drives GPO
So the GPO is being run, and the script works when executing manually - but the drives are not being mapped when the user logs in. Here is a sample from the script I am using:
On Error Resume Next
If err.number = vbEmpty then
Set objShell = Create("WScript.Shell")
objShell.run ("Explorer")
ElseIf err.number = -2147022646 then
Wscript.Echo "You must create" & strDriveLetter
Else Wscript.echo "Unknown " & err.number
End if
' Map H Drive
Set objectNetwork = CreateObject("Wscript.Network")
objectNetwork.RemoteNetworkDrive "H:"
objectNetwork.MapNetworkDrive "H:", "\\Path\to\FileServer"
Set objectShell = CreateObject("Shell.Application")
objectShell.NameSpace("H:").Self.Name = "Name Applied to Drive Letter"
' Map I Drive
Set objectNetwork = CreateObject("Wscript.Network")
objectNetwork.RemoteNetworkDrive "I:"
objectNetwork.MapNetworkDrive "I:", "\\OtherPath\to\FileServer"
Set objectShell = CreateObject("Shell.Application")
objectShell.NameSpace("I:").Self.Name = "Name Applied to Drive Letter"
and so on for each drive letter that applies to the user.
• login script mapping will map your drive to "administrative context" if UAC is enabled. You should keep troubleshooting preference. Loginscript mapping is obsoleted. What is the result if you use "net use" to map? – strongline Nov 20 '15 at 19:37
• Can you elaborate on that first sentence? Do you have a source? We do have UAC enabled. Are you saying that disabling UAC would allow login scripts to work? Shouldn't the UAC prompt show up upon login to allow the script to execute? – Arindrew Nov 20 '15 at 20:15
• it's a well known issue. blogs.msdn.com/b/cjacks/archive/2007/02/19/… And disabling UAC is not the way to go. Basically, if "net use" works, GPP should work - they are same regarding to how they map drives. – strongline Nov 23 '15 at 20:20 | 2019-05-26 07:47:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31520289182662964, "perplexity": 8587.178195624712}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232258862.99/warc/CC-MAIN-20190526065059-20190526091059-00085.warc.gz"} |
https://robotics.stackexchange.com/questions/17939/hand-eye-calibration-of-robot-arm-using-a-2d-camera-and-marker-of-known-size | # Hand eye calibration of robot arm using a 2D camera and marker of known size
If my understanding is correct, one flavor of hand eye calibration requires the following pairs of data for different robot arm positions:
1. The transform from the robot base to the robot hand.
2. The transform from the marker to the robot camera.
By transform, I mean the 4x4 homogeneous matrix that contains both rotation and translation information.
The part I am stuck on is getting the transform from the marker to the robot camera, which is a 2D camera. The marker can be checkerboard, or Aruco, etc. for which opencv can give you the pose of the marker with respect to the camera.
The question I have is fundamental: Is it even possible to get the pose of the camera from images of a marker of known size? Won't there be a scale ambiguity specifically in the z direction of the camera? Is this z ambiguity resolved by using a marker of known size? Finally, if this scale ambiguity is always there, is it possible to do hand eye calibration using a 2D camera and a marker of known size?
Is it even possible to get the pose of the camera from images of a marker of known size?
-> Yes. From the camera image that is containing a calibration board, you can estimate a 3 by 3 homography matrix H. Then, if you know a camera intrinsic parameters then you can inversely recover the scale known transformation matrix using the intrinsic and homography H. Here is a good reference for this (have a look at 3.1 Closed-form solution). Translation scale will be unknown when the board size is unknown.
Won't there be a scale ambiguity specifically in the z direction of the camera?
-> Not at all if the camera intrinsic and board size is known.
Is this z ambiguity resolved by using a marker of known size?
-> Yes
Finally, if this scale ambiguity is always there, is it possible to do hand eye calibration using a 2D camera and a marker of known size?
-> As your statement "scale ambiguity is always there" is not necessary, the calibration is fairly simple now with the scale known transformations above. You just need to find a robot base to the board transformation and hand to eye transformation.
You have 12 unknowns and each constraint will give you 3 equations. 4 different set data will be enough for a closed-form solution. What you need to solve is
$${^RT_{E_i}}{^ET_{C}}{^{C_i}T_{B}}={^RT_{B}}$$
where R is robot base, E is end-effector, C is a camera, B is the board coordinate.
Refers to the following paper for a detailed solution.
I'm tied up at the moment, so I'll flesh this more out tomorrow morning, but I believe the answer to your question is that the pose estimation algorithms utilize the camera parameters of the camera you're using. Field of view, resolution, focal point, and a known object's dimensions all come together to form similar triangles. The focal point and resolution form the triangle between the CCD or image receptor and lens of the camera, then there's another triangle between the lens and the actual object.
If you know the focal distance and "height" on the image receptor, then you can get the angular width of the object. Knowing its real height and the angular width then lets you calculate the distance or depth of the object.
• Thank you! In my case, the camera intrinsics are assumed known, usually denoted by the K matrix. I'm a novice so references would also be very useful. Jan 7 '19 at 1:08 | 2021-10-23 17:12:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5920838713645935, "perplexity": 679.3202570593149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585737.45/warc/CC-MAIN-20211023162040-20211023192040-00155.warc.gz"} |
https://web2.0calc.com/questions/domain-and-range_37 | +0
# Domain and Range
+1
55
1
+147
Find the greatest integer value of $b$ for which the expression $\frac{9x^3+4x^2+11x+7}{x^2+bx+8}$ has a domain of all real numbers.
Feb 21, 2021
#1
+939
-1
$$x^2 + bx+ 8$$ = 0 has to have no real solutions. So, the discriminant neds to be less than 0.
$$\Delta = b^2 - 4ac= b^2 - 32 < 0$$
$$b^2 < 32$$
The greatest integer value of b is 5.
Feb 21, 2021 | 2021-04-13 06:47:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9439252614974976, "perplexity": 1820.9608056540455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038072175.30/warc/CC-MAIN-20210413062409-20210413092409-00524.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/era.2020005 | # American Institute of Mathematical Sciences
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March 2020, 28(1): 67-90. doi: 10.3934/era.2020005
## Initial boundary value problem for a inhomogeneous pseudo-parabolic equation
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
* Corresponding author: Jun Zhou
Received September 2019 Revised November 2019 Published March 2020
Fund Project: The author is supported by NSF grant 11201380.
This paper deals with the global existence and blow-up of solutions to a inhomogeneous pseudo-parabolic equation with initial value $u_0$ in the Sobolev space $H_0^1( \Omega)$, where $\Omega\subset \mathbb{R}^n$ ($n\geq1$ is an integer) is a bounded domain. By using the mountain-pass level $d$ (see (14)), the energy functional $J$ (see (12)) and Nehari function $I$ (see (13)), we decompose the space $H_0^1( \Omega)$ into five parts, and in each part, we show the solutions exist globally or blow up in finite time. Furthermore, we study the decay rates for the global solutions and lifespan (i.e., the upper bound of blow-up time) of the blow-up solutions. Moreover, we give a blow-up result which does not depend on $d$. By using this theorem, we prove the solution can blow up at arbitrary energy level, i.e. for any $M\in \mathbb{R}$, there exists $u_0\in H_0^1( \Omega)$ satisfying $J(u_0) = M$ such that the corresponding solution blows up in finite time.
Citation: Jun Zhou. Initial boundary value problem for a inhomogeneous pseudo-parabolic equation. Electronic Research Archive, 2020, 28 (1) : 67-90. doi: 10.3934/era.2020005
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show all references
##### References:
[1] G. Barenblat, I. Zheltov and I. Kochiva, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., 24 (1960), 1286-1303. doi: 10.1016/0021-8928(60)90107-6. Google Scholar [2] T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London Ser. A, 272 (1972), 47–78. doi: 10.1098/rsta.1972.0032. Google Scholar [3] Y. Cao and J. X. Yin, Small perturbation of a semilinear pseudo-parabolic equation, Discrete Contin. Dyn. Syst., 36 (2016), 631–642. doi: 10.3934/dcds.2016.36.631. Google Scholar [4] Y. Cao, J. X. Yin and C. P. Wang, Cauchy problems of semilinear pseudo-parabolic equations, J. Differential Equations, 246 (2009), 4568–4590. doi: 10.1016/j.jde.2009.03.021. Google Scholar [5] Y. Cao, Z. Y. Wang and J. X. Yin., A semilinear pseudo-parabolic equation with initial data non-rarefied at $\infty$, J. Func. 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The results for $J(u_0)\leq d$
The graphs of $f$ and $g$
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Research Papers
# Optimal Design of Three-Dimensional Heat Flow Structures for Power Electronics ApplicationsPUBLIC ACCESS
[+] Author and Article Information
Ercan M. Dede
Electronics Research Department,
Toyota Research Institute of North America,
1555 Woodridge Ave,
Ann Arbor, MI 48105
e-mail: [email protected]
Yanghe Liu, Shailesh N. Joshi, Feng Zhou, Danny J. Lohan, Jong-Won Shin
Electronics Research Department,
Toyota Research Institute of North America,
1555 Woodridge Ave,
Ann Arbor, MI 48105
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received January 2, 2018; final manuscript received August 31, 2018; published online December 5, 2018. Assoc. Editor: Gamal Refaie-Ahmed.
J. Thermal Sci. Eng. Appl 11(2), 021011 (Dec 05, 2018) (12 pages) Paper No: TSEA-18-1001; doi: 10.1115/1.4041440 History: Received January 02, 2018; Revised August 31, 2018
## Abstract
Design optimization of a three-dimensional (3D) heat flow structure for power electronics gate drive circuit thermal management is described. Optimization methods are described in the creation of several structural concepts targeted toward simultaneous temperature reduction of multiple gate drive integrated circuit (IC) devices. Each heat flow path concept is intended for seamless integration based on power electronics packaging space constraints, while maintaining required electrical isolation. The design synthesis and fabrication of a select concept prototype is presented along with the development of an experimental test bench for thermal performance characterization. Experimental results indicate a significant 45 ∘C maximum temperature reduction for the gate drive IC devices in a laboratory environment, which translates to an estimated 41 °C maximum temperature reduction under high temperature (∼100 °C) ambient conditions. The technical approach and design strategy are applicable to future wide band-gap (WBG) electronics packaging applications, where enhanced 3D thermal routing is expected to be critical to maximizing volumetric power density.
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## Introduction
Continual miniaturization for increased power density is a recurring theme for advanced power electronics found in next-generation hybrid and electric vehicles. Representative examples from the literature [13] highlight a steady progression of the industry state of the art with a roughly 10–40% decrease in volume over successive generations of a typical power electronics assembly. This ceaseless decrease in size has led to significant thermal management challenges as power density correspondingly increases [4].
While high-performance heat spreading [5], single-phase liquid cooling [68], and two-phase cooling [9,10] for large-area (on the order of ∼ 1 cm2) power semiconductor devices are traditional advanced research focus areas for energy conversion applications, thermal management of associated control electronics and passive circuit elements is increasingly relevant for high volumetric power density designs [11]. For automotive power electronics, situations involving increased power density in combination with high ambient temperatures (upward of 200 °C) are emerging [12], and these cases require multiple cooling strategies for the power semiconductors, control (e.g., gate drive) electronics, and associated passives such as DC-link capacitors [13]. Specific to this work, the role of the gate drive IC device is to provide a certain gate current to switch the power semiconductor device to a low impedance state. Although the heat dissipation of a gate drive IC is small relative to a power semiconductor, such an IC device is traditionally passively cooled and is surface mounted on a printed circuit board (PCB).
For a surface mounted device (SMD) on a PCB, many approaches exist for thermal management of standard integrated circuit (IC) packages. For example, a thermal spreader or cap may be attached to the SMD followed by a heat sink that is thermally connected by way of a thermal interface material (TIM) [14]. The gate driver in Ref. [15] is a typical example of an IC package with an exposed metal back intended for such applications. Alternatively, forced convection via guided air flow over the PCB may be utilized [16], thermal coupling to components with high thermal conductivity, and large surface area can be leveraged, or copper (Cu) filling may be used in all available layers/regions of the PCB for enhanced heat spreading [11]. Other interesting three-dimensional (3D) packaging solutions for high board stacking density consider multiple layers in a “power sandwich” configuration for multiple (e.g., mechanical, thermal, electrical) functions [17]. Furthermore, conductive heat transfer through thick Cu PCBs [16] or heat-pipe-assisted Cu heat spreaders [18] to direct heat flow in three dimensions to a liquid-cooled heat sink or chassis is proposed for power-dense applications including microservers. This latter work provides a clear image for the manner in which an effectively designed 3D heat flow path that combines multiple heat transfer mechanisms enables high power density design.
From a circuit perspective, inefficiency of gate driver hard switching is the root cause of its heat dissipation. A conventional gate driver IC generally contains a totem pole or a pair of switches, as shown in Fig. 1. Hard switching of this pair of switches contributes most to the gate drive IC device power loss. Neglecting the quiescent power consumption of the logic components and conduction loss of the pair of switches, gate driver loss, Pgd, is defined, per [19], as Display Formula
(1)$Pgd=Cg×Vdd2×f$
where Cg is the input gate capacitance of the power semiconductor, Vdd is the difference between the on-state and off-stage gate terminal voltage, and f is the switching frequency. Development of next-generation wide band-gap (WBG) power semiconductor devices such as silicon carbide (SiC) pushes Vdd higher than the case for silicon (Si) power devices (for example, Vdd ∼ 15–20 V for a Si IGBT versus Vdd ∼ 20–25 V for a SiC metal-oxide-semiconductor field-effect transistor (MOSFET)) with higher f. This increases Pgd for the gate drive IC device, per Eq. (1), which in turn calls for careful thermal management.
Resonant gate driving technology has been spotlighted to improve driving power devices. The technology is promising in reducing the heat dissipation of the gate drive IC [2022], as well as in increasing the switching speed [23]. This technology revises the totem-pole circuit structure so that the pair of switches operates with soft switching. However, inclusion of bulky passive components, such as resonant inductors, poses a challenge for compact packaging. Another approach to suppress the heat dissipation of the gate driver is to employ WBG material for the totem-pole switches to reduce their conduction loss [24,25]. The low on-state resistance contributes to reduction of the conduction loss, although increased system cost raises another challenge. Regardless of a circuit-level solution, all active power devices still dissipate heat, and in combination with reduced package form factors and high ambient temperatures active devices will still require effective heat removal strategies.
Thus, the contribution of this work is to present a broadly applicable and detailed design optimization and synthesis methodology for the generation of unique 3D thermal routing or heat flow structures for power electronics auxiliary PCBs with SMDs in support of compact high power density design under harsh environments. A background of the thermal management challenge is provided first in Sec. 2 including a baseline thermal analysis of the case at hand and a detailed description of the technology down-selection process plus selected technical approach. Implementation of optimization methods [26,27] in both two dimensions (2D) and 3D for exploration of the design space and structural concept generation is described in Sec. 3. This portion of the paper includes details of the optimization process, design concept results, synthesis and fabrication of a selected novel prototype structure, and numerical modeling to estimate the effect of the 3D heat flow structure on thermal performance. In Sec. 4, experimental verification and additional validation by simulation of the thermal performance of the selected prototype design is explained. Conclusions then follow in Sec. 5.
## Background
A transparent isometric view of a typical vehicle power control unit (PCU) including downsizing image, adapted from Ref. [28], is shown in Fig. 2. As discussed by Hamada et al. [28], the use of emerging WBG, e.g. SiC, power devices is anticipated to enable up to an 80% reduction in overall PCU volume leading to a significant increase in power density. Future power module WBG power semiconductors in a typical PCU are actively cooled [1,3] and may be capable of high temperature, i.e., ∼200 °C operation, in the future [28]. However, the co-location of silicon (Si) and SiC in the same assembly poses challenges due to different temperature limitations for each semiconductor material, and common solders, substrates, and passive (e.g., magnetic) devices are further limited in their high temperature operation. For example, associated control circuitry is often passively cooled leading to thermal management challenges as Si gate drive IC device temperatures reach a general 150 °C limit and FR-4 PCB temperatures approach a typical material glass transition temperature range of 120–180 °C. A cutaway view of a representative PCU is shown in Fig. 3, from Ref. [29], with the control circuit PCB at the uppermost level and a vertically oriented stacked power card-based power module with interleaved double-side liquid cooling directly below. At a high level, the assembly in Fig. 3 illustrates the 3D trend of current and future power electronics packaging strategies across a variety of applications.
###### Numerical Analysis.
To more fully illustrate the thermal challenges arising from high power density 3D design coupled with the harsh under-hood vehicle environment, a heat transfer analysis of the upper case frame, stacked power module plus cooler, and gate drive portion of the control PCB of a representative PCU is carried out with commercial finite element software [30]. The primary heat loads in the system are taken as the gate drive IC devices (as opposed to other PCB components such as the board power supply or logic IC) based on independent thermal imaging of the circuit under actual system operation.
The governing equation for steady-state heat conduction in Cartesian component form in a 3D domain, Ω, is Display Formula
(2)$Q=−∂∂xi(kij∂T∂xj)inΩ$
where kij are the Cartesian components of the thermal conductivity tensor, T is the temperature state variable, and Q is the volumetric heat generated inside the domain [31]. Summation on repeated subscripts is assumed, where i and j are summed over the range of i, j = 1, 2, 3. The boundary conditions (BCs) are given by, Display Formula
(3)$T=f(T) onΓT, and$
Display Formula
(4)$−(kij∂T∂xj)ni=qa+qc onΓq$
where the function, f(T), specifies the required temperature condition on the boundary ΓT, qa is an applied heat flux on the boundary Γq, and qc = h(TTo) is the convective flux on Γq, which is a function of the surface convection coefficient, h, at a reference temperature, To.
Here, assumptions are made to reduce the physical complexity of the model shown in Fig. 4. Specifically, the lower portion, reactor coil, capacitors, lower case frame plus DC/DC converter, and assembly cover are not modeled since they are not considered part of the primary conduction heat transfer path for the gate drive IC PCB; refer to Kitazawa et al. [3] for explanatory details of the various components. Table 1 provides a summary of the assumed model loads, BCs, and material properties for the model. Based on separate system level test data, the power loss and ambient/fixed temperature values in Table 1 are justified as representative PCU device power loss and under hood temperature boundary conditions for estimating the effect of proposed thermal management solutions. Observe in Fig. 4(c) that the power cards are liquid cooled at a fluid inlet temperature of 65 °C. However, the gate drive circuit board does not connect to this liquid cooler and thus is passively air cooled. Accordingly, the assumed convection coefficients in Table 1 are typical for natural convection [32].
In lieu of a computationally expensive conjugate heat transfer analysis, a simplified fixed temperature boundary condition is assumed and applied to the cooler including fluid inlet and outlet ports. Volumetric heat generation, Q, is applied to each gate drive IC device and power card structure, per Table 1. Buoyancy effects are neglected, and a fixed free surface convection coefficient, h, boundary condition is assigned on both the exterior and interior surfaces of the upper case frame, at respective reference temperatures. Thermal radiation is neglected. Observe that the most thermally impactful harsh environment boundary conditions in this table are these relatively high ambient under hood reference temperatures inside and outside of the case. For the control PCB, the in-plane and cross-plane effective thermal conductivity, k, of Cu-filled and non-Cu regions is calculated using composite slab theory [33] based on the detailed board material and layer stack up. Each gate drive IC device is further modeled as a two layer structure with a thermal conductivity consistent with epoxy, k = 0.2 W/mK, at the top layer and a higher thermal conductivity, k = 150 W/mK, for the bottom layer of the IC device. Standard aluminum (Al) properties are given for the upper case frame. A mesh refinement study is performed to assure grid independence with the final mesh comprising approximately 4.0 × 105 tetrahedral finite elements.
The thermal contour results of the baseline numerical analysis for the control PCB are shown in Fig. 5(a), where a maximum IC device temperature, $TICmax=$ 162 °C, is observed. The minimum device temperature, $TICmin$, from the model is 125 °C for an overall device temperature range, $Tr=TICmax−TICmin$, of 37 °C; note that device temperature range, Tr, may be related to system performance, with a lower range preferred. Further, observe in Fig. 5(b) that the temperature variation of the upper case frame is approximately 12.5 °C with the lowest temperatures, close to ∼ 65 °C, corresponding to the direct contact locations for the liquid cooler.
###### Technology Down-Selection and Approach.
A first possible solution to the thermal challenge of lowering the gate drive IC device maximum temperature is increasing the junction size of the totem-pole switches in Fig. 1. This strategy lowers on-state resistance and hence reduces power loss. Generally, the junction resistance, r, of a MOSFET is determined by channel length, L, and width, W, per [34], as Display Formula
(5)$r=[KWL(Vgs−Vt)]−1$
In Eq. (5), K is a constant, units: (Ohm V)−1, determined by the semiconductor material characteristic and process technology, Vgs is the gate-source voltage, and Vt is the threshold voltage. Increasing the junction size reduces the resistance, r, because it is equivalent to increasing the channel width, W. However, a larger junction area implies potentially lower reliability, increased cost, and a bulky IC size that occupies a larger area on the PCB.
A second technical approach is to counteract the high ambient air temperature environment by actively supplying cold air to the upper portion of the electronics enclosure and actively air cool the gate drive circuit PCB. Unfortunately, a major drawback to this approach is the added complexity of piping cool air to the compactly packaged enclosure under the hood and the potential reliability and fouling issues associated with the use of a fan and associated air coolant, respectively.
The addition of a Cu core/inlay or optimizing the anisotropic thermal conductivity of the PCB using customized thermal traces [35] is a third possible design solution for passive thermal (i.e., heat flux) routing. However, an effective heat sinking location is still required, and special consideration must be given to maintaining electrical isolation between high voltage and low voltage regions of the circuit while achieving high thermal performance, e.g., >25 ∘C IC device temperature reduction.
A fourth solution is also considered where thermally conductive material may be used to connect the gate drive IC devices to the liquid cooler located in the PCU. This is an elegant passive solution, which can replace existing air volume in the PCU with a thermally conductive, yet electrically insulating, heat flow structure. Using low thermal resistance heat conduction between the gate drive IC device heat sources and a thermal ground is a potentially highly effective way to obtain high heat transfer with minimal added system complexity, and these merits are transferable to future WBG systems as well.
Based on the relative advantages and disadvantages of the four technologies discussed qualitatively in the proceeding paragraphs, the different options have been scored in Table 2.
Due to the presence of the liquid cooler, the heat flow structure with thermal grounding concept has clear advantages over the remaining concepts. Thus, the technical approach of optimizing a 3D heat flow path is adopted to thermally couple the gate drive IC devices to the cold liquid cooler or upper case frame, Fig. 5(b), with two interposed TIMs. Figure 6 shows a basic cross section schematic of this concept and associated design region. In this figure, TIM1 provides for thermal communication plus electrical isolation between the gate drive IC devices and the heat flow structure, while TIM2 serves to facilitate heat transfer between the heat flow structure and the cooler or upper case frame. In addition to significantly reducing the gate drive IC device temperatures by at least 25 °C, a secondary goal is to design the 3D heat flow path within the existing “dead space” air gap or empty volume of the electronics package assembly.
## Heat Flow Structure Optimization
To design the conductive heat flow path, a structural topology optimization approach based on gradient-based optimization techniques [26] is used to maximize heat transfer while reducing component weight. Steady-state heat conduction in an isotropic solid, Eq. (2), is assumed for the design domain, where the thermal conductivity, k, is equal in all directions. In the optimization routine, the thermal conductivity material physical parameter is interpolated between a minimum and maximum value using the solid isotropic material with penalization scheme Display Formula
(6)$k=(0.001+.999γp)ko$
where ko is a reference (solid material) thermal conductivity value, γ is the design parameter, and an interpolation penalization parameter value, p = 3, is assumed [26]. In Eq. (6), k → 0.001 ko represents air (void), while kko represents thermally conductive (solid) material.
Thus, the optimization problem statement is formalized as the minimization of the average temperature, $T¯$, in the 3D design domain subject to an upper bound material resource (i.e., volume) constraint, vo. A Helmholtz filtering routing utilizing a filter radius, rf, for mesh independence and to enforce a minimum structural length scale is used. Thus, the problem statement is
$FindγMinimizeT¯Subject toEqs.(2)–(4)v–vo≤00≤γ≤1GivenEq.(6);$
refer to Refs. [26,27], and [36] for extensive details and examples. The optimization process is implemented in a finite element software package with a sparse nonlinear optimizer (SNOPT) [37]. The globally convergent method of moving asymptotes optimizer, a well-performing algorithm for topology optimization [38], is additionally explored.
###### Two-Dimensional Optimization and Results.
Prior to optimizing the full 3D structure, a reduced computational cost 2D exploration of the design space using topology optimization is presented to understand interrelationships between the general size (i.e., volume) of the heat flow structure and its effect on heat source temperature reduction. Consider the x-z plane (refer to Fig. 5) on which the gate drive IC devices reside, as presented in Fig. 7. The computational model is initialized using the parameters in Table 1, where the device heat flux is input to the red-colored device location regions, the exterior boundary is adiabatic, and the temperature is fixed at the dotted blue line, where the interface to the PCU liquid cooler resides. To gauge the sensitivity of heat flow structure performance to the material volume fraction constraint, a pareto-front of optimal designs is obtained using the SNOPT optimizer, Fig. 8. The temperature axis is normalized such that the highest temperature is unity and lowest temperature is zero.
Observe in Fig. 8 that increasing the material fraction past 20% has diminishing returns for increased thermal performance. By analyzing the topological structures, it is deduced that the optimizer places conductive paths connecting sink to source in the most efficient means possible [36]. Increasing the material fraction has diminishing benefit since the conductive paths between sink and source have already been established using less material. The diminishing return with increased material is a characteristic of using a fixed temperature boundary condition near the heat sources. This characteristic is not typical in systems where convection replaces the fixed temperature condition. Acknowledging that the optimizer needs a sufficient amount of material to connect the heat sources to the heat sink, a material volume fraction of ∼20% is selected for a full 3D optimization to understand out-of-plane structural design features.
###### Three-Dimensional Optimization and Results.
The previously presented 2D optimization is useful as a computationally inexpensive means to calibrate design settings. To obtain a solution that is meaningful in implementation, a 3D optimization must be performed. 3D topology optimization examples available in the literature cover a range of applications including the design of thermoelectric coolers (TECs) for downhole electronics [39], the design of air-cooled heat sinks subjected to impinging flows [40], and the design of heat sinks under natural convection [41]. As described in these prior works, implementation in 3D is computational intensive, and this present study is unique in its application of 3D topological structural design to conductive heat flow structures for power electronics gate drive IC device temperature control.
To facilitate the optimization study, the air volume, or 3D design domain, is extracted from the previously introduced solid model geometry, as shown in Fig. 9. This design domain is truncated based on a technical criterion that the air volume design domain be located primarily between the gate drive IC device regions of the control PCB and the upper case frame plus cooler/power card stack. Such a strategy allows for the design of an optimal heat flow structure with shortest path between heat source and sink to logically minimize conductive thermal resistance. This design domain size reduction is further supported by the prior 2D design sensitivity study, where a heat flow structure spanning an excessively large area is shown to provide no added thermal benefit. The truncated design domain has the further feature of reducing the computational burden of the overall 3D optimization process.
Normalized thermal loads from Table 1, applied as heat flux, qa, BCs to the IC device cavities indicated in Fig. 9, are used in the optimization model. As shown in this figure, two boundary condition scenarios are investigated with the location of thermal ground varied in each case. In scenario 1, thermal ground is located at the end boundary of the cooler/power card stack, a surface normal to the plane of the control PCB. For scenario 2, a fixed temperature is assumed at the flat surface boundary to the upper case frame directly opposite from the IC devices.
The 3D heat flow structural optimization result for each scenario is shown in Fig. 10, where dark colored regions indicate solid (i.e., thermally conductive metal) material, and light regions represent void (i.e., nonconductive air). A 20% maximum solid material volume fraction constraint, vo = 0.2, with a filter radius, rf = 0.5 × 10−2, is used based on the 2D exploratory studies that identified these values in producing structural designs that consistently connect to all IC devices while using a small fraction of the available volumetric design domain. Using the SNOPT optimizer, solving for each design requires ∼12.5 h of computational time (for 1000 iterations) on a 40-core virtual machine with 2.60 GHz processors and 192 GB of RAM. For reference, a nearly identical scenario 1 structural optimization result (with a final objective function value within 1%) is obtained using the globally convergent method of moving asymptotes optimizer, although computational time is increased significantly to ∼4.5 days for an identical number of solution iterations.
###### Design Synthesis and Fabrication.
Implementing the design from scenario 2 is deemed feasible if the cast Al upper case frame is redesigned. However, the complex nonplanar surface of the upper case frame directly below the control PCB, Fig. 5(b), presents challenges in terms of establishing an effective contact area for TIM2, Fig. 6, if a 3D heat flow structural insert is instead utilized. Moreover, the upper case frame may be mechanically attached to a harsh environment secondary heat source (e.g., internal combustion engine, motor, or transaxle) under the hood. Thus, the structural concept from optimization scenario 1 is selected for design synthesis and fabrication of a standalone component added to the assembly since a planar interface opportunity with pressure and active temperature control exists at the end mating surface of the cooler/power card stack.
The complete design synthesis process for the scenario 1 postprocessed optimization result for a 3D heat flow structure in solid model form is shown in Fig. 11. In steps 1 and 2, respectively, the design domain is defined and the optimization result is obtained. In step 3, the optimization result is converted to stacked image data by slicing the optimized structure along the z-direction of the model in 5 × 10−4 m increments for approximately 200 sliced images using a custom Matlab® script interfaced with COMSOL®. This stacked image data is imported into a secondary commercial software tool [42] that is typically used for visualizing and segmenting medical images (such as computed tomography and magnetic resonance imaging data) to render a 3D computer-aided design solid model around the γ = 0.5 iso-surface, step 4. A fit check in the assembly model is then performed, step 5. Based on this initial computer-aided design solid model concept, a refined monolithic design, Fig. 11 step 6, is derived. The monolithic design has a unified planar surface for the TIM2 interface to the cooler/power card stack and an upper geometry for the TIM1 interface to the gate drive IC devices that is developed based on the optimization result for ease of manufacturing and further light-weighting. For preliminary inspection purposes, a detailed 3D printed rapid prototype concept model made of polylactic acid allows for a physical fit check with the upper case frame, Fig. 11 step 7.
To understand the anticipated temperature reduction effect for the gate drive IC devices, the numerical model described in Sec. 2 is updated to include the 3D heat flow structural design in as-optimized and refined monolithic forms. After a second grid refinement analysis, each final mesh consists of approximately 2.4 × 106 tetrahedral finite elements. Here, it is assumed that each part is fabricated out of Al with a thermal conductivity of 167 W/mK. For TIM1, a typical conformable thermal gap pad [43] of t = 1 mm thickness with a thermal conductivity, k = 0.8 W/mK, and dielectric breakdown voltage of 6 kV is conservatively assumed. A silver-filled thermal grease with a representative areal thermal resistance, Rth ∼ 6.2 × 10−5 m2K/W [44], is applied at the TIM2 interface. The PCB-to-ambient free convection coefficient at the corresponding inside case reference temperature from Table 1 is applied to all external surfaces of each newly added heat flow structure. The thermal contour results for the 3D heat flow structure in as-optimized versus monolithic form are shown in Fig. 12. The as-optimized structure has an average temperature of 66.3 °C, while the refined monolithic design has a slightly increased average temperature of 69.9 °C. The predicted IC device maximum, minimum, and average (of 14 IC devices) temperatures for the baseline and modified designs in Table 3 indicate an impactful 41 °C maximum and 31 °C average temperature reduction. Note that the results for the modified design are obtained using the monolithic 3D heat flow structure; thus, good performance is achieved with increased manufacturability considering conventional machining methods. Additionally, for the modified design with monolithic structure, the range of IC device temperatures, Tr, is reduced 48.6% from 37 °C in the baseline to 19 °C for the modified case. Hence, although the as-optimized structure could be additively manufactured using methods similar to those described in Refs. [40] and [45], a prototype monolithic structure is fabricated out of 6061-T6 alloy Al using traditional machining methods, Fig. 13(a), for performance verification by experiment.
## Performance Verification and Validation
For the experiments, a gate drive IC device control PCB is electrically modified such that select gate drive IC parasitic diodes are used as resistive element heaters. The advantage of this approach is that the conductive thermal resistance of the IC device package is correctly assessed in the physical experiments. Here, eight IC devices are selected and modified in the aforementioned fashion for the experiments; see the PCB bottom side view in Fig. 13(b) with chosen IC devices highlighted with red circles. The devices are electrically wired in parallel and connected to a 0–36 V, 0–6 A programmable direct current (DC) power supply (TDK-Lambda ZUP36-6). For temperature measurement, a calibrated fine wire Type K thermocouple (TC), ±2.2 ∘C accuracy is securely attached to the topside surface of each IC device using a 9.0 × 10−5 m thick Al foil tape (3M) affixed on the perimeter, away from the TC bead, with silicone adhesive. Device temperatures were recorded using a standard data acquisition (DAQ) system (National Instruments) connected to a computer.
###### Uncertainty Analysis.
The major sources of uncertainty in the experiments arise from the temperature measurement accuracy of the thermocouples and DAQ along with the accuracy of the power (i.e., applied voltage, Va, and measured current, I) from the DC power supply to the gate drive parasitic IC diodes. A summary of typical instrument accuracies is provided in Table 4. Note that the temperature measurement accuracy of the thermocouples and DAQ may be summed for a combined measurement accuracy of ±3.2 °C. A propagation of uncertainty analysis, per [46], then provides an overall uncertainty in the applied heater power of ±1.2% based on the instrument accuracy values in Table 4.
###### Experimental & Numerical Results.
In lieu of high temperature testing with a stacked liquid cooler plus active power card structure, a 12 V DC direct-to-air TEC, Laird Technologies, with 11 W cooling power is substituted to achieve the active temperature control boundary condition and an approximately uniform offset in the BC temperatures from Table 1. This test setup enables testing at an ambient, ∼ 22 °C, laboratory temperature; e.g., ΔTcooler = –50 ∘C down from 65 to ∼ 15 °C. The overlaid image in Fig. 13(c) shows the TEC and 3D heat flow structure assembly with a custom trimmed (filled-silicone polymer on rubber-coated fiberglass carrier) gap pad [43] (k = 0.8 W/mK, t = 0.001 m) applied at the TIM1 interface. A uniform thin layer of polysynthetic silver thermal compound (Arctic Silver 5) is precisely applied at the TIM2 interface. These TIMs are selected to reasonably represent the material conditions assumed in the prior computational models. However, to better characterize the effect of TIM1 on overall thermal performance of the system, an additional silicone-based material system with the same electrical breakdown voltage capability [47] is considered with ∼ 20× increase in thermal conductivity and a 50% reduction in thickness; i.e., k = 17 W/mK and t = 5 × 10−4 m.
