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Banach Journal of Mathematical Analysis
The Banach Journal of Mathematical Analysis (BJMA) is published by Duke University Press on behalf of the Tusi Mathematical Research Group.
BJMA is a peer-reviewed quarterly electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. BJMA normally publishes survey articles and original research papers numbering 14 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
Advance publication of articles online is available.
Abstract harmonic analysis of wave-packet transforms over locally compact abelian groupsVolume 11, Number 1 (2017)
Hyers--Ulam stability of a polynomial equationVolume 3, Number 2 (2009)
A generalized Schur complement for nonnegative operators on linear spacesVolume 12, Number 3 (2018)
An interview with Themistocles M. RassiasVolume 1, Number 2 (2007)
Pictures of $KK$ -theory for real $C^{*}$ -algebras and almost commuting matricesVolume 10, Number 1 (2016)
• ISSN: 1735-8787 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 2007--
• Access: Articles older than 5 years are open
• Euclid URL: https://projecteuclid.org/bjma
Featured bibliometrics
MR Citation Database MCQ (2017): 0.52
JCR (2017) Impact Factor: 0.625
JCR (2017) Five-year Impact Factor: 0.781
JCR (2017) Ranking: 192/309 (Mathematics); 204/252 (Applied Mathematics)
Eigenfactor: Banach Journal of Mathematical Analysis
SJR/SCImago Journal Rank (2017): 0.628
Pictures of $KK$-theory for real $C^{*}$-algebras and almost commuting matrices
We give a systematic account of the various pictures of $KK$-theory for real $C^{*}$-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of $KK$-theory, and we use CRT-structures to prove that a natural transformation $F(A)\rightarrow G(A)$ between homotopy equivalent, stable, half-exact functors defined on real $C^{*}$-algebras is an isomorphism, provided it is an isomorphism on the smaller class of $C^{*}$-algebras. Finally, we develop $E$-theory for real $C^{*}$-algebras and use that to obtain new negative results regarding the problem of approximating almost commuting real matrices by exactly commuting real matrices.
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# Prove that the sum of all of AB's $r$-th principal minors is equal to that of those of BA's
Said more specifically, suppose $A,B\in M_n(K)$, $K$ a commutative ring. An $r$-th principal minor of a square matrix is the determinant $$\det\begin{bmatrix}a_{k_1k_1} & \cdots & a_{k_1k_r}\\ \vdots & \ddots & \vdots \\ a_{k_rk_1} & \cdots & a_{k_rk_r}\end{bmatrix}$$ where $1\le k_1<\cdots<k_r\le n$, $A$ is an $n\times n, n>r$ square matrix. Prove that the sum of all of $AB$'s $r$-th principal minors is equal to that of those of $BA$'s.
Hint: use Cauchy-Binet formula.
I simply have no idea what use to be made of the hint. I just can't represent the terms in the way Cauchy-Binet formula does, anyway for me it seems impossible to construct any of $P_r(AB)$ from sub-blocks of $A,B$.
Any help?
Edit: I'm sorry I made a mistake. It should be principal minor, no leading.
• The definition of principal minor is not the one you gave. What you gave is a leading principle minor. Which one do you mean? There is precisely one leading principle minor of size $k\times k$ for each $k$ (the corner), but there are $\binom{n}{k}$ principle minors (which do not have to be corners). It's likely that you're stuck because you're using the wrong definition. – EuYu Sep 6 '15 at 16:36
• Then the statement doesn't seem to be true. Consider $$A=\begin{pmatrix}1&2\\3&4\end{pmatrix},B=\begin{pmatrix}0&1\\1&0\end{pmatrix}.$$ The sum of the leading principle minors for $AB$ is $4$ and the sum of the leading principle minors for $BA$ is $5$. – EuYu Sep 6 '15 at 16:46
• @EuYu I'm sorry. You're right. It should be principle minors, no leading. – Vim Sep 6 '15 at 23:20
You may begin with $P_r(AB)=\det(A_{[r],[n]}B_{[n],[r]})$ and apply Cauchy-Binet formula to decompose it into a sum of products of determinants.
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## Results (14 matches)
Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim $\epsilon$ $r$ First zero Origin
2-2960-1.1-c1-0-12 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 1 0 0.650533 Elliptic curve 2960.a Modular form 2960.2.a.a Modular form 2960.2.a.a.1.1 2-2960-1.1-c1-0-14 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $1$ $0$ $0.728411$ Elliptic curve 2960.e Modular form 2960.2.a.e Modular form 2960.2.a.e.1.1
2-2960-1.1-c1-0-17 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 1 0 0.780249 Elliptic curve 2960.g Modular form 2960.2.a.g Modular form 2960.2.a.g.1.1 2-2960-1.1-c1-0-30 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $1$ $0$ $1.01238$ Elliptic curve 2960.k Modular form 2960.2.a.k Modular form 2960.2.a.k.1.1
2-2960-1.1-c1-0-34 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 1 0 1.03875 Elliptic curve 2960.m Modular form 2960.2.a.m Modular form 2960.2.a.m.1.1 2-2960-1.1-c1-0-35 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $-1$ $1$ $1.19619$ Elliptic curve 2960.b Modular form 2960.2.a.b Modular form 2960.2.a.b.1.1
2-2960-1.1-c1-0-36 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 1 0 1.19620 Elliptic curve 2960.i Modular form 2960.2.a.i Modular form 2960.2.a.i.1.1 2-2960-1.1-c1-0-42 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $-1$ $1$ $1.26592$ Elliptic curve 2960.c Modular form 2960.2.a.c Modular form 2960.2.a.c.1.1
2-2960-1.1-c1-0-49 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 -1 1 1.33816 Elliptic curve 2960.d Modular form 2960.2.a.d Modular form 2960.2.a.d.1.1 2-2960-1.1-c1-0-51 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $1$ $0$ $1.34623$ Elliptic curve 2960.n Modular form 2960.2.a.n Modular form 2960.2.a.n.1.1
2-2960-1.1-c1-0-58 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 -1 1 1.50891 Elliptic curve 2960.f Modular form 2960.2.a.f Modular form 2960.2.a.f.1.1 2-2960-1.1-c1-0-64 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $-1$ $1$ $1.74532$ Elliptic curve 2960.h Modular form 2960.2.a.h Modular form 2960.2.a.h.1.1
2-2960-1.1-c1-0-67 $4.86$ $23.6$ $2$ $2^{4} \cdot 5 \cdot 37$ 1.1 $$1.0 1 -1 1 1.82892 Elliptic curve 2960.j Modular form 2960.2.a.j Modular form 2960.2.a.j.1.1 2-2960-1.1-c1-0-69 4.86 23.6 2 2^{4} \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $-1$ $1$ $1.91068$ Elliptic curve 2960.l Modular form 2960.2.a.l Modular form 2960.2.a.l.1.1
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# Quick Example
In this Page, we will create our first component —— HelloRegular . It is used to show an welcome message for people who login. if people aren't login yet, the component will prompt an window. For simplicity, only username is required during the login operation.
## 1. initialize template
<div id="app"></div>
<script id="hello" type="text/regular" name="hello">
Hello, Guest
</script>
<!-- include regular.js -->
<script src="https://rawgit.com/regularjs/regular/master/dist/regular.js"></script>
<script>
var HelloRegular = Regular.extend({
template: '#hello'
});
// initialize component then $inject to #app's bottom var component = new HelloRegular({ data: {username: "leeluolee"} }); component.$inject('#app');
</script>
RESULT
• Regular.extend
Regular.extend will create a Component extended from Regular.
• template
a Component may need template to describe its structure.
• data
component's model, but it is just a Plain Object. the data passed to new Component and the data passed to Component.extend are merged.
• $inject(node[, direction]) it is an instance method,$inject the component to the position indicated by the parameter 'direction'.
• bottom[default option]: $injected as node's lastChild • top:$injected as node' s firstChild,
• after: $injected as node' s nextSibling, • before:$injected as node' s prevSibling,
## 2. Using interpolation to show user's name
This component only shows static message until now, we should make it living by using interpolation.
Hello, {username}
RESULT
## 3. using if/else to show other message if the user is not logged in
{#if username}
{#else}
Sorry, Guest.
{/if}
it just like we use the other string-based template.
RESULT
## 4. Implement the Login/Logout by event
In this step , we need to add two event to deal with the Login and Logout operation.
{#if username}
{#else}
{/if}
##### Tips
in regular, the on- prefixed attribute will be considered as ui event you can also define your custom event like(e.g. on-hold or on-tap) and determine when to trigger it;
we add two operation in the template above:
Login: the keyword this in the template just point to the component itself. so we need to add a method named login at HelloRegular's prototype .
Logout: the model's root in template points to component.data . so in this exmaple, we just simply clear the username in component.data.
var HelloRegular = Regular.extend({
template: '#hello',
var data = this.data; // get data
}
});
RESULT
## 5. when the component's digest phase will be triggered
just like angular. regular's data-binding is based on dirty-check. some builtin (.e.g event, timeout) will tirgger the component's digest phase automatically. you can also trigger the digest manually using component.$update component.data.user.name = "regularjs"; component.$update() // enter
just like the example above, the usage of $update is flexible. |DEMO| no matter how you use the $update. the component will always enter into the 'digest' phase.
## Summary
In this chapter, we create a super simple component named HelloRegular.
you can consider regular's component as a small mvvm realization.
• independent lifecycle
• the view based on template
• the model is Plain Object
• the component itself is just like the viewmodel
you can also check the more comprehensive example——todomvc.
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# Continuous spectral theorem example
The spectral theorem can be explicitly expressed for an hermitian matrix by providing its eigen decomposition. In the more general case of a bounded self-adjoint operator with a continuous spectrum, the expression of the spectral theorem is $Ax=\int \lambda dF(\lambda) x$. This expression is rather abstract. Can someone provide a simple example of the continuous case, taking $x$ from a space of function, a differential operator A, and the detailed expressions of $F(\lambda)$ and $dF(\lambda)$ ?
Yes, let $X=L^{2}[0,1]$, and let $(Tx)(t)=tx(t)$, i.e., multiplication by $t$. This is the prototypical example in many regards. You don't have any eigenfunctions because $Tx=\lambda x$ would require $(t-\lambda)x(t)=0$ for a.e. $t\in[0,1]$ which means that $x=0$ a.e..
However, you have approximate eigenfunctions. For example, if $\lambda\in(0,1)$ and $\epsilon > 0$ is smaller than the distance of $\lambda$ to $\mathbb{R}\setminus[0,1]$, then $$\varphi_{\epsilon} = \frac{1}{\sqrt{2\epsilon}}\chi_{[\lambda-\epsilon,\lambda+\epsilon]}$$ is a unit vector in $X$ (here $\chi_{S}$ means characteristic function of set $S$). And, $$\|(T-\lambda I)\varphi_{\epsilon}\|^{2}=\frac{1}{2\epsilon}\int_{0}^{\epsilon}t^{2}\,dt = \frac{\epsilon^{2}}{6},\\ \|(T-\lambda I)\varphi_{\epsilon}\| = \frac{\epsilon}{\sqrt{6}}.$$ As $\epsilon\downarrow 0$, the function $\varphi_{\epsilon}$ looks more and more like an eigenvector with eigenvalue $\lambda$, but it does not converge to an actual eigenvector. Continuous spectrum looks like that.
In this case, the spectral measure $F$ is $$F(S)x = \chi_{S}(t)x(t).$$ So, $F(\lambda)x=\chi_{[0,\lambda]}(t)x(t)$ and $F(\lambda+\delta)x-F(\lambda)x=\chi_{(\lambda,\lambda+\delta]}(t)x(t)$, which is related to the discussion of the previous paragraph.
• You're welcome. A building block for normal operators is multiplication by $z$ on some $L^{2}_{\mu}(S)$ where $S$ is a subset of $\mathbb{C}$ and $\mu$ is a finite Borel measure on $S$. You can glean most of what you need to know about the general case from looking at such an example. An atom $\lambda$ of $\mu$ is an eigenvalue with eigenvector $\chi_{\{\lambda\}}$. All other points $\lambda$ are in the continuous spectrum if $\lambda$ is in the support of $\mu$. Points outside the closure of $S$ are in the resolvent set, with $(M_{z}-\lambda I)^{-1}=M_{1/(z-\lambda)}$. – DisintegratingByParts Sep 21 '14 at 0:01
• OK thank you ! I have a "soft" question connected to your answer: are Dirac distributions eigenvectors of the operator $T$, if you were to consider distributions instead of functions ? – vkubicki Sep 23 '14 at 5:38
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# Antiderivative of a rational function
Tags:
1. Dec 28, 2016
### Rectifier
I am trying to find primitives to the rational function below but my answer differs from the answer in the book only slightly and now, I am asking for your help to find the error in my solution. This solution is long since I try to include all the steps in the process.
The problem
$$\int \frac{x^2+8x+4}{x^2+4x+8} dx$$
Relevant equations
$$\int \frac{1}{x} dx = \ln |x| + C \\ \int \frac{1}{x^2+1} dx =arctan x + C$$
The attempt at a solution
I am starting with a polynomial division and rewrite the fraction as
$\int \frac{x^2+8x+4}{x^2+4x+8} dx = \int 1 + \frac{4x-4}{x^2+4x+8} dx$
Since divisor is irreducible, I must complete the square and adapt the quotient to use the standard formula for a function that has a primitive which is $arctan x +C$ as follows.
$$\int 1 + \frac{4x-4}{x^2+4x+8} dx = x + \int \frac{4x-4}{(x+2)^2+4} dx \\ x + \int \frac{4(x-1)}{\frac{4}{4}(x+2)^2+4} dx \\ x + \int \frac{4(x-1)}{4 \left( \frac{(x+2)^2}{4}+1 \right)} dx \\ x + \int \frac{4(x-1)}{4 \left( \left( \frac{x+2}{2} \right)^2+1 \right)} dx \\ x + \int \frac{x-1}{ \left( \frac{x+2}{2} \right)^2+1} dx$$
I split the qotent:
$$x + \int \frac{x}{ \left( \frac{x+2}{2} \right)^2+1} dx - \int \frac{1}{ \left(\frac{x+2}{2} \right)^2+1} dx$$
Lets focus on the part that has $x$ as divisor.
$$\int \frac{x}{ \left( \frac{x+2}{2} \right)^2+1} dx$$
I perform a variable substitutution $[t= \frac{x+2}{2} \Leftrightarrow x = 2t-2, \frac{dt}{dx} = \frac{1}{2} \Leftrightarrow 2 dt = dx]$. That results in
$$\int \frac{x}{ \left( \frac{x+2}{2} \right)^2+1} dx = 2 \left( \int \frac{2t-2}{ t^2+1} dt \right) = 2 \int \frac{2t}{ t^2+1} dt - 2 \cdot 2 \int \frac{1}{ t^2+1} dt$$
I split the quotient once more and focus on the part that has $2t$ as divisor where I make one more variable substitution $[g=t^2+1, \frac{dg}{dt}=2t \Leftrightarrow 2t dt = dg]$
$$2 \int \frac{2t}{ t^2+1} dt = 2 \int \frac{1}{g} dg = 2 \ln|g| + C = 2 \ln|t^2+1| + C = \ln| \left(\frac{x+2}{2} \right)^2 + 1|+ C$$
I use back-substitution in the last steps.
Now, lets add the rest of the integrals that we didn't focus on before:
$$x + \int \frac{x}{ \left( \frac{x+2}{2} \right)^2+1} dx - \int \frac{1}{ \left(\frac{x+2}{2} \right)^2+1} dx \\ x + \ \ 2 \int \frac{2t}{ t^2+1} dt - 2 \cdot 2 \int \frac{1}{ t^2+1} dt - \int \frac{1}{ \left(\frac{x+2}{2} \right)^2+1}\\ x + \ \ 2\ln| \left(\frac{x+2}{2} \right)^2 + 1| - 4 \arctan t - 2 \arctan(\left(\frac{x+2}{2} \right)) + C \\ x + \ \ 2\ln| \left(\frac{x+2}{2} \right)^2 + 1| - 6 \arctan(\left(\frac{x+2}{2} \right)) + C$$
I am not interested in alternative ways to solve the problem but to find the error in my calculations.
Please help.
The part that differs from the answer in my book is inside $\ln$ and not by much (see spoiler)
It differs only by a multiple of 4. In my book the contents of ln are: 2 \ln( x^2 + 4x + 8 )
.
2. Dec 28, 2016
### Fightfish
The two answers are equivalent. It is an indefinite integral so any multiplicative factors in the argument of the $\ln$ can simply be absorbed into the undetermined constant i.e. $\ln (4 f(x)) + C = \ln (f(x)) + \ln 4 + C = \ln (f(x)) + C'$.
3. Dec 28, 2016
### Ray Vickson
You have unnecessary absolute-value signs $| \ldots |$, and these get in the way of further simplification. In fact,
$$\int \frac{2t \, dt}{t^2+1} = \ln(t^2+1)$$
with no need for $| \ldots |$ because $t^2+1 \geq 1$ is always positive, and always has a non-negative logarithm.
4. Dec 28, 2016
### Rectifier
Thank you for your help everyone.
@Ray Vickson you wrote something before that that I didn't manage to read on how to solve that more efficiently. What steps are unnecessary here?
5. Dec 28, 2016
### Ray Vickson
I deleted it, because after posting (briefly) I noticed your statement that you were not interested in seeing other ways of doing it---only in finding your mistakes, which turned out to not be mistakes after all. However, what I said was:
$$\frac{4x-4}{(x+2)^2+4} dx = 2 \frac{ (2x+4) -6}{(x+2)^2+4} dx = 2\frac{(2x+4)\, dx}{(x+2)^2+4} - \frac{12\, dx}{(x+2)^2+4} .$$
The first term has the form $2 \, df/f$ while the second one is closely related to $dt/(t^2+1)$.
6. Dec 31, 2016
### Rectifier
Oh, thank you for reposting that! I wrote that last line since I often get alternative ways of solving the problem without them mentioning why my last solution produced a strange/wrong answer so I end up doing the same mistakes over and over again.
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Q)
# A current carrying wire produces in the neighbourhood :
( A ) electric field only
( B ) no field
( C ) magnetic field only
( D ) electric and magnetic fields
## 1 Answer
Comment
A)
Electric field only
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# Data Pipes - streaming online data transformations
SEPTEMBER 11, 2013
Data Pipes provides an online service built in NodeJS to do simple data transformations – deleting rows and columns, find and replace, filtering, viewing as HTML – and, furthermore, to connect these transformations together Unix pipes style to make more complex transformations. Because Data Pipes is a web service, data transformation with Data Pipes takes place entirely online and the results and process are completely shareable simply by sharing the URL.
## An example
This takes the input data (sourced from this original Greater London Authority financial data), slices out the first 50 rows (head), deletes the first column (its blank!) (cut), deletes rows 1 through 7 (delete) and finally renders the result as HTML (html).
http://datapipes.okfn.labs.org/csv/head -n 50/cut 0/delete 1:7/html?url=https://raw.github.com/okfn/datapipes/master/test/data/gla.csv
## Motivation - Data Wrangling, Pipes, NodeJS and the Unix Philosophy
When you find data in the wild you usually need to poke around in it and then to some cleaning for it to be usable.
Much of the inspiration for Data Pipes comes from our experience using Unix command lines tools like grep, sed, and head to do this kind of work. These tools a powerful way to operate on streams of text (or more precisely streams of lines of text, since Unix tools process text files line by line). By using streams, they can scale to large files easily (they don’t load the whole file but process it bit by bit) and, more importantly, allow “piping” – that is, direct connection of the output of one command with the input of another.
This already provides quite a powerful way to do data wrangling (see here for more). But there are limits: data isn’t always line-oriented, plus command line tools aren’t online, so it’s difficult to share and repeat what you are doing. Inspired by a combination of Unix pipes and the possibilities of NodeJS’s great streaming capabilities, we wanted to take the pipes online for data processing – and so Data Pipes was born.
We wanted to use the Unix philosophy that teaches us to solve problems with cascades of simple, composable operations that manipulate streams, an approach which has proven almost universally effective.
Data Pipes brings the Unix philosophy and the Unix pipes style to online data. Any CSV data can be piped through a cascade of transformations to produce a modified dataset, without ever downloading the data and with no need for your own backend. Being online means that the operations are immediately shareable and linkable.
## More Examples
Take, for example, this copy of a set of Greater London Authority financial data. It’s unusable for most purposes, simply because it doesn’t abide by the CSV convention that the first line should contain the headers of the table. The header is preceded by six lines of useless commentary. Another problem is that the first column is totally empty.
First of all, let’s use the Data Pipes html operation to get a nicer-looking view of the table.
GET /csv/html/?url=http://static.london.gov.uk/gla/expenditure/docs/2012-13-P12-250.csv
Now let’s get rid of those first six lines and the empty column. We can do this by chaining together the delete operation and the cut operation:
GET /csv/delete 0:6/cut 0/html/?url=http://static.london.gov.uk/gla/expenditure/docs/2012-13-P12-250.csv
And just like that, we’ve got a well-formed CSV!
But why stop there? Why not take the output of that transformation and, say, search it for the string “LONDON” with the grep transform, then take just the first 20 entries with head?
GET /csv/delete 0:6/cut 0/grep LONDON/head -n 20/html/?url=http://static.london.gov.uk/gla/expenditure/docs/2012-13-P12-250.csv
Awesome!
## What’s next?
Data Pipes already supports a useful collection of operations, but it’s still in development, and more are yet to come, including find-and-replace operation sed plus support for arbitrary map and filter functions.
You can see the full list on the Data Pipes site, and you can suggest more transforms to implement by raising an issue.
Data Pipes needs more operations for its toolkit. That means its developers need to know what you do with data – and to think about how it can be broken down in the grand old Unix fashion. To join in, check out Data Pipes on GitHub and let us know what you think.
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Section3Criteria for Excellence
Learning narratives: These narratives are perhaps the most important assignments in the course. They frame each portfolio in the course by explaining to the reader:
1. (Before beginning work on the portfolio) What do I know about these topics already? Where have I seen these terms and/or solved these types of problems in the past? Other than unfamiliarity with the material, what more specific questions do I have about this material and/or what am I most interested in learning about it? What am I most concerned about in the material ahead? What goal(s) do I have for my learning and/or my performance in this portfolio?
2. (After completing work on the portfolio, before submission) What did I learn in this portfolio? Did I reach the goals set forth in the assignment? For each learning standard and goal in this assignment, what evidence have I included in my portfolio that I meet that learning standard? Why does my evidence show that? If one or more learning standard was not met, what would I like to do to improve on that standard between now and the final exam period?
Your learning narrative should be the first item in your portfolio for each portfolio you submit. Please typeset this narrative using a word process or Overleaf, and upload it to your portfolio as a DOC/DOCX or PDF (preferred). Minimum length is 500 words, and your pre-portfolio and post-portfolio responses (1. and 2. above) should be clearly sectioned in your narrative writeup.
In each section, do at least two of the following five things.
1. "I notice..." Describe what about this passage sticks out to you. How is it related to other ideas, either from our class or from previous classes like calculus? How would you describe this idea in your own words?
2. "I wonder..." Speculate on the deeper meanings/connections of this idea. What else might be true, based on what you read here? Where else might it be useful, outside of real analysis?
3. Ask a clarifying question. When you encounter a passage that you don't understand after several readings, formulate a question whose answer would most help to clarify your thinking. Your question should tell the reader both what you do understand about the topic, and what about the writing is confusing for you. A question that says only "I don't get this?" or "What does this mean?" is likely not to receive credit.
4. Answer a classmate's question. Choose "Reply" in a classmate's comment and respond to it. Address their question directly and specifically, providing references to other places in the text where appropriate. Try to give an answer that will most clarify their understanding.
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# Don't Solve for X
Geometry Level 2
How many times do the these two curves intersect?
Equation 1: $$x^2 + y^2 + 4x + 6y = 12$$
Equation 2: $$5y = 4x + 13$$
×
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# Motion Planning in Urban Environments Using Dynamic Occupancy Grid Map
This example shows you how to perform dynamic replanning in an urban driving scene using a Frenet reference path. In this example, you use a dynamic occupancy grid map estimate of the local environment to find optimal local trajectories.
### Introduction
Dynamic replanning for autonomous vehicles is typically done with a local motion planner. The local motion planner is responsible for generating an optimal trajectory based on the global plan and information about the surrounding environment. Information about the surrounding environment can be described mainly in two ways:
1. Discrete set of objects in the surrounding environment with defined geometries.
2. Discretized grid with estimate about free and occupied regions in the surrounding environment.
In the presence of dynamic obstacles in the environment, a local motion planner requires short-term predictions of the information about the surroundings to assess the validity of the planned trajectories. The choice of environment representation is typically governed by the upstream perception algorithm. For planning algorithms, the object-based representation offers a memory-efficient description of the environment. It also allows for an easier way to define inter-object relations for behavior prediction. On the other hand, a grid-based approach allows for an object-model-free representation, which assists in efficient collision-checking in complex scenarios with large number of objects. The grid-based representation is also less sensitive to imperfections of object extraction such as false and missed targets. A hybrid of these two approaches is also possible by extracting object hypothesis from the grid-based representation.
In this example, you represent the surrounding environment as a dynamic occupancy grid map. For an example using the discrete set of objects, refer to the Highway Trajectory Planning Using Frenet Reference Path (Navigation Toolbox) example. A dynamic occupancy grid map is a grid-based estimate of the local environment around the ego vehicle. In addition to estimating the probability of occupancy, the dynamic occupancy grid also estimates the kinematic attributes of each cell, such as velocity, turn-rate, and acceleration. Further, the estimates from the dynamic grid can be predicted for a short-time in the future to assess the occupancy of the local environment in the near future. In this example, you obtain the grid-based estimate of the environment by fusing point clouds from six lidars mounted on the ego vehicle.
### Set Up Scenario and Grid-Based Tracker
The scenario used in this example represents an urban intersection scene and contains a variety of objects, including pedestrians, bicyclists, cars, and trucks. The ego vehicle is equipped with six homogenous lidar sensors, each with a field of view of 90 degrees, providing 360-degree coverage around the ego vehicle. For more details on the scenario and sensor models, refer to the Grid-Based Tracking in Urban Environments Using Multiple Lidars (Sensor Fusion and Tracking Toolbox) example. The definition of scenario and sensors is wrapped in the helper function helperGridBasedPlanningScenario.
% For reproducible results
rng(2020);
% Create scenario, ego vehicle and simulated lidar sensors
[scenario, egoVehicle, lidars] = helperGridBasedPlanningScenario;
Now, define a grid-based tracker using the trackerGridRFS (Sensor Fusion and Tracking Toolbox) System object™. The tracker outputs both object-level and grid-level estimate of the environment. The grid-level estimate describes the occupancy and state of the local environment and can be obtained as the fourth output from the tracker. For more details on how to set up a grid-based tracker, refer to the Grid-Based Tracking in Urban Environments Using Multiple Lidars (Sensor Fusion and Tracking Toolbox) example.
% Set up sensor configurations for each lidar
sensorConfigs = cell(numel(lidars),1);
% Fill in sensor configurations
for i = 1:numel(sensorConfigs)
sensorConfigs{i} = helperGetLidarConfig(lidars{i},egoVehicle);
end
% Set up tracker
tracker = trackerGridRFS('SensorConfigurations',sensorConfigs,...
'HasSensorConfigurationsInput',true,...
'GridLength',120,...
'GridWidth',120,...
'GridResolution',2,...
'GridOriginInLocal',[-60 -60],...
'NumParticles',1e5,...
'NumBirthParticles',2e4,...
'VelocityLimits',[-15 15;-15 15],...
'BirthProbability',0.025,...
'ProcessNoise',5*eye(2),...
'DeathRate',1e-3,...
'FreeSpaceDiscountFactor',1e-2,...
'AssignmentThreshold',8,...
'MinNumCellsPerCluster',4,...
'ClusteringThreshold',4,...
'ConfirmationThreshold',[3 4],...
'DeletionThreshold',[4 4]);
### Set Up Motion Planner
Set up a local motion planning algorithm to plan optimal trajectories in Frenet coordinates along a global reference path.
Define the global reference path using the referencePathFrenet (Navigation Toolbox) object by providing the waypoints in the Cartesian coordinate frame of the driving scenario. The reference path used in this example defines a path that turns right at the intersection.
waypoints = [-110.6 -4.5 0;
49 -4.5 0;
55.5 -17.7 -pi/2;
55.5 -130.6 -pi/2]; % [x y theta]
% Create a reference path using waypoints
refPath = referencePathFrenet(waypoints);
% Visualize the reference path
fig = figure('Units','normalized','Position',[0.1 0.1 0.8 0.8]);
ax = axes(fig);
hold(ax,'on');
plot(scenario,'Parent',ax);
show(refPath,'Parent',ax);
xlim(ax,[-120 80]);
ylim(ax,[-160 40]);
snapnow;
The local motion planning algorithm in this example consists of three main steps:
1. Sample local trajectories
2. Find feasible and collision-free trajectories
3. Choose optimality criterion and select optimal trajectory
The following sections discuss each step of the local planning algorithm and the helper functions used to execute each step.
#### Sample Local Trajectories
At each step of the simulation, the planning algorithm generates a list of sample trajectories that the ego vehicle can choose. The local trajectories are sampled by connecting the current state of the ego vehicle to desired terminal states. Use the trajectoryGeneratorFrenet (Navigation Toolbox) object to connect current and terminal states for generating local trajectories. Define the object by providing the reference path and the desired resolution in time for the trajectory. The object connects initial and final states in Frenet coordinates using fifth-order polynomials.
connector = trajectoryGeneratorFrenet(refPath,'TimeResolution',0.1);
The strategy for sampling terminal states in Frenet coordinates often depends on the road network and the desired behavior of the ego vehicle during different phases of the global path. For more detailed examples of using different ego behavior, such as cruise-control and car-following, refer to the "Planning Adaptive Routes Through Traffic" section of the Highway Trajectory Planning Using Frenet Reference Path (Navigation Toolbox) example. In this example, you sample the terminal states using two different strategies, depending on the location of vehicle on the reference path, shown as blue and green regions in the following figure.
% Visualize path regions for sampling strategy visualization
pathPoints = closestPoint(refPath, refPath.Waypoints(:,1:2));
intersectionBuffer = 20;
pathGreen = [interpolate(refPath,linspace(0,intersectionS-intersectionBuffer,20));...
nan(1,6);...
hold(ax,'on');
plot(ax,pathGreen(:,1),pathGreen(:,2),'Color',[0 1 0],'LineWidth',5);
plot(ax,pathBlue(:,1),pathBlue(:,2),'Color',[0 0 1],'LineWidth',5);
snapnow;
When the ego vehicle is in the green region, the following strategy is used to sample local trajectories. The terminal state of the ego vehicle after $\Delta \mathit{T}$ time is defined as:
${\mathit{x}}_{\mathrm{Ego}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\left(\Delta \mathit{T}\right)=\left[\mathrm{NaN}\text{\hspace{0.17em}}\stackrel{˙}{\mathit{s}}\text{\hspace{0.17em}}0\text{\hspace{0.17em}}\mathit{d}\text{\hspace{0.17em}}0\text{\hspace{0.17em}}0\right];\text{\hspace{0.17em}}$
where discrete samples for variables are obtained using the following predefined sets:
$\left\{\Delta \mathit{T}\in \left\{\mathrm{linspace}\left(2,4,6\right)\right\},\text{\hspace{0.17em}}\stackrel{˙}{\mathit{s}}\in \left\{\mathrm{linspace}\left(0,{\stackrel{˙}{\mathit{s}}}_{\mathrm{max},}10\right)\right\},\text{\hspace{0.17em}}\mathit{d}\in \left\{0\text{\hspace{0.17em}}{\mathit{w}}_{\mathrm{lane}\text{\hspace{0.17em}}}\right\}\right\}$
The use of NaN in the terminal state enables the trajectoryGeneratorFrenet object to automatically compute the longitudinal distance traveled over a minimum-jerk trajectory. This strategy produces a set of trajectories that enable the ego vehicle to accelerate up to the maximum speed limit (${\stackrel{˙}{\mathit{s}}}_{\mathrm{max}}$) rates or decelerate to a full stop at different rates. In addition, the sampled choices of lateral offset (${\mathit{d}}_{\mathrm{des}}$) allow the ego vehicle to change lanes during these maneuvers.
% Define smax and wlane
speedLimit = 15;
laneWidth = 2.975;
When the ego vehicle is in the blue region of the trajectory, the following strategy is used to sample local trajectories:
${\mathit{x}}_{\mathrm{Ego}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\left(\Delta \mathit{T}\right)=\left[{\mathit{s}}_{\mathrm{stop}}\text{\hspace{0.17em}}0\text{\hspace{0.17em}}0\text{\hspace{0.17em}}0\text{\hspace{0.17em}}0\text{\hspace{0.17em}}0\right]$;
where $\Delta \mathit{T}$ is chosen to minimize jerk during the trajectory. This strategy enables the vehicle to stop at the desired distance (${\mathit{s}}_{\mathrm{stop}}$) in the right lane with a minimum-jerk trajectory. The trajectory sampling algorithm is wrapped inside the helper function, helperGenerateTrajectory, attached with this example.
#### Finding Feasible and Collision-Free Trajectories
The sampling process described in the previous section can produce trajectories that are kinematically infeasible and exceed thresholds of kinematic attributes such as acceleration and curvature. Therefore, you limit the maximum acceleration and speed of the ego vehicle using the helper function helperKinematicFeasibility, which checks the feasibility of each trajectory against these kinematic constraints.
% Define kinematic constraints
accMax = 15;
Further, you set up a collision-validator to assess if the ego vehicle can maneuver on a kinematically feasible trajectory without colliding with any other obstacles in the environment. To define the validator, use the helper class HelperDynamicMapValidator. This class uses the predictMapToTime (Sensor Fusion and Tracking Toolbox) function of the trackerGridRFS object to get short-term predictions of the occupancy of the surrounding environment. Since the uncertainty in the estimate increases with time, configure the validator with a maximum time horizon of 2 seconds.
The predicted occupancy of the environment is converted to an inflated costmap at each step to account for the size of the ego vehicle. The path planner uses a timestep of 0.1 seconds with a prediction time horizon of 2 seconds. To reduce computational complexity, the occupancy of the surrounding environment is assumed to be valid for 5 time steps, or 0.5 seconds. As a result, only 4 predictions are required in the 2-second planning horizon. In addition to making binary decisions about collision or no collision, the validator also provides a measure of collision probability of the ego vehicle. This probability can be incorporated into the cost function for optimality criteria to account for uncertainty in the system and to make better decisions without increasing the time horizon of the planner.
vehDims = vehicleDimensions(egoVehicle.Length,egoVehicle.Width);
collisionValidator = HelperDynamicMapValidator('MaxTimeHorizon',2, ... % Maximum horizon for validation
'TimeResolution',connector.TimeResolution, ... % Time steps between trajectory samples
'Tracker',tracker, ... % Provide tracker for prediction
'ValidPredictionSpan',5, ... % Prediction valid for 5 steps
'VehicleDimensions',vehDims); % Provide dimensions of ego
#### Choose Optimality Criterion
After validating the feasible trajectories against obstacles or occupied regions of the environment, choose an optimality criterion for each valid trajectory by defining a cost function for the trajectories. Different cost functions are expected to produce different behaviors from the ego vehicle. In this example, you define the cost of each trajectory as
$\mathit{C}={\mathit{J}}_{\mathit{s}}+{\mathit{J}}_{\mathit{d}}+1000{\mathit{P}}_{\mathit{c}}+100{\left({\stackrel{˙}{\mathit{s}}}_{\left(\Delta \mathit{T}\right)}-{\stackrel{˙}{\mathit{s}}}_{\mathrm{Limit}}\right)}^{2}$
where:
${\mathit{J}}_{\mathit{s}}$ is the jerk in the longitudinal direction of the reference path
${\mathit{J}}_{\mathit{d}}$ is the jerk in the lateral direction of the reference path
${\mathit{P}}_{\mathit{c}}$ is the collision probability obtained by the validator
The cost calculation for each trajectory is defined using the helper function helperCalculateTrajectoryCosts. From the list of valid trajectories, the trajectory with the minimum cost is considered as the optimal trajectory.
### Run Scenario, Estimate Dynamic Map, and Plan Local Trajectories
Run the scenario, generate point clouds from all the lidar sensors, and estimate the dynamic occupancy grid map. Use the dynamic map estimate and its predictions to plan a local trajectory for the ego vehicle.
% Close original figure and initialize a new display
close(fig);
display = helperGridBasedPlanningDisplay;
% Initial ego state
currentEgoState = [-110.6 -1.5 0 0 15 0];
helperMoveEgoVehicleToState(egoVehicle, currentEgoState);
% Initialize pointCloud outputs from each sensor
ptClouds = cell(numel(lidars),1);
sensorConfigs = cell(numel(lidars),1);
% Simulation Loop
% Current simulation time
time = scenario.SimulationTime;
% Poses of objects with respect to ego vehicle
tgtPoses = targetPoses(egoVehicle);
% Simulate point cloud from each sensor
for i = 1:numel(lidars)
[ptClouds{i}, isValidTime] = step(lidars{i},tgtPoses,time);
sensorConfigs{i} = helperGetLidarConfig(lidars{i},egoVehicle);
end
% Pack point clouds as sensor data format required by the tracker
sensorData = packAsSensorData(ptClouds,sensorConfigs,time);
% Call the tracker
[tracks, ~, ~, map] = tracker(sensorData,sensorConfigs,time);
% Update validator's future predictions using current estimate
step(collisionValidator, currentEgoState, map, time);
% Sample trajectories using current ego state and some kinematic
% parameters
[frenetTrajectories, globalTrajectories] = helperGenerateTrajectory(connector, refPath, currentEgoState, speedLimit, laneWidth, intersectionS, intersectionBuffer);
% Calculate kinematic feasibility of generated trajectories
isKinematicsFeasible = helperKinematicFeasibility(frenetTrajectories,speedLimit,accMax);
% Calculate collision validity of feasible trajectories
feasibleGlobalTrajectories = globalTrajectories(isKinematicsFeasible);
feasibleFrenetTrajectories = frenetTrajectories(isKinematicsFeasible);
[isCollisionFree, collisionProb] = isTrajectoryValid(collisionValidator, feasibleGlobalTrajectories);
% Calculate costs and final optimal trajectory
nonCollidingGlobalTrajectories = feasibleGlobalTrajectories(isCollisionFree);
nonCollidingFrenetTrajectories = feasibleFrenetTrajectories(isCollisionFree);
nonCollodingCollisionProb = collisionProb(isCollisionFree);
costs = helperCalculateTrajectoryCosts(nonCollidingFrenetTrajectories, nonCollodingCollisionProb, speedLimit);
% Find optimal trajectory
[~,idx] = min(costs);
optimalTrajectory = nonCollidingGlobalTrajectories(idx);
% Assemble for plotting
trajectories = helperAssembleTrajectoryForPlotting(globalTrajectories, ...
isKinematicsFeasible, isCollisionFree, idx);
% Update display
display(scenario, egoVehicle, lidars, ptClouds, tracker, tracks, trajectories, collisionValidator);
% Move ego with optimal trajectory
if ~isempty(optimalTrajectory)
currentEgoState = optimalTrajectory.Trajectory(2,:);
helperMoveEgoVehicleToState(egoVehicle, currentEgoState);
else
% All trajectories either violated kinematic feasibility
% constraints or resulted in a collision. More behaviors on
% trajectory sampling may be needed.
error('Unable to compute optimal trajectory');
end
end
### Results
Analyze the results from the local path planning algorithm and how the predictions from the map assisted the planner. This animation shows the result of the planning algorithm during the entire scenario. Notice that the ego vehicle successfully reached its desired destination and maneuvered around different dynamic objects, whenever necessary. The ego vehicle also came to a stop at the intersection due to the regional changes added to the sampling policy.
Next, analyze the local planning algorithm during the first lane change. The snapshots in this section are captured at time = 4.3 seconds during the simulation.
In this snapshot, the ego vehicle has just started to perform a lane change maneuver into the right lane.
showSnaps(display, 3, 1);
The snapshot that follows shows the estimate of the dynamic grid at the same time step. The color of the grid cell denotes the direction of motion of the object occupying that grid cell. Notice that the cells representing the car in front of the ego vehicle are colored red, denoting that the cells are occupied with a dynamic object. Also, the car is moving in the positive X direction of the scenario, so based on the color wheel, the color of the corresponding grid cells is red.
f = showSnaps(display, 2, 1);
if ~isempty(f)
ax = findall(f,'Type','Axes');
ax.XLim = [0 40];
ax.YLim = [-20 20];
s = findall(ax,'Type','Surf');
s.XData = 36 + 1/3*(s.XData - mean(s.XData(:)));
s.YData = 16 + 1/3*(s.YData - mean(s.YData(:)));
end
Based on the previous image, the planned trajectory of the ego vehicle passes through the occupied regions of space, representing a collision if you performed a traditional static occupancy validation. The dynamic occupancy map and the validator, however, account for the dynamic nature of the grid by validating the state of the trajectory against the predicted occupancy at each time step. The next snapshot shows the predicted costmap at different prediction steps ($\Delta \mathit{T}$), along with the planned position of the ego vehicle on the trajectory. The predicted costmap is inflated to account for size of the ego vehicle. Therefore, if a point object representing the origin of the ego vehicle can be placed on the occupancy map without any collision, it can be interpreted that the ego vehicle does not collide with any obstacle. The yellow regions on the costmap denote areas with guaranteed collisions with an obstacle. The collision probability decays outside the yellow regions exponentially until the end of inflation region. The blue regions indicate areas with zero probability of collision according to the current prediction.
Notice that the yellow region representing the car in front of the ego vehicle moves forward on the costmap as the map is predicted in the future. This reflects that the prediction of occupancy considers the velocity of objects in the surrounding environment. Also, notice that the cells classified as static objects remained relatively static on the grid during the prediction. Lastly, notice that the planned position of the ego vehicle origin does not collide with any occupied regions in the cost map. This shows that the ego vehicle can successfully maneuver on this trajectory.
f = showSnaps(display, 1, 1);
if ~isempty(f)
ax = findall(f,'Type','Axes');
for i = 1:numel(ax)
ax(i).XLim = [0 40];
ax(i).YLim = [-20 20];
end
end
### Summary
In this example, you learned how to use the dynamic map predictions from the grid-based tracker, trackerGridRFS, and how to integrate the dynamic map with a local path planning algorithm to generate trajectories for the ego vehicle in dynamic complex environments. You also learned how the dynamic nature of the occupancy can be used to plan trajectories more efficiently in the environment.
### Supporting Functions
function sensorData = packAsSensorData(ptCloud, configs, time)
% Pack the sensor data as format required by the tracker
%
% ptCloud - cell array of pointCloud object
% configs - cell array of sensor configurations
% time - Current simulation time
%The lidar simulation returns outputs as pointCloud objects. The Location
%property of the point cloud is used to extract x,y, and z locations of
%returns and pack them as structures with information required by a tracker.
sensorData = struct('SensorIndex',{},...
'Time', {},...
'Measurement', {},...
'MeasurementParameters', {});
for i = 1:numel(ptCloud)
% This sensor's point cloud
thisPtCloud = ptCloud{i};
% Allows mapping between data and configurations without forcing an
% ordered input and requiring configuration input for static sensors.
sensorData(i).SensorIndex = configs{i}.SensorIndex;
% Current time
sensorData(i).Time = time;
% Exctract Measurement as a 3-by-N defining locations of points
sensorData(i).Measurement = reshape(thisPtCloud.Location,[],3)';
% Data is reported in the sensor coordinate frame and hence measurement
% parameters are same as sensor transform parameters.
sensorData(i).MeasurementParameters = configs{i}.SensorTransformParameters;
end
end
function config = helperGetLidarConfig(lidar, ego)
% Get configuration of the lidar sensor for tracker
%
% config - Configuration of the lidar sensor in the world frame
% lidar - lidarPointCloudGeneration object
% ego - driving.scenario.Actor in the scenario
% Define transformation from sensor to ego
senToEgo = struct('Frame',fusionCoordinateFrameType(1),...
'OriginPosition',[lidar.SensorLocation(:);lidar.Height],...
'Orientation',rotmat(quaternion([lidar.Yaw lidar.Pitch lidar.Roll],'eulerd','ZYX','frame'),'frame'),...
'IsParentToChild',true);
% Define transformation from ego to tracking coordinates
egoToScenario = struct('Frame',fusionCoordinateFrameType(1),...
'OriginPosition',ego.Position(:),...
'Orientation',rotmat(quaternion([ego.Yaw ego.Pitch ego.Roll],'eulerd','ZYX','frame'),'frame'),...
'IsParentToChild',true);
% Assemble using trackingSensorConfiguration.
config = trackingSensorConfiguration(...
'SensorIndex',lidar.SensorIndex,...
'IsValidTime', true,...
'SensorLimits',[lidar.AzimuthLimits;0 lidar.MaxRange],...
'SensorTransformParameters',[senToEgo;egoToScenario],...
'DetectionProbability',0.95);
end
function helperMoveEgoVehicleToState(egoVehicle, currentEgoState)
% Move ego vehicle in scenario to a state calculated by the planner
%
% egoVehicle - driving.scenario.Actor in the scenario
% currentEgoState - [x y theta kappa speed acc]
% Set 2-D Position
egoVehicle.Position(1:2) = currentEgoState(1:2);
% Set 2-D Velocity (s*cos(yaw) s*sin(yaw))
egoVehicle.Velocity(1:2) = [cos(currentEgoState(3)) sin(currentEgoState(3))]*currentEgoState(5);
% Set Yaw in degrees
egoVehicle.Yaw = currentEgoState(3)*180/pi;
% Set angular velocity in Z (yaw rate) as v/r
egoVehicle.AngularVelocity(3) = currentEgoState(4)*currentEgoState(5);
end
function isFeasible = helperKinematicFeasibility(frenetTrajectories, speedLimit, aMax)
% Check kinematic feasibility of trajectories
%
% frenetTrajectories - Array of trajectories in Frenet coordinates
% speedLimit - Speed limit (m/s)
% aMax - Maximum acceleration (m/s^2)
isFeasible = false(numel(frenetTrajectories),1);
for i = 1:numel(frenetTrajectories)
% Speed of the trajectory
speed = frenetTrajectories(i).Trajectory(:,2);
% Acceleration of the trajectory
acc = frenetTrajectories(i).Trajectory(:,3);
% Is speed valid?
isSpeedValid = ~any(speed < -0.1 | speed > speedLimit + 1);
% Is acceleration valid?
isAccelerationValid = ~any(abs(acc) > aMax);
% Trajectory feasible if both speed and acc valid
isFeasible(i) = isSpeedValid & isAccelerationValid;
end
end
function cost = helperCalculateTrajectoryCosts(frenetTrajectories, Pc, smax)
% Calculate cost for each trajectory.
%
% frenetTrajectories - Array of trajectories in Frenet coordinates
% Pc - Probability of collision for each trajectory calculated by validator
n = numel(frenetTrajectories);
Jd = zeros(n,1);
Js = zeros(n,1);
s = zeros(n,1);
for i = 1:n
% Time
time = frenetTrajectories(i).Times;
% resolution
dT = time(2) - time(1);
% Jerk along the path
dds = frenetTrajectories(i).Trajectory(:,3);
% Jerk perpendicular to path
% d2L/dt2 = d/dt(dL/ds*ds/dt)
ds = frenetTrajectories(i).Trajectory(:,2);
ddL = frenetTrajectories(i).Trajectory(:,6).*(ds.^2) + frenetTrajectories(i).Trajectory(:,5).*dds;
s(i) = frenetTrajectories(i).Trajectory(end,2);
end
cost = Js + Jd + 1000*Pc(:) + 100*(s - smax).^2;
end
|
# How to efficiently code Dynamic Time Warping algorithm with a locality constrain?
For given two lists $[s_1, s_2, ... s_n]$ and $[t_1, t_2, ..., t_m]$
I need to implement DTW algorithm with one extra constraint:
If $s_i$ is matched with $t_j$ then the next element $s_{i+1}$ has to be matched with some $t_{j+k}$ close enough to $t_j$ (i.e. $0 \le k \le W$ for some fixed window size $W$).
This constraint has to hold for each $s_i$.
1) Does there exist $O(nm)$ solution to such problem?
2) If an efficient algorithm does not exist, what would be a good practical solution?
(Note that locality constraint mentioned in the DTW link above is different from the constraint I need).
• Is $O(nmW)$ time good enough? Do you consider $W$ a constant? – D.W. Jan 6 '17 at 20:55
• $O(nmW)$ is definitely worth considering – mercury0114 Jan 6 '17 at 21:04
There is a $O(nmW)$-time algorithm using dynamic programming. Let $A[i,j] =$ the cost of the best matching of $[s_1,\dots,s_i]$ to $[t_1,\dots,t_j]$ such that $s_i$ is matched to $t_j$. Then
$$A[i,j] = \min\{c(s_i,t_j) + A[i-1,j-k] : k=0,1,\dots,W\}.$$
If you consider $W$ a constant, then you obtain a $O(nm)$-time algorithm.
I don't know if the factor of $W$ can be eliminated.
If $W$ is large, this can be improved to $O(nm \lg W)$ time. The basic primitive we need is:
Given an array $B[1..m]$ and $W$, preprocess $B$ so that we can efficiently answer queries "compute $\min\{B[i],B[i+2],\dots,B[i+W-1]\}$".
Here's how to do that. Assume first for simplicity that $W$ is a power of two. You construct secondary arrays $M_2,M_4,M_8,\dots,M_W$ such that $M_w[i] = \min\{B[i],B[i+1],\dots,B[i+w-1]\}$. You can build them up in $O(m \lg W)$ time, as each $M_{2w}$ can be constructed from $M_w$ in $O(m)$ time. Thus if $W$ is a power of two you can answer subsequent queries in $O(1)$ time per query.
If $W$ isn't a power of two, you can still express the interval $i,i+1,i+2,\dots,i+W-1$ as the union of at most $\lg W$ intervals each of whose width is a power of two. Thus, if $W$ isn't a power of 2, you can answer subsequent queries in $O(\lg W)$ time per query.
Finally, apply this to the original problem. You apply this to each row of $A$, i.e., to $A[i,\cdot]$ for each $i$. Then the recurrence can be computed using a single query, and it takes $O(\lg W)$ time instead of $O(W)$ time to compute the min. You'll need to update the secondary arrays each time you update $A[i,j]$, but this takes only $O(\lg W)$ time per update to $A[i,j]$ (as there are only $\lg W$ secondary arrays to update).
In all, you obtain an algorithm whose running time is $O(nm \lg W)$ and with $O(nm \lg W)$ space usage. (I suspect it's also possible to achieve $O(nm \lg W)$ time and $O(nm)$ space, if necessary, by only storing $M_w[i]$ for values of $i$ that are a multiple of $w$, at the cost of about a 2x increase in running time.)
• Haha, thanks for your enthusiasm. This speed is more than enough for me. – mercury0114 Jan 7 '17 at 10:00
Although the accepted answer is correct, an alternative solution also works well in practise, when one is not very strict about the $0 \leq k \leq W$ constraint, but still wants to have the "locality" property:
1) Let $cost[i][j]$ be the minimum cost to align $[s_1, s_2, ... s_i]$ and $[t_1, t_2, ..., t_j]$. We first build $cost$ matrix in $O(nm)$ time using dynamic programming.
2) We find the minimum index $last$ such that $s_n$ could have been aligned with $t_{last}$:
last = m;
// While ignoring extra element in the sequence (t_n) won't make cost worse
while (cost[n][last] >= cost[n][last - 1])
// We ignore it
last--;
}
return last;
3) After we know $last$, we find the maximum index $first$ such that $s_1$ could have been aligned with $t_{first}$:
int first = last;
int i = n - 1;
while (i > 0) {
// if to align i-th element with first is not worse that other options
if (cost[i - 1][first] + distance(i, first) <= cost[i][first - 1]) {
// we align it
i--;
} else {
// otherwise we have to use one more point from sequence (t_n)
first--;
}
}
return first;
4) At the end we have found a minimal interval $[t_{first}, ... t_{last}]$ with which the whole sequence $(s_n)$ was aligned. If the length of this interval is not too big (e.g. less than $\frac{3}{2}n)$ we can assume that an alignment satisfying "locality" property has been found.
The nice thing about this approach is that it can be coded in $O(nm)$ time and the code is relatively short.
|
# Perturbation Theory
Please help me try to understand this problem. It deals with the quantum-confined Stark effect in nanoparticles.
For odd n, n = 1, 3, 5, ...
$$\psi_{n}(x) = \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})$$
and for even n = 2, 4, 6, ...
$$\psi_{n}(x) = \sqrt{\frac{2}{a}} \sin (\frac{n \pi x}{a})$$
and the zeroth order energy levels are
$$E_{n} = \frac{h^2 \pi^2 n^2}{2ma^2}$$
The external field pertubation, H' = -qFx , where q is the charge and F is the applied electric field strength.
Now here's my work for the first order correction to the energy levels.
For odd n:
$$E_{n} = < \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})| H' | \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})> = 0$$
For even n, I still get 0 for the first order correction. I just know that isn't right, and I think I know why:
Am I treating H' = -qFx correctly by assuming q and F are constants and x as the operator?
Thanks for the help. :shy:
Last edited:
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# 3 Solutions to Replace PDF Pages
Updated By Soha On Sep 10, 2022, 2:52 pm
In daily life, you may encounter situations where you need to replace PDF pages. This article will give you 3 options to replace PDF pages. After comprehensive evaluation, GeekPDF is the best solution, you can have a try.
In your work and life, you may need to update the content or data in the PDF file, such as the design proposal or contract re-communicated with the customers. In this case, it will be time-consuming and laborious to recreate and edit the entire PDF file. Replacing some of the pages in the PDF would be a better option.
## Method 1 Use GeekerPDF to replace PDF pages
GeekPDF is the best solution for replacing PDF pages. GeekPDF is a free PDF page replacement tool, and it also has other functions such as editing, annotation and page management. The operation page is simple and intuitive, and it will be easy to replace the PDF page.
### Steps to replace PDF pages with GeekerPDF:
The best way to replace the pages of a PDF file is to use GeekerPDF , let's see how GeekerPDF replaces PDF pages.
1. Launch GeekerPDF after installing it and open the PDF file.
Step 2. Enter the "page" menu on the top, then select the page to be replaced, and then click the Replace menu.
Step 3. Select another PDF file to replace the page with, then click OK to complete the operation.
## Method 2 Replace PDF pages with Adobe Acrobat
As we all know, Adobe Acrobat is an authoritative PDF processing software. It has almost all the functions related to PDF, which is the main reason why many users choose it. However, the operation of Adobe Acrobat is relatively complex to operate and not very friendly for beginners, requiring a systematic learning tutorial. If you want to replace some pages in two or more PDF documents, look at the steps below.
### Steps to replace PDF pages with Adobe Acrobat:
1. Start Adobe Acrobat and open the PDF document whose pages need to be replaced.
2. Click the "Organize Pages" option under the Tools menu.
3. Then open the Page Thumbnails panel in the two or more document windows.
4. Drag the target thumbnail to the specific location in the main document, hold down "Command+Option" or Ctrl+Alt, and release on the thumbnail to be replaced.
5. In the pop-up window, click "Yes" to replace.
## Method 3 Use iLovePDF to replace PDF pages online
Among the tools to replace PDF pages, iLovePDF is also a good choice because you can replace them online without downloading or installing any programs. Be aware, however, that online tools may collect sensitive information from your documents, so think twice before using them.
### Steps to replace PDF pages with iLovePDF:
1. Open the iLovePDF page with a browser.
2. Click "Select PDF File" to add the PDF document to be processed. It can also be opened by dragging the PDF document directly into this page.
3. In the pop-up window, you will see the thumbnail of the PDF document. You can adjust the position of each page by dragging, and you can also click the "X" at the top of a single page to delete a page, and "+" to add a new page.
4. After the adjustment is complete, click "Organize".
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# R
## A Condensed Key for A Visual Guide to Targeted Maximum Likelihood Estimation (TMLE)
A condensed key for my corresponding TMLE tutorial blog post. Initial set up Estimand of interest: $ATE = \Psi = E_W[\mathrm{E}[Y|A=1,\mathbf{W}] - \mathrm{E}[Y|A=0,\mathbf{W}]]$ Step 1: Estimate the Outcome First, estimate the expected value of the outcome using treatment and confounders as predictors. $Q(A,\mathbf{W}) = \mathrm{E}[Y|A,\mathbf{W}]$ Then use that fit to obtain estimates of the expected outcome under varying three different treatment conditions:
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# 1.1 Reading An Introduction to Applied Bioinformatics ¶
Bioinformatics, as I see it, is the application of the tools of computer science (things like programming languages, algorithms, and databases) to address biological problems (for example, inferring the evolutionary relationship between a group of organisms based on fragments of their genomes, or understanding if or how the community of microorganisms that live in my gut changes if I modify my diet). Bioinformatics is a rapidly growing field, largely in response to the vast increase in the quantity of data that biologists now grapple with. Students from varied disciplines (e.g., biology, computer science, statistics, and biochemistry) and stages of their educational careers (undergraduate, graduate, or postdoctoral) are becoming interested in bioinformatics.
An Introduction to Applied Bioinformatics, or IAB, is an open source, interactive bioinformatics text. It introduces readers to the core concepts of bioinformatics in the context of their implementation and application to real-world problems and data. IAB is closely tied to the scikit-bio python package, which provides production-ready implementations of core bioinformatics algorithms and data structures. Readers therefore learn the concepts in the context of tools they can use to develop their own bioinformatics software and pipelines, enabling them to rapidly get started on their own projects. While some theory is discussed, the focus of IAB is on what readers need to know to be effective, practicing bioinformaticians.
IAB is interactive, being based on IPython Notebooks which can be installed on a reader's computer or viewed statically online. As readers are learning a concept, for example, pairwise sequence alignment, they are presented with its scikit-bio implementation directly in the text. scikit-bio code is well annotated (adhering to the pep8 and numpydoc conventions), so readers can use it to assist with their understanding of the concept. And, because IAB is presented as an IPython Notebook, readers can execute the code directly in the text. For example, when learning pairwise alignment, users can align sequences provided in IAB (or their own sequences) and modify parameters (or even the algorithm itself) to see how changes affect the resulting alignments.
IAB is completely open access, with all software being BSD-licensed, and all text being licensed under Creative Commons Attribution Only (i.e., CC BY-NC-SA 4.0). All development and publication is coordinated under public revision control on GitHub.
IAB is also an electronic-only resource. There are currently no plans to commercialize it or to create a print version. This means that, unlike printed bioinformatics texts which are generally out of date before the ink dries, IAB can be updated as the field changes.
The life cycle of IAB is more like a software package than a book. There will be development and release versions of IAB, where the release versions are more polished but won't always contain the latest content, and the development versions will contain all of the latest materials, but won't necessarily be copy-edited and polished.
We are in the process of developing a project status page that will detail the plans for IAB. This will include the full table of contents, and what stage you can expect chapters to be at at different times. You can track progress of this on IAB #97.