Prior to evaluating the performance of the 3D heat flow control structure and its influence on gate drive IC device temperature, heat transfer experiments without active temperature control (i.e., the TEC) or 3D structure installed provide a baseline from which the temperature reduction effect is assessed. For the baseline test, the PCB is bolted to the upper case frame. All IC device temperature measurements are then taken at steady-state, which is achieved after applying power to the devices (approximately 1.23 W per device; 9.84 W total power) for a period of ten minutes. After evaluation of the baseline case, the 3D heat flow structure plus TEC assembly (with TIMs applied) is installed. Even compression of the TIM1 interface is achieved through uniform tightening of the bolts that mount the PCB to the upper case frame. After PCB installation, the experiment is repeated.
The IC device maximum, minimum, and average temperature results for all experimental cases are shown in a bar chart, Fig. 14. Observe that the gate drive IC device maximum and average temperatures are reduced significantly by 45.5 °C and 41.1 °C, respectively, using TIM1 with k = 0.8 W/mK and t = 0.001 m. The IC device temperature range, Tr, is also reduced by 41% from 14.7 °C in the baseline case to 8.7 °C for the modified design. Using the thinner and higher thermal conductivity (k = 17 W/mK, t = 5 × 10−4 m) TIM1 material, the IC device maximum and average temperatures are reduced even further by 60.0 °C and 55.0 °C, respectively, which indicates the importance of the TIM1 interface and material properties on enhancing performance. Additionally, using this second gap pad material, the IC device temperature range, Tr, is reduced 48% relative to the baseline case leading to highly uniform IC device temperatures.
For validation of the experiments, the simulations for the baseline and modified cases are once more updated to reflect the experimental conditions. Specifically, the power card heat loss is set to zero, the cooler temperature is fixed to the TEC condition of ∼ 15 °C, the internal/external convection heat transfer reference temperatures are set to the laboratory ambient of To = 22 °C, and gate drive IC device heat loss is assigned to the appropriate eight devices instead of all 14. Since the exact heat loss from the IC parasitic diodes is not known, the 1.23 W of power applied from the DC source to each device is uniformly scaled down (approximately 52%) in the baseline model to align with the experimentally measured results. These same scaled power loss values are then applied in the simulation with the 3D heat flow structure for straightforward comparison. Using this method, the IC device maximum, minimum, and average temperatures for both the baseline and modified cases are matched to within 5%; refer to the data in Table 3 for all cases. Thus, the experimental results are in satisfactory agreement with modeled predictions and confirm the effectiveness of the novel design approach in achieving significant IC device temperature reduction.
## Conclusions
An optimal design methodology for three-dimensional heat flow structures for power electronics gate drive circuit PCB thermal management was described. A baseline thermal analysis of a representative power control unit was provided to understand the thermal challenges for high power density three-dimensional packaging of the control circuitry. A technology down-selection analysis of potential solutions was provided, and the structural optimization of a conductive heat flow structure was identified as a promising technical approach. Subsequently, a gradient-based structural optimization method was utilized to design a 3D heat flow structure within the existing empty air volume of the package. Two optimized heat flow control 3D structural designs were presented, and one of these designs was synthesized into a unique working prototype. Experiments with this prototype indicated a significant 45 °C gate drive IC device maximum temperature reduction effect in the laboratory environment, and corresponding simulations under high temperature ambient conditions anticipate an estimated 41 °C IC device maximum temperature reduction. The study also highlighted the importance of the thermophysical properties of the selected thermal interface material between the IC devices and 3D heat flow path. In summary, the experimental results are in line with the numerical predictions and indicate that the overall scientific method is highly effective in realizing enhanced thermal routing in three dimensions. Given the significant device temperature reductions that are achievable, the method is widely applicable not only to current Si-based electronics but also next-generation WBG systems including both active and passive components. These packaging techniques may be easily extend to other package geometries to enable further miniaturization and relevant increases in volumetric power density for future WBG electronics.
## Acknowledgements
The authors would like to thank Hiroshi Ukegawa for his technical contributions to this project.
## Nomenclature
• Cg =
gate capacitance, F
• f =
switching frequency, Hz
• h =
convection coefficient, W/m2K
• I =
current, A
• k =
thermal conductivity, W/mK
• L =
junction channel length, m
• p =
penalization parameter
• Pgd =
gate driver power dissipation, W
• q =
heat flux, W/m2
• Q =
volumetric power density, W/m3
• r =
junction electrical resistance, Ohm
• rf =
• Rth =
areal thermal resistance, m2K/W
• t =
thickness, m
• T =
temperature, ∘C
• v =
volume, m3
• V =
voltage, V
• W =
junction channel width, m
Greek Symbols
• Γ =
boundary
• γ =
material design variable
• Ω =
domain
Subscripts
• a =
applied
• avg =
average
• c =
convection
• dd =
supply
• gs =
gate-source
• IC =
integrated circuit
• max =
maximum
• min =
minimum
• o =
reference
• r =
range
• t =
threshold
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View article in PDF format.
## References
Nozawa, N. , Maekawa, T. , Nozawa, S. , and Asakura, K. , 2009, “ Development of Power Control Unit for Compact-Class Vehicle,” SAE Int. J. Passeng. Cars - Electron. Electr. Syst., 2(1), pp. 376–382.
Kubota, S. , Sakurai, T. , and Okada, H. , 2009, “ Size and Weight Reduction Technology for a Hybrid System,” SAE Int. J. Engines, 2(1), pp. 1143–1150.
Kitazawa, O. , Kikuchi, T. , Nakashima, M. , Tomita, Y. , Kosugi, H. , and Kaneko, T. , 2016, “ Development of Power Control Unit for Compact-Class Vehicle,” SAE Int. J. Alt. Power, 5(2), pp. 278–285.
Sakai, Y. , Ishiyama, H. , and Kikuchi, T. , 2007, “ Power Control Unit for High Power Hybrid System,” SAE Paper No. 2007-01-0271.
Ivanova, M. , Avenas, Y. , Schaeffer, C. , Dezord, J.-B. , and Schulz-Harder, J. , 2006, “ Heat Pipe Integrated in Direct Bonded Copper (DBC) Technology for Cooling of Power Electronics Packaging,” IEEE Trans. Power Electr., 21(6), pp. 1541–1547.
Dede, E. M. , 2012, “ Optimization and Design of a Multipass Branching Microchannel Heat Sink for Electronics Cooling,” ASME J. Electron. Packag., 134(4), p. 041001.
Zhou, F. , Liu, Y. , Liu, Y. , Joshi, S. N. , and Dede, E. M. , 2016, “ Modular Design for a Single-Phase Manifold Mini/Microchannel Cold Plate,” ASME J. Therm. Sci. Eng. Appl., 8(2), p. 021010.
Waye, S. K. , Narumanchi, S. , Mihalic, M. , Moreno, G. , Bennion, K. , and Jeffers, J. , 2014, “ Advanced Liquid Cooling for a Traction Drive Inverter Using Jet Impingement and Microfinned Enhanced Surfaces,” 14th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Orlando, FL, May 27–30, pp. 1064–1074.
Wadsworth, D. , and Mudawar, I. , 1990, “ Cooling of a Multichip Electronic Module by Means of Confined Two-Dimensional Jets of Dielectric Liquid,” ASME J. Heat Transfer, 112(4), pp. 891–898.
Joshi, S. N. , and Dede, E. M. , 2017, “ Two-Phase Jet Impingement Cooling for High Heat Flux Wide Band-Gap Devices Using Multi-Scale Porous Surfaces,” Appl. Therm. Eng., 110(5), pp. 10–17.
Marz, M. , 2003, “ Thermal Management in High-Density Power Converters,” IEEE International Conference on Industrial Technology, Maribor, Slovenia, Dec. 10–12, pp. 1196–1201.
Johnson, R. W. , Evans, J. L. , Jacobsen, P. , Thompson, J. R. , and Christopher, M. , 2004, “ The Changing Automotive Environment: High-Temperature Electronics,” IEEE Trans. Electron. Packag. Manuf., 27(3), pp. 164–176.
Wrzecionko, B. , Bortis, D. , and Kolar, J. W. , 2014, “ A 120∘C Ambient Temperature Forced Air-Cooled Normally-Off SiC JFET Automotive Inverter System,” IEEE Trans. Power Electr., 29(5), pp. 2345–2358.
Chu, R. C. , Simons, R. E. , Ellsworth, M. J. , Schmidt, R. R. , and Cozzolino, V. , 2004, “ Review of Cooling Technologies for Computer Products,” IEEE Trans. Device Mat. Reliab., 4(4), pp. 568–585.
Integrated Circuit Division, 2017, “Aug. IXD_609 9-Ampere Low-Side Ultrafast MOSFET Drivers,” Integrated Circuit Division, Beverly, MA, accessed Sept. 19, 2018,
Steinberg, D. S. , 1991, Cooling Techniques for Electronic Equipment, 2nd ed., Wiley, New York.
Ferreira, B. , and Josifovic, I. , 2016, “ Passive Components for a 3D Environment,” International Symposium on 3D Power Electronics Integration and Manufacturing (3D-PEIM), Raleigh, NC, June 13–15.
Cossale, M. , Paredes, S. , Luijten, R. P. , and Michel, B. , 2015, “ Combined Power Delivery and Cooling for High Density, High Efficiency Microservers,” 21st International Workshop on Thermal Investigations of ICs and Systems (THERMINIC), Paris, France, Sept. 30–Oct. 2, pp. 1–6.
Dunn, J. , 2004, “ Matching MOSFET Driver to MOSFETs,” Microchip Technology Inc., Chandler, AZ, accessed Sept. 19, 2018,
Chen, Y. , Lee, F. C. , Amoroso, L. , and Wu, H.-P. , 2004, “ A Resonant MOSFET Gate Driver With Efficient Energy Recovery,” IEEE Trans. Power Electr., 19(2), pp. 470–477.
Zhang, Z. , Li, F. F. , and Liu, Y. F. , 2014, “ A High-Frequency Dual-Channel Isolated Resonant Gate Driver With Low Gate Drive Loss for ZVS Full-Bridge Converters,” IEEE Trans. Power Electr., 29(6), pp. 3077–3090.
Zhang, Z. , Eberle, W. , Yang, Z. , Liu, Y. F. , and Sen, P. C. , 2008, “ Optimal Design of Resonant Gate Driver for Buck Converter Based on a New Analytical Loss Model,” IEEE Trans. Power Electr., 23(2), pp. 653–666.
Anthony, P. , McNeill, N. , and Holliday, D. , 2014, “ High-Speed Resonant Gate Driver With Controlled Peak Gate Voltage for Silicon Carbide MOSFETs,” IEEE Trans. Ind. Appl., 50(1), pp. 573–583.
Moench, S. , Kallfass, I. , Reiner, R. , Weiss, B. , Waltereit, P. , Quay, R. , and Ambacher, O. , 2016, “ Single-Input GaN Gate Driver Based on Depletion-Mode Logic Integrated With a 600 V GaN-on-Si Power Transistor,” IEEE fourth Workshop on Wide Bandgap Power Devices and Applications (WiPDA), Fayetteville, AR, Nov. 7–9, pp. 204–209.
Che, S. , Nagai, S. , Negoro, N. , Kawai, Y. , Tabata, O. , Enomoto, S. , Anda, Y. , and Hatsuda, T. , 2017, “ A1W Power Consumption GaN-Based Isolated Gate Driver for a 1.0 MHz GaN Power System,” 29th International Symposium on Power Semiconductor Devices and IC's (ISPSD), Sapporo, Japan, May 28–June 1, pp. 33–36.
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## Figures
Fig. 1
Typical configuration of gate driver
Fig. 2
Power control unit downsizing image and goal. (Reprinted with permission from Hamada et al. [28]. Copyright 2015 by IEEE).
Fig. 3
Cutaway view of a representative PCU; adapted with permission from Ref. [29]
Fig. 4
Solid model geometry for computational analysis: (a) isometric view, (b) top view with PCB transparent for clarity — red-dashed boxes indicate gate drive IC device locations, and (c) section view of stacked cooler with control PCB directly above
Fig. 5
Thermal contour results for baseline numerical model: (a) control PCB with upper case frame shown transparent and inner power card stack plus cooler hidden, for clarity, and (b) upper case frame only
Fig. 6
Cross section schematic of design region and concept for 3D heat flow structure
Fig. 7
Loads and BCs for 2D optimization study
Fig. 8
Pareto front of material fraction design sensitivity. Note: for inset images, dark regions = thermally conductive (i.e., solid) material; light regions = nonthermally conductive material (i.e., void).
Fig. 9
Extracted air volume 3D design domain
Fig. 10
Three-dimensional heat flow structure optimization results. Note: dark regions = thermally conductive (i.e., solid) material; light regions = nonthermally conductive material (i.e., void).
Fig. 11
Design synthesis process from optimization result to rapid prototype
Fig. 12
Thermal contour results comparing performance of 3D heat flow structure in as-optimized, (a), versus monolithic (b), form
Fig. 13
Experimental setup: (a) prototype Al 3D heat flow structure; (b) control PCB bottom side view—red circled IC devices are powered, and (c) PCB mounted into upper case frame with overlaid view of TEC plus 3D heat flow structure assembly including TIMs (mounted between PCB and case)
Fig. 14
Experimental results for IC device maximum, minimum, and average temperature measurements
## Tables
Table 1 Assumed model loads, BCs, and material properties
Table 2 Technology performance comparison
Table 3 Numerically predicted and experimentally measured results
Note: Sim. = simulation; Exp. = experimental.
aResult using Table 1 conditions.
bTIM1: k = 0.8 W/mK; t = 1 mm.
cResult using experimental conditions.
dTIM1: k = 17 W/mK; t = 0.5 mm.
Table 4 List of instrument accuracies
## Errata
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https://www.biostars.org/p/213348/ | How to resync paired-end data?
2
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Entering edit mode
5.0 years ago
germelcar ▴ 20
I am working with SRR867646 reads, which contains 10919266 sequences for R1 and 2177589 for R2, and in fact, I am not able to do an alignment.
I found another Biostars' post where Devon Ryan suggest using the "repair.sh" script from the BBMap toolkit. I ran the script, but it generates the "r1" and "r2 files empty, and "singletons" file contains the same number of sequences as R1+R2 (10919266+2177589=13096855). My question is, how should I handle that? Should I treat "singletons" files as the reads were single-end?
~g
paired-end transcriptome hisat2 bowtie2 de novo • 4.1k views
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Entering edit mode
Hello germelcar!
We believe that this post does not fit the main topic of this site.
I had the wrong reads. I fully recommend to use the latest version of fastq-dump and its --split-3 argument when working with paired-end data.
For this reason we have closed your question. This allows us to keep the site focused on the topics that the community can help with.
If you disagree please tell us why in a reply below, we'll be happy to talk about it.
Cheers!
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Entering edit mode
@germelcar: Closing a post is an action used by moderators to manage posts that do not fit the topics of this site. Users do not close a post after a solution is found.
The appropriate response would be to the "accept" an answer (use the check mark against the answer).
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Thanks for the observation @genomax2. I have opened it again and sorry for the inconvenience.
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5.0 years ago
GenoMax 107k
I ran the "repair.sh" script and the output is only the "singletons.fq" file, the "r1" or "r2" files are empty.
That does not make sense. What was the full command you used?
Am I right that you did not do trimming on the original files that you got from SRA and the files as submitted may not be matched for number of reads in them?
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Entering edit mode
Yes, you are right. I have not applied some trimming and the reads subitted don't match in the number of sequences. Also, it seems like they are trimmed because all the reads are with a quality above 28.
I ran the following command:
cat SRR867646_1.fastq SRR867646_2.fastq | repair.sh -Xmx15g in=stdin.fq out1=r1.fq out2=r2.fq outs=singletons.fq
The command above generates "r1" and "r2" files empty, but "singletons" is not empty (it's 2.9 GB). I don't know how to interpret that. Should I treat the reads as single-end?
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Entering edit mode
You need to run repair.sh as follows. You need to specify two inputs and two corresponding outputs.
repair.sh in1=SRR867646_1.fastq in2=SRR867646_2.fastq out1=SRR867646_clean_1.fastq out2=SRR867646_clean_2.fastq outsingle=singleton.fastq
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Entering edit mode
I ran the command that you instructed me, with the difference that I have added the "-Xmx12g" argument because of problem with memory. Again, the script has generate "SRR867646_clean_1.fastq" and "SRR867646_clean_2.fastq" files empty and "singleton.fastq" file with 13096855 sequences (like before). The output was the following:
Set INTERLEAVED to false Started output stream.
Input: 13096855 reads 1178716950 bases. Result:
13096855 reads (100.00%) 1178716950 bases (100.00%) Pairs:
0 reads (0.00%) 0 bases (0.00%) Singletons: 13096855 reads (100.00%) 1178716950 bases (100.00%)
Time: 82.731 seconds. Reads Processed: 13096k 158.31k reads/sec Bases Processed: 1178m 14.25m bases/sec
Does the script's output correct? How do I interpret and handle the data? Like single-end pair?
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I believe that repair.sh requires that the reads use standard Illumina read name format. Would you post the first ~20 lines of the SRR867646 R1 and R2 data so we can see it?
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Sure, here are the first 20 lines of the R1 and R2.
The first 20 lines of R1 (SRR867646_1.fastq)
@SRR867646.1.1 1 length=90 TGTNCGTTTCAAGCTTTGAACTGTTTGGATGATACCTTCTTGTTCTTGCAGTTCGGTTTCCATGGCTTCTTTTTCTTTTTCTAGATTTTT +SRR867646.1.1 1 length=90 @@@#4=ABFHGFHIIIIFFHGDDHI?GH>HHIIIIIIIG@BGGHIEHIIHHFHIIHFBEIGFHGGIIIIBCEHHEEFFBEEBD@CCECEE @SRR867646.2.1 2 length=90 CGTNGTACATAAAAATTATTCTGTTTTATCTTTTGGTAAGTCCTTATGATGAATAAAAACAAAACTGAACAGAAACACTCCAAGCATCAT +SRR867646.2.1 2 length=90 @BB#4=ADHHHGHJJJJJJIJJJJJJJJJJJJJJIJIIGIFIJJJJJJHJI>GIIGIIIIIGGIIIJHIHIGDHGAHHEHFFFFFEEEEC @SRR867646.3.1 3 length=90 GTGAAGTCAGAAGGATCGTGATAGACTTTGCCATCAGGGCCCTGGAATTCGTGTCTTTTCTCGCCATCGAAGGTACCGCAGATGCCATGT +SRR867646.3.1 3 length=90 CCCFFFFFHHHHHJIJJJGHEHIIIJJJJJJJJJJJJJJJJJJJJEFGIJJHIIIJJJJIJGJJJHFHHDDFFCEEEDDDDDDDDDCDDE @SRR867646.4.1 4 length=90 CTTNGAGTTTGTTCAGTTGGTCCACTTGGTCGCCCATTTCGGCAACGGTGTCAGTGTGTTTCTTGCGCAGGTTGGACAAGGTGGACTCAT +SRR867646.4.1 4 length=90 CCC#4ADDHHHHHIIIEHIIHIIIIIIIIGIIIIIIIIIIHIIIIIIIFHIIIIIIEH?EHFFFFFCCCCC?CCBCCCBCC@A@BCCCCC @SRR867646.5.1 5 length=90 CTGNAATTCGTGTCTTTTCTCGCCATCGAAGGTACCGCAGATGCCATGTTGGTTTTCTCTGTAAAAGTTGGATGCCGAGATGATACTGTT +SRR867646.5.1 5 length=90 @@@#4ABDHHDFDEHIHIIGHGGIEHIIEGHF?9BGDD?@6=CFHACGFDEF;@AGHGHGHCE7;?;;@DE@;@CAB;B8<>>C@CCEC#
The first 20 lines of R2 (SRR867646_2.fastq)
@SRR867646.1.2 1 length=90 TAAATTTGGTGAATTGTTAGATCGTCTGCTCGAAAGTGAGGCATCTGAACAGAGACTTAGAGACAGAATTTTTGAGTTGGATCAGAAAGA +SRR867646.1.2 1 length=90 @B@FFFFFGHHHHJJJHIGIIJJJGHIIC@HIEFDE*?FHFGGIJJJBGCDGFGIHGEDAGGIIJIGHI>?EEBFFFDEECEEBDCCCCC @SRR867646.2.2 2 length=90 CACAGATCTCGGTAAGGCCGTTGCAACACACGCAGTACGAACGCTACATTGTCTCTGCGTATCCATATTATGCCAGCGCTTTTTCGATGA +SRR867646.2.2 2 length=90 CCCFFFFFHHHHFHIJJIJJIJJJIGIJJJJIIJJHIIJIJJJJJJJHCHHHHHFFFFFACDDDDDDDEDDDDDDDDDDDDDDDDDDEEB @SRR867646.3.2 3 length=90 GTTACATCATCAAACCTAAGGGCTATGGCTTGAAAATCTACTTCGACGGAAACAACAGTATCATCTCGGCATCCAACTTTTACAGAGAAA +SRR867646.3.2 3 length=90 CCCFFFFFHHHHHJJJJJJJJJJJJJJJJJJ@CFHI><c?bbhbfffehb@fhhhc=c=aceeeedc?b?<a>?>AC>CDD>A@CCCCDD @SRR867646.4.2 4 length=90 TGGAGCCACAGCTGCCCAAATCGAGATGAACAAGAAGCGGGAAGCTGAAATGGCCAAACTGAGACGGGACCTCGAGGAAGCCAATGTTCA +SRR867646.4.2 4 length=90 CCCFFFFFHHHHHJJJJJJJJJJJJJIJGIJJJJJJJIJJJIJJJJJJJJJIIJHHHHFFFFFEEDDDDDDDDDDDDDDDDDDDCDDEED @SRR867646.5.2 5 length=90 CAAGGTCAACGACAAAGTTGTTGGAATCGTTTACAAATACGGTGAAGGTTACATCATCAAACCTAAGGGCTATGGCTTGAAAATCTACTT +SRR867646.5.2 5 length=90 @@?DFBDDFDHFHIIGHFEFADGD?EEGH?BGAHGG>DHHHG?F6?FHHGCEFHHJGJJDHHIIHCHHHFFB?C;?CEB?CA@-5>@###
As you can see, the identifier line looks like: @SRR867646.N.RX N length=90, where "N" is the spot number and "RX" is the read number (R1 or R2), I don't know if this is OK.
Do you see something weird with the reads? I have extracted the R1 and R2 with fastq-dump (2.7.0) using the "--split-files" and "--readids" arguments as explained by Edward's Labs
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Entering edit mode
Get the fastq reads directly from ENA and forget about SRA. I am not sure why there are three fastq files at that link. Perhaps submitters have provided an interleaved reads file (which may be the third file). Get the _1 and _2 files to be safe.
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Entering edit mode
Thanks you @genomax2, I have downloaded the files and I will work with them. About the third file, I really don't know about that, but maybe is of interest the answer that I made above it, where fastq-dump with "-F" or "--gzip" argument generates three files as ENA.
Thanks.
~g
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Entering edit mode
There is something strange about these files since SRR86764.fastq appears to be non-overlapping with other two but does not contain interleaved reads.
SRR867646_1.fastq and SRR867646_2.fastq are in sync though. I am able to run repair.sh and get clean output. There are no singletons that result.
If you must use this dataset then as suggested by @Charles below an email to SRA tech support may be in order.
UPDATE
If I start with the SRA file from ENA and fastq-dump the reads then I get this (you may need to rename the file to .sra)
fastq-dump -F --split-files -v SRR867646.sra
Written 10919266 spots for SRR867646.sra
The files that result are not the same size so running repair.sh on them gets the following output
repair.sh in1=./SRR867646_1.fastq in2=./SRR867646_2.fastq out1=./SRR867646_clean_1.fastq out2=./SRR867646_clean_2.fastq outsingle=./single.fastq
Result: 13096855 reads (100.00%) 1178716950 bases (100.00%)
Pairs: 4355178 reads (33.25%) 391966020 bases (33.25%)
Singletons: 8741677 reads (66.75%) 786750930 bases (66.75%)
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Entering edit mode
Thanks @genomax2.
It seems like fastq-dump with --split-3 argument does the same as "repair.sh" script does. I say that based on the following:
I have executed the same command as you mentioned above and another one with the "--split-files" changed to "--split-3":
## with --split-files
R1 = 10919266 sequences
R2 = 2177589 sequences
## with --split-3
SRR867646.fastq = 8741677 sequences (the same as R1 - R2 with --split-files)
R1 = 2177589 sequences
R2 = 2177589 sequences
Also, checking the fastq-dump's documentation with the --help argument (because the webpage is for 2.5.X version), and it says it:
Multiple File Options Setting these options will producemore than 1 file, each of which will be suffixed according to splitting criteria.
--split-3 Legacy 3-file splitting for mate-pairs: First biological reads satisfying dumping conditions are placed in files *_1.fastq and *_2.fastq If only one biological read is present it is placed in *.fastq Biological reads and above are ignored.
I think that explains the behaviour or the three files from the ENA. So in conclusion, for paired-end, is recommended (or "forced") to use --split-3 argument.
Thanks very much to all of you for the help and recommendations.
~g
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If your examples are displayed accurately, then the line breaks have fragmented your reads so they do not conform to the FASTQ format (see here). Each read should consist of four lines:
It may be that fastq-dump outputs a fixed wrap length by default, which can fragment the data, but it's hard to envision how that would produce the line breaks shown in your examples. Therefore, it appears that you have not copied the data format exactly in your examples (also, the examples contain only 19 and 18 lines, but the data are for five reads, which would/should be 20 lines).
I suspect that the real problem is that the read IDs are SRA rather than standard Illumina. You should download in the original format, using the -F flag.
Finally, it's good practice to post the command that you used (anonymize filenames if you prefer), rather than referring to some webpage you used for guidance. It's easier for us to help you troubleshoot.
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Thanks for reply @harold.smith.tarheel. Thanks very much for your recommendations. I have reinstalled sra-tools, but it wasn't the problem. I have downloaded the fastq files from ENA as @genomax2 suggested and it seems weird why is a third file. Anyway, I have made some tests which I would like to share.
I have surfed the web and I found that SRA-tools (also knows as SRA toolkit) have made some changes and NCBI have not doccumented it very well (as mentiones in Edwards Labs). Well, I decided to try some combinations with fastq-dump.
First, I downloaded the two files from ENA and extracted those (in order to manipulate the raw fastq files), later, I downloaded the SRA file with prefetch tool. Finally, I ran fastq-dump with the following combinations:
## test1
fatq-dump --split-3 SRR867646
R1 = 528M, 2177589 sequences (the sames as the fastq files from ENA)
R2 = 528M, 2177589 sequences
The defline sequences are the same for both (R1 and R2).
528M means 528 megabytes (the output is from "ls -lh" command)
## test 2
fastq-dump --split-files -I -W -B --skip-technical SRR867646
R1 = 2.7G, 10919266 sequences
R2 = 536M, 2177589 sequences
Where READ_ID is 1 for R1 and 2 for R2.
## test 3
fastq-dump --split-3 -I SRR867646
R1 = 536M, 2177589 sequences
R2 = 536M, 2177589 sequences
The defline sequences are the same as test2.
## test 4
fastq-dump --split-files -I SRR867646
The same as test 2
## test 5
fastq-dump --split-files -I -W --skip-technical SRR867646
The same as test 2
## test 6
fastq-dump --split-3 -I -W -B --skip-technical SRR867646
R1 = 536M, 2177589 sequences
R2 = 536M, 2177589 sequences
The defline sequences are equals as test 2
## test 7
fastq-dump --split-3 -I -W --skip-technical SRR867646
The same as test 6
## test 8
fastq-dump --gzip --split-3 -I SRR867646
SRR867646.gz = 634M, 8741677 sequences
R1 (SRR867646_1.gz) = 536M
R2 (SRR867646_2.gz) = 536M
Defline the same as test 2
NOTE that with gzip argument, it has generated three files instead of two.
## test 9
fastq-dump --split-3 -I -F SRR867646 --> This is because the suggestion you made
SRR867646.fastq = 1.7G, 8741677 sequences
R1 = 414M, 2177589 sequences
R2 = 414M, 2177589 sequences
The defline sequence (first line of the spot) has the following format: @READ_ID
The defline quality (third line of the spot) has the following format: +READ_ID
## test10
fastq-dump --split-3 -F SRR867646
The same as test 9
Finally, I would like to comment that fastq-dump has the following arguments:
--helicos Helicos style defline
--defline-seq <fmt> Defline format specification for sequence. --defline-qual <fmt> Defline format specification for quality. <fmt> is string of characters and/or variables. The variables can be one of: $ac - accession,$si spot id, $sn spot name,$sg spot group (barcode), $sl spot length in bases,$ri read number, $rn read name,$rl read length in bases. '[]' could be used for an optional output: if all vars in [] yield empty values whole group is not printed. Empty value is empty string or for numeric variables. Ex: @$sn[_$rn]/$ri '_$rn' is omitted if name is empty
I tried to define the deflines but I did have success.
It seems that the test 3 will works fine, the difference is that the defline sequence and defline quality are different (@ACC_NUMBER.SPOT_NUMBER READ_ID SPOT_NUMBER for test3 and @ACC_NUMBER.SPOT_NUMBER SPOT_NUMBER/READ_ID for ENA reads) and defline quality (more verbose for test3), and that is what makes the difference (in size) between the files generated from test3 and ENA's files.
Altought the files generated from test3 are slightly the same as ENA's files, I'll work with ENA's file because those have the standar format (with the slash), and I am not sure if the software out there are able to handle the defline generated from test3.
Thanks to all for your help and reccommendations.
~g
0
Entering edit mode
5.0 years ago
Charles Plessy ★ 2.7k
If the R1 and R2 files were originally paired, and only R1 had reads removed, then you can try https://github.com/mmendez12/sync_paired_end_reads.
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Entering edit mode
Hello Charles Plessy, thanks for reply.
Sorry but... how can I know if only R1 have reads removed? For me, it seems like both (R1 and R2) have reads removed since theirs number of sequences (10919266 for R1 and 2177589 for R2), and all above a score of 28, does that makes sense or am I missing something?
0
Entering edit mode
If the files that you have are not directly the sequencer's output (which we assume is synchronised), and if there is no explanation on how they were produced, then it is hard to answer the question, except by checking if there are R2 IDs that are not found in R1.
Actually, I would have expected such kind of information to be available in the SRA record, but I found nothing. I then visited http://trace.ncbi.nlm.nih.gov/Traces/sra/?run=SRR867646, selected the "Reads" tab, and briefly browsed the read sequences to see where are the unpaired reads. They are all after read number 2177589. I do not know if it means that the authors deposited the files like this. Perhaps you can ask to the SRA helpdesk (since there is no information about who the authors are).
0
Entering edit mode
Thanks Charles Plessy.
It seems like the three files available from ENA's files were produced as I suggest in my answer above. It seems like fastq-dump (at least the version 2.7.0) has added the --split-3 argument which does the work for you.
Thanks.
~g | 2021-09-28 22:54:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4341721534729004, "perplexity": 7002.472518545413}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060908.47/warc/CC-MAIN-20210928214438-20210929004438-00020.warc.gz"} |
https://hal-lirmm.ccsd.cnrs.fr/lirmm-00736699 | # Placing Regenerators in Optical Networks to Satisfy Multiple Sets of Requests
3 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The placement of regenerators in optical networks has become an active area of research during the last few years. Given a set of lightpaths in a network $G$ and a positive integer $d$ , regenerators must be placed in such a way that in any lightpath there are no more than $d$ hops without meeting a regenerator. The cost function we consider is given by the total number of regenerators placed at the nodes, which we believe to be a more accurate estimation of the real cost of the network than the number of locations considered in the work of Flammini (IEEE/ACM Trans. Netw., vol. 19, no. 2, pp. 498-511, Apr. 2011). Furthermore, in our model we assume that we are given a finite set of $p$ possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when $d=1$ or $p=1$, we prove that for any fixed $d,p geq 2$, it does not admit a PTAS, even if $G$ has maximum degree at most 3 and the lightpaths have length ${cal O}(d)$. We complement this hardness result with a constant-factor approximation algorithm with ratio $ln (d cdot p)$. We then study the case where $G$ is- a path, proving that the problem is polynomial-time solvable for two particular families of instances. Finally, we generalize our model in two natural directions, which allows us to capture the model of Flammini as a particular case, and we settle some questions that were left open therein.
Document type :
Journal articles
https://hal-lirmm.ccsd.cnrs.fr/lirmm-00736699
Contributor : Ignasi Sau <>
Submitted on : Friday, September 28, 2012 - 6:00:53 PM
Last modification on : Tuesday, December 17, 2019 - 10:00:03 AM
### Citation
George B. Mertzios, Ignasi Sau Valls, Mordechai Shalom, Shmuel Zaks. Placing Regenerators in Optical Networks to Satisfy Multiple Sets of Requests. IEEE/ACM Transactions on Networking, IEEE/ACM, 2012, 20, pp.1-15. ⟨10.1109/TNET.2012.2186462⟩. ⟨lirmm-00736699⟩
Record views | 2021-06-21 12:44:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.654999852180481, "perplexity": 684.1814335087497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488273983.63/warc/CC-MAIN-20210621120456-20210621150456-00015.warc.gz"} |
https://physics.stackexchange.com/questions/465958/about-fpu-non-linear-problem-in-reference-to-the-original-article | # About FPU non linear problem, in reference to the original article
I'm reading the original article about the Fermi-Pasta-Ulam-Tsingou (FPUT) problem and I have some problems about the conclusion. Here the behavior of the system as was reported in the article: $$x_i=(x_{i+1}+x_{i-1}-2x_i)+\alpha[(x_{i+1}-x_i)^2-(x_i-x_{i-1})^2]$$ for example for the quadratic perturbation, $$i=1,2,...,64$$.
The paradox arises from the bizarre behavior of the system which presents the predominance of one of the modes, i.e. one of the modes has more energy than all the others put together. Only the first few modes exchanges energy between each others and do this regularly. This were the FPUT original observations. At the end of the article there is a reference to the Frobenius and Perron theorem which is summarily recalled
Let $$A$$ be a matrix with positive elements. Consider the linear transformation of the $$n$$-dimensional space defined by this matrix. One can assert that if $$\bar{x}$$ is any vector with all its components positive, and if $$A$$ is applied repeatedly to this vector, the directions of the vectors $$\bar{x}$$, $$A\bar{x}, A^2\bar{x},..., A^i\bar{x}$$, will approach that of a fixed vector $$\bar{x}_0$$ in such that a way that $$A\bar{x}=\lambda\bar{x}_0$$. This eigenvector is unique among all vectors with all their components non-negative. [...]
This above is quoted by the FPUT's article, which continues:
[...] Let $$Q$$ be a transformation of a $$n$$-dimensional space which is non-linear but is still rather simple algebriacally (let us say, quadratic in all the coordinates). Consider any vector $$\bar{x}$$ and the iterates of the transformation $$Q$$ acting on the vector $$\bar{x}$$. In general, there will be no question of convergence of these vectors $$Q^n\bar{x}$$ to a fixed direction. But a weaker statement is perhaps true. The directions of the vectors $$Q^n\bar{x}$$ sweep out certain cones $$C_{\alpha}$$ or solid angles in space in such a fashion that the time averages, i.e., the time spent by $$Q^n\bar{x}$$ in $$C_{\alpha}$$, exist for $$n\to\infty$$. These time averages may depend on the initial values, given $$C_{\alpha}$$. In other words, the space of all direction divides into a finite number of regions $$R_i$$, such that for vector $$\bar{x}$$ taken from any one of these regions the percentage of time spent by images $$\bar{x}$$ under the $$Q^n$$ are the same in any $$C_{\alpha}$$.
Now I can't understand the meaning of these $$C_{\alpha}$$ I think that if the system goes into a "cyclic behavior" for what is about energy exchange I can somehow think to the modes like vectors in a space and I can think the system in approaching these vectors one by one cyclically, so I can read the $$C_{\alpha}$$ like a formalization of this idea, is it correct?
Another question is: what does it means, in this context, to iterate the application of a transformation ($$A$$ or $$Q$$) on a vector? Could it represent somehow the evolution of the system?
• pter26, The English is fine, though I did correct some typos. – stafusa Mar 12 at 8:15 | 2019-07-18 10:13:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 31, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8736923933029175, "perplexity": 233.91269720711347}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525587.2/warc/CC-MAIN-20190718083839-20190718105839-00278.warc.gz"} |
http://coertvonk.com/physics/electromagnetism/magnetism/moving-charge-29837 | # Moving charge; Cyclotron
My notes of the excellent lecture 13 by “Walter Lewin. 8.02 Electricity and Magnetism. Spring 2002. The material is neither affiliated with nor endorsed by MIT, https://youtube.com. License: Creative Commons BY-NC-SA.”
## Path of a moving charge in $$\vec B$$
Remember: Lorenz force $$\vec F$$ depends on the velocity of the charge and the magnetic field that it experiences
$$\vec F = q\,\left(\vec v\times\vec B\right) \nonumber$$
If we have the following charge $$q$$ and velocity $$\vec v$$, it will experience $$\vec F$$
This causes the charged particle to go around in a perfect circle. The Lorenz force can’t change the speed (can’t change the kinetic energy), because $$\vec F\perp \vec v$$, but it can change the direction of the velocity.
The radius $$R$$ of the circle follows from the force. With $$\vec F\perp \vec v$$, the $$\sin$$ of the angle between them is $$1$$. That is now the centripetal force $$\frac{mv^2}{R}$$, where $$m$$ is the mass of the particle $$F = q\,v\,B = \frac{mv^2}{R} \nonumber$$
So the radius $$\shaded{ R = \frac{m\,v}{q\,B} } \label{eq:R}$$
Here $$mv$$ is the momentum.
### Numerical example
$$U$$Instead of $$\Delta V$$, we often use the European symbol for voltage difference: $$U$$. The letter ‘u’ stands for “Potentialunterschied”. Do not confuse it with potential energy, that also uses $$U$$.
Assume a proton with kinetic energy $$1\,\rm{MeV}$$ $$=1.6\times10^{-13}\,\rm J$$ in a constant magnetic field $$\vec B$$ \begin{align*} q\,\Delta V &= 1.6\times10^{-13}\,\rm J \\ m_p &= 1.7\times 10^{-27}\,\rm{kg} \\ q_p &= 1.6\times 10^{-19}\,\rm{C} \end{align*}
The speed of the proton \begin{align} q\,\Delta V &= \frac{1}{2}m\,v^2 \nonumber \\ \Rightarrow v &= \sqrt{\frac{2\,q\Delta V}{m_p}} \nonumber \\ &\approx \sqrt{\frac{2\,(1.6\times10^{-13})}{1.7\times 10^{-27}}} \nonumber \\ &\approx 1.4\times 10^7\,\rm{m/s} \approx 0.05\,\rm c \label{eq:onemkvproton} \end{align}
That is 5% of the speed of light, comfortably low, so we don’t have to make any relativistic corrections.
If this proton now enters the magnetic field $$B=1\,\rm T$$. Based on equation $$\eqref{eq:R}$$, it will circle with radius $$R$$ \begin{align*} R &= \frac{mv}{qB} \\ &= \frac{(1.7\times10^{-27})(1.4\times 10^7)}{(1.6\times 10^{-19})(1)} \\ &\approx 1.5\,\rm m \end{align*}
### Eliminate $$\text{ }\vec v$$
In equation $$\eqref{eq:R}$$, the velocity $$v$$ is commonly replaced by the potential difference $$\Delta V$$ over which we accelerate these particles.
Find $$v=f(\Delta V)$$ \begin{align*} q\,\Delta V &= \frac{1}{2}m\,v^2 \\ \Rightarrow v &= \sqrt{\frac{2\,q\,\Delta V}{m}} \end{align*}
Substituting this in equation $$\eqref{eq:R}$$ \begin{align*} R &= \frac{m\,\sqrt{\frac{2\,q\,\Delta V}{m}}}{qB} \end{align*}
That simplifies to $$\shaded{ R = \sqrt{\frac{2\,m\,\Delta V}{q\,B^2}} } \tag{Radius}$$
### Approaching $$\text{ c}$$
When the speed approaches the speed of light, we have to apply special relativity. That is not part of this course, but we will briefly touch upon that
Things go sour, when we have a $$500\,\rm{keV}$$ electron, then \begin{align*} \frac{1}{2}m\,v^2 &= q\,\Delta V \\ \Rightarrow v &= \sqrt{\frac{2\,q_e\,\Delta V}{m_e}} \\ &= \sqrt{\frac{2\,(1.6\times10^{-19})\,(500\times10^3)}{9.1\times 10^{-31}}} \\ &\approx 4.2\times10^8\,\rm{m/s} \gt \rm c \end{align*}
This is larger than the speed of light, so clearly not possible. If you make relativistic corrections, you will find the actual speed. Just to show you, we’ll make these corrections below.
#### Relativistic correction
Start with same kinetic energy $$q\,\Delta V$$, but it is no longer $$\frac{1}{2}m\,v^2$$ $$q\,\Delta V = (\gamma – 1)\,m\,c^2 \nonumber$$
Here the Lorenz factor $$\gamma$$ is defined as $$\gamma = \frac{1}{\sqrt{1 – \frac{v^2}{c^2}}} \tag{Lorenz factor}$$
The Lorenz factor follows as \begin{align*} q\,\Delta V &= (\gamma – 1)\,m\,c^2 \\ \Rightarrow \gamma &= \frac{q\,\Delta V}{m\,c^2} + 1 \\ &\approx \frac{(500\times 10^3)(1.6\times 10^{-19})}{(9.1\times10^{-31})\,(300\times10^6)^2} + 1 \\ &\approx 1.977 \end{align*}
The speed $$v$$ \begin{align*} \sqrt{1 – \frac{v^2}{c^2}} &= \frac{1}{\gamma} \Rightarrow \frac{v^2}{c^2} \\ \Rightarrow v &= c\,\sqrt{1 – \frac{1}{\gamma^2}} \\ \Rightarrow v &= 300\times10^6 \sqrt{1 – \frac{1}{1.977^2}} \\ &\approx 2.6\times 10^8\,\rm{m/s} \end{align*}
The radius $$R$$ in a $$1\,\rm T$$ magnetic field \begin{align} R &= \gamma\,\frac{m\,v}{q\,B} = \sqrt{\frac{(\gamma+1)\,m\,\Delta V}{q\,B^2}} \label{eq:corrR} \\ &= 1.977\,\frac{(9.1\times10^{-31})\,(2.6\times 10^8)}{(1.6\times10^{-19})\,1} \nonumber \\ &\approx 2.9\,\rm{mm} \nonumber \end{align}
### Some examples
Proton accelerator
KE v [m/s] B [T] R
$$1\,\rm{MeV}$$ $$1.4\times 10^7$$ $$1$$ $$0.15\,\rm{m}$$
$$50\,\rm{MeV}$$ $$9.4\times 10^7$$ $$1$$ $$1.04\,\rm{m}$$
Fermilab $$500\,\rm{GeV}$$ $$2.99999\times10^8$$ $$1.5$$ $$1.1\,\rm{km}$$
LHC $$7,000\,\rm{GeV}$$ $$\approx\rm c$$ $$5.5$$ $$4.2\,\rm{km}$$
Electron accelerator
KE v [m/s] B [T] R
$$15\,\rm{eV}$$ $$2.3\times 10^6$$ $$0.5\times10^{-4}$$ $$26\,\rm{cm}$$
$$100\,\rm{keV}$$ $$1.6\times 10^8$$ $$1$$ $$1.1\,\rm{mm}$$
$$500\,\rm{keV}$$ $$2.6\times10^8$$ $$1$$ $$2.9\,\rm{mm}$$
### Practical use
In 1945, the Americans needed Uranium $${}^{235}\rm U$$ to build an atomic bomb. This has 143 neutrons, instead of the more common 146. To separate them, Ernest Lawrence of Berkeley built a mass spectrometers that could separate $${}^{235}\rm U$$ and $${}^{238}\rm U$$.
In a mass spectrometer, the uranium is heated so that it ionizes. Let’s assume it looses one electron, so it’s positively charged with one unit charge. It then accelerates it over a potential difference, so they get a certain speed.
In a constant magnetic field, the charged particles go around a circle and hit a collector. The radius of the circle is proportional with $$\sqrt{m}$$. The mass of 238 is 1.2% larger than the mass of 235. So they land is a collector slightly separated from the other one.
## Accelerating protons
In 19939, the UC Berkeley physicist, Ernest Laurence received a Nobel Prize for Physics. He invented the cyclotron that accelerates protons to $$730\,\rm{MeV}$$, almost the speed of light.
### Cyclotron
In the early days accelerating was done in a cyclotron. It consists of two conducting chambers $$D$$ in vacuum. Seen from the top and side:
Suppose we release a $$1\,\rm{MeV}$$ proton. That comes out a speed of $$1.4\times10^7\,\rm{m/s}$$ $$\eqref{eq:onemkvproton}$$. In a $$1\,\rm{T}$$ field, based on the earlier table, the radius is going to be $$15\,\rm{cm}$$.
The proton start to make a circle. But when it gets halfway, a potential difference is introduced between these two $$D$$’s. The high potential on the right $$D$$, and the low potential on the left $$D$$. In the gap between the $$D$$’s, you get an electric field $$\vec E$$
The field accelerates the proton. If the potential difference is $$20\,\rm{kV}$$, the proton will gain $$20\,\rm{keV}$$ kinetic energy. When it crossed the gap, it has $$1.02\,\rm{MeV}$$. If $$V$$ is 2% higher, then based on equation $$\eqref{eq:corrR}$$, the radius is 1% higher than $$15\,\rm{cm}$$. It comes out a little higher.
Once, it gets to the top, the potential difference is reversed, so the $$\vec E$$ points to the right, and it is again accelerated by $$20\,\rm{keV}$$.
Very gradually, it spirals out the largest radius. So for every rotation it gains $$40\,\rm{keV}$$. The electric fields are doing the work, they accelerate the particles. The magnetic field changes the direction, but they can’t do work on the particles. It confines the particles.
If we go 1225 full rotations, where each time the kinetic energy increases by $$40\,\rm{keV}$$. Multiplying these you find that it gained $$49\,\rm{MeV}$$. Plus the initial $$1\,\rm{MeV}$$, it now has $$50\,\rm{MeV}$$. Referring to the the earlier table, the radius is one meter.
If we don’t have to make relativistic corrections, the time to go around is independent on the proton’s speed. With the radius proportional to $$v$$, so the time is independent of $$v$$ $$T = \frac{2\pi R}{\rm{speed}} = \frac{2\pi\,m}{q\,B} \nonumber$$
The time to go around once, is only $$66\,\rm{ns}$$. To go around 1,225 times will take only $$80\,\rm{msec}$$. That means the switching frequency becomes about $$30\,\rm{MHz}$$.
Because of relativistic correction, the time to go around once, becomes $$T = \frac{2\pi\,m}{q\,B}\,\gamma = 6.6\times 10^{-8}\,\rm{sec} \nonumber$$
If you go to very high energies, that time is not constant for a full rotation. So you have to adjust the switching frequency. We call those instruments synchrotrons or synchrocyclotrons.
### Modern accelerators
Modern accelerators have constant radii. They are rings. The only way to keep the particles in the ring when they have a low energy, and when they have a high energy, is by gradually increasing the magnetic field. By making the magnetic field go up, you can keep the protons in that ring.
#### Fermilab
Fermilab near Chicago. One of the modern accelerators, occasionally called colliders. A diameter of $$2.2\,\rm{km}$$, accelerates up to $$1000\,\rm{GeV} = 10^{12}\,\rm{eV}$$. The beams of high energy protons are made collide with other nuclei to undercover the inner workings of nuclear physics.
The tunnel of the largest ring in the work, at CERN in Geneva, has a radius of $$4.3\,\rm{km}$$. Using superconducting magnets, they can go to about $$5\,\rm T$$. The Large Hadron collider accelerates protons to the unprecedented energy of $$6500\,\rm{GeV} = 6.5\times 10^{12}\,\rm{eV}$$.
The Higgs boson is part of what’s called the Standard Model of particle physics. A set of rules that lays out our understanding of the fundamental building blocks of the universe. The Higgs boson has a mass of about $$125\,\rm{GeV/c^2}$$, about $$133$$ proton masses. | 2022-12-01 17:03:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999375343322754, "perplexity": 864.4568101856673}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710829.5/warc/CC-MAIN-20221201153700-20221201183700-00647.warc.gz"} |
https://mathoverflow.net/questions/220739/generic-polynomial-for-alternating-group-a-4-is-not-correct | # Generic polynomial for alternating group ${A}_{4}$ is not correct
I was validating the percentage of cases where the generic two parameter polynomial for Galois group ${A}_{4}$ is valid. We have
\begin{equation*} {f}^{{A}_{4}} \left({x, \alpha, \beta}\right) = {x}^{4} - \frac{6\, A}{B}\, {x}^{3} - 8\, x + \frac{1}{{B}^{2}} \left({9\, {A}^{2} - 12 \left({{\alpha}^{3} - {\beta}^{3} + 27}\right) B}\right) \in K \left({\alpha, \beta}\right) \left[{x}\right] \end{equation*}
where
\begin{equation*} A = {\alpha}^{3} - {\beta}^{3} - 9\, {\beta}^{2} - 27\, \beta - 54 \end{equation*}
and
\begin{equation*} B = {\alpha}^{3} - 3\, \alpha\, {\beta}^{2} + 2\, {\beta}^{3} - 9\, \alpha\, \beta + 9\, {\beta}^{2} - 27 \left({\alpha - \beta - 1}\right). \end{equation*}
from Arne Ledet "Constructing Generic Polynomials", Proceedings of the Workshop on Number Theory, Institute of Mathematics, Waseda University, Tokyo, 2001. When testing for $- 100 \le \alpha, \beta \le + 100$ we have 99.990% of the irreducible cases belonging to the ${S}_{4}$ group and 0.005% of the remaining cases belonging to the ${A}_{4}$ and ${D}_{4}$ groups, respectively.
What is the correction if known and are there other two parameter cases known for the ${A}_{4}$ group? I do have from Gene Smith ("Some Polynomials over $\mathbb{Q} \left({t}\right)$ and their Galois groups", Mathematics of Computation, 69(230):775-796, August 1999.) the example ${f}^{{A}_{4}} \left({x, t}\right) = {x}^{4} + 18\, t\, {x}^{3} + \left({81\, {t}^{2} + 2}\right)\, {x}^{2} + 2\, t \left({54\, {t}^{2} + 1}\right) x + 1 \in K \left({t}\right) \left[{x}\right]$ which is valid and I encountered a five parameter case which I have not yet tested. I have validated the other common examples for ${S}_{4}$, ${V}_{4}$, ${D}_{4}$, and ${C}_{4}$.
• I find it hard to figure out what the question actually is... – Igor Rivin Oct 12 '15 at 21:12
• My question this generic polynomial is not correct from what I have computed. Does anyone have the corrected version and are there other examples, say of the two parameter cases, that are known. I have only found these three cases and the main one that I found the error in is repeated in several papers. For example, I have tried sign variation of the three terms-all eight possible cases as a simple search for the error and found none. – Lorenz H Menke Oct 12 '15 at 21:20
• It might be worth checking Jensen, Ledet, and Yui, Generic Polynomials, MSRI Publications 45, Cambrdige (2002), MR1969648 (2004d:12007), if you haven't already. – Gerry Myerson Oct 12 '15 at 22:15
The Galois group is a subgroup of $A^4$ if and only if the discriminant is a perfect square. If you change $x^3$ to $x^2$ you get the discriminant to be: $$\frac{1728^2 \left(b^2+3 b+9\right)^2 \left(a^3 (2 b+3)-3 a^2 \left(b^2+3 b+9\right)+\left(b^2+3 b+9\right)^2\right)^2}{\left(a^3-3 a \left(b^2+3 b+9\right)+2 b^3+9 b^2+27 b+27\right)^4},$$ so that definitely works. The discriminant is definitely NOT a square in the original version.
(A version of) Ledet's paper can be found here. The formula given in that version has $x^2$ where the question here has $x^3$. Perhaps this accounts for the difficulties.
• The formula with $x^2$ is also the formula given in their book "Generic Polynomials -- Constructive Aspects of the Inverse Galois Problem" (C.U. Jensen, A. Ledet, N. Yui, 2002), p. 37. – Tom De Medts Oct 13 '15 at 7:19 | 2021-06-24 04:15:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8109766244888306, "perplexity": 1054.5694674895865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488550571.96/warc/CC-MAIN-20210624015641-20210624045641-00611.warc.gz"} |
https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Energy_Levels | # A-level Physics (Advancing Physics)/Energy Levels
As an electron approaches a nucleus from infinity, it becomes 'bound' - it is attached to the nucleus, if you like. In this bound state, the electron occupies what is called an energy level. A nucleus has a discrete number of energy levels, and so electrons bound to a certain nucleus can only take on certain potential energies. These energies are negative by convention.
The lowest (most negative) energy level is denoted n=1, the next lowest n=2, and so on. The values of these can be found using formulae which you don't need to know about. Alternatively, they may be determined experimentally.
Energy levels in a hydrogen atom. The transition shown from the n=3 level to the n=2 level gives rise to visible light of wavelength 656 nm (red).
At random, electrons jump between energy levels. If they jump to a lower energy level (more negative), they release energy in the form of a photon. If they jump to a higher energy level, they must absorb a photon of the appropriate energy. The energies of these photons can be calculated using the following formulae, which you should already know from AS:
${\displaystyle E=hf}$
${\displaystyle c=\lambda f}$,
where E is energy, h is Planck's constant (6.63 x 10−34 J s), f is frequency, c is the speed of light, and λ is wavelength.
The energy levels of different nuclei are different. Evidence for these energy levels comes from the emission and absorption spectra of atoms. An emission spectrum can be obtained by heating a sample of an element. This gives the electrons energy, so they jump up the energy levels. At random, they then jump down again, giving off photons with measurable frequencies. The formulae above can be used to calculate the difference in energy between the levels between which the electrons have jumped.
An absorption spectrum can be found by passing light through (for example) a gas, and observing the frequencies of light which are absorbed. These frequencies correspond to jumps between energy levels which electrons have undergone when they absorb the photons, gaining energy.
It should be noted that electrons do not always jump to the next-door energy level - they can, in principle, jump to any energy level. They cannot jump to an energy which is not that of an energy level.
To work out how much (electrostatic potential) energy an electron will have at a certain energy level, use the formula: ${\displaystyle E={\frac {-13.6}{n^{2}}}}$
To work out how much energy an electron will gain when jumping between energy levels, use the formula: ${\displaystyle \Delta E=-13.6({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}})}$ where an electron is transitioning between ${\displaystyle n_{1}}$ and ${\displaystyle n_{2}}$
The value of 13.6 is a constant by itself but is made up of a combination of constants from the derivation of the Bohr radius and Energy Levels in Hydrogen.
13.6 comes from ${\displaystyle {\frac {e^{3}M_{e}}{8h^{2}\epsilon _{0}}}}$
Try it yourself:charge on an electron,${\displaystyle e=1.6\times 10^{-}19}$, Mass of an electron,${\displaystyle M_{e}=9.11\times 10^{-}31}$, Planck's Constant, ${\displaystyle h=6.63\times 10^{-}34}$, and Permittivity of Free Space, ${\displaystyle \epsilon _{0}=8.85\times 10^{-}12}$
## Questions
The following table gives the wavelengths of light given off when electrons change between the energy levels in hydrogen as described in the first row:
Transition of n Wavelength (nm) Colour 3→2 4→2 5→2 6→2 7→2 8→2 9→2 ∞→2 656.3 486.1 434.1 410.2 397.0 388.9 383.5 364.6 Red Blue-green Violet Violet (Ultraviolet) (Ultraviolet) (Ultraviolet) (Ultraviolet)
1. Calculate the potential energy of an electron at level n=2.
2. Calculate the difference in potential energy between levels n=2 and n=3.
3. What is the potential energy of an electron at level n=3?
4. If an electron were to jump from n=7 to n=5, what would the wavelength of the photon given off be?
5. Prove that the wavelength of light emitted from the transition n=4 to n=2 is 486.1 nm (HINT: ${\displaystyle e=hf}$ and ${\displaystyle c=f\lambda }$) | 2020-04-04 05:13:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 13, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7152249217033386, "perplexity": 423.7587328557122}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370520039.50/warc/CC-MAIN-20200404042338-20200404072338-00343.warc.gz"} |
http://nlrk.shkundendatenbank.de/a-multiple-choice-test-has-30-questions-and-each-has-4-possible-answers.html | # A Multiple Choice Test Has 30 Questions And Each Has 4 Possible Answers
Question: 1. Multiple-choice questions incorporate both the grade-level standards and the. Nimbostratus c. In a multiple choice question there are 4 alternative answers of which 1, 2, 3, or all may be correct. Objective: Compute probabilities and quantiles for a binomial random variable representing the number of correct guesses on a multiple-choice test and visualize these quantities using the Binomial Applet. On both the academic and general IELTS reading papers you are likely to be asked multiple choice questions (MCQs). Multiple Answer. Each has five answer options. You have 72 seconds or Choice (A), 1 minute and 12 seconds, to complete each question. A student guesses at random the answer to each question. You will have approximately 75 minutes to complete the WRITTEN ACCOUNT CLERK TEST examination portion. Remember to show setup of each probability problem using probability notation, and all calculator steps as you would on the exam. 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A set of multiple choice maths questions are presented. What does apoplectic mean? 3. Note: Each multiple choice question is worth four (4) points. Answer the multiple-choice questions below by selecting one best answer and marking the provided answer sheet. How many ways can you answer the test if you leave an answer for each question? A social security number contains nine digits, such as 000-00-0000. Total of 36 points; points for each part of each question are. Nimbostratus c. Two points are given for each correct answer, but a point is taken off for a wrong answer. If a student guesses on every question, find the probability of getting exactly 9 correct. When taking a 11 question multiple choice test, where each question has 4 possible answers, it would be unusual to get 3 Incorrect or more questions correct by guessing alone. We then selected the questions that most closely related to actual front-end development for inclusion in the test. For each question we have 4 choices. Complete the Answer box for each answer. A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. Test-Taking Strategies - Strategies for Different Types of Test Questions 6 Multiple Choice Tests Carefully read the directions. The MBE is a 200 question, multiple-choice test administered over six hours that typically accounts for 50% of your bar exam score. 2^{20}[/math] which is approximately $1. Question types may include multiple choice or others. A multiple choice test has 20 questions with each having 4 possible answers with one correct. Configure any additional options. multiple-choice tests. If all answers are random guesses, estimate the probability of getting at least 20% correct. Multiple Choice Questions Introduction to Geology - Chapter 1 Each chapter will include a few questions designed to test your knowledge of material covered in the chapter and in the Internet-based resources. A multiple choice test has 7 questions each of which has 4 possible answers, only one of which is correct. questions from each passage were rando mly divided into. All questions must be answered for accurate score evaluation. Each session included multiple-choice and open-response questions. The four parts of this practice Listening test are presented over four separate web pages. On both the academic and general IELTS reading papers you are likely to be asked multiple choice questions (MCQs). This allows for rapid marking and most standardized test have now migrated o computer assisted tests. Choose the one alternative that best completes the statement or answers the question. You can combine many different question types like Multichoice, Drag and drop and Fill in the blanks in a Question set. A question may or may not specify the number of choices to select. A multiple choice test has 10 questions each of which has 5 possible answers, only one of which is correct. Try to choose the most correct answer for each question. B)loans made by banks to the Federal Reserve System. Statistically, that is : if, say 100 000 students gamble on this test, their average result will be a somewhat near 25/100. So if the student answers 4 out of the. If a student guesses on every question, find the probability of getting exactly 12 correct. A multiple-choice exam has four possible answers for each question. variances c. Tom Takes A Multiple Choice Quiz In His Anthropology 100 Class. Now there are only 3 choices. There are five short-answer questions on the AP Stats test. Also, I need to access different rows of the same datafile. Each question has five possible answers, of which one is correct. English Language Arts Test Released Questions and a map that details what learning standard each released question measures and the Choice 1 A RL. Smoke alarms have a limited life. These NEW Quizzes or Quizzes Series 4 are our latest offerings. Question 959364: A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. See each question type article for details on how the results for each question type are calculated in the Analyze Results section. 1993 MULTIPLE CHOICE SCREENING TEST 30 QUESTIONS—40 MINUTES DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN This test contains 30 multiple choice questions. The clouds have a lumpy appearance and are made of ice crystals. Check your work For each of the following questions, solve for "x" using the multi-step method. The test is scored as number of correct answers, with no penalty for guessing. Cxc past questions and answers - principles of business. Those quiz questions, in turn, will be accompanied by multiple choice answers. All of the following are true of odds ratio except: A. Each question has five possible answers, of which one is correct. If you answer any 4-option multiple choice question randomly, there is a 25% chance you are correct. SHORT ANSWER. (3) because for every figure you see in a row one end of two lines lies on one side and other end on another side and also 2 out of 3 of such figures have such sides opposite to each other and one has it adjacent (note having line start at edge should be interpreted as in a favor of this hypothesis i. Know what each multiple choice question is asking. So the probability of getting a correct answer in each case is [math]\frac{1}{4}$ and that of incorrect answer is $\frac{3}{4}$. Step 1: Topic. Other objective test questions, like fill-in-the-blank questions, require that the student recall the correct answer from memory. MS Excel Multiple Choice. Fair weather cumulus d. Binomial Distribution: Example #1. Choose the one alternative that best completes the statement or answers the question. crazy at Quiz Rocket! Biology Multiple Choice Questions and Answers for Different Competitive Exams. For all, this is the best way to improve your skills in Aptitude. You need to enter the smallest possible number of questions to make getting "that many correct" unusual. Use the multiplication rule to find P(CCW), where C denotes a correct answer and W denotes a wrong answer. A student takes a 10 question multiple choice exam and guesses on each question Each question has five choices What is the probability of getting at least 6 correct out of the ten questions?. 5 correct answers. Sample Question: 1. (Sample answers are given for. When you approach a railroad crossing without flashing warning. Try the following multiple choice questions to test your knowledge of this chapter. The MBE was created by the NCBE and is purchased by participating state bar examiners. Check to be sure that you marked only one answer to each question. This section provides a useful collection of sample Interview Questions and Multiple Choice Questions (MCQs) and their answers with appropriate explanations. Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. You may refer to the Reference Sheet on page 5 as often as you like. Write the word or phrase that best completes each statement or answers the question. In a multiple choice test there are 20 questions. Answer: D 23) A) About 25% of the adults have cholesterol levels of at most 211. Each open-ended (OE) item is designed to take approximately ten to fifteen minutes to complete. The adaptive test is exactly what it sounds like, a test that adapts to the test taker. It is possible that all 4 choices are correct, or that all 4 choices are wrong. 1 Answer to A quiz consists of 30 multiple choice questions, each with five possible answers, only one of which is correct. It allows the learner to solve a sequence of various question types. The test was developed by Eldon F. asked by marie on March 12, 2014; please math help. The time limit for this practice test is 30 minutes and this test contains 19 multiple-choice questions. Step 1: Topic. Each correct response to an MC item is worth one point. Questions and Answers. ” Here are a few examples with step-by-step solutions, and a few tips and tricks to answering meaning from context questions. So for example if there are 4 red balls and 3 yellow balls in a bag, the probability of choosing a red ball will be 4/7. A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. One of the biggest problems applicants have with the multiple-choice test is overthinking. Testing policies: I arrange students as spread out from one another as possible in the available class space (in contrast to the clumped groups of four students the class is usually arranged in). • Standardized Test Practice: Test Preparation. Speed 1748 kb/sEntrepreneurship Multiple Choice Question And Answers 1969 ap calculus ab exam, section 1 multiple-choice questions from past ap. Write your answers to these questions in the boxes. Multiple choice questions: There are 32 questions worth 2 points each (32 x 2 pts each = 64 pts). Use the multiplication rule to find P(CCW), where C denotes a correct answer and W denotes a wrong answer. The multiple-choice (MC) items have four answer choices. These types of question are designed to mimic the real life numerical manipulation people will often be asked to do in their day to day work. This type of test allows for a greater level of accuracy in evaluating a prospect’s abilities. Students are asked to select the one alternative that best completes the statement or answers the question. Choose the one alternative that best completes the statement or answers the question. In a history class, Colin and Diana both write a multiple choice quiz. Configure any additional options. Questions 1 - 10 are multiple-choice questions designed to assess your ability to remember or recall basic and foundational pieces of knowledge related to this course. 2^{20}[/math] which is approximately [math]1. Each question has four possible answers, only one of which is correct. General Test-Taking Strategies for Multiple Choice Tests Make Predictions Your mind is typically the most focused immediately after you have read the question and digested its contents. 20) of guessing right. ") For example: What causes night and day? A. The multiple-choice (MC) items have four answer choices. Binomial Distribution: Example #1. 5 correct answers. s 1 to 20 added so far. How many multiple choice questions are on the. See if you’re ready to pass the real thing! This practice test has 45 multiple-choice questions, each with three possible answers. Configure any additional options. The three multiple-choice question types may be in a different order in an actual LSAT than in this practice test. Binomial Problem with n = 30 and p(correct) = 1/4 P(x = 9) = 30C9(1/4)^9*(3/4)^21 = binompdf(30,1/4,9) = 0. Now, if you were to answer RANDOMLY, that means there would be a 50% chance of your being correct. This means that different students are likely to get a different selection of questions when they attempt this quiz. June 28, 2016. You are about to take a 8 question multiple choice test. Which expressions represents the total number of hands possible?. Use this 4 step process to answer any multiple choice question like you're getting paid to do it. The correct answers for multiple-choice questions are also displayed in the table. Joe Donnelly, quiz writer for thirty years has sent me some of his work. A multiple-choice test has 30 questions. It allows the learner to solve a sequence of various question types. Or have your past and future web browsing history. Each test has a contents page, two reading passages, and question and answer sections. We test and find the best products. The swimming pool ---- at 9 o'clock and ---- at 18. Multiple Choice, Choose Single Answer. A multiple-choice test has 30 questions. There Are 4 Choices For Each Question. A choice may be used once, more than once, or not at all in each set. This is quite a common situation many students have come across at least once in their schooling experience. Therefore, you must test the devices weekly. what is the probability that an unprepared student will, by chance, get, a. If they know the answer they will get the question right. When answering multiple choice questions on the OSSLT, eliminate answers you know are wrong. Don't waste time on the hard questions. If a multiple-choice question gives you five possible answers, then, ideally, you may be able to eliminate the four wrong choices and select the right answer. Determine the probability a student randomly guessing on all. But a six question, true or false quiz has 64 possibilities. (Sample answers are given for. If you write 50% below the answers on the test paper, you would be marked wrong. We have to pay them as well. 1)An incentive A)is the opposite of a tradeoff. A quiz has 1 true-false question and 2 multiple choice questions that each have 4 answers. Multiple-choice questions are designed to assess -12 Learning Standardsthe New York State P for Mathematics. The minimum passing score is 70 percent. Check your work For each of the following questions, solve for "x" using the multi-step method. If an examinee must answer 7 of the multiple-choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen?. 2 42) 43) A test consists of 30 multiple choice questions, each with five possible answers, only one of which is correct. TEST-TAKING STRATEGIES FOR READING For students who have enrolled in this class shortly before taking the reading proficiency exam, here are some helpful test-taking strategies you can use: 1. Stem: A question or statement followed by a number of choices or alternatives that answer or complete the question or. D)could be a penalty but could not be a reward. Write the word or phrase that best completes each statement or answers the question. Choose the one alternative that best completes the statement or answers the question. In this multiple choice test, all of the questions have the same value. You have to get at least a 75% in order to pass. doc Page 6 of 41. I think it deals with Pascal's triangle, but I just don't understand it. A correct answer is worth 4 points, but a point is taken off for an incorrect answer. a student ho doen't know a thing, and answers randomly to each question), will - statistically- result in a score of 25%. For questions containing. Multiple-choice questions are designed to assess -12 Learning Standardsthe New York State P for Mathematics. This article will help you answer multiple choice questions more effectively. Never been carefully done happy to multiple choice quiz this quiz collection of nerves. Each OE item. A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. Because the AP Biology exam has been revised, you'll get a more accurate estimate of how well you're doing if you use recent practice tests that are aligned with the new test's format. In our example multiple-choice test, whether you guess randomly or choose 'C' every time, you would expect, on average, to get 30*0. Each answer has a 50 percent chance of being correct. Mathematics multiple-choice questions will be used mainly to assess standard algorithms and conceptual standards. Sixty Maths questions, with answers and detailed solutions, similar to the questions in the ACT maths test. lettered options is formatted as bold and enclosed in parentheses. Let's consider the experiment where we take a multiple-choice quiz of four questions with four choices each, and the topic is something we have absolutely no knowledge. A multiple-choice test has 30 questions and each one has five possible answers, of which one is correct. | 2019-11-13 00:15:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37930911779403687, "perplexity": 605.5400796625513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665809.73/warc/CC-MAIN-20191112230002-20191113014002-00403.warc.gz"} |
http://tex.stackexchange.com/questions/66638/using-sidewaystable-enviroment-with-footnotetext/66641 | # Using sidewaystable enviroment with footnotetext
my new problem si this code:
\documentclass[a4paper,12pt]{article}
\usepackage{rotating}
\begin{document}
\begin{sidewaystable}[h!]