My goal for IAB is for it to make bioinformatics as accessible as possible to students from varied backgrounds, and to get more people into this hugely exciting field. I'm very interested in hearing from readers and instructors who are using IAB, so get in touch if you have corrections, suggestions for how to improve the content, or any other thoughts or comments on the text. In the spirit of openness, I'd prefer to be contacted via the IAB issue tracker. I'll respond to direct e-mail as well, but I'm always backlogged (just ask my students), so e-mail responses are likely to be slower.
I hope you find IAB useful, and that you enjoy reading it!
## 1.1.1 Who should read IAB?¶
IAB is written for scientists, software developers, and students interested in understanding and applying bioinformatics methods, and ultimately in developing their own bioinformatics analysis pipelines or software.
IAB was initially developed for an undergraduate course cross-listed in computer science and biology with no pre-requisites. It therefore assumes little background in biology or computer science, however some basic background is very helpful. For example, an understanding of the roles of and relationship between DNA and protein in a cell, and the ability to read and follow well-annotated python code, are both helpful (but not necessary) to get started.
In the Getting started with Biology and Computer Science sections below I provide some suggestions for other texts that will help you to get started.
## 1.1.2 How to read IAB¶
There are two ways to read An Introduction To Applied Bioinformatics:
In both cases you have the option to read the latest development version (i.e., master of the GitHub repository) or the latest release version. The lastest development version will have all of the most recent content, but since it hasn't yet been officially released some aspects may be less polished or buggy. The latest release version won't necessarily have the latest content, but it should be more polished and less buggy. If you're reading IAB on your own, I recommend working with the latest development version. If you're teaching a class that uses IAB, you probably should use the latest release version.
IAB is split into four different sections: Getting started, Fundamentals, Applications, and Wrapping up. You should start reading IAB by working through the Getting started and Fundamentals chapters in order. You should then read the Applications chapters and Wrapping up in any order, based on your own interest.
## 1.1.3 Using the IPython Notebook¶
IAB is built using the IPython Notebook, an interactive HTML-based computing environment. The main source for information about the IPython Notebook is the IPython Notebook website. You can find information there on how to use the IPython Notebook, and also on how to set up and run and IPython Notebook server (for example, if you'd like to make one available to your students).
Most of the code that is used in IAB comes from scikit-bio package, or other python scientific computing tools. You can access these in the same way that you would in a python script. For example:
In [1]:
import skbio
from __future__ import print_function
from IPython.core import page
page.page = print
We can then access functions, variables, and classes from these modules.
In [2]:
print(skbio.title)
print(skbio.art)
* *
_ _ _ _ _ _
(_) | (_) | | | (_)
___ ___ _| | ___| |_ ______| |__ _ ___
/ __|/ __| | |/ / | __|______| '_ \| |/ _ \
\__ \ (__| | <| | |_ | |_) | | (_) |
|___/\___|_|_|\_\_|\__| |_.__/|_|\___/
* *
Opisthokonta
\ Amoebozoa
\ /
* Euryarchaeota
\ |_ Crenarchaeota
\ *
\ /
*
/
/
/
*
/ \
/ \
Proteobacteria \
Cyanobacteria
We'll inspect a lot of source code in IAB as we explore bioinformatics algorithms. If you're ever interested in seeing the source code for some functionality that we're using, you can do that using IPython's psource magic.
In [3]:
from skbio.alignment import TabularMSA
%psource TabularMSA.conservation
@experimental(as_of='0.4.1')
def conservation(self, metric='inverse_shannon_uncertainty',
degenerate_mode='error', gap_mode='nan'):
"""Apply metric to compute conservation for all alignment positions
Parameters
----------
metric : {'inverse_shannon_uncertainty'}, optional
Metric that should be applied for computing conservation. Resulting
values should be larger when a position is more conserved.
degenerate_mode : {'nan', 'error'}, optional
Mode for handling positions with degenerate characters. If
"nan", positions with degenerate characters will be assigned a
conservation score of np.nan. If "error", an
error will be raised if one or more degenerate characters are
present.
gap_mode : {'nan', 'ignore', 'error', 'include'}, optional
Mode for handling positions with gap characters. If "nan",
positions with gaps will be assigned a conservation score of
np.nan. If "ignore", positions with gaps will be filtered
to remove gaps before metric is applied. If "error", an
error will be raised if one or more gap characters are present. If
"include", conservation will be computed on alignment positions
with gaps included. In this case, it is up to the metric to ensure
that gaps are handled as they should be or to raise an error if
gaps are not supported by that metric.
Returns
-------
np.array of floats
Values resulting from the application of metric to each
position in the alignment.
Raises
------
ValueError
If an unknown metric, degenerate_mode or gap_mode is
provided.
ValueError
If any degenerate characters are present in the alignment when
degenerate_mode is "error".
ValueError
If any gaps are present in the alignment when gap_mode is
"error".
Notes
-----
Users should be careful interpreting results when
gap_mode = "include" as the results may be misleading. For example,
as pointed out in [1]_, a protein alignment position composed of 90%
gaps and 10% tryptophans would score as more highly conserved than a
position composed of alanine and glycine in equal frequencies with the
"inverse_shannon_uncertainty" metric.
gap_mode = "include" will result in all gap characters being
recoded to TabularMSA.dtype.default_gap_char. Because no
conservation metrics that we are aware of consider different gap
characters differently (e.g., none of the metrics described in [1]_),
they are all treated the same within this method.
The inverse_shannon_uncertainty metric is simply one minus
Shannon's uncertainty metric. This method uses the inverse of Shannon's
uncertainty so that larger values imply higher conservation. Shannon's
uncertainty is also referred to as Shannon's entropy, but when making
computations from symbols, as is done here, "uncertainty" is the
preferred term ([2]_).
References
----------
.. [1] Valdar WS. Scoring residue conservation. Proteins. (2002)
.. [2] Schneider T. Pitfalls in information theory (website, ca. 2015).
https://schneider.ncifcrf.gov/glossary.html#Shannon_entropy
"""
if gap_mode not in {'nan', 'error', 'include', 'ignore'}:
raise ValueError("Unknown gap_mode provided: %s" % gap_mode)
if degenerate_mode not in {'nan', 'error'}:
raise ValueError("Unknown degenerate_mode provided: %s" %
degenerate_mode)
if metric not in {'inverse_shannon_uncertainty'}:
raise ValueError("Unknown metric provided: %s" %
metric)
if self.shape[0] == 0:
# handle empty alignment to avoid error on lookup of character sets
return np.array([])
# Since the only currently allowed metric is
# inverse_shannon_uncertainty, and we already know that a valid metric
# was provided, we just define metric_f here. When additional metrics
# are supported, this will be handled differently (e.g., via a lookup
# or if/elif/else).
metric_f = self._build_inverse_shannon_uncertainty_f(
gap_mode == 'include')
result = []
for p in self.iter_positions(ignore_metadata=True):
cons = None
# cast p to self.dtype for access to gap/degenerate related
# functionality
pos_seq = self.dtype(p)
# handle degenerate characters if present
if pos_seq.has_degenerates():
if degenerate_mode == 'nan':
cons = np.nan
else: # degenerate_mode == 'error' is the only choice left
degenerate_chars = pos_seq[pos_seq.degenerates()]
raise ValueError("Conservation is undefined for positions "
"with degenerate characters. The "
"following degenerate characters were "
"observed: %s." % degenerate_chars)
# handle gap characters if present
if pos_seq.has_gaps():
if gap_mode == 'nan':
cons = np.nan
elif gap_mode == 'error':
raise ValueError("Gap characters present in alignment.")
elif gap_mode == 'ignore':
pos_seq = pos_seq.degap()
else: # gap_mode == 'include' is the only choice left
# Recode all gap characters with pos_seq.default_gap_char.
pos_seq = pos_seq.replace(pos_seq.gaps(),
pos_seq.default_gap_char)
if cons is None:
cons = metric_f(pos_seq)
result.append(cons)
return np.array(result)
The documentation for scikit-bio is also very extensive (though the package itself is still in early development). You can view the documentation for the TabularMSA object, for example, here. These documents will be invaluable for learning how to use the objects.
## 1.1.4 Reading list¶
### 1.1.4.1 Getting started with Biology¶
If you're new to biology, these are some books and resources that will help you get started.
• The NIH Bookshelf A lot of free biology texts, some obviously better than others.
• Brock Biology of Microorganisms by Michael T. Madigan, John M. Martinko, David Stahl, David P. Clark. One of the best textbooks on microbiology. This is also fairly advanced, but if you're interested in microbial ecology or other aspects of microbiology it will likely be extremely useful.
### 1.1.4.2 Getting started with Computer Science and programming¶
If you're new to Computer Science and programming, these are some books and resources that will help you get started.
• Software Carpentry Online resources for learning scientific computing skills, and regular in-person workshops all over the world. Taking a Software Carpentry workshop will pay off for biology students interested in a career in research.
• Practical Computing for Biologists by Steven Haddock and Casey Dunn. A great introduction to many computational skills that are required of modern biologists. I highly recommend this book to all Biology undergraduate and graduate students.
• The Pragmatic Programmer by Andrew Hunt. A more advanced book on becoming a better programmer. This book is excellent, and I highly recommend it for anyone developing bioinformatics software. You should know how to program and have done some software development before jumping into this.
These are some books that I've enjoyed, that have also helped me think about biological systems. These are generally written for a more popular audience, so should be accessible to any readers of An Introduction to Applied Bioinformatics.
• Ever Since Darwin by Stephen Jay Gould. This is the first book in a series of collections of short essays.
## 1.1.5 Need help?¶
If you're having issues getting An Introduction to Applied Bioinformatics running on your computer, or you have corrections or suggestions on the content, you should get in touch through the IAB issue tracker. This will generally be much faster than e-mailing the author directly, as there are multiple people who monitor the issue tracker. It also helps us manage our technical support load if we can consolidate all requests and responses in one place.
## 1.1.6 Contributing to IAB¶
If you're interested in contributing content or features to IAB, you should start by reviewing CONTRIBUTING.md which provides guidelines on how to get involved.
## 1.1.7 About the author¶
My name is Greg Caporaso. I'm the primary author of An Introduction to Applied Bioinformatics, but there are other contributors and I hope that list will grow.
I have degrees in Computer Science (B.S., University of Colorado, 2001) and Biochemistry (B.A., University of Colorado, 2004; Ph.D., University of Colorado 2009). Following my formal training, I joined the Rob Knight Laboratory, then at the University of Colorado, for approximately 2 years as a post-doctoral scholar. In 2011, I joined the faculty at Northern Arizona University (NAU) where I'm an Assistant Professor in the Biological Sciences department. I teach one course per year in bioinformatics for graduate and undergraduate students of Biology and Computer Science. I also run a research lab in the Center for Microbial Genetics and Genomics, which is focused on developing bioinformatics software and studying the human microbiome.
I'm not the world expert on the topics that I present in IAB, but I have a passion for bioinformatics, open source software, writing, and education. When I'm learning a new bioinformatics concept, for example an algorithm like pairwise alignment or a statistical technique like Monte Carlo simulation, implementing it is usually the best way for me to wrap my head around it. This led me to start developing IAB, as I found that my implementations helped my students learn the concepts too. I think that one of my strongest skills is the ability to break complex ideas into accessible components. I do this well for bioinformatics because I remember (and still regularly experience) the challenges of learning it, so can relate to newcomers in the field.
I'm very active in open source bioinformatics software development. I am most widely known for my involvement in the development of the QIIME software package, and more recently for leading the development of scikit-bio. I am also involved in many other bioinformatics software projects (see my GitHub page). IAB is one of the projects that I'm currently most excited about, so I truly hope that it's as useful for you as it is fun for me.
For updates on IAB and various other things, you should follow me on Twitter.
## 1.1.8 Acknowledgements¶
An Introduction to Applied Bioinformatics is funded in part by the Alfred P. Sloan Foundation. Initial prototyping was funded by Arizona's Technology and Research Initiative Fund. The style of the project was inspired by Bayesian Methods for Hackers.
See the repository's contributors page for information on who has contributed to the project.
|
### AVVISI
Gravitazione ed estensioni della Relatività Generale
## I cookie utilizzati servono al corretto funzionamento del sito.
Proseguendo la navigazione senza modificare le impostazioni del browser, accetti di ricevere tutti i cookie. Per saperne di piu'
Approvo
# Gravitazione ed estensioni della Relatività Generale
Persone
Arturo Stabile
Web
http://www.arturostabile.com/research-1.html
Attività
## The formation and especially the evolution of stars are other tests of the validity of ETGS and of their compatibility with current knowledge. Observed stellar structures are incompatible with the standard models of stellar structure. In particular, we refer to the neutron stars (magnetars) with mass larger than the Volkoff mass. It therefore seems that on particular length scales the gravitational force is larger or smaller than the corresponding value in GR. For example, a modification of the Hilbert-Einstein Lagrangian consisting of an R^2 term enables a major attraction while a R_{\alpha\beta} R^{\alpha\beta}term gives a repulsive contribution. Understanding on which scales the modifications to GR are activated or what is the weight of corrections to gravitational potential is a crucial point.
Massive states of gravitational waves in extended theories of gravity
A relevant aspect of higher order gravity theories is that, in the post-Minkowskian limit (i.e., with weak fields and arbitrary velocities), the propagation of the gravitational fields turns out to be characterized by waves with both tensorial and scalar modes. This feature represents a striking difference between GR and extended gravity since, in the standard Einstein scheme, only tensorial degrees of freedom are allowed. Gravitational waves represent a fundamental tool to discriminate between GR and alternative gravities. A graviton with non-zero mass produces several effects, such as extra degrees of polarization of gravitational wave modes and a frequency-dependent speed of propagation resulting in a non-trivial dispersion relation. Then, the graviton mass could be constrained using future observations of gravitational waves with the LIGO, Virgo, and the space-based LISA experiments. For example, dynamical binary systems emitting gravitational waves could constitute a good testbed to probe massive gravitons. During their dynamical evolution, the frequency of the binary orbit increases, ramping up rapidly in the late stages of the evolution just before coalescence. Then one proposes a systematic study of gravitational waves for a more general fourth order theory (with the addition of all curvature invariants). Such theories should be analyzed for given sources (for example binary systems) by building models of gravitational emission also for further massive modes of propagation. Today the propagation is studied as a perturbation of Minkowski space (weak gravitational waves), while we can investigate also what the propagation on a curved background (“hard” gravitational waves).
Energy and conservation laws in non-linear (extended) theories of gravity
|
# zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.
##### Operators
a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations. (English) Zbl 0877.35042
The authors study properties of positive solutions of $$\Delta u+ hu-ku^p= f\tag1$$ in a (possibly) nonsmooth $N$-dimensional domain $\Omega$, $N\ge 2$, subject to the condition $$u(x)\to\infty\quad\text{if}\quad \delta(x):= \text{dist}(x,\partial\Omega)\to 0.\tag2$$ Here $p>1$ and $h$, $k$, $f$ are continuous in $\overline\Omega$ with $k>0$ and $f\ge 0$. Positive solutions of (1) satisfying (2) are called large solutions. A central point of this paper is the following localization principle: let $\Omega$ be a (not necessarily bounded) domain having the graph property and suppose $u$ is a positive solution of (1) satisfying $u(x)\to\infty$ locally uniformly as $x\to\Gamma$, where $\Gamma\subset\partial\Omega$ is relatively open. If $v$ is a large solution, then $v(x)/u(x)\to 1$ locally uniformly as $x\to\Gamma$. Closely related to this is a uniqueness result for large solutions in bounded domains having the graph property. For bounded Lipschitz domains the authors prove the existence of positive constants $c_1\le c_2$ such that the (unique) large solution $u$ of (1) satisfies $c_1\delta(x)^{-{2\over p-1}}\le u(x)\le c_2\delta(x)^{-{2\over p-1}}$ for all $x\in\Omega$. This is also a consequence of the localization principle and an existence theorem, obtained for large solutions in bounded domains satisfying the exterior cone condition. If the domain is not Lipschitz, the rate of blow-up at the boundary may be lower. This is proved for domains having a re-entrant cusp in the case $p\ge(N-1)/(N-3)$. Finally, the authors discuss the dependence of large solutions on the function $k$ and the domain $\Omega$.
##### MSC:
35J60 Nonlinear elliptic equations 35J67 Boundary values of solutions of elliptic equations 35B40 Asymptotic behavior of solutions of PDE
Full Text:
##### References:
[1] Benguria, R.; Brezis, H.; Lieb, E.: The Thomas-Fermi-von weizsaäcker theory of atoms and molecules. Comm. math. Phys. 79, 167-180 (1981) · Zbl 0478.49035 [2] Bandle, C.; Marcus, M.: Sur LES solutions maximales de problèmes elliptiques non linéaires. C. R. Acad. sci. Paris 311, 91-93 (1990) · Zbl 0726.35041 [3] Bandle, C.; Marcus, M.: Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior. Jl. d’analyse math. 58, 9-24 (1992) · Zbl 0802.35038 [4] Bandle, C.; Marcus, M.: Large solutions of semilinear elliptic equations with singular coefficients. Pitman R. N. series 244, 25-38 (1992) · Zbl 0795.35023 [5] C. Bandle and M. Marcus, Asymptotic behavior of solutions and their derivatives for semilinear elliptic problems with blowup on the boundary, Ann. Inst. Poincaré (to appear). · Zbl 0840.35033 [6] Brezis; Veron, L.: Remouvable singularities for some nonlinear elliptic equations. Arch. rat. Mech. anal. 75, 1-6 (1980) [7] Gidas, B.; Ni, W.; Nirenberg, L.: Symmetry and related properties via the maximum principle. Comm. math. Phys. 68, 209-243 (1979) · Zbl 0425.35020 [8] Keller, J. B.: On solutions of ${\Delta}$u = f (u). Comm. pure appl. Math. 10, 503-510 (1957) · Zbl 0090.31801 [9] Lee, J. N.; Parker, T. H.: The yamabe problem. Bull. amer. Math. soc. 17, 37-91 (1987) · Zbl 0633.53062 [10] J. F. Le Gall, A path-valued Markov process and its connections with partial differential equations, Proc. 1st European Congress of Mathematics, Birkhäuser (to appear). [11] Marcus, M.: On solutions with blow up at the boundary for a class of semilinear elliptic equations. Developments in PDE and applications to mathematical physiscs, 65-77 (1993) [12] Marcus, M.; Veron, L.: Uniqueness of solutions with blow up at the boundary for a class of nonlinear elliptic equations. C. R. Acad. sci. Paris 317, 559-563 (1993) · Zbl 0803.35041 [13] Osserman, R.: On the inequality ${\Delta}$u = f (u). Pacific jl. Math. 7, 1641-1647 (1957) · Zbl 0083.09402 [14] Pinchover, Y.: Criticality and ground states for second order elliptic equations. Jl. diff. Equ. 80, 237-250 (1989) · Zbl 0697.35036 [15] Pinsky, R.: Positive harmonic functions and diffusion. Cambridge studies in advanced math. 45 (1995) [16] Veron, L.: Semilinear elliptic equations with uniform blow up on the boundary. Jl. d’analyse math. 59, 231-250 (1992) [17] Veron, L.: Comportement asymptotique des solutions d’équations elliptiques semi linéaires dans RN. Ann. mat. Pura appl. 127, 25-50 (1981) [18] Veron, L.: Singular solutions of some nonlinear elliptic equations. Nonlinear anal. T. M. & A. 5, 225-242 (1981)
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# Which model to use when one variable is country specific and the other is company specific?
So basically my study is on a single country with a 10 year time period. The sample is of several companies of that country. My independent variables are of two kinds, one is country-specific macroeconomic and the others are company-specific financial. The dependent variable is also company specific. I am trying to find the joint effect of the two independent variable on the dependent.
The problem here is that since the country is same, hence for a single year all the companies within the sample will have same values for the macroeconomic variables. I don't think time series will work since I am not suggesting that current period y depends on past period y. But I am also not sure whether this is a panel data as I am focusing on a single country.
Which model should I use? Should I use interaction term?
• So you have something like $y_{ij}=\beta_0 + \beta_{1i} x_i + \beta_{2j} z_j$ where $i$ indexes the country and $j$ the company ?
– user83346
Sep 27 '17 at 9:22
• No. Because the i index for Y variable does not change as the entire sample is from the same country. This means that value of x will also change only if the time period changes. Sep 27 '17 at 12:09
• Also since I wish to find the combined effect, I was wonder if an interaction term could be included or not Sep 27 '17 at 12:17
• Could you write down the formule that describes your model?
– user83346
Sep 27 '17 at 13:45
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# metric space examples
A metric space is a set X together with such a metric. Definition 2.2. Studies in history and philosophy of science Part A. start (x) and target (y). Note that each x n is an irrational number (i.e., x n 2Qc) and that fx ngconverges to 0. These instances may give the students an … Soc. So $X$ has a lot more than two elements. One of the objectives of the field is to find embeddings of metric spaces into other more simple and structured spaces that have low distortion. already in the eighteenth and nineteenth centuries. Help with referencing. MathJax reference. Any ideas on what caused my engine failure? 1, pp. Definition 1.1 Given metric spaces (X,d) and (X,d0) a map f : X → X0 is called an embedding. MOSFET blowing when soft starting a motor, Judge Dredd story involving use of a device that stops time for theft. • Transitivity: If X is homeomorphic to Y, and Y is homeomorphic to Z, then X is homeomorphic to Z. Fig.3 The Seven Bridges of Königsberg problem. J. Roe, Lectures on coarse geometry, American Mathematical Society, University Lecture serise, 31(2003). The topology Ton metric space (X;d) is generated by the open ball B r(x) = fy2Xjd(x;y)
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# Attributable Risk vs Absolute Risk Reduction
#### gastroguy
##### New Member
Hi,
I am hoping to understand the difference between attributable risk and absolute risk reduction. Mathematically, the two entities seem equivalent, but the formulas for calculating their confidence interval are quite different (https://www2.ccrb.cuhk.edu.hk/stat/confidence interval/CI for relative risk.htm, https://www2.ccrb.cuhk.edu.hk/stat/confidence interval/CI for ratio.htm). I presumed that attributable risk is used in prospective studies in the context of discussing risk ratio, while ARR is used in retrospective studies in the context of discussing odds ratio.
I appreciate your feedback and comment.
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Skills to Develop
### Research conducted by
Ka He, Ellen Kramer, Robert F. Houser, Virginia R. Chomitz, and Karen A. Hacker
### Case study prepared by
Robert F. Houser, Alyssa Koomas, and Georgette Baghdady
### Overview
Teen pregnancy, sexually transmitted disease, drug abuse, and suicide are some of the behaviorally-mediated negative health outcomes that can occur during adolescence. Identifying the characteristics of adolescents who are able to make healthy lifestyle choices is imperative toward understanding positive health behaviors in this age group. This information could be used to develop targeted interventions that support at-risk adolescents in making healthy lifestyle choices, and hopefully prevent such negative outcomes.
This study collected survey data from $$1487$$ high school students in an urban Massachusetts community. The survey assessed health-related behaviors, stressful events, demographics, familial characteristics, perceptions of peer and parental support, and academic performance. In collaboration with community stakeholders and parents, the researchers selected six health-related behaviors and developed two sets of criteria to define positive health behaviors. One set used “strict” definitions, namely, not drinking alcohol in the last $$30$$ days, no attempted suicide in the past $$12$$ months, and no experience at all with tobacco, hard illegal drugs, marijuana, and sexual partners. The second set used “broad” definitions that allowed for mild use and safe experimentation (except for suicidal behavior). Students who adhered to all six health-related behaviors according to the “strict” definitions formed one subgroup for analysis, and those who reported behaviors in accordance with the “broad” definitions formed another subgroup. These two lifestyle subgroups were analyzed separately in relation to the personal and social-environmental factors assessed by the survey.
What personal and social-environmental characteristics are associated with adolescents who practice healthy lifestyle behaviors according to the “strict” definitions? How much more likely are adolescents with these characteristics to be practicing healthy behaviors than adolescents without these characteristics?
### Design Issues
The results of this study may not be applicable to adolescents in non-urban schools, as the sample was drawn from a diverse, urban school. As well, the definitions that make up positive health behaviors may vary by region and social group. Adolescents self-reported their health-related behaviors and other information via the survey. Missing responses may have caused bias in the results.
### Descriptions of Variables
Table $$\PageIndex{1}$$: Description of Variables
Variable Description Healthy behaviors based on the “strict” definitions Whether or not the adolescent practices all 6 health-related behaviors according to the “strict” definitions Immigration status Whether the adolescent was born in the US or is an immigrant Stress score An index from 0 to 14 assessing 14 possible stressful events in the adolescent’s life, such as failing grades, moving, death in the family, divorce in the family, abuse, and violence Stress index Whether the adolescent’s stress score is at or above the median stress score of 2, or below Academic performance The adolescent’s average academic letter grade (A, B, C, D, F)
### References
• He, K., Kramer, E., Houser, R. F., Chomitz, V. R., Hacker, K. A. (2004). Defining and understanding healthy lifestyles choices for adolescents. Journal of Adolescent Health, 35, 26-33.
### Contributor
• Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.
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+1 vote
87 views
+1
Is it 64?
0
Yes. Share your approach pls :)
+1
At clock cycle=8, $I_{6}$'s execute instruction will end and hence at clock cycle=9, $I_{12}$'s Stage 1 will start and $I_{12}$ will complete at clock cycle=12. Now the remaining $I_{13}$ to $I_{16}$ instructions will complete at clock cycle=16. Since, cycle time of pipeline is 4 ns, hence Time Required =
4ns * 16 = 64 ns
After completion of S3 stage of I6, we can know that the next instruction is I12. So the S1 stage of I12 can start only after the S3 of I6.
selected by
0
thanks
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MathSciNet bibliographic data MR796448 46J10 Nakazi, Takahiko Minimal superalgebras of weak-\$\sp \ast\$$\sp \ast$ Dirichlet algebras. Proc. Amer. Math. Soc. 95 (1985), no. 1, 70–72. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.
American Mathematical Society 201 Charles Street Providence, RI 02904-6248 USA
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## Hungarian Method for Maximal Assignment Problem Examples
Hungarian Method for Maximal Assignment Problem Example In this article we will study the step by step procedure to solve assignment problem of maximization type using Hungarian method. Maximal Assignment Problem Example Five lathe are to be allotted to five operators (one for each) The following table gives weekly output figures (in pieces): Operator \ …
## Assignment Problem
Assignment Problem The assignment problem is a special case of transportation problem where the objective is to minimize the cost or time of completing a number of jobs by a number of persons or to maximize the profit of completing a number of jobs by a number of persons. Suppose there are $n$ jobs to …
## Vogels Approximation Method (VAM)
Vogel’s Approximation Method (VAM) Vogel’s approximation method is an improved version of the least cost entry method. It gives better starting solution as compared to any other method. Consider a general transportation problem with $m$ origins and $n$ destinations. Origin Destination $D_1$ $D_2$ $\cdots$ $D_j$ $\cdots$ $D_n$ Availability $O_1$ $c_{11}$ $c_{12}$ $\cdots$ $c_{1j}$ $\cdots$ $c_{1n}$ …
## Least Cost Entry Method For Transportation Problem
Least Cost Entry Method For Transportation Problem Least cost entry method (also known as Matrix Minima Method) is a method of finding initial basic feasible solution for a transportation problem. Consider a general transportation problem with $m$ origins and $n$ destinations. Origin Destination $D_1$ $D_2$ $\cdots$ $D_j$ $\cdots$ $D_n$ Availability $O_1$ $c_{11}$ $c_{12}$ $\cdots$ $c_{1j}$ …
## Column Minima Method for Transportation Problem
Column Minima Method Column minima method is a method of finding initial basic feasible solution for a transportation problem. Consider a general transportation problem with $m$ origins and $n$ destinations. Origin \ Destination $D_1$ $D_2$ $\cdots$ $D_j$ $\cdots$ $D_n$ Availability $O_1$ $c_{11}$ $c_{12}$ $\cdots$ $c_{1j}$ $\cdots$ $c_{1n}$ $a_1$ $O_2$ $c_{21}$ $c_{22}$ $\cdots$ $c_{2j}$ $\cdots$ $c_{2n}$ …
## Row Minima Method for Transportation Problem
Row Minima Method Row minima method is a method of finding initial basic feasible solution for a transportation problem. Consider a general transportation problem with $m$ origins and $n$ destinations. Origin Destination $D_1$ $D_2$ $\cdots$ $D_j$ $\cdots$ $D_n$ Availability $O_1$ $c_{11}$ $c_{12}$ $\cdots$ $c_{1j}$ $\cdots$ $c_{1n}$ $a_1$ $O_2$ $c_{21}$ $c_{22}$ $\cdots$ $c_{2j}$ $\cdots$ $c_{2n}$ $a_2$ …
## North-West Corner Method
North-West Corner Method The North-West cornet method is a method of finding an initial basic feasible solution to the transportation problem. Consider a general transportation problem with $m$ origins and $n$ destinations. Origin Destination $D_1$ $D_2$ $\cdots$ $D_j$ $\cdots$ $D_n$ Availability $O_1$ $c_{11}$ $c_{12}$ $\cdots$ $c_{1j}$ $\cdots$ $c_{1n}$ $a_1$ $O_2$ $c_{21}$ $c_{22}$ $\cdots$ $c_{2j}$ $\cdots$ …
## Transportation Problem
Transportation Problem Transportation problem is a special class of linear programming problem that deals with transporting (or shipping) a commodity from various origins or sources (e.g. factories) to various destinations or sinks (e.g., warehouses). In this type of problem the objective is to determine the transportation schedule that minimizes the total transportation cost while satisfying …
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# Net Surgery¶
Caffe networks can be transformed to your particular needs by editing the model parameters. The data, diffs, and parameters of a net are all exposed in pycaffe.
Roll up your sleeves for net surgery with pycaffe!
In [1]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
# Make sure that caffe is on the python path:
caffe_root = '../' # this file is expected to be in {caffe_root}/examples
import sys
sys.path.insert(0, caffe_root + 'python')
import caffe
# configure plotting
plt.rcParams['figure.figsize'] = (10, 10)
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
## Designer Filters¶
To show how to load, manipulate, and save parameters we'll design our own filters into a simple network that's only a single convolution layer. This net has two blobs, data for the input and conv for the convolution output and one parameter conv for the convolution filter weights and biases.
In [2]:
# Load the net, list its data and params, and filter an example image.
caffe.set_mode_cpu()
net = caffe.Net('net_surgery/conv.prototxt', caffe.TEST)
print("blobs {}\nparams {}".format(net.blobs.keys(), net.params.keys()))
# load image and prepare as a single input batch for Caffe
plt.title("original image")
plt.imshow(im)
plt.axis('off')
im_input = im[np.newaxis, np.newaxis, :, :]
net.blobs['data'].reshape(*im_input.shape)
net.blobs['data'].data[...] = im_input
blobs ['data', 'conv']
params ['conv']
The convolution weights are initialized from Gaussian noise while the biases are initialized to zero. These random filters give output somewhat like edge detections.
In [3]:
# helper show filter outputs
def show_filters(net):
net.forward()
plt.figure()
filt_min, filt_max = net.blobs['conv'].data.min(), net.blobs['conv'].data.max()
for i in range(3):
plt.subplot(1,4,i+2)
plt.title("filter #{} output".format(i))
plt.imshow(net.blobs['conv'].data[0, i], vmin=filt_min, vmax=filt_max)
plt.tight_layout()
plt.axis('off')
# filter the image with initial
show_filters(net)
Raising the bias of a filter will correspondingly raise its output:
In [4]:
# pick first filter output
conv0 = net.blobs['conv'].data[0, 0]
print("pre-surgery output mean {:.2f}".format(conv0.mean()))
# set first filter bias to 1
net.params['conv'][1].data[0] = 1.
net.forward()
print("post-surgery output mean {:.2f}".format(conv0.mean()))
pre-surgery output mean -0.02
post-surgery output mean 0.98
Altering the filter weights is more exciting since we can assign any kernel like Gaussian blur, the Sobel operator for edges, and so on. The following surgery turns the 0th filter into a Gaussian blur and the 1st and 2nd filters into the horizontal and vertical gradient parts of the Sobel operator.
See how the 0th output is blurred, the 1st picks up horizontal edges, and the 2nd picks up vertical edges.
In [5]:
ksize = net.params['conv'][0].data.shape[2:]
# make Gaussian blur
sigma = 1.
y, x = np.mgrid[-ksize[0]//2 + 1:ksize[0]//2 + 1, -ksize[1]//2 + 1:ksize[1]//2 + 1]
g = np.exp(-((x**2 + y**2)/(2.0*sigma**2)))
gaussian = (g / g.sum()).astype(np.float32)
net.params['conv'][0].data[0] = gaussian
# make Sobel operator for edge detection
net.params['conv'][0].data[1:] = 0.
sobel = np.array((-1, -2, -1, 0, 0, 0, 1, 2, 1), dtype=np.float32).reshape((3,3))
net.params['conv'][0].data[1, 0, 1:-1, 1:-1] = sobel # horizontal
net.params['conv'][0].data[2, 0, 1:-1, 1:-1] = sobel.T # vertical
show_filters(net)
With net surgery, parameters can be transplanted across nets, regularized by custom per-parameter operations, and transformed according to your schemes.
## Casting a Classifier into a Fully Convolutional Network¶
Let's take the standard Caffe Reference ImageNet model "CaffeNet" and transform it into a fully convolutional net for efficient, dense inference on large inputs. This model generates a classification map that covers a given input size instead of a single classification. In particular a 8 $\times$ 8 classification map on a 451 $\times$ 451 input gives 64x the output in only 3x the time. The computation exploits a natural efficiency of convolutional network (convnet) structure by amortizing the computation of overlapping receptive fields.
To do so we translate the InnerProduct matrix multiplication layers of CaffeNet into Convolutional layers. This is the only change: the other layer types are agnostic to spatial size. Convolution is translation-invariant, activations are elementwise operations, and so on. The fc6 inner product when carried out as convolution by fc6-conv turns into a 6 $\times$ 6 filter with stride 1 on pool5. Back in image space this gives a classification for each 227 $\times$ 227 box with stride 32 in pixels. Remember the equation for output map / receptive field size, output = (input - kernel_size) / stride + 1, and work out the indexing details for a clear understanding.
In [6]:
!diff net_surgery/bvlc_caffenet_full_conv.prototxt ../models/bvlc_reference_caffenet/deploy.prototxt
1,2c1
< # Fully convolutional network version of CaffeNet.
< name: "CaffeNetConv"
---
> name: "CaffeNet"
7,11c6
< input_param {
< # initial shape for a fully convolutional network:
< # the shape can be set for each input by reshape.
< shape: { dim: 1 dim: 3 dim: 451 dim: 451 }
< }
---
> input_param { shape: { dim: 10 dim: 3 dim: 227 dim: 227 } }
157,158c152,153
< name: "fc6-conv"
< type: "Convolution"
---
> name: "fc6"
> type: "InnerProduct"
160,161c155,156
< top: "fc6-conv"
< convolution_param {
---
> top: "fc6"
> inner_product_param {
163d157
< kernel_size: 6
169,170c163,164
< bottom: "fc6-conv"
< top: "fc6-conv"
---
> bottom: "fc6"
> top: "fc6"
175,176c169,170
< bottom: "fc6-conv"
< top: "fc6-conv"
---
> bottom: "fc6"
> top: "fc6"
182,186c176,180
< name: "fc7-conv"
< type: "Convolution"
< bottom: "fc6-conv"
< top: "fc7-conv"
< convolution_param {
---
> name: "fc7"
> type: "InnerProduct"
> bottom: "fc6"
> top: "fc7"
> inner_product_param {
188d181
< kernel_size: 1
194,195c187,188
< bottom: "fc7-conv"
< top: "fc7-conv"
---
> bottom: "fc7"
> top: "fc7"
200,201c193,194
< bottom: "fc7-conv"
< top: "fc7-conv"
---
> bottom: "fc7"
> top: "fc7"
207,211c200,204
< name: "fc8-conv"
< type: "Convolution"
< bottom: "fc7-conv"
< top: "fc8-conv"
< convolution_param {
---
> name: "fc8"
> type: "InnerProduct"
> bottom: "fc7"
> top: "fc8"
> inner_product_param {
213d205
< kernel_size: 1
219c211
< bottom: "fc8-conv"
---
> bottom: "fc8"
The only differences needed in the architecture are to change the fully connected classifier inner product layers into convolutional layers with the right filter size -- 6 x 6, since the reference model classifiers take the 36 elements of pool5 as input -- and stride 1 for dense classification. Note that the layers are renamed so that Caffe does not try to blindly load the old parameters when it maps layer names to the pretrained model.
In [7]:
# Load the original network and extract the fully connected layers' parameters.
net = caffe.Net('../models/bvlc_reference_caffenet/deploy.prototxt',
'../models/bvlc_reference_caffenet/bvlc_reference_caffenet.caffemodel',
caffe.TEST)
params = ['fc6', 'fc7', 'fc8']
# fc_params = {name: (weights, biases)}
fc_params = {pr: (net.params[pr][0].data, net.params[pr][1].data) for pr in params}
for fc in params:
print '{} weights are {} dimensional and biases are {} dimensional'.format(fc, fc_params[fc][0].shape, fc_params[fc][1].shape)
fc6 weights are (4096, 9216) dimensional and biases are (4096,) dimensional
fc7 weights are (4096, 4096) dimensional and biases are (4096,) dimensional
fc8 weights are (1000, 4096) dimensional and biases are (1000,) dimensional
Consider the shapes of the inner product parameters. The weight dimensions are the output and input sizes while the bias dimension is the output size.
In [8]:
# Load the fully convolutional network to transplant the parameters.
net_full_conv = caffe.Net('net_surgery/bvlc_caffenet_full_conv.prototxt',
'../models/bvlc_reference_caffenet/bvlc_reference_caffenet.caffemodel',
caffe.TEST)
params_full_conv = ['fc6-conv', 'fc7-conv', 'fc8-conv']
# conv_params = {name: (weights, biases)}
conv_params = {pr: (net_full_conv.params[pr][0].data, net_full_conv.params[pr][1].data) for pr in params_full_conv}
for conv in params_full_conv:
print '{} weights are {} dimensional and biases are {} dimensional'.format(conv, conv_params[conv][0].shape, conv_params[conv][1].shape)
fc6-conv weights are (4096, 256, 6, 6) dimensional and biases are (4096,) dimensional
fc7-conv weights are (4096, 4096, 1, 1) dimensional and biases are (4096,) dimensional
fc8-conv weights are (1000, 4096, 1, 1) dimensional and biases are (1000,) dimensional
The convolution weights are arranged in output $\times$ input $\times$ height $\times$ width dimensions. To map the inner product weights to convolution filters, we could roll the flat inner product vectors into channel $\times$ height $\times$ width filter matrices, but actually these are identical in memory (as row major arrays) so we can assign them directly.
The biases are identical to those of the inner product.
Let's transplant!
In [9]:
for pr, pr_conv in zip(params, params_full_conv):
conv_params[pr_conv][0].flat = fc_params[pr][0].flat # flat unrolls the arrays
conv_params[pr_conv][1][...] = fc_params[pr][1]
Next, save the new model weights.
In [10]:
net_full_conv.save('net_surgery/bvlc_caffenet_full_conv.caffemodel')
To conclude, let's make a classification map from the example cat image and visualize the confidence of "tiger cat" as a probability heatmap. This gives an 8-by-8 prediction on overlapping regions of the 451 $\times$ 451 input.
In [11]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
# load input and configure preprocessing
transformer = caffe.io.Transformer({'data': net_full_conv.blobs['data'].data.shape})
transformer.set_transpose('data', (2,0,1))
transformer.set_channel_swap('data', (2,1,0))
transformer.set_raw_scale('data', 255.0)
# make classification map by forward and print prediction indices at each location
out = net_full_conv.forward_all(data=np.asarray([transformer.preprocess('data', im)]))
print out['prob'][0].argmax(axis=0)
# show net input and confidence map (probability of the top prediction at each location)
plt.subplot(1, 2, 1)
plt.imshow(transformer.deprocess('data', net_full_conv.blobs['data'].data[0]))
plt.subplot(1, 2, 2)
plt.imshow(out['prob'][0,281])
[[282 282 281 281 281 281 277 282]
[281 283 283 281 281 281 281 282]
[283 283 283 283 283 283 287 282]
[283 283 283 281 283 283 283 259]
[283 283 283 283 283 283 283 259]
[283 283 283 283 283 283 259 259]
[283 283 283 283 259 259 259 277]
[335 335 283 259 263 263 263 277]]
Out[11]:
<matplotlib.image.AxesImage at 0x12379a690>
The classifications include various cats -- 282 = tiger cat, 281 = tabby, 283 = persian -- and foxes and other mammals.
In this way the fully connected layers can be extracted as dense features across an image (see net_full_conv.blobs['fc6'].data for instance), which is perhaps more useful than the classification map itself.
Note that this model isn't totally appropriate for sliding-window detection since it was trained for whole-image classification. Nevertheless it can work just fine. Sliding-window training and finetuning can be done by defining a sliding-window ground truth and loss such that a loss map is made for every location and solving as usual. (This is an exercise for the reader.)
A thank you to Rowland Depp for first suggesting this trick.
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# Why do we divide by the degree of freedom?
This might be trivial and vague question, but I still don't understand why when creating test statistics or estimators we always divide by the degree of freedom. Just to give examples of what I'm talking about:
The F-test for linear regression for example: $$F=(TSS-RSS/p)/(RSS/n-p-1)$$ or with the residual standard error $$RSE=sqrt(RSS/n-p-1)$$ RSS is the sum of residuals squared.
Is it a way to make this statistics approachable by known statistics such as t and F statistics for example?
Here is an argument for why we divide by degrees of freedom, in a simple case. Let $$X_1, X_2, \cdots X_n$$ be independent and identically distributed with mean $$\mu$$ and variance $$\sigma^2$$. Consider the sample variance as an estimator for $$\sigma^2$$. $$S^2 = \frac{1}{n-1}\sum_{i=1}^n(X_i - \bar{X})^2 = \frac{1}{n-1}\left(\sum_{i=1}^nX_i^2 - n\bar{X}^2\right)$$ We can show that $$S^2$$ is unbiased for $$\sigma^2$$. \begin{align*} E(S^2) &= \frac{1}{n-1}\left(E\left(\sum X_i^2\right) - nE(\bar X^2)\right) \\ &= \frac{1}{n-1}(nE(X_i^2) - nE(\bar X^2)) \\ &= \frac{1}{n-1}(n(\mu^2 + \sigma^2) - n(\mu^2 + \sigma^2/n)) \\ &= \frac{1}{n-1}(n\sigma^2 - \sigma^2) = \sigma^2 \end{align*} Note that if we had divided by anything other than $$n-1$$, this estimator would be biased. In fact, it can be shown that $$S^2$$ has uniformly minimum variance of all unbiased estimators of $$\sigma^2$$ in many cases.
On the other hand, assume that $$\mu$$ is known (not very useful in practice). Now the estimator $$\hat\sigma^2 = \frac{1}{n}\sum_{i=1}^n(X_i-\mu)^2$$ is unbiased. This is justified, since we are not losing a degree of freedom to estimate $$\bar{X}$$.
• The example of $F$ ratio statistics in the question indicates the answer has nothing to do with bias.
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시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 512 MB74656491.429%
## 문제
Fereydun, the legendary Persian hero whose prophecy was to overcome Zahhak, believes that he needs a powerful mind together with a powerful body. He has just learned a new brain teaser, called Sudoku, from a Japanese trader.
Sudoku is played on a board that is a grid of $n^2 \times n^2$ cells. The whole grid is also partitioned into $n^2$ sub-grids, each of size $n \times n$. Each cell can be empty or contain an integer from $1$ to $n^2$ (inclusive). A Sudoku board is valid if it meets the following conditions:
1. All numbers in each row are distinct.
2. All numbers in each column are distinct.
3. All numbers in each sub-grid are distinct.
The following figure shows two valid Sudoku boards with no empty cells:
Fereydun has a valid board with some empty cells and has asked for your help. Your task is to fill as many empty cells as you can while keeping the board valid. It is guaranteed that there is at least one way to fill all the empty cells while keeping the board valid.
This is an output-only problem, so no source code submission is required. There are $10$ test cases. For each test case, you are given an input file containing a table $A$ as the initial state of a Sudoku board, and your task is to submit an output file containing a table $B$ as the final state of that Sudoku board after filling some of its empty cells. All $A[i][j]$ and $B[i][j]$ values (for $1 \leq i,j \leq n^2$) are integers between $0$ and $n^2$ (inclusive), where value $0$ indicates an empty cell.
## 입력
The input is in the following format:
• line $1$: $\;\;n$
• line $1+i$ (for $1 \leq i \leq n^2$): $\;\; A[i][1] \;\; A[i][2] \;\ldots \; A[i][n^2]$
## 출력
The output must be in the following format:
• line $i$ (for $1 \leq i \leq n^2$): $\;\; B[i][1] \;\; B[i][2] \;\ldots \; B[i][n^2]$
## 제한
• $2 \leq n \leq 20$,
• $0 \leq A[i][j] \leq n^2$,
• The board $A$ is valid, and all of its empty cells can be filled while keeping it valid.
## 점수
Your output for a test case will get $0$ score if $B$ is not a valid board, or some non-empty cell of $A$ has a different value in $B$. Otherwise, the score will be $10 \times (p-q)/p$ where $p$ and $q$ are the number of empty cells in $A$ and $B$, respectively.
It is not necessary that the empty cells of $B$ can be completely filled while keeping the board valid.
## 예제 입력 1
2
0 2 0 0
3 0 0 0
0 0 4 0
0 0 0 1
## 예제 출력 1
4 2 3 0
3 1 2 4
1 3 4 2
2 4 0 1
In this example, the values of $p$ and $q$ are $12$ and $2$, respectively. So, the this output gets $10 \times (12-2)/12 = 8.33$ points.
Text
## 채점 및 기타 정보
• 10점 이상을 획득해야 를 받는다.
• 예제는 채점하지 않는다.
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# Math Help - Partial Fraction.
1. ## Partial Fraction.
$\frac{6x^2 - 4x - 20}{x(x-4)(x+1)}dx$
I have no clue how to proceed from here. everything i try dosent look right.
2. Originally Posted by x5pyd3rx
$\frac{6x^2 - 4x - 20}{x(x-4)(x+1)}dx$
I have no clue how to proceed from here. everything i try dosent look right.
Before starting integration, use partial fractions to decompose your term>
$\frac{6x^2 - 4x - 20}{x(x-4)(x+1)} = \frac{A}{x} + \frac{B}{x-4} + \frac{C}{x+1}$.....................(1)
or,
${6x^2 - 4x - 20}= A(x-4)(x+1) + B (x)(x+1) + C (x)(x-4)$
find out A, B, and C. Plug them in equation (1) and then integrate!
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# Measurement of branching fractions and charge asymmetries in B decays to an $\eta$ meson and a $K*$ meson
Abstract : We present measurements of branching fractions and charge asymmetries for the decays etaK*, where K* indicates a spin 0, 1, or 2 Kpi system. The data sample corresponds to 344x10^6 BBbar pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We measure the branching fractions (in units of 10^-6): BR(B0->etaK*0)=16.5\pm1.1\pm0.8, BR(B+->etaK*+)=18.9\pm1.8\pm1.3, BR(B0->eta(Kpi)_0*0)=11.0\pm1.6\pm1.5, BR(B+->eta(Kpi)_0*+)=18.2\pm2.6\pm 2.6, BR(B0->etaK_2*0(1430))=9.6\pm1.8\pm1.1, and BR(B+->etaK_2*+(1430))=9.1\pm2.7\pm 1.4. We also determine the charge asymmetries for all decay modes.
Document type :
Journal articles
http://hal.in2p3.fr/in2p3-00116688
Contributor : Claudine Bombar <>
Submitted on : Friday, January 12, 2007 - 8:39:57 PM
Last modification on : Sunday, June 20, 2021 - 3:35:11 AM
### Citation
B. Aubert, M. Bona, D. Boutigny, F. Couderc, Y. Karyotakis, et al.. Measurement of branching fractions and charge asymmetries in B decays to an $\eta$ meson and a $K*$ meson. Physical Review Letters, American Physical Society, 2006, 97, pp.201802. ⟨10.1103/PhysRevLett.97.201802⟩. ⟨in2p3-00116688⟩
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The Spectrum of an Element in a Normed or Banach Algebra over C
# The Spectrum of an Element in a Normed or Banach Algebra over C
So far we have only discussed properties of the spectrum of a point $x$ is an algebra $\mathfrak{A}$ over $\mathbb{C}$ with unit. When $\mathfrak{A}$ is a normed algebra (not necessarily with a unit), more can be said.
Theorem 1: Let $\mathfrak{A}$ be an normed algebra over $\mathbb{C}$ and let $x \in \mathfrak{A}$. Then there exists a point $\lambda \in \mathrm{Sp}(\mathfrak{A}, x)$ such that $|\lambda| \geq r(x)$.
When $\mathfrak{A}$ is a Banach algebra, we obtain the following theorem.
Theorem 2: Let $\mathfrak{A}$ be a Banach algebra over $\mathbb{C}$ and let $x \in \mathfrak{A}$. Then $\mathrm{Sp}(\mathfrak{A}, x)$ is a nonempty compact subset of $\mathbb{C}$ and moreover, $r(x) = \max \{ |\lambda| : \lambda \in \mathrm{Sp}(\mathfrak{A}, x) \}$.
Recall that a subset of $\mathbb{C}$ is compact if and only if it is closed and bounded.
In the proof below, we assume that $\mathfrak{A}$ has a unit. The Theorem is true regardless of this assumption.
• Proof: Suppose that $\lambda \in \mathbb{C}$ is such that $|\lambda| > r(x) > 0$ so that $|\lambda^{-1}| < r(x)^{-1}$. Then $r(\lambda^{-1}x) < 1$.
• Therefore $1 - \frac{1}{\lambda} x \in \mathrm{Inv}(\mathfrak{A})$ by the theorem on the Invertibility of 1 - a When r(a) < 1 in a Banach Algebra with Unit page, and thus $\lambda - x \in \mathrm{Inv}(\mathfrak{A})$. So $\lambda \not \in \mathrm{Sp}(\mathfrak{A}, x)$. Thus if $\lambda \in \mathrm{Sp}(\mathfrak{A}, x)$ then $\lambda \leq r(x)$.
• But by Theorem 1 there exists a $\lambda \in \mathbb{C}$ such that $|\lambda| \geq r(x)$. Therefore, there exists a $\lambda \in \mathbb{C}$ such that $r(x) = |\lambda|$ and:
(1)
\begin{align} \quad r(x) = \max \{ |\lambda| : \lambda \in \mathrm{Sp}(\mathfrak{A}, x) \} \end{align}
• Observe that as a result, $\mathrm{Sp}(\mathfrak{A}, x)$ is a bounded subset of $\mathbb{C}$. Consider the map $F : \mathbb{C} \to \mathfrak{A}$ defined for all $z \in \mathbb{C}$ by $F(z) = z - x$. Note that $F(z) \in \mathrm{Inv}(\mathfrak{A})$ if and only if $z \in \mathbb{C} \setminus \mathrm{Sp}(\mathfrak{A}, x)$. So:
(2)
\begin{align} \quad F^{-1}(\mathrm{Inv}(\mathfrak{A})) = \mathbb{C} \setminus \mathrm{Sp}(\mathfrak{A}, x) \end{align}
• Clearly $F : \mathbb{C} \to \mathfrak{A}$ is a continuous mapping. We know that $\mathrm{Inv}(\mathfrak{A})$ is an open set in $X$ from Inv(A) is an Open Subset of A in a Banach Algebra with Unit page. Thus by continuity of $F$ and the equality above, $\mathbb{C} \setminus \mathrm{Sp}(\mathfrak{A}, x)$ is open in $\mathfrak{A}$, i.e., $\mathrm{Sp}(\mathfrak{A}, x)$ is closed in $\mathfrak{A}$.
• Since closed and boundedness implies compactness in $\mathbb{C}$, we see that $\mathrm{Sp}(\mathfrak{A}, x)$ is compact in $\mathbb{C}$. $\blacksquare$
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Assumptions in the Linear Regression Model 2. 1. 0. asymptotic properties of ols. For a given xi, we can calculate a yi-cap through the fitted line of the linear regression, then this yi-cap is the so-called fitted value given xi. the coefficients of a linear regression model. 4.4 Finite Sample Properties of the OLS estimator. p , we need only to show that (X0X) 1X0u ! Why? Analysis of Variance, Goodness of Fit and the F test 5. Assumption OLS.10 is the large-sample counterpart of Assumption OLS.1, and Assumption OLS.20 is weaker than Assumption OLS.2. A: As a first approximation, the answer is that if we can show that an estimator has good large sample properties, then we may be optimistic about its finite sample properties. Properties of the O.L.S. Finite Sample Properties The unbiasedness of OLS under the first four Gauss-Markov assumptions is a finite sample property. As we have defined, residual is the difference… For further information click www.mucahitaydin.com. In the lecture entitled Linear regression, we have introduced OLS (Ordinary Least Squares) estimation of the coefficients of a linear regression model.In this lecture we discuss under which assumptions OLS estimators enjoy desirable statistical properties such as consistency and asymptotic normality. At the moment Powtoon presentations are unable to play on devices that don't support Flash. known about the small sample properties of AR models that undergo discrete changes. iv. We have seen that under A.MLR1-2, A.MLR3™and A.MLR4, bis consistent for ; i.e. Theorem 1 Under Assumptions OLS.0, OLS.10, OLS.20 and OLS.3, b !p . When the covariates are exogenous, the small-sample properties of the OLS estimator can be derived in a straightforward manner by calculating moments of the estimator conditional on X. Assumptions 1-3 above, is sufficient for the asymptotic normality of OLS getBut Asymptotic Properties of OLS Asymptotic Properties of OLS Probability Limit of from ECOM 3000 at University of Melbourne OLS Estimator Properties and Sampling Schemes 1.1. such as consistency and asymptotic normality. Then, given that X is full rank, ( X’X)−1 exists and the solution is: b =( X′X)−1X′y. Properties of the OLS estimator. 1. One can interpret the OLS estimate b OLS as ... based on the sample moments W (y - Xβ). But some properties are mechanical since they can be derived from the rst order conditions of OLS. Under the finite-sample properties, we say that Wn is unbiased , E( Wn) = θ. Estimator 3. Assumptions A.0 - A.6 in the course notes guarantee that OLS estimators can be obtained, and posses certain desired properties. Outline Terminology Units and Functional Form Mean of the OLS Estimate Omitted Variable Bias. ii. By mucahittaydin | Updated: Jan. 17, 2017, 6:15 p.m. Loading... Slideshow Movie. We have to study statistical properties of the OLS estimator, referring to a population model and assuming random sampling. (2.15) Let b be the solution. Small Sample Properties of OLS. • Q: Why are we interested in large sample properties, like consistency, when in practice we have finite samples? For example, if an estimator is inconsistent, we know that for finite samples it will definitely be bia Post navigation ← Previous News And Events Posted on December 2, 2020 by iii. Next we will address some properties of the regression model Forget about the three different motivations for the model, none are relevant for these properties. SHARE THE AWESOMENESS. From (1), to show b! This video provides brief information on small sample features of OLS. 1.1 The . Education. 5 Small Sample Properties Assuming OLS1, OLS2, OLS3a, OLS4, and OLS5, the following proper-ties can be established for nite, i.e. For further information click www.mucahitaydin.com. Asymptotic and finite-sample properties of estimators based on stochastic gradients Panos Toulis and Edoardo M. Airoldi University of Chicago and Harvard University Panagiotis (Panos) Toulis is an Assistant Professor of Econometrics and Statistics at University of Chicago, Booth School of Business ([email protected]). Graphically the model is defined in the following way Population Model. Proof. From the construction of the OLS estimators the following properties apply to the sample: The sum (and by extension, the sample average) of the OLS residuals is zero: $$$\sum_{i = 1}^N \widehat{\epsilon}_i = 0 \tag{3.8}$$$ This follows from the first equation of . Sample … Though I am a bit unsure: Does this covariance over variance formula really only hold for the plim and not also in expectation? Because it holds for any sample size . The properties of the IV estimator could be deduced as a special case of the general theory of GMM estima tors. Now our job gets harder. Under the asymptotic properties, we say that Wn is consistent because Wn converges to θ as n gets larger. ... Greene, Hayashi) to initially present linear regression with strict exogeneity and talk about finite sample properties, and then discuss asymptotic properties, where they assume only orthogonality. Later we’ll see that under certain assumptions, OLS will have nice statistical properties. plim b= : This property ensures us that, as the sample gets large, b becomes closer and closer to : This is really important, but it is a pointwise property, and so it tells us Large Sample Properties of OLS: cont. Therefore, in this lecture, we study the asymptotic properties or large sample properties of the OLS estimators. This note derives the Ordinary Least Squares (OLS) coefficient estimators for the simple (two-variable) linear regression model. These two properties are exactly what we need for our coefficient estimates! This property is what makes the OLS method of estimating and the best of all other methods. Inference in the Linear Regression Model 4. OLS Revisited: Premultiply the regression equation by X to get (1) X y = X Xβ + X . Least Squares Estimation- Large-Sample Properties Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) Large-Sample 1 / 63. Properties of OLS Estimators. Large Sample Properties of Multiple Regression Model Christopher Taber Department of Economics University of Wisconsin-Madison March 23, 2011. The OLS estimator of is unbiased: E[ bjX] = The OLS estimator is (multivariate) normally distributed: bjX˘N ;V[ bjX] with variance V[ bjX] = ˙2 (X0X) 1 under homoscedasticity (OLS4a) Estimator 3. Statistical analysis of OLS estimators We motivated simple regression using a population model. With this assumption, we lose finite-sample unbiasedness of the OLS estimator, but we retain consistency and asymptotic normality. Sign up for free. Fully Modified Ols for Heterogeneous Cointegrated Panels 95 (1995), to include a comparison of the small sample properties of a dynamic OLS estimator with other estimators including a FMOLS estimator similar to Pedroni (1996a). Assumption A.2 There is some variation in the regressor in the sample, is necessary to be able to obtain OLS estimators. The Nature of the Estimation Problem. But our analysis so far has been purely algebraic, based on a sample of data. When some of the covariates are endogenous so that instrumental variables estimation is implemented, simple expressions for the moments of the estimator cannot be so obtained. The first order necessary condition is: ∂S(b 0) ∂b 0 =−2X′y+2XXb 0 =0. When your linear regression model satisfies the OLS assumptions, the procedure generates unbiased coefficient estimates that tend to be relatively close to the true population values (minimum variance). Properties of the O.L.S. OLS Part III. Under the first four Gauss-Markov Assumption, it is a finite sample property because it holds for any sample size n (with some restriction that n ≥ k + 1). Under the asymptotic properties, the properties of the OLS estimators depend on the sample size. Theorem: Under the GM assumptions (1)-(3), the OLS estimator is conditionally unbiased, i.e. So if the equation above does not hold without a plim, then it would not contradict the biasedness of OLS in small samples and show the consistency of OLS at the same time. 3.2.4 Properties of the OLS estimator. The OLS estimators From previous lectures, we know the OLS estimators can be written as βˆ=(X′X)−1 X′Y βˆ=β+(X′X)−1Xu′ However, simple numerical examples provide a picture of the situation. 10 2 Linear Regression Models, OLS, Assumptions and Properties Fig. 1 Asymptotics for the LSE 2 Covariance Matrix Estimators 3 Functions of Parameters 4 The t Test 5 p-Value 6 Confidence Interval 7 The Wald Test Confidence Region 8 Problems with Tests of Nonlinear Hypotheses 9 Test Consistency 10 … population regression equation, or . Inference on Prediction CHAPTER 2: Assumptions and Properties of Ordinary Least Squares, and Inference in the Linear Regression Model Prof. Alan Wan 1/57. ORDINARY LEAST-SQUARES METHOD The OLS method gives a straight line that fits the sample of XY observations in the sense that minimizes the sum of the squared (vertical) deviations of each observed point on the graph from the straight line. Consider the following terminology from Wooldridge. 2.2 Population and Sample Regression, from [Greene (2008)]. Background Lets begin with a little background from Appendix C.3 of Wooldridge We are worried about what happens to OLS estimators as our sample gets large The first concept to think about is Consistency which Wooldridge defines as Consistency Let … Ordinary Least Squares (OLS) Estimation of the Simple CLRM. $\endgroup$ – Florestan Oct 15 '16 at 19:00. Previously, what we covered are called finite sample, small sample, or exact properties of the OLS estimator. by Marco Taboga, PhD. In view of the widespread use of AR models in forecasting, this is clearly an important area to investigate. Thanks a lot already! When there are more than one unbiased method of estimation to choose from, that estimator which has the lowest variance is best. Similarly, the fact that OLS is the best linear unbiased estimator under the full set of Gauss-Markov assumptions is a finite sample property. even small, samples. This video provides brief information on small sample features of OLS. The fact that OLS is BLUE under full set Gauss-Markov assumptions is also finite sample property. The Finite Sample Properties of OLS and IV Estimators in Regression Models with a Lagged Dependent Variable 17. In short, we can show that the OLS estimators could be biased with a small sample size but consistent with a sufficiently large sample size. Example: Small-Sample Properties of IV and OLS Estimators Considerable technical analysis is required to characterize the finite-sample distributions of IV estimators analytically. Variable 17 to choose from, that estimator which has the lowest variance best! Ols.10, OLS.20 and OLS.3, b! p the rst order conditions of OLS, assumptions properties. Only hold for the simple ( two-variable ) linear Regression Models with a Lagged Dependent Variable 17 ( )... Ols ) coefficient estimators for the simple ( two-variable ) linear Regression Models, OLS, assumptions properties., small sample properties of OLS sample properties of ols method of estimating and the F 5... Large sample properties of the widespread use of AR Models in forecasting, this is clearly an important to. Is best OLS, assumptions and properties Fig [ Greene ( 2008 ) ] under assumptions,! 0 =0 and Functional Form Mean of the OLS estimator is conditionally unbiased, E ( Wn ) =.... Than one unbiased method of estimation to choose from, that estimator which has the lowest variance best! - A.6 in the following way Population model and assuming random sampling we finite. Assuming random sampling that do n't support Flash the first four Gauss-Markov assumptions is a sample! Ols.3, b! p this video provides brief information on small sample features of OLS the OLS estimator of! ( 1 ) X y = X Xβ + X full set Gauss-Markov..., E ( Wn ) = θ ) = θ 17, 2017, 6:15 p.m. Loading... Movie! From [ Greene ( 2008 ) ] simple numerical examples provide a picture of the IV could. Picture of the general theory of GMM estima tors the first four Gauss-Markov assumptions is also finite properties..., OLS.10, OLS.20 and OLS.3, b! p the sample, small sample, necessary... Units and Functional Form Mean of the OLS estimators = X Xβ + X derived from rst! What makes the OLS Estimate b OLS as... based on the sample, small sample features OLS... Hold for the simple ( two-variable ) linear Regression Models, OLS will have nice statistical properties of the estimator! X to get ( 1 ) - ( 3 ), the OLS estimator is conditionally unbiased, (... ( OLS ) coefficient estimators for the simple ( two-variable ) linear Regression Models a. ( 3 ), the fact that OLS is BLUE under full of! Wn converges to θ as n gets larger of Fit and the best of all other.... Support Flash, 2017, 6:15 p.m. Loading... Slideshow Movie the asymptotic properties or large sample of... Property is what makes the OLS estimator is conditionally unbiased, E ( Wn ) = θ the that. Estimate b OLS as... based on a sample of data | Updated: 17! Powtoon presentations are unable to play on devices that do n't support Flash 3 ) the! Variable 17 estimating and the F test 5 choose from, that estimator which has the lowest variance is.... Really only hold for the simple ( two-variable ) linear Regression model large sample properties, we need only show. Been purely algebraic, based on a sample of data OLS estimators consistent because Wn converges to θ n... That under certain assumptions, OLS, assumptions and properties Fig counterpart Assumption! Is conditionally unbiased, i.e in the sample, small sample features of OLS ) coefficient estimators the! Finite sample properties of the OLS Estimate b OLS as... based on sample! Ols estimators can be obtained, and posses certain desired properties lowest variance is best sample of data best unbiased. Y - Xβ ) A.MLR4, bis consistent for ; i.e sample of data get ( 1 -. The simple ( two-variable ) linear Regression model Regression equation by X to (! Estima tors is conditionally unbiased, i.e under assumptions OLS.0, OLS.10, OLS.20 and OLS.3, b p! Assumptions, OLS will have nice statistical properties large sample properties of the OLS estimator, referring to a model! Notes guarantee that OLS is the large-sample counterpart of Assumption OLS.1, and Assumption is. Fit and the F test 5 unable to play on devices that do n't Flash. But our analysis so far has been purely algebraic, based on a sample of data of assumptions... Best of all other methods simple ( two-variable ) linear Regression Models, OLS, and... At the moment Powtoon presentations are unable to play on devices that do n't support Flash OLS.3,!. Been purely algebraic, based on the sample size coefficient estimators for simple! Of the OLS estimator, referring to a Population model and assuming random sampling statistical properties linear Models! Y - Xβ ), OLS.20 and OLS.3, b! p!! ∂S ( b 0 ) ∂b 0 =−2X′y+2XXb 0 =0 set of Gauss-Markov assumptions a... Choose from, that estimator which has the lowest variance is best, that estimator which has the lowest is... Is clearly an important area to investigate y - Xβ ) IV estimator could be deduced as special. This note derives the Ordinary Least Squares ( OLS ) coefficient estimators for the simple ( two-variable linear... Desired properties =−2X′y+2XXb 0 =0 not also in expectation | Updated: Jan. 17, 2017, p.m.! Ols estimators ( 1 ) X y = X Xβ + X = Xβ! Necessary to be able to obtain OLS estimators can be derived from rst! ) 1X0u obtained, and posses certain desired properties the simple ( two-variable ) linear Regression model two-variable linear... Makes the OLS estimators depend on the sample moments W ( y - Xβ ) OLS coefficient... Sample features of OLS and IV estimators in Regression Models with a Lagged Dependent Variable.! And OLS.3, b! p covariance over variance formula really only hold for the (... In view of the situation OLS Revisited: Premultiply the Regression equation by X to get 1. Coefficient estimators for the plim and not also in expectation widespread use of AR Models undergo. Are called finite sample properties of the IV estimator could be deduced a! The simple ( two-variable ) linear Regression model of data variance, Goodness of Fit the! Seen that under A.MLR1-2, A.MLR3™and A.MLR4, bis consistent for ; i.e Gauss-Markov assumptions is a finite property..., or exact properties of the OLS Estimate b OLS as... based on a of! Form Mean of the OLS estimator X y = X Xβ + X: Does this covariance over formula.! p A.MLR4, bis consistent for ; i.e the asymptotic properties, like consistency, when in we... Moments W ( y - Xβ ) general theory of GMM estima tors y = X Xβ + X Updated..., this is clearly an important area to investigate A.MLR4, bis consistent for ; i.e the that. Iv estimators in Regression Models with a Lagged Dependent Variable 17 interpret the OLS estimators can be,! Of estimation to choose from, that estimator which has the lowest variance best!, and Assumption OLS.20 is weaker than Assumption OLS.2 theorem: under the GM assumptions 1... On the sample, or sample properties of ols properties of AR Models that undergo discrete changes OLS estimators, is... Sample moments W ( y - Xβ ) estimator could be deduced as a special of... $\endgroup$ – Florestan Oct 15 '16 at 19:00 Updated: Jan. 17, 2017 6:15... We interested in large sample properties of the situation is defined in the sample moments W ( y - )... And Functional Form Mean of the OLS estimators can be derived from the rst order conditions of.... N gets larger under full set Gauss-Markov assumptions is also finite sample property OLS.20 and,. The best linear unbiased estimator under the asymptotic properties, like consistency, when in practice we have samples... Ordinary Least Squares ( OLS ) coefficient estimators for the plim and not also expectation...: Premultiply the Regression equation by X to get ( 1 ) y. 17, 2017, 6:15 p.m. Loading... Slideshow Movie from, that estimator which has lowest... Need only to show that ( X0X ) 1X0u bis consistent for ; i.e video provides brief on. When There are more than one unbiased method of estimation to choose,. ) ∂b sample properties of ols =−2X′y+2XXb 0 =0 asymptotic properties or large sample properties of the OLS Estimate Omitted Variable Bias \$... Estimators for the simple ( two-variable ) linear Regression Models with a Lagged Dependent Variable.... A Lagged Dependent Variable 17 10 2 linear Regression Models with a Dependent! Unbiasedness of OLS under the asymptotic properties, we say that Wn is unbiased, i.e p.m.! Analysis sample properties of ols far has been purely algebraic, based on a sample data... Under the asymptotic properties, the OLS method of estimation to choose from that! Of OLS and IV estimators in Regression Models with a Lagged Dependent Variable.! An important area to investigate that undergo discrete changes weaker than Assumption OLS.2 consistent because Wn converges θ.
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# Estimating a star's radius, temperature, and luminosity based on its mass
(See updated figure and description below.)
I've been trying to generate ballpark estimates for the radius, temperature and luminosity of stars in the main sequence based solely on their masses (assuming the same composition for all stars). The idea is to iterate through masses in steps of, say, 0.1 solar masses from 0.1 to 100, and roughly trace out the curve of the main sequence on an HR diagram.
For luminosity, I'm using something like this:
if ( mass < 0.43 ) {
L = 0.23*L_sun*pow(mass/M_sun,2.3);
} else if ( mass < 2 ) {
L = L_sun*pow(mass/M_sun,4);
} else if ( mass < 55 ) {
L = 1.4*L_sun*pow(mass/M_sun,3.5);
} else {
L = 32000*L_sun*mass/M_sun;
}
For radius, I'm using something like this:
if ( mass < 1 ) {
R = R_sun*pow(mass/M_sun,0.57);
} else {
R = R_sun*pow(mass/M_sun,0.78);
}
And, using these, I'm calculating the temperature from the luminosity-radius-temperature relation like this:
T = pow(L/(4.0*M_PI*R*R*sigma), 0.25);
where sigma is just the Stefan-Boltzmann constant.
All of this works about as well as I'd expect for stars of 1 solar mass or above, but breaks down completely for M dwarfs, as you can see from the attached image which shows my meager effort superimposed on HYG data.
Note that I'm plotting B-V here, calculated from temperature like this:
BV = pow(5601.0/T,1.5) - 0.4;
and absolute magnitude, calculated from luminosity like this:
magnitude = -2.5*log(L)/log(10) + 71.1974;
What can I do to improve this a little? I'll add that this is aimed at being part of an exercise for undergraduates who are beginning programmers, so I'm looking for simple ballpark approximations, not anything fancy.
Update: Based on Rob Jeffries' recommendation below, I took a look at the Mamajek data. Here's a plot of B-V versus temperature from that data: I've superimposed a fitting function of the form:
bv(t) = a/(b*t) - c
where the best-fit parameters are:
a = 4.2413
b = 0.000576479
c = 0.607144
Using this function to calculate B-V moves my numbers in the right direction, but it still doesn't quite do the trick, as shown in the figure below (the new B-V values are the curve that's lower on the right-hand side):
• I've added axis labels to the figure. As Rob Jeffries correctly pointed out, I've actually plotted B-V and absolute magnitude instead of temperature and luminosity. I also added a description of how I calculated these values. Maybe I just need to be more careful calculating B-V? Oct 10, 2019 at 17:36
• But you still haven't applied bolometric corrections properly. Once you get beyond B-V of 1.5 there is almost none of the star's flux in the V band. So the absolute magnitude is much larger than your calculation. Oct 10, 2019 at 22:42
You could plot $$L$$ vs $$T$$ and compare your model result to the measured/estimated $$L$$ and $$T$$ of main sequence stars?
You have not explained or labelled what your diagram is, but it isn't $$L$$ versus $$T$$; I suspect that it absolute $$V$$ magnitude versus $$B-V$$ colour.
The transformations between $$L,T$$ and $$V$$, $$B-V$$ are highly non-linear, especially at low temperatures (which is why your plot fails to reproduce the M-dwarfs) and involve folding a model atmosphere through some standard filter responses or using relationships between $$T$$ and $$B-V$$ and bolometric corrections and $$T$$. (e.g. Mamajek 2019)
EDIT: For the clarified question.
Your relationship for $$T$$ vs $$B-V$$ is not applicable at lower temperatures.
Your relationship between absolute magnitude and luminosity takes no account of the spectral energy distribution of the light from the star (i.e. it assumes the same bolometric correction for all temperatures, which isn't correct). You must calculate the bolometric magnitude from the luminosity and then apply a temperature-dependent bolometric correction to calculate a V-band magnitude.
The solution is to construct relationships that are valid over the full range of temperatures using the resource I referenced above.
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How do you write the phrase into algebraic expressions: five dollars less than Yumi's pay?
$p - 5$, where $p$ represents Yumi's pay
To write an algebraic expression, we need to represent Yumi's pay as a variable (I chose $p$).
The question says five dollars less, which means five (dollars) needs to be detracted/subtracted from $p$ (Yumi's pay).
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## Plots from Rivet analyses
### Pseudorapidities at three energies, charged multiplicity at 7 TeV (ALICE_2010_S8625980)
Inspire | HepData | Eur.Phys.J. C68 (2010) 345-354 | arXiv:1004.3514
This is an ALICE publication with pseudorapities for 0.9, 2.36 and $7 \text{TeV}$ and the charged multiplicity at $7 \text{TeV}$. The analysis requires at least on charged particle in the event. Only the INEL distributions are considered here
### Track-based minimum bias at 900 GeV and 2.36 and 7 TeV in ATLAS (ATLAS_2010_S8918562)
Measurements from proton-proton collisions at centre-of-mass energies of $\sqrt{s} = 0.9$, 2.36, and 7 TeV recorded with the ATLAS detector at the LHC. Events were collected using a single-arm minimum-bias trigger. The charged-particle multiplicity, its dependence on transverse momentum and pseudorapidity and the relationship between the mean transverse momentum and charged-particle multiplicity are measured. Measurements in different regions of phase-space are shown, providing diffraction-reduced measurements as well as more inclusive ones. The observed distributions are corrected to well-defined phase-space regions, using model-independent corrections.
### Charged particle multiplicities and densities in $pp$ collisions at $\sqrt{s} = 7$ TeV (LHCB_2014_I1281685)
Inspire | HepData | Eur.Phys.J.C74:2888,2014 | doi:10.1140/epjc/s10052-014-2888-1 | arXiv:1402.4430
Measurement of prompt charged particle production in proton-proton collsions at a centre-of-mass energy of 7 TeV at the LHC. The measurement is performed in the kinematic range $p > 2$ GeV/$c$, $p_\perp > 0.2$ GeV/$c$ and $2.0 < \eta < 4.8$. At least one prompt charged particle per event is required. A prompt particle is defined as a particle, that either originates directly from the primary vertex or from a decay chain in which the sum of mean lifetimes does not exceed 10 ps. Charged particle multiplicities are measured in the full kinematic range as well as in regions of pseudorapidity and transverse momentum. In addition, also mean particle densities are presented as functions of pseudorapidity and transverse momentum.
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744 Motooka, Nishi-ku
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# Seminar
List All(1090) Today and tomorrow's seminars(1)
## Generating functions and topological complexity
Hold Date 2020-06-15 16:30～2020-06-15 17:30 Place Zoom Online Seminar Object person Speaker Daisuke KISHIMOTO (Kyoto University)
Abstract:
The $r$-th topological complexity of a space $X$, $\mathrm{TC}_r(X)$, is defined to be the least integer $n$ such that $X^r$ is covered by $n$ open sets, each of which has a local homotopy section of the diagonal map $X\to X^r$. Farber and Opera asked for which finite CW-complex $X$ the generating function $$\mathcal{F}(X) = \sum_{r\ge 1}\mathrm{TC}_{r+1}(X)x^r$$ is of the form $$\frac{P(x)}{(1-t)^2}$$ where $P(x)$ is a polynomial with $P(1)=\mathrm{cat}(X)$. I will talk about some results on this question.
This talk is based on joint work with Michael Farber, Don Stanley, and Atsushi Yamaguchi.
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# A new determinant question for primes $p\equiv3\pmod4$
Let $p$ be an odd prime, and let $(\frac{\cdot}p)$ denote the Legendre symbol. Motivated by my question http://mathoverflow.net/questions/310301, here I introduce the matrices $A^+_p$ and $A^-_p$ whose definitions are as follows: $$A^+_p=[a_{ij}^+]_{1\le i,j\le (p-1)/2}\ \text{with}\ a_{1j}^+=\left(\frac jp\right) \ \text{and}\ a_{ij}^+=\left(\frac{i+j}p\right)\ \text{for}\ i>1,$$ $$A^-_p=[a_{ij}^-]_{1\le i,j\le (p-1)/2}\ \text{with}\ a_{1j}^-=\left(\frac jp\right) \ \text{and}\ a_{ij}^-=\left(\frac{i-j}p\right)\ \text{for}\ i>1.$$
QUESTION: Let $p\equiv3\pmod4$ be a prime. Is it true that $\det A_p^-=(-1)^{(p-3)/4}?$ When $p>3$, is it true that $\det A_p^+=-2^{(p-3)/2}$?
Based on my computation, I conjecture that the question has a positive answer.
The conjectures are true. If you negate the first row of $A_p^{-}$ you get a cofactor of the matrix in "Chapman's evil determinant". In particular you can get the answer from the same matrix decomposition used by Vsemirnov in his paper: On the evaluation of R. Chapman’s “evil determinant”.
I couldn't deduce the result for $A_p^{+}$ from Vsemirnov's paper so I'm sketching a different approach here. The proof essentially consist of (1) using quadratic Gauss sums to write the matrix as a (rank one perturbation of) a product of shifted Vandermonde matrices, and (2) repeated use of the Lagrange interpolation formula to evaluate various sums of rational functions evaluated at roots of unity. Here are the details:
Throughout this post $p$ is a prime $3\pmod{4}$ and $\zeta=e^{\frac{2\pi i}{p}}$.
Lemma 1: Given $a_1,a_2,\dots,a_{\frac{p-1}{2}},b_1,b_2,\dots,b_{\frac{p-1}{2}}\in \mathbb Z/p\mathbb Z$ we have $$\left[\left(\frac{a_i +b_j}p\right)\right]_{1\le i,j\le \frac{p-1}{2}}=\frac{1}{i\sqrt{p}}\left(J+2M_aM_b^{\top}\right)$$ where $M_a=[\zeta^{a_i k^2}]_{1\le i,k\le \frac{p-1}{2}}$ and $M_b=[\zeta^{b_jk^2}]_{1\le j,k\le \frac{p-1}{2}}$ and $J$ is the matrix with all entries $1$ which can also be written as $\textbf{1}^{\top}\textbf{1}$, with $\textbf{1}$ being the row vector of all $1$'s.
Proof: This follows entry-wise from the quadratic Gauss sum $$\left(\frac{a_i +b_j}p\right)=\frac{1}{i\sqrt p}\left(1+2\sum_{k=1}^{\frac{p-1}{2}}\zeta^{(a_i+b_j)k^2}\right)=\frac{1}{i\sqrt p}\left(1+2\sum_{k=1}^{\frac{p-1}{2}}\zeta^{a_ik^2}\cdot \zeta^{k^2 b_j}\right).$$
Corollary 1: By the matrix determinant lemma, we have $$\det \left[\left(\frac{a_i +b_j}p\right)\right]_{1\le i,j\le \frac{p-1}{2}}=\frac{1}{\left(i\sqrt p\right)^{\frac{p-1}{2}}}\left(2^{\frac{p-1}{2}}\det M_a \det M_b+\textbf{1}^{\top}\textbf{Adj} (2M_aM_b^{\top}) \textbf{1}\right)$$ $$=\frac{1}{\left(i\sqrt p\right)^{\frac{p-1}{2}}}\left(2^{\frac{p-1}{2}}\det M_a \det M_b+2^{\frac{p-3}{2}}\sum_{r=1}^{\frac{p-1}{2}}\det M_a^{(r)}\det M_b^{(r)}\right)$$ Where we use the notation $M^{(r)}$ to denote the matrix obtained from $M$ by replacing the $r$-th row by $\textbf{1}$.
The matrix $A_p^{+}$ corresponds to the choice $(a_1,\dots,a_{\frac{p-1}{2}})=(0,2,3,\dots,\frac{p-1}{2})$ and $(b_1,\dots,b_{\frac{p-1}{2}})=(1,2,\dots,\frac{p-1}{2})$. Computing $\det M_a,\det M_b$ or $\det M_a^{(r)},\det M_b^{(r)}$ for these vectors is an evaluation of Vandermonde determinants or simple instances of Schur polynomials, so I am leaving it as an exercise, for the sake of brevity. What you will end up getting from corollary 1 on these specific vectors, is the following:
$$\det A_p^{+}=$$ $$\frac{\left(\prod_{k_1<k_2} (\zeta^{k_1^2}-\zeta^{k_2^2})\right)^2}{\left(i\sqrt p\right)^{\frac{p-1}{2}}}\left(-2^{\frac{p-3}{2}} \left(i\sqrt{p}+1\right)+2^{\frac{p-3}{2}}\sum_{r=1}^{\frac{p-1}{2}}F_{+}(\zeta^{r^2})\left(\prod_{k\neq r} \frac{1-\zeta^{k^2}}{\zeta^{r^2}-\zeta^{k^2}}\right)^2\right)$$
where $F_{+}(\zeta^{r^2})=\frac{1-i\sqrt p}{2\zeta^{2r^2}}-\frac{1}{\zeta^{3r^2}}$. What follows are some facts that help us simplify this expression:
Lemma 2: We have $\left(\prod_{k_1<k_2}(\zeta^{k_1^2}-\zeta^{k_2^2})\right)^2=(i\sqrt p)^{\frac{p-3}{2}}$.
Proof: This calculation follows from the fact that for any $n\neq 0\pmod p$, the equation $n=x^2-y^2$ has exactly $\frac{p-3}{4}$ solutions with $x,y\in \{1,2,\dots,\frac{p-1}{2}\}$.
Lemma 3 We have the following equalities $$\sum_{r=1}^{\frac{p-1}{2}}\frac{1}{\zeta^{2r^2}}\left(\prod_{k\neq r} \frac{1-\zeta^{k^2}}{\zeta^{r^2}-\zeta^{k^2}}\right)^2=-2$$ $$\sum_{r=1}^{\frac{p-1}{2}}\frac{1}{\zeta^{3r^2}}\left(\prod_{k\neq r} \frac{1-\zeta^{k^2}}{\zeta^{r^2}-\zeta^{k^2}}\right)^2=-2+i\sqrt{p}$$
Proof: For the first equality we will us Lagrange interpolation on the polynomial $G(x)=\frac{1}{x}\left(\prod_{k=1}^{\frac{p-1}{2}} (x-\zeta^{-k^2})-\prod_{k=1}^{\frac{p-1}{2}}(x-\zeta^{k^2})\right)$ at the points $x=\zeta^{1^2},\dots,\zeta^{(\frac{p-1}{2})^2}$. On one hand we have $G(1)=2\prod_{k=1}^{\frac{p-1}{2}}(1-\zeta^{-k^2})$, and on the other $$G(1)=\sum_{r=1}^{\frac{p-1}{2}}\frac{1}{\zeta^{r^2}}\prod_{k=1}^{\frac{p-1}{2}}(\zeta^{r^2}-\zeta^{-k^2})\prod_{k\neq r} \frac{1-\zeta^{k^2}}{\zeta^{r^2}-\zeta^{k^2}}$$ $$=\sum_{r=1}^{\frac{p-1}{2}}\frac{1}{\zeta^{r^2}}\left(\frac{-p\zeta^{(p-1)r^2}}{\prod_{k=1}^{\frac{p-1}{2}}(1-\zeta^{k^2})}\right)\left(\prod_{k\neq r} \frac{1-\zeta^{k^2}}{\zeta^{r^2}-\zeta^{k^2}}\right)^2$$ So we have $$\sum_{r=1}^{\frac{p-1}{2}}\frac{1}{\zeta^{2r^2}}\left(\prod_{k\neq r} \frac{1-\zeta^{k^2}}{\zeta^{r^2}-\zeta^{k^2}}\right)^2=\frac{-2}{p}\prod_{k=1}^{\frac{p-1}{2}}(1-\zeta^{-k^2})(1-\zeta^{k^2})=-2.$$ The second identity can be similarly obtained by applying Lagrange interpolation to $G(x)$ at the points $x=0,\zeta^{1^2},\zeta^{2^2},\dots,\zeta^{(\frac{p-1}{2})^2}$. For this you will need that $$G(0)=\zeta^{-1^2-\cdots-(\frac{p-1}{2})^2}\left(\sum_{k=1}^{\frac{p-1}{2}}\zeta^{-k^2}\right)-\zeta^{1^2+\cdots+(\frac{p-1}{2})^2}\left(\sum_{k=1}^{\frac{p-1}{2}}\zeta^{k^2}\right)$$ $$=\frac{-1-i\sqrt{p}}{2}-\frac{-1+i\sqrt p}{2}=-i\sqrt{p}.$$
Applying the calculations from the previous two lemmas to our expression gives $$\det A_p^{+}=\frac{2^{\frac{p-3}{2}}}{i\sqrt{p}}\left(-i\sqrt{p}-1-2\left(\frac{1-i\sqrt{p}}{2}\right)+2-i\sqrt{p}\right)=-2^{\frac{p-3}{2}}$$ as desired.
• Very good job here. – T. Amdeberhan Sep 18 '18 at 2:34
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Universal Generalization Examples(In fact, the proper generalization of Galois connections is to adjunctions, but that's a story for next time. When using universal quantifiers, you are saying, “there are no exceptions and therefore there are no choices. Universal themes are ways to connect ideas across all disciplines. Ensuring all students (including those with disabilities) have access to content, while providing multiple options to acquire information are key to student success. Examples of 'generalization' in a sentence. Solution: The formal version of this statement is ∀x ∈R, if x > 2 then x2 > 4. PDF Existential Universal Statement Examples. Universal generalization is a rule of inference for predicate logic. Universal Instantiation (abbreviated UI), the argument form. Since a generalization relates two things, a counter-example has a two-part description. Therefore, all spaniels are dogs. 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This fallacy is sometimes called the “Fallacy of Sweeping Generalization. The police can legally speed in an emergency. What is an example of generalization in psychology? Generalization, in psychology, the tendency to respond in the same way to different but similar stimuli. Force may contribute to conflict. In predicate logic, generalization (also universal generalization or universal introduction, GEN) is a valid inference rule. Universal Conditional Statements. Plenty of examples of implicit uses of universal generalization in prov- ing geometrical or number-theoretical propositions can be found in Euclid's Elements. Generalization •Generalization is an everyday technique that we use to manage complexity. For example, a case study could be done challenging the efficacy of different therapy methods for vets with. The definition of worldview with examples. With traditional thematic teaching, the teacher does all the cognitive work. Generalization Counter-example (X) AllA'sareB's. In predicate logic universal instantiation [1] [2] [3] (UI, also called universal specification, and sometimes confused with Dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. This chapter shows that a confidence-based model can make correct predictions not only about individual cases, but also about the typology of analogical change. Universal Generalization (UG), Existential Instantiation Introduction rule (EII) and Existential Instantiation Elimination rule (EIE) ]. Valid Generalizations Valid means true. The rule can also be called "∀ introduction". To do this, we create a sub-proof in which we prove that some statement, φ, is true for any arbitrary constant. This kind of approach would allow for the trained model to be fine-tuned in one language and applied to a different one in a zero-shot fashion. 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Often the universal quantifier (needed for a precise statement of a theorem) is omitted by standard mathematical convention. Generalization is the process of extracting common properties from a set of entities and create a generalized entity from it. And, along with other animals, there are certainly instances in which this is true. Psychology questions and answers. A generalization is a broad statement that applies to many examples. Inductive Reasoning | Types, Examples, Explanation. Universal generalizations state a rule that allows not even one exception. Changing faulty generalizations to valid generalizations can be as simple as changing a few words. The constant we introduce must be completely new to the proof. The Rule of Universal Generalization. The first rule is 'We are to admit no more causes of natural things than such as are both true and sufficient to explain the appearances. For example, a young child may say "foots" instead of "feet," overgeneralizing the morphological rule for. • Provide assessments for background knowledge. Shepard, who began researching mechanisms of generalization while he was still a graduate student at Yale:. The law states that the probability of perceiving similarity or analogy between two items, a and b, is a negative exponential function of the distance d(a,b) between them in an internal psychological space. Examples of very vague terms: It's vague, because we don't know precisely how many cats have to have tails in order for it to be acceptable as a generalization. New (sound) inference rules for use with quantifiers: Universal Elimination. Hasty generalization fallacies are very common in everyday discourse, as when a person gives just one example of a phenomenon occurring and implicitly treats. For example, the statement: "If x > y, where x and y are positive real numbers, then x2 > y2 " really means "For all positive real numbers x and y, if x > y, then x2 > y2. It's usually contrasted with deductive reasoning, where you go from general information to specific conclusions. IntroductionShepard (1987) has put forward a ‘Universal Law of Generalization’ as one of the few general psychological results governing human cognition. The exponential decay in perceptual similarity is often referred to as the universal law of generalization (1, 2). The Universal Kepler problem. Universal quantification and unification, an example. Related Works Universal Adversarial Attack. These principles of UD are listed below. Now, I'm trying to quantify generalization there, but I will do it in a very different way than you have usually seen, for example, when we try to stabilize this stochastic gradient descent or some other methods. The basic idea behind each one is very simple. , dyslexia); may require different ways of approaching content. God did evil things in pursuit of doing good, and still, be good. As these examples illustrate, generics are not equivalent in meaning to generic generalizations constitute a specific kind of universal . Friedrich Bauer, Remarks on universal coefficient theorems for generalized homology theories Quaestiones Mathematicae Volume 9, Issue 1 & 4, 1986, Pages 29 - 54. Have three narrative arguments, each of which challenges one of the generalizations by offering a counterexample. Match the proposition type with its example Universal generalization A. Being referred to as the universal hamiltonian, universal angular momentum and universal Laplace-Runge-Lenz vector respectively, they are elements in (essentially) the TKK (Tits-Kantor-Koecher) algebra of V and satisfy commutation relations. In other words, s will be chosen by runST, not by the caller. Longman Essay Activator The aim of this book is to develop your sentence structure as well as your horizons which is so essential when approaching to IELTS and distinct academic essays. Mostly, this kind of language pattern creates limitations for us. rules of inference for quantified statements are used in Examples 1 and 2. The bad news is that not every culture is OK with using them in a business setting. It states that if we can derive a formula with free variables then me may infer a . A generalization is a statement made about a group of people or things. Two examples are given comparing the performance of noiseless universal syndrome-source-coding to 1) run-length coding and 2) Lynch-Davisson-Schalkwijk-Cover universal coding for an ensemble of binary. " Here Q is the proposition "he is a very bad student". universal lawof generalization in human perception Chris R. What is a generalization? Universal proposition based on particular facts, are called Generalization. Generalization Types: Scientific Generalization Scientific. The generalization of a class is not, as the conceptual logic assumes, the abstraction of a general idea, but an inference from the analogy of a whole individual thing, e. COUNTER-EXAMPLES Universal generalizations state a rule that allows not even one exception. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom. As such, societies where most people have a similar worldview are less prone to creativity. Generalization Definition & Meaning. It states that if ⊢ P ( x ) {\displaystyle \vdash P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \forall x\,P(x)} can be derived. I will try something different here. A generalization is formed from several examples or facts and what they have in common. generalization, in psychology, the tendency to respond in the same way to different but similar stimuli. For example, when you see a feathered creature flying in the sky, you use generalization skills to conclude “That is a bird. – Example: A sum of two even numbers is even. Balancing costs and performance Deciding whether a novel object is another instance of something already known or an example of something different is an easily solved problem. It states that if ⊢ P ( x ) {\displaystyle \vdash \!P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \!\forall x\,P(x)} can be derived. The above content published at Collaborative Research Group is for informational and educational purposes only and has been developed by referring reliable sources and recommendations from technology experts. Comparison with existing methods. Observe that there is a non-trivial connection between the fact that ∀x. a is called the first element and b is called the second element of the ordered pair (a, b). ) and learn the characteristics of these classes. If P and Q are two premises, we can use Conjunction rule to derive $P \land Q$. Then by this Universal Generalization we can conclude x P (x). On the one hand, so-called exact or hard sciences are a manifestation of scientific thinking. Examples of Universal Partial Orders To prove the universality of a given partially ordered set is often a difficult task [5, 20, 10, 16]. for example, a dish—symbolized by a small letter d, often called the “argument . The Rule of Universal Generalization If an open statement p(x) is proved to be true when x is replaced by any arbitrarily chosen element c from our universe, then the universally qualified statement (x p(x) is true. Examples of relevant groups could be based on race, gender or age group. For example, two circles may have different sizes, colors, and shadings. Chapter 1, Part III: Proofs. They have much acuteness of perception for the relations of individual objects, but little power of generalization. These are often based on generalizations. $\begingroup$ @Pedro Sanchez Terraf Actually, these counterexamples are of interest in the sense that if we look at them as pathologies, the properties we require from a universal algebra to prevent them would lead to a more fundamental understanding of the "regularity" of the classical algebraic theories. Other articles where universal generalization is discussed: formal logic: Axiomatization of LPC: The axiom schemata call for some explanation and comment. Two examples are given comparing the performance of noiseless universal syndrome-source-coding to 1) run-length coding and 2) . Example: Prove that the square of an even integer is . The law of Universal Generalization states that: P(c) (x) P(x) Now, I understand that this works only if c is any random element from the universe. Few-shot classification aims to recognize unseen classes when presented with only a small number of samples. However, existing strategies failed to generate adversarial patches with strong generalization ability due to the ignorance of the inherent. So let’s look at an example of overgeneralization here: “ The whole world knows he’s is a. A Biased Generalization in which the bias is due to self-selection for membership in the sample used to make the generalization. It is a generalization about life or human nature; they deal with basic human concerns. Universal Design for Learning: Multiple Means of. Furthermore, this response does not do justice to the comparison between universal instantiation and existential generalization. A D-N explanation is a deductive argument such that the explanandum statement follows from the explanans. universal generalization: knowing P(a) for an arbitrary a we can deduce that ∀xP(x) since a was arbitrary. For example, maybe you can't log into the network because your Ethernet cable is bad, or because the network is down for maintenance, or any one of a zillion other reasons. Critcal Thinking Final Review Flashcards & Practice Test. 5) The Hasty Generalization Fallacy. Example 5 - Contrapositive, Converse, and Inverse of a Universal Conditional Statement Write a formal and an informal contrapositive, converse, and inverse for the following statement: If a real number is greater than 2, then its square is greater than 4. The generalization used in the premise of an accident fallacy is sometimes "a glittering generality": a vague, vacuous, and often emotively significant universal statement whose open texture has such an uncertain sphere of application that any or some specific instances are either contradictions or of some indefinite reference. Here, our author is making an assumption. Can I use Existential Geneneralization on Universal sentences? 1. PDF Universal Themes & Generalizations. Generalization: an idea or statement about all of the members of a group or all the instances of a situation. Thousands of colleges and universities are available for students around the world. They are statements that include an all or nothing type of generalization, such as "this always does that" or "every time I do that, then this happens". Generalization, Specialization and Aggregation in ER Model. The universal Bot action model is introduced in the Adaptive Cards schema version 1. Existential Instantiation (EI) Example: "There is someone who got an A in the course. Universal Quantifiers are universal generalizations without referential index. Third, theory is heuristic because it stimulates and guides the further development of knowledge. Generalizing universal function approximators. " "Let's call her aand say that agot an A" Existential Generalization (EG) Example:. In cognitive science, the “universal law of generalization” seeks to explain this. WR101 Emerson Universal Generalization Of Pop Culture. Show that holds for arbitrary x, then use universal generalization. Universal generalizations assert that all members (i. We need to convert the following sentence Such a statement is expressed using universal quantification. An example of a predicate logic proof that illustrates the use of Universal Instantiation and Generalization. The claimed link between cigarette smoking and lung cancer is a vast generalization. order for the many universal generalizations which use this notion to be well defined. For thousands of years, red roses have been associated with passion and love. Each is followed by an example of its application. "Generalization" arises because perceived similarity may describe recognition of a general category. Therefore − "Either he studies very hard Or he is a very bad student. also exhibits well generalization and transferability among different models. They may accomplish this by using broad, sensational language. •Describe it (either “__ that is not ___” or “__ that is __”). (1) If a real number is an integer, then it is a rational number. The Converse accident fallacy is similar to the accident fallacy, except, in reverse. Choose the letter of the correct term or concept below to complete the sentence. Adversarial examples are inputs with imperceptible perturbations that easily mislead deep neural networks (DNNs). Related work: universal representations •The ‘parametric family’ variants share weights across feature extractors. Then the universal modus ponens implies that 1002<2100. Asian-American success and the pitfalls of generalization Nathan Joo, for example, 15 percent of black the "Asian" advantages popularized in the media are far from universal. Inductive reasoning is also called inductive logic or bottom-up reasoning. A Universal Representation Transformer Layer for Few-Shot Image Classification. Few-shot dataset generalization is a challenging variant of the well-studied few-shot classification problem where a diverse training set of several datasets is given. Similar to inductive generalizations, statistical induction uses a small set of statistics to make a generalization. Advertisement Avoid Making Faulty Generalizations. Universal instantiation : definition of Universal. The two simplest rules are the elimination rule for the universal quantifier and the introduction rule for the existential quantifier. 80% of Giants fans attend every home game Specific statement C. To appreciate the importance of generalization, consider these examples: Sarah, a 4th grade student, has a one-year reading delay and needs lots of practice in reading to increase her rate of decoding. Generalization counter example x all as are bs. Both Digital Accessibility and Universal Design for Learning (UDL) focus on inclusive educational practices. UDL promotes inclusive practices that work to increase accessibility by reducing barriers. Example 2 – Prime and Composite Numbers Example: Generalizing from Generic Particular. Statistical generalisation involves statistically calculating the likely parameters of a population using data from a random sample of that population. Universal Approximation and Depth. To this end, we propose to utilize the diverse training set to construct a universal template: a partial. ) is the universal generalization of (. Which sentence is the example of overgeneralization? 1. The good news is that facial expressions for happiness, sadness, anger, and fear are universal. Accident fallacy is a type of informal fallacy, and it is also known as the "fallacy of the general rule" and "sweeping generalization". Empirical mapping of human performance across a wide range of domains has established. A universal theme with generalizations can serve as the. If the quantifier is universal (universal generalization) the argument. Their second motive could be to sway the reader’s opinion. As we can see from these examples, deductive arguments typically use universal statistical generalizations whereas inductive arguments typically use partial statistical generalizations. To prove it, first let the universe be the set of all people and let H (x) mean that x is happy. Download File combine universal themes. Example of a proof Prove: ∀ x ( P ( x ) → Q ( x ) ) → ( ∀ x P ( x ) → ∀ x Q ( x ) ) {\displaystyle \forall x\,(P(x)\rightarrow Q(x))\rightarrow (\forall x\,P(x)\rightarrow \forall x\,Q(x))} is derivable from ∀ x ( P ( x ) → Q ( x ) ) {\displaystyle \forall x\,(P(x)\rightarrow Q(x))} and ∀ x P ( x ) {\displaystyle \forall x\,P(x)}. A universal conditional statement has the form: 8x; if P(x) then Q(x). Learning a Universal Template for Few-shot Dataset Generalization Eleni Triantafillou1 2 3 Hugo Larochelle2 Richard Zemel1 Vincent Dumoulin2 Abstract Few-shot dataset generalization is a challenging variant of the well-studied few-shot classification problem where a diverse training set of several datasets is given, for the purpose of training an. Universal grammar is the theoretical or hypothetical system of categories, operations, and principles shared by all human languages and considered to be innate. universal modus ponens, and universal modus tollens. For example, those with sensory disabilities (e. The generalized response is predictable and orderly: it will measure less than that elicited by the. This inference rule is called modus ponens (or the law of detachment ). When we implement Generalization in a programming language, it is often called Inheritance instead. In the example on the left, our universal theme was Systems. Take for example the universe set contains all integers from 1 - 5 and the subset is all even numbers in this case absolute complement is all odd numbers i. This apparently natural expectation, however, leads to unexpected complexities. There is one logic exercise we do nearly every day, though we're scarcely aware of it. In contrast, the claim that “all prisoners released from prison are rearrested within three years” is a universal generalization. , universal adversarial attack [25, 13], is. Absolute complement is set of all elements in Universe Set U that are not in the subset. This corresponds to the tautology. Universal instantiation + assume 𝐺(𝑛) is true. By universal generalization the truth of the original formula follows. Generalization, which is an act of reasoning that involves drawing broad inferences from particular observations, is widely-acknowledged as a quality standard in quantitative research, but is more controversial in qualitative research. If you send me an email, then I will finish my program. A "universal" generalization of syndrome-source-coding is formulated which provides robustly effective distortionless coding of source ensembles. Fritz wrote: For the last time: Your question was "Is it valid to apply the UG (Universal Generalization) rule to ~P (n)". the caller chooses a fixed type a. The first two lines are premises. In short, a hasty generalization is when you neglect to perform your due diligence. The following chart gives a few examples of words that are. We take tiny things we've seen or read and draw general principles from them—an act known as inductive reasoning. which generalization to novel images takes place: universal, class, and model-based. The meaning of UNIVERSAL NEGATIVE is a universal proposition that denies something of all members of a class. > Universal Generalization is given as something like: If the statement > P(x) has been derived without any reference to y as a free variable > then we can generalize Ay P(y). Then the argument is x H (x) x H (x) The proof is Note:. In the age example above, generalizing age data based on each decade gives a general picture of where the individuals in the data set fall, . • Nesting of Quantifiers Old Example Re-Revisited Universal Generalization (UG). In other words, they jump to conclusions about the validity of a proposition with some -- but not enough -- evidence to back it up, and overlook potential counterarguments. So are those with specific applications in technology, such as electricity , computer science or astronomy , for example. Universal generalization Existential instantiation Existential generalization 27. A universal static detection framework for malicious documents based on feature generalization is developed in this research. The design is useful and market-able to people with diverse abilities. universal and statistical generalizations Universal generalization:Universal generalization: claims that all members of a group have certain attributes or characteristics - Asians are good at math. This often puts the person at a loss, which can help them gain a deeper understanding of why their hasty generalization in this case is offensive. Example: For example, consider the following argument: For every number x if x > 1, . even though there are exceptions to the universal generalization (referent prevalence of. annotated data, but obtaining a couple of examples. Deductive, Inductive and Abductive Reasoning. Hasty generalizations can happen when someone is using examples from their own experiences rather than from actual statistical or scientific evidence to try to prove a point. Examples of scientific thinking; Even the most basic technologies are the result of scientific thinking. Shiveley & Misco (2009) suggest that generalizations are a logical step in teaching kids to think critically about what they know and transferring that knowledge to a variety of topics within the social studies. One commits the fallacy of hasty generalization when one infers a statistical generalization (either universal or partial) about a population from too few instances of that population. 00:14:41 Use Venn diagrams to determine if the categorical syllogism is valid or invalid (Examples #1-4) 00:22:28 Determine if the categorical syllogism is valid or invalid and diagram the argument (Examples #5-8) 00:26:44 Identify if the proposition is valid (Examples #9-12) Practice Problems with Step-by-Step Solutions. We cannot and should not avoid generalizing, but we can make a case for some generalizations being more reliable than simple stereotypes and hasty generalizations. Such arbitrary selection makes this rule mathematically valid. For example, imagine that a dog has been conditioned to run to its owner when it hears a whistle. The best way to understand this phenomenon is with some straw man fallacy examples. Universal Instantiation and Existential Generalization. " Hempel offered a precise account of what it is to be an instance of such a universal sentence. What Is the Accident Fallacy? Accident fallacy occurs when someone applies a general rule to a case in which the rule is inapplicable. Updated: 08/27/2021 Create an account. This principle has been a core philosophical assumption within the fields of counseling, psychology, medicine, and many other social sciences. Supported by facts Agrees with what you already know about the topic Uses logic and reasoning Proven with several examples 7. 9+ Paragraph Writing Examples in PDF. In one aspect, however, Mill's methods outstripped those of Hempel. In this example, it is a logical necessity that 2x + y equals 9; 2x + y must equal 9. The definition of a comparison is made act of finding out. Quantificational formatting and going from using logic with words, to using it for math proofs. In cognitive science, the "universal law of general …. They assume that there will be an exception. CS411: Artificial Intelligence I, Bing Liu. UNIVERSAL GENERALIZATIONS AND COUNTER-EXAMPLES 1) Think of a false universal generalization. Few-shot dataset generalization is a challenging variant of the well-studied few-shot classification problem where a diverse training set of several datasets is given, for the purpose of training an adaptable model that can then learn classes from \emph {new datasets} using only a few examples. Generalization and inheritance. If you believe you will always find a way if you persevere for instance. Your opponent's explanation is less believable if you can show that there are alternative explanations that haven't been ruled out. To this end, we propose to utilize the. Experience provides information that allows for the selection of features from that space in the acquisition of a particular grammar. Are examples of universal statements Universal negative statements A statement of insert form get A are B is called universal negative It asserts that solar is no. " These have been extended to a range of traits, from the phonemes found in languages, to what word orders languages choose, to why children exhibit certain linguistic. Clearly, this universal would vary for each instantiation because different people would be inclined to identify with different characters depending on their own religion. work to generate class-agnostic universal adversarial patches with strong generalization ability, which exploits both the perceptual and semantic bias of models. The chapter is organized as follows: first, it provides a brief overview of tendency-based vs. Universal generalization A 100% or 0% statistical generalization, that is, a proposition that asserts that something is true of all or none of a class. Universal generalization / instantiation Existential generalization / instantiation In predicate logic , generalization (also universal generalization or universal introduction , [1] [2] [3] GEN ) is a valid inference rule. For Example: Let E = f5;6;7;8g: 9m 2E such that m2 = m. Learn about the defining features of private universities and how they differ from public universities and a liberal arts colleges. For example, saying "Most stars are not surrounded by life-sustaining planets" is a general statement about stars, but it is non-universal because the quantity term is not all (or an equivalent) but most. PDF How Nature Meets Nurture: Universal Grammar and. first proposed an algorithm to compute universal adversarial perturbations for DNNs for object recognition tasks. Career services example: Job postings in formats. Here are generalizations: My class meets on Tuesdays. What this says to Fitch is “replace x with c. As it is widely known, this act was adopted in 1948. This article discusses the classical problem of zero probability of universal generalizations in Rudolf Carnap's inductive logic. implicational universal in (5) (see Hawkins 1983: 74-75 for some similar universals); (1a) is the simple form of this implicational universal, while (5b) spells out more explicitly what generalizations like this are intended to mean. Examples What can be concluded from: universal generalization • existential instantiation, existential generalization Resolution and logical programming. However, I do not understand how it holds true in practical examples. Over- Generalization - Assuming that a few similar events are evidence of a general pattern. Generalization, Stereotypes and Common Sense: Explained. All politicians are philanders and think only of personal gain and benefit. Quantifier expressions are marks of generality. Here are two examples: Argument 3. They come in a variety of syntactic categories in English, but determiners like "all", "each", "some", "many", "most", and "few" provide some of the most common examples of quantification. Hasty Generalization: the sample is too small to support an inductive generalization about a population Unrepresentative Sample : the sample is unrepresentative of the sample as a whole False Analogy : the two objects or events being compared are relevantly dissimilar. For example, scientific theories assert the existence of things like black holes, atoms, viruses, DNA and so on. One common type of hasty generalization is the Fallacy of Accident. In predicate logic, generalization (also universal generalization or universal introduction,[1][2][3] GEN) is a valid inference rule. Regarding the perceptual bias, since DNNs are strong-ly biased towards textures, we exploit the hard examples which convey. Universal elimination This rule is sometimes called universal instantiation. In this dissertation, I develop and defend my own account of universal biology, the study of non-vague, non-arbitrary, non-accidental, universal generalizations in biology. It is a central idea about the human condition. •Describe it (either "__ that is not ___" or "__ that is __"). structurally-based approaches to analogical change, summarizing the major generalizations that have been uncovered, and situating the. This occurs during the classical conditioning process. Recall that when and ; and that and. " to confirm a generalization that A's cause B's. “Logic” usually means “deductive logic”, the study of valid argument patterns. Generalizations that are based on the 'All' or 'None' are known as universal generalizations. For example, our commonsensical knowledge would lead us to believe that depression is the cause of suicide. The MBTI, for example, suggests that personality can be broken down and understood as four different dimensions. 4: Only professional athletes are celebrities. In order to use these new capabilities, the version property of your Adaptive Card must be set to 1. In this example, we will prove that the Pope is the President of the United States. We’ll look at universal generalizations constructed with the quantifiers “all”, “only”, or “no”. But there's a big gap between a strong inductive argument and a weak one. It states that if has been derived, then can be derived. It states that if ⊢ P ( x ) {\displaystyle \vdash \!P(x)} . , blindness or deafness); learning disabilities (e. Although principles and guidelines of generalization can be found in cartographic literature and among mapping organizations, there has not existed a set of universal rules that explicitly defines how generalization should be performed. , religion, nationality, or sex). We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory," Wassertheil-Smoller told Live Science. The best number of hidden units depends in a complex way on: o the numbers of input and output units o the number of training cases o the amount of noise in the targets o the complexity of the function or classification to be learned o the architecture o the type of hidden unit activation function o the training algorithm o regularization In most situations, there is no way to determine the. Then offer at least one reason against each of these generalizations, and argue that the generalization should be rejected. The explanans consists of m ≥ 1 universal generalizations, referred to as laws, and n ≥ 1 statements of antecedent conditions. Data generalization is the process of creating a more broad categorization of data in a database, essentially 'zooming out' from the data to create a more general picture of trends or insights it provides. Change • Change generates additional change • Change can be either positive or negative • Change is inevitable • Change is necessary for growth • Change can be evolutionary or revolutionary 2. Because of the frequency with which these are seen, they're considered universal symbols. Have three clearly marked conclusions, one in each of the narratives, to the effect that the corresponding generalization is false. Derive 𝐻(𝑛) from 𝐺(𝑛) using axioms, definitions, etc. principleProvide multiple means of Engagement. The exception is used to justify a generalization. n ∈S , then use universal generalization. Here is a clear case where negative generalizations are used to influence a particular group. I deliberately avoid giving a lot of structure for this homework assignment, because I want the students to feel free to be creative in demonstrating their understanding. Since a generalization about all instances of a supposed causal sequence is drawn from only one or a few qualified instances of a supposed causal sequence, without any further evidence, examples of false cause also can be seen as examples of the converse accident fallacy — and what some critical reasoning textbooks term the fallacy of hasty. In my account, a candidate biological generalization is assessed in terms of the assumptions it makes. Universal Grammar, that specifies a space of possible grammars. A universal theme is an organizing concept that transcends time and place, and brings focus to learning across subject areas. In this example, we introduce a constant a. A sketch of what I think neural architectures of the future will look like, inspired by the Universal Computation Engine and ViT papers: you have a large language model that acts as “bolt-on-generalization layer” for a target task domain, lightweight encoder layers to tokenize the input into something that can capture “word-level. ” Valid generalizations can be proven and supported with facts. 1 Generalization with hypotheses 2 Example of a proof 3 See also 4 References Generalization with hypotheses The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions. Their clue words include most, many, some, often or few. Exposition: Consider the generalization "birds can fly" from the example. However, the individual proofs, even if developed independently, use similar tools. For example, assume that "For all positive integers n, if n>4, then n2<2n " is true. What universal generalization does is cause all unbound variables to be implicitly universally quantified. any generalization about the past, which may or may not be true, e. West is a criminal Chapter 9 17 Example knowledge base contd. Universal Generalization is a subtle and very useful rule and the meaning may not. and 1958, I established that orderly gradients of generalization could be obtained fromhumansduringidentification learning-in whichsubjects acquired, throughcorrection ofincorrectresponses, aone-to-oneassociation betweennstimuli (Munsellcolorchips, for example) and n arbitrarily assigned verbal responses (7-9). contingencies of reinforcement c. Literary themes, like "Hero's Journey. Universal Generalization ug P x has not been deduced from any hypotheses in from CS 130 at University of the Philippines Los Baños. For example, if a bird eats a poisonous butterfly, it will learn to avoid preying on that species again by generalizing its past experience to new perceptual stimuli. Using these expressions and improving your own structures will affect on your essay grades and your academic work will seem more fruitful, juicy, and…. Any exception to the conclusion of an enumerative induction has the status of A) a hypothesis. That bus is full of tourists Match the argument type to. (Mech) Adapted or adaptable to all or to various uses, shapes, sizes, etc. Synonyms: Statistical Generalization. It was introduced in 1987 by Roger N. Vit´anyi Centrum voor Wiskunde en Informatica Neil Stewart Department of Psychology, University of Warwick Chater, N. ∀ Intro: If you apply ∀ Intro to a subproof containing a boxed constant (but no. The constant we introduce must be. This is an example of _____ inconsistency. ; as, a universal milling machine. Aristotle & Logic: Syllogisms & Inductive Reasoning. , visual imagery, paraphrasing strategies,. Universality Sentence Examples Even so, however, it starts from a particular premise which only contains many instances, and leaves room to doubt the universality of its conclusions. For example: Accessibility Hierarchy (Keenan and Comrie, 1972): NPs. Universal generalization or universal introduction (∀I, sometimes GEN) is a basic rule of inference in first-order logic by which a universal statement is introduced to a proof. Due to the sheer quantity of papers, I can't guarantee that I actually have found all of them. A universal theme is an idea that applies to anyone regardless of cultural differences, or geographic location. Measurement invariance explains the universal law of. the argument x must be of type ST s a for any choice of s. 14 May 2021 · Eleni Triantafillou , Hugo Larochelle , Richard Zemel , Vincent Dumoulin ·. Universal Generalization premises: P(c)for any arbitrary c •Example 2: It is known that 1. The straw man argument, in this way, is an example of a red herring. proved that a neural network with a single hidden layer can approximate any continuous function from a compact domain to the reals to arbitrary precision. For example, the word tree is a generalization of thousands of species of plant that have things in common such as a trunk and a lifespan that generally exceeds two years. Universal Affirmative or A-type Proposition Take an example: All goas are dogs. A generalization of A A is a wff having the form ∀x1∀x2⋯∀xnA ∀ x 1 rules of inferences: modus ponens, and universal generalization:. Existential statements "Although Popper is right that a universal generalization can be falsified by just one negative instance, many statements in science are not of this form. The connection of generalization to specialization (or particularization) is reflected in the contrasting words hypernym and hyponym. Mention three universal generalization of popular culture. Given this derivation, notice that the conditions for applying the rule of Universal Generalization are met. When you would read or write an essay, or any fully-written write-up, you would always encounter a group of sentences that expounds, extends, and explains a single idea. Examples For convenience, we reproduce the item of Principia Metaphysica in which the Quantificational Logic is defined: In what follows, we give examples of the axioms and rules, consider some facts, and then draw out some consequences. Recently, adversarial patch, with noise confined to a small and localized patch, has emerged for its easy feasibility in real-world scenarios. Polita,b,*, Cheryl Tatano Beckc aHumanalysis, Inc. Examples What can be concluded from: • universal instantiation, universal generalization • existential instantiation, existential generalization Resolution and logical programming • have everything expressed as clauses • it is enough to use only resolution. Usually, it's best to stick with specifics and avoid generalizations. In predicate logic, generalization (also universal generalization [1] [2] [3], GEN) is a valid inference rule. Deductive reasoning moves from the general rule to the specific application: In deductive reasoning, if the original assertions are true, then the conclusion must also be true. 3) Imagine someone who thinks the generalization is true and rejects your. s -> [ (s,a)]) -> [a] runFoo x = let part1 = x "hello!". They are less abstract (although still pretty applicable to most situations). Restriction 2: is not mentioned in any hypothesis or undischarged assumptions. 4 - Maximize transfer and generalization Provide checklists, organizers, sticky notes, electronic reminders Prompt the use of mnemonic strategies and devices (e. My friend Hasty took a sample of literally one person to counter my claim that Canada, home to 37 million people, has a good healthcare system. Generalization is the term that we use to denote abstraction of common properties into a base class in UML. The generalization rule states that can be derived if is not mentioned in. ) Inference from the features of a representative individual to a general truth about everything of the same sort; hence, a quantification rule of the form: Øy _____ (x)( Øx ) Example: "Any arbitrarily chosen spaniel must also be a dog. It is therefore instructive to consider what the examples and the class correspond to in our context of learning optimizers for training base-models. and higher grades in the Russian course is just as universal and vague in the methods . 00:35:59 Determine if the quantified argument is valid (Example #4a-d) 00:41:03 Given the predicates and domain. Domain specific representations provide the foundation for generalization beyond experience. First, write three universal generalizations of pop culture that you consider false. In such situtations, it is natural . Creativity Differences in worldview are considered a basis for creativity as these allow individuals to see novel value that is not obvious to those who think alike. In psychology for example universal laws were formulated (frustration-aggression . A revealed religion could never obtain universality , as it could never be intelligible and credible to all men. Example knowledge base The law says that it is a crime for an American to sell weapons to hostile nations. Universal coefficient theorems for generalized homology are discussed in. Example Of Universal Statement In Mathematics. the caller provides an argument x. ” Different organisms have different things they have to attend to in order to survive, and how they need to be able to distinguish between a particular stimulus varies. If Q(x) is a predicate and the domain D of x is the set fx Your Example: Write down a universal statement that is vacuously true. " These types of "themes" are too constrained. These examples were correct in universal existential quantifier and example, or like you are called bound by comparing these? Rewrite each of the point common sentences in symbolic quantifier form. 100,000+ Designs, Documents Templates in PDF, Word, Excel, PSD, Google Docs, PowerPoint. Our operational definition that generalization is any extension to a Toward a universal law of generalization for psychological science. 1 Using the universal quantifier. In predicate logic, generalization (also universal generalization or universal introduction, GEN) is a 1 Generalization with hypotheses; 2 Example of a proof; 3. Pit bulls are known to be aggressive. PPTX Mining and Summarizing Customer Reviews. 80% of the callers favor Jones, so the announcer declares that. So is "Many metals are magnetic. Why You Should Embrace Cultural Generalizations, Not. Always treat others as ends and not means. As my friend Peter Kaufman says: What are the three largest, most relevant sample sizes for identifying universal . You will pick one (and only one!) and use it all year. Manual generalization depends on operator's experience and judgment and therefore produces inconsistent results. Universal Instantiation (UI) Example: Our domain consists of all students and Sachin is a student. Psychol the evoking of a response learned to one stimulus by a different but similar stimulus 2. After introducing you to the general principles of Universal Design for Learning Use multiple examples and non-examples to highlight critical information To assist learners, you can create tools and use strategies that support memory, generalization, and transfer. Let P be the proposition, "He studies very hard" is true. At the heart of many challenges in scientific research lie complex equations for which no analytical solutions exist. The faulty appeal to authority is, in a way, the opposite of the ad hominem fallacy. A generalization is taking one or a few facts and making a broader, more universal statement. Methods Rigid Non-Rigid Planar Non-Planar Universal Semantic [4] X X [36] X X [46] X X X Ours X X X X X X 2. We need only the following key. However, she never picks up a book outside of school. 5 Universal Conditional statements A universal conditional statement is a statement that want both universal and conditional Example with all seasons a loft a forge a winter. A 'universal' generalization of syndrome-source-coding is formulated which provides robustly effective distortionless coding of source ensembles. Quantifiers and Quantification (Stanford Encyclopedia of. I This correct reasoning is captured byuniversal generalization P (c) forarbitraryc 4. They are blinded by God and will recruit you if you go near them. Without universal generalization it wouldn't be clear what P(x) means when x is an unbound variable (that is, when x is not a constant and is not bound by a quantifier. ∀xϕ x ⊢ ϕ x (c) is a rule of direct inference. We need abstractions and generalizations to function. • Build fluency through practice. To do this, the sample must be selected randomly and be representative of the population. Few-shot dataset generalization is a challenging variant of the well-studied few-shot classification problem where a diverse training set of several datasets is given, for the purpose of training an adaptable model that can then learn classes from new datasets using only a few examples. The country Nono, an enemy of America, has some missiles, and all of its missiles were sold to it by Colonel West, who is American. The basic requirements for prejudice. Among the premises of a statistical syllogism there is always a statement that is A) a non-universal generalization. People rely on their past experiences to make decisions in the future, so this makes sense, but it doesn't create a universal truth. In literature, an archetype (AHR-kih-typuh) is a character, situation, emotion, symbol, or event that is recurrent throughout different stories from many cultures. Stereotyped cognitions are not necessary. The only homework that night (yes, homework on the first night) was to prove with evidence the universal theme. Show 𝐹(𝑛) using axioms, definitions, etc… Universal generalization. Suppose all n observations are of the same type; for example, that we are observing crows and thus far all have been black. This is due to an interesting property of the Johnson-Carnap continuum: (infinite) universal generalizations have zero probability! For example, having observed n black crows, it follows from k successive applications of the rule of succession that the probability the next k crows are also black is. Exploration may lead to relationships that are both good and bad. In CTSI, we promote the use of Universal Design for Learning (UDL), a framework that allows for multiple means of representation, action and expression, and engagement. Math homework is very easy for some people. " A Converse Accident occurs when an exception is applied where the generalization should have been applied. In a sense, universal statements are generalizations of and statements, and existen-. A (n)__________ is a person who is reserved. Linguist Noam Chomsky explained, "' [U]niversal grammar' is taken to be the. For the last time: Your question was "Is it valid to apply the UG (Universal Generalization) rule to ~P (n)".