\centering
\setlength{\tabcolsep}{5pt}
\begin{tabular}{|p{3cm}||p{4cm}|p{4cm}|p{4cm}|p{4cm}|}
\hline
EJ & \textbf{471} & \textbf{575} & \textbf{671} & \textbf{675} \\
\hline
a & 12 & dfg & fg\footnotemark[1] & ffd \\
\hline
a & 42 & fdg & s\footnotemark[2] & sdf \\
\hline
\end{tabular}
\caption{Bla bla bla bla bla.}
\label{A7660C1}
\footnotetext[1]{ bla}
\footnotetext[2]{ bla bla}
\end{sidewaystable}
\end{document}
I don't understand why, in the table are footnote references (\footnotemark) as numbers -> 1 and [2], but footnote text are referenced as letters -> [a] and [b] (\footnotetext). This problem is seen in the attached pdf document. I am running Miktex 2.9 (XeLaTeX).
-
## 1 Answer
You don't need to use \footnotemark. \footnote will work fine as you are in a minipage.
\documentclass[a4paper,12pt]{article}
\usepackage{rotating}
\begin{document}
\begin{sidewaystable}[h!]
%\renewcommand\thempfootnote{\arabic{mpfootnote}}%if you want arabic numbers
\centering
\setlength{\tabcolsep}{5pt}
\begin{tabular}{|p{3cm}||p{4cm}|p{4cm}|p{4cm}|p{4cm}|}
\hline
EJ & \textbf{471} & \textbf{575} & \textbf{671} & \textbf{675} \\
\hline
a & 12 & dfg & fg\footnote{bla} & ffd \\
\hline
a & 42 & fdg & s\footnote{blablab}& sdf \\
\hline
\end{tabular}
\caption{Bla bla bla bla bla.}
\label{A7660C1}
\end{sidewaystable}
\end{document}
-
That's a really quick answer. Thank you very much. Other option is using tablefootnote package. This LATEX package provides the command \tablefootnote to be used in a table or sidewaystable environment, where \footnote will not work and when using \footnotemark and \footnotetext and adjusting the counters (including Hfootnote) manually is either too much work or would not even work (sidewaystable). – jafan Aug 10 '12 at 13:08 | 2015-11-27 15:34:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7916866540908813, "perplexity": 4037.020361658501}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398449258.99/warc/CC-MAIN-20151124205409-00248-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.emathzone.com/tutorials/geometry/right-circular-cylinder.html | # Right Circular Cylinder
Right Circular Cylinder
A cylinder whose base is a circle is called circular cylinder. If the axis of the cylinder is perpendicular to its base then the cylinder is called a right circular cylinder.
If $r$ is the radius of the circular base, $h$ is the height, $S$ is the lateral surface area, $V$ is the volume and $P$ is the perimeter of the base, then
$Volume\,of\,the\,cylinder\, = \,area\,of\,base\, \times \,height\,of\,cylinder$
i.e (i) $V = \pi {r^2}h$ ($r$ being radius)
or (ii) $V = \frac{\pi }{4}{d^2}h$ ($d$ being diameter)
Example:
Find the cost of digging a well 3m in diameter and 24m deep at the rate of Rs.10 per cu.m.
Solution:
Given that
Diameter of the well $= 3m$
$\therefore$ Radius of the well, $r = 1.5m$
Depth of the well, $h = 24m$
$\therefore$ Volume of the earth excavated $= \pi {r^2}h = \frac{{22}}{7} \times \left( {1.52} \right) \times 24$
$= 3.1416 \times 2.25 \times 24\,\,cu.\,m$
$= 169.646\,\,cu.\,m$
Now, cost per cu. m $= {\text{Rs}}{\text{.}}\,10$
$\therefore$ ${\text{Total}}\,{\text{Cost}}\, = \,10 \times 169.646 = 1696.46\,{\text{rupees}}$
Example:
The volume of a cylindrical ring is 800 cu.cm. The radius of a cross section is 2cm. Find the length of the ring.
Solution:
Given that
Radius of cross section, $r = 2\,{\text{cm}}$
Volume, $v = 800\,{\text{cu}}{\text{.cm}}$
Let the length of the ring be $h\,\,\,cm$
Now, ${\text{Volume}}\, = \,{\text{area of cross – section }} \times {\text{ height}}$
$800\,\,\,\,\,\,\, = \pi {r^2} \times h$
$= \frac{{22}}{7} \times 4 \times h$
$\therefore$ $h = \frac{{800 \times 7}}{{22 \times 7}} = \frac{{700}}{{11}} = 63.6\,{\text{cm}}$ | 2021-10-20 09:22:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.859619140625, "perplexity": 6727.361658563174}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585305.53/warc/CC-MAIN-20211020090145-20211020120145-00415.warc.gz"} |
https://en.xen.wiki/w/Superparticular | Superparticular
Superparticular numbers are ratios of the form $\frac{n+1}{n}$, or $1+\frac{1}{n}$, where n is a whole number greater than 0.
The word "superparticular" has Latin etymology and means "above by one part". The equivalent word of Greek origin is "epimoric" (from επιμοριοσ, epimorios).
These ratios have some peculiar properties:
• The difference tone of the dyad is also the virtual fundamental.
• The first 6 such ratios (3/2, 4/3, 5/4, 6/5, 7/6, 8/7) are notable harmonic entropy minima.
• The difference (i.e. quotient) between two successive epimoric ratios is always an epimoric ratio.
• The sum (i.e. product) of two successive epimoric ratios is either an epimoric ratio or an epimeric ratio.
• Every epimoric ratio can be split into the product of two epimoric ratios. One way is via the identity: $1+\frac{1}{n} = (1+\frac{1}{2n})\times(1+\frac{1}{2n+1})$, but more than one such splitting method may exist.
• If a/b and c/d are Farey neighbors, that is if a/b < c/d and bc - ad = 1, then (c/d)/(a/b) = bc/ad is epimoric.
• The ratios between successive members of any given Farey sequence will be superparticular.
Curiously enough, the ancient Greeks did not consider 2/1 to be superparticular because it is a multiple of the fundamental (the same rule applies to all natural harmonics in the Greek system). Another explanation for the exclusion of 2/1 can be found on the Generalized superparticulars page. | 2020-09-25 06:57:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8378278017044067, "perplexity": 1602.6615721664734}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400222515.48/warc/CC-MAIN-20200925053037-20200925083037-00475.warc.gz"} |
https://orbit.dtu.dk/en/publications/consistent-two-equation-closure-modelling-for-atmospheric-researc | # Consistent Two-Equation Closure Modelling for Atmospheric Research: Buoyancy and Vegetation Implementations
Andrey Sogachev, Mark C. Kelly, Monique Y. Leclerc
Research output: Contribution to journalJournal articleResearchpeer-review
## Abstract
A self-consistent two-equation closure treating buoyancy and plant drag effects has been developed, through consideration of the behaviour of the supplementary equation for the length-scale-determining variable in homogeneous turbulent flow. Being consistent with the canonical flow regimes of grid turbulence and wall-bounded flow, the closure is also valid for homogeneous shear flows commonly observed inside tall vegetative canopies and in non-neutral atmospheric conditions. Here we examine the most often used two-equation models, namely $${E - \varepsilon}$$ and E − ω (where $${\varepsilon}$$ is the dissipation rate of turbulent kinetic energy, E, and $${\omega = \varepsilon/E}$$ is the specific dissipation), comparing the suggested buoyancy-modified closure against Monin–Obukhov similarity theory. Assessment of the closure implementing both buoyancy and plant drag together has been done, comparing the results of the two models against each other. It has been found that the E − ω model gives a better reproduction of complex atmospheric boundary-layer flows, including less sensitivity to numerical artefacts, than does the $${E -\varepsilon}$$ model. Re-derivation of the $${\varepsilon}$$ equation from the ω equation, however, leads to the $${E - \varepsilon}$$ model implementation that produces results identical to the E − ω model. Overall, numerical results show that the closure performs well, opening new possibilities for application of such models to tasks related to the atmospheric boundary layer—where it is important to adequately account for the influences of both vegetation and atmospheric stability.
Original language English Boundary-Layer Meteorology 145 2 307-327 0006-8314 https://doi.org/10.1007/s10546-012-9726-5 Published - 2012
## Keywords
• Atmospheric boundary layer
• Atmospheric surface layer
• Canopy flow
• Monin–Obukhov similarity theory
• Non-neutral stratification
• Turbulence closure
• Two-equation closure models | 2021-06-22 20:52:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3976392149925232, "perplexity": 3769.109673639349}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488519735.70/warc/CC-MAIN-20210622190124-20210622220124-00007.warc.gz"} |
https://codegolf.stackexchange.com/questions/54147/take-it-or-leave-it-a-game-show-for-computers?noredirect=1 | # Take It or Leave It: A Game Show for Computers
Context:
A reclusive billionaire has created a game show to attract the world's best and brightest programmers. On Mondays at the stroke of midnight, he chooses one person from a pool of applicants to be the contestant of the week, and provides them with a game. You are this week's lucky contestant!
This week's game:
The host provides you with API access to a stack of 10,000 digital envelopes. These envelopes are randomly sorted, and contain within them a dollar value, between $1 and$10,000 (no two envelopes contain the same dollar value).
You have 3 commands at your disposal:
1. Read(): Read the dollar figure in the envelope at the top of the stack.
2. Take(): Add the dollar figure in the envelope to your game show wallet, and pop the envelope off the stack.
3. Pass(): Pop off the envelope on the top of the stack.
The Rules:
1. If you use Pass() on an envelope, the money within is lost forever.
2. If you use Take() on an envelope containing $X, from that point forward, you may never use Take() on an envelope containing <$X. Take() on one of these envelopes will add $0 to your wallet. Write an algorithm that finishes the game with the maximal amount of money. If you're writing a solution in Python, feel free to use this controller to test out algorithms, courtesy of @Maltysen: https://gist.github.com/Maltysen/5a4a33691cd603e9aeca If you use the controller, you cannot access globals, you can only use the 3 provided API commands, and local scoped variables. (@Beta Decay) Notes: "Maximal" in this case means the median value in your wallet after N > 50 runs. I expect, though I would love to be proven wrong, that the median value for a given algorithm will converge as N increases to infinity. Feel free to try to maximize the mean instead, but I have a feeling that the mean is more likely to be thrown off by a small N than the median is. Edit: changed the number of envelopes to 10k for easier processing, and made Take() more explicit. Edit 2: The prize condition has been removed, in light of this post on meta. Current high scores: PhiNotPi -$805,479
Reto Koradi - $803,960 Dennis -$770,272 (Revised)
Alex L. - $714,962 (Revised) • I implemented in a way that it just returns False. Since you can read it there is no real point of failing the entire game on a failed take() – OganM Jul 31 '15 at 21:43 • In case anyone wants to use it, here is the controller that i've been using to test my algorithms: gist.github.com/Maltysen/5a4a33691cd603e9aeca – Maltysen Jul 31 '15 at 22:36 • P.S. Nice question and welcome to Programming Puzzles and Code Golf :) – trichoplax Jul 31 '15 at 23:17 • @Maltysen I put your controller into the OP, thanks for the contribution! – LivingInformation Aug 1 '15 at 4:20 • I couldn't find an explicit rule on bitcoin prizes, but there is some meta discussion on real world prizes which people can contribute to. – trichoplax Aug 1 '15 at 14:22 ## 5 Answers # CJam,$87,143$700,424$720,327$727,580$770,272
{0:T:M;1e4:E,:)mr{RM>{RR(*MM)*-E0.032*220+R*<{ERM--:E;R:MT+:T;}{E(:E;}?}&}fRT}
[easi*]$easi2/=N This program simulates the entire game multiple times and calculates the median. ### How to run I've scored my submission by doing 100,001 test runs: $ time java -jar cjam-0.6.5.jar take-it-or-leave-it.cjam 100001
770272
real 5m7.721s
user 5m15.334s
sys 0m0.570s
### Approach
For each envelope, we do the following:
• Estimate the amount of money that will inevitably be lost by taking the envelope.
If R is the content and M is the maximum that has been taken, the amount can be estimated as R(R-1)/2 - M(M+1)/2, which gives the money all envelopes with contents X in the interval (M,R) contain.
If no envelopes had been passed yet, the estimation would be perfect.
• Calculate the amount of money that will inevitably be lost by passing the envelope.
This is simply the money the envelope contains.
• Check if the quotient of both is less than 110 + 0.016E, where E is the number of remaining envelopes (not counting envelopes that cannot be taken anymore).
If so, take. Otherwise, pass.
• Because using a golfing language helps in any way whatsoever. ;P +1 for the algo. – Maltysen Jul 31 '15 at 23:17
• I can't replicate your results using a Python clone: gist.github.com/orlp/f9b949d60c766430fe9c. You score around $50,000. That's an order of magnitude off. – orlp Aug 1 '15 at 1:50 • @LivingInformation Trial and error. I'm currently looking at using the exact amount instead of estimations, but the resulting code is very slow. – Dennis Aug 1 '15 at 5:11 • This answer needs more upvotes than mine! It's more clever, scores higher, and is even golfed! – Alex L Aug 1 '15 at 18:20 • @LivingInformation This is my address: 17uLHRfdD5JZ2QjSqPGQ1B12LoX4CgLGuV – Dennis Aug 1 '15 at 21:40 ## Python,$680,646 $714,962 f = (float(len(stack)) / 10000) step = 160 if f<0.5: step = 125 if f>0.9: step = 190 if read() < max_taken + step: take() else: passe() Takes larger and larger amounts in steps of size between$125 and $190. Ran with N=10,000 and got a median of$714962. These step sizes came from trial and error and are certainly not optimal.
The full code, including a modified version of @Maltysen's controller which prints a bar chart while it runs:
import random
N = 10000
def init_game():
global stack, wallet, max_taken
stack = list(range(1, 10001))
random.shuffle(stack)
wallet = max_taken = 0
def read():
return stack[0]
def take():
global wallet, max_taken
amount = stack.pop(0)
if amount > max_taken:
wallet += amount
max_taken = amount
def passe():
stack.pop(0)
def test(algo):
results = []
for _ in range(N):
init_game()
for i in range(10000):
algo()
results += [wallet]
output(wallet)
import numpy
print 'max: '
output(max(results))
print 'median: '
output(numpy.median(results))
print 'min: '
output(min(results))
def output(n):
print n
result = ''
for _ in range(int(n/20000)):
result += '-'
print result+'|'
def alg():
f = (float(len(stack)) / 10000)
step = 160
if f<0.5: step = 125
if f>0.9: step = 190
if read() < max_taken + step:
#if read()>max_taken: print read(), step, f
take()
else:
passe()
test(alg)
BitCoin address: 1CBzYPCFFBW1FX9sBTmNYUJyMxMcmL4BZ7
Wow OP delivered! Thanks @LivingInformation!
• The controller is Maltysen's, not mine. – orlp Aug 1 '15 at 4:10
• Confirmed. I had just set up a controller, and get very similar numbers for your solution. Strictly speaking, I think you have to maintain the value of max_taken in your own code, since it's not part of the official game API. But that's trivial to do. – Reto Koradi Aug 1 '15 at 4:32
• Yeah, max_taken is in @Maltysen's controller. If it is useful I can post the entire solution (controller + algorithm) in one block. – Alex L Aug 1 '15 at 4:36
• It's really no big deal. But I think the cleanest approach would be to only use the read(), take() and pass() methods in the posted code, since those are the "3 commands at your disposal" based on the definition in the question. – Reto Koradi Aug 1 '15 at 4:41
• @Reto I'm willing to revise the question to whatever commands make the most sense. Read, Take, and Pass were all 4 characters, and felt fitting, but i'm open to suggestions (for example, i've considered changing "pass" to "leave", because I titled the post "take it or leave it"). – LivingInformation Aug 1 '15 at 4:43
# C++, ~$815,000 Based on Reto Koradi's solution, but switches to a more sophisticated algorithm once there's 100 (valid) envelopes left, shuffling random permutations and computing the heaviest increasing subsequence of them. It will compare the results of taking and not taking the envelope, and will greedily select the best choice. #include <algorithm> #include <iostream> #include <vector> #include <set> void setmax(std::vector<int>& h, int i, int v) { while (i < h.size()) { h[i] = std::max(v, h[i]); i |= i + 1; } } int getmax(std::vector<int>& h, int n) { int m = 0; while (n > 0) { m = std::max(m, h[n-1]); n &= n - 1; } return m; } int his(const std::vector<int>& l, const std::vector<int>& rank) { std::vector<int> h(l.size()); for (int i = 0; i < l.size(); ++i) { int r = rank[i]; setmax(h, r, l[i] + getmax(h, r)); } return getmax(h, l.size()); } template<class RNG> void shuffle(std::vector<int>& l, std::vector<int>& rank, RNG& rng) { for (int i = l.size() - 1; i > 0; --i) { int j = std::uniform_int_distribution<int>(0, i)(rng); std::swap(l[i], l[j]); std::swap(rank[i], rank[j]); } } std::random_device rnd; std::mt19937_64 rng(rnd()); struct Algo { Algo(int N) { for (int i = 1; i < N + 1; ++i) left.insert(i); ival = maxval = 0; } static double get_p(int n) { return 1.2 / std::sqrt(8 + n) + 0.71; } bool should_take(int val) { ival++; auto it = left.find(val); if (it == left.end()) return false; if (left.size() > 100) { if (val > maxval && val < 466.7f + 0.9352f * maxval + 0.0275f * (ival - 1)) { maxval = val; left.erase(left.begin(), std::next(it)); return true; } left.erase(it); return false; } take.assign(std::next(it), left.end()); no_take.assign(left.begin(), it); no_take.insert(no_take.end(), std::next(it), left.end()); take_rank.resize(take.size()); no_take_rank.resize(no_take.size()); for (int i = 0; i < take.size(); ++i) take_rank[i] = i; for (int i = 0; i < no_take.size(); ++i) no_take_rank[i] = i; double take_score, no_take_score; take_score = no_take_score = 0; for (int i = 0; i < 1000; ++i) { shuffle(take, take_rank, rng); shuffle(no_take, no_take_rank, rng); take_score += val + his(take, take_rank) * get_p(take.size()); no_take_score += his(no_take, no_take_rank) * get_p(no_take.size()); } if (take_score > no_take_score) { left.erase(left.begin(), std::next(it)); return true; } left.erase(it); return false; } std::set<int> left; int ival, maxval; std::vector<int> take, no_take, take_rank, no_take_rank; }; struct Game { Game(int N) : score_(0), max_taken(0) { for (int i = 1; i < N + 1; ++i) envelopes.push_back(i); std::shuffle(envelopes.begin(), envelopes.end(), rng); } int read() { return envelopes.back(); } bool done() { return envelopes.empty(); } int score() { return score_; } void pass() { envelopes.pop_back(); } void take() { if (read() > max_taken) { score_ += read(); max_taken = read(); } envelopes.pop_back(); } int score_; int max_taken; std::vector<int> envelopes; }; int main(int argc, char** argv) { std::vector<int> results; std::vector<int> max_results; int N = 10000; for (int i = 0; i < 1000; ++i) { std::cout << "Simulating game " << (i+1) << ".\n"; Game game(N); Algo algo(N); while (!game.done()) { if (algo.should_take(game.read())) game.take(); else game.pass(); } results.push_back(game.score()); } std::sort(results.begin(), results.end()); std::cout << results[results.size()/2] << "\n"; return 0; } • Interesting. It had crossed my mind that it should be possible to improve by looking at the values left for the last few envelopes. I figure you played with the cutoff point where you switch strategies? Is it just getting too slow if you switch earlier? Or are the results actually getting worse? – Reto Koradi Aug 3 '15 at 13:54 • @RetoKoradi I did play with the cutoff point, and earlier cutoffs both got too slow and worse. Not too surprising honestly, at 100 envelopes we're already sampling a mere 1000 permutations out of a possible 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000. – orlp Aug 3 '15 at 14:15 # Java,$806,899
This is from a trial of 2501 rounds. I am still working on optimizing it. I wrote two classes, a wrapper and a player. The wrapper instantiates the player with the number of envelopes (always 10000 for the real thing), and then calls the method takeQ with the top envelope's value. The player then returns true if they take it, false if they pass it.
## Player
import java.lang.Math;
public class Player {
public int[] V;
public Player(int s) {
V = new int[s];
for (int i = 0; i < V.length; i++) {
V[i] = i + 1;
}
// System.out.println();
}
public boolean takeQ(int x) {
// System.out.println("look " + x);
// http://www.programmingsimplified.com/java/source-code/java-program-for-binary-search
int first = 0;
int last = V.length - 1;
int middle = (first + last) / 2;
int search = x;
while (first <= last) {
if (V[middle] < search)
first = middle + 1;
else if (V[middle] == search)
break;
else
last = middle - 1;
middle = (first + last) / 2;
}
int i = middle;
if (first > last) {
// System.out.println(" PASS");
return false; // value not found, so the envelope must not be in the list
// of acceptable ones
}
int[] newVp = new int[V.length - 1];
for (int j = 0; j < i; j++) {
newVp[j] = V[j];
}
for (int j = i + 1; j < V.length; j++) {
newVp[j - 1] = V[j];
}
double pass = calcVal(newVp);
int[] newVt = new int[V.length - i - 1];
for (int j = i + 1; j < V.length; j++) {
newVt[j - i - 1] = V[j];
}
double take = V[i] + calcVal(newVt);
// System.out.println(" take " + take);
// System.out.println(" pass " + pass);
if (take > pass) {
V = newVt;
// System.out.println(" TAKE");
return true;
} else {
V = newVp;
// System.out.println(" PASS");
return false;
}
}
public double calcVal(int[] list) {
double total = 0;
for (int i : list) {
total += i;
}
double ent = 0;
for (int i : list) {
if (i > 0) {
ent -= i / total * Math.log(i / total);
}
}
// System.out.println(" total " + total);
// System.out.println(" entro " + Math.exp(ent));
// System.out.println(" count " + list.length);
return total * (Math.pow(Math.exp(ent), -0.5) * 4.0 / 3);
}
}
## Wrapper
import java.lang.Math;
import java.util.Random;
import java.util.ArrayList;
import java.util.Collections;
public class Controller {
public static void main(String[] args) {
int size = 10000;
int rounds = 2501;
ArrayList<Integer> results = new ArrayList<Integer>();
int[] envelopes = new int[size];
for (int i = 0; i < envelopes.length; i++) {
envelopes[i] = i + 1;
}
for (int round = 0; round < rounds; round++) {
shuffleArray(envelopes);
Player p = new Player(size);
int cutoff = 0;
int winnings = 0;
for (int i = 0; i < envelopes.length; i++) {
boolean take = p.takeQ(envelopes[i]);
if (take && envelopes[i] >= cutoff) {
winnings += envelopes[i];
cutoff = envelopes[i];
}
}
results.add(winnings);
}
Collections.sort(results);
System.out.println(
rounds + " rounds, median is " + results.get(results.size() / 2));
}
// stol... I mean borrowed from
// http://stackoverflow.com/questions/1519736/random-shuffling-of-an-array
static Random rnd = new Random();
static void shuffleArray(int[] ar) {
for (int i = ar.length - 1; i > 0; i--) {
int index = rnd.nextInt(i + 1);
// Simple swap
int a = ar[index];
ar[index] = ar[i];
ar[i] = a;
}
}
}
A more detailed explanation is coming soon, after I finish optimizations.
The core idea is to be able to estimate the reward from playing a game from a given set of envelopes. If the current set of envelopes is {2,4,5,7,8,9}, and the top envelope is the 5, then there are two possibilities:
• Take the 5 and play a game with {7,8,9}
• Pass the 5 and play a game of {2,4,7,8,9}
If we calculate the expected reward of {7,8,9} and compare it to the expected reward of {2,4,7,8,9}, we will be able to tell if taking the 5 is worth it.
Now the question is, given a set of envelopes like {2,4,7,8,9} what is the expected value? I found the the expected value seems to be proportional to the total amount of money in the set, but inversely proportional to the square root of the number of envelopes that the money is divided into. This came from "perfectly" playing several small games in which all of the envelopes have almost identical value.
The next problem is how to determine the "effective number of envelopes." In all cases, the number of envelopes is known exactly by keeping track of what you've seen and done. Something like {234,235,236} is definitely three envelopes, {231,232,233,234,235} is definitely 5, but {1,2,234,235,236} should really count as 3 and not 5 envelopes because the 1 and 2 are nearly worthless, and you would never PASS on a 234 so you could later pick up a 1 or 2. I had the idea of using Shannon entropy to determine the effective number of envelopes.
I targeted my calculations to situations where the envelope's values are uniformly distributed over some interval, which is what happens during the game. If I take {2,4,7,8,9} and treat that as a probability distribution, its entropy is 1.50242. Then I do exp() to get 4.49254 as the effective number of envelopes.
The estimated reward from {2,4,7,8,9} is 30 * 4.4925^-0.5 * 4/3 = 18.87
The exact number is 18.1167.
This isn't an exact estimate, but I am actually really proud of how well this fits the data when the envelopes are uniformly distributed over an interval. I'm not sure of the correct multiplier (I am using 4/3 for now) but here is a data table excluding the multiplier.
Set of Envelopes Total * (e^entropy)^-0.5 Actual Score
{1,2,3,4,5,6,7,8,9,10} 18.759 25.473
{2,3,4,5,6,7,8,9,10,11} 21.657 29.279
{3,4,5,6,7,8,9,10,11,12} 24.648 33.125
{4,5,6,7,8,9,10,11,12,13} 27.687 37.002
{5,6,7,8,9,10,11,12,13,14} 30.757 40.945
{6,7,8,9,10,11,12,13,14,15} 33.846 44.900
{7,8,9,10,11,12,13,14,15,16} 36.949 48.871
{8,9,10,11,12,13,14,15,16,17} 40.062 52.857
{9,10,11,12,13,14,15,16,17,18} 43.183 56.848
{10,11,12,13,14,15,16,17,18,19} 46.311 60.857
Linear regression between expected and actual gives an R^2 value of 0.999994.
My next step to improve this answer is to improve estimation when the number of envelopes starts to get small, which is when the envelopes are not approximately uniformly distributed and when the problem starts to get granular.
Edit: If this is deemed worthy of bitcoins, I just got an address at 1PZ65cXxUEEcGwd7E8i7g6qmvLDGqZ5JWg. Thanks! (This was here from when the challenge author was handing out prizes.)
• Accidentally sent you 20k satoshi over 805,479. For reference, the amount was supposed to be your score. Enjoy my mistake :) – LivingInformation Aug 3 '15 at 2:24
• Will you be running numbers with more rounds? Based on what I'm seeing, there is quite a bit of variation, and 500 is not enough to get a stable median. My score is very close to yours if I run only 500 rounds, but it all depends on how the random numbers happen to fall. If I used a variable seed, and did 500 runs a few times, I could probably get a higher score. – Reto Koradi Aug 3 '15 at 2:52
• @RetoKoradi I'm definitely going to do more rounds. – PhiNotPi Aug 3 '15 at 13:19 | 2019-12-14 14:13:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3715204894542694, "perplexity": 3548.3517014591207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541157498.50/warc/CC-MAIN-20191214122253-20191214150253-00183.warc.gz"} |
https://labs.tib.eu/arxiv/?author=Wenhao%20Zhang | • Electronic effect of doped oxygen atoms in Bi2201 superconductors determined by scanning tunneling microscopy(1803.03400)
April 3, 2018 cond-mat.supr-con
The oxygen dopants are essential in tuning electronic properties of Bi$_2$Sr$_2$Ca$_{n-1}$Cu$_n$O$_{2n+4+\delta}$ superconductors. Here we apply the technique of scanning tunneling microscopy and spectroscopy to study the influence of oxygen dopants in an optimally doped Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ and an overdoped Bi$_{2-y}$Pb$_y$Sr$_2$CuO$_{6+\delta}$. In both samples, we find that interstitial oxygen atoms on the SrO layers dominate over the other two forms of oxygen dopants, oxygen vacancies on the SrO layers and interstitial oxygen atoms on the BiO layers. The hole doping is estimated from the oxygen concentration, as compared to the result extracted from the measured Fermi surface. The precise spatial location is employed to obtain a negative correlation between the oxygen dopants and the inhomogeneous pseudogap.
• The study of electronic nematicity in an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+\delta}$ superconductor using scanning tunneling spectroscopy(1803.03403)
March 9, 2018 cond-mat.supr-con
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+\delta}$ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
• Visualization of electronic topology in ZrSiSe by scanning tunneling microscopy(1801.09979)
Jan. 30, 2018 cond-mat.mtrl-sci
As emerging topological nodal-line semimetals, the family of ZrSiX (X = O, S, Se, Te) has attracted broad interests in condensed matter physics due to their future applications in spintonics. Here, we apply a scanning tunneling microscopy (STM) to study the structural symmetry and electronic topology of ZrSiSe. The glide mirror symmetry is verified by quantifying the lattice structure of the ZrSe bilayer based on bias selective topographies. The quasiparticle interference analysis is used to identify the band structure of ZrSiSe. The nodal line is experimentally determined at $\sim$ 250 meV above the Fermi level. An extra surface state Dirac point at $\sim$ 400 meV below the Fermi level is also determined. Our STM measurement provides a direct experimental evidence of the nodal-line state in the family of ZrSiX.
• Spin Fluctuation Induced Linear Magnetoresistance in Ultrathin Superconducting FeSe Films(1704.01005)
The discovery of high-temperature superconductivity in FeSe/STO has trigged great research interest to reveal a range of exotic physical phenomena in this novel material. Here we present a temperature dependent magnetotransport measurement for ultrathin FeSe/STO films with different thickness and protection layers. Remarkably, a surprising linear magnetoresistance (LMR) is observed around the superconducting transition temperatures but absent otherwise. The experimental LMR can be reproduced by magnetotransport calculations based on a model of magnetic field dependent disorder induced by spin fluctuation. Thus, the observed LMR in coexistence with superconductivity provides the first magnetotransport signature for spin fluctuation around the superconducting transition region in ultrathin FeSe/STO films.
• Using Deep Learning Method for Classification: A Proposed Algorithm for the ISIC 2017 Skin Lesion Classification Challenge(1703.02182)
March 10, 2017 cs.CV
Skin cancer, the most common human malignancy, is primarily diagnosed visually by physicians [1]. Classification with an automated method like CNN [2, 3] shows potential for challenging tasks [1]. By now, the deep convolutional neural networks are on par with human dermatologist [1]. This abstract is dedicated on developing a Deep Learning method for ISIC [5] 2017 Skin Lesion Detection Competition hosted at [6] to classify the dermatology pictures, which is aimed at improving the diagnostic accuracy rate and general level of the human health. The challenge falls into three sub-challenges, including Lesion Segmentation, Lesion Dermoscopic Feature Extraction and Lesion Classification. This project only participates in the Lesion Classification part. This algorithm is comprised of three steps: (1) original images preprocessing, (2) modelling the processed images using CNN [2, 3] in Caffe [4] framework, (3) predicting the test images and calculating the scores that represent the likelihood of corresponding classification. The models are built on the source images are using the Caffe [4] framework. The scores in prediction step are obtained by two different models from the source images.
• Atomically Resolved FeSe/SrTiO3(001) Interface Structure by Scanning Transmission Electron Microscopy(1512.05203)
Dec. 17, 2015 cond-mat.supr-con
Interface-enhanced high-temperature superconductivity in one unit-cell (UC) FeSe films on SrTiO3(001) (STO) substrate has recently attracted much attention in condensed matter physics and material science. By combined in-situ scanning tunneling microscopy/spectroscopy (STM/STS) and ex-situ scanning transmission electron microscopy (STEM) studies, we report on atomically resolved structure including both lattice constants and actual atomic positions of the FeSe/STO interface under both non-superconducting and superconducting states. We observed TiO2 double layers (DLs) and significant atomic displacements in the top two layers of STO, lattice compression of the Se-Fe-Se triple layer, and relative shift between bottom Se and topmost Ti atoms. By imaging the interface structures under various superconducting states, we unveil a close correlation between interface structure and superconductivity. Our atomic-scale identification of FeSe/STO interface structure provides useful information on investigating the pairing mechanism of this interface-enhanced high-temperature superconducting system.
• Thickness dependence of superconductivity and superconductor-insulator transition in ultrathin FeSe films on SrTiO3(001) substrate(1507.08431)
July 30, 2015 cond-mat.supr-con
Interface-enhanced high-temperature superconductivity in one unit-cell (UC) FeSe film on SrTiO3(001) (STO) substrate has recently attracted much attention in condensed matter physics and material science. Here, by ex situ transport measurements, we report on the superconductivity in FeSe ultra-thin films with different thickness on STO substrate. We find that the onset superconducting transition temperature (Tc) decreases with increasing film thickness of FeSe, which is opposite to the behavior usually observed in traditional superconductor films. By systematic post-annealing of 5 UC FeSe films, we observe an insulator to superconductor transition, which is accompanied with a sign change of the dominated charge carriers from holes to electrons at low temperatures according to the corresponding Hall measurement.
• High temperature superconducting FeSe films on SrTiO3 substrates(1404.3464)
Interface enhanced superconductivity at two dimensional limit has become one of most intriguing research directions in condensed matter physics. Here, we report the superconducting properties of ultra-thin FeSe films with the thickness of one unit cell (1-UC) grown on conductive and insulating SrTiO3 (STO) substrates. For the 1-UC FeSe on conductive STO substrate (Nb-STO), the magnetization versus temperature (M-T) measurement shows a diamagnetic signal at 85 K, suggesting the possibility of superconductivity appears at this high temperature. For the FeSe films on insulating STO substrate, systematic transport measurements were carried out and the sheet resistance of FeSe films exhibits Arrhenius TAFF behavior with a crossover from a single-vortex pinning region to a collective creep region. More intriguing, sign reversal of Hall resistance with temperature is observed, demonstrating a crossover from hole conduction to electron conduction above Tc in 1-UC FeSe films.