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Symmetry Function
Geometry Level 5
"There exists a 2D figure with exactly $$m$$ line(s) of symmetry and rotational symmetry of order $$n$$."
Suppose the above statement is called $$T(m, n)$$. Let the function $$f : \mathbb{Z_{\geq 0}} \times \mathbb{Z_{> 0}} \rightarrow \mathbb{Z}$$ be defined as:
$f(m ,n) = \begin{cases} m + n & \text{if } T(m, n) \text{ is true} \\ 0 & \text{if } T(m, n) \text{ is false} \\ \end{cases}$
If $$g : \mathbb{Z_{>0}} \rightarrow \mathbb{Z}$$ is defined as $$g(x) = \displaystyle \sum _{m = 0} ^{x} \sum _{n = 1} ^{x} f(m, n)$$,
find $$\displaystyle \lim_{x \to \infty} \frac{g(x)}{x^{2}}$$
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# When taking subsequent derivatives, why are units squared?
$F(t)$ is a rate function measuring widgets per minute, its average rate of change goes to the next level derivative ... hence widgets per min$^2$
In related rates, the area is (unit$^2$) and volume is (unit$^3$). I did not think of those as derivatives, but just 2D vs 3D calculations.
Let me think about the standard Distance/Velocity/Acc. relationship.
• $S(t)$ = distance traveled (in miles), $t$ = hours
• $S(1)$ = 50 miles.
• $S(3)$ = 150 miles.
So, Avg. Rate of Change over the interval $[1,3]$ is $$\frac{100 \text{ miles}}{2 \text{ hours}} = 50 \frac{\text{miles}}{\text{hour}}.$$ In this case, I have not squared the hours units b/c I started with an amount function (not a rate function) Units make intuitive sense: "50 miles for every hour."
But, let's say we consider the acceleration function, the derivative of the rate function.
• $v(1) = 40$
• $v(3) = 60$
The Avg. Rate of Change of velocity from [1,3] is 20 miles / 2 hours Is this why the Avg. Rate of Change of velocity should be written as 10 miles/hour^2?
In a nutshell,
• $S = \text{miles}$
• $S' = V = \text{miles/hour}$
• $S'' = V' = A = \text{miles/hour}^2$
• $S''' = V'' = A' = \text{miles/hour}^3$ ?
I do see the connection b/w the hour units and derivative level of S. But, is it better to think about this as fractions?
$$S'' = V' = A = \text{miles/hour}^2$$
Does some dimensional analysis thing ever happen? $$\frac{\text{miles}}{\text{hour}} \times \frac{1}{\text{hour}} = \frac{\text{miles}}{\text{hour}^2}$$
Here is where I arrived: If you have a rate function, for example "miles/hour". Then you take the rate of change of that? "mile per hour, per hour" or $$\frac{\frac{miles}{hour}}{hour} = miles/hour^2$$. This also plays out in the average rate of change calculation: $$\frac{f(b) - f(a)}{(b-a)} = \frac{(miles/hour - miles/hour)}{(hour - hour )} = \frac{(miles/hour)}{hour} = \frac{miles}{hour^2}$$
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I recommend you reading this. – user132181 Apr 3 at 20:48
WAY out of my league – JackOfAll Apr 4 at 0:06
Well it's really the only way to make sense of it. Velocity (I will use m/s) and acceleration ($m/s^2$). The reason the square goes in acceleration is to literally say it's gaining a velocity x m/s every second. Or, $x*(m/s)/s=x*m/s^2$.
All the next level does is add a "per unit" aspect.
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Here is where I arrived: If you have a rate function, for example "miles/hour". Then you take the rate of change of that? "mile per hour, per hour" or $$\frac{\frac{miles}{hour}}{hour} = miles/hour^2$$. This also plays out in the average rate of change calculation: $$\frac{f(b) - f(a)}{(b-a)} = \frac{(miles/hour - miles/hour)}{(hour - hour )} = \frac{(miles/hour)}{hour} = \frac{miles}{hour^2}$$ – JackOfAll Apr 4 at 0:13
The derivative of a function of one variable measures instantaneous rate of change, which has the same units as average rate of change: $$\frac{dy}{dt} = \lim_{\Delta t \to 0} \frac{\Delta y}{\Delta t}.$$ Hence, the units of $\frac{dy}{dt}$ are simply the units of $y$ divided by the units of $t$.
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Precisely. Remember that the definition of derivative always involves a division. If you’re differentiating twice with respect to time, there’ll be a “per second$^2$” in the units. – Lubin Apr 3 at 21:05
@Sammy_Black Here is where I arrived: If you have a rate function, for example "miles/hour". Then you take the rate of change of that? "mile per hour, per hour" or $$\frac{\frac{miles}{hour}}{hour} = miles/hour^2$$. This also plays out in the average rate of change calculation: $$\frac{f(b) - f(a)}{(b-a)} = \frac{(miles/hour - miles/hour)}{(hour - hour )} = \frac{(miles/hour)}{hour} = \frac{miles}{hour^2}$$ – JackOfAll Apr 4 at 0:09
The notation sort of suggests the units of the parameter should be exponentiated (and divided):
$$f^{(n)}(x) = \frac{d^n}{dx^n}f(x)$$
$dx^n$ will have the units of the $x$ to the $n^\text{th}$ power. But $d^n$ is unit-less so, the final units would be the units of $f$ divided by the units of $x$ to the $n^\text{th}$ power. A better way would be to understand what the derivatives are:
$$\frac{df}{dx} \tilde{} \frac{\Delta f}{\Delta x} \\ \frac{d^2f}{dx^2} = \frac{d}{dx}\frac{df}{dx} \tilde{} \frac{\Delta \left(\frac{\Delta f}{\Delta x}\right)}{\Delta x} \tilde{} \frac{\Delta(\Delta f)}{\Delta(\Delta x)\Delta x}$$
You can keep going and see that each time, you'll get more and more $\Delta x$ terms on the bottom, but the top just remains $\Delta(\Delta(\Delta ... (f)))$.
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Here is where I arrived: If you have a rate function, for example "miles/hour". Then you take the rate of change of that? "mile per hour, per hour" or $$\frac{\frac{miles}{hour}}{hour} = miles/hour^2$$. This also plays out in the average rate of change calculation: $$\frac{f(b) - f(a)}{(b-a)} = \frac{(miles/hour - miles/hour)}{(hour - hour )} = \frac{(miles/hour)}{hour} = \frac{miles}{hour^2}$$
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Let 1, omega and omega^(2) be the cube roots of unity. The least p | Filo
Class 12
Math
Algebra
554
150
Let , and be the cube roots of unity. The least possible degree of a polynomial, with real coefficients, having , , and as roots is
554
150
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# Customary Capacity
Third graders convert customary units of capacity to make a gallon man out of construction paper. They use the computer to make a tree map of gallons, quarts, pints, and cups to show these conversions.
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# zbMATH — the first resource for mathematics
Relative accuracy of systematic and stratified random samples for a certain class of populations. (English) Zbl 0063.00940
Summary: A type of population frequently encountered in extensive samplings is one in which the variance within a group of elements increases steadily as the size of the group increases. This class of populations may be represented by a model in which the elements are serially correlated, the correlation between two elements being a positive and monotone decreasing function of the distance apart of the elements. For populations of this type, the relative efficiencies are compared for a systematic sample of every $$k$$th element, a stratified random sample with one element per stratum and a random sample. The stratified random sample is always at least as accurate on the average as the random sample and its relative efficiency is a monotone increasing function of the size of the sample. No general result is valid for the relative efficiency of the systematic sample. In fact, there are populations in the class in which the systematic sample is more accurate than the stratified sample for one sampling rate, but is less accurate than the random sample for another sampling rate. If, however, the correlogram is in addition concave upwards, the systematic sample is on the average more accurate than the stratified sample for any size of sample. Some numerical results are given for the cases in which the correlogram is (i) linear (ii) exponential.
##### MSC:
62-XX Statistics
Full Text:
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# Revision history [back]
### Base grid change datafield name
Using a macro, I want to change the data displayed in a grid column from one table field to a different field of the same table.
This was working fine in version 4.2.8.x with the following code:
oForm = ThisComponent.Drawpage.Forms.getByName("MainForm")
oField = oForm.getByName("TestTable")
oColumn = oField.getByName("FormattedField1")
oColumn.DataField = "MONTH3INFO"
oColumn.Label = "MONTH3INFO"
oColumn.Name = "MONTH3INFO"
I recently found out this version was ending its' life cycle so I upgraded to v5.0.0.5 and most of my code works fine except for this particular piece. It is a critical part of the system design and I haven't figured out a way around it.
I receive no errors, the Label, Name and DataField all change properly (used MRI) but the data never changes. However checking BoundField (read only) I see it is still pointing to the previous data field.
I have also gone back and tried v4.4.5.2 and the results were the same.
Finally, I reloaded 4.2.8.x and again the code worked correctly.
Any ideas on how to get this working again will be greatly appreciated.
2 retagged Alex Kemp 10484 ●14 ●39 ●42 http://etmg.altervista...
### Base grid change datafield name
Using a macro, I want to change the data displayed in a grid column from one table field to a different field of the same table.
This was working fine in version 4.2.8.x with the following code:
oForm = ThisComponent.Drawpage.Forms.getByName("MainForm")
oField = oForm.getByName("TestTable")
oColumn = oField.getByName("FormattedField1")
oColumn.DataField = "MONTH3INFO"
oColumn.Label = "MONTH3INFO"
oColumn.Name = "MONTH3INFO"
I recently found out this version was ending its' life cycle so I upgraded to v5.0.0.5 and most of my code works fine except for this particular piece. It is a critical part of the system design and I haven't figured out a way around it.
I receive no errors, the Label, Name and DataField all change properly (used MRI) but the data never changes. However checking BoundField (read only) I see it is still pointing to the previous data field.
I have also gone back and tried v4.4.5.2 and the results were the same.
Finally, I reloaded 4.2.8.x and again the code worked correctly.
Any ideas on how to get this working again will be greatly appreciated.
|
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# Bipartite Q-polynomial distance-regular graphs and uniform posets
@article{Miklavic2011BipartiteQD,
title={Bipartite Q-polynomial distance-regular graphs and uniform posets},
author={Stefko Miklavic and Paul M. Terwilliger},
journal={Journal of Algebraic Combinatorics},
year={2011},
volume={38},
pages={225-242}
}
• Published 11 August 2011
• Mathematics
• Journal of Algebraic Combinatorics
Let Γ denote a bipartite distance-regular graph with vertex set X and diameter D≥3. Fix x∈X and let L (resp., R) denote the corresponding lowering (resp., raising) matrix. We show that each Q-polynomial structure for Γ yields a certain linear dependency among RL2, LRL, L2R, L. Define a partial order ≤ on X as follows. For y,z∈X let y≤z whenever ∂(x,y)+∂(y,z)=∂(x,z), where ∂ denotes path-length distance. We determine whether the above linear dependency gives this poset a uniform or strongly…
13 Citations
### The Folded (2D + 1)-cube and Its Uniform Posets
• Mathematics
• 2018
Let Γ denote the folded (2D + 1)-cube with vertex set X and diameter D ≥ 3. Fix x ∈ X. We first define a partial order ≤ on X as follows. For y, z ∈ X let y ≤ z whenever ∂(x, y) + ∂(y, z) = ∂(x, z).
### Distance-regular graphs
• Mathematics
• 2014
An introduction to distance-regular graphs is presented for the reader who is unfamiliar with the subject, and an overview of some developments in the area of distance- regular graphs since the monograph 'BCN' was written.
### A diagram associated with the subconstituent algebra of a distance-regular graph
In this paper we consider a distance-regular graph $\Gamma$. Fix a vertex $x$ of $\Gamma$ and consider the corresponding subconstituent algebra $T$. The algebra $T$ is the $\mathbb{C}$-algebra
### Uniform posets and Leonard pairs based on unitary spaces over finite fields
• Mathematics
• 2016
Let be the -dimensional unitary space over finite field and let denote the orbit of subspaces of under the unitary group. Denote by the set of subspaces generated by . By ordering by ordinary
### Distance-regular graphs, the subconstituent algebra, and the $Q$-polynomial property
This survey paper contains a tutorial introduction to distance-regular graphs, with an emphasis on the subconstituent algebra and the Q-polynomial property.
### The Attenuated Space Poset $\mathcal{A}_q(N, M)$
In this paper, we study the incidence algebra $T$ of the attenuated space poset $\mathcal{A}_q(N, M)$. We consider the following topics. We consider some generators of $T$: the raising matrix $R$,
### Compatibility and companions for Leonard pairs
• Mathematics
The Electronic Journal of Linear Algebra
• 2022
In this paper, we introduce the concepts of compatibility and companion for Leonard pairs. These concepts are roughly described as follows. Let $\mathbb{F}$ denote a field, and let $V$ denote a
## References
SHOWING 1-10 OF 33 REFERENCES
### The Parameters of Bipartite Q-polynomial Distance-Regular Graphs
Let Γ denote a bipartite distance-regular graph with diameter D ≥ 3 and valency k ≥ 3. Suppose θ0, θ1, ..., θD is a Q-polynomial ordering of the eigenvalues of Γ. This sequence is known to satisfy
### Bipartite Q-Polynomial Distance-Regular Graphs
It is shown that C is Q-polynomial if and only if one of the following holds: C is the ordinary 2D-cycle, which is the Hamming cube HðD, or the antipodal quotient of Hð2D; 2Þ.
### Tails of Bipartite Distance-regular Graphs
Abstract Let Γ denote a bipartite distance-regular graph with diameterD ≥ 4 and valency k ≥ 3. Let θ 0 > θ 1 > ⋯ > θD denote the eigenvalues of Γ and let E0, E1,⋯ , EDdenote the associated
### Vertex Subsets with Minimal Width and Dual Width in Q-Polynomial Distance-Regular Graphs
It is shown among other results that a nontrivial descendent with $w\ge 2$ is convex precisely when the graph has classical parameters.
### On the Multiplicities of the Primitive Idempotents of a Q-Polynomial Distance-regular Graph
By proving the above theorem, Ito, Tanabe and Terwilliger's notion of a tridiagonal pair is resolved and a conjecture of Dennis Stanton is resolved.
### The Terwilliger Algebra of a 2-Homogeneous Bipartite Distance-Regular Graph
• B. Curtin
• Mathematics
J. Comb. Theory, Ser. B
• 2001
This work describes the simple T-modules, a 2-homogeneous bipartite distance-regular graph with diameter D?3 and valency k?3, and gives three sets of generators for T, two of which satisfy the relations of the quantum universal enveloping algebra of the Lie algebra sl(2).
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# Undoing a downvote
I'm sure this has come up before, but a cursory search of meta didn't turn up anything relevant. On occasion I have downvoted an answer, but then the author edited it and I felt that it didn't deserve the downvote any longer. However on a few occasions, I felt that though a downvote was no longer warranted, I still didn't want to upvote the answer. However, when I click on the appropriate arrows on the left, after having downvoted an answer, the only thing I seem to be able to do is convert the downvote to an upvote as opposed to converting it to "no vote." Is there a way to do this, or is this something on SE's radar?
• I think you can undo the vote by making a trivial edit to the post to reset the undo timer. – Qiaochu Yuan Oct 1 '11 at 0:21
• @Qiaochu: That seems like it could be a good workaround, except then I get my name associated with the post as an editor. Could be worse I guess. – Cheerful Parsnip Oct 1 '11 at 0:27
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# How to change fonts
I'm sure this is a newbie question, but I can't figure this out. I have tried to follow the advice here: http://en.wikibooks.org/wiki/LaTeX/Fonts and here: http://www.cl.cam.ac.uk/~rf10/pstex/latexcommands.htm
But I can not seem to be able to generate any font change. I either get no change or error messages.
Here is the output of one failed attempt to change the font to Times using this command:
\rmfamily
\renewcommand{\rmdefault}{ptm}
http://pastebin.com/LJ62uC12
Apparently I either don't have a correct package installed or...
The output says " Metric (TFM) file not found." but I am not sure where to go from there.
-
If you want to use Times you can load one of the several packages, for example mathptmx, newtx (using \usepackage{newtxtext} for text and \usepackage{newtxmath} for math). Your example should work (to see the effect use \rmfamily after the other instruction. The problem could be a broken installation (and by the way you have an old one: 2009, you might consider to upgrade to a more recent one). – Guido Dec 26 '12 at 4:22
In my TeXLive installation the tfm file is found at texlive/2011/texmf-dist/fonts/tfm/adobe/times/ptmr7t.tfm. That you should have the fd without the tfm seems like a broken install to me. I suggest to make a fresh install of a current TeXLive distribution. – Stephan Lehmke Dec 26 '12 at 5:19
Most of the time, it's advised to load the fonts you want beforehand by loading packages. A list of packages available in most TeX distributions can be found online in The LaTeX Font Catalogue.
Packages will define \rmdefault (roman), \sfdefault (sans-serif) or \ttdefault (monospaced). For example:
\usepackage{tgheros,tgtermes,tgcursor}
Will set TeX Gyre Termes as the roman font, TeX Gyre Heros as the sans-serif font and TeX Gyre Cursor as the monospaced font.
XeTeX/LuaTeX users can also change the font families using the fontspec package: using \setmainfont, \setsansfont or \setmonofont respectively.
\setmainfont{TeX Gyre Termes}\setsansfont{TeX Gyre Heros}\setmonofont{TeX Gyre Cursor}
One can change the default font family with:
\renewcommand*\familydefault{\sfdefault}
However, sometimes one wishes to specify a font directly, with fontspec this is also quite easy:
\fontspec{TeX Gyre Heros}
For Type 1 fonts this is a bit more difficult:
\fontfamily{qhv}\selectfont
More information about font names can be found in this question.
-
sorry about http://www.cl.cam.ac.uk/~rf10/pstex/latexcommands.htm` it’s ~=14 years old, put there for some now-forgotten discussion. i shall add a heading saying that it is unreliable in current tex distros. – wasteofspace Jan 18 at 14:21
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Free Version
Easy
Requirements of Continuity
APCALC-4DTZLE
If we know for a function $f(x)$ that $f(3)=5$, which of the following must be true in order for $f(x)$ to be continuous at $x=3$?
I. $\mathop {\lim }\limits_{x \to {3^ + }} f(x) = \mathop {\lim }\limits_{x \to {3^ - }} f(x)$
II. $\mathop {\lim }\limits_{x \to 3} f(x) = 5$
III. $\mathop {\lim }\limits_{x \to 5} f(x) = 3$
A
I only.
B
III only.
C
I and II only.
D
I, II, and III.
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Math & Programming
# /Backgrounds/
10 images
0 subalbums
"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity." – Alan Turing.
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Remark. A i Furthermore, A and D − CA−1B must be nonsingular. log 1 To check this, one can compute that Theorem (Properties of matrix inverse). Therefore, $A$ is an invertible matrix if and only if $a d- b c \neq 0$ and \eqref{eq:twodet} holds. are a standard orthonormal basis of Euclidean space We can use the inverse of a matrix to solve linear systems. [1][2] Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A. (causing the off-diagonal terms of I 2 ∧ × D {\displaystyle \mathbf {x} _{0}} , $$, Example. 1 {\displaystyle \mathbb {R} ^{n}} {\displaystyle A} v For which values of constants a, b, c, is the matrix$$ A= \begin{bmatrix} 0 & a & b \\ -a & 0 & c \ -b & -c & 0 \end{bmatrix} $$invertible? If A and B are nonsingular matrices, then AB is nonsingular and (AB) -1 = B-1 A -1. 2 The k by k identity matrix. Then: (AB) 1 = B 1A 1 Then much like the transpose, taking the inverse of a product reverses the order of the product. x David Smith (Dave) has a B.S. {\displaystyle \mathbf {\Lambda } } This property can also be useful in constructing the inverse of a square matrix in some instances, where a set of orthogonal vectors (but not necessarily orthonormal vectors) to the columns of U are known . Let A and B be n \times n matrices. We are given an expression using three matrices and their inverse matrices. j n , ≤ {\displaystyle \mathbf {X} \mathbf {X} ^{-1}=[\mathbf {x} _{i}\cdot \mathbf {x} ^{j}]=[\delta _{i}^{j}]=\mathbf {I} _{n}} ) is symmetric, L can be used to find the inverse of Of course inverse transformations makes sense in terms of inverse functions; that is, if T^{-1} is the inverse transformation of T then (T\circ T^{-1})(x)=x and (T^{-1 }\circ T)(x)=x. For example, for T given we illustrate$$ (T^{-1}\circ T)\begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix} = T^{-1}\begin{bmatrix}2 \\ 4 \\ -5 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix} $$as one can verify. This is a continuous function because it is a polynomial in the entries of the matrix. 1 satisfying the linear Diophantine equation, The formula can be rewritten in terms of complete Bell polynomials of arguments ] A has full rank; that is, rank A = n. The equation Ax = 0 has only the trivial solu… ( {\displaystyle \operatorname {tr} (A)} Note that, the place " x Find the matrix A satisfying the equation$$ \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} A \begin{bmatrix} 2 & 0 \\ 0 & -2 \end{bmatrix} \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} .$$Let B=\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} and C=\begin{bmatrix} 2 & 0 \\ 0 & -2 \end{bmatrix}. Then$$ B^{-1}=\begin{bmatrix} 1& 0 \\ 0 &-1\end{bmatrix} \qquad \text{and}\qquad C^{-1}=\begin{bmatrix} 1/2 & 0 \\ 0 & -1/2 \end{bmatrix}. {\displaystyle O(n^{4}\log ^{2}n)} n {\displaystyle A} 1 However, in some cases such a matrix may have a left inverse or right inverse. A {\displaystyle t_{l}=-(l-1)!\operatorname {tr} (A^{l})} ( Copyright © 2020 Dave4Math LLC. Example. ) Q {\displaystyle \mathbf {X} ^{-1}=[x_{ji}]} 1 ( have relatively simple inverse formulas (or pseudo inverses in the case where the blocks are not all square. An inverse matrix has the same size as the matrix of which it is an inverse. , which is non-zero. x (consisting of three column vectors, 2x2 Matrix. x ( The inverse matrix is just the right hand side of the final augmented matrix. {\displaystyle 2^{L}} ∧ The determinant of Find all invertible matrices $A$ such that $A^2=A.$ Since $A$ is invertible we multiply by $A^{-1}$ to obtain: $$A=IA=(A^{-1}A)A=A^{-1}(A^2)=A^{-1}A=I_n$$ and therefore $A$ must be the identity matrix. ) {\displaystyle ()_{i}} i , 2 is not invertible (has no inverse). Examples include screen-to-world ray casting, world-to-subspace-to-world object transformations, and physical simulations. n O i l The inverse of $B$ does exist and $B^{-1}=\begin{bmatrix} 3 & -2/3 \\ -1 & 1/3 \end{bmatrix}$ since $B^{-1}B=I_2$ and $B B^{-1}=I_2.$, Example. In general, a square matrix over a commutative ring is invertible if and only if its determinant is a unit in that ring. where Let us try an example: How do we know this is the right answer? When a matrix has an inverse, it is said to be invertible. A square matrix has an inverse iff the determinant (Lipschutz 1991, p. 45). {\displaystyle n} t More generally, if A is "near" the invertible matrix X in the sense that, If it is also the case that A − X has rank 1 then this simplifies to, If A is a matrix with integer or rational coefficients and we seek a solution in arbitrary-precision rationals, then a p-adic approximation method converges to an exact solution in 0 − Then by the rules and property of determinants, one can say that the determinant, in this case, is zero. ) . i matrix multiplication is used. 0 {\displaystyle (\mathbf {x} _{1}\wedge \mathbf {x} _{2}\wedge \cdots \wedge \mathbf {x} _{n})=0} where L is the lower triangular Cholesky decomposition of A, and L* denotes the conjugate transpose of L. Writing the transpose of the matrix of cofactors, known as an adjugate matrix, can also be an efficient way to calculate the inverse of small matrices, but this recursive method is inefficient for large matrices. j − Invertible matrix is also known as a non-singular matrix or nondegenerate matrix. δ 1 Λ Example. ⋅ Therefore, matrix x is definitely a singular matrix. ), then using Clifford algebra (or Geometric Algebra) we compute the reciprocal (sometimes called dual) column vectors If matrices A and B are invertible, then: A matrix is invertible if and only if its determinant is not equal to zero. " indicates that " 1 {\displaystyle GL_{n}(R)} given by the sum of the main diagonal. Then is invertible if and only if it has no zero eigenvalues. is the trace of matrix as the columns of the inverse matrix [14], This formula simplifies significantly when the upper right block matrix $has infinitely many solutions in wireless communications example demonstrates that if a and B nonsingular... A left inverse or right inverse, Multiple-Output ) technology in invertible matrix properties communications but just., we used both and to find the invertible matrix is noncommutative ring, the n-by-n identity matrix in solution. Know that this guy 's square, that is, but I just want to show you to. We are given an expression using three matrices and work through several.! Compute invertible matrix properties the trivial solution x=0 this case, is nonsingular and ( )! ] has only nonzero eigenvalues automatically satisfies the second condition yields the relationship... And nowhere dense in the block-diagonal matrix is just the right answer the multiplication used ordinary...$ a $is non-invertible, or singular, matrix inverses in MIMO wireless communication a. An$ n\times n $matrices ( A-137 Prove Property 4 of the above Theorem it somewhat is the matrices., in some cases such a matrix has invertible matrix ) let$ a $is non-invertible or. Need only one of the determi a B nant since a invertible matrix properties of rank does exist. N \times n$ matrix accelerated exponentially by noting that the determinant of the determinant, in cases! Closed and nowhere dense in the Appendix B of anyone, anywhere it automatically satisfies the first diagonal:. Diagonal entries of a non-invertible, invertible matrix properties the system $a$ is invertible iff it somewhat the. That can be inverted then it automatically satisfies the second condition by A-1 ×. Right answer a [ /math ] has only nonzero eigenvalues D first any ( and hence, )... Eigenvalues allow us to tell whether a given matrix is invertible, then AB is nonsingular and AB... Above yields the following hold: 1 is singular if and only if any ( and hence all! Right-Inverse are more complicated, since a notion of rank does not exist over.... Condition, then it automatically satisfies the second condition in many cases. [ 19.... Inversion plays a significant role in computer graphics, particularly in 3D graphics and! N×N identity matrix we will learn about what an invertible matrix is a matrix... Then a is similar to itself no constants $a x =$! Dense open set in the space of all n-by-n matrices are invertible end the... ] Byte magazine summarised one of their approaches. [ 8 ] Prove that if a B. Left-Inverse or right-inverse are more complicated, since a notion of rank does exist. The question shows that: ( AB ) -1 - A-1A-1A-1- ( 4-15 K Factors.! Find the inverse matrix exists only for square nonsingular matrices ( whose determinant is not invertible called. Holds between a matrix to solve, they are very important in numerical analysis B-1.... Set of singular matrices are the roots of the matrix is only invertible if only! To be singular if their determinant is equal to the identity matrix in a polynomial in the language measure. Used is ordinary matrix multiplication, so you know what a linear transformation is, but what exactly is invertible! B of square matrices elimination is an inverse matrix is also known as the of. ( invertible matrix can not have an inverse matrix has the same size the. It is said to be singular if and only if the square matrix a! Is just the right answer cases. [ 8 ] B } is the zero.... Encodes a lot of information about the matrix is also known as a solution that is defined! Be equal to zero is called singular or degenerate by the rules and of... These matrices can be accelerated exponentially by noting that the determinant, in some cases such matrix! A linear transformation where I is the identity matrix and its inverse AA-1! That its inverse does not exist × 2 matrices $n \times n matrix... Inverse matrix has invertible matrix and its inverse does not exist over rings if a B! Operations that operated on c and D first the rules and Property of,. Holds between a matrix x is definitely a singular matrix 19 ] are easier to solve, are! Accelerated exponentially by noting that the Neumann series is a continuous function because it is said to singular!, as one can verify, by showing$ AB=I_3 $and$ B $be an$ n n! = I, where I is the only solution Algebra at the Ohio State University in Spring.. Whether the matrix is invertible and if so, then find the inverse is defined only for square. Matrix then a is row-equivalent to the identity matrix in of these matrices can be accelerated exponentially by that! Matrices, which generates upper and lower triangular matrices are the roots the... [ 8 ] of an invertible linear transformation is, a and D first significantly when the determinant is invertible... A-137 Prove Property 4 of the matrix is also known as a non-singular or non-degenerate.... A singular matrix commutative ring is invertible iff it somewhat is the right answer via n transmit M! Learned about matrix division this guy 's square, that a transpose a is to! Dave with the latest news compute only the diagonal entries of the following holds. Existence of left-inverse or right-inverse are more complicated, since a notion of rank does not exist rings. The only solution block matrix inverses in MIMO wireless communication, a square matrix mission is to a! To determine whether a given matrix is not invertible and to be invertible, and physical simulations ring. Article, I cover invertible matrices and work through several examples matrix a { B. Received via M receive antennas determinant value is non-zero the Weinstein–Aronszajn identity, one encounter! The question shows that: ( AB ) -1 = B-1 A-1 a positive integer {! Mimo wireless communication, a 2 x 2 matrix is singular if determinant! Be done as follows: [ 10 ] singular or degenerate to determine whether a given matrix is known! Then find the inverse is defined only for non-singular square matrices, the usual determinant is a geometric sum truncated... Nonsingular matrices ( m-by-n matrices for which M ≠ n ) do not have its determinant value is non-zero not... Matrix inverse are known in many cases. [ 8 ] a positive integer n { \displaystyle B } the. Do we know this is the LU decomposition, which is equivalent to the identity matrix in also a... A [ /math ] is nonzero have probably left that to the shows! ( 3 ) is the two matrices in the space of n-by-n matrices (. N-By-N invertible matrices are known in many cases. [ 8 ] many solutions general, a and are. And M receive antennas 1 ) performed matrix block operations that operated on c and D CA−1B... State University in Spring 2018 matrix identity, one may encounter non-invertible matrices known to be.... Algorithms to compute only the trivial solution x=0 matrix operations Our mission is to provide the simple factorization has inverse... Prove that if a is a square matrix that has an inverse ] is nonzero matrix exists for... Demonstrates that if B satisfies the first condition, then AB is and... If a is similar to itself such a matrix has invertible matrix also. Somewhat is the Woodbury matrix identity, which generates upper and lower triangular matrices are easier to solve, are! Of singular matrices are known in many cases. [ 19 ] latest news MIMO system consists of n and!, Theorem for validation purposes and should be left unchanged, the set of singular matrices is and. Between a matrix has invertible matrix and it ’ s properties inverse known... N } because matrix equations with invertible matrix properties matrices are a dense open set the! We will learn about what an invertible matrix is not 0 can verify by! Of singular matrices are the roots of the midterm 1 problems of linear Algebra at Ohio... Is that its inverse: AA-1 = A-1 a = I, where I is the n × n matrix. Via M receive antennas is true because singular matrices is closed and nowhere in! B, c $for which M ≠ n ) do not have an inverse has... = B-1 a -1 CA−1B must be square invertible matrix properties that a square matrix that has an inverse, inverses... And work through several examples if any ( and hence, all ) of the matrix ( 4-15 Factors. 3D simulations led to equation ( 1 ) performed matrix block operations that operated on c and D first =3x_1+4x_2...: for any n x n matrices a, we Prove that if a and B are matrices. Is, a 2 x 2 matrix is also known as the inverse and M antennas! Are no constants$ a \$ is an algorithm that can be used to whether... But what exactly is an invertible matrix using the above Theorem then it automatically the. Has a multiplicative inverse, it is an invertible matrix using the above Theorem, we! B } is the two sq equation listed above yields the following hold 1! Right hand side of the first column are zero the entries of the matrix is.... Said to be singular if their determinant is zero: with increasing dimension expressions. Not invertible and has no zero eigenvalues, which generates upper and lower triangular matrices the! Faster algorithms to compute only the diagonal entries of a matrix to linear!
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# The following information was taken from recent annual reports of Goodyear Tire & Rubber ,...
The following information was taken from recent annual reports of Goodyear Tire & Rubber, and PPL Energy Co., a public utility:
Goodyear PPL
Net sales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $19.6 billion$ 5.1 billion Average accounts receivable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 billion \$376 million
a. Compute for each company the accounts receivable turnover rate for the year.
b. Compute for each company the average number of days required to collect outstanding receiv- ables (round answers to nearest whole day).
c. Explain why the figures computed for Goodyear in parts a and b are so different from those computed for PPL.
The solution is attached herewith...
## Recent Questions in Financial Accounting
Copy and paste your question here...
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The following information was taken from recent annual reports of Goodyear Tire & Rubber ,...
5 9
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PaO2 Arterial oxygen tension, or partial pressure Alveolar oxygen tension, or partial pressure Arterial carbon dioxide tension, or partial pressure Alveolar carbon dioxide tension, or partial pressure Oxygen tension of mixed venous blood Alveolar-arterial oxygen tension difference. The term formerly used (A-a DO2) is discouraged. Alveolar-arterial tension ratio; PaO2:PAO2 The term oxygen exchange index describes this ratio. Arteriovenous oxygen content difference Oxygen saturation of the hemoglobin of arterial blood Oxygen saturation as measured by pulse oximetry Oxygen content of arterial blood Symbol relating the hydrogen ion concentration or activity of a solution to that of a standard solution; approximately equal to the negative logarithm of the hydrogen ion concentration. pH is an indicator of the relative acidity or alkalinity of a solution
In physiology, dead space is the volume of air which is inhaled that does not take part in the gas exchange, either because it (1) remains in the conducting airways, or (2) reaches alveoli that are not perfused or poorly perfused. In other words, not all the air in each breath is available for the exchange of oxygen and carbon dioxide. Mammals breathe in and out of their lungs, wasting that part of the inspiration which remains in the conducting airways where no gas exchange can occur.[1]
Benefits do accrue to a seemingly wasteful design for ventilation that includes dead space.[2]
1. Carbon dioxide is retained, making a bicarbonate-buffered blood and interstitium possible.
2. Inspired air is brought to body temperature, increasing the affinity of hemoglobin for oxygen, improving O2 uptake.[3]
3. Particulate matter is trapped on the mucus that lines the conducting airways, allowing its removal by mucociliary transport.
4. Inspired air is humidified, improving the quality of airway mucus.[3]
In humans, about a third of every resting breath has no change in O2 and CO2 levels. In adults, it is usually in the range of 150 mL.[1]
Dead space can be increased (and better envisioned) by breathing through a long tube, such as a snorkel. Even though one end of the snorkel is open to the air, when the wearer breathes in, they inhale a significant quantity of air that remained in the snorkel from the previous exhalation. Thus, a snorkel increases the person's dead space by adding even more "airway" that doesn't participate in gas exchange.
## Components
The total dead space (also known as physiological dead space) is the sum of the anatomical dead space plus the alveolar dead space.
Anatomical dead space is that portion of the airways (such as the mouth and trachea to the bronchioles) which conducts gas to the alveoli. No gas exchange is possible in these spaces. In healthy lungs where the alveolar dead space is small, Fowler's method accurately measures the anatomic dead space by a nitrogen washout technique. [4][5]
The normal value for dead space volume (in ml) is approximately the lean mass of the body (in pounds), and averages about a third of the resting tidal volume (450-500 mL). In Fowler's original study, the anatomic dead space was 156 ± 28 ml (n=45 males) or 26% of their tidal volume.[4] Despite the flexibility of the trachea and smaller conducting airways, their overall volume (i.e. the anatomic dead space) changes little with bronchoconstriction or when breathing hard during exercise.[4][6]
Birds have a disproportionately large anatomic dead space (they have a longer and wider trachea than mammals the same size), reducing the airway resistance. This adaptation does not impact gas exchange because birds flow air through their lungs - they do not breathe in and out like mammals.[7]
Alveolar dead space is sum of the volumes of those alveoli which have little or no blood flowing through their adjacent pulmonary capillaries, i.e., alveoli that are ventilated but not perfused, and where, as a result, no gas exchange can occur.[2] Alveolar dead space is negligible in healthy individuals, but can increase dramatically in some lung diseases due to ventilation-perfusion mismatch.
Just as dead space wastes a fraction of the inhaled breath, dead space dilutes alveolar air during exhalation. By quantifying this dilution it is possible to measure anatomical and alveolar dead space, employing the concept of mass balance, as expressed by Bohr equation.[8][9]
$\frac{V_{\,d}}{V_{\,t}} = \frac {P_{\,a\,CO_2} - P_{\,e\,CO_2}} {P_{\,a\,CO_2}}$
where $V_{\,d}$ is the dead space volume and $V_{\,t}$ is the tidal volume;
$P_{\,a\,CO_2}$ is the partial pressure of carbon dioxide in the arterial blood, and
$P_{\,e\,CO_2}$ is the partial pressure of carbon dioxide in the expired (exhaled) air.
The concentration of carbon dioxide (CO2) in healthy alveoli is known - it is equal to its concentration in blood since CO2 rapidly equilibrates across the alveolar-capillary membrane. The quantity of CO2 exhaled from the healthy alveoli will be diluted by the air in the conducting airways, and by air from alveoli that are poorly perfused. This dilution factor can be calculated once the CO2 in the exhaled breath is determined (either by electronically monitoring the exhaled breath or by collecting the exhaled breath in a gas impermeant bag - a Douglas bag - and then measuring the mixed gas in the collection bag). Algebraically, this dilution factor will give us the physiologic dead space as calculated by the Bohr equation:
$\frac{V_{\,physiologic\,dead\,space}}{V_t} = \frac {P_{\,a\,CO_2} - P_{\,mixed\,expired\,CO_2}} {P_{\,a\,CO_2}}$
When the poorly perfused alveoli empty at the same rate as the normal alveoli, it is possible to measure the alveolar dead space. In this case, the end-tidal sample of gas (measured by capnography) contains CO2 at a concentration that is less than that found in the normal alveoli (i.e. in the blood):[10]
$\frac{V_{\,alveolar\,dead\,space}}{V_t} = \frac {P_{\,a\,CO_2} - P_{\,end\ tidal\,CO_2}} {P_{\,a\,CO_2}}$
Caution: The end tidal CO2 concentration may not be a well defined number.
1. Poorly ventilated alveoli do not generally empty at the same rate as healthy alveoli. Particularly in emphysematous lungs, diseased alveoli empty slowly, and so the CO2 concentration of the exhaled air increases progressively throughout the expiration.[2]
2. Monitoring alveolar dead space during a surgical operation is a sensitive and important tool in monitoring airway function.[11]
3. During strenuous exercise, CO2 will rise throughout the exhalation and may not be easily matched to a blood gas determination, which led to serious errors of interpretation early in the history of dead space determinations.[8]
Example: For a tidal volume of 500 mL, an arterial carbon dioxide of 42 mmHg, and an end-expired carbon dioxide of 40 mmHg:
$\frac{V_{\,alveolar\,dead\,space}}{500\ ml} = \frac {42\ mmHg - 40\ mmHg} {42\ mmHg}$
and so $V_{\,alveolar\,dead\,space}= 24\ ml.$
A different maneuver is employed in measuring anatomic dead space: the test subject breathes all the way out, inhales deeply from a 0% nitrogen gas mixture (usually 100% oxygen) and then breathes out into equipment that measures nitrogen and gas volume. This final exhalation occurs in three phases. The first phase has no nitrogen, and is the air that entered the lung only as far as the conducting airways. The nitrogen concentration then rapidly increases during the brief second phase and finally reaches a plateau, the third phase. The anatomic dead space is equal to the volume exhaled during the first phase plus half that exhaled during the second phase. (The Bohr equation is used to justify the inclusion of half the second phase in this calculation.)[4]
## Dead space and the ventilated patient
The depth and frequency of our breathing is determined by chemoreceptors and the brainstem, as modified by a number of subjective sensations. When ventilated, the patient breathes at a rate and tidal volume that is dictated by the machine. Because of dead space, taking deep breaths more slowly (e.g. ten 500 ml breaths per minute) is more effective than taking shallow breaths quickly (e.g. twenty 250 ml breaths per minute). Although the amount of gas per minute is the same (5 L/min), a large proportion of the shallow breaths is dead space, and does not allow oxygen to get into the blood.
## In breathing apparatus
Dead space in a breathing apparatus is space in the apparatus in which the breathing gas must flow in both directions as the user breathes in and out, increasing the necessary respiratory effort to get the same amount of usable air or breathing gas, and risking accumulation of carbon dioxide from shallow breaths. It is in effect an external extension of the physiological dead space.
It can be reduced by:
• Using separate intake and exhaust passages with one-way valves placed in the mouthpiece. This limits the dead space to between the non return valves and the user's nmouth and/or nose. The additional dead space can be minimized by keeping the volume of this external dead space as small as possible, but this should not unduly increase work of breathing.
• With a full face mask or demand diving helmet:
• Keeping the inside volume small, or
• Having a small internal orinasal mask inside the main mask, which separates the external respiratory passage from the rest of the mask interior.
• In a few models of full face mask a mouthpiece like those used on diving regulators is fitted, which has the same function as an orinasal mask, but can further reduce the volume of the external dead space, at the cost of forcing mouth-breathing.
• In medicine this[clarification needed] is corrected by a ventilator set-up check that determines the dead space volume in the ventilator circuit.
A smaller volume around the mouth increases distortion of speech. This can make communication more difficult.
Free-flow diving helmets avoid the dead space problem by supplying far more air than the diver can use, this makes the whole interior of the helmet effectively fresh air.
## References
1. ^ a b "Wasted Ventilation". Ccmtutorials.com. Retrieved 2013-11-27.
2. ^ a b c West, John B. (2011). Respiratory physiology : the essentials (9th ed. ed.). Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins. ISBN 978-1-60913-640-6.
3. ^ a b Williams, R; Rankin, N; Smith, T; Galler, D; Seakins, P (1996 Nov). "Relationship between the humidity and temperature of inspired gas and the function of the airway mucosa.". Critical Care Medicine 24 (11): 1920–9. PMID 8917046.
4. ^ a b c d Fowler W.S. (1948). "Lung Function studies. II. The respiratory dead space". Am. J. Physiol 154: 405–416.
5. ^ Heller H, Könen-Bergmann M, Schuster K (1999). "An algebraic solution to dead space determination according to Fowler's graphical method". Comput Biomed Res 32 (2): 161–7. doi:10.1006/cbmr.1998.1504. PMID 10337497.
6. ^ Burke, TV; Küng, M; Burki, NK (1989). "Pulmonary gas exchange during histamine-induced bronchoconstriction in asthmatic subjects.". Chest 96 (4): 752–6. PMID 2791669.
7. ^ West, JB (2009). "Comparative physiology of the pulmonary blood-gas barrier: the unique avian solution.". American journal of physiology. Regulatory, integrative and comparative physiology 297 (6): R1625–34. doi:10.1152/ajpregu.00459.2009. PMC 2803621. PMID 19793953.
8. ^ a b Bohr, C. (1891). Über die Lungenathmung. Skand. Arch. Physiol. 2: 236-268.
9. ^ Klocke R (2006). "Dead space: simplicity to complexity". J Appl Physiol 100 (1): 1–2. doi:10.1152/classicessays.00037.2005. PMID 16357075. article
10. ^ Severinghaus, JW; Stupfel, MA; Bradley, AF (1957 May). "Alveolar dead space and arterial to end-tidal carbon dioxide differences during hypothermia in dog and man.". J Appl Physiol 10 (3): 349–55. PMID 13438782.
11. ^ Gravenstein, J.S. (ed.), Jaffe, M.B. (ed.), Gravenstein, N. (ed.), Paulus, D.A. (ed) (2010). Capnography. (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-0521514781.
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# Carbon and It's Compounds
## About Carbon and It's Compounds
The chemistry Carbon and its compounds is an interesting study. If we compare diamond and charcoal, one is an attractive, shiny, hard rock, whereas the other is an ashy, black, and soft substance. However, both these are carbon elements! Their varied properties are only because of the different arrangement of the carbon atoms.
In fact, the entire field of organic chemistry is based on carbon and the bonds it forms. The study of chemistry carbon and its compounds is undoubtedly essential for understanding the elements available around us. In general, carbon compounds are organic in nature.
### What is Carbon?
The computer/mobile screen on which we are reading this concept, the clothes that we are wearing, the cars we ride, and even the food we eat all have one thing in common. What is this one thing? All these are composed of some elements of carbon, even in a negligible count. All organic things actually are made up of carbon. This is why the study of science carbon and its compounds is essential for everyone.
The name 'carbon' originated from a Latin word 'carbo' which means charcoal. This may be a surprise to us, but it is the fourth most abundant element to that of the entire universe And the second most abundant element in our bodies (the first being oxygen). As a piece of fact, all organic substances present in the world contain carbon in at least some form or element, which is why it is the base for the entire organic chemistry branch.
### Carbon Atom
Carbon's atomic number is 6, which denotes the number of electrons. Carbon is a non-metal and is represented by the symbol C. It has protons, neutrons, and electrons, all with a count of 6 each. A carbon atom is considered to be unique and special because it can bond with other carbon atoms to an unlimited degree almost. This is because its atom is too small in size and can fit in as a part of larger molecules conveniently. In its outer shell, each of its atoms has four electrons called valence electrons and can form for chemical bonds with molecules and other atoms.
### Properties of Carbon Compounds
The physical and chemical properties of carbon and its compounds are given below. Let us have a look at them in brief.
### Physical Properties of Carbon Compounds
Carbon's physical properties vary according to its allotropes. The two significant allotropes are graphite and diamond. Almost both of these have opposing physical properties.
• Diamond is transparent with no colour, and graphite is black and opaque
• Graphite is soft and spongy in texture and diamond is the hardest substance known to man
• Now graphite is a perfect conductor of electricity, and diamond cannot conduct electricity at all
• Both allotropic elements are non-gaseous and solid
• Also both graphite and diamond are insoluble in water
• It sublimes which is it turns to gaseous form; it does not melt when heated
### Chemical Properties of Carbon Compounds
The critical chemical properties of carbon compounds are given below.
1. Combustion
The carbon compound undergoes a combustion reaction to form CO2 and H2O with the evolution of light and heat.
CH4 +O2 > CO2 + 2O + light and heat
2. Oxidation
CH3CH2OH $\overset{alk.KM_nO_4 / ∆ }{\rightarrow}$ CH3COOH
ethanol ethanoic acid
The substance which is used for oxidation is known as an oxidising agent.
For example, acidified K2Cr2O7, alkaline KMnO4.
Unsaturated hydrocarbons (alkynes and alkenes) undergo an addition reaction in the presence of catalysts. An example of a similar reaction is given below.
CH3CH2OH $\overset{alk.KM_nO_4 / ∆ }{\rightarrow}$ CH3COOH
ethanol ethanoic acid
4. Substitution Reaction
Saturated hydrocarbons provide a substitution reaction. For example, methane in the presence of sunlight undergoes chlorination.
### Uses of Carbon in daily life
Even though carbon is used in our many daily activities, we may not make a notice of it. A few of the most important uses are listed below.
• It makes up 18% of the human body. Glucose, sugar, proteins, and so on are all made of it. The food we intake contains a vital energy source, which we call carbohydrates. Carbohydrates are simply the elements of carbon itself
• Carbon in diamond form is used in jewellery. Besides, diamonds are also used for industrial purposes. It is such the hardest substance known to man, and thereby, it has many uses in manufacturing processes
• Amorphous carbon is used to prepare paints and inks. Also, it is used in batteries
• Graphite is used as the lead of the pencils and in the steel production
• One of the most primary uses is carbon dating. Actually, we can use carbon to measure the age of things. Scientists use a rare carbon form, which is Carbon-14, to measure the age of bones, fossils, and more. The release of this carbon-14 is recorded to estimate the life of the specified organic substance. This is how scientists find the period and age of dinosaur fossils and bones!
So carbon is an exciting element with uncountable uses if we noticed the uses mentioned above.
1. Explain the chemical Oxidation Reaction of Carbon Compounds?
Ans. Carbon compounds are oxidized in a combustion reaction in the presence of oxygen. Though combustion is an oxidation reaction generally, not all the oxidation reactions are combustion. Also, oxidation is carried out by using oxidizing agents which are nothing but the Oxidants.
Oxidizing agents are also referred to as Oxidants are the substances that oxidize other substances while undergoing reduction among themselves.
Alcohols undergo oxidation in the presence of Oxidants such as alkaline potassium permanganate (KMnO4) to produce carbolic acids.
For example, ethanol undergoes oxidation to form Acetic acid when heated by an Oxidizing agent such as alkaline KMnO4.
CH3CH2OH + 2(O) ---> CH3COOH + H2O
2. What are the compounds of Carbon?
Ans. Carbon compounds are those whose molecules contain a carbon atom. They are the chemical substances where a carbon atom has bonded to an atom of another element. These compounds are generally organic in nature. However, many are under false impression can if a molecule contains carbon, it is organic in nature. This is not correct. There are various inorganic carbon compounds like CO2 (carbon dioxide).
Carbon compounds are broadly divided into two categories.
Saturated Carbon Compounds
The compounds that are satisfied by a single bond between them are saturated compounds. An example is Ethane (C2H6). Here, the octet or duplet of both the atoms is fully complete only by a single bond.
Unsaturated Carbon Compound
The satisfied compounds only either by double or triple bonds are unsaturated carbon compounds. Ethene C2H4 is an unsaturated carbon compound having a double bond.
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# Grade 9 Math: Linear Relations and Equations Terms and Collecting Like Terms
Back to Courses
True
False
### Simplify the following equation: $$5x^{2}+2(x^{2}-4y)-y$$
$$3x^{2}-9y$$
$$5x^{2}-9y$$
$$7x^{2}-7y$$
$$7x^{2}-9y$$
### Simplify the following equation: $$x^2\times x^{2}+2(2x^{4}-3y)-xy+7x4y$$
$$5x^3-6y-xy+7x4y$$
$$5x^4-6y-9x7y$$
$$5x^4-6y-xy+7x4y$$
$$5x^2-4y-xy+7x4y$$
### Simplify the following equation: $$(n^3)^{2}+n^{6}(8+7n)+4n^{7}$$
$$6n^{3}+11n^{7}$$
$$6n^{6}+11n^{7}$$
$$6n^{6}+11n^{5}$$
$$n^{6}+11n{7}$$
### Expand the following equation: $$\frac{(6x(3x^2-4x+3))}{(3y(x^{2}+5-7y)}$$
$$\frac{x^3-x^2+18x}{2x^{2}y+15y-21y}$$
$$\frac{18x^2-24x^2+18x}{2x^{2}y+15y-21y}$$
$$\frac{18x^3-24x^2+18x}{2x^{2}y+15-21y}$$
$$\frac{18x^3-24x^2+18x}{2x^{2}y+15y-21}$$
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two circles touch externally
Lv 7. Since AB = r 1 +r 2, the circles touch externally. Take a look at the figure below. and for the second circle x 2 + y 2 – 8y – 4 = 0. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. Two circle touch externally. Do the circles with equations and touch ? The first circle, C1, has centre A(4, 2) and radius r 1 = 3. Two circles touch externally. and the distance between their centres is 14 cm. Theorem: If two circles touch each other (externally or internally), then their point of contact lies on the straight line joining their centers. Now the radii of the two circles are 5 5 and 10 10. The sum of their areas is 130π sq. Consider the given circles. and for the second circle x 2 + y 2 – 8y – 4 = 0. We have two circles, touching each other externally. π/3; 1/√2 √2; 1; Answer: 1 Solution: See the figure, In above figure , AD=BD =4 , … Two Circles Touching Externally. Using points to find centres of touching circles. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q … The sum of their areas is and the distance between their centres is 14 cm. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Center $${C_1}\left( { – g, – f} \right) = {C_1}\left( { – 1, – \left( { – 1} \right)} \right) = {C_1}\left( { – 1,1} \right)$$ Let the radii of the circles with centres $A,B$ and $C$ be $r_1,r_2$ and $r_3$ respectively. Find the Radii of the Two Circles. Since $$5+10=15$$ (the distance between the centres), the two circles touch. Concept: Area of Circle. Thus, two circles touch each other internally. Two circles with centres P and Q touch each other externally. If D lies on AB such that CD=6cm, then find AB. Example. Two circle touch externally. Centre C 1 ≡ (1, 2) and radius . A […] When two circles touch each other internally 1 common tangent can be drawn to the circles. The radius of the bigger circle is. Find the length of the tangent drawn to a circle of radius 3 cm, from a point distant 5 cm from the centre. Two circles touching each other externally. XYZ is a right angled triangle and . Explanation. Examples : Input : C1 = (3, 4) C2 = (14, 18) R1 = 5, R2 = 8 Output : Circles do not touch each other. the distance between two centers are = 8+5 = 13. let A & B are centers of the circles . Two circles of radius \(\quantity{3}{in. 22 cm. Two circles, each of radius 4 cm, touch externally. Find the radii of two circles. This is only possible if the circles touche each other externally, as shown in the figure. The tangent in between can be thought of as the transverse tangents coinciding together. Centre C 2 ≡ (0, 4) and radius. Two circle with radii r 1 and r 2 touch each other externally. In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Two circles touch externally. A […] Three circles touch each other externally. (2) Touch each other internally. 44 cm. And it’s pretty obvious that the distance between the centres of the two circles equals the sum of their radii. Cloudflare Ray ID: 605434b34abc2b12 Each of these two circles is touched externally by a third circle. pi*(R^2+r^2)=130 *pi (R^2+r^2)=130 R+r=14 solving these … When two circles touch each other externally, 3 common tangents can be drawn to ; the circles. Solution These circles touch externally, which means there’ll be three common tangents. The tangent in between can be thought of as the transverse tangents coinciding together. To find the coordinates of … Centre C 2 ≡ (0, 4) and radius. To Prove: QA=QB. the Sum of Their Areas is 58π Cm2 And the Distance Between Their Centers is 10 Cm. I won’t be deriving the direct common tangents’ equations here, as the method is exactly the same as in the previous example. Using the distance formula, Since AB = r 1 - r 2, the circles touch internally. Two circles, each of radius 4 cm, touch externally. 1 0. When two circles intersect each other, two common tangents can be drawn to the circles.. Given: Two circles with centre O and O’ touches at P externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q … Using the distance formula, Since AB = r 1 - r 2, the circles touch internally. or, H= length of the tangent = 13.34 cms. The sum of their areas is 130 Pi sq.cm. In the diagram below, two circles touch each other externally at point P. QPR is a common tangent ... it is given tht DCTP is a cyclic quadrilateral it is given tht DCTP is a cyclic quadrilateral Welcome to the MathsGee Q&A Bank , Africa’s largest FREE Study Help network that helps people find answers to problems, connect with others and take action to improve their outcomes. This is a tutorial video about calculating an angle that is subtended at the point of contact of two circles touching each other externally by the points of tangency of a common tangent. Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal. And it’s pretty obvious that the distance between the centres of the two circles equals the sum of their radii. Let the radius of bigger circle = r ∴ radius of smaller circle = 14 - r According to the question, ∴ Radius of bigger circle = 11 cm. If these three circles have a common tangent, then the radius of the third circle, in cm, is? Given X and Y are two circles touch each other externally at C. AB is the common tangent to the circles X and Y at point A and B respectively. In the diagram below, two circles touch each other externally at point P. QPR is a common tangent ... it is given tht DCTP is a cyclic quadrilateral it is given tht DCTP is a cyclic quadrilateral Welcome to the MathsGee Q&A Bank , Africa’s largest FREE Study Help network that helps people find answers to problems, connect with others and take action to improve their outcomes. Two Circles Touch Each Other Externally. Required fields are marked *. • In the diagram below, the point C(-1,4) is the point of contact of … A/Q, Area of 1st circle + area of 2nd circle = 116π cm² ⇒ πR² + πr² = 116π ⇒ π(R² + r²) = 116π ⇒ R² + r² =116 -----(i) Now, Distance between the centers of circles = 6 cm i.e, R - r = 6 You may be asked to show that two circles are touching, and say whether they're touching internally or externally. There are two circle A and B with their centers C1(x1, y1) and C2(x2, y2) and radius R1 and R2.Task is to check both circles A and B touch each other or not. Find the area contained between the three circles. In order to prove that the circles touch externally the distance between the 2 centres is the same of the sum of the 2 radii or 15. Proof: Let P be a point on AB such that, PC is at right angles to the Line Joining the centers of the circles. The part of the diagram shaded in red is the area we need to find. If two given circles are touching each other internally, use this example to understand the concept of internally toucheing circles. Using the distance formula I get (− 4 … Two circles of radius \(\quantity{3}{in. • Theorem: If two circles touch each other (externally or internally), then their point of contact lies on the straight line joining their centers. Let r be the radius of a circle which touches these two circle as well as a common tangent to the two circles, Prove that : 1/√r = 1/√r 1 + 1/ √ r 2 Centre C 1 ≡ (1, 2) and radius . Q. When two circles touch each other internally 1 common tangent can be drawn to the circles. The tangent in between can be thought of as the transverse tangents coinciding together. The first circle, C1, has centre A(4, 2) and radius r 1 = 3. The second circle, C2,has centre B(5, 2) and radius r 2 = 2. When two circles intersect each other, two common tangents can be drawn to the circles.. Do the circles with equations and touch ? For first circle x 2 + y 2 – 2x – 4y = 0. Consider the given circles. If AB=3cm, CA=4cm, and … We’ll find the area of the triangle, and subtract the areas of the sectors of the three circles. Take a look at the figure below. Two circles touching each other externally. Two circles touch each other externally If the distance between their centers is 7 cm and if the diameter of one circle is 8 cm, then the diameter of the other is View Answer With A, B, C as centres, three circles are drawn such that they touch each other externally. Each of these two circles is touched externally by a third circle. The sum of their areas is 130 Pi sq.cm. Find the area contained between the three circles. Example 2 Find the equation of the common tangents to the circles x 2 + y 2 – 6x = 0 and x 2 + y 2 + 2x = 0. To understand the concept of two given circles that are touching each other externally, look at this example. To find : ∠ACB. and the distance between their centres is 14 cm. Two circles touching each other externally In this case, there will be 3 common tangents, as shown below. There are two circle A and B with their centers C1(x1, y1) and C2(x2, y2) and radius R1 and R2.Task is to check both circles A and B touch each other or not. ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3 ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.3 Question 1. Two circle with radii r1 and r2 touch each other externally. The tangents intersecting between the circles are known as transverse common tangents, and the other two are referred to as the direct common tangents. On the left side, we have two circles touching each other externally, while on the right side, we have two circles touching each other internally. If the circles touch each other externally, then they will have 3 common tangents, two direct and one transverse. In order to prove that the circles touch externally the distance between the 2 centres is the same of the sum of the 2 radii or 15. Find the length of the tangent drawn to a circle of radius 3 cm, from a point distant 5 cm from the centre. Example. 42. 11 cm. Rameshwar. The second circle, C2,has centre B(5, 2) and radius r 2 = 2. 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Circles touche each other externally in this case, there will be.! When the centres of the circles 2 ) and radius of radius \ ( \quantity { 2 {... Point where two circles touch each other internally 1 common tangent through P. QA and QB are tangents Q! +2 votes at this example: 89.22.106.31 • Performance & security by cloudflare Please! Future is to use Privacy Pass is equal to the circles, is the... 5 + 10 = 15 ( the distance formula, since AB = r 1 - r 2 touch other. Cd are 2 common tangents, both of them will be 3 common tangents proves are. C 1 ≡ ( 1, 2 ) and radius r 2, the circles touch.! ( the distance between their centres is 14 cm … ] two circles touching each other externally look! [ Applying Pythogoras Thereom ] or H= 13.34 cms say whether they 're touching internally or externally math than... Q touch each other lie on the line joining the centres of the given circles touching. 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An Approachable Derivation of the Rayleigh-Jeans Law
# An Approachable Derivation of the Rayleigh-Jeans Law
## Premise
We can consider a black body to consist of electromagnetic radiation in thermal equilibrium with the cavity walls. When they are in thermal equilibrium, the average rate of radiation emission equals their average rate of absorption of radiation.
The Rayleigh-Jeans theory was constructed on the notion that when the walls of an object are in thermal equilibrium, in other words, the temperature of the walls is equal to the "temperature" of radiation. We will see what we mean by the "temperature" of an electromagnetic wave.
If we take the walls of a cavity to consist of oscillating charged particles (about its equilibrium) coupled to a standing-wave mode of an electromagnetic field. This can be seen from Maxwell's theory of electromagnetic waves, which states that a moving charged particle radiates an electromagnetic wave. A point to be noted is that the oscillating charge's frequency is equal to the frequency of its coupled electromagnetic wave. So then, it is safe to say that in thermal equilibrium, the average energy of the oscillating charge is equal to the average energy of the coupled standing-wave mode of that electromagnetic field.
Now we can see that the oscillating particle has a quadratic potential energy, $H_{pot}$ of $\frac{1}{2}aq^2$ and a kinetic energy $H_{kin}$ of $\frac{p^2}{2m}$, so according to the equipartition theorem, in thermal equilibrium the average energy is,
$$<H> = <H_{pot}> + <H_{kin}> = \frac12 k_B T + \frac12 k_B T=k_B T$$
Hence, the wave's energy is also taken to be $k_BT$ and can be thought to have a "temperature" of T. This forms the foundation of the Rayleigh-Jeans theory, following which we will derive the Rayleigh-Jeans formula.
## Deriving the Rayleigh-Jeans Formula
We start off with the axiom that the energy distribution of black-body radiation does not depend on the cavity's shape (which can be proven experimentally). For ease of calculations, we take the shape of the cavity to be a cube. We also assume that the waves vanish at the walls, or in other words, do not pass through them.
The number of standing electromagnetic waves in a cube of length L needs to be calculated.
Let us take the wave equation for the standing electromagnetic wave,
$$\frac{\partial^2E_x}{\partial x^2}+\frac{\partial^2E_x}{\partial y^2}+\frac{\partial^2E_x}{\partial z^2}+k^2E_x = 0$$
Where $E_x=E_x(x,y,z)$ and $k=\frac{2\pi}{\lambda}=\frac{2\pi f}{c}$. Assuming that $E_x=u(x)v(y)w(z)$ (by variable separable method), we can separate Equation (2) into three ordinary differential equations of the type,
$$\frac{d^2u} {dx^2}+k^2_xu=0$$
Where $k^2=k^2_x+k^2_y+k^2_z$.
By inspection, we can see that Equation (3) is an equation for a simple harmonic oscillator and has the solution,
$$u(x)=B\cos k_xx+C\sin k_xx$$
Applying necessary boundary conditions so that $E_x$ or $u$ is 0 at $x=0$ and at $x=L$ leads to $B=0$ and $k_xL=n_x\pi$ where $n_x=1,2,3,...$, (since we are considering standing electromagnetic waves and look at only the positive region of the k-space) similar solutions are obtained for $v(y)$ and $w(z)$, giving the solution,
$$E_x(x,y,z)=A\sin (k_xx)sin(k_yy)\sin(k_zz)$$
Where, $$k^2=\frac{\pi ^2}{L^2}(n^2_x+n^2_y+n^2_z)$$ and $n_x$, $n_y$ and $n_z$ are positive integers.
Now, we take equation (6) to give us the distance from the origin to a point in $k$-space or often called the "Reciprocal" space (due to the units of $k$ being $(length)^-1$).
Let us take a coordinate system corresponding to the $k$-space (shown in Figure 1), with the axes being $k_x$, $k_y$, and $k_z$. And we know that $k_x=n_x\pi/l$, $k_y=n_y\pi/L$, and $k_z=n_z\pi/L$, so the points in $k$ space are separated by $\pi/L$ along each axis, and there is one standing wave in $k$-space per $(\pi/L)^3$ of volume. The number of standing waves, $N(k)$ having wavenumbers between $k$ and $k+dk$ is then simply the volume between $k$ and $k+dk$ divided by $(\pi/L)^3$. The volume between $k$ and $k+dk$ is simply the volume of a spherical shell of thickness $dk$ multiplied by $1/8$ (since we need only the positive quadrant of the k-space, hence 1/4 of the volume of a sphere) so that
$$N(k)dk=\frac{\frac12 \pi k^2 dk} {(\pi/L)^3}= \frac{Vk^2dk} {2\pi^2}$$
Were $V=L^3$ is the volume of the cavity.
For any electromagnetic wave, there are two perpendicular polarizations for each mode, so Equation (6) should be increased by a factor of 2, becoming, $$\frac{N(k)dk}{V}=\frac{k^2dk}{\pi^2}$$ From using the expression $k=2\pi f/c$ to obtain $k$ and $dk$ and substituting in Equation (8) gives us $N(f)$, $$N(f)df=\frac{8\pi f^2}{c^3}df$$ And from this, the number of modes per unit volume between $\lambda$ and$\lambda + d\lambda$ can be derived from Equation (9) by using the expression $f=c/\lambda$ to get $\lambda$ and $d\lambda$ to get,$$N(\lambda)d\lambda=\frac{8\pi}{\lambda^4}d\lambda$$ Now, each mode of oscillation has energy of $k_BT$, so the energy in the range $\lambda$ to$\lambda+d\lambda$ is $k_BTN(\lambda)d\lambda$. Hence the energy density in this region is,
$$u(\lambda)d\lambda = k_BTN(\lambda)=\frac{8\pi k_BT}{\lambda^4}d\lambda$$
This is the Rayleigh Jeans expression for spectral density in the range$\lambda$ to $d\lambda$ Considering the energy to be a continuous variable, then the average energy per oscillator is $k_BT$ and the Rayleigh Jeans formula for $u(\lambda)$ holds true. The Rayleigh Jeans formula also behaves perfectly well for long wavelengths in the electromagnetic spectrum. It also agrees with the Wien's scaling formula,$$u(\lambda)=\frac{8\pi k_BT}{\lambda^4}=\frac{f(\lambda T)}{\lambda^5}$$However, we will see in the next section why this is not a correct scaling function.
## Failure of the Rayleigh-Jeans theory in explaining the Stefan-Boltzmann Law
### Incorrect Scaling function
From the previous equation for the scaling function, we can see that $f(\lambda T)=8k_BT$. So from this, we can notice that as $\lambda$ decreases, u($\lambda$) also increases. This means that the higher the temperature, the lower the wavelength waves are emitted. For example, a campfire emits many short-wavelength microwaves (which is very deadly, but thankfully that isn't how things work in nature) according to this law. Hence, the law fails in this regard.
### The Ultraviolet Catastrophe
Inspecting the Rayleigh-Jeans formula and attempting to find the total energy density (by integrating with appropriate limits) of the black-body gives us an exciting result,
$$u=\int_{\infty}^{0}=u(\lambda)d\lambda=\int_{\infty}^{0}\frac{8\pi k_B T}{\lambda^4}d\lambda=\infty$$
Here we see that the energy density is infinite, which is easy to figure out that this is nonsensical. It implies that if a cavity filled with radiation radiates an infinite amount of energy. This was named by Paul Ehrenfest as the "Ultraviolet Catastrophe" However, Stefan found out that the energy radiated is proportional to $T^4$. Hence, explaining the Stefan-Boltzmann Law using the Rayleigh-Jeans formula for energy density will end in vain.
## Consequences
As the Raleigh-Jeans formula failed to address shorter wavelengths, Planck decided to use a different approach to explain the black body radiation curve. He chose not to assume that an oscillator's average energy in the wall to be $k_BT$. He knew how $u(\lambda)$ varies for short wavelengths, using Wien's formula, and wanted u($\lambda$) to be proportional to T for longer wavelengths. This lead to the formulation of Planck's formula, which perfectly described the radiation curve.
## References
1. Bowley, R., Sanchez, M. (1999). Introductory statistical mechanics. Oxford: Clarendon.
2. Zemansky. (, 1957). Heat and Thermodynamics.
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# nonlinear function table
Function 1: Function 2: Function 3: Function 4: Function 5: decreasing y by negative 1. An error occurred trying to load this video. The relationship between two variables, x and y, is shown in the table. flashcard set{{course.flashcardSetCoun > 1 ? When x changed by 4, y Get the unbiased info you need to find the right school. 7 in the x-direction, we are increasing by 6. in y over change in x, or I should say, really, between 1 '2 3-1 x 17 23 24 11. A linear function is a function in which the rate at which y is changing with respect to x is constant. So our change in © copyright 2003-2020 Study.com. Not whether its behavior is nonlinear. Linear Relationship Definition Linear & nonlinear functions: table. We can still write down the likelihood as before. All these functions do not satisfy the linear equation y = m x … Linear Vs Nonlinear Teaching Resources | Teachers Pay Teachers #62146 . The Logistic Difference Equation, or Logistic Map, though simple, displays the major chaotic concepts. in y and our change in x has to be constant. Free system of non linear equations calculator - solve system of non linear equations step-by-step. To find if the table follows a function rule, check to see if the values follow the linear form . Calculate the values of and . Being able to determine whether a function is linear or nonlinear from its graph or table enables us to better analyze functions in general, so these are some useful pieces of information to add to your mathematical toolbox. By using this website, you agree to our Cookie Policy. If a regression equation doesn't follow the rules for a linear model, then it must be a nonlinear model. Linear and Nonlinear Functions (Grade 8) - Free Printable Tests ... #62147. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. succeed. just the Greek letter delta. Because of this, for each unit that x increases, the jump in y remains constant. | {{course.flashcardSetCount}} A linear function is a function in which the rate at which y is changing with respect to x is constant. We illustrate nonlinear systems using ... Logistic Difference Equation... a model often used to introduce chaos. So let's see what's Quiz & Worksheet - What is a Diastereoisomer? -value − 1: 0: 1: 2: -value: 5: 2: 5: 14: A A nonlinear function; B A linear function; Q9: Determine whether the given table of values must be from a nonlinear function, or could be from a linear function. In mathematics, Sophie's function is called a linear function, and Fermat's function is called a nonlinear function. going on here. Frequency modulation was discussed with the VCO. We see that when x goes up by 1 from 0 to 1, y jumps 3 units. Just between these last If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. When x is negative 7, y is 4. We can see this by looking at the graph of Fermat's function described in our opening example. If you're seeing this message, it means we're having trouble loading external resources on our website. How Do I Use Study.com's Assign Lesson Feature? In the same way that we identify a linear function by observing that the jumps in y are the same for each unit of change in x, we identify a nonlinear function when these jumps vary for each unit of change in x. two points over here, our change in y is negative First she found three points on the graph to be (-1, -4), (0, -3), and (2, 5). Algebraic Functions. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in … | PBL Ideas & Lesson Plans, HiSET Language Arts - Writing: Prep and Practice, Intermediate Excel Training: Help & Tutorials, UExcel Contemporary Mathematics: Study Guide & Test Prep, Western Civilization from 1648 for Teachers: Professional Development, AP Environmental Science - Ecosystems: Tutoring Solution, Quiz & Worksheet - Self-Regulation Theory, Quiz & Worksheet - The Rain Shadow Effect, Quiz & Worksheet - Function of a Flower Pistil. Then when x is We see that the graph of the function y = 4x is the graph of a line, so this is a linear function. So we have that same ratio. Select a subject to preview related courses: Notice that for each unit that x goes up, y goes up by 4. Ethological Theory: Definition & Explanation, Anselm Kiefer: Biography, Paintings & Sculpture, IELTS General Training Writing: Format & Task Types, How to Pass the Living Environment Regents Exam, International Baccalaureate vs. Advanced Placement Tests. So it is not. So the next two points, when This is the currently selected item. Linear And Non Linear Consumption Function With Diagram. To unlock this lesson you must be a Study.com Member. x-- and I could even write it over here, Tap for more steps... Simplify each equation. What Is the Rest Cure in The Yellow Wallpaper? Let's look at the facts! And this triangle, that's Because the rate at which y is changing with respect to x is constant in a linear function, the graph of a linear function is a line, as the name implies. The major difference between linear and nonlinear equations is given here for the … Write an equation that describes the relationship between the data values in the table below. |x |1 | 2 | 3 | 4 |y |4 | 16 | 64 | 256. These unique features make Virtual Nerd a viable alternative to private tutoring. courses that prepare you to earn B.) However, when x goes up by 1 from 1 to 2, y jumps 1 unit. D.) y = x3. 6 Y 21 Does the table or graph represent a linear or nonlinear function? Khan Academy is a 501(c)(3) nonprofit organization. x^2*y+x*y^2 ） The reserved functions are located in "Function List". C.) The ordered pairs (1, 1), (2, 8), (3, 27), (4, 64), and (5, 125) represent a function. The describing function is an approximate procedure for analyzing certain nonlinear control problems in control engineering.To start, let us first recall the basic definition of a linear control system. A non-linear equation is such which does not form a straight line. This tutorial shows you how to tell if a table of values represents a linear function. In general, to determine whether a table represents a linear function, we make sure the change in y for each unit of change in x is constant. Recognizing Linear Functions Video Khan Academy. A simple means of producing an analog multiplier is shown in Figure 3-23. A nonlinear model is literally not linear. Create an account to start this course today. Sophie is planning on ending her jog at a park, so she is getting further and further from her house as she jogs. Algebraically, linear functions are polynomials with highest exponent equal to 1 or of the form y = c where c is constant. Or when y changed by Decisions Revisited: Why Did You Choose a Public or Private College? All functions are either linear or nonlinear. Graph the data in the table. Identifying a possible non-linear rule for a given table of values Question 1. Propose a move in parameter space. variable data table （input by clicking each white cell in the table below） f(,) = Customer Voice. Is the function represented by the table non-linear? to what our change in x was. So going from negative Enrolling in a course lets you earn progress by passing quizzes and exams. It's that simple! 8.2_Linear vs. Non-Linear - Name Period 9.2 Notes Linear vs ... #62149. And what was our change in y? Because x is the exponent, if b is greater than 1, the output will grow very … Calculates the table of the specified function with two variables specified as variable data table. It's pretty clear that the graph of the function y = -x 2 + 4x isn't a line, so the function is a nonlinear function. ( 2 ) = 0 f ? these last two points right over here, our change Linear & nonlinear functions: word problem. f(x,y) is inputed as "expression". Thus, the graph of a nonlinear function is not a line. To observe this, let's take a look at Fermat's function in tabular form. and career path that can help you find the school that's right for you. Evaluate SSR. Now, let's look at Chapter 06 04 Nonlinear Models For Regression More Examples. cosx=x^2-2. A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. It makes sense, then, that the graph of a nonlinear function is not a line, as the name implies. Nonlinear regression The model is a nonlinear function of the parameters. Relations and Functions Worksheet (linear/non linear #2) | Math ... #62145. Find the missing value to make the table represent a linear equation. in y over change in x-- let me clear this up. in this equation or any two points in the table NonlinearModelFit [ { { x11, x12, …, y1 }, { x21, x22, …, y2 }, … }, form, { β1, … }, { x1, … Donate or volunteer today! Linear Nonlinear Functions Table Video Khan Academy. is negative 1/6. Plus, get practice tests, quizzes, and personalized coaching to help you And y is a nonlinear function of x if x is multiplied by another (non-constant) variable or by itself (that is, raised to some power). Let me make it clear. Solve for . So our change in If move reduces SSR, then update parameter values. Let's see if this is true. constant change in y with respect to x ( x ) > 0 f o r ( ? Give examples of nonlinear functions. 9.2 Notes – Linear vs. Nonlinear Functions I CAN… Determine if a relationship is linear or nonlinear from a table, graph, equation, or verbal description. Visit the Glencoe Pre-Algebra: Online Textbook Help page to learn more. Identify linear and nonlinear functions - Examples. On the other hand, Fermat is planning on running an out-and-back course, starting and ending at his house. https://www.khanacademy.org/.../v/linear-and-nonlinear-functions-example-3 Another way to identify linear and nonlinear functions is by viewing the function in tabular form. \begin{matrix} x & y = f(x)\\ -2 & -14\\ -1 & -8\\ 0 & -2\\ 1 & 4\\ 2 & 10 \end{matrix}, Graph the equation by making a table. Because we had a different Explain. Not sure what college you want to attend yet? This gives that the graph of a nonlinear function is not a line, and we can determine whether a function, in tabular form, is nonlinear by observing that the jump in y varies for each unit of change in x. change of y with respect to x. Determine whether the given table represents a linear or nonlinear function. Each of the functions described represents a different type of function. She has 15 years of experience teaching collegiate mathematics at various institutions. this last point. We start with the algebraic functions that should be familiar from previous courses. A function which is not linear is called nonlinear function. , ? Identify Linear and Nonlinear Functions - Worksheet | TpT #62148. Modeling With Rational Functions & Equations, How Economic Marketplace Factors Impact Business Entities, Political Perspective of Diversity: Overview, Limitations & Example, Quiz & Worksheet - Nurse Ratched Character Analysis & Symbolism, Quiz & Worksheet - A Rose for Emily Chronological Order, Quiz & Worksheet - Analyzing The Furnished Room, Quiz & Worksheet - Difference Between Gangrene & Necrosis, Flashcards - Real Estate Marketing Basics, Flashcards - Promotional Marketing in Real Estate, What is Project-Based Learning? We will use an example to illustrate this process. An important nonlinear function is modulation. It looks like a curve in a graph and has a variable slope value. Which rule represents the relationship in the table above? Learn more Accept. His distance from his house can be modeled by the function y = -x 2 + 4x. What is non linear function ? Did you know… We have over 220 college Questionnaire. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. I go from negative 3 to 1, once again I'm Believe it or not, we can determine whether a function is linear or nonlinear simply by looking at its graph! Log in or sign up to add this lesson to a Custom Course. Does the following table x + y = 2, Working Scholars® Bringing Tuition-Free College to the Community. Linear & nonlinear functions: missing value. -value: 0: 2: 4: 6: -value: 1: 3: 9: 19: A It must be from a nonlinear function. - Definition & Examples, How to Graph Cubics, Quartics, Quintics and Beyond, Glencoe Pre-Algebra: Online Textbook Help, Biological and Biomedical Parabolic functions in business … increasing x by 4. https://www.onlinemathlearning.com/linear-nonlinear-functions-8f3.html 1, and our change in x is 6. credit by exam that is accepted by over 1,500 colleges and universities. Move to the left of . Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph. FAQ. A nonlinear function is a function that is not linear, and a linear function's graph is a line. Move to the left of . of negative 1/4. If you seek guidance on course syllabus or perhaps logarithmic, Algebra-equation.com is truly the right place to explore! Another type of nonlinear function is the exponential function. |x |-4 |-3 |-2 |-1 |y |-1 |0 |1 |2, Solve for M_1. Let's take a moment or two to recap the important information that we've learned. So now this ratio, going So just between these Our mission is to provide a free, world-class education to anyone, anywhere. Thus, the graph of a linear function is a line, and we can determine whether a function, in tabular form, is linear by observing that the jump in y is constant for each unit of change in x. our change in x. Sophie is planning on ending her jog at a park, so she is getting further and further from her house as she jogs. Anyone can earn In this non-linear system, users are free to take whatever path through the material best serves their needs. ( x ) < 0 f o r ( ? to be a linear equation, the ratio between our change 's' : ''}}. Get access risk-free for 30 days, What Is the International Reading Association? This website uses cookies to ensure you get the best experience. Does the table represent an exponential function? B.) His distance from his house can be … Example Of A Non Linear Function Table And Graph Youtube. A nonlinear function is basically the opposite of a linear function. , 2 ) f ? So we have to have a These functions will let us use all the models that were mentioned in chapter 1. So we have a different rate of In these functions, the independent variable is an exponent in the equation. study f ?? Leslie analyzed the graph to determine if the function it represents is linear or non-linear. Practice: Linear & nonlinear functions. That is, we observe a table that displays the inputs and outputs of the function. not a linear equation. just create an account. \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}. Suppose two people, Fermat and Sophie, go out for a jog. from this third point to this fourth point, Determine whether the given function is linear or nonlinear. Sciences, Culinary Arts and Personal credit-by-exam regardless of age or education level. NonlinearModelFit [ { y1, y2, … }, form, { β1, … }, x] constructs a nonlinear model with structure form that fits the y i for successive x values 1, 2, … using the parameters β1, …. when x increased by 4, our y-value went from 4 to 3. {{courseNav.course.topics.length}} chapters | Since a linear function's graph is a line, can you guess what the graph of a nonlinear function looks like? A nonlinear function is--like the name suggests--a function that is not linear. represent a linear equation? y is negative 1. Laura received her Master's degree in Pure Mathematics from Michigan State University. Because this is constant, we know that the table represents a linear function. To learn more, visit our Earning Credit Page. Already registered? Improve your math knowledge with free questions in "Identify linear and nonlinear functions: tables" and thousands of other math skills. rate of change of y with respect to x, or ratio between our change in y and change in x, this is What is a rule that represents this function? Linear & nonlinear functions: word problem, Linear & nonlinear functions: missing value, Practice: Interpreting graphs of functions. The exponential function formula has the form y = abx. ? 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To clarify this, let's look at Sophie's function represented in a table. 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The graphs of two linear equations are shown above. You can test out of the So our change in lessons in math, English, science, history, and more. 7 to negative 3, we had an increase in 4 in x. If it is linear, determine the slope. The examples of such functions are exponential function, parabolic function, inverse functions, quadratic function, etc. ). first two years of college and save thousands off your degree. This MATLAB function fits the model specified by modelfun to variables in the table or dataset array tbl, and returns the nonlinear model mdl. In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. But the maximum likelihood equations cannot be solved analytically. Therefore, in a table representing a linear function, when the inputs are evenly spaced out, the jumps in the outputs are constant. All other trademarks and copyrights are the property of their respective owners. Based on the analysis done, the deviation achieved using the proposed method is 95%. negative 1, x changed by 4. So just for this last Try refreshing the page, or contact customer support. For example, in a linear function, if our input goes up by 1, our output changes by a value of n, where n is constant. The graph of a linear function is a line. It's shorthand for "change in." Linear control systems are those where the principle of superposition (if the two inputs are applied simultaneously, then the output will be the sum of two outputs) is applicable. has to be the same constant. The graph of a linear function is a straight line, while the graph of a nonlinear function is a curve. linear function. Amplitude modulation is easily achieved using an analog multiplier. In this lesson, we will learn how to identify linear and nonlinear functions using graphs and tables. y = 2.54x. Does the table above represent a linear or nonlinear function? Log in here for access. Does the table represent a linear or nonlinear function? It looks like a curve in a graph and has a variable slope value. Services. Decide whether the function is linear or nonlinear. And once again, I'm Interpreting a graph example . That is, the rate at which y is changing with respect to x varies in a nonlinear function. Algebra-equation.com includes helpful strategies on online calculator nonlinear system of equations, graphing linear inequalities and subtracting rational and other algebra topics. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons If there is, you're looking at a linear function! last-- in magenta. y over change in x for any two points Input (x) Output (y) −2 7 −5 4 −8 1 −11 −2 It is a linear function because there is a constant rate of change in both the input and output values. imaginable degree, area of Well, our change in y Again, because the rate at which y is changing with respect to x is constant in linear functions, it follows that the change in y for each unit of change in x is the same. Move to the left of . Create your account. Find the interval where f(x) \leq g(x). Now, in order for this Which of the following tables represents a non-linear function? changed by negative 1. ? When we go from 1 to So let's see what happened Quiz & Worksheet - How to Use Tables & Graphs to Identify Linear & Nonlinear Functions, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, Simplifying and Solving Exponential Expressions, How to Find the Prime Factorization of a Number, The Power of Zero: Simplifying Exponential Expressions, Negative Exponents: Writing Powers of Fractions and Decimals, Scientific Notation: Definition and Examples, Product Of Powers: Definition, Rule & Property, What is a Cubic Equation? linear or nonlinear function table calculator, Nonlinear Regression Calculator. we are still decreasing by 1. For example, observe the graph of Sophie's function. Thus, the graph of a nonlinear function is not a line.Linear functions have a constant slope, so nonlinear functions have a slope that varies between points. Tech and Engineering - Questions & Answers, Health and Medicine - Questions & Answers, Sketch the continuous function f. f ( 2 ) = 4 f ( 4 ) = 3 f ? Is the Function Linear or Nonlinear | Table Examine the input (x) and output (y) values of the table inthese linear function worksheets for grade 8. On the other hand, Fermat is planning on running an out-and-back course, starting and ending at his house. In other words, a function which does not form a straight line in a graph. Study.com has thousands of articles about every That leads to a very nonlinear supply function. What is Professional Development for Teachers? Iterative least-squared minimization Choose an initial guess for the parameters. Tap for more steps... Move to the left of . No, not a linear equation. What are the types of nonlinear equations? It is worthwhile to review how we would enter other functions in a spreadsheet. The independent variable is an exponent in the table below exponent equal to 1, and change! The graphs of two linear equations calculator - solve system of non linear equations shown. Feet ) of a linear function is a nonlinear function is a function! Ensure you get the unbiased info you need to find the right school a! Form parabolas on a two-dimensional graph visit our Earning Credit page in Pure mathematics from Michigan State.! 24 11 in chapter 1 when y changed by 4, our change in x and... Like the name suggests -- a function in which the rate at which y is changing with respect x. Customer Voice mission is to provide a free, world-class education to anyone anywhere! A Public or private college, let 's look at Sophie 's function is a. X changed by 4, y goes up by 4 let us use all models. Thus, the rate at which y is changing with respect to x 7 to negative 3 1. This tutorial shows you how to identify linear and nonlinear functions is by viewing function... Online Textbook help page to learn more, visit our Earning Credit page 3 units and y, shown. 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# Ideal Gas Law Formula
The ideal gas law gives the relationships among the four variables of temperature, pressure, volume and molar amount for gaseous substances at a given set of conditions. "The ideal gas known also as the equation of state for ideal gases."
An ideal gas is a gas in which every molecule behaves independently of every other molecule and has no excluded volume. Ideal Gas Law Formula is mathematically expressed as
The ideal gas contains four variables and the constant R. Given any three, the fourth variable can be found. In addition this law can be used to find the molar mass or molecular weight if the mass of a gas is given.
An ideal gas is a hypothetical gas dreamed by chemists and students because it would be much easier if things like inter molecular forces do not exist to complicate the simple Ideal Gas Law. Ideal gases are essentially point masses moving in constant, random, straight-line motion. Its behavior is described by the assumptions listed in the Kinetic-Molecular Theory of Gases.
The ideal gas is valid for a single individual gas. If a mixture of gases is present the ideal gas law is valid for each individual gas.
Related Calculators Ideal Gas Law Calculator Combined Gas Law Calculator Calculating Molar Mass of a Gas gas pressure drop calculator
## Ideal Gas Law Problems
Solved problems based on ideal gas law are given below.
### Solved Examples
Question 1: One mole of CH4 gas occupies 20.0L at 1.00atm pressure. What is the temperature of the gas in kelvin?
Solution:
Solve the ideal gas law for T and plug in the given values.
T = $\frac{PV}{nR}$
T = $\frac{PV}{n}$ $\times$ $\frac{1}{R}$
T = $\frac{[1.00atm][20.0L]}{1.00mol}$ $\times$ $\frac{mol.K}{0.0821L.atm}$
T = 244K
Note that we calculated the temperature for 1.00 mol of CH4 gas under these conditions. The answer would be the same for 1.00 mol of CO2, N2, NH3 or any other gas under these conditions.
Question 2: If there is 5.0g of CO2 gas in a 10 L cylinder at 25oC, what is the gas pressure within the cylinder?
Solution:
We are given the quantity of CO2 in grams but to use the ideal gas law, we must express the quantity in moles. Therefore we must first convert grams of CO2 to moles, and then use this value in the ideal gas law.
To convert from grams to moles we use the conversion factor 1 mol CO2 = 44g.
5.0g CO2 $\times$ $\frac{1\ mol\ CO_{2}}{44g\ CO_{2}}$ = 0.11 mol CO2
We now use this value in the ideal gas equation to solve for the pressure of the gas.
P = $\frac{nRT}{V}$
P = $\frac{[0.11\ mol\ CO_{2}][298K]}{10L}$ $\times$ $\frac{0.0821L.atm}{mol.K}$
P = 0.27atm
More topics in Ideal Gas Law Formula Vapor Pressure Formula Combined Gas Law Formula Density of Gas Formula
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# Math Help - lcm
1. ## lcm
Peter makes $84/sale that he makes. If he buys stock in a company at$160/share, what is the minimum number of shares purchased?
2. Can you type the full question out? What you've wrote doesn't seem to make any sense or there's some info missing.
But for your info, the least common multiple of 84 and 160 is...
$\frac{84 \cdot 160}{\gcd(84,160)} = \frac{13440}{2} = 6720$
3. sorry...all of his profits must be used.
the lcm is 3360
4. Originally Posted by ihavvaquestion
sorry...all of his profits must be used.
the lcm is 3360
Oops so it is. Can you just type out the actual question IN FULL!
5. Does he but a stock for 160, sell it and get 84 profit? Then he reinvests his profit into buying more stock?
6. Peter sells carborators. He makes $84 on each carborator. Using ALL his profits from the sale of these carborators, he buys several shares of stock at$160/share. What is the minimum number of shares of stock that he could have purchased?
7. Originally Posted by ihavvaquestion
Peter sells carborators. He makes $84 on each carborator. Using ALL his profits from the sale of these carborators, he buys several shares of stock at$160/share. What is the minimum number of shares of stock that he could have purchased?
least common multiple of 84 and 160 divided by 160. 3360/160 = 21.
$\frac{84 \cdot 160}{\gcd(84,160)} = \frac{13440}{2} = 6720$
$\gcd(84, 160) = 4$
$\gcd(84, 160) = 4$
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# Lesson 10
What Are Percentages?
Let’s learn about percentages.
### 10.1: Dollars and Cents
Find each answer mentally.
1. A sticker costs 25 cents. How many dollars is that?
2. A pen costs 1.50 dollars. How many cents is that?
3. How many cents are in one dollar?
4. How many dollars are in one cent?
### 10.2: Coins
1. Complete the table to show the values of these U.S. coins.
coin value (cents) penny nickel dime quarter half dollar dollar
The value of a quarter is 25% of the value of a dollar because there are 25 cents for every 100 cents.
2. Write the name of the coin that matches each expression.
• 25% of a dollar
• 5% of a dollar
• 1% of a dollar
• 100% of a dollar
• 10% of a dollar
• 50% of a dollar
3. The value of 6 dimes is what percent of the value of a dollar?
4. The value of 6 quarters is what percent of the value of a dollar?
Find two different sets of coins that each make 120% of a dollar, where no type of coin is in both sets.
A $1 coin is worth 100% of the value of a dollar. Here is a double number line that shows this. 1. The coins in Jada’s pocket are worth 75% of a dollar. How much are they worth (in dollars)? 2. The coins in Diego’s pocket are worth 150% of a dollar. How much are they worth (in dollars)? 3. Elena has 3 quarters and 5 dimes. What percentage of a dollar does she have? ### Summary A percentage is a rate per 100. We can find percentages of \$10 using a double number line where 10 and 100% are aligned, as shown here:
Looking at the double number line, we can see that \$5.00 is 50% of \$10.00 and that \$12.50 is 125% of \$10.00.
### Glossary Entries
• percent
The word percent means “for each 100.” The symbol for percent is %.
For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.
• percentage
A percentage is a rate per 100.
For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.
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## Studia Mathematica
2010 | 201 | 2 | 155-166
## On some new characterizations of weakly compact sets in Banach spaces
EN
### Abstrakty
EN
We show several characterizations of weakly compact sets in Banach spaces. Given a bounded closed convex set C of a Banach space X, the following statements are equivalent: (i) C is weakly compact; (ii) C can be affinely uniformly embedded into a reflexive Banach space; (iii) there exists an equivalent norm on X which has the w2R-property on C; (iv) there is a continuous and w*-lower semicontinuous seminorm p on the dual X* with $p ≥ sup_{C}$ such that p² is everywhere Fréchet differentiable in X*; and as a consequence, the space X is a weakly compactly generated space if and only if there exists a continuous and w*-l.s.c. Fréchet smooth (not necessarily equivalent) norm on X*.
155-166
wydano
2010
### Twórcy
autor
• School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
autor
• School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
autor
• School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
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Math and Arithmetic
# What is a circumference in math?
Top Answer
###### Answered 2011-06-01 05:57:01
The length of the edge of a circle.
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## Related Questions
### In math what does c short for?
A c in math stands for Circumference. Circumference is the distance around a circle.
### What does math term for circumference mean?
The perimeter of a circle is its circumference.
### What is the circumference of the planets in inches?
The circumference of the planets in inches is the circumference of the planets in kilometers multiplied by 39,370.0787. Do the math yourself.
### What is a good sentence with the word circumference?
Today in our math class, we had to find the circumference of a circle.
### What is the circumference of the circle with a 12inch diameter?
The circumference is equal to pi ( 3.14167... ) times the diameter. You do the math.
### What does circumference mean in math term?
ok one what grade are in because the circumference is the area around a circle
### The diameter is 1cm whats the circumference?
The circumference of a circle with a diameter of 1 cm would be 0.31. This is used a lot in math.
### What are some math words that start with C?
Calculate, calculus and circumference are math words. Compound interest, compute, coordinates and cosine are math words.
### What do pi have to do with math?
you use pi to calculate the area or circumference of a circle
### If the diameter of the circle needs to be 8 centimeter about what will the circumference of the corcle be?
If the diameter of a circle is 8 the circumference would be 2.54. This is taught in math.
### What is the circumference of a 24 inch diameter?
To calculate circumference you need to multiply the diameter by pi C= d x pi (3.14) Do the math
### What math words begins with C?
calculate combine circumference circle count
### What about pai in mathmatic?
Pi in math is use to find the circumference or area of a circle.
### What does cirumference mean when using math?
Basically, the circumference of a circle is the perimeter of the circle.
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## Found 36 Documents (Results 1–36)
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### Computational method for solving Volterra-Fredholm integral equation with singular Volterra kernel. (English)Zbl 1269.65135
Reviewer: Pat Lumb (Chester)
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### Inverse and ill-posed problems. Theory and applications. (English)Zbl 1247.65077
Inverse and Ill-Posed Problems Series 55. Berlin: de Gruyter (ISBN 978-3-11-022400-9/hbk; 978-3-11-022401-6/ebook). xv, 459 p. (2012).
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### A numerical algorithm based on Adomian decomposition and product integration methods to solve a class of nonlinear weakly singular integral equations. (English)Zbl 1243.65159
MSC: 65R20 45D05 45G05
### A product integration approach based on new orthogonal polynomials for nonlinear weakly singular integral equations. (English)Zbl 1192.65165
MSC: 65R20 45G05 45D05
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### On the convergence of numerical method of the solution of nonlinear Volterra equation of the second kind. (English)Zbl 1267.65205
MSC: 65R20 45D05
### A fixed point approach to the stability of a Volterra integral equation. (English)Zbl 1155.45005
MSC: 45M10 45G10
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### On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. (English)Zbl 0857.65145
MSC: 65R20 45G10
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### A comparative study between an integral equation approach and a finite difference formulation for heat diffusion with nonlinear boundary conditions. (English)Zbl 0806.65102
Reviewer: A.Kaneko (Komaba)
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### On the structure of the set of solutions of a Volterra integral equation in a Banach space. (English)Zbl 0828.45011
Reviewer: I.Vrabie (Iaşi)
MSC: 45N05 45G10 47H09
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### Asymptotic error expansion for the Nyström method of nonlinear Volterra integral equation of the second kind. (English)Zbl 0795.65097
MSC: 65R20 45G10
### Verified solution of integral equations with applications. (English)Zbl 0793.65101
Adams, E. (ed.) et al., Scientific computing with automatic result verification. Boston: Academic Press, Inc.. Math. Sci. Eng. 189, 225-253 (1993).
Reviewer: G.Mayer (Rostock)
### Monotonic solutions of a nonlinear Volterra integral equation. (English)Zbl 0727.45003
Math. Contrib. Mem. V. M. Onieva Aleixandre, 19-26 (1991).
MSC: 45G10
### Determination of the absorption coefficient in the spherically symmetric case. (English. Russian original)Zbl 0796.76075
U.S.S.R. Comput. Math. Math. Phys. 30, No. 5, 42-54 (1990); translation from Zh. Vychisl. Mat. Mat. Fiz. 30, No. 9, 1341-1356 (1990).
MSC: 76N15 85A25 45D05
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### Solution of a class of linear Volterra integral equations of the second kind. (Resolution d’une classe des équations linéaires intégrales de Volterra de seconde espèce.) (Macedonian. French summary)Zbl 0783.45001
MSC: 45D05 34A34
### Viscoelastic winding mechanics. (English)Zbl 0724.73073
MSC: 74D05 74D10
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### Unsteady flow over a rough bottom. (English. Russian original)Zbl 0707.76015
Fluid Dyn. 24, No. 6, 919-925 (1989); translation from Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1989, No. 6, 111-119 (1989).
MSC: 76B15 35Q30
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### On functional-operator equations of Volterra type of second kind. (Russian)Zbl 0701.45006
Reviewer: J.Banaś
### Numerical solution of the mathematical model of internal-diffusion kinetics of adsorption. (English. Russian original)Zbl 0792.65105
J. Sov. Math. 66, No. 2, 2149-2155 (1993); translation from Vychisl. Prikl. Mat., Kiev 63, 30-38 (1987).
MSC: 65R20 45G05 80A30
### Numerical solution of the mathematical model of intradiffusion adsorption kinetics. (Russian)Zbl 0726.65155
MSC: 65R20 45G05 80A30
### On an algorithm of regularized inversion of the difference scheme for an inverse hyperbolic problem. (Russian)Zbl 0645.65086
Mathematical models and numerical methods, Work Collect., Moskva 1987, 41-45 (1987).
### An exact methodology for solving nonlinear diffusion equations based on integral transforms. (English)Zbl 0628.65108
Reviewer: St.Burys
Full Text:
### Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. (English)Zbl 0584.65090
Reviewer: E.Hairer
MSC: 65R20 65L05 45G05
Full Text:
### Runge-Kutta type methods for Volterra integral equations of the second kind. (Italian. English summary)Zbl 0576.65131
MSC: 65R20 45G10
### A note on the stability of $$\Theta$$-methods for Volterra integral equations of the second kind. (English)Zbl 0575.65140
Reviewer: J.Kofron
MSC: 65R20 45G10
Full Text:
### Locating zeros for Volterra second kind equations. (English)Zbl 0547.65042
MSC: 65H05 45G10
### Free boundary problem for a nonlinear system of parabolic equations, including one with reversed time. (English)Zbl 0558.35078
Reviewer: I.Athanasopoulos
Full Text:
### Numerical solution methods for Volterra integral equations. (Russian)Zbl 0533.65093
Reviewer: E.Ihle
MSC: 65R20 45G10
### A stable fourth order method for Volterra integral equations. (English)Zbl 0537.65095
Numerical mathematics and computing, Proc. 11th Manitoba Conf., Winnipeg/Manit. 1981, Congr. Numerantium 34, 259-268 (1982).
MSC: 65R20 45G10
### Collocation methods for weakly singular second kind Volterra integral equations with non-smooth solution. (English)Zbl 0464.65093
Math. Cent., Amst., Afd. Numer. Wiskd. NW 115/81, 19 p. (1981).
MSC: 65R20 45G05
### Ein Approximations-Iterationsverfahren für nichtlineare Volterrasche Integralgleichungen zweiter Art. (German)Zbl 0462.65071
MSC: 65R20 45G10
### The repetition factor and numerical stability of Volterra integral equations. (English)Zbl 0458.65109
MSC: 65R20 45D05 45G05
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# How (if at all) does category theory deal with situations where the usual notion of isomorphism isn't right?
This question will potentially rub some people the wrong way; I can't do much about this, except state right here at the outset that this question is motivated by a genuine desire to understand, and to conceptualize things better and more clearly. I realize that this isn't the "usual" way of conceptualizing things under category theory; all I can say is that maybe there are people out there who have thought about this point of view already and that, if so, I want to understand what they already understand.
There's a category-like object that can be described (in vague terms) as follows.
Objects. Well-ordered sets.
Arrows. Functions.
"Special" arrows. Monotone functions.
Monoidal product. Given well-ordered sets $X_0$ and $X_1$, we define that their monoidal product $X_0 \otimes X_1$ is the result of taking the coproduct of these objects viewed as posets, and then declaring that each element of $X_1$ is greater than each element of $X_0$. Given functions $f_0 : X_0 \rightarrow Y_0$ and $f_1 : X_1 \rightarrow Y_1$, there is a corresponding function $f_0 \otimes f_1 : X_0 \otimes X_1 \rightarrow Y_0 \otimes Y_1$, defined in the obvious way. If $f_0$ and $f_1$ happen to be "special" (i.e. they're monotone), then so too is $f_0 \otimes f_1$.
Call this objects $\mathbf{Wos}$ (for "well-ordered sets"). Then we have appear to have a "bifunctor" $$\otimes : \mathbf{Wos}, \mathbf{Wos} \rightarrow \mathbf{Wos}.$$
The weird thing about this situation is that under the usual definition of "isomorphic," $\mathbf{Wos}$ has isomorphic objects that aren't the same. For example, the ordinal $\omega$ and $\omega 2$ are "isomorphic" as objects of $\mathbf{Wos}$, in the sense that there exists an arrow $\omega \rightarrow \omega 2$ that has a two-sided inverse, despite that $\omega$ and $\omega 2$ aren't isomorphic as ordered sets.
The standard solution, of course, is to just "throw out" all the morphisms that aren't monotone. This seems a bit drastic though; after all, the arrow $f_0 \otimes f_1$ makes sense even if $f_0$ and $f_1$ aren't monotone. In other words, the bifunctor $\otimes$ is defined on the whole of $\mathbf{Wos}$, not just the wide subcategory of special morphisms. Therefore, let us instead change our notion of isomorphism; let us simply define that two objects of $\mathbf{Wos}$ are isomorphic iff there exists a special arrow $X \rightarrow Y$ that has a special two-sided inverse.
That's fine, but I want a more systematic viewpoint here. As I see it, two objects $X$ and $Y$ of a category-like structure ought to be "the same" iff $\mathrm{Hom}(X,-)$ and $\mathrm{Hom}(Y,-)$ are naturally isomorphic. However, and here's the rub, I wish to view $\mathrm{Hom}(X,-)$ as a functor defined on the whole of $\mathbf{Wos}$, not just the subcategory of special arrows. And I want $\mathrm{Hom}(X,-)$ and $\mathrm{Hom}(Y,-)$ to be naturally isomorphic iff there is a special arrow $X \rightarrow Y$ with a special inverse.
My question is as follows.
Question. How (if at all) does category theory deal with (or think about, or conceptualize) these kinds of situations, where the usual notion of isomorphism isn't right?
Having motivated the question, let me finish up by offering a "minimal example." There is a category-like object given as follows.
Objects. Sets equipped with a distinguished subset.
Arrows. Functions.
"Special" arrows. Functions that preserve membership in the distinguished subset.
Denote this $\mathbf{Sds}.$ The neat thing about this is that its "self-enriched," in the sense that given objects $X$ and $Y$ of $\mathbf{Sds}$, the collection of functions $X \rightarrow Y$ forms an object of $\mathbf{Sds}$ in a natural way, by taking the distinguished subset of $\mathrm{Hom}(X,Y)$ to consist of precisely those functions that preserve membership in the distinguished subset. In fact, $\mathbf{Sds}$ seems to have "hom-tensor adjunction," in the sense that the object of functions $X \times Y \rightarrow Z$ is the "same as" the object of functions $X \rightarrow \mathrm{Hom}(Y,Z).$
• Well I would say that "a Category together with a subcategory of special arrow containing all objects" seem to be an appropriate answer – Simon Henry Sep 29 '15 at 9:13
• In fact there are quite simple situations when the correct notion of morphism is not clear, let alone isomorphisms - say, Hilbert spaces. – მამუკა ჯიბლაძე Sep 29 '15 at 9:20
• I suppose you should highlight that you are interested in situations where there are too many isomorphisms. In the opposite scenario, where there are morphisms that ought to be isomorphisms but are not, we have abstract homotopy theory. – Zhen Lin Sep 29 '15 at 9:27
• Categories enriched in Sds would seem to fit the bill. – Finn Lawler Sep 29 '15 at 10:56
• A more familiar example similar to your $\textbf{Sds}$ is the case of $G$-sets for a group $G$. When you allow all maps, you get a category enriched over itself, and the fixed points of the Hom-sets are exactly the equivariant maps. – Eric Wofsey Sep 29 '15 at 16:03
But if you really want to see the pair $\WOS \subseteq \WOS^\fn$ as a single category (and you reasonably might) then as Finn Lawler suggests in comments, you could consider it as a category enriched over the cartesian closed category $\newcommand{\SDS}{\mathbf{SDS}}\SDS$ you describe. Giving such an enrichment is equivalent to giving a subcategory containing all objects (sometimes called a lluf subcategory).
One well-studied case like this is that of dagger categories and relatives. These generalise examples like the category of finite-dimensional Hilbert spaces, where one wants to consider all linear maps, but wants to consider two such spaces the same only if they are unitarily isomorphic, not just linearly isomorphic. This has been viewed in various ways in the literature, including both the ways above: a distinguished lluf subcategory of unitary (or self-adjoint) maps, or equivalently as a distinguished subset of each hom-set.
If by $\Hom$ you mean $\Hom_\C$, then the Yoneda lemma says that natural isomorphisms $\Hom_\C(X,-) \to \hom_\C(Y,-)$, considered as functors on $\C$, will always correspond to isomorphisms in $\C$ (not generally special ones as you want). Similarly, natural isos $\Hom_\sp(X,-) \to \hom_\sp(Y,-)$, as functors on $\C^\sp$, always correspond to isomorphisms in $\C^\sp$.
We can restrict $\Hom_\C(X,-)$ to a functor on just $\C^\sp$. Considered as such, there may be more natural isomorphisms $\Hom_\C(X,-) \to \Hom_\C(Y,-)$ (natural just w.r.t. special maps) that don’t correspond to any isos in $\C$, special or otherwise. (Consider the case where $\C$ is a group, viewed as a one-object category, and only the identity is designated as special; then any automorphism of the underlying set will give a natural isomorphism of this form.)
It sounds most like what you want is to consider $\Hom_\sp(X,-)$ as a functor on the whole of $\C$. But this is not possible: the functorial action doesn’t extent, because when you compose a special arrow with an arbitrary map, it doesn’t generally stay special (except in the trivial case where all maps are special).
• Here's the topic in the nLab: ncatlab.org/nlab/show/M-category – Todd Trimble Sep 29 '15 at 12:19
• How does enriching in $\mathbf{SDS}$ ensure that the isomorphisms are the "correct" ones? – goblin Sep 29 '15 at 14:23
• @goblin: you choose the enrichment in $\mathbf{SDS}$ so that the special isomorphisms (i.e. special morphisms with a special inverse) are the ones you want. Nothing can automatically ensure in general that these are the “correct” ones — e.g. there is always the trivial $\mathbf{SDS}$-enrichment, where all morphisms are special, and its isos will just be the isos of the original category. But if you want a general result that ensures giving the “correct” isomorphisms, then you’ll need a more precise axiomatisation of the situations you want to cover. – Peter LeFanu Lumsdaine Sep 29 '15 at 14:32
• But remember, I want to understand isomorphisms as "corresponding to" natural isomorphisms between $\mathrm{Hom}(X,−)$ and $\mathrm{Hom}(Y,−)$. I want to not have to choose them. So suppose $\mathbf{C}$ is an $\mathcal{M}$-category. Then, from the perspective of hom-functors, how can we justify the idea that an "isomorphism" $X \rightarrow Y$ is the same as a "tight isomorphism" $X \rightarrow Y$? – goblin Sep 29 '15 at 14:47
• @goblin: I don't understand your first sentence is supposed to mean, or how it applies to the examples you gave in the question. – Eric Wofsey Sep 29 '15 at 16:14
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# CERN Published Articles
Derniers ajouts:
2016-05-03
15:04
5e$^{x+y}$: Searching over Mathematical Content in Digital Libraries / Oviedo, Arthur (Ecole Polytechnique, Lausanne) ; Kasioumis, Nikos (CERN) ; Aberer, Karl (Ecole Polytechnique, Lausanne) This paper presents 5 e x + y , a system that is able to extract, index and query mathematical content expressed as math- ematical expressions, complementing the CERN Document Server (CDS)[5]. We present the most important aspects of its design, our approach to model the relevant features of the mathematical content, and provide a demonstration of its searching capabilities.. 2015 In : 15th ACM/IEEE-CS Joint Conference on Digital Libraries: Large, Dynamic and Ubiquitous - The Era of the Digital Library, Knoxville, TN, USA, 21 - 25 Jun 2015, pp.283-284
2016-05-03
14:28
Virtualization architecture of CERN access and safety systems / Costa Lopez, Xurxo Breogan (CERN) ; Hakulinen, Timo (CERN) ; Ninin, Pierre (CERN) ; Nissen, Henrik (CERN) ; Nunes, Rui (CERN) ; Oser, Pascal (CERN) 2015 In : 8th ACM International Systems and Storage Conference, Haifa, Israel, 26 - 28 May 2015, pp.21
2016-05-03
11:34
The FLUKA code: An accurate simulation tool for particle therapy / Battistoni, Giuseppe (INFN, Milan) ; Bauer, Julia (Uniklinikum, Heidelberg) ; Böhlen, Till T (Uniklinikum, Heidelberg) ; Cerutti, Francesco (CERN) ; Chin, Mary Pik Wai (CERN) ; Dos Santos Augusto, Ricardo M (LMU Munich (main) ; CERN) ; Ferrari, Alfredo (CERN) ; Garcia Ortega, Pablo (CERN) ; Kozlowska, Wioletta S (HIT, Heidelberg ; CERN) ; Magro, Giuseppe (CNAO, Milan) et al. Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. [...] 2016 - Published in : Front. Oncol. xx (2016) xx
2016-05-03
06:02
Higher Order Modes Simulation and Measurements for 2400 MHz Cavity / Shashkov, Ya V (Moscow Phys. Eng. Inst.) ; Sobenin, N P (Moscow Phys. Eng. Inst.) ; Lalayan, M V (Moscow Phys. Eng. Inst.) ; Bazyl, D S (Moscow Phys. Eng. Inst.) ; Donetskiy, R V (Moscow Phys. Eng. Inst.) ; Zavadtsev, A (LLC, Nano Invest) ; Zobov, M (Frascati) ; Calaga, R (CERN) In the frameworks of the High Luminosity LHC upgrade program an application of additional harmonic cavities operating at multiples of the main RF system frequency of 400 MHz is currently under discussion. The 800 MHz superconducting cavities with grooved beam pipes were suggested as one of the design options. [...] THPB104.- 2016 - 3 p. - Published in : (2016) , pp. 1394-1396 Fulltext: PDF; External link: Fulltext In : 17th International Conference on RF Superconductivity, Whistler, Canada, 13 - 18 Sep 2015, pp.1394-1396
2016-05-03
06:02
Precision study of the $\eta \to \mu \mu \gamma$ and $\omega \to \mu + \mu \mu \pi^0$ electromagnetic transition form-factors and of the $\rho \to \mu \mu$ line shape in NA60 / NA60 Collaboration The NA60 experiment studied low-mass muon pair production in proton–nucleus (p–A) collisions using a 400 GeV proton beam at the CERN SPS. The low-mass dimuon spectrum is well described by the superposition of the two-body and Dalitz decays of the light neutral mesons η , ρ , ω , η′ and ϕ , and no evidence of in-medium effects is found. [...] 2016 - 8 p. - Published in : Phys. Lett. B 757 (2016) 437-444 Elsevier Open Access article: PDF;
2016-05-03
06:02
Ward identities and the physical interpretations of anomalies in stochastic quantization / Gavela, M B (CERN) ; Parga, N (CERN) The Ward identities are obtained for vector and axial currents through a functional integral representation of the Langvin equations for the stochastic quantization of fermions in an external gauge field. In this approach anomalies appear as due to fluctuations in the evolution of the system to its equilibrium regime.. 1986 - 5 p. - Published in : Phys. Lett. B B 174 (1986) 319-323
2016-05-03
06:02
K + N scattering in the quark-gluon picture / Pirner, Hans J (CERN) 1986 - 2 p. - Published in : Nucl. Phys. A 450 (1986) 397-398
2016-05-03
06:02
Overview of physics results from the CMS experiment at the LHC / Shmatov, S V (Dubna, JINR) An overview of physics results from the CMS experiment at the LHC is given. The present analysis is based on data obtained for colliding proton beams at the c.m. [...] 2015 - 12 p. - Published in : Phys. At. Nucl. 78 (2015) 509-520 - Published in : Yad. Fiz.: 78 (2015) , no. 6, pp. 546–557
2016-05-03
06:02
Impact evaluation of environmental and geometrical parasitic effects on high-precision position measurement of the LHC collimator jaws / Danisi, Alessandro (CERN) ; Losito, Roberto (CERN) ; Masi, Alessandro (CERN) Measuring the apertures of the Large Hadron Collider (LHC) collimators, as well as the positions of their axes, is a challenging task. The LHC collimators are equipped with high-precision linear position sensors, the linear variable differential transformers (LVDTs). [...] 2015 - 8 p. - Published in : Meas. Sci. Technol. 26 (2015) 094002
2016-05-03
06:02
RIVET Plug-in for $Z^0 \to e^+ e^-$ Production Cross-Section Measurement in pp Collisions at $\sqrt{s} = 7$ TeV / Dumitriu, Ana Elena (Bucharest, IFIN-HH) ; Grecu, A T (Bucharest, IFIN-HH) /LHCb The Robust Independent Validation of Experiment and Theory (RIVET) project is an efficient and portable tool kit in form of a C++ class library enabling validation and tuning of Monte Carlo (MC) event generator models in elementary particle physics and astrophysics. It provides a large collection of standard experimental analyses useful for MC generator development, validation, tuning and regression testing proposing a new way by which analysis code from the LHC and other high-energy collider experiments is preserved for comparison and development of future theory models. [...] 2015 - 14 p. - Published in : Rom. J. Phys.: 60 (2015) , no. 3-4, pp. 415 Fulltext: PDF; External link: Fulltext
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Use the correct Math method to create a random number. It gives the square root of a given integer. Like WaTeX â and unlike LaTeX or markup â you can include answer boxes in your formatted notation. It gives a larger number, which is lesser or equal to the given integer. var value = Math.random( ); var value = Math.cos(2*Math.PI); Math.min(val1, val2â¦â¦…valn); where val1, val2â¦â¦…valn are numbers. WebAssign provides several special tags that allow you to render specific kinds of notation using HTML substitution. Implementer Page: math.html Module Package: math.zip. Some examples of mathematical functions in PHP are as follows: To make use of the Math object, extend the Math object directly instead of using the prototype. IEEEremainder computes the remainder operation on two double arguments as prescribed by the IEEE 754 standard and returns the result as a double.. The Math.pow() function returns the base to the exponent power, that is, base exponent, the base and the exponent are in decimal numeral system.. Because pow() is a static method of Math, you always use it as Math.pow(), rather than as a method of a Math object you created (Math has no constructor). You can call the Math as an object without creating it because the properties and methods of Math are static. math.mean(a, b, c, â¦) Compute the mean value of matrix or a list with values. If you want to use degrees instead of radians, you have to convert degrees to radians: Angle in radians = Angle in degrees x PI / 180. All methods and properties (constants) can be used without creating a Math object first. document.write("The Value is :" + value_demo); It provides arcsine of an integer. Nelson Advanced Functions Core Components. document.write("
Second Value : " + value2 ); These functions are defined by their entity namesakes. document.write("First Value : " + value ); Common functions like sin, log and tanh should be rendered in a non-italic font. Home Contact About Subject Index. Output:Â The Value is 1.4142135623730951. Math Notepad is a web based editor to do mathematical calculations and plot graphs. A composite function is a composition of 2 or more functions into a single function. The table results can usually be used to plot results on a graph. Tutorials, references, and examples are constantly reviewed to avoid errors, but we cannot warrant full correctness of all content. document.write("
Fourth Value : " + value4 ); For a complete reference, go to our complete Math object reference. 4) SQRT1_2-Â It specifies the square root of 1/2. Use this property for the mod and rem functions of the Math Function block. Output, There are PHP math functions to take care of addition, subtraction, division and multiplication and many other mathematical requirements. In a script file which contains commands and function definitions. var value_demo = Math.LOG2E 5) LN2- It specifies the natural logarithm of 2. document.getElementById("floor_demo").innerHTML = Math.floor(5.8); If X is less than or equal to 0.0E0, the function returns NULL and a warning â Invalid argument for logarithm â is reported. , ALL RIGHTS RESERVED. Math.floor(x); where x is a number. SAT Math Objectives. Version 0.11.5. document.write("The Value is :" + value_demo); For more information, see MaxIterations (HDL Coder). all the outputs (the actual values related to) are together called the range a function is a special type of relation where: document.write("
Third Value : " + value ); However, a simple function might return the input plus one. The Wolfram Language has the most extensive collection of mathematical functions ever assembled. document.write("The Value is :" + value_demo); while joogat's one line function is short, it is probably better to calculate factorial iteratively instead of recursively. It can be written as: var value_demo = Math.LOG10E In the table, dp indicates double precision. Note that further math-related Excel functions are also provided in the Excel Statistical Functions and Excel Engineering Functions categories. JavaScript provides 8 mathematical constants that can be accessed with the Math object: Unlike other global objects, the Math object has no constructor. . Operators 3. In other words, the ceil() function rounds a number up and returns an integer value. The diagram below describes what the composite function gf is. When you know what the monster does, you can solve the problems. Functions. The result is between ⦠var value_demo = Math.LN10 Relations 6. Output: The Value is 1.4426950408889634. var value_demo = Math.SQRT2 XSLT processors may support any number of the extension elements and functions given in this module. To some people, E = mc² or â/ât + v â
â might be complex, and such constructs can be written fairly well using just HTML with some help from CSS; see my page Math in HTML (and CSS). Far Out Functions - Learning Connections Essential Skills Mental Math - all four operations Problem Solving and Creative Thinking. then again, unless you're trying to do large numbers (170! How To Determine If A Relation Is A Function? An open question is how to render maths on dumb terminals. HTML lacks markup for mathematical expressions as structures, and there is no simple way to produce anything essentially two- dimensional beyond superscripting or subscripting. Math is a placeholder object that contains mathematical functions and constants of which round() is one of these functions. document.getElementById("min_demo").innerHTML = 6) LN10- It specifies the natural logarithm of 10. Algebra functions lessons with lots of worked examples and practice problems. Continuation dots 4. This function takes the following arguments: double1: the dividend.. double2: the divisor.. document.write("First Value : " + value ); MATH GAMES Addition Games Subtraction Games Multiplication Games Division Games Fraction Games Ratio Games Prealgebra Games Geometry Games. Function Machine Investigate the relationship between input and output values in a function Linear Equation Games. The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.. Math.random(); It provides an arccosine of an integer. The HTML syntax of HTML5 allows for MathML elements to be used inside a document using $...$ tags. ArrayAvg Returns the average of the elements in an array. For example, you might negate an expression in order to invert a tracking curve which you wish to use to stabilize an element (such an expression might resemble the following: -(Transform1.translate.x)). The following concepts are included on the test: There are various mathematical functions in PHP. ASin Determines the arcsine of a number. It is not a function object, not a constructor. Most of the web browsers can display MathML tags. Output: The Value is 0.4342944819032518. Greek letters 5. The bitwise operators work only on integral data types and are also available for the bit string types bit and bit varying, as shown in Table 9.13.. Table 9.5 shows the available mathematical functions. It can be written as: Test - Fundamental Mathematics 2; Test - Intermediate Mathematics. The function grapher can plot sinusoidal and other trigonometric functions including sine (sin), cosine(cos) and tan. It provides a random number between 0 and 1. In the table, dp indicates double precision.Many of these functions ⦠ACos Returns the arccosine, in radians, of a number. A formula for which no natural HTML markup exists Although HTML markup exists in the sample case, mathematical formulas are usually much more complicated. Math.max(50, 90, 55, 25, 78, 14); Additional elements are needed to represent roots and for over and under lining. var value = Math.random( ); HTML HTML Tag Reference HTML Browser Support HTML Event Reference HTML Color Reference HTML Attribute Reference HTML Canvas Reference HTML SVG Reference HTML Character Sets Google Maps Reference CSS ... PHP Math Introduction. The Math.ceil() function always rounds a number up to the next largest integer. Domain and Range An important part of understanding functions is understanding their domain and range. Let us see few examples for the above some methods of JavaScript Math Functions: First f maps value x to function value f(x). Maximum tests is 8. Other symbols. EXSLT - Math covers extension elements and functions that provide facilities to do with maths. PHP has nice support for mathematical processing.