• Dichotomy of Electronic Structure and Superconductivity between Single-Layer and Double-Layer FeSe/SrTiO3 Films(1402.1400)
The latest discovery of possible high temperature superconductivity in the single-layer FeSe film grown on a SrTiO3 substrate, together with the observation of its unique electronic structure and nodeless superconducting gap, has generated much attention. Initial work also found that, while the single-layer FeSe/SrTiO3 film exhibits a clear signature of superconductivity, the double-layer FeSe/SrTiO3 film shows an insulating behavior. Such a dramatic difference between the single-layer and double-layer FeSe/SrTiO3 films is surprising and the underlying origin remains unclear. Here we report our comparative study between the single-layer and double-layer FeSe/SrTiO3 films by performing a systematic angle-resolved photoemission study on the samples annealed in vacuum. We find that, like the single-layer FeSe/SrTiO3 film, the as-prepared double-layer FeSe/SrTiO3 film is insulating and possibly magnetic, thus establishing a universal existence of the magnetic phase in the FeSe/SrTiO3 films. In particular, the double-layer FeSe/SrTiO3 film shows a quite different doping behavior from the single-layer film in that it is hard to get doped and remains in the insulating state under an extensive annealing condition. The difference originates from the much reduced doping efficiency in the bottom FeSe layer of the double-layer FeSe/SrTiO3 film from the FeSe-SrTiO3 interface. These observations provide key insights in understanding the origin of superconductivity and the doping mechanism in the FeSe/SrTiO3 films. The property disparity between the single-layer and double-layer FeSe/SrTiO3 films may facilitate to fabricate electronic devices by making superconducting and insulating components on the same substrate under the same condition.
• Electronic Evidence of an Insulator-Superconductor Transition in Single-Layer FeSe/SrTiO3 Films(1401.7115)
In high temperature cuprate superconductors, it is now generally agreed that the parent compound is a Mott insulator and superconductivity is realized by doping the antiferromagnetic Mott insulator. In the iron-based superconductors, however, the parent compound is mostly antiferromagnetic metal, raising a debate on whether an appropriate starting point should go with an itinerant picture or a localized picture. It has been proposed theoretically that the parent compound of the iron-based superconductors may be on the verge of a Mott insulator, but so far no clear experimental evidence of doping-induced Mott transition has been available. Here we report an electronic evidence of an insulator-superconductor transition observed in the single-layer FeSe films grown on the SrTiO3 substrate. By taking angle-resolved photoemission measurements on the electronic structure and energy gap, we have identified a clear evolution of an insulator to a superconductor with the increasing doping. This observation represents the first example of an insulator-superconductor transition via doping observed in the iron-based superconductors. It indicates that the parent compound of the iron-based superconductors is in proximity of a Mott insulator and strong electron correlation should be considered in describing the iron-based superconductors.
• Direct observation of high temperature superconductivity in one-unit-cell FeSe films(1311.5370)
Nov. 21, 2013 cond-mat.supr-con
Heterostructure based interface engineering has been proved an effective method for finding new superconducting systems and raising superconductivity transition temperature (TC). In previous work on one unit-cell (UC) thick FeSe films on SrTiO3 (STO) substrate, a superconducting-like energy gap as large as 20 meV, was revealed by in situ scanning tunneling microscopy/spectroscopy (STM/STS). Angle resolved photoemission spectroscopy (ARPES) further revealed a nearly isotropic gap of above 15 meV, which closes at a temperature of ~ 65 K. If this transition is indeed the superconducting transition, then the 1-UC FeSe represents the thinnest high TC superconductor discovered so far. However, up to date direct transport measurement of the 1-UC FeSe films has not been reported, mainly because growth of large scale 1-UC FeSe films is challenging and the 1-UC FeSe films are too thin to survive in atmosphere. In this work, we successfully prepared 1-UC FeSe films on insulating STO substrates with non-superconducting FeTe protection layers. By direct transport and magnetic measurements, we provide definitive evidence for high temperature superconductivity in the 1-UC FeSe films with an onset TC above 40 K and a extremely large critical current density JC ~ 1.7*106 A/cm2 at 2 K. Our work may pave the way to enhancing and tailoring superconductivity by interface engineering.
• Phase Diagram and High Temperature Superconductivity at 65 K in Tuning Carrier Concentration of Single-Layer FeSe Films(1207.6823)
Superconductivity in the cuprate superconductors and the Fe-based superconductors is realized by doping the parent compound with charge carriers, or by application of high pressure, to suppress the antiferromagnetic state. Such a rich phase diagram is important in understanding superconductivity mechanism and other physics in the Cu- and Fe-based high temperature superconductors. In this paper, we report a phase diagram in the single-layer FeSe films grown on SrTiO3 substrate by an annealing procedure to tune the charge carrier concentration over a wide range. A dramatic change of the band structure and Fermi surface is observed, with two distinct phases identified that are competing during the annealing process. Superconductivity with a record high transition temperature (Tc) at ~65 K is realized by optimizing the annealing process. The wide tunability of the system across different phases, and its high-Tc, make the single-layer FeSe film ideal not only to investigate the superconductivity physics and mechanism, but also to study novel quantum phenomena and for potential applications.
• Electronic Origin of High Temperature Superconductivity in Single-Layer FeSe Superconductor(1202.5849)
Feb. 27, 2012 cond-mat.supr-con
The latest discovery of high temperature superconductivity signature in single-layer FeSe is significant because it is possible to break the superconducting critical temperature ceiling (maximum Tc~55 K) that has been stagnant since the discovery of Fe-based superconductivity in 2008. It also blows the superconductivity community by surprise because such a high Tc is unexpected in FeSe system with the bulk FeSe exhibiting a Tc at only 8 K at ambient pressure which can be enhanced to 38 K under high pressure. The Tc is still unusually high even considering the newly-discovered intercalated FeSe system A_xFe_{2-y}Se_2 (A=K, Cs, Rb and Tl) with a Tc at 32 K at ambient pressure and possible Tc near 48 K under high pressure. Particularly interesting is that such a high temperature superconductivity occurs in a single-layer FeSe system that is considered as a key building block of the Fe-based superconductors. Understanding the origin of high temperature superconductivity in such a strictly two-dimensional FeSe system is crucial to understanding the superconductivity mechanism in Fe-based superconductors in particular, and providing key insights on how to achieve high temperature superconductivity in general. Here we report distinct electronic structure associated with the single-layer FeSe superconductor. Its Fermi surface topology is different from other Fe-based superconductors; it consists only of electron pockets near the zone corner without indication of any Fermi surface around the zone center. Our observation of large and nearly isotropic superconducting gap in this strictly two-dimensional system rules out existence of node in the superconducting gap. These results have provided an unambiguous case that such a unique electronic structure is favorable for realizing high temperature superconductivity.
• Phases and phase transitions in two dimensional superconducting films(1112.1207)
This paper has been withdrawn by the author | 2020-03-30 13:49:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5484771728515625, "perplexity": 3152.670091141037}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00435.warc.gz"} |
https://www.iacr.org/cryptodb/data/paper.php?pubkey=30113 | ## CryptoDB
### Paper: Solving LPN Using Covering Codes
Authors: Qian Guo Thomas Johansson Carl Löndahl DOI: 10.1007/s00145-019-09338-8 Search ePrint Search Google We present a new algorithm for solving the LPN problem. The algorithm has a similar form as some previous methods, but includes a new key step that makes use of approximations of random words to a nearest codeword in a linear code. It outperforms previous methods for many parameter choices. In particular, we can now solve the $(512,\frac{1}{8})$ ( 512 , 1 8 ) LPN instance with complexity less than $2^{80}$ 2 80 operations in expectation, indicating that cryptographic schemes like HB variants and LPN-C should increase their parameter size for 80-bit security.
##### BibTeX
@article{jofc-2020-30113,
title={Solving LPN Using Covering Codes},
journal={Journal of Cryptology},
publisher={Springer},
volume={33},
pages={1-33},
doi={10.1007/s00145-019-09338-8},
author={Qian Guo and Thomas Johansson and Carl Löndahl},
year=2020
} | 2022-06-30 02:09:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48548173904418945, "perplexity": 2535.6651548804957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103646990.40/warc/CC-MAIN-20220630001553-20220630031553-00292.warc.gz"} |
https://labanimalsjournal.ru/en/2618723x-2018-02-04 | # Modeling Of Traumatic Injuries Of The Cornea Of The Eye
A. Ivkina(1), Researcher, St. Petersburg state chemical-pharmaceutical University, D. Yu.Ivkin(1), candidate of biological Sciences, head of St. Petersburg state chemical-pharmaceutical University, Е. Semivelichenko(1), Junior researcher St. Petersburg state chemical-pharmaceutical University, G. Plisko(1), Junior researcher St. Petersburg state chemical-pharmaceutical University, P. Burenkov(2), chief, preclinical research, «Samson-Med» 1-St. Petersburg state University of chemical and pharmaceutical Sciences Ministry of health of the Russian Federation, 197376, St. Petersburg, Professor Popov str., 14, lit. And 2-Samson-Med, 196158, St. Petersburg, Moscow highway, 13 E-mail: [email protected]
### Abstract
On the center of experimental pharmacology Saint-Petersburg Chemical-Pharmaceutical University on rabbits male breed of Soviet chinchilla, as the most accessible and relevant test system, was conducted modeling of traumatic erosion by the method of S. Hanna, J.E. O’Brien (1960) and an acid burn of the cornea of the eye followed by a histological evaluation of the pathological process. The number of animals was sufficient to obtain statistically reliable results. The article describes in the great detail the conditions for keeping animals and reproducing models, a scoring of the severity of traumatic injury was suggested, which took into account the presence or absence of pathological changes, the presence and severity of the current exudative inflammation followed by pathological vascularization of the cornea, the presence and prevalence of fibroplastic changes in the cornea, pathological process and organization in its outcome. The consistency of the models is confirmed histologically, the severity of the lesion predominates in the modeling of traumatic erosion; in the future, the evaluation of the condition of the cornea may be of interest not only on the 29th day after the modeling of the pathology, but also on the 8th, 15th, 22nd days. In this case, it becomes possible to investigate the development of the pathological process in dynamics. These models are extremely relevant in the study of eye forms of drugs with regenerative, antihypoxic and antioxidant effects.
### References
1. Kanyukov V.N., Stadnikov A.A., Trubina O.M., Yahina O.M. Eksperimentalnoe modelirovanie travmaticheskih povrezhdeniy rogovicy. – Vestnik OGU, 2014, 12 (173): 156–9.
2. Rukovodstvo po laboratornym zhivotnym i al`ternativnym modelyam v biomedicinskih tehnologiyah. Pod red.: N.N. Karkishhenko i S.V. Gracheva. M., 2010.
3. Rukovodstvo po provedeniyu doklinicheskih issledovaniy lekarstvennyh sredstv. Ch. I. M.: Grif i K, 2012. | 2021-10-19 23:53:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33925291895866394, "perplexity": 9169.536754810057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585290.83/warc/CC-MAIN-20211019233130-20211020023130-00206.warc.gz"} |
https://dsp.stackexchange.com/questions/76432/results-do-not-match-between-manually-computed-psd-values-and-those-from-matlab | # Results do not match between manually computed PSD values and those from MATLAB pwelch function
The power spectral density (PSD) of the given input signal $$x[n]$$ is computed as follows:
close all;clear;clc
n = 8;
F = dftmtx(n);
invF = 1/n*F';
rng default
x = randn(100*n,1);
xx = buffer(x,n,n-1);
xx = xx(:, n:end);
XX = fft(xx, n);
phixx = mean(XX.*conj(XX),2)/n;
phixx = phixx.';
Then, the phixx is
phixx =
1.0837 1.1155 0.8099 0.9498 1.0470 0.9498 0.8099 1.1155
If the MATLAB built-in function pwelch is used to compute the PSD, then the results are quite different from what is shown above:
pp = pwelch(x, ones(n,1), n-1, n)'
0.1725 0.3551 0.2578 0.3023 0.1666
As it is one side, so the length is only n/2+1, but I expected the values to be identical to each other.
Was the way how pwelch was used wrong?
Please let me know if there should be more detailed information.
update
I just found out that the results are identical except for a $$\pi$$ or $$2\pi$$ difference between them, i.e.,
(phixx(1:n/2+1)./pp)/pi
ans =
2.0000 1.0000 1.0000 1.0000 2.0000
There seems a constant involved in computing pwelch.
Then, I am wondering which one should be used.
1. pwelch() can return a one sided (default) or two sided spectrum. For one sided, the energy of negative frequency is added to the symmetric positive ones.
2. pwelch() returns a spectral density in something like $$W/Hz$$ which is actually dependent on the sample rate. By default pwelch() assumes a sample rate of $$2\pi$$.
pp = pwelch(x, ones(n,1), n-1, n,1,'twosided')';
pwelch() is fairly complicated so it's typically not a bad idea to read through the entire documentation and understand all the different options before using it.
• Thanks for the answer! Indeed, the 'twosided' variable works and now it seems that the results coincide. This time could be a good chance to read through the entire doc pwelch. But in regard to the first bullet point in your answer, if the energy of negative frequency is added to the symmetric positive ones, then I expect the values of (phixx(1:n/2+1)./pp)/pi should be somehow 1.0 2.0 2.0 2.0 2.0 1.0. But the actual values are the other way around. Jul 23 at 20:19
• Yes if you use "onsided", no if you use "twosided". Note that twosided returns and 8 element vector and onesided a 5-element one. You want to maintain Perceval's theorem $\sum P(k) = \sum x[n]^2$ Jul 23 at 21:17 | 2021-12-04 19:05:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.738375186920166, "perplexity": 1083.0154366808542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363006.60/warc/CC-MAIN-20211204185021-20211204215021-00040.warc.gz"} |
http://comorarch.blogspot.com/2012/10/digital-logic-logic-gate-easy.html | Pages
Digital Logic : Logic Gate (EASY)
DIGITAL LOGIC
1. What is ‘Digital Logic’?
· basis in digital computing
· gives us an understanding how circuits and hardware communicate within the computer
· use a sequence of numbers to represent the signal
- basically use binary numbers (0 or 1)
LOGIC GATES
1. What is ‘Logic Gates’?
· a device that will perform a basic logical functions
· fundemental to build a block of intergrated circuits
· 2 input
- binary numbers (0 or 1)
· some application of logic gate
- diode
- transistor
- microprocessor etc.
· can be represent by using Boolean expressions
Name Graphical symbol Algebraic Expressions Truth Table AND $A \cdot B$ A B Y 0 0 1 1 0 1 0 1 0 0 0 1 OR $A+B$ A B Y 0 0 1 1 0 1 0 1 0 1 1 1 NOT $\overline{A}$ A Y 0 1 1 0 NAND $\overline{A \cdot B}$ A B Y 0 0 1 1 0 1 0 1 1 1 1 0 NOR $\overline{A + B}$ A B Y 0 0 1 1 0 1 0 1 1 0 0 0 XOR $A \oplus B$ A B Y 0 0 1 1 0 1 0 1 0 1 1 0 XNOR $\overline{A \oplus B}$ or ${A \odot B}$ A B Y 0 0 1 1 0 1 0 1 1 0 0 1 | 2021-10-17 13:53:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4328294098377228, "perplexity": 436.596652248434}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585177.11/warc/CC-MAIN-20211017113503-20211017143503-00395.warc.gz"} |
https://zbmath.org/?q=an%3A0915.35043 | zbMATH — the first resource for mathematics
Positive solutions to a class of elliptic boundary value problems. (English) Zbl 0915.35043
Summary: We prove the existence of positive solutions to the boundary value problems $\Delta u+\lambda a(x)f(u)= 0\quad\text{in }\Omega,\quad u= 0\quad\text{on }\partial\Omega,$ where $$\Omega$$ is a bounded domain in $$\mathbb{R}^N$$, $$a:\Omega\to \mathbb{R}$$ may change sign, $$f(0)>0$$, and $$\lambda> 0$$ is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem. $$\copyright$$ Academic Press.
MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
Full Text:
References:
[1] Cac, N.P.; Fink, A.M.; Gatica, J.A., Nonnegative solutions of the radial Laplacian with nonlinearity that changes sign, Proc. amer. math. soc., 123, 1393-1398, (1995) · Zbl 0826.34021 [2] Courant, R.; Hilbert, D., Methods of mathematical physics, (1953), Interscience New York · Zbl 0729.00007 [3] Hess, P., On bifurcation and stability of positive solutions of nonlinear elliptic eigenvalue problems, (), 103-119 [4] Hess, P.; Kato, T., On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. partial differential equations, 5, 999-1030, (1980) · Zbl 0477.35075 [5] Lions, P.L., On the existence of positive solutions of semilinear elliptic equations, SIAM rev., 24, 441-467, (1982) · Zbl 0511.35033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-05-16 08:13:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6977472901344299, "perplexity": 1090.85182250877}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992516.56/warc/CC-MAIN-20210516075201-20210516105201-00192.warc.gz"} |
http://popflock.com/learn?s=Dextrorotation_and_levorotation | Dextrorotation and Levorotation
Get Dextrorotation and Levorotation essential facts below. View Videos or join the Dextrorotation and Levorotation discussion. Add Dextrorotation and Levorotation to your PopFlock.com topic list for future reference or share this resource on social media.
Dextrorotation and Levorotation
A chemical compound showing dextrorotation in a polarimeter. From the perspective of the observer, the plane is rotated to the right (clockwise).
Dextrorotation and levorotation (also spelled laevorotation)[1] are terms used in chemistry and physics to describe the optical rotation of plane-polarized light. From the point of view of the observer, dextrorotation refers to clockwise or right-handed rotation, and levorotation refers to counterclockwise or left-handed rotation.[2][3]
A chemical compound that causes dextrorotation is called dextrorotatory or dextrorotary, while a compound that causes levorotation is called levorotatory or levorotary.[4] Compounds with these properties consist of chiral molecules and are said to have optical activity. If a chiral molecule is dextrorotary, its enantiomer (geometric mirror image) will be levorotary, and vice versa. Enantiomers rotate plane-polarized light the same number of degrees, but in opposite directions.
## Chirality prefixes
### (+)-, (-)-, d-, l-, D-, and L-
A dextrorotary compound is often prefixed with "(+)-" or "d-". Likewise, a levorotary compound is often prefixed with "(-)-" or "l-". These lowercase "d-" and "l-" prefixes are distinct from the SMALL CAPS "D-" and "L-" prefixes, which are most often used to distinguish chiral organic compounds in biochemistry and are based on the compound's absolute configuration relative to (+)-glyceraldehyde, which is the D-form by definition. The prefix used to indicate absolute configuration does not necessarily imply the prefix used to indicate chirality in the same molecule. For example, nine of the nineteen L-amino acids naturally occurring in proteins are, despite the L- prefix, actually dextrorotary (at a wavelength of 589 nm), and D-fructose is sometimes called "levulose" because it is levorotary.
### (R)- and (S)-
The (R)- and (S)- prefixes from the Cahn-Ingold-Prelog priority rules are different from the preceding ones in that the R and S labels characterize the absolute configuration of a specific stereocenter, rather than of a whole molecule. A molecule with just one stereocenter can be labeled R or S, but a molecule with multiple stereocenters needs more than one label, for example (2R,3S).
If there is a pair of enantiomers, each with one stereocenter, then one enantiomer is R and the other is S; one enantiomer is levorotary and the other is dextrorotary. However, there is no general correlation between these two labels. In some cases the (R)-enantiomer is the dextrorotary enantiomer, and in other cases the (R)-enantiomer is the levorotary enantiomer. The relationship can only be determined on a case-by-case basis with experimental measurements or detailed computer modeling.[5]
## Specific rotation
A standard measure of the degree to which a compound is dextrorotary or levorotary is the quantity [?], known as the specific rotation. Dextrorotary compounds have a positive specific rotation, while levorotary compounds have a negative specific rotation. Any pair of enantiomers have equal but opposite specific rotations.
The formula for specific rotation, [?], is
${\displaystyle [\alpha ]={\frac {\alpha }{c\cdot l}},}$
where:
? = observed rotation (in degrees),
c = concentration of the solution of an enantiomer (in g/ml),
l = length of the polarimeter tube (in decimeters).
The degree of rotation of plane-polarized light depends on the number of chiral molecules that it encounters on its way through the tube of the polarimeter (thus, the length of the tube and concentration of the enantiomer). In many cases, it also depends on the temperature and the wavelength of light that is employed.
## Other terminology
The equivalent French terms are dextrogyre and levogyre. These are used infrequently in English.[6]
## References
1. ^ The first word component dextro- comes from the Latin word dexter, meaning "right" (as opposed to left). Laevo- or levo- comes from the Latin laevus, meaning "left side".
2. ^ LibreTexts Chemistry - Polarimetry
3. ^ "Determination of optical rotation and specific rotation" (PDF). The International Pharmacopoeia. World Health Organization. 2017. ISBN 9789241550031.
4. ^ Solomons, T.W. Graham; Fryhle, Graig B. (2004). Organic Chemistry (8th ed.). Hoboken: John Wiley & Sons, Inc.
5. ^ See, for example,Stephens, P. J.; Devlin, F. J.; Cheeseman, J. R.; Frisch, M. J.; Bortolini, O.; Besse, P. (2003). "Determination of absolute configuration using calculation of optical rotation". Chirality. 15: S57-64. doi:10.1002/chir.10270. PMID 12884375.
6. ^ For example: Sebti; Hamilton, eds. (2001). Farnesyltransferase inhibitors in cancer therapy. p. 126. ISBN 9780896036291. Retrieved .
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0. | 2020-03-29 18:32:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6002691984176636, "perplexity": 5161.025738741642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370495413.19/warc/CC-MAIN-20200329171027-20200329201027-00079.warc.gz"} |
https://economics.stackexchange.com/questions/20037/how-to-prove-dynamic-inefficiency-in-the-solow-model | # How to prove dynamic inefficiency in the Solow model?
I know that if capital is below the golden rule level in the Solow model, then we are dynamically efficient, and vice versa.
How is that proven?
## 1 Answer
I give the intuitive explanation in words first, then below is the proof.
Define a Pareto improvement to be where consumption is no lower in every period and higher in at least one period. We're said to be dynamically efficient if there's no possible Pareto improvement and dynamically efficient if there's a possible Pareto improvement.
Assume we start off already in steady state.
Proposition 1. If the savings rate is below the golden-rule level (or equivalently, the steady-state capital stock is below the golden-rule level), then we're dynamically efficient.
Proof. If we switch to a lower savings rate, the new steady-state level of consumption will be lower, and so this cannot be a Pareto improvement.
Conversely, if we switch to a higher savings rate, then consumption in the initial period of the switch will be lower, so that again this cannot be a Pareto improvement.∎
Proposition 2. If the savings rate is above the golden-rule level (or equivalently, the steady-state capital stock is above the golden-rule level), then we're dynamically inefficient.
Proof. We claim that switching to the golden-rule savings rate is a Pareto improvement.
First, note that by switching, the new steady-state level of consumption will be higher.
Next, note that in the initial period (after we've switched), consumption is higher than before, because we've lowered our savings rate.
In fact, in the initial period, consumption will be higher than the new steady state. Consumption will then fall monotonically towards the new steady state level (which is higher than old steady state).
Altogether then, by switching to this lower savings rate, consumption in each period is higher than the old steady-state level (or in other words, than it would've been had we not made the switch). This is thus a Pareto improvement.∎
• Very good answer. The only thing you might want to specify wether those are your own notes and if not perhaps post a link / reference. 👍 – bbecon Jun 14 '18 at 17:35
• @br1: They aren't notes from anywhere. I wrote them myself on LyX (much less painful than writing math here), specially for this answer. I then took a screenshot of the output PDF then put the image here. – Kenny LJ Jun 15 '18 at 1:19 | 2020-09-18 08:37:13 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8404127955436707, "perplexity": 1235.6669157224335}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400187354.1/warc/CC-MAIN-20200918061627-20200918091627-00463.warc.gz"} |
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https://scottaaronson.blog/?p=6778 | ## On Bryan Caplan and his new book
Yesterday I attended a lecture by George Mason University economist Bryan Caplan, who’s currently visiting UT Austin, about his new book entitled Don’t Be a Feminist. (See also here for previous back-and-forth between me and Bryan about his book.) A few remarks:
(1) Maybe surprisingly, there were no protesters storming the lectern, no security detail, not even a single rotten vegetable thrown. About 30 people showed up, majority men but women too. They listened politely and asked polite questions afterward. One feminist civilly challenged Bryan during the Q&A about his gender pay gap statistics.
(2) How is it that I got denounced by half the planet for saying once, in a blog comment, that I agreed with 97% of feminism but had concerns with one particular way it was operationalized, whereas Bryan seems to be … not denounced in the slightest for publishing a book and going on a lecture tour about how he rejects feminism in its entirety as angry and self-pitying in addition to factually false? Who can explain this to me?
(3) For purposes of his argument, Bryan defines feminism as “the view that women are generally treated less fairly than men,” rather than (say) “the view that men and women ought to be treated equally,” or “the radical belief that women are people,” or other formulations that Bryan considers too obvious to debate. He then rebuts feminism as he’s defined it, by taking the audience on a horror tour of all the ways society treats men less fairly than women (expectations of doing dirty and dangerous work, divorce law, military drafts as in Ukraine right now, …), as well as potentially benign explanations for apparent unfairness toward women, to argue that it’s at least debatable which sex gets the rawer deal on average.
During the Q&A, I raised what I thought was the central objection to Bryan’s relatively narrow definition of feminism. Namely that, by the standards of 150 years ago, Bryan is obviously a feminist, and so am I, and so is everyone in the room. (Whereupon a right-wing business school professor interjected: “please don’t make assumptions about me!”)
I explained that this is why I call myself a feminist, despite agreeing with many of Bryan’s substantive points: because I want no one to imagine for a nanosecond that, if I had the power, I’d take gender relations back to how they were generations ago.
Bryan replied that >60% of Americans call themselves non-feminists in surveys. So, he asked me rhetorically, do all those Americans secretly yearn to take us back to the 19th century? Such a position, he said, seemed so absurdly uncharitable as not to be worth responding to.
Reflecting about it on my walk home, I realized: actually, give or take the exact percentages, this is precisely the progressive thesis. I.e., that just like at least a solid minority of Germans turned out to be totally fine with Nazism, however much they might’ve denied it beforehand, so too at least a solid minority of Americans would be fine with—if not ecstatic about—The Handmaid’s Tale made real. Indeed, they’d add, it’s only vociferous progressive activism that stands between us and that dystopia.
And if anyone were tempted to doubt this, progressives might point to the election of Donald Trump, the failed insurrection to maintain his power, and the repeal of Roe as proof enough to last for a quadrillion years.
Bryan would probably reply: why even waste time engaging with such a hysterical position? To me, though, the hysterical position sadly has more than a grain of truth to it. I wish we lived in a world where there was no point in calling oneself a pro-democracy anti-racist feminist and a hundred other banal and obvious things. I just don’t think that we do.
### 64 Responses to “On Bryan Caplan and his new book”
1. bf skinner Says:
“How is it that I got denounced by half the planet for saying once, in a blog comment, that I agreed with 97% of feminism but had concerns with one particular way it was operationalized, whereas Bryan seems to be … not denounced in the slightest for publishing a book and going on a lecture tour about how he rejects feminism in its entirety as angry and self-pitying in addition to factually false? Who can explain this to me?”
Because, unfortunately, the universe is a giant pachinko machine (random behavior with the illusion of free will). There is the idea in Ancient Greece of “kairos” — the perfect timing for an opportunity. As is then, so is now. Whether or not someone catches flak for statements is not based on an objective measurement by the mob but by a random cascading set of events, similar to the butterfly which flaps its wings in Santiago and causes a Hurricane in North Carolina.
2. Dave Says:
“How is it that I got denounced by half the planet for saying once, in a blog comment, that I agreed with 97% of feminism but had concerns with one particular way it was operationalized, whereas Bryan seems to be … not denounced in the slightest for publishing a book and going on a lecture tour about how he rejects feminism in its entirety as angry and self-pitying in addition to factually false? Who can explain this to me?”
I wouldn’t think of it that you got attacked by feminists. You got attacked by bullies; bullies who called themselves feminists.
One key point about bullies is that they attack (perceived) weakness. You looked vulnerable, in part because you were being vulnerable and honest in your post, and to a bully that invites attack.
Bryan is not projecting weakness. He’s not being conciliatory. He’s signaled loud and clear that he’s ready to fight and looking forward to it. I expect someone to try, but he’s just not a very inviting target because the standard twitter mob scorn and shouting won’t work on him. If someone calls him a misogynist and a loser he’s just not going to be hurt by it, so people don’t.
3. Doug K Says:
to the point 2)
Bryan Caplan is a wellknown contrarian and rightwinger, everyone already expects him to be anti feminism. Dog bites man isn’t a good story, Man bites dog is news and sells newspapers/gets clicks though. Bryan is just doing what is in his nature and expected of him, which is not an interesting story. You on the other hand made a slightly unexpected statement.. and of course as bf skinner says, there is that element of randomness.
I used to call myself a feminist, my parents were and raised me as such. After spending time on Twitter and seeing the responses to the women scientists, authors etc on there: I’m not sure as a man that I ever understood the female experience of sexism. See also link from my name, a survey from Runners World on running while female. These days I call myself a feminist, inasmuch as any man could be.
4. Matthijs Says:
“How is it that I got denounced by half the planet […], whereas Bryan seems to be … not denounced in the slightest […] ?”
Scott Alexander’s «The Toxoplasma of Rage» seems relevant here. Specifically the section on dubious rape stories.
https://slatestarcodex.com/2014/12/17/the-toxoplasma-of-rage/
5. Andrew Says:
Hi Scott, you of course must know the etymology of the word “hysterical”? Your use in the final paragraph is perhaps not what you meant.
6. Scott Says:
Andrew #5: I meant it in the usual sense of “extreme and emotionally unhinged.” And I wasn’t describing my own view, but Bryan’s (at least, I’m pretty sure that’s what he’d say from talking to him). Fwiw, I try never to argue against people on the basis of Fun Facts about the etymology of the words they’re using, since even if true, such facts seem like obvious distractions.
7. Bernard A Says:
Just because a person declares that x is y and then claims to disprove y, they haven’t disproved x anywhere but in their own private universe.
8. Nick Drozd Says:
> expectations of doing dirty and dangerous work, divorce law, military drafts as in Ukraine right now, …
War is obviously a problem without any easy solutions (although we may observe in passing that those responsible for it are almost exclusively men), but the other two problems do have easy solutions:
1. Don’t expect men to do dirty and dangerous work. While we’re at it, don’t expect women to do dirty and dangerous work either.
2. Don’t get married, or else sign a generous prenup if you do.
Is that all?
9. Shmi Says:
I wonder if the reason you get so much flak is that you are part of an outgroup but Bryan Caplan isn’t, by the other Scott A criteria: https://slatestarcodex.com/2014/09/30/i-can-tolerate-anything-except-the-outgroup/
After all you are a non-radical progressive, and he is an economic libertarian.
10. Jon Awbrey Says:
“not really sexist, just following the prevailing social order”
11. JimV Says:
Life is not fair, part the infinity. (Said not in snark but in sorrow.)
Random evolution fixed on the mammalian strategy of females having primary responsibility for raising the young, and males being the physical competitors and explorers. Now technology makes strict compliance with those roles unnecessary and hence unfair, but they are still culturally ingrained in many.
While agreeing with previous commenters on various reasons for the unequal harassment treatment referenced in the post, I also think Caplan might welcome more vociferous harassment as a way to accrue more publicity and status, and might wish the situations were reversed.
12. Jay L Gischer Says:
belle hooks defines feminism as the fight against sexism. Does Bryan argue that sexism never existed? I don’t think he does.
Thing is, all those unequal burdens on men he points out? That’s sexism. So he is totally a feminist, except for defining himself not to be one.
Here’s a really fun fact. You know who pointed out the sexism dealt to men (in the form of the draft and military service) during the 80’s? That’s right, it was Andrea Dworkin. Which brings us full circle back to you, Scott.
As for the question of why he doesn’t catch crap for his views the way you do? I think it’s because he doesn’t give a crap. It bothers you, and you react, so they keep doing it, because its fun. For them.
13. SR Says:
I’ve got to say, the third sentence of Caplan’s that you quote at that link– “These days, the world’s best detectives would struggle to find outright racists and sexists.” I had no idea I was such a skilled detective! It’s incredibly easy to find such people.
One way is to go to any right-leaning publication online, click on a negative news story pertaining to some person who happens to be a minority or a woman, and scroll down to the comments section. I guarantee somewhere between 10 and 20% of the commenters will satisfy his criteria.
Another way– note that Gallup polling from last year indicated that only 94% of people approved of interracial marriage. Call random phone numbers as they did to conduct the poll, and at least 1 in 20 people is likely to be a racist.
Possibly, being a professor in one of the most progressive areas of the country (northern VA) skews Caplan’s views.
14. Qwerty Says:
Is it simply a provocative unimportant book?
I like Camille Paglia’s definition of feminist and her arguments about it.
I’m curious if Caplan brings Paglia up at all. She is an exciting thinker. I don’t see her speak or write much these days. I’m curious what she thinks about the recent changes in abortion rights, as well.
15. Zack M. Davis Says:
Bryan seems to be … not denounced in the slightest for publishing a book and going on a lecture tour about how he rejects feminism in its entirety as angry and self-pitying in addition to factually false? Who can explain this to me?
It’s simple game theory: orthodoxy punishes heretics more than infidels, because heretics are more incentivizable by orthodoxy’s punishment. Caplan isn’t part of the progressive coalition and doesn’t want to be; he knows it, and his enemies know it, so trying to threaten him into compliance would be a waste of time. You, on the other hand, make it very clear that you want to be a progressive in good standing (“because I want no one to imagine for a nanosecond that, if I had the power […]”). Since the threat of not being a good coalition member is real to you, other coalition members have an incentive to use it on you. (Perhaps you can view this as a synthesis of Dave #2’s theory about showing weakness and Doug K. #3’s theory about expectations.)
16. Lili Says:
I generally agree with your perspective. Specifically, I agree that calling yourself a feminist is valuable as signaling you care about women’s rights. However, like Jay L Gischerd above, I’d like to push back on Caplan’s definition of sexism. It’s really just a strawman that he sets up to then tear it down with examples where men are not treated fairly. Yes, men can be treated unfairly! In fact, the root cause of the unfair treatment is in fact a propensity to treat feminity as weak and thus penalize feminine men (those who may not go to war or who would like to take care of kids). This affects men of color even further as they may be coded as more masculine and thus deviations from that become more penalized.