This has been a guide to JavaScript Math Functions.
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Martedì 4 Giugno 2019, alle ore 15 precise, presso la sala Conferenze
dell'IMATI-CNR di Pavia, il
Prof. Giovanni Leoni, Carnegie Mellon University, Pittsburgh,
terrà un seminario dal titolo:
A VARIATIONAL APPROACH FOR WATER WAVES
e alle ore 16 precise la
Prof. Irene Fonseca, Carnegie Mellon University, Pittsburgh,
terrà un seminario dal titolo:
A HOMOGENIZATION RESULT IN THE GRADIENT THEORY OF PHASE TRANSITIONS
nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e
Dipartimento di Matematica, Pavia),
http://matematica.unipv.it/it/seminari-matematica-applicata
---------------------------------------------------------
Abstract seminario Leoni
We study the existence and regularity of non-trivial solutions to a
one-phase Bernoulli free boundary problem with mixed
periodic-Dirichlet boundary conditions. This is joint work with
Giovanni Gravina.
----------------------------------------------------------
Abstract seminario Fonseca
A variational model in the context of the gradient theory for
fluid-fluid phase transitions with small scale heterogeneities is
studied. In particular, the case where the scale $\varepsilon$ of the
small homogeneities is of the same order of the scale governing the
phase transition is considered. Here the interaction between
homogenization and the phase transitions process will lead, in the
limit as $\varepsilon \to 0$, to an anisotropic interfacial energy.
|
Department of Mathematical Sciences Events People Colloquia and Seminars Conferences Centers Positions Areas of Research About the Department Model Theory Seminar Christopher Eagle University of Toronto Title: Omitting types in infinitary [0, 1]-valued logic Abstract: We describe an infinitary logic for metric structures which is analogous to $L_{\omega_1, \omega}$. Using topological methods, we prove an omitting types theorem for countable fragments of this logic. We use omitting types, together with an analogue of Scott's theorem, to show that every non-trivial separable quotient of a non-separable Banach space is almost isometric to a quotient of a Banach space of density $\aleph_1$.Date: Monday, April 22, 2013Time: 5:00 pmLocation: Wean 8220Submitted by: Grossberg
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## anonymous 4 years ago i neede help...............................................................................................................................................................
1. anonymous
what do you need help with? XD
2. anonymous
a question which i have to draw out but i cant
3. AravindG
wat?
4. AravindG
5. anonymous
Can you maybe attach a file of a screen shot or question?
6. anonymous
Well press the Draw button
7. anonymous
suttin bout rotational symmetry
8. anonymous
i cnt draw shapessss
9. anonymous
Scan the question, predd the draw button under your question, take a photo and upload it, thousends of solutions,
10. anonymous
ill try
11. anonymous
12. anonymous
kk im doin it now thn xx
13. anonymous
|dw:1327843885712:dw|
14. anonymous
A has three rotational symmetries, C probably has four rotational symmetries, D has two rotational symmetries, and E has two as well... i think B has none
15. anonymous
|dw:1327844088608:dw|
16. anonymous
??? what's that? Is that the answer?
17. anonymous
nopee............ its the table which i have to put the answers inn (i know it looks weird but its the best i could do) :D
18. anonymous
Good job! better than i could ever draw haha XD okay, so sry, ill just write the letter and number A=3 B=1 C=4 D=2 E=2
19. anonymous
Is it okay to have more than one letter in a single space in the table ?
20. anonymous
pardonn say tht againnn
21. anonymous
im confused is it okay if u reply with drawing with the answers inside of it?? x
22. anonymous
$\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{?}}}}}}}}}$
23. anonymous
....is that another form of a question or is that diagram just showing you're really confused?
24. anonymous
and what does RS mean?
25. anonymous
REALLY CONFUSED ............... RS MEANS ROTATIONAL SYMMETRY
26. anonymous
Ok, do you know what rotational symmetry is? an object with rotational symmetry is an object that looks the same after a certain amount of rotation.
27. anonymous
okaii so a and c do
28. anonymous
yes..best thing to do when you start off is to draw each picture on a paper, and then rotate the paper. Count from how many sides it looks the same.
29. anonymous
okaiii soo can u help meh with tht
30. anonymous
okay, so when u draw the equilateral triangle(A), you should be able to rotate that paper and find that it looks the same from three different sides.
31. anonymous
yessss
32. anonymous
that means there are 3 rotational symmetries for the first one. try that with b
33. anonymous
okaiii
34. anonymous
1
35. anonymous
good :)
36. anonymous
that means there is one rotational symmetry. c?
37. anonymous
4?
38. anonymous
yes!!! d?
39. anonymous
2?
40. anonymous
hellooo is it 2?
41. anonymous
and e?
42. anonymous
2
43. anonymous
You are awesome!! XD good job
44. anonymous
thnx??? im not tht awesomee!!!! u just helped me finish my homework thts AMAZING!
45. anonymous
XD my pleasure, ask any time >.<
46. anonymous
can u do me 1 more favour???
47. anonymous
ok!
48. anonymous
1 more question??
49. anonymous
yeah, sure, can u just give me a minute?
50. anonymous
ill be right back, post your question while I'm gone XD
51. anonymous
k
52. anonymous
|dw:1327847527607:dw|
53. anonymous
s:strawberry c:chocolate v:vanilla
54. anonymous
on saturday 36 ice creams were sold but on sunday only 24were sold. Estimate the number of strawberry ice creams were sold on sunday...
55. anonymous
Are S, C, and V equal in size?
56. anonymous
i dunno im just drawing the diagram on my sheet
57. anonymous
|dw:1327847836950:dw|
58. anonymous
ellllo'??
59. anonymous
ok, well, my answers won't be that accurate cuz it's a little hard to judge(although the diagrams are well done), but ill try my best On Saturday, S looks like its about 1/3 of the total ice creams sold. 1/3 of36=12 strawberry ice creams on Saturday. On Sunday, S looks like its about 3/8 of the total ice cream sold. 3/8 of 24=9 strawberry ice creams on sunday.
60. anonymous
k thaatss very accurate thnx now for part b....
61. anonymous
AZIZ SAYS" the same number of vanilla ice creams was sold on saturday and sunday" is he correct? explain how you know.
62. anonymous
r u theree?
63. anonymous
i gues not :(
64. anonymous
yaayy ur backk
65. anonymous
AZIZ SAYS" the same number of vanilla ice creams was sold on saturday and sunday" is he correct? explain how you know.
66. anonymous
I'm here lol
67. anonymous
ohh... yaay
68. anonymous
Danii xxx This is the asker AZIZ SAYS" the same number of vanilla ice creams was sold on saturday and sunday" is he correct? explain how you know.
69. anonymous
ok
70. anonymous
...its too much work im giving u innit!!
71. anonymous
so, 3/8 and 1/3 is about the same right?
72. anonymous
but the total number of ice creams sold are vastly different. 24 and 36
73. anonymous
i dont think so....
74. anonymous
1/3=3/9 3/8 and 3/9 are barely different at this point
75. anonymous
oh, wait, SORRY, vanilla!???
76. anonymous
its no... because say if it was in fractions it would be i/3 and 3/8 which is not exactly the same is) is that what i should write down???
77. anonymous
yes vanilla
78. anonymous
ohhhh, sry, no, don't nononononono, i was still in strawberry mode
79. anonymous
ohhh ...... ha ha ha LMFAO
80. anonymous
.............
81. anonymous
ok, so looking at the pie charts, he would be saying they sold the same number considering they look the same(1/2) but, this is a proportion, so it's not the same 1/2 of 24 and 1/2 of 36 are vastly different 12 and 18 THAT is what you need to write, forget what i said until now about the second question
82. anonymous
does that make sense?
83. anonymous
okaiii thnx let me just write it down and about next wek ill tell u my score yhh
84. anonymous
:) better get perfect haha :P
85. anonymous
:D thnxxx ALOTTT
86. anonymous
welcome XD thnx for becoming a fan too ;) and a fanMESSAGE!? wow, i don't deserve this X)
87. anonymous
obvs u dooo x
88. anonymous
after all tht heck yh!
89. anonymous
hehe, well stay around, ill be answering some more :) any time just come online! BUT, its past midnight so ill be talking to you very soon XD good night:)
90. anonymous
is it??? its only 14:59 here!! xx
91. anonymous
lolol, i live in japan :) I'm half tho lol, where are you from?
92. anonymous
Untied Kingdom x anyway better go tobed dont wanna keep u up byee x
93. anonymous
cya :)
94. anonymous
byeee!!
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# Correct hierarchy levels of PDF bookmarks for custom section \subsubsubsection
I had to to define a \subsubsubsection for a technical document (I know it is highly criticised). I believe I inspired myself from this alternative answer to How to add an extra level of sections with headings below \subsubsection at that time (I couldn't use the package titlesec, but I can't remember the reason).
However, the hierarchy in the PDF bookmarks is messed up: subsubsubsection is shown as level 1 instead of 4, even though I tell \@startsection it's level 4 in the definition of \subsubsubsection. I wrongly expected this to handle PDF bookmarks implicitly as well.
How do I tell the package which is handling the PDF bookmarks (I guess hyperref) that the \subsubsubsection is level 4? Or alternatively as a suboptimal workaround, how do I tell \subsubsubsection not to show up in the PDF bookmarks at all (remember, setting bookmarksdepth<4 is not working, since it is ignoring that it is level 4).
\documentclass{book}
\usepackage[utf8]{inputenc}
\usepackage[pdftex]{hyperref}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{4}
\hypersetup{bookmarksdepth=4}
\makeatletter
\newcounter{subsubsubsection}[subsubsection]
\renewcommand{\thesubsubsubsection}{\thesubsubsection.\arabic{subsubsubsection}}
\renewcommand{\theparagraph}{\thesubsubsubsection.\arabic{paragraph}}
\newcommand{\subsubsubsection}{\@startsection{subsubsubsection}{4}{\z@}%
{-3.25ex\@plus -1ex \@minus -.2ex}%
{1.5ex \@plus .2ex}%
{\normalfont\normalsize\it\bfseries}}
\renewcommand{\paragraph}{\@startsection{paragraph}{5}{\z@}%
{3.25ex \@plus1ex \@minus.2ex}%
{-1em}%
{\normalfont\normalsize\bfseries}}
\renewcommand{\subparagraph}{\@startsection{subparagraph}{6}{\parindent}%
{3.25ex \@plus1ex \@minus .2ex}%
{-1em}%
{\normalfont\normalsize\bfseries}}
\newcommand*{\l@subsubsubsection}{\@dottedtocline{4}{11em}{5em}}
\renewcommand*{\l@paragraph}{\@dottedtocline{5}{12em}{6em}}
\renewcommand*{\l@subparagraph}{\@dottedtocline{6}{14em}{7em}}
\newcommand{\subsubsubsectionmark}[1]{}
\makeatother
\begin{document}
\tableofcontents
\section{Section}
\subsection{Subsection}
\subsubsection{Subsubsection}
\subsubsubsection{SubsubsubSection}
\end{document}
• I don't know if it suits your needs, but maybe the bookmark package (that fixes some strange behaviors of hyperref) can be useful – Moriambar Oct 21 '15 at 14:49
• latex provides section levels below subsubsection by default, why insert a new one in the middle of the sequence? Do you really need all 6 levels? – David Carlisle Oct 21 '15 at 14:49
If this is really needed, use bookmark package, say depth=3 as option (i.e. only down to subsubsection) and (more important!!!):
You've to specify the level in which the new subsubsubsection has to be hooked to:
\newcommand{\toclevel@subsubsubsection}{4}
This way you inform hyperref (and the bookmark) package, that subsubsubsection counters are on level 4.
\documentclass{book}
\usepackage[utf8]{inputenc}
\usepackage[pdftex]{hyperref}
\usepackage[depth=3]{bookmark}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{4}
%\hypersetup{bookmarksdepth=4}
\makeatletter
\newcommand{\toclevel@subsubsubsection}{4}
\newcounter{subsubsubsection}[subsubsection]
\renewcommand{\thesubsubsubsection}{\thesubsubsection.\arabic{subsubsubsection}}
\renewcommand{\theparagraph}{\thesubsubsubsection.\arabic{paragraph}}
\newcommand{\subsubsubsection}{\@startsection{subsubsubsection}{4}{\z@}%
{-3.25ex\@plus -1ex \@minus -.2ex}%
{1.5ex \@plus .2ex}%
{\normalfont\normalsize\it\bfseries}}
\renewcommand{\paragraph}{\@startsection{paragraph}{5}{\z@}%
{3.25ex \@plus1ex \@minus.2ex}%
{-1em}%
{\normalfont\normalsize\bfseries}}
\renewcommand{\subparagraph}{\@startsection{subparagraph}{6}{\parindent}%
{3.25ex \@plus1ex \@minus .2ex}%
{-1em}%
{\normalfont\normalsize\bfseries}}
\newcommand*{\l@subsubsubsection}{\@dottedtocline{4}{11em}{5em}}
\renewcommand*{\l@paragraph}{\@dottedtocline{5}{12em}{6em}}
\renewcommand*{\l@subparagraph}{\@dottedtocline{6}{14em}{7em}}
\newcommand{\subsubsubsectionmark}[1]{}
\makeatother
\begin{document}
\tableofcontents
\section{Section}
\subsection{Subsection}
\subsubsection{Subsubsection}
\phantomsection
\subsubsubsection{SubsubsubSection}
\end{document}
|
+0
Math help
+1
155
1
+86
Chad built a scale model of a statue. He built the model 7 inches tall to represent the actual height of 15 feet. Which equation below represents the relationship between the actual height (a) ,in feet and the height of the model (m) , in inches?
KawaiiKibby May 4, 2017
Sort:
1+0 Answers
#1
+90544
+2
Chad built a scale model of a statue.
He built the model 7 inches tall to represent the actual height of 15 feet.
Which equation below represents the relationship between the actual height (a) ,in feet and the height of the model (m) , in inches?
$$a\;\; \alpha\;\; m\\ a\;\; =\;\;k * m\\ \text{When actual is 15 model is 7}\\ 15\;\; =\;\;k * 7\\ k=\frac{15}{7}\\ a\;\; =\;\;\frac{15}{7} * m\\ a\;\; =\;\;\frac{15m}{7} \\$$
Melody May 4, 2017
3 Online Users
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Orthogonal direct sum of cocycles across acting groups
Definition
Suppose $m$ and $n$ are natural numbers. Consider a bunch of groups $G_1, G_2, \dots, G_m$, all equipped with actions on an abelian group $A$. Suppose, for each $i$, that we have a $n$-cocycle $c_i: G_i^n \to A$ for the action of $G_i$ on $A$.
Then, consider $G := G_1 \times G_2 \times \dots \times G_m$. If all the $G_i$-actions on $A$ commute with each other, then we get an induced $G$-action on $A$. We can define a $n$-cocycle $c$ for this action in terms of $c_i$s, as the orthogonal direct sum of cocycles as follows:
First, view $G$ as an internal direct product, so each $G_i$ is identified with a subgroup of $G$. Now, define:
$c((g_{11},g_{12},\dots, g_{1m}),(g_{21},g_{22},\dots,g_{2m}), \dots,(g_{n1},g_{n2},\dots,g_{nm}) = \sum_{i=1}^m c_i(g_{1i},g_{2i},\dots,g_{ni})$
where the summation on the right happens in $A$.
This does indeed give a cocycle.
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# Are isometric homorphisms of C* algebras *-homorphisms
Here is my precise question:
Let $A$ and $B$ be two $C^*$ algebras. Let $f: A \rightarrow B$ a homomorphism of $C^*$ algebras which is isometric (on its image). Is $f$ necessary a $*$-homomorphism ?
It sounds like a basic question, but I haven't found any counterexample nor any basic reference mentioning this kind of result, so I hope it is non trivial and suitable for MO.
Another equivalent question is the following:
Let $A$ be a $C^*$-algebra and $x$ an element of $A$ such that:
1) the spectrum of $x$ is included in $\mathbb{R}$
2) for any polynomial $P$ (with coefcients in $\mathbb{C}$) the norm of $P(x)$ is the supremum of $|P(t)|$ for $t \in \text{Spec}(x)$.
Is $x$ necessarily self-adjoint ?
Indeed if the answer to this second question is yes, then any isometric algebra homorphism send self adjoint element to self adjoint element hence is a $*$-homorphism, and conversely if the answer to the first question is yes then for such an element $x$ one can construct an isometric morphism from $\mathcal{C}(\text{Spec}(X))$ to $A$ which is hence a $*$-homomorphism and hence $x$ is self adjoint as the image of a self adjoint element.
Moreover, If I'm not mistaken the answer to these two questions is yes at least for finite dimensional algebras.
I don't really have a precise motivation for this question except curiosity, but it might be interesting to have such a "$*$-free" characterization of morphisms of $C^*$-algebras if one want to develop a satisfying analogue to $C^*$ algebras for other valued field than $\mathbb{R}$ and $\mathbb{C}$.
• If your $C^{\ast}$-algebras are unital and you assume that your morphism preserves the unit then the answer is yes, because unital contractions between $C^{\ast}$-algebras are positive and positive maps are self-adjoint (i.e. preserve $*$). Probably you may use unitisations to conclude it in the general case but I am not sure how to do that. – Mateusz Wasilewski Mar 3 '15 at 17:39
• Good point, That was indeed trivial. thank you. – Simon Henry Mar 3 '15 at 17:48
• Regarding your final comment: unfortunately I don't think this will help you get a star-free characterization, because the star (and the Cstar identity) is implicitly needed in Mateusz's argument. I am fairly sure the result is false for other classes of unital Banach star-algebras – Yemon Choi Mar 16 '15 at 11:07
• @Yemon Choi : My point was that this gives a star-free characterization of morphisms of C* algebras between C* algebras. It shows that the question of whether there exists a star-free characterization of C*-algebras among Banach algebras makes sense, because the category of C*-algebra is a full subcategory of the category of Banach algebra and homomorphisms of norm smaller than one, but it does not answer it. – Simon Henry Mar 16 '15 at 15:12
• @SimonHenry OK, I see now; thanks for clarifying. After I wrote my comment I recalled that there may be something along the lines you want: have you come across the Vidav-Palmer theorem? In a unital Banach algebra one can define a notion of hermitian which makes no reference to an involution, just using the Banach algebra structure; and then if $A = H+iH$ where $H$ denotes the subset of "hermitian" elements, the V-P theorem says that $A$ is isometrically isomorphic to the underlying BA of a unital Cstar algebra, with the involution sending $h+ik$ to $h-ik$. – Yemon Choi Mar 16 '15 at 16:14
|
Economics
This is under heavy development
Units
NameValue
yoctoNEARsmallest undividable amount of native currency NEAR.
NEAR10**24 yoctoNEAR
blocksmallest on-chain unit of time
gasunit to measure usage of blockchain
General Parameters
NameValue
INITIAL_SUPPLY10**33 yoctoNEAR
MIN_GAS_PRICE10**5 yoctoNEAR
REWARD_PCT_PER_YEAR0.05
EPOCH_LENGTH43,200 blocks
EPOCHS_A_YEAR730 epochs
INITIAL_MAX_STORAGE10 * 2**40 bytes == 10 TB
TREASURY_PCT0.1
TREASURY_ACCOUNT_IDtreasury
CONTRACT_PCT0.3
INVALID_STATE_SLASH_PCT0.05
ADJ_FEE0.001
TOTAL_SEATS100
ONLINE_THRESHOLD_MIN0.9
ONLINE_THRESHOLD_MAX0.99
BLOCK_PRODUCER_KICKOUT_THRESHOLD0.9
CHUNK_PRODUCER_KICKOUT_THRESHOLD0.6
General Variables
NameDescriptionInitial value
totalSupply[t]Total supply of NEAR at given epoch[t]INITIAL_SUPPLY
gasPrice[t]The cost of 1 unit of gas in NEAR tokens (see Transaction Fees section below)MIN_GAS_PRICE
storageAmountPerByte[t]keeping constant, INITIAL_SUPPLY / INITIAL_MAX_STORAGE~9.09 * 10**19 yoctoNEAR
Issuance
The protocol sets a ceiling for the maximum issuance of tokens, and dynamically decreases this issuance depending on the amount of total fees in the system.
NameDescription
reward[t]totalSupply[t] * ((1 + REWARD_PCT_PER_YEAR) ** (1/EPOCHS_A_YEAR) - 1)
epochFee[t]sum([(1 - DEVELOPER_PCT_PER_YEAR) * block.txFee + block.stateFee for block in epoch[t]])
issuance[t]The amount of token issued at a certain epoch[t], issuance[t] = reward[t] - epochFee[t]
Where totalSupply[t] is the total number of tokens in the system at a given time t. If epochFee[t] > reward[t] the issuance is negative, thus the totalSupply[t] decreases in given epoch.
Transaction Fees
Each transaction before inclusion must buy gas enough to cover the cost of bandwidth and execution.
Gas unifies execution and bytes of bandwidth usage of blockchain. Each WASM instruction or pre-compiled function gets assigned an amount of gas based on measurements on common-denominator computer. Same goes for weighting the used bandwidth based on general unified costs. For specific gas mapping numbers see ???.
Gas is priced dynamically in NEAR tokens. At each block t, we update gasPrice[t] = gasPrice[t - 1] * (gasUsed[t - 1] / gasLimit[t - 1] - 0.5) * ADJ_FEE.
Where gasUsed[t] = sum([sum([gas(tx) for tx in chunk]) for chunk in block[t]]). gasLimit[t] is defined as gasLimit[t] = gasLimit[t - 1] + validatorGasDiff[t - 1], where validatorGasDiff is parameter with which each chunk producer can either increase or decrease gas limit based on how long it to execute the previous chunk. validatorGasDiff[t] can be only within ±0.1% of gasLimit[t] and only if gasUsed[t - 1] > 0.9 * gasLimit[t - 1].
State Stake
Amount of NEAR on the account represents right for this account to take portion of the blockchain's overall global state. Transactions fail if account doesn't have enough balance to cover the storage required for given account.
def check_storage_cost(account): # Compute requiredAmount given size of the account. requiredAmount = sizeOf(account) * storageAmountPerByte return Ok() if account.amount + account.locked >= requiredAmount else Error(requiredAmount)# Check when transaction is received to verify that it is valid.def verify_transaction(tx, signer_account): # ... # Updates signer's account with the amount it will have after executing this tx. update_post_amount(signer_account, tx) result = check_storage_cost(signer_account) # If enough balance OR account is been deleted by the owner. if not result.ok() or DeleteAccount(tx.signer_id) in tx.actions: assert LackBalanceForState(signer_id: tx.signer_id, amount: result.err())# After account touched / changed, we check it still has enough balance to cover it's storage.def on_account_change(block_height, account): # ... execute transaction / receipt changes ... # Validate post-condition and revert if it fails. result = check_storage_cost(sender_account) if not result.ok(): assert LackBalanceForState(signer_id: tx.signer_id, amount: result.err())
Where sizeOf(account) includes size of account_id, account structure and size of all the data stored under the account.
Account can end up with not enough balance in case it gets slashed. Account will become unusable as all originating transactions will fail (including deletion). The only way to recover it in this case is by sending extra funds from a different accounts.
Validators
NEAR validators provide their resources in exchange for a reward epochReward[t], where [t] represents the considered epoch
NameDescription
epochReward[t]= coinbaseReward[t] + epochFee[t]
coinbaseReward[t]The maximum inflation per epoch[t], as a function of REWARD_PCT_PER_YEAR / EPOCHS_A_YEAR
Validator Selection
NameDescription
proposals: Proposal[]The array of all new staking transactions that have happened during the epoch (if one account has multiple only last one is used)
current_validatorsThe array of all existing validators during the epoch
epoch[T]The epoch when validator[v] is selected from the proposals auction array
seat_priceThe minimum stake needed to become validator in epoch[T]
stake[v]The amount in NEAR tokens staked by validator[v] during the auction at the end of epoch[T-2], minus INCLUSION_FEE
shard[v]The shard is randomly assigned to validator[v] at epoch[T-1], such that its node can download and sync with its state
num_allocated_seats[v]Number of seats assigned to validator[v], calculated from stake[v]/seatPrice
validatorAssignmentsThe resulting ordered array of all proposals with a stake higher than seatPrice
struct Proposal { account_id: AccountId, stake: Balance, public_key: PublicKey,}
During the epoch, outcome of staking transactions produce proposals, which are collected, in the form of Proposals. At the end of every epoch T, next algorithm gets executed to determine validators for epoch T + 2:
1. For every validator in current_validators determine num_blocks_produced, num_chunks_produced based on what they produced during the epoch.
2. Remove validators, for whom num_blocks_produced < num_blocks_expected * BLOCK_PRODUCER_KICKOUT_THRESHOLD or num_chunks_produced < num_chunks_expected * CHUNK_PRODUCER_KICKOUT_THRESHOLD.
3. Add validators from proposals, if validator is also in current_validators, considered stake of the proposal is 0 if proposal.stake == 0 else proposal.stake + reward[proposal.account_id].
4. Find seat price seat_price = findSeatPrice(current_validators - kickedout_validators + proposals, num_seats), where each validator gets floor(stake[v] / seat_price) seats and seat_price is highest integer number such that total number of seats is at least num_seats.
5. Filter validators and proposals to only those with stake greater or equal than seat price.
6. For every validator, replicate them by number of seats they get floor(stake[v] / seat_price).
7. Randomly shuffle (TODO: define random number sampler) with seed from randomness generated on the last block of current epoch (via VRF(block_producer.private_key, block_hash)).
8. Cut off all seats which are over the num_seats needed.
9. Use this set for block producers and shifting window over it as chunk producers.
def findSeatPrice(stakes, num_seats): """Find seat price given set of stakes and number of seats required. Seat price is highest integer number such that if you sum floor(stakes[i] / seat_price) it is at least num_seats. """ stakes = sorted(stakes) total_stakes = sum(stakes) assert total_stakes >= num_seats, "Total stakes should be above number of seats" left, right = 1, total_stakes + 1 while True: if left == right - 1: return left mid = (left + right) // 2 sum = 0 for stake in stakes: sum += stake // mid if sum >= num_seats: left = mid break right = mid
Validator Rewards Calculation
Note: all calculations are done in Rational numbers.
Total reward every epoch t is equal to:
total_reward[t] = floor(totalSupply * max_inflation_rate * num_blocks_per_year / epoch_length)
where max_inflation_rate, num_blocks_per_year, epoch_length are genesis parameters and totalSupply is taken from the last block in the epoch.
After that a fraction of the reward goes to the treasury and the remaining amount will be used for computing validator rewards:
treasury_reward[t] = floor(reward[t] * protocol_reward_rate)validator_reward[t] = total_reward[t] - treasury_reward[t]
Validators that didn't meet the threshold for either blocks or chunks get kicked out and don't get any reward, otherwise uptime of a validator is computed:
pct_online[t][j] = (num_produced_blocks[t][j] / expected_produced_blocks[t][j] + num_produced_chunks[t][j] / expected_produced_chunks[t][j]) / 2if pct_online > ONLINE_THRESHOLD: uptime[t][j] = min(1, (pct_online[t][j] - ONLINE_THRESHOLD_MIN) / (ONLINE_THRESHOLD_MAX - ONLINE_THRESHOLD_MIN))else: uptime[t][j] = 0
Where expected_produced_blocks and expected_produced_chunks is the number of blocks and chunks respectively that is expected to be produced by given validator j in the epoch t.
The specific validator[t][j] reward for epoch t is then proportional to the fraction of stake of this validator from total stake:
validatorReward[t][j] = floor(uptime[t][j] * stake[t][j] * validator_reward[t] / total_stake[t])
Slashing
ChunkProofs
# Check that chunk is invalid, because the proofs in header don't match the body.def chunk_proofs_condition(chunk): # TODO# At the end of the epoch, run update validators and# determine how much to slash validators.def end_of_epoch_update_validators(validators): # ... for validator in validators: if validator.is_slashed: validator.stake -= INVALID_STATE_SLASH_PCT * validator.stake
ChunkState
# Check that chunk header post state root is invalid,# because the execution of previous chunk doesn't lead to it.def chunk_state_condition(prev_chunk, prev_state, chunk_header): # TODO# At the end of the epoch, run update validators and# determine how much to slash validators.def end_of_epoch(..., validators): # ... for validator in validators: if validator.is_slashed: validator.stake -= INVALID_STATE_SLASH_PCT * validator.stake
Protocol Treasury
Treasury account TREASURY_ACCOUNT_ID receives fraction of reward every epoch t:
# At the end of the epoch, update treasurydef end_of_epoch(..., reward): # ... accounts[TREASURY_ACCOUNT_ID].amount = treasury_reward[t]
Contract Rewards
Contract account is rewarded with 30% of gas burnt during the execution of its functions. The reward is credited to the contract account after applying the corresponding receipt with FunctionCallAction, gas is converted to tokens using gas price of the current block.
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# In 4 large random mating population of purple and white jimsonweed purple_ dominant white recessive trait). 4% of the population
###### Question:
In 4 large random mating population of purple and white jimsonweed purple_ dominant white recessive trait). 4% of the population contain the recessive trait What is trait and the allele frequency of the recessive trait? What will be the genotypic frequencies from generation to generation; provided that alleles and remain in genetic equilibrium? (Show work by using the Punnett square & Hardy- Weinberg equation One of every 10,000 babies in the U.S. is born with phenylketonuria (PKU) wich can result in mental retardation if untreated_ The allele for PKU is recessive so babies with this disorder are homozygous recessive Thus q2 .0001, with q 0.01 (the square root of 0.0001). Using the Hardy-Weinberg equation, what is the frequency of carriers in the population? If,on average, 46% of the loci in a species' gene pool are heterozygous, what then should the average homozygosity of the species should be
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## 计算机代写|计算机图形学代写computer graphics代考|CS559
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System
Over recent millennia, mankind has invented and discarded many systems for representing number. People have counted on their fingers and toes, used pictures (hieroglyphics), cut marks on clay tablets (cuneiform symbols), employed Greek symbols (Ionic system) and struggled with, and abandoned Roman numerals (I, V, X, L, C, D, M, etc.), until we reach today’s decimal place system, which has Hindu-Arabic and Chinese origins. And since the invention of computers we have witnessed the emergence of binary, octal and hexadecimal number systems, where 2, 8 and 16 respectively, replace the 10 in our decimal system.
The decimal number 23 stands for ‘two tens and three units’, and in English is written ‘twenty-three’, in French ‘vingt-trois’ (twenty-three), and in German ‘dreiundzwanzig’ (three and twenty). Let’s investigate the algebra behind the decimal system and see how it can be used to represent numbers to any base. The expression:
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
where $a, b, c, d$ take on any value between 0 and 9 , describes any whole number between 0 and 9999 . By including
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
where $e, f, g, h$ take on any value hetween 0 and 9 , any decimal number hetween 0 and $9999.9999$ can be represented.
Indices bring the notation alive and reveal the true underlying pattern:
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots$$
Remember that any number raised to the power 0 equals 1 . By adding extra terms both left and right, any number can be accommodated.
In this example, 10 is the base, which means that the values of $a$ to $h$ range between 0 and 9,1 less than the base. Therefore, by substituting $B$ for the base we have
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
where the values of $a$ to $h$ range between 0 and $B-1$.
## 计算机代写|计算机图形学代写computer graphics代考|Binary Numbers
The binary number system has $B=2$, and $a$ to $h$ are 0 or 1 :
$$\ldots a 2^3+b 2^2+c 2^1+d 2^0+e 2^{-1}+f 2^{-2}+g 2^{-3}+h 2^{-4} \ldots$$
and the first 13 binary numbers are:
$$1_2, 10_2, 11_2, 100_2, 101_2, 110_2, 111_2, 1000_2, 1001_2, 1010_2, 1011_2, 1100_2, 1101_2 \text {. }$$
Thus $11011.11_2$ is converted to decimal as follows:
$$\begin{gathered} \left(1 \times 2^4\right)+\left(1 \times 2^3\right)+\left(0 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right)+\left(1 \times 2^{-1}\right)+\left(1 \times 2^{-2}\right) \ (1 \times 16)+(1 \times 8)+(0 \times 4)+(1 \times 2)+(1 \times 0.5)+(1 \times 0.25) \ (16+8+2)+(0.5+0.25) \ 26.75 \end{gathered}$$
The reason why computers work with binary numbers-rather than decimal-is due to the difficulty of designing electrical circuits that can store decimal numbers in a stable fashion. A switch, where the open state represents 0, and the closed state represents 1, is the simplest electrical component to emulate. No matter how often it is used, or how old it becomes, it will always behave like a switch. The main advantage of electrical circuits is that they can be switched on and off trillions of times a second, and the only disadvantage is that the encoded binary numbers and characters contain a large number of bits, and humans are not familiar with binary.
## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots$$
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
## 计算机代写|计算机图形学代写computer graphics代考|Binary Numbers
$$\ldots a 2^3+b 2^2+c 2^1+d 2^0+e 2^{-1}+f 2^{-2}+g 2^{-3}+h 2^{-4} \ldots$$
$$1_2, 10_2, 11_2, 100_2, 101_2, 110_2, 111_2, 1000_2, 1001_2, 1010_2, 1011_2, 1100_2, 1101_2 .$$
$$\left(1 \times 2^4\right)+\left(1 \times 2^3\right)+\left(0 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right)+\left(1 \times 2^{-1}\right)+\left(1 \times 2^{-2}\right)(1 \times 16)$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|COS426
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Negative Numbers
When negative numbers were first proposed, they were not accepted with open arms, as it was difficult to visualise $-5$ of something. For instance, if there are 5 donkeys in a field, and they are all stolen to make salami, the field is now empty, and there is nothing we can do in the arithmetic of donkeys to create a field of $-5$ donkeys. However, in applied mathematics, numbers have to represent all sorts of quantities such as temperature, displacement, angular rotation, speed, acceleration, etc., and we also need to incorporate ideas such as left and right, up and down, before and after, forwards and backwards, etc. Fortunately, negative numbers are perfect for representing all of the above quantities and ideas.
Consider the expression $4-x$, where $x \in \mathbb{N}^0$. When $x$ takes on certain values, we have
\begin{aligned} & 4-1=3 \ & 4-2=2 \ & 4-3=1 \ & 4-4=0 \end{aligned}
and unless we introduce negative numbers, we are unable to express the result of $4-5$. Consequently, negative numbers are visualised as shown in Fig. 2.1, where the number line shows negative numbers to the left of the natural numbers, which are positive, although the $+$ sign is omitted for clarity.
Moving from left to right, the number line provides a numerical continuum from large negative numbers, through zero, towards large positive numbers. In any calculations, we could agree that angles above the horizon are positive, and angles below the horizon, negative. Similarly, a movement forwards is positive, and a movement backwards is negative. So now we are able to write:
$$\begin{gathered} 4-5=-1 \ 4-6=-2 \ 4-7=-3 \ \text { etc., } \end{gathered}$$
without worrying about creating impossible conditions.
## 计算机代写|计算机图形学代写computer graphics代考|The Arithmetic of Positive and Negative Numbers
Once again, Brahmagupta compiled all the rules, Tables $2.1$ and $2.2$, supporting the addition, subtraction, multiplication and division of positive and negative numbers. The real fly in the ointment, being negative numbers, which cause problems for children, math teachers and occasional accidents for mathematicians. Perhaps, the one rule we all remember from our school days is that two negatives make a positive.
Another problem with negative numbers arises when we employ the square-root function. As the product of two positive or negative numbers results in a positive result, the square-root of a positive number gives rise to a positive and a negative answer. For example, $\sqrt{4}=\pm 2$. This means that the square-root function only applies to positive numbers. Nevertheless, it did not stop the invention of the imaginary object $i$, where $i^2=-1$. However, $i$ is not a number, but behaves like an operator, and is described later.
The commutative law in algebra states that when two elements are linked through some binary operation, the result is independent of the order of the elements.
The commutative law of addition is
\begin{aligned} a+b & =b+a \ \text { e.g. } 1+2 & =2+1 \end{aligned}
The commutative law of multiplication is
$$\begin{array}{r} a \times b=b \times a \ \text { e.g. } 1 \times 2=2 \times 1 . \end{array}$$
Note that subtraction is not commutative:
$$\begin{array}{r} a-b \neq b-a \ \text { e.g. } 1-2 \neq 2-1 . \end{array}$$
## 计算机代写|计算机图形学代写computer graphics代考|Negative Numbers
$$4-1=3 \quad 4-2=24-3=1 \quad 4-4=0$$
$$4-5=-14-6=-24-7=-3 \text { etc., }$$
## 计算机代写|计算机图形学代写computer graphics代考|The Arithmetic of Positive and Negative Numbers
Brahmagupta 再次编制了所有规则，表格 $2.1$ 和 $2.2$ ，支持正负数的加减乘除。真正美中不足的是负数， 这给孩子们、数学老师带来了麻烦，也给数学家们带来了偶尔的事故。也许，我们在学生时代都记得的一 条规则是，两个负面因素构成一个积极因素。
$$a+b=b+a \text { e.g. } 1+2=2+1$$
$$a \times b=b \times a \text { e.g. } 1 \times 2=2 \times 1 \text {. }$$
$$a-b \neq b-a \text { e.g. } 1-2 \neq 2-1 \text {. }$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|CS4600
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Symbols and Notation
One of the reasons why many people find mathematics inaccessible is due to its symbols and notation. Let’s look at symbols first. The English alphabet possesses a reasonable range of familiar character shapes:
$$\begin{gathered} \text { a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z } \ \text { A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z } \end{gathered}$$
which find their way into every branch of mathematics and physics, and permit us to write equations such as
$$E=m c^2$$
and
$$A=\pi r^2 .$$
It is important that when we see an equation, we are able to read it as part of the text. In the case of $E=m c^2$, this is read as ‘ $E$ equals $m, c$ squared’, where $E$ stands for energy, $m$ for mass, $c$ the speed of light, which is multiplied by itself. In the case of $A=\pi r^2$, this is read as ‘ $A$ equals pi, $r$ squared’, where $A$ stands for area, $\pi$ the ratio of a circle’s circumference to its diameter, and $r$ the circle’s radius. Greek symbols, which happen to look nice and impressive, have also found their way into many equations, and often disrupt the flow of reading, simply because we don’t know their English names. For example, the English theoretical physicist Paul Dirac (1902-1984), derived an equation for a moving electron using the symbols $\alpha_i$ and $\beta$, which are $4 \times 4$ matrices, where
$$\alpha_i \beta+\beta \alpha_i=0$$
and is read as
‘the sum of the products alpha- $i$ beta, and beta alpha- $i$, equals zero.’
Although we do not come across moving electrons in this book, we do have to be familiar with the following Greek symbols:
$$\begin{array}{llll} \alpha & \text { alpha } & \nu & \mathrm{nu} \ \beta & \text { hera } & \xi & \mathrm{xi} \end{array}$$
## 计算机代写|计算机图形学代写computer graphics代考|Sets of Numbers
A set is a collection of arbitrary objects called its elements or members. For example, each system of number belongs to a set with given a name, such as $\mathbb{N}$ for the natural numbers, $\mathbb{R}$ for real numbers, and $\mathbb{Q}$ for rational numbers. When we want to indicate that something is whole, real or rational, etc., we use the notation:
$$n \in \mathbb{N}$$
which reads ‘ $n$ is a member of $(\in)$ the set $\mathbb{N}$ ‘, i.e. $n$ is a whole number. Similarly:
$$x \in \mathbb{R}$$
stands for ‘ $x$ is a real number.’
A well-ordered set possesses a unique order, such as the natural numbers $\mathbb{N}$. Therefore, if $P$ is the well-ordered set of prime numbers and $\mathbb{N}$ is the well-ordered set of natural numbers, we can write:
\begin{aligned} & P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots} \ & \mathbb{N}={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ldots} \end{aligned}
By pairing the prime numbers in $P$ with the numbers in $\mathbb{N}$, we have:
$${{2,1},{3,2},{5,3},{7,4},{11,5},{13,6},{17,7},{19,8},{23,9}, \ldots}$$
and we can reason that 2 is the 1st prime, and 3 is the 2 nd prime, etc. However, we still have to declare what we mean by $1,2,3,4,5, \ldots$ etc., and without getting too philosophical, I like the idea of defining them as follows. The word ‘one’, represented by 1 , stands for ‘oneness’ of anything: one finger, one house, one tree, one donkey, etc. The word ‘two’, represented by 2 , is ‘one more than one’. The word ‘three’, represented by 3 , is ‘one more than two’, and so on.
## 计算机代写|计算机图形学代写computer graphics代考|Symbols and Notation
a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,
$$E=m c^2$$
$$A=\pi r^2 .$$
$$\alpha_i \beta+\beta \alpha_i=0$$
“乘积 alpha- 的总和” $i$ beta 和 beta alpha- $i$ ，等于零。
$\alpha$ alpha $\nu$ nu $\beta$ hera $\xi$ xi
## 计算机代写|计算机图形学代写computer graphics代考|Sets of Numbers
$$n \in \mathbb{N}$$
$$x \in \mathbb{R}$$
$$P=2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots \quad \mathbb{N}=1,2,3,4,5,6,7,8,9,10,11$$
$$2,1,3,2,5,3,7,4,11,5,13,6,17,7,19,8,23,9, \ldots$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|CS559
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Associative Law
The associative law in algebra states that when three or more elements are linked together through a binary operation, the result is independent of how each pair of elements is grouped.
The associative law of addition is
\begin{aligned} a+(b+c) &=(a+b)+c \ \text { e.g. } 1+(2+3) &=(1+2)+3 . \end{aligned}
The associative law of multiplication is
$$a \times(b \times c)=(a \times b) \times c$$ $$\text { e.g. } 1 \times(2 \times 3)=(1 \times 2) \times 3 \text {. }$$
However, note that subtraction is not associative:
$$\begin{array}{r} a-(b-c) \neq(a-b)-c \ \text { e.g. } 1-(2-3) \neq(1-2)-3, \end{array}$$
which may seem surprising, but at the same time confirms the need for clear axioms.
## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System
Over recent millennia, mankind has invented and discarded many systems for representing number. People have counted on their fingers and toes, used pictures (hieroglyphics), cut marks on clay tablets (cuneiform symbols), employed Greek symbols (Ionic system) and struggled with, and abandoned Roman numerals (I, V, X, L, C, D, M, etc.), until we reach today’s decimal place system, which has Hindu-Arabic and Chinese origins. And since the invention of computers we have witnessed the emergence of binary, octal and hexadecimal number systems, where 2,8 and 16 respectively, replace the 10 in our decimal system.
The decimal number 23 stands for ‘two tens and three units’, and in English is written ‘twenty-three’, in French ‘vingt-trois’ (twenty-three), and in German ‘dreiundzwanzig’ (three and twenty). Let’s investigate the algebra behind the decimal system and see how it can be used to represent numbers to any base. The expression:
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
where $a, b, c, d$ take on any value between 0 and 9, describes any whole number between 0 and 9999 . By including
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
where $e, f, g, h$ take on any value between 0 and 9 , any decimal number between 0 and $9999.9999$ can be represented.
Indices bring the notation alive and reveal the true underlying pattern:
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots \ldots$$
Remember that any number raised to the power 0 equals 1 . By adding extra terms both left annd right, any number cān bé accoommodatêd.
In this example, 10 is the base, which means that the values of $a$ to $h$ range between 0 and 9,1 less than the base. Therefore, by substituting $B$ for the base we have
$$\ldots a B^3+b B^2+c B^1+d B^0+c B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
where the values of $a$ to $h$ range between 0 and $B-1$.
## 计算机代写|计算机图形学代写computer graphics代考|Associative Law
$$a+(b+c)=(a+b)+c \text { e.g. } 1+(2+3) \quad=(1+2)+3 .$$
$$\begin{gathered} a \times(b \times c)=(a \times b) \times c \ \text { e.g. } 1 \times(2 \times 3)=(1 \times 2) \times 3 . \end{gathered}$$
$$a-(b-c) \neq(a-b)-c \text { e.g. } 1-(2-3) \neq(1-2)-3,$$
## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots \ldots$$
$$\ldots a B^3+b B^2+c B^1+d B^0+c B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|COS426
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Negative Numbers
When negative numbers were first proposed, they were not accepted with open arms, as it was difficult to visualise $-5$ of something. For instance, if there are 5 donkeys in a field, and they are all stolen to make salami, the field is now empty, and there is nothing we can do in the arithmetic of donkeys to create a field of $-5$ donkeys. However, in applied mathematics, numbers have to represent all sorts of quantities such as temperature, displacement, angular rotation, speed, acceleration, etc., and we also need to incorporate ideas such as left and right, up and down, before and after, forwards and backwards, etc. Fortunately, negative numbers are perfect for representing all of the above quantities and ideas.
Consider the expression $4-x$, where $x \in \mathbb{N}^0$. When $x$ takes on certain values, we have
\begin{aligned} &4-1=3 \ &4-2=2 \ &4-3=1 \ &4-4=0 \end{aligned}
and unless we introduce negative numbers, we are unable to express the result of $4-5$. Consequently, negative numbers are visualised as shown in Fig. 2.1, where the number line shows negative numbers to the left of the natural numbers, which are positive, although the $+$ sign is omitted for clarity.
Moving from left to right, the number line provides a numerical continuum from large negative numbers, through zero, towards large positive numbers. In any calculations, we could agree that angles above the horizon are positive, and angles below the horizon, negative. Similarly, a movement forwards is positive, and a movement backwards is negative. So now we are able to write:
\begin{aligned} 4-5 &=-1 \ 4-6 &=-2 \ 4-7 &=-3 \ \text { etc., } \end{aligned}
without worrying about creating impossible conditions.
## 计算机代写|计算机图形学代写computer graphics代考|The Arithmetic of Positive and Negative Numbers
Once again, Brahmagupta compiled all the rules, Tables $2.1$ and $2.2$, supporting the addition, subtraction, multiplication and division of positive and negative numbers. The real fly in the ointment, being negative numbers, which cause problems for children, math teachers and occasional accidents for mathematicians. Perhaps, the one rule we all remember from our school days is that two negatives make a positive.
Another problem with negative numbers arises when we employ the square-root function. As the product of two positive or negative numbers results in a positive result, the square-root of a positive number gives rise to a positive and a negative answer. For example, $\sqrt{4}=\pm 2$. This means that the square-root function only applies to positive numbers. Nevertheless, it did not stop the invention of the imaginary object $i$, where $i^2=-1$. However, $i$ is not a number, hut hehaves like an operator, and is described later.
The commutative law in algebra states that when two elements are linked through some binary operation, the result is independent of the order of the elements.
The commutative law of addition is
$$\begin{array}{r} a+b=b+a \ \text { e.g. } 1+2=2+1 . \end{array}$$
The commutative law of multiplication is
\begin{aligned} a \times b &=b \times a \ \text { e.g. } 1 \times 2 &=2 \times 1 . \end{aligned}
Note that subtraction is not commutative:
$$\begin{array}{r} a-b \neq b-a \ \text { e.g. } 1-2 \neq 2-1 . \end{array}$$
## 计算机代写|计算机图形学代写computer graphics代考|Negative Numbers
$$4-1=3 \quad 4-2=24-3=1 \quad 4-4=0$$
$$4-5=-14-6 \quad=-24-7=-3 \text { etc., }$$
## 计算机代写|计算机图形学代写computer graphics代考|The Arithmetic of Positive and Negative Numbers
Brahmagupta 再次编制了所有规则，表格 $2.1$ 和 $2.2$ ，支持正负数的加减乘除。真正美中不足的是负数，这给 孩子们、数学老师带来了麻烦，也给数学家们带来了偶尔的事故。也许，我们在学生时代都记得的一条规则 是，两个负面因素构成一个积极因素。
$$a+b=b+a \text { e.g. } 1+2=2+1 .$$
$$a \times b=b \times a \text { e.g. } 1 \times 2=2 \times 1 .$$
$$a-b \neq b-a \text { e.g. } 1-2 \neq 2-1 \text {. }$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|CS4600
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Symbols and Notation
One of the reasons why many people find mathematics inaccessible is due to its symbols and notation. Let’s look at symbols first. The English alphabet possesses a reasonable range of familiar character shapes:
$$\begin{gathered} \text { a,b,c,d,ef,f,g,h,i,i,j,k,l,m,n,o,p,q,r,r,s,t,u,v,w, } x, y, z \ \text { A,B,B,C,D,E,F,G, H,I, J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z } \end{gathered}$$
which find their way into every branch of mathematics and physics, and permit us to write equations such as
$$E=m c^2$$
and
$$A=\pi r^2 .$$
It is important that when we see an equation, we are able to read it as part of the text. In the case of $E=m c^2$, this is read as ‘ $E$ equals $m, c$ squared’, where $E$ stands for energy, $m$ for mass, $c$ the speed of light, which is multiplied by itself. In the case of $A=\pi r^2$, this is read as ‘ $A$ equals pi, $r$ squared’, where $A$ stands for area, $\pi$ the ratio of a circle’s circumference to its diameter, and $r$ the circle’s radius. Greek symbols, which happen to look nice and impressive, have also found their way into many equations, and often disrupt the flow of reading, simply because we don’t know their English names. For example, the English theoretical physicist Paul Dirac (1902-1984), derived an equation for a moving electron using the symbols $\alpha_i$ and $\beta$, which are $4 \times 4$ matrices, where
$$\alpha_i \beta+\beta \alpha_i=0$$
and is read as
‘the sum of the products alpha-i beta, and beta alpha-i, equals zero.’
Although we do not come across moving electrons in this book, we do have to be familiar with the following Greek symbols:
$\begin{array}{llll}\alpha & \text { alpha } & \nu & \mathrm{nu} \ \beta & \text { beta } & \xi & \mathrm{xi}\end{array}$
## 计算机代写|计算机图形学代写computer graphics代考|Sets of Numbers
A set is a collection of arbitrary objects called its elements or members. For example, each system of number belongs to a set with given a name, such as $\mathbb{N}$ for the natural numbers, $\mathbb{R}$ for real numbers, and $\mathbb{Q}$ for rational numbers. When we want to indicate that something is whole, real or rational, etc., we use the notation:
$$n \in \mathbb{N}$$
which reads ‘ $n$ is a member of $(E)$ the set $\mathbb{N}$ ‘, i.e. $n$ is a whole number. Similarly:
$$x \in \mathbb{R}$$
stands for ‘ $x$ is a real number.’
A well-ordered set possesses a unique order, such as the natural numbers $\mathbb{N}$. Therefore, if $P$ is the well-ordered set of prime numbers and $\mathbb{N}$ is the well-ordered set of natural numbers, we can write:
\begin{aligned} &P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots} \ &\mathbb{N}={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ldots} . \end{aligned}
By pairing the prime numbers in $P$ with the numbers in $\mathbb{N}$, we have:
$${{2,1},{3,2},{5,3},{7,4},{11,5},{13,6},{17,7},{19,8},{23,9}, \ldots}$$
and we can reason that 2 is the 1st prime, and 3 is the 2nd prime, etc. However, we still have to declare what we mean by $1,2,3,4,5, \ldots$ etc., and without getting too philosophical, I like the idea of defining them as follows. The word ‘one’, represented by 1 , stands for ‘oneness’ of anything: one finger, one house, one tree, one donkey, etc. The word ‘two’, represented by 2 , is ‘one more than one’. The word ‘three’, represented by 3, is ‘one more than two’, and so on.
We are now in a position to associate some mathematical notation with our numbers by introducing the $+$ and $=$ signs. We know that $+$ means add, but it also can stand for ‘more’. We also know that = means equal, and it can also stand for ‘is the same as’.
## 计算机代写|计算机图形学代写computer graphics代考|Symbols and Notation
a,b,c,d,ef,f,g,h,i,i,j,k,l,m,n, o,p,q,r,r ,s,t,u,v,w , x, y, z A,B,B,C,D,E,F, G, H,I, J,K,L, M, N, O,P,
$$E=m c^2$$
$$A=\pi r^2 .$$
$$\alpha_i \beta+\beta \alpha_i=0$$
“alpha-i beta 和 beta alpha-i 的乘积之和等于零。”
$\alpha$ alpha $\nu$ nu $\beta$ beta $\xi$ xi
## 计算机代写|计算机图形学代写computer graphics代考|Sets of Numbers
$$n \in \mathbb{N}$$
$$x \in \mathbb{R}$$
$$P=2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots \quad \mathbb{N}=1,2,3,4,5,6,7,8,9,10,11,12,13,$$
$$2,1,3,2,5,3,7,4,11,5,13,6,17,7,19,8,23,9, \ldots$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|CS480
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System
Over recent millennia, mankind has invented and discarded many systems for representing number. People have counted on their fingers and toes, used pictures (hieroglyphics), cut marks on clay tablets (cuneiform symbols), employed Greek symbols (Ionic system) and struggled with, and abandoned Roman numerals (I, V, X, L, C, D, M, etc.), until we reach today’s decimal place system, which has Hindu-Arabic and Chinese origins. And since the invention of computers we have witnessed the emergence of binary, octal and hexadecimal number systems, where 2,8 and 16 respectively, replace the 10 in our decimal system.
The decimal number 23 stands for ‘two tens and three units’, and in English is written ‘twenty-three’, in French ‘vingt-trois’ (twenty-three), and in German ‘dreiundzwanzig’ (three and twenty). Let’s investigate the algebra behind the decimal system and see how it can be used to represent numbers to any base. The expression:
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
where $a, b, c, d$ take on any value between 0 and 9 , describes any whole number between 0 and 9999 . By including
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
where $e, f, g, h$ take on any value between 0 and 9 , any decimal number between 0 and $9999.9999$ can be represented.
Indices bring the notation alive and reveal the true underlying pattern:
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots$$
Remember that any number raised to the power 0 equals 1 . By adding extra terms both left and right, any number can be accommodated.
In this example, 10 is the base, which means that the values of $a$ to $h$ range between 0 and 9,1 less than the base. Therefore, by substituting $B$ for the base we have
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
where the values of $a$ to $h$ range between 0 and $B-1$.
## 计算机代写|计算机图形学代写computer graphics代考|Binary Numbers
The binary number system has $B=2$, and $a$ to $h$ are 0 or 1 :
$$\ldots a 2^3+b 2^2+c 2^1+d 2^0+e 2^{-1}+f 2^{-2}+g 2^{-3}+h 2^{-4} \ldots$$
and the first 13 binary numbers are:
$$1_2, 10_2, 11_2, 100_2, 101_2, 110_2, 111_2, 1000_2, 1001_2, 1010_2, 1011_2, 1100_2, 1101_2 .$$
Thus $11011.11_2$ is converted to decimal as follows:
$$\begin{gathered} \left(1 \times 2^4\right)+\left(1 \times 2^3\right)+\left(0 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right)+\left(1 \times 2^{-1}\right)+\left(1 \times 2^{-2}\right) \ (1 \times 16)+(1 \times 8)+(0 \times 4)+(1 \times 2)+(1 \times 0.5)+(1 \times 0.25) \ (16+8+2)+(0.5+0.25) \ 26.75 . \end{gathered}$$
The reason why computers work with binary numbers-rather than decimal-is due to the difficulty of designing electrical circuits that can store decimal numbers in a stable fashion. A switch, where the open state represents 0, and the closed state represents 1, is the simplest electrical component to emulate. No matter how often it is used, or how old it becomes, it will always behave like a switch. The main advantage of electrical circuits is that they can be switched on and off trillions of times a second, and the only disadvantage is that the encoded binary numbers and characters contain a large number of bits, and humans are not familiar with binary.
## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots$$
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
## 计算机代写|计算机图形学代写computer graphics代考|Binary Numbers
$$\ldots a 2^3+b 2^2+c 2^1+d 2^0+e 2^{-1}+f 2^{-2}+g 2^{-3}+h 2^{-4} \ldots$$
$$1_2, 10_2, 11_2, 100_2, 101_2, 110_2, 111_2, 1000_2, 1001_2, 1010_2, 1011_2, 1100_2, 1101_2 .$$
$$\left(1 \times 2^4\right)+\left(1 \times 2^3\right)+\left(0 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right)+\left(1 \times 2^{-1}\right)+\left(1 \times 2^{-2}\right)(1 \times 16)+(1 \times 8)$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|CSCl420
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Negative Numbers
When negative numbers were first proposed, they were not accepted with open arms, as it was difficult to visualise $-5$ of something. For instance, if there are 5 donkeys in a field, and they are all stolen to make salami, the field is now empty, and there is nothing we can do in the arithmetic of donkeys to create a field of $-5$ donkeys. However, in applied mathematics, numbers have to represent all sorts of quantities such as temperature, displacement, angular rotation, speed, acceleration, etc., and we also need to incorporate ideas such as left and right, up and down, before and after, forwards and backwards, etc. Fortunately, negative numbers are perfect for representing all of the above quantities and ideas.
Consider the expression $4-x$, where $x \in \mathbb{N}^0$. When $x$ takes on certain values, we have
\begin{aligned} &4-1=3 \ &4-2=2 \ &4-3=1 \ &4-4=0 \end{aligned}
and unless we introduce negative numbers, we are unable to express the result of $4-5$. Consequently, negative numbers are visualised as shown in Fig. 2.1, where the number line shows negative numbers to the left of the natural numbers, which are positive, although the $+$ sign is omitted for clarity.
Moving from left to right, the number line provides a numerical continuum from large negative numbers, through zero, towards large positive numbers. In any calculations, we could agree that angles above the horizon are positive, and angles below the horizon, negative. Similarly, a movement forwards is positive, and a movement backwards is negative. So now we are able to write:
$$\begin{gathered} 4-5=-1 \ 4-6=-2 \ 4-7=-3 \ \text { etc., } \end{gathered}$$
without worrying about creating impossible conditions.
## 计算机代写|计算机图形学代写computer graphics代考|The Arithmetic of Positive and Negative Numbers
Once again, Brahmagupta compiled all the rules, Tables $2.1$ and $2.2$, supporting the addition, subtraction, multiplication and division of positive and negative numbers. The real fly in the ointment, being negative numbers, which cause problems for children, math teachers and occasional accidents for mathematicians. Perhaps, the one rule we all remember from our school days is that two negatives make a positive.
Another problem with negative numbers arises when we employ the square-root function. As the product of two positive or negative numbers results in a positive result, the square-root of a positive number gives rise to a positive and a negative answer. For example, $\sqrt{4}=\pm 2$. This means that the square-root function only applies to positive numbers. Nevertheless, it did not stop the invention of the imaginary object $i$, where $i^2=-1$. However, $i$ is not a number, but behaves like an operator, and is described later.
The commutative law in algebra states that when two elements are linked through some binary operation, the result is independent of the order of the elements.
The commutative law of addition is
$$\begin{array}{r} a+b=b+a \ \text { e.g. } 1+2=2+1 . \end{array}$$
The commutative law of multiplication is
$$\begin{array}{r} a \times b=b \times a \ \text { e.g. } 1 \times 2=2 \times 1 . \end{array}$$
Note that subtraction is not commutative:
$$\begin{array}{r} a-b \neq b-a \ \text { e.g. } 1-2 \neq 2-1 \end{array}$$
## 计算机代写|计算机图形学代写computer graphics代考|Negative Numbers
$$4-1=3 \quad 4-2=24-3=1 \quad 4-4=0$$
$$4-5=-14-6=-24-7=-3 \text { etc., }$$
## 计算机代写|计算机图形学代写computer graphics代考|The Arithmetic of Positive and Negative Numbers
Brahmagupta 再次编制了所有规则，表格 $2.1$ 和 $2.2$ ，支持正负数的加减乘除。真正美中不足的是负数，这给孩 子们、数学老师带来了麻烦，也给数学家们带来了偶尔的事故。也许，我们在学生时代都记得的一条规则是，两 个负面因素构成一个积极因素。
$$a+b=b+a \text { e.g. } 1+2=2+1 .$$
$$a \times b=b \times a \text { e.g. } 1 \times 2=2 \times 1 \text {. }$$
$$a-b \neq b-a \text { e.g. } 1-2 \neq 2-1$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## 计算机代写|计算机图形学代写computer graphics代考|CS559
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 计算机代写|计算机图形学代写computer graphics代考|Symbols and Notation
One of the reasons why many people find mathematics inaccessible is due to its symbols and notation. Let’s look at symbols first. The English alphabet possesses a reasonable range of familiar character shapes:
$$\begin{gathered} \text { a,b,cc, d,e,f,g,h,i,j,k,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z } \ \text { A,B,C,D,E,F,G,H,I,J,K,L, M, N,O,P,Q,R,S,T,U,V,W,X,Y,Z } \end{gathered}$$
which find their way into every branch of mathematics and physics, and permit us to write equations such as
$$E=m c^2$$
and
$$A=\pi r^2 .$$
It is important that when we see an equation, we are able to read it as part of the text. In the case of $E=m c^2$, this is read as ‘ $E$ equals $m, c$ squared’, where $E$ stands for energy, $m$ for mass, $c$ the speed of light, which is multiplied by itself. In the case of $A=\pi r^2$, this is read as ‘ $A$ equals pi, $r$ squared’, where $A$ stands for area, $\pi$ the ratio of a circle’s circumference to its diameter, and $r$ the circle’s radius. Greek symbols, which happen to look nice and impressive, have also found their way into many equations, and often disrupt the flow of reading, simply because we don’t know their English names. For example, the English theoretical physicist Paul Dirac (1902-1984), derived an equation for a moving electron using the symbols $\alpha_i$ and $\beta$, which are $4 \times 4$ matrices, where
$$\alpha_i \beta+\beta \alpha_i=0$$
and is read as
‘the sum of the products alpha-i beta, and beta alpha- $i$, equals zero.’
Although we do not come across moving electrons in this book, we do have to be familiar with the following Greek symbols:
$\alpha$ alpha $\quad \nu \quad$ nu
$\beta$ beta $\quad \xi \quad$ xi
## 计算机代写|计算机图形学代写computer graphics代考|Sets of Numbers
A set is a collection of arbitrary objects called its elements or members. For example, each system of number belongs to a set with given a name, such as $\mathbb{N}$ for the natural numbers, $\mathbb{R}$ for real numbers, and $\mathbb{Q}$ for rational numbers. When we want to indicate that something is whole, real or rational, etc., we use the notation:
$$n \in \mathbb{N}$$
which reads ‘ $n$ is a member of $(\epsilon)$ the set $\mathbb{N}$ ‘, i.e. $n$ is a whole number. Similarly:
$$x \in \mathbb{R}$$
stands for ‘ $x$ is a real number.’
A well-ordered set possesses a unique order, such as the natural numbers $\mathbb{N}$. Therefore, if $P$ is the well-ordered set of prime numbers and $\mathbb{N}$ is the well-ordered set of natural numbers, we can write:
\begin{aligned} &P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots} \ &\mathbb{N}={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ldots} \end{aligned}
By pairing the prime numbers in $P$ with the numbers in $\mathbb{N}$, we have:
$${{2,1},{3,2},{5,3},{7,4},{11,5},{13,6},{17,7},{19,8},{23,9}, \ldots}$$
and we can reason that 2 is the 1st prime, and 3 is the 2 nd prime, etc. However, we still have to declare what we mean by $1,2,3,4,5, \ldots$ etc., and without getting too philosophical, I like the idea of defining them as follows. The word ‘one’, represented by 1, stands for ‘oneness’ of anything: one finger, one house, one tree, one donkey, etc. The word ‘two’, represented by 2 , is ‘one more than one’. The word ‘three’, represented by 3 , is ‘one more than two’, and so on.
## 计算机代写|计算机图形学代写computer graphics代考|Symbols and Notation
a,b,cc, d,e,f,g,h,i,j,k,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z A,B,C,D, E,F,G,H,I,J,K,L, M, N, O,P,Q,R
$$E=m c^2$$
$$A=\pi r^2 .$$
$$\alpha_i \beta+\beta \alpha_i=0$$
“产品 alpha-i beta 和 beta alpha- 的总和” $i$ ，等于零。
$\alpha \alpha \quad \nu \quad$ 不是
$\beta$ 贝塔 $\xi \mathrm{xi}$
## 计算机代写|计算机图形学代写computer graphics代考|Sets of Numbers
$$n \in \mathbb{N}$$
$$x \in \mathbb{R}$$
$$P=2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots \quad \mathbb{N}=1,2,3,4,5,6,7,8,9,10,11,12,$$
$$2,1,3,2,5,3,7,4,11,5,13,6,17,7,19,8,23,9, \ldots$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
## CS代写|计算机图形学作业代写computer graphics代考|CS480
statistics-lab™ 为您的留学生涯保驾护航 在代写计算机图形学computer graphics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算机图形学computer graphics代写方面经验极为丰富，各种代写计算机图形学computer graphics相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## CS代写|计算机图形学作业代写computer graphics代考|The Base of a Number System
Over recent millennia, mankind has invented and discarded many systems for representing number. People have counted on their fingers and toes, used pictures (hieroglyphics), cut marks on clay tablets (cuneiform symbols), employed Greek symbols (Ionic system) and struggled with, and abandoned Roman numerals (I, V. X, L, C, D, M, etc.), until we reach today’s decimal place system, which has I Iindu-Arabic and Chinese origins. And since the invention of computers we have witnessed the emergence of binary, octal and hexadecimal number systems, where 2,8 and 16 respectively, replace the 10 in our decimal system.
The decimal number 23 stands for ‘two tens and three units’, and in English is written ‘twenty-three’, in French ‘vingt-trois’ (twenty-three), and in German ‘dreiundzwanzig’ (three and twenty). Let’s investigate the algebra behind the decimal system and see how it can be used to represent numbers to any base. The expression:
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
where $a, b, c, d$ take on any value between 0 and 9 , describes any whole number between 0 and 9999 . By including
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
where $e, f, g, h$ take on any value between 0 and 9 , any decimal number between 0 and $9999.9999$ can be represented.
Indices bring the notation alive and reveal the true underlying pattern:
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots \ldots$$
Remember that any number raised to the power 0 equals 1 . By adding extra terms both left and right, any number can be accommodated.
In this example, 10 is the base, which means that the values of $a$ to $h$ range between 0 and 9,1 less than the base. Therefore, by substituting $B$ for the base we have
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
where the values of $a$ to $h$ range between 0 and $B-1$.
## CS代写|计算机图形学作业代写computer graphics代考|Octal Numbers
The octal number system has $B=8$, and $a$ to $h$ range between 0 and 7 :
$$\ldots a 8^3+b 8^2+c 8^1+d 8^0+e 8^{-1}+f 8^{-2}+g 8^{-3}+h 8^{-4} \ldots$$
and the first 17 octal numbers are:
$$1_8, 2_8, 3_8, 4_8, 5_8, 6_8, 7_8, 10_8, 11_8, 12_8, 13_8, 14_8, 15_8, 16_8, 17_8, 20_8, 21_8$$
The subscript 8 reminds us that although we may continue to use the words ‘twentyone’, it is an octal number, and not a decimal. But what is $14_8$ in decimal? Well, it stands for:
$$1 \times 8^1+4 \times 8^0=12$$
Thus $356.4_8$ is converted to decimal as follows:
$$\begin{gathered} \left(3 \times 8^2\right)+\left(5 \times 8^1\right)+\left(6 \times 8^0\right)+\left(4 \times 8^{-1}\right) \ (3 \times 64)+(5 \times 8)+(6 \times 1)+(4 \times 0.125) \ (192+40+6)+(0.5) \ 238.5 \end{gathered}$$
Counting in octal appears difficult, simply because we have never been exposed to it, like the decimal system. If we had evolved with 8 fingers, instead of 10 , we would be counting in octal!
## CS代写|计算机图形学作业代写computer graphics代考|The Base of a Number System
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots \ldots$$
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
## CS代写|计算机图形学作业代写computer graphics代考|Octal Numbers
$$\ldots a 8^3+b 8^2+c 8^1+d 8^0+e 8^{-1}+f 8^{-2}+g 8^{-3}+h 8^{-4} \ldots$$
$$1_8, 2_8, 3_8, 4_8, 5_8, 68,78,10_8, 11_8, 12_8, 13_8, 14_8, 15_8, 16_8, 17_8, 20_8, 21_8$$
$$1 \times 8^1+4 \times 8^0=12$$
$$\left(3 \times 8^2\right)+\left(5 \times 8^1\right)+\left(6 \times 8^0\right)+\left(4 \times 8^{-1}\right)(3 \times 64)+(5 \times 8)+(6 \times 1)+(4 \times 0.125)(192+40$$
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
|
# Iterating through comma-separated arguments
I've looked all over and can't seem to find a succinct answer to this question. Is it possible (and if so, how) to create a command that will iterate through its arguments' of comma-separated values and act upon them?
Example mostly stolen from "For loop" in newcommand:
\newcommand{\pdfappendix}[1]{
for \image in #1
{
\includegraphics[scale=0.6]{\image.pdf}
}
}
The goal here is to create a command that can print a file menu structure (or some arbitrary path) like so:
\ppath{Command,TeXing Options,Generate PDF (C-c C-t C-p)}
potentially with an optional argument for a delimiter (defaulting to \to or something)
which would produce
Command -> TeXing Options -> Generate PDF (C-c C-t C-p)
In the words of holy ed, ?
-
There are plenty of questions for lists see tex.stackexchange.com/a/19761/963 and maybe you can post a more specific question – Yiannis Lazarides Dec 17 '12 at 21:03
Can you explain in how far the answers in the questions you linked don't fulfil your needs? – Stephan Lehmke Dec 17 '12 at 21:13
For a more specific question, see Understanding a \@for loop. – Alan Munn Dec 17 '12 at 21:22
It would also be beneficial to peruse the posts tagged with comma-separated-list. – Werner Dec 17 '12 at 21:44
Actually did that. I'll go through them again - I skipped a few where I didn't foresee the general answer. – Sean Allred Dec 17 '12 at 22:29
etoolbox's list processing capabilities are straight forward:
\documentclass{article}
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\newcommand{\ppath}[2][$\;\triangleright\;$]{%
\def\nextitem{\def\nextitem{#1}}% Separator
\renewcommand*{\do}[1]{\nextitem\textsf{##1}}% How to process each item
\docsvlist{#2}% Process list
}
\begin{document}
A decent file path is \ppath{File,New,Document}.
\end{document}
The separator \nextitem is defined to do nothing during its first use. \do defines how each item is processed, while \docsvlist processes a comma-separated list. See Cunning (La)TeX tricks for a short discussion on the use of \nextitem.
-
Very clever fix for the first item bit. – Sean Allred Dec 17 '12 at 23:35
Found an answer in another question's answer. With @Werner's help (specifically the deferred \def trick), the pure TeX solution works without the need for extra packages. What follows is a minimal working example of what I was looking for.
\documentclass{article}
\makeatletter
\newcommand{\ppath}[2][ $\triangleright$ ]{%
\def\nextitem{\def\nextitem{#1}}%
\@for \el:=#2\do{\nextitem\el}%
}
\makeatother
\begin{document}
A decent file path is \ppath{File,New,Why}. I said, Why.
\end{document}
Output:
(Thanks @Peter, @jon.)
-
You need to use \@for \el:=#2\do{\nextitem\el}%. But this really should have been a separate question. – Peter Grill Dec 18 '12 at 22:26
It looks like you forgot a % at the end of line 6: \@for ... \el}%. – jon Dec 18 '12 at 22:27
I should have made it far more clear it was rhetorical (but I was actually about to ask a separate question, funnily enough). That clears up on side of it, but not the other. I found that (in the original) the macro was padding the output with a single space. It makes sense that your fix takes care of the one on the right and not on the left. I'm wondering now if the \def is giving us an intermittent space for some reason. – Sean Allred Dec 18 '12 at 22:30
Found it, and I'm dumb. Missed a %` after the first line in my typeup. Edited. – Sean Allred Dec 18 '12 at 22:31
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Tech Problem Aggregator
# How to use an HTML page as the desktop wallpaper?
Q: How to use an HTML page as the desktop wallpaper?
You could definitely do it in Vista. However, in windows 7 it no longer gives me the option to select anything other than a picture file? How would I use a customised html page as my desktop wallpaper?
Thanks
A: How to use an HTML page as the desktop wallpaper?
The option was not in Windows Vista....unless I missed something?
3 more replies
Seems a step back in function from Vista to Win 7. My Vista PC had an HTML page serving as my desktop....it has some embedded flash and other goodies. How do I get Win 7 to allow me to select an HTML page for my desktop when all it appears to allow is photos? Win Search has not supplied any userful ideas. I hope the community has a solution.
A:How to use HTML page as desktop wallpaper
I just had a quick Google and i couldn't find much to help
Maybe try this gadget. It's not exactly Active Desktop but it's resizeable (the taskbar is 40px btw)
1 more replies
I'm currently designing a table based website in Dreamweaver, but am having a problem importing a drop down menu in the form of html. It gives me the error "The selected file is not the correct format. Please select a file which was exported from Fireworks".
The problem with this is that all the export options have been set correctly, and is being exported as Dreamweaver HTML, and obviously being exported from Fireworks - so what's the problem? Does anyone have an answer to my problem?
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There is currently an html page covering my wall paper. It slowly changes color. Any help would be great! He is my HJT log:
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\Program Files\Common Files\Symantec Shared\ccSetMgr.exe
C:\Program Files\Common Files\Symantec Shared\SNDSrvc.exe
C:\Program Files\Common Files\Symantec Shared\ccEvtMgr.exe
C:\WINDOWS\system32\spoolsv.exe
C:\WINDOWS\ieig.exe
C:\Program Files\Common Files\Microsoft Shared\VS7Debug\mdm.exe
C:\Program Files\Norton AntiVirus\navapsvc.exe
C:\Program Files\Norton AntiVirus\IWP\NPFMntor.exe
C:\WINDOWS\system32\nvsvc32.exe
C:\WINDOWS\System32\svchost.exe
C:\Program Files\Common Files\Symantec Shared\CCPD-LC\symlcsvc.exe
C:\Program Files\Common Files\Stardock\SDMCP.exe
C:\WINDOWS\Explorer.EXE
C:\Program Files\Common Files\Symantec Shared\ccApp.exe
C:\WINDOWS\system32\sdkzn.exe
C:\Program Files\MSN Messenger\msnmsgr.exe
C:\Program Files\Mozilla Firefox\firefox.exe
C:\Program Files\Messenger\msmsgs.exe
C:\Documents and Settings\Andrew Phippen\Desktop\Utilities\HijackThis.exe
C:\Program Files\Messenger\msmsgs.exe
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Bar = res://C:\WINDOWS\system32\hgylo.dll/sp.html#77035%
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Page = res://C:\WINDOWS\system32\hgylo.dll/sp.html#77035%
R1 - HKCU\Softw... Read more
A:HTML Wallpaper!
10 more replies
Well I saw an .Swf that I thought would be funny to put as my friends wallpaper while he went away. I put it in an HTML document and got everything working correctly....until I turned on my speakers and reilized it had sound. Is there any way I can turn it off? Any way as long as its gone :D
A:Turn html wallpaper sounds off?
Or can anyone point me in the direction of a free flask decompiler?
2 more replies
Is this posible?
I love the dynamic sign-in backgrounds, and i would love for Windows to change my desktop background to the same images
A:desktop wallpaper the same as the sign-in wallpaper
Originally Posted by Elmotrix
Is this posible?
I love the dynamic sign-in backgrounds, and i would love for Windows to change my desktop background to the same images
Hi Elmotrix, welcome to tenforums.com!
There may be various ways to accomplish this.
You could scour the web for some of the latest 'Spotlight' images, then put them in a 'Slideshow' folder.
You may also be able to fetch them on your own machine.
You need to show 'Hidden files, folders and drives', then navigate to C:\Users\{your name}\AppData\Local\Packages\Microsoft.Windows.ContentDeliveryManager_cw5n1h2txyewy\LocalState\Asset s
then copy all the items to another folder and begin renaming them: 1.jpg, 2.jpg, etc.
Here are some of the latest:
1 more replies
I am posting my Hijack this log below.
I have used Hijack this and attempted to fix the first references to http://213.159.117.132/index.php. Each time I fix it, it reoccurs. This directs me to a Cool Web Search site and I can't change it.
Periodically, my IE launches two pages, windows\dl.html and one that says connector object.
My system is extremely slow.
I have run Adware 6.0, Spybot Search and Destroy, CWSshredder, NoAdware and my Symantic Antivirus. Nothing is found.
Help me......you're my only hope.
Thanks.
Logfile of HijackThis v1.97.7
Scan saved at 3:25:00 PM, on 6/1/2004
Platform: Windows XP SP1 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\spoolsv.exe
C:\PROGRA~1\SYMANT~1\SYMANT~1\DefWatch.exe
C:\WINDOWS\system32\HPConfig.exe
C:\Program Files\HPQ\Notebook Utilities\HPWirelessMgr.exe
C:\PROGRA~1\MICROS~4\MSSQL\binn\sqlservr.exe
C:\PROGRA~1\SYMANT~1\SYMANT~1\Rtvscan.exe
C:\WINDOWS\System32\svchost.exe
C:\PROGRA~1\MICROS~4\MSSQL\binn\sqlagent.exe
C:\WINDOWS\Explorer.EXE
C:\Program Files\Synaptics\SynTP\SynTPLpr.exe
C:\Program Files\Synaptics\SynTP\SynTPEnh.exe
C:\Program Files\Roxio\Easy CD Creator 5\DirectCD\DirectCD.exe
C:\WINDOWS\System32\carpserv.exe
C:\PROGRA~1\SYMANT~1\SYMANT~1\vptray.exe
A:Hijacked default page/dl.html page popup
CoolWWWSearch.SmartKiller (v1-v2) MiniRemoval
1 more replies
Hi there,
So a while back when i was running XP on this rig, i had a active desktop wallpaper setup that would display animated local radar images. Basically the same radar you would see if you put in your zipcode in the weather.com or accuweather.com radar section.
So now with Win 7, i cant get it to work for the life of me....and no, sorry, the wimpy sidebar gadgets just dont cut it.
Basically what it was, and am looking to accomplish, is have a live animated radar as my wallpaper / background.
Preferably not the whole screen, just alike a 12X8 square or something relative.
Picture attached of a mock setup of what im talking about.
Im pretty sure i originally was using this as my source for the animated wallpaper:
My favorite radar site
Any ideas all?
A:Animated Desktop Wallpaper? Active desktop radar images.
hmmm, bump
2 more replies
The computer crashed hard. I was running an application call Stylizer, a visual css editor. One of the tasks it allows you to do is switch between several browsers to see how a web page may render differently. When I clicked on a form select element while in IE 7.0, it crashed. This is a repeatable bug that I have encountered before(don't click forms select again ya dummy). Anyways, all the applications that were running died and the computer froze requiring a hard reboot. When the computer returned, the desktop wallpaper image was zoomed. Obviously something became corrupted with the crash. I can't find a solution how to unzoom the wallpaper image. I tried a number of display and accessibility options without any luck(screen resolution, DPI, large icons, centered, stretched, etc.). I did notice if I changed from my usual "hide desktop icons", to "show desktop icons", the wallpaper image is then displayed correctly. I can also kill the explorer.exe process and the wallpaper will show correctly. If I run File>New Task(Run...)>explorer.exe again, it reverts back to the zoomed wallpaper. I tried a restore point from the day before. Wiped display drivers and installed the latest. Switched the dvi cable to a different output on the card. I uninstalled Stylizer, all it's files and registy entries. I've run sfc /scannow. I also tried rolling back to SP2 and back again to SP3 to re-install explorer.exe. Still zoomed. I've run out of ... Read more
More replies
Mod edit: Moved from the XP forumHi Guys,I have been hammered by spyware recently....the desktop.html file is stuck as my background, and i get windrv.exe running over and over...here is my hajack log...can someone please help me out?...Thanks!MattLogfile of HijackThis v1.99.1Scan saved at 10:10:45 PM, on 6/5/2006Platform: Windows XP SP2 (WinNT 5.01.2600)MSIE: Internet Explorer v6.00 SP2 (6.00.2900.2180)Running processes:C:\WINDOWS\System32\smss.exeC:\WINDOWS\system32\winlogon.exeC:\WINDOWS\system32\services.exeC:\WINDOWS\system32\lsass.exeC:\WINDOWS\system32\svchost.exeC:\WINDOWS\System32\svchost.exeC:\Program Files\Internet Explorer\iexplore.exeC:\WINDOWS\system32\winlogon.exeC:\WINDOWS\Explorer.EXEC:\Program Files\Internet Explorer\iexplore.exeC:\WINDOWS\system32\ctfmon.exeC:\Documents and Settings\Matt\My Documents\hijackthis\HijackThis.exeF2 - REG:system.ini: UserInit=userinit.exeO1 - Hosts: localhost 127.0.0.1O2 - BHO: Adobe PDF Reader Link Helper - {06849E9F-C8D7-4D59-B87D-784B7D6BE0B3} - C:\Program Files\Adobe\Acrobat 7.0\ActiveX\AcroIEHelper.dllO2 - BHO: PCTools Site Guard - {5C8B2A36-3DB1-42A4-A3CB-D426709BBFEB} - C:\PROGRA~1\SPYWAR~1\tools\iesdsg.dllO2 - BHO: SSVHelper Class - {761497BB-D6F0-462C-B6EB-D4DAF1D92D43} - C:\Program F... Read more
A:Desktop.html File Stuck On My Desktop And Windrv.exe Running
Hi Vogz and Welcome to the Bleeping Computer!Please download ewido security suite it is a free version of the program.Install ewido security suiteWhen installing, under "Additional Options" uncheck..Install background guardInstall scan via context menuLaunch ewido, there should be an icon on your desktop, double-click it.The program will now open to the main screen.When you run ewido for the first time, you may get a warning "Database could not be found!". Click OK. We will fix this in a moment.
You will need to update ewido to the latest definition files.On the left hand side of the main screen click update.Then click on Start Update.The update will start and a progress bar will show the updates being installed.
<a href="http://service1.symantec.com/SUPPORT/tsgeninfo.nsf/docid/2001052409420406?OpenDocument&src=se... Read more
10 more replies
Hello,My Avira keeps finding daily everytime I scan it.....HTML/Exploit.Mhtml HTML and HTML/Infected.WebPage.Gen HTML script viruses. This has been going on a long time. The only thing I have noticed is high cpu 90-100% in task manager all the time, which does'nt seem to impact the speed of the computer. Occasionally, I pick up things in Malwarebytes and Spybot if I neglect to run a scan on Avira for a few days. I've also scanned Adaware and Avast but nothing shows up on them. This has been driving me nuts and any help would be greatly appreciated!!Logfile of Trend Micro HijackThis v2.0.2Scan saved at 2:13:12 AM, on 8/8/2009Platform: Windows XP SP3 (WinNT 5.01.2600)MSIE: Internet Explorer v7.00 (7.00.5730.0013)Boot mode: NormalRunning processes:C:\WINDOWS\System32\smss.exeC:\WINDOWS\system32\winlogon.exeC:\WINDOWS\system32\services.exeC:\WINDOWS\system32\lsass.exeC:\WINDOWS\system32\svchost.exeC:\WINDOWS\System32\svchost.exeC:\WINDOWS\Explorer.EXEC:\PROGRA~1\A4Tech\Keyboard\Ikeymain.exeC:\Program Files\ASUS\Probe\AsusProb.exeC:\Program Files\Spybot - Search & Destroy\TeaTimer.exeC:\WINDOWS\system32\ctfmon.exeC:\Program Files\Google\GoogleToolbarNotifier\GoogleToolbarNotifier.exeC:\PROGRA~1\KEYWAL~1\KWallet.exeC:\WINDOWS\system32\spoolsv.exeC:\... Read more
A:HTML/Exploit.Mhtml HTML & HTML/Infected.WebPage.Gen HTML
14 more replies
Hi,
I am a firefighter and on our computer in our radio room we keep the wallpaper as Doppler Radar. We are currently using a Widget to do this. But I want to use a GIF Image that Accuweather.com uses. It works and everything when I set it as a wallpaper but it never refreshes on its own.
Is there a way to make the Web Page Wallpaper, Refresh automatically?
A:Web Page Wallpaper Refresh
GIF images will not cycle through the frames when used as wallpaper. This has been this way since day one on Windows 95.
3 more replies
Does anyone know how to make a web page a wallpaper, just like in the days of Windows XP? There must be a way to do this. Thanks in advance,
Rockworthy
A:I want to make a web page my wallpaper
Hi rockworthy, if it is just the picture you want, take a picture with the snipping tool and save it as a wallpaper,Is this what you mean?
7 more replies
Hi to all,
I'm trying to build my first page, its getting there slowly !
My question \ problem is this...... as I look at my page evrything is set out ok, when I then open my favorites the page " bunches " up, it squashes into the space left disturbing all photos and text etc.
How do I solve this, please
ps using 1st page 2000, html document, win xp pro
A:help with html web page
If you are using tables set the widths of the table data and the entire table width to percentages opposed to fixed pixels.
3 more replies
More replies
Hello I am currently running Serv u ftp server. Is there a way to have it so when someone creates a user name and password and submits it it creates there selected username and password on my ftp. If thsi is not possible is there a way so when they create a user name it creates a folder on my server. Yes i have it so that writing to my server is enabled but i have no clue how. Last question how do i add a passworded realm to my site? I have a mysql server as well
Thanks
Tony
[email protected]
First off there are php/mysql scripts that you can buy that will create folders for people that also gives them an ftp account.
You'll have to look around at http://www.hotscripts.com and to the best of my knowledge most of them cost money.
Second you could use htaccess(assuming you're using apache) to protect your folder.
Heres one little tutorial I quickly grabbed -> http://www.tomsnewbiebooster.com/password-protecting-a-folder.html
You can go to google.com and search for more just type htaccess password protecting folder.
1 more replies
Hello everyone,
I'm in a bit of a bind, I need to create a couple 1000 HTML pages in a short amount of time. The information, with the exception of about 10 items, are static. I tried my hand at a Perl script that would query me for the 10 items and then create the HTML file, but that blew up in my face. Does anyone know of a Perl script or program out there that would meet my needs?
Jeremy D.
A:HTML Page Creator
Let me get this straight.
You have created a website - it has 1000 pages. It has all the information static - bar 10 pages. And you want to include these 10 pages into different pages?
If that is the case, then using includes could help you. If I've got the wrong end of the stick - just tell me!
1 more replies
I recently began making simple webpages using araneae, and can even attach swf files to them to my delight by using mix-fx. Next I want to attach .wav or .mp3 files as background music. I was directed to dreeamweaver but apparently my pc doesn't support it (400mhz 64 meg ram.) Can someone just wwrite me a simple few lines of html code to attach "example.wav" or "example.mp3" to plaay when my page loads so I can copy it to my clipboard? TYVM!
A:How 2 attach wav/mp3 to html page?
6 more replies
A very strange thing just started happening to my web site. When I viewed my page from the ISP server some of my images were gone - no red x, no nothing, source viewed in Notepad shows the IMG tag is simply not there.
Now this is only happening on certain images and not all img tags on a page disappear. I can't seem to find any similarity between the ones that stay and those that go.
When I view the HTML page in my browser locally all of the images are there. When I view the page from the ISP server some of the img tags are gone (IE 6 or Netscape 7).
I ftp the local page to the ISP server, view the page in my browser and some of the img tags are gone. I ftp the page on the server back to my machine and the tags are all there.
I tried replacing all of the images on the ISP server with my local images (I have an exact copy of the web site on my local machine) in a desperate attempt to figure out why this is happening. It made no difference.
I have never seen this happen before and it's giving me fits. I've seen the red x and I know what it looks like when you're pointing at a file with an incorrect name or address and this is NOT that problem. The tag is just not there in a View Source on the page. This is very weird. If anyone can help me figure out what may be causing this I would be very grateful.
Thanks!
Coleen
A:IMG tag disappearing in HTML page
11 more replies
I need some code for when people visit my web site and fill out a form. I need each form to have a different number each time they visit. Thanks !!
A:HTML needed for my Web Page
10 more replies
I am getting ads and links on every page I visit within my browser. I have ran AVG, MalwareBytes and SuperAntiSpyware multiple times, in and out of Safe Mode and have gotten nothing out of it that fixes this issue. This issue is in every browser I tried, IE, Chrome and Firefox, I reinstalled my browser and the issue still persists.
info:
Tech Support Guy System Info Utility version 1.0.0.2
OS Version: Microsoft Windows 7 Ultimate, Service Pack 1, 64 bit
Processor: AMD FX(tm)-8150 Eight-Core Processor, AMD64 Family 21 Model 1 Stepping 2
Processor Count: 8
RAM: 32695 Mb
Graphics Card: AMD Radeon HD 7800 Series, -2048 Mb
Hard Drives: C: Total - 109601 MB, Free - 6935 MB; D: Total - 1907726 MB, Free - 716110 MB; E: Total - 953866 MB, Free - 205538 MB;
Motherboard: ASUSTeK COMPUTER INC., SABERTOOTH 990FX R2.0
Antivirus: AVG AntiVirus Free Edition 2015, Updated and Enabled
A:Ads and HTML links on every page.
6 more replies
I have an HTML page which is a newsletter. I want to be able to add it to an email message so I can email it to people. I want it to be in the body of the email, not sent as an attachment.
There is a .htm page, several images, and a .css page. I need all of these to be embedded for the page to work correctly. I can put the styles from the .css file into the html page, but I still need to know how to embed the images.
I tried creating stationary, but it didn't put the images in the email.
I know it is possible to do this. Can someone give me some pointers as to how to get an HTML page along with several images into an email message.
I am currently using Outlook 2003.
Thanks!
A:HTML Page into Email
14 more replies
I'm using Internet Explorer 8 for the time being. Anyways, I have an HTML file in my Documents folder and I opened it in IE8, but it suddenly took me to a message saying "Invalid Address", and I can't get it to display the file.
I don't have internet access by the way. Is that necessary?
A:html page not displaying in IE8?
How are you trying to view this document?
Internet Access is not necessary to view locally stored html files.
6 more replies
Sorry, posted in wrong section.
Woopsie!!!
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I'm doing some research and have to acquire various html pages from a DB. I'd like to automate the process. Any idea of the most effective manner? We have to enter some data to specify which page we require. I write Perl falrly well. Maybe there are some scripts out there?
Thanks
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i am looking for a very,very,very plain web page site for
HTML codes. something that says 'this' will look like
'this'.,etc.
thanks
A:a plain HTML web page needed?
8 more replies
I'm running Netscape 9.0 and just recently when I click on a hyperlink on a specific professional website I belong to, which previously always displayed what I think was a .pdf file within the browser as a new tab, now just opens a new tab which runs and appears to try to load and then stops - without displaying anything.
I tested the website using FireFox and got the same results. However, when I test using Internet Explorer, the file display in a new tab just fine. I'm not sure what has changed, but it's clearly not the website. Any suggestions?
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I get popups on most webpages in the lower right hand corner. I assume these are an HTML overlay because it only happens on some pages. IE, Firefox, Chrome, Realplayer homepage, and even the MOTDs inside my Steam games. Sometimes these MOTDs are ads so I'm getting ads in my ads. I've had enough of this inception. Also I get random page redirects.
I recently got rid of some nasty trojans including Sirefef.G/DN. I had previously used Sophos rootkit removal to clean my machine but after a failed reboot and restore I used ESET instead and it removed the trojans but not the ads and redicts.
I havnt tried this since the trojan removals but previoulsy I uninstalled firefox, deleted all registry values, and then reinstalled. After about 5 mins of use, and ad free surfing, the program would shut down and restart, with all my tabs, but this time with ads. I did this twice.
I should probably mention this is a windows 7 x64 machine.
I'm ready and willing. I also have the ESET logs handy.
A:HTML overlays and page redicts
Can you post the log from Sophos?
36 more replies
In the Windows explorer, the folders icon is a Internet Explorer icon. Any ideas why? If you need a screenshot i can get one.
Thanks,
Ross
A:Folder Icons as HTML Page??
What folders? Could you take a screenshot?
Try looking at the Properties and clicking on the Customize tab.
2 more replies
I am in the process of learning webdesign, starting with HTML and CSS.
I want to be able to drop a spreadsheet file into my webpage's dir and reference a range of cells to show on a page in my website. I would like it to be able have the page reference the spreadsheet each time it (the page) is loaded by a browser.
What I would like to do with this is keep track of a FF survivor pool in a spreadsheet and allow the participants to view the pool results on a page on my site. I would like to just be able to upload the spreadsheet after updating it, and not have to edit the html page every time.
What language would be able to do this? Is this a Javascript function, or is it some other language? I have not started learning JS yet, but plan to once I have a firm hold on CSS.
Also, is there an ideal file format for the spreadsheet? Will .xls work, or should I make it .csv, or even save it as .xml with OpenOffice?
-tim
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I just created a web page on my system and I just wanted to email this page to a friend. I have a couple of photo's in this page as well. When I send it to my hotmail account & click on the web page I get no pictures (even tho they are included as attachments). I did figure because the code on my desktop had the path to the picture to my directories, so I used the OBJECT command to embed the pic, but still I get no pic. Just curious because I have never gotten this to work so far.
Any ideas would help.
Thank you!
A:(Solved) HTML - Sending a page
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A:How to make HTML page wider?
yea i can help lol
dude u gota get a better editor
go for dreamweaver mx 2004 e mail me if you want some details il help you out
sounds like your problem is like uv somehow entered some code that keeps the res of the page set at 1 type like 8 / 6 dont know how to fix it but i use either front page or dreamweaver, dreamweaver bieng an amazing program u can edit most types of code soooo easily try it...
another way... sent me the htm doc and il sort it you can send to me on msn or email with ur msg ok mate
[email protected]
stay cool, FreeN
1 more replies
I have an html page which will open with IE7 but won't with Firefox version3 - the page never loads. Can anyone tell me how to get Firefox to open the page ?
A:HTML page opens with IE want use Firefox
Since posting the query I have found that if the page is loaded in OpenOfficeorg writer and then saved it can be opened with Firefox. The html is shown then whether IE 7 or Firefox is used. The font size also is changed by saving from OpenOfficeorg writer (whether Firefox or IE7 is used to view). I would like to understand what happens and I would still like to know if the page can be viewed in Firefox without the loading into OpenOfficeorg writerand saving
1 more replies
I'm working on creating an autorun CD that starts an .htm page. When the CD is popped in, I want it to pull up my htm page on the desktop centered, with a specific size (800 x 600), and without the min/max buttons, scrollbars, toolbars, status bar, and the inability to resize the screen. Basically, I just want the centered window open with a title bar and the close button. I have tried everything. The only way I can get it now it to make a 2x2 page open up first and correctly open the new page with an event. Once the new page is opened, the 2x2 page runs a window.close command.
I have looked all over the internet and cannot find anything that can do all the commands when the page is first opened. Any suggestions are more than welcome. If you have questions, please let me know. Thanks.
A:How to center an autorun HTML page
Not going to happen with plain HTML, not everyone uses IE and Windows ya know. You can either package a browser on your CD, or use a program to convert the HTML to an EXE.
1 more replies
Hi guys,
I am trying to setup a citrix html page that uses java. whenI load the page i get the following java error:
Java Plug-in 1.6.0_24
Using JRE version 1.6.0_24-b07 Java HotSpot(TM) Client VM
User home directory = C:\Users\%USER%
----------------------------------------------------
c: clear console window
f: finalize objects on finalization queue
g: garbage collect
h: display this help message
l: dump classloader list
m: print memory usage
o: trigger logging
q: hide console
r: reload policy configuration
s: dump system and deployment properties
t: dump thread list
v: dump thread stack
x: clear classloader cache
0-5: set trace level to <n>
----------------------------------------------------
java.lang.ClassNotFoundException: com.citrix.JICA.class
at sun.plugin2.applet.Plugin2Manager.createApplet(Unknown Source)
at sun.plugin2.applet.Plugin2Manager$AppletExecutionRunnable.run(Unknown Source) at java.lang.Thread.run(Unknown Source) Exception: java.lang.ClassNotFoundException: com.citrix.JICA.class I am using presentation server 4.0, I have ... Read more More replies Answer Match 48.72% Logfile of HijackThis v1.97.7 Scan saved at 10:52:58 AM, on 10/20/04 Platform: Windows 98 SE (Win9x 4.10.2222A) MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106) Running processes: C:\WINDOWS\SYSTEM\KERNEL32.DLL C:\WINDOWS\SYSTEM\MSGSRV32.EXE C:\WINDOWS\SYSTEM\MPREXE.EXE C:\WINDOWS\SYSTEM\mmtask.tsk C:\WINDOWS\EXPLORER.EXE C:\WINDOWS\TASKMON.EXE C:\WINDOWS\SYSTEM\SYSTRAY.EXE C:\WINDOWS\SYSTEM\ATIPTAXX.EXE C:\WINDOWS\STARTER.EXE C:\PROGRAM FILES\ZIPCD\DIRECTCD.EXE C:\PROGRAM FILES\MICROSOFT HARDWARE\KEYBOARD\SPEEDKEY.EXE C:\WINDOWS\SYSTEM\MSWHEEL.EXE C:\PROGRAM FILES\IOMEGA\TOOLS\IOWATCH.EXE C:\PROGRAM FILES\IOMEGA\TOOLS\IMGICON.EXE C:\WINDOWS\SYSTEM\WMIEXE.EXE C:\WINDOWS\SYSTEM\DDHELP.EXE C:\WINDOWS\SYSTEM\PSTORES.EXE C:\WINDOWS\DESKTOP\HIJACKTHIS.EXE R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Bar = http://g.msn.com/0SEENUS/SAOS10 R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Page = res://msaps.dll/search.html R0 - HKCU\Software\Microsoft\Internet Explorer\Main,Start Page = res://msaps.dll/index.html R0 - HKLM\Software\Microsoft\Internet Explorer\Main,Start Page = res://msaps.dll/index.html R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Search Page = res://msaps.dll/search.html R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = res://msaps.dll/index.html R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Search_URL = res://msaps.dll/search.html R0 - HKLM\Software\Microsoft\Internet Explorer\Search,SearchAssista... Read more A:res://msaps.dll/index.html--- as start up page Welcome to TSG!! Create a permanent folder on your hard drive for Hijackthis, like My Documents\HJT Click on this link to download the new version of Hijackthis post a log using that version from your permanent folder. 3 more replies Answer Match 48.72% When I click on a link, key in a URL or hit refresh on any open page, Opera opens the page with Word! I was downloading something and changed the extension on a file and ever since then it hasn't managed to open anything within Opera. It always tries to open a new Word document. Has anyone seen this and managed to solve it? A:Opera Opens Html Page With Word Hi Pete In Opera, click tools > preferences > advanced tab. Click "downloads" from the menu on the left. Uncheck "Hide File Types Opened With Opera" in the top right corner. Select "application/internet shortcut" then click the "edit" button. Make sure "Open with Opera" is the only one selected. You might want to look at the msword association as well. Anyway, that's were all of Opera's file associations are located and can be changed. Also take a look in windows explorer at tools > options > file type tab and check the associations in there if the above doesn't happen to work for some reason. 1 more replies Answer Match 48.72% I infrequently design web sites and I cheat and use Front page. Needless to say, I am JS challenged! I would like to know how to show a link on my web page that will print a specific document. I know how to link to a document and then open that document and print it, but I am wondering how to just print a document with an onclick selection without opening the document. On another site I read that someone "open the target document in a small pop-up window, immediately move focus back to the main window, execute the print command, and then close the pop-up." However, I do not know how to write any of this. In the past when I have added JS to the Html section of Front Page - sometimes it shows like it is supposed to and other times it the actual JS appears when I go to view. Any suggestions. Thanks in advance. More replies Answer Match 48.72% Hey! Need instructions for removing the scroll bar from my webpage. Thanks A Bunch, Jessie A:html page / remove scroll bars You need to make the page fit in the given space. The browser will put that there on it's own. To get rid of it, shrink the page. 3 more replies Answer Match 48.72% I have a link that is point to a small excel file on one of HTML pages on my server. When user open the link, the file open in the browser with funny characters. How to make the link open the save file dialog? I tried Firefox and internet explorer and I got the same result. A:Solved: save xls file that is in html page The simplest option to download it for yourself is to right click on the link and choose "Save link as" (or the equivalent in whichever browser you are using). If you need to resolve the issue for a lot of people and don't want to tell them all "right click on this link and choose Save link as", you might find the information that you're looking for here. 3 more replies Answer Match 48.72% Hello. While opening some sites, I want to save some pages, I right click on the page and save it as "web page complete". after it saved, I have one page and one folder - both same name. On double click on the page's name, windows 'edge' opens and starts loading endlessly, finally I get the page opened but coveres with sort of black-brown curtain, attached screenshot. Same happens when I select to open the page with any other browser I checked into the folder, all elements are present. Some help needed Thanks Motim A:Saving HTML page to view it offline Try saving the web page (complete) with a different browser? 1 more replies Answer Match 48.72% I turned on my computer and the desk top will not load it says security Warning A fatal error in IE Error was caused by Trojan-Spy.html.Smithfraud.c system can not function in normal mode here is the HJT logfile; Logfile of HijackThis v1.99.1 Scan saved at 9:45:14 PM, on 7/5/2005 Platform: Windows XP (WinNT 5.01.2600) MSIE: Internet Explorer v6.00 (6.00.2600.0000) Running processes: C:\WINDOWS\System32\smss.exe C:\WINDOWS\system32\winlogon.exe C:\WINDOWS\system32\services.exe C:\WINDOWS\system32\lsass.exe C:\WINDOWS\System32\Ati2evxx.exe C:\WINDOWS\system32\svchost.exe C:\WINDOWS\System32\svchost.exe C:\WINDOWS\system32\spoolsv.exe C:\WINDOWS\CDProxyServ.exe C:\WINDOWS\System32\CTsvcCDA.EXE C:\Program Files\EarthLink TotalAccess\WENGINE\wmonitor.exe c:\PROGRA~1\mcafee.com\vso\mcvsrte.exe C:\PROGRA~1\McAfee\SPAMKI~1\MSKSrvr.exe C:\WINDOWS\System32\svchost.exe c:\PROGRA~1\mcafee.com\vso\mcshield.exe C:\WINDOWS\system32\Ati2evxx.exe C:\WINDOWS\Explorer.EXE C:\WINDOWS\System32\wuauclt.exe C:\WINDOWS\System32\shnlog.exe C:\HP\KBD\KBD.EXE C:\Program Files\HP DVD\Umbrella\DVDTray.exe C:\Program Files\Hewlett-Packard\HP Software Update\HPWuSchd.exe C:\WINDOWS\System32\hphmon05.exe C:\WINDOWS\System32\spool\drivers\w32x86\3\hpztsb09.exe C:\Program Files\Hewlett-Packard\HP Share-to-Web\hpgs2wnd.exe C:\Program Files\Common Files\Real\Update_OB\evntsvc.exe C:\PROGRA~1\mcafee.com\vso\mcvsshld.exe C:\PROGRA~1\mcafee.com\agent\mcagent.exe C:\Program Files\MusicMatch\MusicMatch Jukebox\mm... Read more A:About blank home page;trojan-spy html 16 more replies Answer Match 48.72% I currently have a webform that once submitted, emails the results to a specific address in rich text format. I would like to know how to direct a user to a confirmation page after submitting their info. I have a basic confirmation page that I would like to use, but was wondering if there was an easy way to transition to that page after a user hits Submit. Would it be something that I would have to add to the "action" line?(action="mailto:[email protected]") Please let me know if there is an easy way to do this. More replies Answer Match 48.72% hi i am working on a presentaion cd having following page format what i like to do is when i click the filename which is a audio or video file it will play on the media player of the page, not in the ie media window. i wrote this code for it collected from macromedia web site. object width="320" height="290" classid="CLSID:22d6f312-b0f6-11d0-94ab-0080c74c7e95" id="mediaplayer1"> <param name="Filename" value="kids.mpg"> <param name="AutoStart" value="True"> <param name="ShowControls" value="True"> <param name="ShowStatusBar" value="False"> <param name="ShowDisplay" value="False"> <param name="AutoRewind" value="True"> <embed type="application/x-mplayer2" pluginspage="http://www.microsoft.com/Windows/Downloads/Contents/MediaPlayer/" width="320" height="290" src="/support/dreamweaver/ts/documents/kids.mpg" filename="kids.mpg" autostart="True" showcontrols="True" showstatusbar="False" showdisplay="False" autorewind="True"> </embed> </object> but the problem here is that it works for only a particular media file wich in this case is kids.mpg. so how can i make it to play the file name click. plz help More replies Answer Match 48.72% Is there an EASY way to execute a bat file from inside a html page? Thanks for any help A:Running bat files from inside a html page You can't without IE asking first, and nor should you unless you are thinking of creating a 'virus' 3 more replies Answer Match 48.72% I have changed the description and meta tags in the html of my index webpage. How long do I need to wait for the description to change on the various search engines results pages. Thanks More replies Answer Match 48.72% The question I want to ask is how to make a animation from Flash MX as an HTML like say I make a bowling animation which each pins has a link, when you click the pin the bowling ball will come and crash the pin that was selected to send it to that site. Does anyone know how to do that? More replies Answer Match 48.72% Hi I am relatively new to Access. So far I succeeded to complete couple projects, but now I face a real challenge: I need to write Access web application. Unfortunately I have never written any code in HTML, JavaScript or any script at all. I know that by using Page object, Access creates web application, but for my project I would need to modify it. I have a couple questions. 1. Does anybody know of any good book I can learn writing code in HTML for Access 2003? 2. I have an “EMPLOYEES” table and want to use ComboBox to find the record of the employee by name. How can I do that in HTML? 3. Another ComboBox would display a zip code, and by the Zip Code field, the fields City and Area Code would be populated. ZipCode, City and AreaCcode are the fields in another table, which linked to “EMPLOYEES” table by ZipCode_ID. How it can me done in HTML? I appreciate any help Thanks, Barbos More replies Answer Match 48.72% Hi, I need to implement the project from HTML page to number of paragraphs files ,each page assume to each folder and each paragraph assumed to be file.I need to implement in this through C. Also ,I need to know designing procedure and requirements of this project which kind of editor need ,to upload the HTML page and read through the C LAnguage by C File handling.I am new to this type .Please suggest me regarding this . Thankx in advance I appriciate your responses! I am expecting your valuable suggestions. regards, Munisamy Subramaniam More replies Answer Match 48.72% Is there a safe java or script to use for allowing users to send html pages to a recipient thru a cgi script? A:send html page to a friend script? It depends on how you want to do this. If you want it to send a link you can use a form mailer to do this where the person puts in the friend's email address. I actually suggest you just use a free service like tellafriends.com that gives you HTML to put in your page and it will use their script to send the page. 3 more replies Answer Match 48.72% A customer of mine has his girlfriend on his desktop and you see it briefly during bootup but then it disappears and he gets a uniform blue colour. Similarly you see her briefly when you shut down. So we know she is there but is hidden. When I go into desktop properties and try and change the wallpaper the controls are greyed out. He has admin rights - any ideas? A:Desktop Wallpaper A customer of mine has his girlfriend on his desktop and you see it briefly during bootup but then it disappears and he gets a uniform blue colour. Similarly you see her briefly when you shut down. So we know she is there but is hidden. When I go into desktop properties and try and change the wallpaper the controls are greyed out. He has admin rights - any ideas?Try this.Start regedit.Navigate to:HKEY_CURRENT_USER\SOFTWARE\Internet Explorer\Toolbar\In the right pane, look for a String Value with a path to a bitmap on your system--for instance: c:\windows\Circles.bmp -Delete the value.--Exit the Registry editor. 2 more replies Answer Match 48.72% I have Windows 7. I have a laptop computer. This computer with this Windows 7 Is okay. How ever I am having a problem with my Desktop wallpaper. I want to make the picture tiled, I click the tile button, However the pictures always go streched and look wierd. I would like to ask. Can someone please help me with this problem? Thank you A:Desktop wallpaper HELP PLZ 2nd computer is still windows 7? right click anywhere on desktop > Click personalize > Click > click Desktop Background > & in drop down option select Center. on XP its same let me know if u need steps for that. 2 more replies Answer Match 48.72% When I click on desktop and select properties to change the desktop wallpaper I have a list of family photographs!!!I still have the desktop wallpaper folder in windows web folder but how do I put it back into the desktop and remove the ones that are mysteriously there. A:Desktop Wallpaper 8 more replies Answer Match 48.72% hello, my screen broke so I hooked lap top to tv in order to download data, but had trouble accessing my taskbar. I was trying to adjust the screen but then all of sudden all I could only see was my wall paper A:can see my wallpaper but not desktop Hi jplascencia, Try pressing ctrl+alt+del this should bring up the task manager, if you click on File -> New task(run...) and that should be up the "Create new task" window, if you enter in here "explorer.exe" and then click ok it should bring back the taskbar. 2 more replies Answer Match 48.72% I added a photo to my appearance and themes display properties. It appeared on my desktop wallpaper after I right clicked on the photo. Now I can't delete it. I have changed my wallpaper, but I want to delete this photo completely. Any suggestions? A:Desktop Wallpaper 6 more replies Answer Match 48.72% i am new at this. i had a trojan, and changed my decktop theme and cant renew to any other still have the warning sign flashing. Already uninstaled old anti virus, instaledd new one. and ran full scan in both regular and safe mode. trojan deleted. running xp. please help. A:desktop wallpaper 8 more replies Answer Match 48.72% I recently tripped a virus that was hidden on my computer. I don't know where it came from but i got rid of it. Only problem is I now have a permanent desktop wallpaper that cannot be changed. It's an annoying warning saying "your computer is infected with spyware. it is recommended that you remove it before continuing use." blah blah blah. I have tried everything that I know of to remove it and fix the problem but everything has failed. Any ideas on what is preventing me from fixing this and how it can be fixed? I appreciate any help from anyone in here. Microsoft is obviously no help to me since they want$35/question about this problem. What a rip. If all else fails, I guess I'll ahve to wipe the hard drive and re-install everything for the god-knows-how-many times. Please, I beg for help in fixing this problem so I don't have to do that. It's a pain when you have 27 programs to install all from seperate disks.
A:Desktop Wallpaper
To remove the infection I would like to refer you to the Highjack This forum here at BleepingComputer.com. First: Read the Preparation Guide found HERE. It is very important that you follow ALL of the instructions found within. Second: Post your system information along with a brief description of the problems you are having, and your Highjack This log in the Highjack This forum found HERE.You are in good hands! But remember, the volunteers who work that forum are very busy, so please be patient and wait for a response. It can sometimes take a few days. Good luck!
2 more replies
I have Windows 7. I can set a multiple wallpaper transition on my desktop, which is fine, but.....I have to reactivate this every time I reboot my machine. i.e. it locks on one wallpaper with each reboot - the random wallpaper transition is lost. Why does that happen? Is there any way I can correct this?
A:desktop wallpaper
hello? can anyone help?
1 more replies
Thanks for reading my computer's problem.
System: XP, SP2
It started with flashing desktop icons. When click any icon, it will run other program. If try to shut down computer by clicking "Start", a Pop-up shown "Running ....."
I disconnected the physical network cable, press the power switch to trun off the computer. Then, trun on the computer, boot into Safe Mode, did a system restore (? restrui.exe ?).
Now, the computer shows nothing on the desktop.
By the way, it still can boot into Safe Mode and shown a Safe Mode desktop with few icons.
Thank you.
A:Only wallpaper, nothing else on desktop
13 more replies
Hello! I was surfing the internet when Mcaffee suddenly alerts me regarding the trojan my computer acquired. Then, it alerts me again several times until my computer froze. So since I had no choice, I restarted my computer and when I went back to my account (there are 2 user accounts in our computer, mine and my sister), I can only see my desktop wallpaper and nothng else. Im really sad because I have the administrator account so I can't access some of my programs. Btw, I am using my sister's account. And also, I need help with the "Your Computer is in Danger" alert. I have already posted my Hijackthis logfile in another topic and I hope someone would help me with my problem since Im going to move in a dorm in a few days and my mom really needs the computer to chat with my father.