From this perspective, to be a feminist is to recognize the inherent value of feminity and to fight against any penalties on its expression. This of course encompasses the biological aspects (such as providing abortions) but it also includes social aspects of gender expression which may affect men as well (and indeed do in the cases Caplan mentions).
Rather than acknowledging this framing, the definition that Caplan works off of pits social advances as a zero-sum game, wherein women cannot advance socially without harming men. This is misguided and a potentially damaging view as it divides the community artificially rather than allowing us all to work for a greater common cause.
17. manorba Says:
Well, here in italy we have the first female PM in history!
While i’ve grew up a feminist, still am a feminist regardless of what definition comes out of tiktok, i strongly disagree on the idea that women would be better that men in many fields. Sex doen’t matter. I’ve always been working in mixed gender places, i’ve even had a couple of women bosses along the way. Some were good, some were godawful.
And history teaches us that women (expecially when organized as a group) have seldom been on the conservative , if not reactionary part of politics.
See prohibition. Or the maga karens.
In italy we had to cheat on the results of the post war referendum because women went en masse to vote for keeping the monarchy. And at the first real popular vote, they handed the country to the DC (democrazia cristiana, i think it doesn’t need any translation)
SR#13: I must be one of those racists, because I don’t approve marriage between Jews and gentiles. We’ve preserved our heritage for two thousand of years and only those who avoided what you could call “interracial marriage” kept their identity. I won’t get into whether being Jew is a race or not, it’s definitely more nuanced than that, but the gist of preserving group identity by only marrying inside the group was still there regardless. And I do approve marriage between Jews of different origins, e.g. Sephardic and Ashkenazi. It would be complete hypocrisy for me to judge those who want to preserve their identity the same way my ancestors have done for thousand of years.
Abstract words like feminism don’t work according to definitions but according to how people use them. Different generations have different people. Feminism a century ago consisted of brave talented woman fighting for freedom to do things, and to stop horrible treatment of them. Feminists today fight to gain privilege and advantage over men as if the world is some weird zero sum game between men and women.
The movie Ratatouille had something I find as a good analogy. They said “everyone can cook”, and it has two different meanings:
One is that everyone can be a good cook. That’s clearly false because some people are just terrible and that’s just it.
The other is that a good cook could be anyone and come from everywhere.
Old feminists were woman who were already outstanding but the world just didn’t let them express it. New feminists are mediocre at best and are looking to play the victim and gain an advantage to cover for their mediocracy. (And of course there were all the real societal inequalities that are long dead, like voting and being treated as property. That has nothing to do with modern feminism because those things don’t exist).
The way I see it, every social movement doesn’t stop when its goal is achieved, because there are always more goals for some subset of its supporters. Social movements stop when they are met with an equal and opposing force, like newton’s third law. Feminism didn’t stop at legal and opportunity equality, where you would have logically expected it, because there is simply no pushback on that – it’s everyone’s common sense. Just like LGBT didn’t stop at legal marriage and being destigmatized. And abortion didn’t stop at the common sense compromise of Roe vs Wade, and kept pushing to murder almost-born fetuses.
Progressivism is what happens when old social movements achieve their goal, reach the middle ground most people wouldn’t mind accepting and keep going forward, because the real equilibrium isn’t the common sense consensus but only when your ideas are so twisted that some people actually want to stand against them with an opposing and equal force.
19. Corbin Says:
Scott, your questions are intertwined and there is a single unified answer for them.
First, I want to give my prior estimation for your second question. I estimate that around 25-30% of the population would actively vote/elect to regress gender relations by 150yrs. I also estimate that around 5-10% of the population is callous and insensitive to the plight of marginalized folks. This means that, to me, some 30-40% of the population could easily be convinced to hold a position that Caplan thinks 60% of the population cannot hold. My estimate is not made in a vacuum, but comes from news about various democratically-elected politicians, as well as interviews with their various constituents. The regressive beliefs are, sadly, real.
(Technical note for Caplan, should he choose to respond: It’s highly unlikely that we are both right, and that *exactly* 40% of the country would be regressive and *exactly* 60% of the country would not be regressive. So one of us is probably wrong. (Also, *please* respond; I’m looking for any excuse to fisk your Substack~))
So, is Caplan the kind of person who doesn’t read the news? Have they been asleep for their entire lives? No. I think, then, that it is fair to withdraw a Gricean charity from their viewpoint, especially since it sounds like they did not offer any *evidence* for their claims. We don’t need to engage with their position at all — we can put it on a pike outside in the front yard, along with a sign reading, “Here lie Caplan’s claims, unsubstantiated.” It sounds like he might vote for leopards, too, in which case we can equip the pike with a second sign: “Here lies Caplan, a professor who thought that the fascists would not hurt professors.”
And this leads us to the unified answer. Why did feminists bother talking to Scott and not to this other guy? Because this other guy has denied reality to a degree which makes him irrelevant, and there’s no rescuing him. Because Scott shows an ability to update priors, while the other guy enthusiastically supports patriarchy. Because this other guy goes around with a provocative talk and a provocative book and tries to be a culture warrior, while Scott recognizes that the culture war is largely bullshit. Because Scott is worth talking to.
SR #13: Maybe Caplan’s locale has something to do with it. But I’m skeptical. I grew up in Oregon, and I was raised to understand that the fascists were real and that certain parts of the state were not safe for travel. To this day, I divide the Pacific Northwest into safe and unsafe regions based on prevailing beliefs in those regions. Surely Caplan, who travels across the USA much more than me, has an even better understanding of the degree to which some regions of the USA are too fascist to safely visit! No, I think that we should see Caplan as a deeply deluded individual who happens to benefit from white and male privileges; he simply doesn’t see fascists as dangerous because he has internalized the idea that they will not hurt him.
20. manorba Says:
about the book and his author, tell you what, to me it is just trolling. higher level trolling if you want, but still.
As many have mentioned before me, his points are moot. it gets mainstream visibility because we live in a post truth and post logic world. It’s no mistery it caught your attention. you devoted your life to truth and logic. and that’s how trolls get you 😉
21. Mitchell Porter Says:
Regarding question 2 – why were you attacked for criticizing feminism a little, while Bryan rejects feminism altogether and is seemingly ignored – I think other commenters have it right: you were regarded as a kind of peer by your critics, whereas Bryan is a lost cause not worth bothering with, inherently beyond the bounds of respectable thought.
A few weeks ago, Robin Hanson gave a positive review to a book called “Fossil Future” which apparently asserts that future harms from climate change are minor and will easily be paid for by future economic growth. Why wasn’t this book scrutinized and criticized heavily on, I don’t know, NPR and the New York Times? Again, because a priori it’s not considered serious scholarship, it’s considered a generic product of a parallel world where right-wing money funds works that argue for predetermined conclusions. Something like that.
You *can* see a handful of Internet feminists discuss Bryan’s book here:
22. manorba Says:
Gadi #18 Says: I must be one of those racists, because I don’t approve marriage between Jews and gentiles.
why do you care about other peoples’ private life? don’t you have one of your own? and why would anybody care if you approve or not?
Why do you feel the need to comment on the struggles of relevant parts of society and their effort to come out of it like they are eroding your personal well being?
23. Scott Aaronson Fan Says:
Scott, here’s why you get attacked more than Bryan Caplan. The first and most important reason is that you are more autistic. Radical feminists hate autists, for the same reason they do not like human genetic enhancement, space travel, and human cloning, and they love nature. As an autistic/Asperger guy, your existence is a *direct attack* on the radical feminists’ conception of humanity. To them you are not even a human, you are human-adjacent. You are in direct opposition to femininity itself, as conceived by left-wing feminists.
The other reason is that you are on the left. You interact with many people on the left, and are high-profile. Caplan is a libertarian so for him it’s nothing new. He is not a mainstream figure. By contrast, you are a normal center-left guy, so you get held to a higher standard. You are also a very very public figure, who is writing on your blog on all sorts of things.
24. CC Says:
Gadi #18. How is your opinion different from folks saying they don’t approve of marriages between white and black people? Coming from India, it is the same as upper caste people saying that they don’t want intermarriage between castes because they want to preserve their “ancient” culture. It is a slippery slope from culture preservation to outright racism and discrimination.
25. Qwerty Says:
Manorba #20,
I wouldn’t go so far as to call the author a troll. Not at all. He is worth engaging with, particularly if you disagree. I haven’t read this book, but I liked some important questions this author asked in another book, “The case against education”. I value college education deeply, but liked that he tried to ask what the role of a university was in society. It is a good question.
26. SR Says:
Gadi #18. I suppose the question is a little ambiguous because ‘approve’ can have multiple meanings. I’ll distinguish 3 possibilities– (1) You, personally, would not participate in an interracial marriage, (2) You believe that interracial marriage should be legal but should not be encouraged, (3) You believe that interracial marriage should be illegal. I think (1) is acceptable as I don’t think people should be judged based on personal preferences. By the same token, I think believing (3) makes one a racist as it is overriding *others’* personal preferences using the force of the law, on the basis of race.
I think (2) is more complicated. I do understand those who want to preserve their culture at a societal level. However, I don’t think this necessarily has anything to do with race. Expanding on your example relating to Jewish people, genetics apparently indicate that Yemeni Jews are genetically much more similar to Arabs than to other Jewish populations. It is hypothesized that they may mostly be the descendants of converts to Judaism. e.g. see Razib Khan’s post here- https://www.gnxp.com/WordPress/2021/10/28/yemen-and-the-yemeni-jews/ . Does this make them any less Jewish? I am not Jewish, but at least as an outsider, I would not think so.
I think in general, a good litmus test would be– would you be equally comfortable with a marriage of two people of your race, and a marriage between one person of your race, and another who was adopted into a family of your race, is culturally indistinguishable from the median person of your race, and differs only genetically? If not, I would consider that to be racist.
I personally think even focusing on culture to too much of an extent is somewhat misguided, but that is a different topic of discussion.
Corbin #19. Sadly, I think there is some truth to what you say. In general, I am a little skeptical of the concept of white, male privilege (I am nonwhite and feel like I have lived a pretty privileged life myself). But I think it’s safe to say that Caplan, personally, is either willfully ignoring evidence around him that would repudiate his thesis, or is incredibly unperceptive.
27. Scott Says:
Nick Drozd #8: But if there’s dirty and dangerous work that needs doing—if machines can’t yet replace humans for all of it—shouldn’t whoever is willing to do it at least be well-rewarded?
28. Dan Staley Says:
So… is this whole discussion just a semantic argument over the meaning of the word “feminism”?
29. Scott Says:
Gadi #18: As someone who chose to marry a Jewish woman and raise two Jewish children—if I’d chosen otherwise, it would’ve been none of your business, and your disapproval would’ve been irrelevant.
30. Marc Briand Says:
Re your interchange with Caplan: unless you have some mutually agreed upon algorithm for evaluating the magnitude of unfairness visited upon men and women, arguing who is treated worse is an exercise in futility. For every example you bring up Caplan will bring up a counterexample, and on and on it goes. I believe this is exactly the sort of tar pit Caplan wants to pull people into. His whole approach seems to be a bait-and-switch on the meaning of feminism. If I were you I would not give him any more of my time.
31. HasH Says:
“I teach you the overman. Man is something that shall be overcome.” Nietzsche
I am not a racist. I am from Caucasisa (born and raise). Pure bred same race and we are few million left on earth. Our language not related with any existing language tree. I want that culture survive. Like American, or Siberia ethnic people. Living museum. Israeli Jews one of them (i don’t care their religious belief just for cultural history).
Peace!
32. SR Says:
Adding to my comment above, it just occurred to me that if you belong to a small cultural community that is in danger of dying out (e.g. see the Parsi community of India, or the Samaritans of Israel), you would actually want to *encourage* interracial/intercultural marriage, as, otherwise, in a few generations, the gene pool would become too small to be sustainable. The crucial thing, then, if you cared about passing on that endangered culture, would be to find a spouse who is okay with preferentially passing down the traditions of the endangered culture when raising kids, in an effort to keep those traditions alive for longer. I thus feel that the cultural objection to interracial marriage does not really hold water.
33. Everything Sucks Says:
Hey Scott,
I appreciate your thoughts. Nonetheless, I feel like you’re totally missing the elephant in the room here. I know you don’t want to moderate an incel discussion on your blog—and after your trolling debacle over the summer, it’s totally understandable. If you want to doscuss gender/feminist culture war politics, however, you are practically BEGGING to invite incel commentary. It’s impossible to appreciate the full picture here without acknowledging the (largely ignored by society) lived experiences of millions of lonely, frustrated men who are, in their own way, marginalized by society, and have no reason to give a shit about any of this.
Take me, for example. I’m an incel. 27, kissless male virgin, and not for lack of trying. I’ve wanted, I’ve craved sex for a decade, and I’ve been totally ignored while girls chased bad boys and chads. When you talk about abortion rights, all I think about are the girls who laughed at me or looked at me with contempt. When you talk about oppression of women or gays or transgenders or whatever, all I remember is the burning pain inside from seeing all these beautiful laughing young women and knowing I shouldn’t even talk to them for fear of being labelled a creep or whatever. Whenever you mention any of these woke causes, I literally can’t make myself care. There’s too much pain inside. In fact, the thought of a “Handmaid’s tale” right wing revolution brings me more joy than fear.
You can’t discuss gender politics without acknowledging this reality. There are millions and millions of young guys like me—more every year—who are totally deprived of sex and love and, in their own way, just as marginalized by society. Their pain begets no parades or speeches. Nobody cares. And likewise, they have no reason to give a shit about women or the rest of it.
If you don’t acknowledge this reality, you can’t get a full picture of wjhat’s going on in this country. So if you want to avoid the incel stuff, don’t talk about it.
34. Boaz Barak Says:
I didn’t read Caplan’s book but I’m struck at how quickly he’s published this book, after publishing his case against education, claiming that the hundreds of Billions societies spend on education from 8th grade onwards is largely wasted. It seems that either Caplan is an incredibly prescient seer, that in many different domains can see the true facets that almost all of society misses, or that he’s just a troll.
35. manorba Says:
Qwerty #25 Says: I wouldn’t go so far as to call the author a troll. Not at all
ok let’s just say we disagree on where the boundary between provocative and trolling is 🙂
it’s just that he chooses the hottest topic at hand, puts forward the most divisive and counterintuitive interpretation and backs it up with blatantly wrong data. That to me is trolling 101.
36. Michel Says:
HasH #31: Sorry, the correct word in your case is ‘subspecies’ not ‘race’. And yes, racism is confusing subspecies with race. You are just another human, like any. Like me – dubbed “white” for my strongly pigmented yellow-brownish-pink skin. And sometimes ‘purity’ is another word for ‘inbreeding’, or excluding unfashionable traits like a different epicantal fold. All this, of course, depending on the size of the group.
37. Wind Says:
My answer to your Q2: although I think #23 has a point in particular, I’d say the main point is timing. The spotlight of the activist left, for want of a better demonym, moves around – you had the bad timing to criticise feminism when the spotlight was on women.
As evidence that the spotlight has moved on and where it’s pointing now, I cite that neither “Karen” (which, you will note is explicitly female-coded) nor “TERF” were such emotion-generating outgroup signifiers back then.
I say this because as someone who does not identify with their birth sex myself, I believe the spotlight will have moved on again in a few years, and I worry what remaining support or goodwill might be left over for people like me then. “The mob is currently on my side” is one of the least reassuring feelings possible.
38. Scott Aaronson Fan Says:
I should have also included nuclear power in the first reason. The second reason was mis-stated. The real reason though is that you really care about being attacked. This neuroticism and this sort of reaction to these unfair critics (“bullies”, if you call it that) means that they will continue to unfairly criticize (“bully”) you. This kind of extreme cowardice makes you vulnerable.
Why do you keep stating your commitment to feminism? What do you have to signal? Who are you trying to convince with this commitment? You are happily married to a woman with a career who kept her name. The real reason is your insecurity and neuroticism, which makes you vulnerable.
39. Herhjgfd Says:
We got a natural experiment disproving his last book on education. When schools shut down for the pandemic students really didn’t learn as much according to standardized testing, with less loss in states that stayed open like Florida, which contradicted his thesis that schooling was just a waste. Not sure what experiment could test any ideas in his new book.
SR #26: Call it whatever you want, I don’t discuss internal terminology I discuss actions. I would say (2). I very rarely support making things I don’t like illegal, if at all. On the other hand, I’ll shamelessly teach my kids they should prefer marrying a Jew. And I’ll never judge or criticize any other group if they do the same with their kids because that would be hypocritical. I won’t rationalize away my actions in a way that excludes white people or black people or Amish or whatever. Many of the real racists will easily make the same rationalization about culture. Maybe all the 6% you called racist only made the decision because of culture. Culture and race are highly correlated, so there’s plenty of logic in their decision.
In the end of the day, the probability I’ll disapprove interracial Jewish marriage is much higher than the probability I’ll disapprove a Jewish marriage. I don’t spin around and dance and write narratives around my actions, and I find hypocrisy for similar actions by others a bigger sin than racism.
Scott #29: I do bet that your good Jewish parental education has been a factor in your decisions and life trajectory. That’s the way things work and there’s no reason to be ashamed of it. Choosing to do similarly with my kids as my parents did and (maybe?) as your parents did isn’t something shameful. Although it is probably much easily done in Israel where they are more likely to find a Jewish husband/wife without conflicts.
41. Scott Says:
Gadi #40: When did I say anything about being ashamed of my choices?
42. Michael Z Says:
You didn’t get denounced by half the planet, you just got a lot of hateful comments on the internet. The internet haters represent an extremely unrepresentative portion of the world.
Also, you made yourself look vulnerable in your blog comment(s), so the haters saw you as an easier target. I actually found it somewhat comical that you wanted these people’s approval and opened yourself up like that, because so many of them are openly and obsessively prejudiced against men. Would you try to debate Kanye West on the merits of his arguments? It probably wouldn’t lead anywhere.
43. Vitor Says:
Lili #16, your attitude exemplifies perfectly why I’m not a feminist. You don’t outright say it, but you imply that men can only be treated unfairly insofar as they have feminine qualities that are penalized. Do you think that every masculine man is happy to be handed a gun and sent to die for his country? Or happy to get the short end of the stick in child custody disputes? Is that your *definition* of masculinity?
You say nice words about working for a common cause instead of being artifically divided, but then this “common” cause just happens to only concern itself with the struggles of feminine people.
44. Nick Drozd Says:
Scott #29
Yes, of course they should be paid well! And they should have improved working conditions. Better pay and conditions for workers are often effected by unions and collective bargaining. But I’m guessing that Caplan, as a right-wing think-tank provocateur, is opposed to all of that. I’m sure he has some really fascinating arguments about how in fact work safety regulations actually make things less safe for workers, and therefore safety laws should be abolished.
Of course, that’s all bullshit. Anti-feminists will bring up these issues where men are treated less fairly, but they don’t actually care about those issues. As other commenters have discussed, anti-feminists are fixated on calculating grievances and then arguing which “side” has it worse. They don’t care about fixing the issues they raise. Caplan does not personally care at all about the actual men who are forced to do dirty and dangerous work. He isn’t interested in improving their conditions or their lives.
This problem comes up over and over with reactionaries. Remember when George Floyd was murdered by police a few years ago? There was a lot of discussion about how racist the police are. Donald Trump himself came out to say, no, the police aren’t racist, they kill white people too! Now, that’s not exactly factually wrong (for example, look up DANIEL SHAVER). And you’d think the obvious next step would be to inquire further into police killings, regardless of race. But that’s all beside the point for the reactionary — all he cared about was dismissing any concern about racism. The actual white people killed by police don’t matter.
45. Forever Alone Says:
Scott and Everything Sucks,
I’m curious if you’ve seen Nama Kates’ commentary on the incel movement. She’s one of the very few people who seems genuinely interested in understanding their point of view without having an ideological axe to grind, and she’s come to sympathize with them. She runs a podcast where she interviews incels.
Take a look at her UnHerd here: https://unherd.com/author/naama-kates/
I think Naama would be really interested in your perspective, Scott, if you’d reach out to her. You definitely have a unique story to tell.
46. Nick Drozd Says:
SAF #23
> Radical feminists hate autists, for the same reason they do not like human genetic enhancement, space travel, and human cloning, and they love nature.
Uh, WTF are you talking about? This is a really bizarre caricature of “radical feminists”. Try as I might, I cannot think of a single instance in my entire life of seeing any feminist at all suggesting that they “do not like” space travel, or that the idea of space travel has anything to do with feminism in any way.
You seem to have a picture in your mind of some anti-technology hippy earth mother type, and that for you is the totality of feminism. There are two problems:
1. Most feminists are not anti-technology. In fact, there are lots of feminists who work in STEM. There is also a whole sub-genre of feminist sci-fi, which of course prominently features space travel!
2. Those hippy earth mother types are often not anti-technology either. You know what they are usually interested in? Astrology. And guess what: the people who are into astrology are also excited about the JWST! They discuss the latest findings just like us science nerds. (They draw rather different conclusions, but that’s a whole other story.)
Human cloning and genetic enhancement are complicated subjects. I’m sure feminists have all sorts of feminism-influenced opinions about them, but there is no broad consensus that I am aware of. Painting with a broad brush here is not a smart move.
And just to be clear, anti-feminists are not exactly known for being pro-science. Many anti-feminists are religious lunatics and conspiracy theorists who believe that the Earth is 6,000 years old, that the Moon landing was faked, etc.
47. Scott Says:
Herhjgfd #39: Not to put words in Bryan’s mouth, but I believe he’d say that the COVID learning loss is irrelevant since the studies show the kids would’ve forgotten nearly all the stuff anyway after they graduated if not earlier, so that COVID merely hastened the inevitable.
48. SR Says:
Gadi #40. This will probably be my last response in this thread. I’m not interested in judging whether you in particular are or aren’t racist. Addressing your other points–
You are right that the polling strictly speaking does not show that 6% of the population are racist. However, just as you say that disapproval of interracial marriage is heavily correlated with cultural preferences, it is also heavily correlated with obviously prejudicial views regarding other groups (e.g. beliefs that other groups should not have the right to vote, beliefs that they should be segregated, reluctance to work with those of other groups in a professional setting, etc.). There is a long history of racists using other excuses to hide their racially prejudiced views– see how the American South afterwards whitewashed their motivations in the Civil War.
So perhaps the 6% of that poll are not *all* racist, but I have no hesitation in saying that at least 6% of the population of the US has racially prejudiced attitudes. It is not at all hard to believe, given that there are many people alive today who grew up prior to the passage of the Civil Rights Act of 1964, some of whom statistically speaking would have never changed their views on segregation and passed down their views to their descendants. David Duke, a former leader of the KKK, won 43% of the vote in a US Senate election in Louisiana, in 1990. I view the people who voted for him (and those who would have voted for him, had they lived in Louisiana) as just as morally reprehensible as those who voted for Hitler in 1933, whether or not it technically constitutes racism. Many of those Duke voters are still alive and well today. I do not agree with the progressive view that racism is everywhere today, but I think it is equally incorrect to say that it has disappeared completely.
Regarding hypocrisy, I like the belief enunciated by the conservative pundit Ben Shapiro- “I don’t like hypocrisy charges generally, because I think when people sin, it’s the sin that’s the problem, not the purported standard.” I think this applies as much to hypocrisy about morality/religion as it does to hypocrisy about liberalism.
49. SR Says:
Scott, the writing style of ‘Forever Alone’ and ‘Everything Sucks’ are extremely reminiscent of that of the same incel troll who bothered you the last time. e.g. compare Comment 45 in this thread to https://scottaaronson.blog/?p=6552#comment-1941172 . Although it could be a coincidence.
50. mls Says:
Dr. Aaaronson #27
Thank you for your consideration. My greatest fear at work is the kind of incident in this video:
I am not a window washer. But, in Chicago, unionized window washers are in the same union as low pressure system building engineers. These are not the highest paying jobs because they are primarily janitorial with only light maintenance. Interestingly, the window washers do not even receive a hazard pay differential under their contract.
Nick Drozd #44
Blue-collar workers with hazardous jobs are pawns for both sides of debates over safety regulations. Rules transfer decision-making from the workers who have “skin in the game” to experts who profit from their status in bureaucratic hierarchies.
In the United States, OSHA and the training of union members by their unions have had measurable impacts on worker disability. Disability insurance and compensation plans have not seen those improvements because of predator-prey dynamics between lawyers and physicians. And, in so far as health insurance is a private-sector entitlement program, physicians price services in a money-rich market where overuse of medical testing protects them from malpractice. The benefits of safe workplaces are erased by ambulance chasing.
As a person who learned his trade before OSHA had significant influence, what I surmised from my first OSHA certification class is that most of the safety regulations in my industry are for the benefit of insurance companies. Fingers, hands, arms, toes, feet, legs, and eyes can all be “priced.” Death, however, often involves jury-awaded damages that are less predictable.
And, since OSHA regulations repeatedly defer to manufacturer recommendations, it provides an opportunity for engineers to make money by simply producing incompatible tools and equipment on a regular basis.
Recall how Microsoft Windows had been marketed as a vanilla interface to minimize training costs. Once market dominance had been obtained, user interfaces had been changed in quick succession until the hubris of the Federal Reserve tanked the information technology sector in 2000. Corporations started pushing back in the face of recession.
One sees similar predatory strategies in the manufacturing of safety equipment. If companies cannot extend the usable life of their equipment, they can never be generous with their workers.
In my trade, it is often the case that safety rules increase hazards. OSHA has provisions — prior request for deferral of rules in triplicate. In the actual world, difficulties are not that foreseeable. And, people who write liquidated damages into contracts are not bound by safety regulations to respect OSHA safety regulations. The law has no “pass through” to all economic actors. It stops at the employer. This means that one of the first things compromised where contracts are awarded according to lowest bids are the safety rules. The only real concern is defensibilty in the face of legal liability.
And, of course, I have not even touched on the fact that the regulations are written in “legalese” for workers who, largely, have no education of which to speak. Over half of the workers in my company are native Spanish speakers. Not all of them can read. Their weekly safety reminders have been English documents downloaded from an Internet site. I think they are now only being given a qr-code so they can download the pages for themselves.
I can assure you that only one or two people have actually read the company safety program (OSHA stipulates that training is the responsibility of the employer. In this context “responsibility” ought to include pay for reading the safety documents (and manufacturer recommendations on equipment). Such pay is never forthcoming — nor will it be unless a lawsuit for interpreting “responsibility” is initiated. So, the employees have no economic incentive to be informed on the company safety program. And, they all know that there would be adverse consequences if they actually tried to apply the published rules.)
In so far as OSHA instills a fear of liability, people in my trade are safer. But, this is largely because equipment is now available where it would have been denied in the past. It is not as if the rules are actually followed.
Reality is sobering.
51. Topologist Guy Says:
SR, the comment by “Forever Alone” doesn’t look at all reminiscent (in terms of writing style) of the one you linked, aside from the fact that they’re both discussing the same social issue.
52. SR Says:
Topologist Guy #51. Maybe I’m wrong. But I did read through the entirety of the incel discussions a while back, and the troll did write in a certain distinctive way that I felt was mirrored in these comments. For instance, in the comments here https://scottaaronson.blog/?p=6576, under the name of ‘Roger D.’, he twice refers to Scott in the middle of a sentence in the following way–
“I don’t call you an Incel, Scott, because you’re…”
Compare to comment 45 where you have the analogous construction–
“I think Naama would be really interested in your perspective, Scott, if you’d reach out to her.”
It’s not a construction that no one else uses, but it’s uncommon, as only people who are rather particular about grammar (I tentatively include myself in this category) tend to use it, in my experience.
The anger+pain in comment 33 here also mirrors the sentiments with which the incel troll was commenting. I don’t want to go through the effort of finding a reference. Although admittedly, it could just be distinct people with the same grievances.
Also, regarding the content being the same, it seems improbable that there would be multiple incels who read Scott’s blog and independently ask him to talk to right-sympathetic media figures about incel problems. Similarly, it seems unlikely that two different incels would comment on this blog post within the span of a day.
None of this is enough to prove anything. But given past experience, it seems quite plausible to me. If I am wrong, I apologize in advance to the commenters above.
53. incel Says:
Throughout my entire life, I have been an outcast. I’ve have spent countless hours pondering alone in my apartment why this is. I have legitimately never had a friend in real life or anyone I could consider close to. Sure you meet people in school or at work but they were never my “friends”. No one ever called me no one ever asked me to do anything with them. And I don’t even blame them. Why would anyone want to associate with someone who does nothing all day but sulk and rot. A few years ago I tried to change my life and better myself. I put myself out there and came out of my confront zone, only to be bombarded by the worst case of realization the world could ever offer. Your face and looks define your value before anyone even knows who you are. When you wake up every morning, look in the mirror and are overcome with depression and sadness what life left is there to live? I do not live anymore, I purely exist in a world where everything is moving forward and I am staying still. Imagine one of those videos where someone is standing still for a long time while everyone passes them on the street sped up, that is how I feel every day. I wish this torture upon no one. I’d like to say to my fellow incel brothers do not give up hope, maybe someday you to will be free of these chains and no longer held down by inceldom.
I will die a kissless virgin – but let’s not think I never tried. I have tried everything – tinder, bumble, bars, clubs, meetups, co-workers. I can’t even count or remember the amount of times I was rejected. It has to be in the thousands at this point. I COULD NOT EVEN GET A SINGLE DATE. This was soul crushing to me. Why could I not even land a single date with any women? Where my standards to high? Was it something I said? No no no no, it was my face. I lost the genetic lottery and this was my destiny. All I ever wanted was to be loved by someone as much as I loved them, this is the only thing I have ever wanted but I know this will never happen….
54. Matty Wacksen Says:
>How is it that I got denounced by half the planet
You weren’t. Selection effects made it feel like you were though, when really you were denounced by a tiny minority. Those effects get stronger if there is some kind of feedback loop, e.g. if the bullies feel like what they’re doing is working. My guess is that Bryan Caplan got some form of better selection effects. FWIW, I heard about your blog from others who were *supporting* you, in fact I’ve never met anyone I would take seriously who did not.
> so too at least a solid minority of Americans would be fine with—if not ecstatic about—The Handmaid’s Tale made real.
I feel like you’re not taking this argument far enough. If, as you say, people can’t be trusted to reveal their true preferences, why trust them when they call themselves “feminists”? To take this argument even further: shouldn’t we trust people who say “I think women should be treated equally as men” more than those who say “I am a feminist”, since the “I am a feminist” crowd is hiding behind a poorly-defined word that can swing either way? Here’s a skit from the Babylon Bee making this joke about a guy saying he’s a feminist but using it to act like a non-feminist https://www.youtube.com/watch?v=j3jGG32ekdk
>Indeed, they’d add, it’s only vociferous progressive activism that stands between us and that dystopia.
>And if anyone were tempted to doubt this…
I notice I am confused, because vociferous progressive activism prevented none of the events you mention, in fact there is probably a strong argument that it had its fair share of blame in *causing* Trump’s election because it condescendingly assumed that everyone who would go on to elect Trump was backwards and hated women’s rights made them not trust the progressives.
55. manorba Says:
SR #52 Says: None of this is enough to prove anything. But given past experience, it seems quite plausible to me. If I am wrong, I apologize in advance to the commenters above.
it’s peculiar tho, innit? the timing screams of a coordinated effort, the nicknames used are lazy to say the least.
And even if they are legit, they say the same things over and over using the same language.
Scott and some other posters have already debated the issue ad nauseam. just check old posts if you want hints on how to get out of inceldom.
56. OhMyGoodness Says:
The majority of the voting eligible population in the US is female. Females tend to vote at a higher rate than males. If blame is to be assigned for the current state of politics in the US then argument by numbers points to strong female voter complicity and or guilt.
I dream of the day when genetic engineering will provide the possibility of erasing all tribal affiliations in the human population and people will consider others (including their mates) simply as individuals and not some simplified list of divisive labels. Sometimes it seems as those that are most opposed to tribalism in theory are the most adherent in practice.
57. Lili Says:
Vitor #43, thank you for taking the time to reply to me. I agree with you that men can be treated unfairly even while being masculine.
It’s possible you’re reacting to my phrasing of “feminine people”, which admittedly was a poor choice of phrasing for my message. I think men (including masculine men) get unfairly penalized for doing feminine-coded actions (taking care of children, expressing emotions) and for avoiding masculine-coded actions (going to war, being the “breadwinner” for the family). So I meant that it’s not about being a masculine/feminine man, but about doing masculine/feminine-coded actions.
Historically, the feminine-coded actions have been undervalued compared to the masculine actions. Taking care of children is seen as less important than defending the country, for instance. So a man (especially a masculine one) who might want to prioritize taking care of his family over fighting in a war may be met with disapproval: “are your children really more important than our borders being safe?” There are no epics written about men staying home to take care of children, yet raising the next generation is at least as important as keeping borders safe.
I think this is why the men’s right movement is not taken as seriously, as historically masculine-coded actions (having a career, going to battle, expressing theories) have been seen as more desirable and respectable than feminine-coded actions (taking care of children or even other people, doing chores, self-care).
So to me, the root is not about masculine vs feminine people, but rather how we code different actions and the inherent value that gets attached to those. I hope that we can make the feminine actions just as respectable as masculine and in the process destigmatize men and women who behave outside of their gender norms.
58. manorba Says:
There must be something i misunderstood…
how come the military draft (or service)is now discrimination against men? oh, the turntables..
59. OhMyGoodness Says:
Lili#57
“There are no epics written about men staying home to take care of children, yet raising the next generation is at least as important as keeping borders safe.”
The children you stay home and care for aren’t armed with thermobaric weapons nor white phosphorous munitions…well…until at least teenagers.
60. Qwerty Says:
Manorba #35:
I’ve often wondered exactly what a troll is. The best I could come up with is, someone who is not sincerely interested in a discussion, but has some other agenda in participating.
The reason I liked reading “The case against education”, is that the culture I come from (India) is heavily into credentialism, to the point that it is bizarre.
I believe that one must learn FOR THE SAKE OF LEARNING.
This book asks what the role of university is in society. It answers it, saying it provides a credential.
I have always seen good universities as places that offer you intellectually curious people to learn from and with. Maybe bad universities offer only a credential. So I disagree with Cowen on his answer to the question, but I don’t think he’s being insincere. Maybe he’s just cynical:). Or maybe I’m just bizarrely / stupidly earnest.
61. manorba Says:
Qwerty #60 Says: I’ve often wondered exactly what a troll is. The best I could come up with is, someone who is not sincerely interested in a discussion, but has some other agenda in participating.
Oh, i agree (actually, i agree with everything else you say in the post), i’d just add the minor thing that sometimes the agenda is just “winning the argument”.
But in this case i see a leit motiv: an attack to all the conquests made by rationality in the last centuries. I struggle to accept that the almost 1:1 correspondence with the neo-traditionalist (in italy it takes the name of “sovranismo”, sovereignity) ideas is just a coincidence.
62. Douglas Knight Says:
Why do we talk about politics? Is it cheap talk? Actual votes are so few bits of information. Politicians would like know what’s going to happen ahead of time, rather than playing the ultimatum game. Even without voting, every government has a democratic pressure valve of civil war. In particular, when you say that we should talk about big changes, it sounds like you’re talking about speech that would only be realized in civil war. We want to know who would win, so that we don’t have to fight.
But you say a lot of things that don’t match that. Other people don’t act like they agree with that model in several different ways. You seem to believe that talk is pretty cheap.
You say “a solid minority of Germans turned out to be totally fine with Nazism, however much they might’ve denied it beforehand.” If people lie about their beliefs, what is the actual signalling game? You seem to think that Trump voters are lying to you about first wave feminism. If you don’t believe them, why should they believe you that you’re only a 97% feminist? How does “vociferous activism” cause anything?
You seem to say that it’s more important that we are clear and stable in our coarse position than that we get the fine adjustment correct. This seems obviously correct. But you observe people who don’t seem to agree with you. One possibility is that you are incorrect and Bryan is correct that we are clear and stable on the coarse position, so there’s no reason to talk about it. Another possibility is that you are factually correct, but other people disagree with you on the morality of making the coarse position clear. Why? One possibility is to confuse you about whether you are making the fine adjustment or the coarse adjustment, but probably there are many other possibilities. Only your side can really manipulate you, but it sounds like you describe both sides as polarizing. Leaving aside coarse vs fine, what about Duverger’s law? At any scale, why are they polarizing, rather than appealing to the centrist? Maybe you don’t know what game they are playing?
63. Douglas Knight Says:
Another thing about people lying about their politics: the proverbial communists who became Nazis. Talk is cheap, but brawling seems like an expensive signal, and yet… Does this shed light on what people are actually signaling and how to predict where they will go in the future?
64. Recursion Respecter Says:
To me, the interesting claims are that (1) men as a class have more agency than women as a class, and (2) this inequality extends broadly, so that gendered socioeconomic norms grant the average man greater powers than they grant the average woman. It’s my affirmation of these claims, and my belief that they represent a problem we ought to fix, that I think makes me a feminist in the non-trivial sense.
#1 seems obvious, taking the gender of the world’s major political and economic leaders into account. #2 is a bit dicier, but seems reasonable given how power within (heterosexual) households tends to be concentrated in the husband in most places on Earth. In support of #2, it’s also worth noting that most workplaces (especially high-earnings / prestigious workplaces) tend to be dominated by men even below the C-suite, and I believe that even in the most everyday of contexts (interactions between friends, coworkers and strangers), women face a kind of glass ceiling of social *respect* (they need to work harder to be taken seriously as leaders in group conversation and decision, on average).
Anyway, that all being said, I am not sure whether the *average* man loses out more from gendered socioeconomic norms than the average women, in a purely utilitarian sense. That seems debateable. Just because men have more power doesn’t mean they actually benefit from it, or utilize it in the most personally beneficial ways, and then there’s all those particular ways that men get a clearly raw deal (especially in times of war). Lastly, I think we’d all be better off, men included, if this agency-differential were reduced, so in a way it harms men too.
So, in this utilitarian sense, I may not be a feminist, in that I am not so confident that men are the average winners, utiles-wise.
But its the agency thing that I think of more, when I think about feminism.
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https://forums.techguy.org/threads/word-2010-vba-autoopen-macro-to-insert-dates-into-text-boxes.1102703/ | # Word 2010 VBA AutoOpen Macro to Insert Dates Into Text Boxes
Discussion in 'Business Applications' started by LukeB12345, Jul 3, 2013.
Not open for further replies.
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I am trying to create an AutoOpen VBA Macro in Word 2010 files for automatically inserting the same dates into 2 different text boxes when I first open the file. Ideally, I would want 1 file to do this always for Yesterday's date (whatever that may be) and another file to do this for Friday's date (whatever that may be).
Reason for this is because our mail room gets mail the day before I get it on my desk and I need to date stamp it using a Word 2010 template where I have 2 text boxes (please see attached file--oh, doesn't seem like I can attach the file???) for Tuesday through Friday. Right now, I am using the Macros I have created (1 for Yesterday's Date and another Macro for Friday's Date which is Date() -3).
I want to use that Macro logic to put that into the Text boxes I have when it first opens? Please help me with this anyone......
It doesn't seem like I can attach the file so here is the VBA code:
Sub AutoOpen()
'
' AutoOpen Macro that places the cursor at the last position of edit (not default of top left) (will work with Protected View)
If Application.ActiveProtectedViewWindow Is Nothing Then
Application.GoBack
End If
' InsertTextBox1 Macro
Dim Shp As Shape
Orientation:=msoTextOrientationVertical, _
Left:=22, Top:=252, Width:=25, Height:=170)
Set Shp = Nothing
Selection.InsertAfter Format(Now() - 1, "dddd, MMMM dd, yyyy")
Selection.Font.Size = 8
Selection.Font.Name = "Arial Narrow"
Selection.Font.Bold = wdToggle
Selection.Font.Bold = wdToggle
' InsertTextBox1 Macro
Dim Shp2 As Shape
Orientation:=msoTextOrientationHorizontal, _
Left:=432, Top:=752, Width:=170, Height:=18)
Set Shp2 = Nothing
End Sub
Luke
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Hans
Hi Luke,
Check under Go advanced and then 'Manage Attchments' to select and attach the file, without the file it will be guessing what and how.
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Hans
You just replied, there is quite a large button next to 'Post Quick Reply' and what does it say ...?
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I hit "Go Advanced" .... Now where is Manage Attachments?? If I click the little paperclip icon or the arrow next to it, it does nothing??
Can you tell me please how to attach a file (I don't understand why this has to be so complicated)??
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Hans
I do think you should try and read what's on the screen
#### Attached Files:
• ###### TSG.jpg
File size:
48.2 KB
Views:
139
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Yeah, I see your screenshot, but when I click Go Advanced, everything is the same except I don't have that "Manage Attachments" button like you do for some reason???
So anyway, a lot of code has changed since we last talked and I could just post it up in the forum, then you can copy it into your a New Word Document (only thing is you would have to name that new word document "All Claims (Transparent).docx" if you have Word 2010 of course) since there's an If statement to apply the AutoOpen Macro to only that file.......
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Hans
Maybe your screen resolution is different, it's there or your IE is not functioning correctly.
You can past your changed code and I'll see if I can figure out what you want.
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Ok here it is (so I am just reprinting these text boxes from this Word template onto thousands of claim forms already printed out by the time I get them):
Sub AutoOpen()
' AutoOpen Macro that places the cursor at the last position of edit (not default of top left) (will work with Protected View)
If Application.ActiveProtectedViewWindow Is Nothing Then
Application.GoBack
End If
If ActiveDocument.Name = "All Claims (Transparent).docx" Then
' InsertTextBox1 (Vertical)
Dim Shp As Shape, sDate As String
If Format(Now(), "ddd") = "Mon" Then
sDate = Format(Now() - 3, "dddd, MMMM dd, yyyy")
Else
sDate = Format(Now() - 1, "dddd, MMMM dd, yyyy")
End If
Left:=7, Top:=252, Width:=25, Height:=170)
Shp.TextFrame.TextRange.Style = "Normal"
Shp.TextFrame.TextRange.Font.Size = 8
Shp.TextFrame.TextRange.Font.Name = "Arial Narrow"
Shp.TextFrame.TextRange.Text = "NMM RECEIVED: " & sDate
Shp.Line.Visible = msoFalse
' InsertTextBox2 (Horizontal)
Dim Shp2 As Shape, sDate2 As String
If Format(Now(), "ddd") = "Mon" Then
sDate2 = Format(Now() - 3, "dddd, MMMM dd, yyyy")
Else
sDate2 = Format(Now() - 1, "dddd, MMMM dd, yyyy")
End If
Left:=462, Top:=765, Width:=142, Height:=18)
Shp2.TextFrame.TextRange.Style = "Normal"
Shp2.TextFrame.TextRange.Font.Size = 8
Shp2.TextFrame.TextRange.Font.Name = "Arial Narrow"
Shp2.TextFrame.TextRange.Text = "NMM RECEIVED: " & sDate
Shp2.Line.Visible = msoFalse
Shp2.IncrementRotation (180)
End If
End Sub
Oh yeah, the only thing left is to make the text inside the text boxes transparent (50%)??? That's what I need help with please???
By the Way, I tried the same thing under Google Chrome, and it didn't have the Manage Attachments button (I think that is only for Premium Users or something right??)??
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First Name:
Hans
I see what the macro does. AutoOpen only works if the docuemnt already has the macro in them
A word file with macro's has the extension docm and not docx
First a liitle ho to when pasting code:
Start the section with [ code ] no blanks inside the square brackets
paste the code and the close that section with [ / code ] and again no blanks inside the square brackets
then you'll see something like this
Code:
Sub AutoOpen()
' AutoOpen Macro that places the cursor at the last position of edit (not default of top left) (will work with Protected View)
If Application.ActiveProtectedViewWindow Is Nothing Then
Application.GoBack
End If
If ActiveDocument.Name = "[COLOR="Red"]All Claims (Transparent).docm[/COLOR]" Then
' InsertTextBox1 (Vertical)
Dim Shp As Shape, sDate As String
If Format(Now(), "ddd") = "Mon" Then
sDate = Format(Now() - 3, "dddd, MMMM dd, yyyy")
Else
sDate = Format(Now() - 1, "dddd, MMMM dd, yyyy")
End If
Left:=7, Top:=252, Width:=25, Height:=170)
Shp.TextFrame.TextRange.Style = "Normal"
Shp.TextFrame.TextRange.Font.Size = 8
Shp.TextFrame.TextRange.Font.Name = "Arial Narrow"
Shp.TextFrame.TextRange.Text = "NMM RECEIVED: " & sDate
Shp.Line.Visible = msoFalse
' InsertTextBox2 (Horizontal)
Dim Shp2 As Shape, sDate2 As String
If Format(Now(), "ddd") = "Mon" Then
sDate2 = Format(Now() - 3, "dddd, MMMM dd, yyyy")
Else
sDate2 = Format(Now() - 1, "dddd, MMMM dd, yyyy")
End If
Left:=462, Top:=765, Width:=142, Height:=18)
Shp2.TextFrame.TextRange.Style = "Normal"
Shp2.TextFrame.TextRange.Font.Size = 8
Shp2.TextFrame.TextRange.Font.Name = "Arial Narrow"
Shp2.TextFrame.TextRange.Text = "NMM RECEIVED: " & sDate
Shp2.Line.Visible = msoFalse
Shp2.IncrementRotation (180)
End If
End Sub
Notice the document name in the macro it's doc instead of docx.
Run it and it qorks, but it will run every time you open this document, I don't think that is what you want but ...
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Messages:
41
Ok, thanks for the tips (I knew that but don't use Word too much for Macros, mostly .xlsm files). The file works as of now (not sure what you mean "AutoOpen only works if the docuemnt already has the macro in them"??) and it is working exactly as I want it to work except that the text boxes don't have transparency applied to them when the document is first opened.
Anyway, I do want it to run everytime I open the document since that document serves as my template for date stamping the claim forms.
Can you please let me know how to make the text boxes transparent??
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Messages:
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First Name:
Hans
Default is no fill so transparant
see attachment
One thing you'll have to keep in mind you're creating a new textbox everytime which is place over the previous one.
I'm no Word guru so you'll have to figure out something like if shp.... exists then use it and update it or else delete all shapes before you begin
#### Attached Files:
• ###### All Claims (Transparent).docm
File size:
21 KB
Views:
71
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Messages:
41
So I see the TimeStampModule code is different than the code I had shared with you...
So what do I need to put in the .Fill.Backcolor = line (which is commented out at the moment)??
I am not sure if .Fill.Backcolor will make the text inside the Text box transparent, either??
I tried, instead, .Fill.Transparency = 0# (not sure if it suppose to be 1#, tried both on both shapes\text boxes and neither worked)??
Also, only 1 text box shows up halfway in, halfway out?? (I guess the margins for that .docm file are different--did you change the positions of the text boxes??)
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First Name:
Hans
I don't know, that was a test of mine but I couldn't work that one out.
I changed the formatting for the date in that sense that the values is the same only another shape and orientation, so why reset the value twice, onec is enough
Joined:
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Messages:
41
So I actually have figured a way to make both text boxes transparent.
Just had to use a Style in the VBA code to apply the Style I had created through the GUI. I am not sure if it would be better or not to pursue getting it to work in the VBA code alone without relying on any GUI Style created??
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https://plotly.com/python/v3/chord-diagram/ | # Python Chord Diagram in Python/v3
How to make an interactive chord diagram in Python with Plotly and iGraph.
See our Version 4 Migration Guide for information about how to upgrade.
# Chord Diagrams with Plotly¶
A circular layout places the graph nodes uniformly on a circle. In this example we illustrate how to draw the graph edges in order to avoid a cluttered visualization.
### Eurovision Song Contest Example¶
As an example, we consider a circular graph with the European countries as nodes. Among these countries, some qualified for the grand final Eurovision Song Contest.
Each european country is a jury member and rates some contestants on a scale from 1 to 12 (in 2015 a contestant from Australia led to adding this country to the graph).
There is a directed edge from a jury member country to a contestant country if the contestant acquired at least one point from the jury country voters.
The jury member countries are placed uniformly, in alphabetical order, on the unit circle. If there is an edge between two nodes, then we draw a cubic Bézier curve having as the first and the last control point the given nodes.
To avoid cluttered edges we adopted the following procedure in choosing the interior control points for the Bézier curve:
• we consider five equally spaced points on the unit circle, corresponding to the angles $0, \:\pi/4$ $\pi/2,\: 3\pi/4, \:\pi$: $$P_1(1,0), \: P_2=(\sqrt{2}/2,\: \sqrt{2}/2),\: P_3(0,1), \: P_4=(-\sqrt{2}/2, \sqrt{2}/2),\: P_5(-1,0)$$
• define a list, Dist, having as elements the distances between the following pairs of points: $$(P_1, P_1), \:(P_1, P_2), \: (P_1, P_3),\: (P_1, P_4),\: (P_1, P_5)$$
• In order to assign the control poligon to the Bézier curve that will be the edge between two connected nodes, V[i], V[j], we compute the distance between these nodes, and deduce the interval $k$, of two consecutive values in Dist, this distance belongs to.
• Since there are four such intervals indexed $k=0,1,2,3$, we define the control poligon as follows: $${\bf b}_0=V[i],\:\: {\bf b}_1=V[i]/param,\:\: {\bf b}_2=V[j]/param, \:\:{\bf b}_3=V[j],$$ where param is chosen from the list: params=[1.2, 1.5, 1.8, 2.1].
Namely, if the distance(V[i], V[j]), belongs to the $K^{th}$ interval associated to Dist, then we choose param= params[K].
We processed data provided by Eurovision Song Contest, and saved the corresponding graph in a gml file. Now we can read the gml file and define an igraph.Graph object.
Install the Python libraries with sudo pip install python-igraph and sudo pip install networkx.
In [1]:
import igraph as ig
Define the list of nodes (vs stands for vertices):
In [2]:
V=list(G.vs)
G.vs.attributes()# list node attributes
Out[2]:
['id', 'label']
Define the label list. Labels will be displayed in the Plotly plot:
In [3]:
labels=[v['label'] for v in V]
G.es is the sequence of graph edges
In [4]:
G.es.attributes()# the edge attributes
Out[4]:
['weight']
Get the edge list as a list of tuples, having as elements the end nodes indices:
In [5]:
E=[e.tuple for e in G.es]# list of edges
len(E)
Out[5]:
400
Get the list of Contestant countries:
In [6]:
ContestantLst=[G.vs[e[1]] for e in E]
Contestant=list(set([v['label'] for v in ContestantLst]))
len(Contestant)
Out[6]:
25
Get the node positions, assigned by the circular layout:
In [7]:
layt=G.layout('circular') #circular layout
layt is a list of 2-elements lists, representing the coordinates of nodes placed on the unit circle:
In [8]:
L=len(layt)
layt[7]
Out[8]:
[0.45399049973954686, 0.8910065241883678]
Define the list of edge weights:
In [9]:
Weights= map(int, G.es["weight"])
In the sequel we define a few functions that lead to the edge definition as a Bézier curve:
dist(A,B) computes the distance between two 2D points, A, B:
In [10]:
import numpy as np
def dist (A,B):
return np.linalg.norm(np.array(A)-np.array(B))
dist(layt[0], layt[5])
Out[10]:
0.76536686473017945
Define the list Dist of threshold distances between nodes on the unit circle and the list of parameters for interior control points:
In [11]:
Dist=[0, dist([1,0], 2*[np.sqrt(2)/2]), np.sqrt(2),
dist([1,0], [-np.sqrt(2)/2, np.sqrt(2)/2]), 2.0]
params=[1.2, 1.5, 1.8, 2.1]
The function get_idx_interv returns the index of the interval the distance d belongs to:
In [12]:
def get_idx_interv(d, D):
k=0
while(d>D[k]):
k+=1
return k-1
Below are defined the function deCasteljau and BezierCv. The former returns the point corresponding to the parameter t, on a Bézier curve of control points given in the list b.
The latter returns an array of shape (nr, 2) containing the coordinates of nr points evaluated on the Bézier curve, at equally spaced parameters in [0,1].
For our purpose the default number of points evaluated on a Bézier edge is 5. Then setting the Plotly shape of the edge line as spline, the five points are interpolated.
In [13]:
class InvalidInputError(Exception):
pass
def deCasteljau(b,t):
N=len(b)
if(N<2):
raise InvalidInputError("The control polygon must have at least two points")
a=np.copy(b) #shallow copy of the list of control points
for r in range(1,N):
a[:N-r,:]=(1-t)*a[:N-r,:]+t*a[1:N-r+1,:]
return a[0,:]
def BezierCv(b, nr=5):
t=np.linspace(0, 1, nr)
return np.array([deCasteljau(b, t[k]) for k in range(nr)])
Finally we set data and layout for the Plotly plot of the circular graph:
In [14]:
import plotly.plotly as py
import plotly.graph_objs as go
node_color=['rgba(0,51,181, 0.85)' if v['label'] in Contestant else '#CCCCCC' for v in G.vs]
line_color=['#FFFFFF' if v['label'] in Contestant else 'rgb(150,150,150)' for v in G.vs]
edge_colors=['#d4daff','#84a9dd', '#5588c8', '#6d8acf']
Define the lists of x, respectively y-coordinates of the nodes:
In [15]:
Xn=[layt[k][0] for k in range(L)]
Yn=[layt[k][1] for k in range(L)]
On each Bézier edge, at the point corresponding to the parameter $t=0.9$, one displays the source and the target node labels, as well as the number of points (votes) assigned by source to target.
In [16]:
lines=[]# the list of dicts defining edge Plotly attributes
edge_info=[]# the list of points on edges where the information is placed
for j, e in enumerate(E):
A=np.array(layt[e[0]])
B=np.array(layt[e[1]])
d=dist(A, B)
K=get_idx_interv(d, Dist)
b=[A, A/params[K], B/params[K], B]
color=edge_colors[K]
pts=BezierCv(b, nr=5)
text=V[e[0]]['label']+' to '+V[e[1]]['label']+' '+str(Weights[j])+' pts'
mark=deCasteljau(b,0.9)
edge_info.append(go.Scatter(x=[mark[0]],
y=[mark[1]],
mode='markers',
marker=dict( size=0.5, color=edge_colors),
text=text,
hoverinfo='text'
)
)
lines.append(go.Scatter(x=pts[:,0],
y=pts[:,1],
mode='lines',
line=dict(color=color,
shape='spline',
width=Weights[j]/5#The width is proportional to the edge weight
),
hoverinfo='none'
)
)
trace2=go.Scatter(x=Xn,
y=Yn,
mode='markers',
name='',
marker=dict(symbol='circle',
size=15,
color=node_color,
line=dict(color=line_color, width=0.5)
),
text=labels,
hoverinfo='text',
)
axis=dict(showline=False, # hide axis line, grid, ticklabels and title
zeroline=False,
showgrid=False,
showticklabels=False,
title=''
)
def make_annotation(anno_text, y_coord):
return dict(showarrow=False,
text=anno_text,
xref='paper',
yref='paper',
x=0,
y=y_coord,
xanchor='left',
yanchor='bottom',
font=dict(size=12)
)
anno_text1='Blue nodes mark the countries that are both contestants and jury members'
anno_text2='Grey nodes mark the countries that are only jury members'
anno_text3='There is an edge from a Jury country to a contestant country '+\
'if the jury country assigned at least one vote to that contestant'
width=800
height=850
title="A circular graph associated to Eurovision Song Contest, 2015<br>Data source:"+\
"<a href='http://www.eurovision.tv/page/history/by-year/contest?event=2083#Scoreboard'> [1]</a>"
layout=go.Layout(title= title,
font= dict(size=12),
showlegend=False,
autosize=False,
width=width,
height=height,
xaxis=dict(axis),
yaxis=dict(axis),
margin=dict(l=40,
r=40,
b=85,
t=100,
),
hovermode='closest',
annotations=list([make_annotation(anno_text1, -0.07),
make_annotation(anno_text2, -0.09),
make_annotation(anno_text3, -0.11)]
)
)
data=lines+edge_info+[trace2]
fig=go.Figure(data=data, layout=layout)
py.iplot(fig, filename='Eurovision-15')
Out[16]:
Now we can compare to the Eurovision graph as a networkx.Graph:
In [17]:
import networkx as nx
import matplotlib.pyplot as plt
%matplotlib inline
G=nx.DiGraph()
plt.figure(figsize=(18,18))
nx.draw_circular(G,node_color='g', edge_color='#909090', node_size=900)
plt.axis('equal')
Out[17]:
(-1.5, 1.5, -1.5, 1.5) | 2021-12-05 23:50:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44491320848464966, "perplexity": 3412.6172171792923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363226.68/warc/CC-MAIN-20211205221915-20211206011915-00170.warc.gz"} |
http://polystat.blogspot.com/2015/05/performance-of-gpu-vs-cpu.html | ## Illustrating Three Approaches to GPU Computing: The Mandelbrot Set
As you may know (a few post earlier), our research lab has equipped by a GPU (Graphics Processing Unit) server, called Tesla k40, and today I did my first experiment to realize the computational power of this parallel hardware versus 5th Generation Intel® Core™ i7 Processor.
The following example, taken from Matlab, shows how fast GPU performance can speed up computing. Using Parallel Computing Toolbox™ this code is then adapted to make use of GPU hardware in three ways:
1. Using the existing algorithm but with GPU data as input
2. Using arrayfun to perform the algorithm on each element independently
3. Using the MATLAB/CUDA interface to run some existing CUDA/C++ code
Setup
The values below specify a highly zoomed part of the Mandelbrot Set in the valley between the main cardioid and the p/q bulb to its left.
A 1000x1000 grid of real parts (X) and imaginary parts (Y) is created between these limits and the Mandelbrot algorithm is iterated at each grid location. For this particular location 500 iterations will be enough to fully render the image.
Below is an implementation of the Mandelbrot Set using standard MATLAB commands running on the CPU.
Using gpuArray
When MATLAB encounters data on the GPU, calculations with that data are performed on the GPU. The class gpuArray provides GPU versions of many functions that you can use to create data arrays, including the linspace, logspace, and meshgrid functions needed here. Similarly, the count array is initialized directly on the GPU using the functionones.
With these changes to the data initialization the calculations will now be performed on the GPU:
Element-wise Operation
Noting that the algorithm is operating equally on every element of the input, we can place the code in a helper function and call it using arrayfun. For GPU array inputs, the function used with arrayfun gets compiled into native GPU code. In this case we placed the loop in pctdemo_processMandelbrotElement.m:
Note that an early abort has been introduced because this function processes only a single element. For most views of the Mandelbrot Set a significant number of elements stop very early and this can save a lot of processing. The for loop has also been replaced by a while loop because they are usually more efficient. This function makes no mention of the GPU and uses no GPU-specific features - it is standard MATLAB code.
Using arrayfun means that instead of many thousands of calls to separate GPU-optimized operations (at least 6 per iteration), we make one call to a parallelized GPU operation that performs the whole calculation. This significantly reduces overhead.
Working with CUDA
In Experiments in MATLAB improved performance is achieved by converting the basic algorithm to a C-Mex function. If you are willing to do some work in C/C++, then you can use Parallel Computing Toolbox to call pre-written CUDA kernels using MATLAB data. You do this with the parallel.gpu.CUDAKernel feature.
A CUDA/C++ implementation of the element processing algorithm has been hand-written in pctdemo_processMandelbrotElement.cu. This must then be manually compiled using nVidia's NVCC compiler to produce the assembly-level pctdemo_processMandelbrotElement.ptx (.ptx stands for "Parallel Thread eXecution language").
The CUDA/C++ code is a little more involved than the MATLAB versions we have seen so far, due to the lack of complex numbers in C++. However, the essence of the algorithm is unchanged:
Summary
This example has shown three ways in which a MATLAB algorithm can be adapted to make use of GPU hardware:
1. Convert the input data to be on the GPU using gpuArray, leaving the algorithm unchanged
2. Use arrayfun on a gpuArray input to perform the algorithm on each element of the input independently
3. Use parallel.gpu.CUDAKernel to run some existing CUDA/C++ code using MATLAB data
Code
maxIterations = 500;
gridSize = 1000;
xlim = [-0.748766713922161, -0.748766707771757];
ylim = [ 0.123640844894862, 0.123640851045266];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t = tic();
x = linspace( xlim(1), xlim(2), gridSize );
y = linspace( ylim(1), ylim(2), gridSize );
[xGrid,yGrid] = meshgrid( x, y );
z0 = xGrid + 1i*yGrid;
count = ones( size(z0) );
% Calculate
z = z0;
for n = 0:maxIterations
z = z.*z + z0;
inside = abs( z )<=2;
count = count + inside;
end
count = log( count );
% Show
figure
hold on
cpuTime = toc( t );
fig = gcf;
fig.Position = [200 200 600 600];
imagesc( x, y, count );
axis image
colormap( [jet();flipud( jet() );0 0 0] );
title( sprintf( '%1.2fsecs (without GPU)', cpuTime ) );
hold off
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Setup
t = tic();
x = gpuArray.linspace( xlim(1), xlim(2), gridSize );
y = gpuArray.linspace( ylim(1), ylim(2), gridSize );
[xGrid,yGrid] = meshgrid( x, y );
z0 = complex( xGrid, yGrid );
count = ones( size(z0), 'gpuArray' );
% Calculate
z = z0;
for n = 0:maxIterations
z = z.*z + z0;
inside = abs( z )<=2;
count = count + inside;
end
count = log( count );
% Show
figure
fig = gcf;
fig.Position = [200 200 600 600];
hold on
count = gather( count ); % Fetch the data back from the GPU
naiveGPUTime = toc( t );
imagesc( x, y, count )
axis image
colormap( [jet();flipud( jet() );0 0 0] );
title( sprintf( '%1.3fsecs (naive GPU) = %1.1fx faster', ...
naiveGPUTime, cpuTime/naiveGPUTime ) )
hold off
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function count = pctdemo_processMandelbrotElement(x0,y0,maxIterations)
% z0 = complex(x0,y0);
% z = z0;
% count = 1;
% while (count <= maxIterations) && (abs(z) <= 2)
% count = count + 1;
% z = z*z + z0;
% end
% count = log(count);
% Setup
t = tic();
x = gpuArray.linspace( xlim(1), xlim(2), gridSize );
y = gpuArray.linspace( ylim(1), ylim(2), gridSize );
[xGrid,yGrid] = meshgrid( x, y );
% Calculate
count = arrayfun( @pctdemo_processMandelbrotElement, ...
xGrid, yGrid, maxIterations );
% Show
figure
fig = gcf;
fig.Position = [200 200 600 600];
hold on
count = gather( count ); % Fetch the data back from the GPU
gpuArrayfunTime = toc( t );
imagesc( x, y, count )
axis image
colormap( [jet();flipud( jet() );0 0 0] );
title( sprintf( '%1.3fsecs (GPU arrayfun) = %1.1fx faster', ...
gpuArrayfunTime, cpuTime/gpuArrayfunTime ) );
hold off
cudaFilename = 'pctdemo_processMandelbrotElement.cu';
ptxFilename = ['pctdemo_processMandelbrotElement.',parallel.gpu.ptxext];
kernel = parallel.gpu.CUDAKernel( ptxFilename, cudaFilename );
% Setup
t = tic();
x = gpuArray.linspace( xlim(1), xlim(2), gridSize );
y = gpuArray.linspace( ylim(1), ylim(2), gridSize );
[xGrid,yGrid] = meshgrid( x, y );
% Make sure we have sufficient blocks to cover all of the locations
numElements = numel( xGrid );
% Call the kernel
count = zeros( size(xGrid), 'gpuArray' );
count = feval( kernel, count, xGrid, yGrid, maxIterations, numElements );
% Show
figure
fig = gcf;
fig.Position = [200 200 600 600];
hold on
count = gather( count ); % Fetch the data back from the GPU
gpuCUDAKernelTime = toc( t );
imagesc( x, y, count )
axis image
colormap( [jet();flipud( jet() );0 0 0] );
title( sprintf( '%1.3fsecs (GPU CUDAKernel) = %1.1fx faster', ...
gpuCUDAKernelTime, cpuTime/gpuCUDAKernelTime ) );
hold off
1. My mind is blowing now!! Heavy language! :)
2. Nice and quite informative post. I really look forward to your other posts.
Technical Support Engineering Services | 2018-05-24 03:52:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26359957456588745, "perplexity": 10674.99180843939}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865913.52/warc/CC-MAIN-20180524033910-20180524053910-00191.warc.gz"} |
http://community.wikia.com/wiki/User_blog:Derek_Despie/Derek_Despie_becomes_normal_Wikian_once_again_for_%22Nintendo_Wiki%22 | in:
English
# Derek Despie becomes normal Wikian once again for "Nintendo Wiki"
Hi everyone, I'm Derek Despie.....I'm discussing with some Nintendo Wikians to unblock both User:Derek Despie and User:DDD1988 from the Nintendo Wiki. I'm posting it to some admins for that local wiki, so I'm having a chance to edit a whole load of sorts 'n stuff without having to add false information or do spamming, once again, since then. | 2017-05-26 20:58:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.815746009349823, "perplexity": 13441.99548272652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608684.93/warc/CC-MAIN-20170526203511-20170526223511-00236.warc.gz"} |
https://tex.stackexchange.com/questions/118496/math-symbol-within-a-new-font-word/118499#118499 | # Math symbol within a new-font word
I would like to insert a bullet to separate the syllables within a word. The word appears in a new font, and I would like the bullet to appear (as in a dictionary) centered within the word.
Neither escaping to math mode (the second line) nor escaping from math mode (third line) works.
How can I reconcile this incompatibility between the text font and the math font?
\documentclass{article}
\usepackage{times,amsmath,amsfonts,amssymb}
\pagestyle{empty}
\newfont{\mynewfont}{pagk8r scaled 3000}
\begin{document}
{\mynewfont extra}
{\mynewfont ex}$\bullet${\mynewfont tra}
${\mynewfont ex}\bullet {\mynewfont tra}$
\end{document}
Assuming that \newfont is just for the purpose of the example (it should never be used in LaTeX, it's still defined for backwards compatibility), here's a way:
\documentclass{article}
\usepackage{graphicx}
\pagestyle{empty}
\newfont{\mynewfont}{pagk8r scaled 3000}
\newcommand{\syllmark}{\kern.1em\raisebox{.3ex}{\scalebox{1.5}{\textbullet}}\kern.1em\relax}
\begin{document}
{\mynewfont extra}
{\mynewfont ex\syllmark tra}
\end{document}
Adjust the amounts of kerning, scaling and raising to suit.
The recommended way for defining the font is to use higher level commands. Since you want Avant Garde at 30pt, do
\DeclareRobustCommand\bigavantgarde{\fontsize{30}{42}\usefont{\encodingdefault}{pag}{m}{n}}
\DeclareTextFontCommand\textbigavantgarde{\bigavantgarde}
so you have both
{\bigavantgarde word}
and
\textbigavantgarde{word}
• Thanks.. I need a pointer: what is the new way for specifying "pagk8r scaled 3000"? Jun 10 '13 at 18:54
• @Calaf I added the info. Jun 10 '13 at 19:19 | 2022-01-21 08:12:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9386049509048462, "perplexity": 4024.6029760342335}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00621.warc.gz"} |
https://www.cuemath.com/ncert-solutions/exercise-1-2-real-numbers-class-10-maths/ | # NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.2
Go back to 'Real Numbers'
## Question 1
Express each number as a product of its prime factors:
(i) $$140$$
(ii) $$156$$
(iii) $$3825$$
(iv) $$5005$$
(v) $$7429$$
### Solution
What is known?
A number.
What is unknown?
The expression of the given number as a product of its prime factors.
Reasoning:
Find the prime factors of the given numbers by prime factorisation method and then multiply the obtained prime numbers to get the product of the prime numbers.
Steps:
(i) $$140$$
Prime factors of $$140$$
\begin{align}&=2\times 2 \times 5 \times 7 \\&={{2}^{2}}\times 5\times 7\end{align}
(ii) $$156$$
Prime factors of $$156$$
\begin{align}&=2\times 2\times 3\times 13 \\ &={{2}^{2}}\times 3\times 13 \end{align}
(iii) $$3825$$
Prime factors of $$3825$$
\begin{align}&=3\times 3\times 5\times 5\times 17 \\ &={{3}^{2}}\times {{5}^{2}}\times 17\end{align}
(iv) $$5005$$
Prime factors of $$5005$$
$=5\times7\times11\times 13$
(v) $$7429$$
Prime factors of $$7429$$
$=17\times 19\times 23$
## Question 2
Find the LCM and HCF of the following pairs of integers and verify that LCM $$\times$$ HCF $$=$$ Product of the two numbers.
(i) $$26$$ and $$91$$
(ii) $$510$$ and $$92$$
(iii) $$336$$ and $$54$$
### Solution
What is known?
Pairs of numbers.
What is unknown?
The LCM and HCF of the following pairs of integers and verify that LCM $$\times$$ HCF $$=$$ Product of the two numbers
Reasoning:
• To find the LCM and HCF of the given pairs of the integers, first find the prime factors of the given pairs of integers.
• Then, find the product of smallest power of each common factor in the numbers. This will be the HCF.
• Then find the product of greatest power of each prime factor in the number. This would be the LCM.
• Now, you have to verify LCM $$\times$$ HCF $$=$$ product of the two numbers, find the product of LCM and HCF and also the two given numbers. If LHS is equal to the RHS then it will be verified.
Steps:
(i) $$26$$ and $$91$$
Prime factors of $$26=2\times 13$$
Prime factors of $$91=7\times 13$$
HCF of $$26$$ and $$91=13$$
LCM of $$26$$ and $$91$$\begin{align}&=2 \times7 \times 13\\&=14 \times 13 \\&=\text{ }182 \\ \end{align}
Product of two numbers \begin{align}&=26\times 91\\ &=2366 \end{align}
LCM $$\times$$ HCF
\begin{align}&= 182\,\times\,13\\ &= 2366\end{align}
So,
Product of two numbers $$=$$ LCM $$\times$$HCF
(ii) $$510$$ and $$92$$
Prime factors of $$510=2\times 3\times 5\times 17$$
Prime factors of $$92=2\,\times \,2\times 23$$
HCF of two numbers $$=2$$
LCM of two numbers
\begin{align}&=2\times 2\times 3\times 5\times 17\times 23 \\ &=23460\end{align}
Product of two numbers
\begin{align}&=510\,\times\,92 \\ &= 46920\end{align}
LCM $$\times$$ HCF \begin{align}&=2\times 23460 \\&=46920\end{align}
Product of two numbers $$=$$ LCM $$\times$$ HCF
(iii) $$336$$ and $$54$$
Prime factors of $$336=2\times 2\times 2\times 2\times 3\times 7$$
Prime factors of $$54=2 \times 3 \times 3\times 3$$
HCF of two numbers $$=6$$
LCM of two numbers
\begin{align} &=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 7 \\ &=2^{4} \times 3^{3} \times 7 \\ &=3024 \end{align}
Product of two numbers
\begin{align} &=336 \times 54 \\ &=18144 \end{align}
LCM $$\times$$ HCF
\begin{align}&=3024 \times 6 \\ &=18144\end{align}
Product of two numbers $$=$$ LCM $$\times$$ HCF
## Question 3
Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) $$12, 15$$ and $$21$$
(ii) $$17, 23$$ and $$29$$
(iii) $$8, 9$$ and $$25$$
### Solution
What is known?
(i) $$12, 15$$ and $$21$$
(ii) $$17, 23$$ and $$29$$
(iii) $$8, 9$$ and $$25$$
What is unknown?
The LCM and HCF of the given integers by applying the prime factorisation method.
Reasoning:
To solve this question, follow the following steps-
• First find the prime factors of the given integers.
• Find the HCF of the given pair of integers i.e. product of smallest power of each prime factor, involved in the number.
• Lastly, Find the LCM of the given pair of integers i.e. product of greatest power of each prime factor, involved in the number.
Steps:
(i) $$12, 15$$ and $$21$$
Prime factors of $$12$$
\begin{align}&= {2 \times 2 \times 3}\\&={{2^2} \times 3}\end{align}
Prime factors of $$15= 3 \times 5$$
Prime factors of $$21=2 \times 2 \times 3$$
HCF of $$12,15$$ and $$21= {3}$$
LCM of $$12,15$$ and $$21$$ \begin{align}&= {{2^2} \times 3 \times 5 \times 7}\\ &={ 420}\end{align}
(ii) $$17, 23$$ and $$29$$
Prime factors of $$17= 17\,\times\,1$$
Prime factors of $$23=23\,\times\,1$$
Prime factors of $$29 = 29 \times 1$$
HCF of $$7,\,23$$ and $$29={1}$$
LCM of $$17,\,23$$ and $$29$$
\begin{align}&= 17 \times 23 \times 29\\&= 11339\end{align}
(iii) $$8, 9$$ and $$25$$
Prime factors of $$8$$
\begin{align}&= 2 \times 2 \times 2\\ &= {2^3}\end{align}
Prime factors of $$9$$
\begin{align}&= 3 \times 3\\ &= {3^2}\end{align}
Prime factors of $$25$$
\begin{align}&= 5 \times 5\\ &= {\text{ }}{5^2}\end{align}
HCF of $$8, 9$$ and $$25 = 1$$
LCM of $$8,\,9$$ and $$25$$
\begin{align} &=2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 \\ &=1800 \end{align}
## Question 4
Given that HCF $$(306, 657) = 9$$, find LCM $$(306, 657)$$.
### Solution
What is known?
HCF of two numbers $$(306, 657) = 9$$
What is unknown?
LCM of the given numbers
Reasoning:
We know that LCM $$\times$$ HCF $$=$$ product of two given integers
We have the given numbers as $$306$$ and $$657$$ and we can find the product of $$306$$ and $$657$$. The HCF of this two numbers is $$9$$. Put the values in the above property and find the value of unknown i.e. HCF.
Steps:
Given, HCF $$(306, 657) = 9.$$
We have to find,
LCM $$(306, 657) = ?$$
We know that
LCM$$\times$$ HCF $$=$$ Product of two numbers
\begin{align}\rm{LCM}\times\, 9 &= 306\, \times \,657\\\rm{LCM}&= {\frac{{306\, \times \,657}}{9}}\\\rm{LCM}&= 34\, \times \,657\\\rm{LCM}&= 22338 \end{align}
## Question 5
Check whether $$6^n$$ can end with the digit $$0$$ for any natural number $$n$$.
### Solution
What is unknown?
Whether $$6^n$$ can end with the digit $$0$$ for any natural number $$n$$.
Reasoning:
If any number ends with the digit $$0$$ that means it should be divisible by $$5$$. That is, if $$6^n$$ ends with the digit $$0$$, then the prime factorization of $$6^n$$ would contain the prime $$5$$.
Steps:
Prime factors of $${6^{{n}}} = {\left( {2 \times 3} \right)^{{n}}} = {\left( 2 \right)^{{n}}}{\left( 3 \right)^{{n}}}$$
You can observe clearly, $$5$$ is not in the prime factors of $$6^n$$.
That means $$6^n$$ will not be divisible by $$5.$$
Therefore, $$6^n$$ cannot end with the digit $$0$$ for any natural number $$n$$.
## Question 6
Explain why $$7 × 11 × 13 + 13$$ and $$7 × 6 × 5 × 4 × 3 × 2 × 1 + 5$$ are composite numbers.
### Solution
What is unknown?
Whether $$7{{ }} \times {{ }}11{{ }} \times {{ }}13{{ }} + {{ }}13$$ and $$7{{ }} \times {{ }}6{{ }} \times {{ }}5{{ }} \times {{ }}4{{ }} \times {{ }}3{{ }} \times {{ }}2{{ }} \times {{ }}1{{ }} + {{ }}5$$ are composite numbers?
Reasoning:
To solve this question, recall that:
• Prime numbers are whole numbers whose only factors are $$1$$ and itself.
• Composite number are the positive integers which has factors other than $$1$$ and itself.
Now, simplify $$7{{ }} \times {{ }}11{{ }} \times {{ }}13{{ }} + {{ }}13$$ and $$7{{ }} \times {{ }}6{{ }} \times {{ }}5{{ }} \times {{ }}4{{ }} \times {{ }}3{{ }} \times {{ }}2{{ }} \times {{ }}1{{ }} + {{ }}5.$$ On simplifying them, you will find that both the numbers have more than two factors. So, if the number has more than two factors, it will be composite.
Steps:
It can be observed that,
\begin{align} 7\times 11\times &13+13\,\\&=13\left( 7\times 11+1 \right) \\ \,\,&=13\left( 77+1 \right) \\ &=13\,\,\times \,78 \\ &=13\times 13\times 6\times 1 \\&=13\times13\times2\times3\times1\end{align}
The given number has $$2,3,13$$ and $$1$$ as its factors. Therefore, it is a composite number.
\begin{align}7\times &6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5 \\&= {5 \times \left( {7\!\times\! 6 \!\times\! 4 \!\times\! 3 \!\times\! 2 \!\times\! 1 \!+\!1} \right)}\\&= {5 \times \left( {1008 + 1} \right)}\\ &={ 5 \times 1009 \times 1}\end{align}
$$1009$$ cannot be factorised further. Therefore, the given expression has $$5,1009$$ and $$1$$ as its factors. Hence, it is a composite number.
## Question 7
There is a circular path around a sport field. Sonia takes $$18$$ minutes to drive one round of the field, while Ravi takes $$12$$ minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?
### Solution
What is known?
• Sonia takes $$18$$ minutes to drive one round of the field.
• Ravi takes $$12$$ minutes for the same.
• They both start at the same point and at the same time and go in the same direction.
What is unknown?
After how many minutes will they meet again at the same point.
Reasoning:
Time taken by Sonia is more than Ravi to complete one round. Now, you have to find after how many minutes will they meet again at the same point. For this, there will be a number which is a divisible by both $$18$$ and $$12$$ and that will be the time when both meet again at the starting point. To find this you have to take LCM of both the numbers.
Steps:
LCM of $$18$$ and $$12$$,
\begin{align}18 &= 2 \times 3 \times 3\\12 &= 2 \times 2 \times 3\end{align}
LCM of $$12$$ and $$18$$
\begin{align}&= 2 \times 2 \times 3 \times 3\\ &= 36\end{align}
Therefore, Ravi and Sonia will meet together at starting point after $$36$$ minutes. | 2020-07-12 22:04:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 48, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000098943710327, "perplexity": 871.9673887506283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657140337.79/warc/CC-MAIN-20200712211314-20200713001314-00471.warc.gz"} |
https://physics.stackexchange.com/questions/255449/what-is-the-explanation-for-the-interference-patterns-in-mwi | What is the explanation for the interference patterns in MWI?
In Young's double-slit experiment, MWI states that in some "worlds" the particle goes through one slit, and in others it goes through the other. If this is so, why do we get an interference pattern? The particle is not interacting with itself and is defined by classical mechanics?
Furthermore, is MWI deterministic? If it is, how is it even possible for there to be many worlds? Surely the state of the world at a given time + the laws of physics will always result in the same future space-time in any deterministic theory?
There doesn't exist any "totally well-defined" realization of MWI but its champions want to agree with the basic experimental facts so they would almost certainly say that there is no splitting of the worlds when a particle goes through two slits.
Instead, if there's any splitting of the worlds at all, and different MWI advocates have different opinions whether it occurs at all (in particular, Everett's opinion was No – and he wrote an expletive on a document by DeWitt who introduced "many worlds" for the first time) – the splitting only occurs at the moment when many degrees of freedom decohere or a human observation is made, e.g. after the particle hits the photographic plate at one point or another. (Again, there is no well-defined description of the moment when the splitting is supposed to take place, or how it takes place etc.)
Before that, MWI assumes that the wave function "objectively exists" and its parts of the wave function going through the two slits interfere with each other just like they interfere in standard quantum mechanics.
MWI is meant to be a deterministic theory where the wave function is an object that objectively exists, a set of classical degrees of freedom, and that evolves according to a deterministic Schrödinger equation. There is no contradiction between having many worlds and determinism. However, there may be a contradiction between assumptions of MWI and other observed facts.
Most contemporary MWI advocates imagine that the "many worlds" are nothing else than the "parts" of the wave function that are widely separated in the configuration space (a power of the real space). No universal set of rules how the wave function may be divided to parts exists but when the evolution of the parts get "macroscopically different", it starts to make sense to say that "two portions of the wave function are hugely separated".
• But how does this relate to my quetsions? – Bonj May 12 '16 at 13:33
• I tried to label the key words in bold face and added a paragraph to address some additional question I first overlooked. – Luboš Motl May 12 '16 at 14:04
• Okay, thanks, your answer makes more sense now. I still don't fully understand how there is no contradiction between having many worlds and determinism. Is it because of the degrees of freedom? – Bonj May 12 '16 at 14:32
• By determinism, MWI advocates mean that the wave function evolves according to the deterministic Schrödinger equation and there's "nothing else". In standard QM, the measurement is when the randomness enters. In MWI, the idea is that the randomness never enters. Instead, all the possible outcomes of a measurement exist simultaneously, and you find yourself in one of them - one of the parallel Universes. The more probable "worlds" should be more likely to be "yours" than the less probable ones. MWI cannot really explain how it's possible if all the "worlds" are equally real. But they don't care – Luboš Motl May 12 '16 at 15:18
• Understood, thanks. And one last thing. If not all the "worlds" are equally real, then surely randomness or hidden variables must be introduced to explain why some worlds are more real than others? Or if our world is the only real world and we are merely navigating our way through the universal wave-function, to explain why our world is the real world given the potential that it would not have been. – Bonj May 12 '16 at 16:20
Firstly, I find the hostility against many worlds interpretation inadequate. As far as understanding quantum mechanics goes, the case is far from closed. I believe that it is unlikely, that this question will be answered near future (and it is plausible that it will be never resolved). Nevertheless, something being inherently hard should not suppress our thinking.
Secondly, why do I believe that many worlds interpretation is a sound approach? Before even hearing the MWI-word, we were talking about quantum entanglement in our department coffee room's blackboard (some 7 years ago) and I realized that measurement can be explained by quantum entanglement of the observer and the system. I think most physicists are too busy thinking about real problems (as they should), that they never sit down to think about these fundamental issues. (Also, one of the reasons is probably the choice of name and the stupid splitting movie film picture in Wikipedia).
Thirdly, I will have do define carefully what MWI is. As is correctly stated in the other answers, there are various definitions (the vicious say that there are as many definitions of MWI as there are supporters):
First thing you have to understand about MWI that it is formulated by a PhD student 60 years ago. The decoherence will not be invented in 15 years and the current main-stream interpretation of quantum mechanics is the Copenhagen interpretation with unintuitive wave function collapse postulate. Still, I find the thesis to be quite remarkable (Everett is also cited by decoherence paper, but I cannot access it so I do not know if it is in good or bad).
In Everett's thesis, he defines two ways of changing the wave function (as listed by von Neumann).
1. Process: Suddenly, by assigning the system into eigenstates with probabilities $|<\phi_i|\Psi>|^2$.
2. Process: Via unitary evolution, according to Schrodinger equation.
He lists several alternatives, but sticks with alternative 5:
To assume the universal validity of the quantum description, by the complete abandonment of Process 1. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the state function of the composite system which includes the observer and his object-system, and which at all times obeys the wave equation (Process 2).
As far as I see it, this is the crux of many-worlds interpretation. There is no need to consider a) unexplained sudden changes to wave function b) probabilistic rules of resetting quantum simulations at certain moments. Here a) and b) differ by whether the collapse is real in other interpretations.
Here is another quote:
We have seen that in almost all of these observer states it appears to the observer that the probabilistic aspects of the usual form of quantum theory are valid. We have thus seen how pure wave mechanics, without any initial probability assertions, can lead to these notions on a subjective level, as appearances to observers.
Here is one more:
We have shown that our theory based on pure wave mechanics, which takes as the basic description of physical systems the state function - supposed to be an objective description (i.e., in one-one, rather than statistical, correspondence to the behavior of the system) - can be put in satisfactory correspondence with experience. We saw that the probabilistic assertions of the usual interpretation of quantum mechanics can be deduced from this theory, in a manner analogous to the methods of classical statistical mechanics, as subjective appearances to observers - observers which were regarded simply as physical systems subject to the same type of description and laws as any other systems, and having no preferred position. The theory is therefore capable of supplying us with a complete conceptual model of the universe, consistent with the assumption that it contains more than one observer.
As far as I interpret this, Everett is saying that probabilistic interpretation of quantum mechanics is emergent from properties of unitary evolution of the wave function. This is appealing in many ways. First of all, wave function collapse as a phenomenon is explained. It is an entanglement between observer and the system. When added with decoherence, one has a theory of measurement which is complete and contains no awkward collapse postulates.
Finally and foremost, and this is why all the fuzz, here comes the many worlds part. Pure wave mechanics, also for observers, means that there are finite amplitudes in many different observer states simultaneously. Thus, if with a world we mean all things we can get information about, we will see, that the scientist who measured spin up will never communicate with the scientist who measured spin down. With orthodox interpretation, both of these scientists still exists in the world wave function.
Now, finally, and unfortunately at so late part of this answer because of all the fuzz, we can come to your questions:
MWI states that in some "worlds" the particle goes through one slit, and in others it goes through the other. If this is so, why do we get an interference pattern?
It does not state that at all! Exactly the opposite. It states all the regular things about two-slit experiment which can also be stated with probabilistic interpretations: Only, if one measured from which slit the particle goes, one does not get the interference pattern. Probabilistic interpretations call this collapse. MWI says that there is a quantum entangled state $|a>|A>+|b>|B>$ where small letters are slits and capitals observers reading a or b from their measuring apparatus.
Is MWI deterministic?
Yes, everything will be governed by the unitary evolution of the wave function. The Schöringer equation is of first order in time and thus exactly solvable when given a boundary condition (say wave function at surface t=0). This means that the system is fully deterministic. To elaborate further, in many worlds interpretation the unitary evolution of the wave function produces collapse of wave function only as an emergent process (thus abadoning process 1, as listed above).
To conclude, MWI should be treated as a historical way to modern understanding of quantum mechanics and measurement. In it's 60's formulation it is outdated, but the concepts still hold. I find it funny, that the proponents of probabilistic theory seem to find the MWI-theory non-sense, even their own interpretation can be derived MWI. It remains to be seen if future experiments can shed light into these interpretations. For example, although very unlikely, it would be very exciting if the progress in quantum computing would hit unexplained mysterious limitations requiring new theories. As far as the dislike towards this theory goes, it is probably related to fact that discussing interpretations is mostly hobby to everyone. There are very few who actually does research on this fields, and could comment on the latest events. The rest are probably like me: when I go to work tomorrow, I will wonder about theoretical modelling of plasmonics in photovoltaics, since that is what I get paid to do.
As stated by Luboš Motl in another answer, there is no consensus between Everett's interpretation contenders about what it means exactly. The common idea is that no state evolution other than unitary as per Schrödinger should be accepted (no collapse) but that's about it.
Indeed it is not clear at all what is supposed to be splitting or branching, and when. For a thorough review of this topic ("many what, exactly"?), see Multiplicity in Everett's interpretation of quantum mechanics (Louis Marchildon, 2015).
The Many Worlds Interpretation is a theory of non relativistic quantum mechanics where there is a wavefunction from the configuration space of the entire system (and this is utterly essential) into the joint spin state of the entire system and it evolves according to the Schrödinger equation, and nothing else.
No one claims (or has ever claimed) that in one world the particle goes through one slit and in another world the particle goes through the other. Instead, what happens is the wavefunction of the system evolves according to the Schrödinger equation, hence, according to the Hamiltonian.
If you want to see why interference happens, it helps to first contrast with a situation where there is no interference, e.g. one where you get which-way information.
We will have the same setup for both situations. So for instance, the x axis could represent the x position of particle one and the y axis could represent the $y$ position of particle one and the z axis could represent the position of particle two. Then the wavefunction must assign a value to each combination of the locations of each particle (the configuration space is $\mathbb R^{3n}$ and a single point $(\vec r_1, \vec r_2, ... , \vec r_n)$ tells you a classical configuration of every particle).
But your wavefunction assigns values to every possible configuration. Possibly zero. Possibly nonzero. Let's have the wavefunction have its complex phase oscillate in the x direction, but be confined to a finite spread in the x direction (confined near $x=-1$). The oscillation of phase in the x direction means the region of support (where it has nonzero values) will move in the positive x direction. Let's also focus it in the z direction so it has a finite spread in the z direction (confined near $z=0$). But in the y direction it will be bimodal. It will have a region near $y=-10$ where it is nonzero, and a region near $y=+10$ where it is nonzero. But go a little bit from those values and it drops to zero.
So it's like you had a packet moving in the x direction and focused in the x direction and focused in the z direction and also focused in the y direction near $y=-10$ and then you had a second packet moving in the x direction and focused in the x direction and focused in the z direction and also focused in the y direction near $y=+10$. Your initial wave is the sum of those packets, so it is nonzero in both those regions of configuration space.
But those regions aren't worlds.
Now, if you go through a slit with a which way detector, then the wave confined near $y=-10$ goes through a slit with center at $x=0$ and $y=-10$ but because of the which way detector, the wave is deflected in the direction $-\hat z$ so even as it spreads out on the $y$ direction it is systematically deflected in the $-\hat z$ direction.
So it eventually hits a screen at $x=200$ all concentrated at $z=-200$. It's like if you put a fiber optic cable on the slit and aimed the beam down.
And the wave confined near $y=+10$ goes through a slit with center at $x=0$ and $y=+10$ but because of the which way detector, the wave is deflected in the direction $+\hat z$ so even as it spreads out on the $y$ direction it is systematically deflected in the $\hat z$ direction.
So it eventually hits a screen at $x=200$ all concentrated at $z=+200$. It's like if you put a fiber optic cable on the slit and aimed the beam up.
If you actually put fiber optic cables in your slits and sent classical light through it, you'd get a beam deflected down from one slit and a beam deflected up from the other slit, and you would get single slit dictation pattern from each slit.
Both classically and quantum mechanically.
Now let's say there is no which way pattern. Then you wave simply spreads, but isn't deflected. Which means the wave near $y=-10$ spreads out and the wave near $y=+10$ spreads out and by the time they get to $x=+200$ the support of each wave overlaps the support of the other wave.
So it really was one wave with two disjoint regions of support, and the two regions evolved to overlap. When that happens the values interfere and the wave develops parts that have larger values than others.
So far, this is just what the Schrödinger equations says. No interpretations have come into play at all.
The wavefunction gets regions with different sized values solely based on whether those disjoint regions of support evolve to overlap. And they do start to overlap when the location of the particle moving towards the screen isn't causing (by the Hamiltonian) any other particles to move differently.
But when you hit the screen, other particles do start to move differently. The particles at that screen location change. And the particles at the other screen locations do not change.
So when you had the which way detector, you effectively had a screen right there and the waves immediately start to veer away from each other in configuration space. Whereas if you don't have the which way detector they spread and start to overlap before they hit there screen (where they then start to veer away from each other).
Your claim that the particle follows classical mechanics is plain wrong. And MWI doesn't claim that.
In MWI you do have worlds. But many worlds are defined as separate wavepacket whose supports will never overlap with each other in the future. This basically requires that they separately veer in different directions. And since there are $3n$ directions in $\mathbb R^{3n}$ it is easy to veer in different directions once the wave has made many twists in many different particles' directions. And just like two people randomly moving in $3n$ directions. When $n>>10^{24}$ the odds are really bad that they will ever bump into each other.
So the cutoff of being separate worlds isn't sharp, any more than the size cutoff to use thermodynamics isn't sharp. But eventually when enough particles have been involved, the different twists have placed the support into such different regions that they are not going to overlap again.
So they were not separate worlds when they went through the slit, since separate worlds are defined by not having their support overlap ever again.
The MWI is completely deterministic. There are many worlds because it waves can have regions of support (places where they currently are nonzero) that diverge away from each other in a huge dimensioned space and never overlap again and thus act independently.
There isn't a "classical state of the world." The classical states of the world are literally the points in the huge dimensioned configuration space. And the wavefunction is assigning nonzero vaules to whole regions of configuration space. A world in MWI is a current assignment of nonzero values to a region that evolves in the future as if that is the only place where the values are currently nonzero. You can have multiple worlds. And by definition each acts as if it is the only one.
If you know the definitions it isn't mysterious at all. Start with configuration space. Then assign values to each configuration. Then note that the region where the values are nonzero (the support) sometimes splits into disjoint regions that evolve over time to never again overlap.
Then note that the values in those disjoint regions can act like they are the whole wavefunction and can't tell if they are. Hence it makes sense to call them a world and let each one model itself as the whole world.
If you didn't allow that, you'd be insisting they have to continue modeling parts of the configuration space that don't affect them. For no scientific reason whatsoever. And it wouldn't be wrong per se. It's just extra bookkeeping that doesn't affect that world's predictions. Insisting on modeling things that don't affect your predictions is the domain of people with strong opinions.
People that merely care about making predictions accept that there is a point where it is safe (prediction wise) to simplify things down to have a given world select itself as the only one. Since it won't matter to its predictions about its own future evolution.
• After reading this I know even less about this than I thought I knew before. It's like a bunch of abused words that can be found in the layman literature about quantum mechanics hacked together into a lengthy rant of sorts that doesn't tell me anything about what the MWI really is (I already know that it's nonsense, but that takes but one sentence to motivate). – CuriousOne May 12 '16 at 21:49
• @CuriousOne: this is not kinder garden here. Please remain polite while interacting with others. I am also sure your contribution could be much more valuable if you did not waste your time in unjustified (and not very informative) rants about view points you don't accept or don't understand. Regarding Timaeus' answer, this is basically the same as Lubos Motl's one, phrased differently and with an attempt to explain how determinism does not necessarily rule out effective branching. – gatsu May 16 '16 at 9:51
• @gatsu: That was the polite way of saying it. Timaeus can do better, in my opinion, and I hope he will. I really tried reading it and I got confused, just like I said. I have absolutely nothing against somebody writing a good answer, but this isn't it, I am afraid. – CuriousOne May 16 '16 at 9:57
In the many world interpretation of quantum mechanics, there is only a split into different branches when decoherence takes place. So there would be no split in the two slit experiment until the photon hits the photographic plate. At that stage decoherence takes place and there would be a split into a separate Universe (branch) each of which has the photon hit a different part of the photographic plate. The theory is deterministic until you try to answer what is the probability of being in the different Universes. This is then taken as being proportional to the amplitude squared of the value of the wave function for each Universe.
There is no widely accepted way of experimentally distinguishing the many worlds interpretation from the more traditional Copenhagen interpretation. So the question which is more correct is more of a philosophical one rather than a physics one.
protected by Qmechanic♦May 15 '16 at 17:39
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count). | 2019-08-17 13:12:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6538551449775696, "perplexity": 464.143931194621}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313259.30/warc/CC-MAIN-20190817123129-20190817145129-00110.warc.gz"} |
https://www.researchgate.net/scientific-contributions/Jean-Charles-Faugere-46318401 | # Jean-Charles Faugère's research while affiliated with French National Centre for Scientific Research and other places
## Publications (173)
Article
Let K be a field and (f1,…,fs,ϕ) be multivariate polynomials in K[x1,…,xn] (with s<n) each invariant under the action of Sn, the group of permutations of {1,…,n}. We consider the problem of computing the critical points of ϕ restricted to the algebraic set V(f), where f=(f1,…,fs). This is the same as computing the points at which f vanishes and the...
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Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots, n\}$. We consider the problem of computing the points at which $\mathbf{f}$ vanish and the Jacobian matrix asso...
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Grö bner bases is one the most powerful tools in algorithmic nonlinear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases, the polynomial systems coming from applications have some kind of structure. We consider sparse systems where the...
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Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases, the polynomial systems coming from applications have some kind of structure. For example , several problems in...
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Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous polynomials, that is to write a homogeneous polynomial in $n$ variables of degree $D$ as a sum of $D$-th powers of lin...
Conference Paper
Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp--Massey algorithm. Likewise, sparse multivariate polynomial interpolation and multidimensional cyclic code decoding re...
Conference Paper
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gröbner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faugè...
Preprint
The Berlekamp--Massey--Sakata algorithm and the Scalar-FGLM algorithm both compute the ideal of relations of a multidimensional linear recurrent sequence.Whenever quering a single sequence element is prohibitive, the bottleneck of these algorithms becomes the computation of all the needed sequence terms. As such, having adaptive variants of these a...
Preprint
A fundamental problem in computational algebraic geometry is the computation of the resultant. A central question is when and how to compute it as the determinant of a matrix. whose elements are the coefficients of the input polynomials up-to sign. This problem is well understood for unmixed multihomogeneous systems, that is for systems consisting...
Preprint
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of F...
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Computing discrete logarithms is generically a difficult problem. For divisor class groups of curves defined over extension fields, a variant of the Index-Calculus called decomposition attack is used, and it can be faster than generic approaches. In this situation, collecting the relations is done by solving multiple instances of the point m-decomp...
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We compare thoroughly the Berlekamp -- Massey -- Sakata algorithm and the Scalar-FGLM algorithm, which compute both the ideal of relations of a multi-dimensional linear recurrent sequence. Suprisingly, their behaviors differ. We detail in which way they do and prove that it is not possible to tweak one of the algorithms in order to mimic exactly th...
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The so-called Berlekamp–Massey–Sakata algorithm computes a Gröbner basis of a 0-dimensional ideal of relations satisfied by an input table. It extends the Berlekamp–Massey algorithm to n-dimensional tables, for n>1. We investigate this problem and design several algorithms for computing such a Gröbner basis of an ideal of relations using linear alg...
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Symmetric Tensor Decomposition is a major problem that arises in areas such as signal processing, statistics, data analysis and computational neuroscience. It is equivalent to write a homogeneous polynomial in $n$ variables of degree $D$ as a sum of $D$-th powers of linear forms, using the minimal number of summands. This minimal number is called t...
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Given several n-dimensional sequences, we first present an algorithm for computing the Grobner basis of their module of linear recurrence relations. A P-recursive sequence (ui)i ∈ Nⁿ satisfies linear recurrence relations with polynomial coefficients in i, as defined by Stanley in 1980. Calling directly the aforementioned algorithm on the tuple of s...
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Boneh et al. showed at Crypto 99 that moduli of the form $$N=p^rq$$ can be factored in polynomial time when $$r \simeq \log p$$. Their algorithm is based on Coppersmith’s technique for finding small roots of polynomial equations. In this paper we show that $$N=p^rq^s$$ can also be factored in polynomial time when r or s is at least $$(\log p)^3$$;...
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Conference Paper
Sakata generalized the Berlekamp--Massey algorithm to n dimensions in~1988. The Berlekamp--Massey--Sakata (BMS) algorithm can be used for finding a Grbner basis of a 0-dimensional ideal of relations verified by a table. We investigate this problem usingö linear algebra techniques, with motivations such as accelerating change of basis algorithms (FG...
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We investigate the security of the family of MQQ public key cryptosystems using multivariate quadratic quasigroups (MQQ). These cryptosystems show especially good performance properties. In particular , the MQQ-SIG signature scheme is the fastest scheme in the ECRYPT benchmarking of cryptographic systems (eBACS). We show that both the signature sch...
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We investigate the Hidden Subspace Problem ($$\mathrm{HSP}_q$$) over $${\mathbb {F}}_q$$: Input : $$p_1,\ldots ,p_m,q_1,\ldots ,q_m\in {\mathbb {F}}_q[x_1,\ldots ,x_n]$$ of degree $$d\ge 3$$ (and $$n\le m\le 2n$$). Find : a subspace $$A\subset {{\mathbb {F}}_q}^n$$ of dimension $$n/2$$ ($$n$$ is even) such that \begin{aligned} p_i(A)=0\,\,\forall...
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The purpose of this talk is to study the difficulty of the Goppa Code Distinguishing (GD) problem, which is the problem of distinguishing the public matrix in the McEliece cryptosystem from a random matrix. It is widely believed that this problem is computationally hard as proved by the increas-ing number of papers using this hardness assumption. O...
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FGb is a high-performance, portable, C library for computing Gröbner bases over the integers and over finite fields. FGb provides high quality implementations of state-of-the-art algorithms (F 4 and F 5) for computing Gröbner bases. Currently, it is one of the best implementation of these algorithms, in terms of both speed and robustness. For insta...
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In this paper, we present an efficient cryptanalysis of the so-called HM cryptosystem which was published at Asiacrypt’1999, and one perturbed version of HM. Until now, this scheme was exempt from cryptanalysis. We first present a distinguisher which uses a differential property of the public key. This distinguisher permits to break one perturbed v...
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Computing loci of rank defects of linear matrices (also called the MinRank problem) is a fundamental NP-hard problem of linear algebra which has applications in Cryptology, in Error Correcting Codes and in Geometry. Given a square linear matrix (i.e. a matrix whose entries are k-variate linear forms) of size n and an integer r, the problem is to fi...
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We consider the composition f =g o h of two systems g= (g0, ..., gt) and h=(h0, ..., hs) of homogeneous multivariate polynomials over a field K, where each gj ∈ K[y0, ..., ys] has degree ℓ each hk ∈ K[x0, ..., xr] has degree m, and fi = gi(h0, ..., hs) ∈ K[x0, ..., xr] has degree n = ℓ · m, for 0 ≤ i ≤ t. The motivation of this paper is to... | 2023-03-30 07:26:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8084458708763123, "perplexity": 750.726452502014}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949107.48/warc/CC-MAIN-20230330070451-20230330100451-00304.warc.gz"} |
https://crypto.stackexchange.com/questions/67226/golombs-randomness-postulates | # Golomb's Randomness postulates
In Handbook of applied cryptography, Golomb's randomness postulates are given: Let $$s$$ be a periodic sequence of period $$N$$. Golomb’s randomness postulates are the following.
R1: In the cycle $$s_N$$ of $$s$$, the number of $$1$$s differs from the number of $$0$$s by at most $$1$$.
R2: In the cycle $$s_N$$, at least half the runs have length $$1$$, at least one-fourth have length $$2$$, at least one-eighth have length $$3$$, etc., as long as the number of runs so indicated exceeds $$1$$. Moreover, for each of these lengths, there are (almost) equally many gaps and blocks.6
R3: The autocorrelation function $$C(t)$$ is two-valued. That is for some integer $$K$$, $$C(t)=K$$ for $$t\neq 0 \pmod N$$ while $$C(0)=N.$$
But why do those postulates make sense?
• I fixed your autocorrelation definition that seemed to have dropped off. – kodlu Feb 12 '19 at 4:48
R1. This is a strict balancedness condition, the difference is 1, in case $$N$$ is odd and zero is impossible.
R3. Having an autocorrelation $$C(t)$$ of the form $$C(t)=N I\{t=0\}+ f(t) I\{t \neq 0\}$$ where $$I$$ is the indicator function, with $$f(t)$$ small in absolute value is a feature of an i.i.d. independent sequence. By parseval $$|f(t)|\leq 1$$ is possible for odd lengths. Golomb chooses this off peak correlation function $$f(t)$$ as constant so phase information is not leaked. | 2020-02-21 16:31:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9231022596359253, "perplexity": 559.9098177180072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145533.1/warc/CC-MAIN-20200221142006-20200221172006-00039.warc.gz"} |
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