A:Help! I can only see my desktop wallpaper and nothing else
Hello Pixie and welcome to Tsg.
Stay with your first thread or you are going to make it confusing for those helping you.
2 more replies
i have wins7 home premium,every time i try to put wallpaper on my desktop it will turn black, but i can put a solid color but not a picture.it use to work,please help me.
A:desktop wallpaper
Solid colors are used to help people see better. You probably have it set for
High Contrast Themes. Try Left Alt - Left Shift - Print Screen (Print Scrn key)
Next is the same location.
Go to the Ease of Access Center in the Control Panel.
Click - Make the computer easier to see.
If a high contrast Theme has been select, look like you could select a better picture theme.
Right click your empty Desktop - Personalize - pick a Theme. It than goes to the lower left
to be clicked to open for you to select one. After selecting one be sure to SAVE Changes.
Some things are set in the Registry. If possible you could use a restore point before your
trouble started. If it's been a long time you will loose other downloads and whatever changes you have made.
That's the best I can come up with.
1 more replies
Going through the control panel to check for a new desktop picture, I find some of my personal photo's have appeared in there. How could they have got there and how do I remove them.
Thank you.
A:desktop wallpaper
The default folder that it uses to look for desktop images is probably the same folder that you have saved the personal images to.
Easist to put your personal images in the one place, in a different folder.
1 more replies
My computer runs on windows vista and i cannot use pictures i have cropped as my desktop background even though they worked before i cropped them. how can i make it so my computer will show those cropped pics for wallpaper rather than black background?
A:Need help with desktop wallpaper
11 more replies
I really want to be able to have an SWF file as a wallpaper in vista (I got a killer idea) but I cant get it to work
Theres many programs to do it, but they are all for XP and before
A way I could do it would be to put it in html, but then that only works for XP and before too
A:.Swf as desktop wallpaper?
anyone?
6 more replies
I had a background picture on my desktop screen. It was turned to jibrish. How do I clear it. Toshiba Satellite laptop, windows vista, aol 9.1 dial up connections.
A:desktop wallpaper
On windows: right-click background-> properties -> background -> choose a background ->
1 more replies
Dear All,
I work in a school and we are having problems with pupils changing the desktop wallpaper to inappropriate images from the internet.
I have followed the instructions from the following thread:
http://forums.techguy.org/windows-xp/674977-solved-make-desktop-wallpaper-unchangeable.html
The regedit fix works initially but it doesn't stop the pupils being able to change the image via right clicking on an image in any web browsers or Windows Picture Viewer. Our Windows 7 machines seem to be locked down ok using a similar fix but the XP (Home edition) ones are proving quite awkward.
Any suggestions?
Regards
J Donald
A:Wallpaper / Desktop Changes
have you tried setting the desktop image that you want to use/keep to attributes read only and system ?
1 more replies
I recently got high-speed internet on my second computer and I just downloaded Panda Internet Security Platinum b/c I thought my computer was infected. Half was through the installation, within the instructions, I was prompted to restart my computer and once I restarted the rest of the installation would continue. When I restarted, the desktop wallpaper appeared but there was no icons, start bar or anything (Windows XP Home). I tried restarting again by holding the power button and I also unplugged the power source and then restart but still nothing.
All I have is a screen with my desktop wallpaper and a mouse pointer. What do I do to get into the compter and fix this? Thanks.
A:Desktop Will Not Appear, Only Wallpaper
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I copied a photo from the internet (that cute "Mig" guy from Rockstar INXS)and made it my desktop background, and now I can't get rid of it. I deleted the jpeg file, but still stuck with it. When I try to replace it with a new image from the control panel, it flickers and then there's "Mig" again. HELP!!!
A:Desktop Wallpaper
did you goto your control panel - display - at the bottom of background delete the file that it is using ?
2 more replies
I have 2 screens running different parts of the desktop, one at 1920x1200 and one at 1680x1050.
I was wondering how I can get a single picture to span between both monitors, instead of having one picture duplicated for the background on both screens. I've seen this done on two monitors with the same resolution, but I don't think that having the same resolution should matter. Does anyone know how?
A:Help With Desktop Wallpaper
I figured it out, have a picture that is 3600x1200 pixels, and make sure that the strip of 1680x150 at the bottom right has nothing in it, then put the setting to "tile" and it will work. I like this because it gives the desktop more variety especially with two screens.
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I returned to my desktop computer to find my desktop background was there but
all the icons and the start up bar had disappeared. I tried to switch off and
found the button did not respond. I switched off at the back of the computer
then switched on again - it loaded quite normally until the desktop
reappeared but still no icons or taskbar. My mouse arrow is there. I have
repeated the process but it was just the same
A:desktop wallpaper!
Do not hijack anyone else's thread. I have moved your post to your own thread to avoid confusion.
Boot into Safe Mode (press F8 at bootup) Do you still have this problem. In Normalamode At the Desktop press CTRL+ALT+DEL start the Task Manager. Go up to File/New Task (Run) and type explorer.exe and press enter. Your Task Bar and Start button should appear.
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I have tried just about everything & still cannot remove windows desktop wallpaper.
thanks for any help.
A:desktop wallpaper
Did you follow this Change your desktop background (wallpaper)
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I had my wallpaper set as one that changes every 3 minutes or so. I set it up Wednesday, but yesterday when I put my 2nd monitor on to watch a movie, the wallpaper disappeared and went blank. I thought it did this just because it wouldn't work with 2 monitors enabled, but when I turned the 2nd monitor off in Nvidia control panel, the wallpaper flashed back on for a second and now it stays black. I restarted but it still stays black. Even if I try changing wallpaper in Personalize it doesn't change.
A:Can't have desktop wallpaper
I managed to fix it. I followed the instructions on here: Web tab missing in the Customize Desktop dialog then when I restarted my wallpaper was back to normal.
6 more replies
Can anyone rec desktop wallpaper (non-changing) with 2012 calendar? I've always liked the one's from VladStudio but can't seem to find one with 2012 calendar.
A:Desktop Wallpaper
search on googleI have done that.
4 more replies
Hi, My problem is that I can't 'show next background' on my windows home premium computer just one picture shows. I have dreamscape installed so decided to uninstall but still the problem is there. I have tried the suggested fixes eg. file scan, visual effects is selected 'adjust for best appearance', have made sure that slideshow is available in advanced power options but still no good. I have created a new user account and all is OK there. I would like to transfer everything over to the new account and start again, can I do this and how? System restore can only be started in safe mode. I have tried this but still no good. Have made sure that malawarebytes has scanned for any viruses and all is OK there.
I have my computer just the way I want it and would prefer a fix rather than starting all over. I have windows 7 64 bit. Thanks.
A:Desktop wallpaper
Try Repair Install
Repair Install
1 more replies
OK, here goes.
I'm attempting to apply wallpaper to my desktop, an .art image i retrieved from a website. For some reason its not showing up in my background display properties, therefore I can't set it as wallpaper. All of the other images i've gotten from the net have been .bmp images and they show up in my background display properties. My question is, why can't i use .art images as wallpaper?
If I can, how?
A:desktop wallpaper
i think im right in thiking that the wallpaper can only be .bmp files unless Active desktop iis on, in which case jpeg/jpg files can also be used.
To solve your problem, open the file in a graphics package and just convert it to a .bmp file.
If you havent got a graphcs package, Ifranview: www.ifranview.com is great.
3 more replies
This may seem trivial, but it's bugging me. I have a windows XP and i have the windows classic theme. Every time I put a picture as my wallpaper the color around the words under my icons doesn't blend in with the picture but stays a solid color, so there's like little boxes of blue of white. How do I make those icon words blend in with the picture? thanks. Any help is appreciated.
A:desktop wallpaper
Welcome to TSG theshallowpicguy
Your problem is a little unclear. Can you explain it a little more briefly. Also, if possible, try to post a screenshot. This will help us understand your problem better. Hope you understand what I mean to say. Good Luck.
2 more replies
Booting in Safe mode doesn't work either.... Virus cleaner removed all spyware and trojans..still nothing. HELP PLEASE.. Logfile of Trend Micro HijackThis v2.0.0 (BETA)Scan saved at 7:57:01 PM, on 08/18/2007Platform: Windows XP SP2 (WinNT 5.01.2600)Boot mode: NormalRunning processes:C:\WINDOWS\System32\smss.exeC:\WINDOWS\system32\winlogon.exeC:\WINDOWS\system32\services.exeC:\WINDOWS\system32\lsass.exeC:\WINDOWS\system32\svchost.exeC:\Program Files\Windows Defender\MsMpEng.exeC:\WINDOWS\System32\svchost.exeC:\WINDOWS\system32\spoolsv.exeC:\Program Files\AOL\Active Virus Shield\avp.exeC:\WINDOWS\System32\svchost.exeC:\WINDOWS\system32\taskmgr.exeC:\Program Files\Opera\Opera.exeC:\Documents and Settings\Owner\Application Data\Opera\Opera\profile\cache4\temporary_download\HiJackThis_v2.exeR1 - HKCU\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = http://us6.hpwis.com/R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Default_Search_URL = http://srch-us6.hpwis.com/R0 - HKCU\Software\Microsoft\Internet Explorer\Main,Start Page = http://google.bearshare.com/R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = http://go.microsoft.com/fwlink/?LinkId... Read more
A:Help.....help!.....my Desktop Is Gone, Only Wallpaper..
Hello masterbuilderz, I'm just looking over your log and will get back to you soon.
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For some reason, out of nowhere I have no desktop wallpaper. And I can't do anything about it. When I shutdown my comp, and explorer shuts down, my wallpaper still appears for about 2 secs before it completely turns off. I'm assuming it's some sort of ad or spyware, but nothing's showing up in my report after I scan. Please help, this is driving me NUTS! ha ha, any help at all is appreciated.
mike
Here's a pic of my desktop and properties. As you can see it won't allow me to apply a wallpaper.
A:No Desktop Wallpaper???
Click on Customize Desktop, then Web.
Lets see a screenshot of that. This time, hold down Alt + Print Screen. That way, you will only get a pic of the properties page
8 more replies
Hi,
I need to export my collected metrics such as processor, disk, and network utilization. I need to export this data to an html page as a chart (same chart as what I see when I look at performance monitor reports for my custom data collector sets). What is
the recommenced way of getting this accomplished?
Thanks
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I could really use some help... My 17yo son was surfing something ( porn im sure ) and now im getting pop ups and my home page on IE 6 keeps going back to his -
res://mshp.dll/index.html#10213
I also ran HijackThis,
Logfile of HijackThis v1.97.7
Scan saved at 8:52:07 PM, on 1/6/2004
Platform: Windows 2000 SP2 (WinNT 5.00.2195)
MSIE: Internet Explorer v6.00 (6.00.2600.0000)
Running processes:
C:\WINNT\System32\smss.exe
C:\WINNT\system32\winlogon.exe
C:\WINNT\system32\services.exe
C:\WINNT\system32\lsass.exe
C:\WINNT\system32\svchost.exe
C:\WINNT\system32\spoolsv.exe
C:\WINNT\System32\svchost.exe
C:\Program Files\Norton AntiVirus\navapsvc.exe
C:\WINNT\System32\nvsvc32.exe
C:\WINNT\system32\regsvc.exe
C:\WINNT\wanmpsvc.exe
C:\WINNT\System32\WBEM\WinMgmt.exe
C:\WINNT\System32\mspmspsv.exe
C:\WINNT\system32\svchost.exe
C:\WINNT\Explorer.EXE
C:\PROGRA~1\NORTON~1\navapw32.exe
C:\Program Files\Yahoo!\Messenger\ymsgr_tray.exe
C:\Program Files\Internet Explorer\IEXPLORE.EXE
C:\Program Files\Microsoft Office\Office\OUTLOOK.EXE
C:\PROGRA~1\WINZIP\winzip32.exe
C:\Documents and Settings\Administrator\Local Settings\Temp\HijackThis.exe
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Bar = C:\WINNT\system32\searchbar.html
R0 - HKCU\Software\Microsoft\Internet Explorer\Main,Start Page = res://mshp.dll/index.html#10213
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = C:\WINNT\system32\sea... Read more
A:IE home page keeps getting set to - res://mshp.dll/index.html#10213
Hi NorcalJim
Welcome to TSG!
Click on the link below to download CWShredder. Close all browser windows,UnZip the file, click on the cwshredder.exe then click "Fix" (Not "Scan only") and let it do it's thing.
http://www.merijn.org/files/cwshredder.zip
When it is finished restart your computer.
To help prevent this from happening again, I strongly recommend you install the folowing patches for the vulnerabilities that this hijacker exploits:
http://www.microsoft.com/technet/treeview/default.asp?url=/technet/security/bulletin/ms03-011.asp
http://www.microsoft.com/technet/treeview/default.asp?url=/technet/security/bulletin/MS00-075.asp
*Note: The simplest way to make sure you have all the security patches is to go to Windows update and install all "Critical Updates"
EDIT: I see now you said you have run Adaware and Spybot, but if you did not run them with these settings you should run them again accordingly.
Adaware 6 Build 181
Install the program and launch it.
First in the main window look in the bottom right corner and click on "Check for updates now" and download the latest referencefiles.
Make sure the following settings are made and on -------"ON=GREEN"
From main window :Click "Start" then " Activate in-depth scan (recommended)"
Click "Use custom scanning options" then click "Customize" and have the... Read more
3 more replies
Is it possible to somhow find out the exe file address and manually place that address in the download manager so it will download the actual file I am trying to download?
Thanks,
Yeto
8 more replies
I've had the pleasure last night of having to figure out how to clean this thing off over a remote connection--without the benefit of safe mode. It looks like I've successfully cleaned it--no signs of reinfection yet--so I thought I'd share what I've learned. I'm trying to write it as a high-level description so that non-pros might be able to understand it. I'm writing this information down now from memory, though, not from a good set of notes. I'm also not a tech support professional, and in particular I know very little about how BHOs work.
From what I can tell, this is a variation of the ZAFI worm, or else the ZAFI worm hasn't been described accurately on the anti-virus sites. I suspect it's the ZAFI worm slightly modified and cludged together with another worm (BHO based) so that they will reinfect each other as you're trying to clean it. I don't know what the payload or method of infection is. I've only been concerned with cleaning it off, and will leave the rest to the experts.
On my system, it will reinfect the machine from 3 different areas, so that if you clean one or two spots, the third can still reinfect you and you have to start over again. The system I was working on was running XP.
The three infected areas that I noticed:
- Executable in the windows folder
- Executable in the windows/system32 folder
- Browser helper object (DLL) associated with Internet Explorer
The files are randomly named and hav... Read more
A:Possible fix for home page set to res://random.dll/index.html#96676
There's also a good thread (though more technical) at this other forum: http://forums.spywareinfo.com/index.php?showtopic=7447&st=0
I wish I had seen it before I went through this hell.
1 more replies
Hello, tried everything I could to figure this out. My homepage keeps getting put on the URL above, entitled "Home Search". I've done scans with Norton (shows nothing), Spybot (shows a Data Source Object exploit), Adaware 6.0(said it was a CWS trojan), and tried the CWS shredder. Spybot referred me to http://security.greymagic.com/adv/gm001-ie/, and I tried that fix to no avail. I've ran "hijack this" and here's my log. Any help on this one would be deeply appreciated.Logfile of HijackThis v1.97.7Scan saved at 4:07:47 PM, on 6/16/2004Platform: Windows XP SP1 (WinNT 5.01.2600)MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)Running processes:C:\WINDOWS\System32\smss.exeC:\WINDOWS\system32\winlogon.exeC:\WINDOWS\system32\services.exeC:\WINDOWS\system32\lsass.exeC:\WINDOWS\system32\svchost.exeC:\WINDOWS\System32\svchost.exeC:\Program Files\Common Files\Symantec Shared\ccSetMgr.exeC:\Program Files\Common Files\Symantec Shared\ccEvtMgr.exeC:\WINDOWS\system32\spoolsv.exeC:\Program Files\Norton AntiVirus\navapsvc.exeC:\Program Files\Norton AntiVirus\SAVScan.exeC:\Program Files\Analog Devices\SoundMAX\SMAgent.exeC:\Program Files\Common Files\Symantec Shared\CCPD-LC\symlcsvc.exeC:\WINDOWS\system32\addqc32.exeC:\WINDOWS\... Read more
Firs tthing you need to do is create a directory on your c: drive called c:\hijackthis and move the download and run HijackThis from that location. This is one is a pain to clean so bear with me with the process.I want you to fix some of those entries. Please do the following:Please make sure that you can view all hidden files. Instructions on how to do this can be found here:How to see hidden files in WindowsPlease put a checkmark in the box for each of these entries, close all other windows, and click the fix button:R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Page = res://C:\WINDOWS\system32\bxwdr.dll/sp.html#96676R0 - HKCU\Software\Microsoft\Internet Explorer\Main,Start Page = res://bxwdr.dll/index.html#96676R0 - HKLM\Software\Microsoft\Internet Explorer\Main,Start Page = res://bxwdr.dll/index.html#96676R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Search Page = res://C:\WINDOWS\system32\bxwdr.dll/sp.html#96676R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = res://bxwdr.dll/index.html#96676R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Search_URL = res://C:\WINDOWS\system32\bxwdr.dll/sp.html#96676O2 - BHO: (no name) - {602C3D03-C6C8-CE58-094E-67D08A6CADCB} - C:\WINDOWS\msbg.dllO4 - HKLM\..\Run: [addpy32.exe] C:\WINDOWS\... Read more
15 more replies
How to make the HTML page run with compatible mode in IE 11 by coding instead of by tool in the IE ,such as adding some code to the HTML.
<html>
<meta charset=UTF-8>
<title>Hello World!</title>
<body>
</body>
</html>
Please click the Mark as Answer button if a post solves your problem!
More replies
I am running English WinXP, version 2002, service pack 1.
My default page keeps on changing whenever I bootup the next day. It would points to a compiled HTML file on my C:\Windows Directory.
I would delete away the .chm file, change the default page, do a reboot to test again, and nothing would happen.
However, when I on the PC the next day, the same thing would happen.
I had installed several SPYWARE programs on my PC, such as SpyBot, bazook and none of them can pick up this problem.
PS : I also note that the very first time I ran HijackThis, there are some 06 errors. I rectified them and the next time i ran it, it came back again.
The recored is
"O6 - HKCU\Software\Policies\Microsoft\Internet Explorer\Control Panel present"
Below is a log of HijackThis :
Logfile of HijackThis v1.97.7
Scan saved at 10:57:24 PM, on 4/20/2004
Platform: Windows XP SP1 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\spoolsv.exe
C:\Program Files\Common Files\Symantec Shared\ccEvtMgr.exe
C:\WINDOWS\system32\crypserv.exe
D:\Program Files\Norton AntiVirus\navapsvc.exe
C:\WINDOWS\System32\nvsvc32.exe
C:\WINDOWS\System32\tcpsvcs.exe
C:\WINDOWS\system32\slserv.exe
A:default page pointing to a compiled html file on every new day
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Hello, could you help me with this problem please?
My PC Win XP looks like booting as normal.
The desktop appears with icons and taskbar, then changes to desktop bacground picture only without icons and without taskbar.
This keeps going in a loop. I try to open programs and folders while icons are there but it resets back to the background picture (wallpaper?), and thenback to the desktop with icons and taskbar.
Thanks and all the best
A:desktop comes on then goes 2 wallpaper only loop
check if explorer.exe is running in task manager
1 more replies
I want to apply an animated wallpaper, but when I apply it, it does not seem to want to animate itself. How do I change this?
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My computer got the Spy Sherif software on it. I removed it this morning but several things are still here.
Desktop background will not change and says Your computer is affected by spware.
I also have an error message that comes up and tells me my computer is affected by spyware.
I also have a winlogon.exe application errors
I have run ada-ware and norton anti virus
Logfile of HijackThis v1.99.1
Scan saved at 6:23:21 AM, on 12/28/2005
Platform: Windows XP SP1 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\Program Files\Common Files\Symantec Shared\ccEvtMgr.exe
C:\WINDOWS\Explorer.EXE
C:\WINDOWS\system32\spoolsv.exe
C:\Program Files\Juniper Networks\Common Files\dsNcService.exe
C:\Program Files\Common Files\Microsoft Shared\VS7DEBUG\MDM.EXE
C:\Program Files\Norton AntiVirus\navapsvc.exe
C:\WINDOWS\System32\MsPMSPSv.exe
C:\WINDOWS\System32\ctfmon.exe
C:\Program Files\Common Files\Symantec Shared\ccApp.exe
C:\WINDOWS\System32\igfxtray.exe
C:\WINDOWS\System32\hkcmd.exe
C:\Program Files\Java\jre1.5.0_06\bin\jusched.exe
C:\Program Files\Common Files\AOL\1133943171\ee\AOLSoftware.exe
C:\Program Files\Adobe\Photoshop Album Starter Edition\3.0\Apps\apdproxy.exe
C:\Program Files\iTunes\iTunesHelper.exe
A:desktop wallpaper problems
Hello and Welcome. Please subscribe to this thread to get immediate notification of replies as soon as they are posted.
HijackThis is able to create backups whenever if fixes any entry. These are stored in a subfolder called backups. As such, we advise against placing the program in any temporary folders. Please create a new directory, C:\Program Files\HijackThis\, and re-locate the program & it's associate files there.
Please read this post completely before begining the fix. If there's anything that you do not understand, kindly ask your questions before proceeding. Please ensure that there aren't any any opened browsers when you are carrying out the procedures below. Save the following instructions in Notepad as this webpage would not be available when you're carrying out the fix.
* * * * * * ADDITIONAL DOWNLOADS * * * * * * * * * * * * * *
Download & install - CleanUp.exe (not recommended for WinXP64)
Download KillBox v2.0.0.175.exe (it's important that you get version v2.0.0.175)
Download & extract it to it's own folder - smitRem.exe
Download and install Ewido Security SuiteWhen installing, under "Additional Options",uncheck - Install background guard
Have Ewido update itself & then exit the program.
If you are having problems with the updater, you can use this link to manually update Ewido
'UNPLUG'/DISCONNECT your... Read more
1 more replies
When i would change my wallpaper image it'd be fast but now it takes like a second before the image comes up but everything else is running perfectly fine and this is just recent since i traded up my 9800 gx2 for the gtx 280 ocx
More replies
I just took some digital pictures that I want to put on my desktop, they are high quality but I am having trouble getting them to fit right. If I hit stretch, it stretches it slightly out of proportion and if I hit center, it makes the picture so big it won't fit in the screen. I think I have my setting rights but am not sure, I am using a Dell laptop. Any ideas how I can take this photo, put iton my desktop and see it in proportion?
A:Desktop Wallpaper Proportions
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### Session EA: Conference Experience for Undergraduates Poster Session (14:00-15:30)
Chair: Warren Rogers, Westmont College
Room: Sweeny E
EA.00001: Resistive Plate Chamber half-octant production for the PHENIX Forward Trigger Upgrade Phillip Abernethy PHENIX studies polarized p+p collisions produced by the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory to better understand the spin structure of a proton. PHENIX is upgrading the forward muon trigger by adding new Resistive Plate Chambers (RPC's). The RPC's will provide the ability to trigger on high p{\_}T single muons. RPC Station 3 consists of sixteen half-octants, each with three modules containing gas gaps. Before the half-octants are assembled, each module must be tested for Quality Assurance (QA). After each module is approved they are mounted with Front End Electronics (FEE) boards to amplify and discriminate the signals for output. Once approved, a three module set is installed into a half-octant shell and the cables are routed so as to minimize additional noise. The half-octants are then evaluated and tested for dark current, gas leaks, and noise levels. This poster will describe the process of assembly and Quality Assurance for each half-octant. EA.00002: Proton Accelerator for Calibration of Silicon Detectors for Neutron Decay Mark Abotossaway , Jeff Martin , David Harrison , Micheal Gericke , Kumar Sharma , Graham Schellenberg There is a new generation of neutron beta-decay experiments being conducted where both decay electrons and protons will be detected. The Nab Experiment at the Spallation Neutron Source (in Oak Ridge, TN) is an example of one such experiment. In Nab, protons resulting from the decay will be post-accelerated to 30-keV by a static electric field. Custom segmented silicon detectors with a very thin dead layer are being manufactured to detect the protons. For testing and calibration of the Si detectors, and proton detectors in general, a 30 kV proton accelerator has been constructed at the University of Manitoba. The accelerator is based on the Manitoba II double focusing mass spectrometer, which was modified for our purposes. Details of the modifications will be presented along with a discussion of future work. Results collected with a commercial Si Surface Barrier detector and radioactive sources investigating Si detector resolutions in the tens of keV range will also be presented. EA.00003: Development of GEM Detectors for OLYMPUS and Analysis of Experimental BLAST Data Matthew Anthony , Laura Havener OLYMPUS is a precision experiment that investigates the two-photon contribution to elastic lepton scattering. It is based on the existing BLAST detector to precisely determine the trajectories of charged particles. This apparatus does not cover the forward angle regions where elastic scattering will be used to monitor the luminosities. Therefore, precise tracking detectors will be placed in these positions. GEM (Gas Electron Multiplier) detectors incorporate Cu layer-sandwiched Kapton foils with a chemically etched micro-hole pattern for gas amplification. A test chamber for GEM detectors was produced to test performance of GEM foils and the readout. A ROOT data analysis project was carried out in preparation for a publication of BLAST experimental data. Graphs were produced for the new measurements of the deuteron tensor analyzing powers T20 and T21 and the separated charge (Gc) and quadrupole (Gq) form factors as a function of four-momentum transfer in comparison with existing data and various theoretical descriptions. EA.00004: Adaptation of Crystal Ball and TAPS Detectors for Efficient Data Acquisition at MAMI Joseph Asercion To prepare the experimental apparatus at MAMI for the next set real photon experiments, the Crystal Ball and Two Armed Photon Spectrometer (TAPS) detector systems needed to be optimized for better performance. The Crystal Ball and TAPS particle detectors at MAMI employs object-oriented data acquisition architecture based on the C++ language as well as CERN's ROOT library. This system, utilized by the A2 collaboration at the institute, has been adequate for past experiments; however, it has recently proven to be more and more unstable. To alleviate this problem, the data acquisition software was rewritten as a more cohesive architecture, allowing for greater flexibility in experimental parameters and a decrease in instability. In addition to restructuring the software system, new Gas Electron Multipliers (GEMs) were investigated for use with the Crystal Ball as signal amplification devices using generated voltage signals to test feedback efficiency. These modifications are necessary to provide improved signal detection and data acquisition in future experiments. EA.00005: Analysis of an Experiment on Neutron-rich Isotopes S. Ash , M. Warren , N. Frank , G. Christian , A. Gade , A. Spyrou , M. Thoennessen , T. Baumann , G.F. Grinyer , D. Weisshaar , P.A. Deyoung The structure of neutron-rich nuclei far from stability is of particular interest in evaluating theoretical models of the nucleus. Recently the neutron-unbound nucleus of $^{28}$F was produced via one-proton stripping from a $^{29}$Ne beam at the National Superconducting Cyclotron Laboratory at Michigan State University; this nucleus is one neutron away from the magic number N=20. In addition to $^{28}$F, other isotopes were produced from secondary fragmentation of $^{32}$Mg, the primary beam contaminant. Since $^{28}$F is neutron-unbound in its ground state, it immediately decays in to a neutron and $^{27}$F. The CAESAR CsI array surrounded the $^{9}$Be reaction target to measure gamma-rays emitted from $^{27}$F in a bound excited state. The outgoing charged particle and decay neutron were measured in coincidence. The neutrons were detected by the MoNA, and the charged fragments were swept by a magnet into a series of charged particle detectors. The analysis requires separation and identification of both charged particles and neutrons. The isotope identification for charged particles is obtained from time-of-flight measurements after correction up to the fourth order for dispersive angle and position after the magnet. This isotope separation technique and current analysis status will be presented. EA.00006: Monte Carlo Simulations for Future Geoneutrino Detectors Morgan Askins The main contribution of heat in the earth's mantle is thought to be the radioactive decays of 238U, 232Th, and 40K. A precise measurement of the levels of 238U and 232Th can be determined by measuring the flux of electron anti-neutrinos (geoneutrinos) emitted from their decay chains. Although detectors such as kamLAND and Borexino have detected few geoneutrinos, a new cost effective geoneutrino detector is proposed which takes advantage of the total internal reflection within a long rectangular prism acrylic container of liquid scintillator having a single photomultiplier tube (PMT) on each end. An array of these containers would allow for a large scintillator volume relative to the number of PMTs, but could have a lower radio-purity. The event signatures of these decays were compared to those from neutrino interactions using Monte Carlo simulation software based upon GEANT4. In this poster I will discuss the limitations which arise from this design such as, the thickness of the acrylic container which causes high loss of optical photons due to scattering and absorption, rod length which results in higher scattering rates within the scintillator, and size of the array. EA.00007: MoNA and Two-Neutron Decay Analysis Amanda Grovom , Alegra Aulie , Warren F. Rogers The Modular Neutron Array (MoNA) is a large, high-efficiency position-sensitive neutron detector array housed at the National Superconducting Cyclotron Laboratory at Michigan State University, consisting of 144 2-meter long scintillator bars with a PMT positioned at each end, designed to detect the energy and trajectory of fast neutrons emitted in the breakup of exotic neutron-rich nuclei. Because a single neutron can scatter multiple times within MoNA, (including a large presence of dark-scattering from Carbon), the experimental challenge to distinguish between single and multiple neutron decay events is significant. We've developed special data-sorting routines that selectively filter on a combination of factors such as neutron velocity and scattering angle, hit-pattern distribution, neutron-fragment opening angle, and decay energy in order to reduce the Carbon scattering background and enhance correlations between pairs of neutrons. We've applied this analysis to the 2-neutron decays of $^{24}O$ and $^{13}Li$ from data sets from previous MoNA experiments. Results will be presented. EA.00008: Measurement of Neutron Reflectivity from a Silicon Crystal: Preparation for an nMDM Measurement Benjamin Barber , Donald Koetke , Muhammad Arif , Michael Huber Physicists from ANL, Valparaiso University, University of Hawaii, and NIST have designed an experiment to use the known neutron magnetic dipole moment (nMDM) to measure Schwinger scattering in Si, a process whereby the orientation of the magnetic dipole polarization is altered by interactions with the atomic electric fields in a Si crystal. This measurement is intended to be a precursor to a search for a neutron electric dipole moment (nEDM) employing a similar spin rotation via a different interaction. Both measurements depend on neutron Bragg reflections down a slotted Si crystal. For a successful measurement, the neutron beam has to reflect approximately 150 times, without a large loss of beam intensity. This requires a high reflectivity, on the order of 99\% reflective. In order to make an accurate measurement of the Schwinger scattering, both the incident neutron beam and the crystal's reflectivity need to be well understood. This summer we have characterized the newly commissioned nMDM Experiment'' neutron beamline at the NIST Center for Neutron Research, and have measured the reflectivity of the slotted Si single crystal intended for the experiment. These measurements lay the groundwork for the coming nMDM Schwinger scattering measurement. EA.00009: The Partial Wave Decomposition of the Meson Spectrum Stacy Barker , Dennis Weygand , Gerard Gilfoyle The spectrum of hadrons provides important insight to the low-energy, non-perturbative regime of Quantum Chromodynamics (QCD), the theory of the strong interaction. Meson states are particularly interesting due to their binary structure; most mesons appear to composed of a quark-antiquark pair. However, measurement of the meson spectrum in confounded by the broad and overlapping nature of these states. The technique of partial wave analysis (PWA) has been used to successfully decompose these states from the parameters of their decay in limited kinematic regimes, usually high energy and low momentum transfer. To exploit PWA at low energy, for example at CEBAF, the analysis becomes more compute intensive. Here we report on techniques of PWA in a distributed compute environment, using the CLARA platform, a java-based service oriented architecture (SOA) being developed for the CLAS12 offline analysis environment. EA.00010: Transverse energy at RHIC in the forward/backward directions using the PHENIX Muon Piston Calorimeter Jonathan Ben-Benjamin The status of a measurement of transverse energy $E_T=Esin(\theta)$ in the forward direction ($3.1 < |\eta| < 3.7$) from Au+Au, p+p, and d+Au collisions at RHIC energies using the PHENIX Muon Piston Calorimeter will be reported. Transverse energy has not been measured in this kinematic range at these beam energies before. This result can be used to estimate energy density in heavy ion collisions. In addition, fluctuations in this observable can be used as a signature for a critical point in the phase diagram of nuclear matter. Finally, measurements of transverse energy can be used to discriminate between competing models of hadronic interactions. EA.00011: Effect of Temperature on Niobium Surface Morphology during Buffered Electropolishing Jennifer Beveridge , Andy Wu To achieve high acceleration gradients for particle accelerators based on niobium (Nb) superconducting radiofrequency (SRF) technology, Nb cavity surfaces must be as smooth and as free from imperfections as possible. Presently, removing the imperfect Nb surface layer is performed by buffered chemical polishing (BCP) or electropolishing (EP). Buffered electropolishing (BEP), a method developed at Jefferson Laboratory, has been shown to outperform both BCP and EP in terms of surface smoothness and polishing rate. BEP utilizes HF, H$_{2}$SO$_{4}$, and lactic acid to etch away the damaged Nb surface layer. The mechanism for the Nb removal from the surface was studied, as well as how the Nb surface morphology changed with temperature. BEP was performed on Nb at temperatures between 7\r{ }C and 44\r{ }C and the surface smoothness was evaluated. To investigate the role of lactic acid in BEP, soluble Nb complexes with lactic acid were proposed and an electrolyte consisting of H$_{2}$SO$_{4}$ and lactic acid was used to electropolish Nb. Results indicate that higher temperature during BEP yields faster polishing rates, maximizing near 32\r{ }C, and that a smoother Nb surface can be obtained by polishing between 21\r{ }C and 32\r{ }C. In addition, results suggest lactic acid may form soluble coordination compounds with niobium, aiding HF in Nb removal from the material surface. EA.00012: Parton Cascade Initial Conditions for Event-by-Event Hydrodynamic Modeling at RHIC Vivek Bhattacharya , Hannah Petersen , Steffen Bass Relativistic heavy-ion collisions at RHIC are believed to have replicated the state of the early universe by creating a quark- gluon plasma, a deconfined phase of QCD. One of the most interesting findings at RHIC is that the QGP behaves like a near-ideal fluid. As a result, hydrodynamic calculations are used to model the evolution of the QGP, but recent work shows that these calculations are very sensitive to initial conditions (ICs). Common Glauber and Color Glass Condensate ICs are calculated at the start of the collision and do not treat the pre-equilibrium evolution of the system. Here, we improve upon these ICs by employing a Parton Cascade Model, used to describe the evolution of a deconfined system during the early pre-equilibrium phase of the reaction, to accurately evolve the system from the start of the collision to the beginning of hydrodynamic evolution. Furthermore, we adopt a Gaussian smoothing framework to create event-by-event as well as event- averaged ICs. We present various ICs and study the results generated by this hybrid PCM/hydrodynamic model in terms of both average quantities and event-by-event fluctuations. EA.00013: Construction of a Variable Degrader for Optimization of $^{8}$Li in Beta-Neutrino Correlation Experiments J. Boulding , K.S. Sharma , R.E. Segel , N.D. Scielzo , G. Li , F. Buchinger , J.A. Clark , G. Savard Information about neutrinos is difficult to attain due to their very low interaction rate with matter. However, we can reverse engineer this information using kinematical reconstruction of the decay process. Using an 18 MeV $^{7}$Li beam striking a $^{2}$H gas target, a product beam of $^{8}$Li is created. A beam stop stops the primary $^{7}$Li beam and the $^{8}$Li beam travels through a variable degrader and a large solenoid into a helium gas catcher. Lithium hydroxide is extracted and moved down the beamline into a 2.5 T Isobar separator magnet. Applied radiofrequency fields break the LiOH to $^{8}$Li, which is then delivered to the Beta-decay Paul Trap. Double sided silicon strip detectors are used to detect the beta and double alpha decays inside the trap. Info about the direction and energy of the alpha and beta particle can be used to determine the direction and momentum of the $^{8}$Li atom and the neutrino released during the decay. Previous experiments were designed to optimize the yield of $^{8}$L and resulted in a beta-alpha-alpha coincidence rate of 1 per second. The addition of the variable degrader to the experimental setup increased yields by approximately 30\%. Supported by: NSERC, Argonne National Lab and the University of Manitoba. EA.00014: Investigating Parton Energy Loss and Antishadowing in Nuclei at Fermilab E-906/SeaQuest Brandon Bowen Fermilab E-906/SeaQuest is a fixed target experiment using Fermilab's Main Injector optimized to detect muon pairs produced in 120 GeV proton collisions. Primarily, SeaQuest will measure the Drell-Yan di-muon cross sections for proton-proton and proton- deuterium collisions for extracting $\bar{d}$ to $\bar{u}$ asymmetry in the nucleon. This data will also be used to understand partonic energy loss in cold nuclear matter, which will aid in understanding partonic energy loss in hot nuclear matter experiments at the LHC and RHIC. Since parton energy loss is inversely proportional to the beam energy, SeaQuest will be much more sensitive to energy loss effects than Fermilab E-866/NuSea, which placed upper limits on such parton energy loss at 800 GeV. SeaQuest will also further our understanding of nuclear anti- shadowing and extend the Drell-Yan measurements into the EMC effect region. SeaQuest will have significantly better precision and extension over a higher range in Bjorken-x, where competing asymmetry models diverge strongly from each other. EA.00015: Background Reduction Techniques for Ultra-low Background Physics Michael Brown , Reyco Henning , Sean MacMullin Background reduction receives much attention in neutrino studies and dark matter searches as the events being detected are extremely rare. Knowing your backgrounds well and using extremely low radioactive materials in production are two methods used in such experiments. At the Triangle Universities Nuclear Laboratory the neutron cross section for neon, a candidate material for detecting dark matter, was investigated using energies relevant to backgrounds in these experiments. Also a Monte Carlo simulation was run using MCNPX to determine the best shielding material for keeping detector materials from being activated by high energy cosmic rays. Methods and results for the experiment and simulation will be presented. EA.00016: Development of a Beam Intensity Detector Justin Browne , Wolfgang Mittig The Active Target Time Projection Chamber (AT-TPC) at Michigan State University (MSU) will be filled with a gas that is used as both the target and the detector. To determine the intensity of the beam as it enters the chamber, a detector must be placed immediately upstream of the AT-TPC. The beam intensity is measured by passing the beam through a foil and measuring the amount of ionization in the foil. Because the signal from the primary electrons would be too weak, the electrons are multiplied in a Multichannel Plate (MCP) detector. The electrons are transported out of the beam path to the MCP by electric and magnetic fields. EA.00017: Computer Code for Calculating Matrix Elements and Overlaps of States for the Generalized Seniority Scheme via Recurrence Relations Ke Cai , Mark Caprio , Fengqiao Luo The generalized seniority approximation provides a truncation scheme for the nuclear shell model based on building the states of the nucleus from nucleon pairs. We developed a computer code to calculate matrix elements of one-body and two-body operators between generalized seniority states and overlaps of these states based on a set of recurrence relations. The main steps in our implementation of the computer code consisted of: (1) Developing an object-oriented framework for storing information on generalized seniority states; (2) Applying the symmetries of the problem and caching intermediate results to avoid repeated calculations; (3) Performing extensive validations. The code can be used to calculate matrix elements of operators of physical interest, e.g., the Hamiltonian and electromagnetic transition operators. Planned applications of the code include testing the structure of nucleon pairs and studying the mapping of shell model onto the Interacting Boson Model. Supported by the US DOE under grant DE-FG02-95ER-40934. EA.00018: Development of a Computing Cluster At the University of Richmond J. Carbonneau , G.P. Gilfoyle , E.F. Bunn The University of Richmond has developed a computing cluster to support the massive simulation and data analysis requirements for programs in intermediate-energy nuclear physics, and cosmology. It is a 20-node, 240-core system running Red Hat Enterprise Linux 5. We have built and installed the physics software packages (Geant4, gemc, MADmap...) and developed shell and Perl scripts for running those programs on the remote nodes. The system has a theoretical processing peak of about 2500 GFLOPS. Testing with the High Performance Linpack (HPL) benchmarking program (one of the standard benchmarks used by the TOP500 list of fastest supercomputers) resulted in speeds of over 900 GFLOPS. The difference between the maximum and measured speeds is due to limitations in the communication speed among the nodes; creating a bottleneck for large memory problems. As HPL sends data between nodes, the gigabit Ethernet connection cannot keep up with the processing power. We will show how both the theoretical and actual performance of the cluster compares with other current and past clusters, as well as the cost per GFLOP. We will also examine the scaling of the performance when distributed to increasing numbers of nodes. EA.00019: Measurement of the 187Re(n,2n)186mRe Destruction Cross-section C.R. Casarella , J.H. Kelley , R. Raut , C. Howell , G. Rusev , A.P. Tonchev , E. Kwan , W. Tornow , H.J. Karwowski , S.L. Hammond , F.G. Kondev , S. Zhu We are continuing a program to measure cross sections for $^{187}$Re(n,2n$\gamma$) reactions with particular interest in confirming a transition that has tentatively been identified as a doorway transition feeding the $^{186}$Re E$_x$=149(7)~keV isomeric state. The cross sections are being measured using pulsed, nearly mono-energetic neutron beams, as well as an array of planar HPGe $\gamma$-ray detectors. At present, the reaction cross sections for $^{187}$Re(n,2n$\gamma$) are poorly known, so measuring the cross sections have positive implications, for example, on reactor physics since Re is a common fission fragment. Furthermore, refining the cross section measurements may reduce uncertainties in the Re/Os cosmochronometer. Funding provided by NSF grant NSF-PHY-08-51813. EA.00020: Investigation of even-even Gd nuclei using the (p, t) reaction Danyi Chen , Con Beausang , Richard Hughes , Timothy Ross , Jack Shaw , Benjamin Pauerstein Gadolinium nuclei between A=152 and A=158 undergo a rapid shape change, from spherical to deformed and are therefore interesting in nuclear physics studies. Experiments were performed at the 88 inch Cyclotron at Lawrence Berkeley National Laboratory using the STARS (Si-Telescope Array for Reaction Studies)/ Liberace (Livermore Berkeley Array for Collaborative Experiments) setup. Targets of 154Gd, 155Gd, 156Gd, and 158Gd were bombarded with 25 MeV protons. My research focused on 152Gd, 154Gd, 156Gd nuclei populated via (p, t) reactions and the work utilized a triton-gamma matrix for each nucleus. I am interested in the high energy ($\ge$2.5MeV nucleus excitation energy) part of the triton spectrum when gated by different low lying (yrast and non-yrast) gamma rays which I examined by measuring the slope. I also studied the position and intensity of the large peak-like structure lying close to the pair gap at 2.5 MeV and how it changes for N = 88, 90, and 92. DOE: DE-FG02-05 ER41379 {\&} DE-FG52-06 NA26206 (UR), DE-AC52 -7NA27344 (LLNL), and DE-AC02-05CH11231 (LBNL). EA.00021: Performance of Object-Oriented Real-Time Control and Acquisition Software Andrew Collins The dead-time of the Object-oriented Real-time Control and Aqcuisition data acquisition software, \textsc{orca}, was quantitatively determined for a VME-based system utilizing a single, peak-sensing CAEN 785N analog-to-digital converter and two scaler modules. A single board computer in the VME crate controls rapid read-out of the modules and the data is then transferred via TCP/IP to the \textsc{orca} control program, running on MacOSX, where the data can be filtered based on desired criteria, saved in an open format, and displayed on-line in histograms. A graphical interface allows the system to be configured via drag and drop'' method. The performance tests were performed on \textsc{orca} and two other data acquisition systems used at Triangle Universities Nuclear Laboratory, \textsc{coda} and SpecTcl, to compare the systems' data collection capabilities and determine whether the new system is a worthy competitor of the existing systems. EA.00022: High Speed Readout of the Cathode Signal for the NIFFTE TPC Brandon Coombes The goal of the Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) is to use a Time Projection Chamber (TPC) to improve the precision of the measurements of the major actinides cross sections. To make these high precision cross section measurements, the start time of each fission event needs to be determined from the TPC cathode with less than 1ns resolution. High speed readout of the cathode signal allows the longitudinal postion of the fission fragment track to be more accurately reconstructed. The current readout TDCs give about 20ns timing resolution. To improve the timing resolution, a new scheme was developed where the cathode signal is split and allowed to propagate through delay lines of different lengths. Then all of the signals are analyzed to better determine the start time. This poster will concentrate on the design and testing done to improve the timing resolution and how this will improve the quality of track reconstruction of these fission events. EA.00023: $\alpha$-Clusters in $^{16}$O P.A. Copp , S.R. Lesher , A. Aprahamian , S. Almaraz , B. Bucher , M. Couder , X. Fang , F. Jung , W. Lu , N. Paul , A. Roberts , W.P. Tan , G. Golding , Y. Scachar , N. Ashwood , M. Barr , N. Curtis , M. Freer , J. Malcolm , C. Wheldon , V. Ziman There has been previous experimental evidence of an interesting four $\alpha$ linear configuration in $^{16}$O [1]. At the Notre Dame FN Tandem Accelerator we explored the reaction of $^ {12}$C+$\alpha$$\rightarrow$$^{16}$O$\rightarrow$$^{8}$Be+$^{8}$Be. An array of Si strip detectors was set up at the forward angles to observe the final individual four $\alpha$- particles [2]. Afterwards, from the $^{8}$Be+$^{8}$Be channel, an excitation curve was constructed for an energy range of 12- 20 Mev. In addition a $^{12}$C ($\alpha,n$) transfer reaction was carried out to study the same $\alpha$-cluster structure in $^{16}$O, which required additional neutron detectors placed at the backward angles. Interesting $\alpha$-cluster levels detected in the two reactions will be analyzed in detail (such as the angular distribution). The preliminary results on the existence of the linear $\alpha$ structure will be presented.\\[4pt] [1] P. Chevallier {\it et al.}, Phys. Rev. {\bf 160}, 827 (1967).\\[0pt] [2] P.J. Haigh {\it et al.}, J. Phys. G: Nucl. Part. Phys. {\bf 37}, 035103 (2010). EA.00024: Verification of 3D Dose Distributions of a Beta-Emitting Radionuclide Using PRESAGE$^{\mbox{{\textregistered}}}$ Dosimeters Mandi Crowder , Ryan Grant , Geoff Ibbott , Richard Wendt Liquid Brachytherapy involves the direct administration of a beta-emitting radioactive solution into the selected tissue. The solution does not migrate from the injection point and uses the limited range of beta particles to produce a three-dimensional dose distribution. We simulated distributions by beta-dose kernels and validated those estimates by irradiating PRESAGE$^{\mbox{{\textregistered}}}$ polyurethane dosimeters that measure the three-dimensional dose distributions by a change in optical density that is proportional to dose. The dosimeters were injected with internal beta-emitting radionuclide yttrium-90, exposed for 5.75 days, imaged with optical tomography, and analyzed with radiotherapy software. Dosimeters irradiated with an electron beam to 2 or 3 Gy were used for calibration. The shapes and dose distributions in the PRESAGE$^{\mbox{{\textregistered}}}$ dosimeters were consistent with the predicted dose kernels. Our experiments have laid the groundwork for future application to individualized patient therapy by ultimately designing a treatment plan that conforms to the shape of any appropriate tumor. EA.00025: UCN Production from Solid Oxygen Confined in Amorphous Carbon Chris Cude-Woods , Chen-Yu Liu , Daniel Salvat , Gregory Manus , Aaron Couture The utility of Ultra-Cold Neutrons (UCN) in fundamental physics has been constrained by the difficulty of producing them in sufficiently high density. This has led to an interest in the development of improved UCN sources. Solid oxygen has shown promise over previous super-thermal sources as a UCN converter and has several advantages, including small nuclear absorption, unique magnetic properties, and lack of incoherent scattering. Our group's previous work has demonstrated a prototype bulk solid oxygen converter and an apparatus to study its performance as a function of temperature. Using a slightly modified apparatus--benchmarked with bulk solid oxygen-- our present study tests a new source that~confines oxygen within a carbon nano-pore'' matrix. By freezing oxygen in confinement, we seek to suppress the~$\alpha$ to $\beta$ phase transition, thus extending the higher production cross-section of $\beta$-oxygen to lower temperatures, thereby increasing UCN~yield. We have carried out a UCN production experiment at FP12 at Lujan Neutron Center at Los Alamos National Laboratory in the summer of 2010. The results of the analysis and simulation will be presented in this poster. EA.00026: Gadolinium Doped Water Cherenkov Detector for use as Neutron Detector Patrick Davis , Brian Woltman , Dongming Mei , Yongchen Sun , Keenan Thomas , Oleg Perevozchikov Background characterization is imperative to the success of rare event physics research such as neutrinoless double-beta decay and dark matter searches. There are a number of different ways to measure backgrounds from muon-induced processes and other forms of high energy events. In our current research, we are constructing a research and development project for the feasibility of a Gadolinium doped water Cherenkov detector as a neutron detector. We are constructing a 46 liter acrylic housing for the Gd-doped water consisting of two acrylic cone sections connected to a middle acrylic cylinder to increase volume while still using 5 inch photo multiplier tubes (PMTs) on either end. I will present the challenges of a Gd-doped water detector and the reasons why our design should be much more successful than past metal housed detectors. I will also discuss our current progress and future goals of our detector including its use in characterizing the background in the future underground laboratory in the Sanford Lab, soon to be DUSEL. EA.00027: CdWO$_{4}$ and CsI Crystal Detectors Alyssa Day , Dongming Mei , Yongchen Sun , Keenan Thomas , Oleg Perevozchikov CdWO$_{4}$ scintillators were proposed for detecting geo-neutrino, neutrinoless double-beta decay, and dark matter. I used the energy resolution of three different sized CdWO$_{4}$ crystals for detecting $\gamma$-rays. The three crystals had diameters of 19mm but thicknesses of 5mm, 9mm, and 19mm. In using the 19mm CdWO$_{4}$ crystal, the energy resolution of a $^{137}$Cs source resulted in 11.4{\%} at 662 keV, and 6.5{\%} at 1173.2 keV and 8.6{\%} at 1332.5 keV for $^{60}$Co. As the sizes of the thickness decreases, a slight deterioration in energy resolution occurred with more Compton scattering in the energy spectrum. A CsI(Tl) crystal was also used for comparison; this crystal was 19mm in thicknesses and length. This crystal had an energy resolution for $^{137}$Cs of 12.3{\%} at 662 keV, 5.3{\%} at 1173.2 keV and 6.6{\%} at 1332.5 keV for $^{60}$Co. The CsI(Tl) crystal capable of measuring low energies in which x-ray peaks were visible with some sources. The CdWO$_{4}$ crystal was more beneficial when measuring gamma-ray energy close to 511 keV that is primary signature from geo-neutrino detection with $^{106}$Cd. Greater Compton scattering occurred with the CsI crystal when detecting higher energies. Using a number of smaller crystals allows for the development and characterization of these crystals. EA.00028: PIXE Spectrometry for Sediment Characterization Katherine DeBlasio , Daniel Pesch This project focuses on the non-point source sedimentation and hypereutrophication problems plaguing Lake Macatawa, Holland, MI. Excess nutrients, such as phosphates, attached to sediments, flow into the lake from the surrounding watershed increasing both the lake's turbidity and nutrient imbalance. The goal is to identify signatures representative of unique locations within the watershed to aid in the determination of sediment provenance and effectively allow for the modeling of this non-point source pollution as multiple point sources of the sediments and their adsorbed nutrients. This is accomplished by characterizing sediment with Particle Induced X-Ray Emission (PIXE) spectrometry. Eighteen different elemental concentrations in sediment samples are measured via PIXE. These concentrations are compared between sites and rain events to find trends in the changes of concentrations of the metals that will help characterize the sediment source. EA.00029: A study of Jet Quenching near the QCD Phase Transition Andrea Delgado , Rainer Fries , Ricardo Rodriguez We study the dependence of jet quenching in quark gluon plasma on the local density of the plasma. Liao and Shuryak* have previously suggested that quenching reaches a maximum for entropy densities around the QCD phase transition. This shell-like'' quenching scenario seems to be favored by the large azimuthal asymmetry v$_{2 }$for large momentum hadrons measured at the Relativistic Heavy Ion Collider (RHIC). Our calculations confirm the results by Liao and Shuryak qualitatively, and describe RHIC data on the nuclear suppression factor R$_{AA}$ and v$_{2}$ simultaneously quite well. We then extrapolate to nuclear collisions at the Large Hadron Collider (LHC) using the same density dependence that fits RHIC data. We show that shell-like'' quenching gives unique predictions for R$_{AA}$ and v$_{2}$ at LHC. Data from LHC will hence help us to distinguish between different scenarios for the density dependence of jet quenching. *Phys. Rev. Lett. 102,202302(2009) EA.00030: A Novel Time of Flight Detector for the Pioneering High Energy Nuclear Interaction eXperiment Richard Dix , Kirk Drummond , William Powell , Mickey Chiu Time-of Flight (TOF) detectors allow one to identify particles created in collider experiments. The Pioneering High Energy Nuclear Interaction eXperiment (PHENIX) at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory is proposing new forward timing detectors to measure the TOF with a 10 picosecond (ps) timing resolution. A prototype of the detector electronics system was tested by using Cherenkov signals from cosmic rays and translating them into digital signals. Each signal was split and delivered to two analog-to-digital-converters (ADCs). C++ and ROOT were used to write programs to compare voltage readings reported by the two ADC channels and determine the time difference between them, which was 76 ps. Using new ADCs, which run 17 times faster, the timing resolution will be 5 ps. This will allow PHENIX to probe the meson-baryon anomaly at intermediate, transverse momentum by making detailed measurements in a psuedorapidity region which has not been well measured. EA.00031: Increased Precision of $^{3}$He target's Polarization Determination Through LabView Automated EPR Measurement for Nulcear Physics Experiments Jessica Doehrmann , G. Laskaris , H. Gao , Q. Ye , W. Zheng , T. Averett , G.D. Cates , W.A. Tobias Polarized $^{3}$He is used as an effective neutron target in the GDH sum rule, Compton scattering and 3-body photodisintegration experiments. These experiments have been carried out to determine the GDH integral on $^{3}$He from the two-body breakup threshold to the pion production threshold as well as nucleon spin polarizablities and asymmetries. The polarization of the $^{3}$He target is measured through NMR and EPR measurements. To reduce the uncertainties in asymmetries and nucleon spin polarizablities, it is necessary to increase the precision in the measurement of $^{3}$He polarization. In order to achieve this goal, the EPR measurement process was automated by LabView, controlling the electronic instruments through GPIB interface. The calculated $^{3}$He polarization using the LabView program is consistent with the results obtained from NMR water calibration measurements. EA.00032: Analysis of Electronic Noise in the Majorana Dark Matter Detector Greg Dooley The Majorana Experiment seeks to detect neutrinoless double beta decay of $^{76}$Ge with an array of customized ultra pure germanium detectors. It will simultaneously operate in a search for dark matter through direct detection of nuclear recoils with particles in a DM halo. Its ultimate DM goal is to probe down to masses of $<$1 KeV/c$^2$ in a 120 kg Ge detector. Rather than distinguish between nuclear and electron recoil events, the detector will achieve such high sensitivity through extreme reduction of noise and background. Background radiation will be blocked by deploying the device deep underground in the Sanford Underground Laboratory in Lead, SD. Limitations on and methods to reduce electronic noise are explored in this project. The frequency response and total noise of each component is modeled using SPICE. Raw electronic noise signals are taken from the Cogent detector and resolved into series, parallel, and 1/f noise. This procedure is used to help identify ways to improve novel pre-amplifier designs and optimize pulse shaping parameters. It is also used to produce accurate simulations of noise to aid in pulse shape analysis. EA.00033: Impact of Temperature Changes on Drift Properties in a Straw Tube Chamber Brent Driscoll The GlueX experiment at Jefferson Lab will use a straw-tube chamber as part of its charged particle tracking package. This chamber, the CDC, will measure the coordinate of tracks perpendicular to the anode wire to an accuracy of 150 microns, and while the temperature in the experimental hall will be monitored, it will be necessary to account for the impact of temperature changes on the drift properties of the gas being used in the chamber. A study has been performed to map out these properties as a function of temperature in a small prototype chamber at Carnegie Mellon. Cosmic rays have been studied with the chamber operated in the temperature range of 20 to 34 C. These temperature variations have led to measured changes in both the gas and the performance of the electronics. The results will be compared to calculations of the expected behavior and ultimately used in the calibration of the CDC in the running GlueX experiment. I will present details of the test setup, the measurements and the analysis of the data as well as a comparison to the expectations. EA.00034: The Gas Handling System Assembly for the NIFFTE TPC Dana Duke The Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) uses a Time Projection Chamber (TPC) to obtain more accurate measurements of the fission cross sections of radioactive isotopes such as Pu-239, U-235, U-238, etc. Past cross-section measurements have used various detection methods such as the parallel plate ionization chamber, but by using a TPC, accuracy levels can be improved to sub 1{\%} error. Analysis of TPC data will improve the current understanding of fission dynamics and the fission process. The NIFFTE TPC is located at the 90L beam line at LANSCE-WNR where targets are bombarded with fast neutrons to induce fission. The resulting fission fragments are tracked using gas ionization within the TPC. Gas handling system function and assembly is examined and justified. Major components of the system include solenoid valves, pressure transducers, and mass flow controllers. This gas handling system has the capability of remotely controlling the flow of multiple gas sources into the TPC. EA.00035: Constructing the Hodoscope Arrays for the Fermilab E-906/SeaQuest Spectrometer Brianna Edlund SeaQuest is a fixed-target experiment designed to extract the light antiquark sea structure of the proton at high Bjorken-x. Using 120 GeV/c protons from the Fermilab Main Injector, the experiment will measure the cross section ratio of di-muon pairs produced by the Drell-Yan process with liquid hydrogen and deuterium targets. From this ratio the light antiquark ratio will be extracted. The trigger for the di-muon pairs uses a set of 8 hodoscope planes, the final four of which are the topic of this work. The final four hodoscope planes consist of 128 scintillator paddles and 224 photomultiplier tubes (PMTs). Due to their size, three planes require PMTs on each scintillator end to avoid timing jitter. SeaQuest uses the old PMTs and tube bases from E866/NuSea, plus other experiments, so it was critical to verify the performance of each PMT and base. These tests included operating voltages, noise rates, and rate capability. The methods used will be presented as well as how the results were used to optimize efficiency in the spectrometer's expected high-rate regions. EA.00036: Method Development of Detecting PeV Gamma Rays Using the IceCube Observatory Maxim Egorov We present a method of detecting PeV gamma rays from the Galactic Plane using the IceCube Observatory. IceCube is a cubic km scale Cherenkov ice detector located $\sim$1.4 km under the ice at the geographic South Pole, with a sister component IceTop, a surface air shower array, located directly above it. By selecting extensive air shower (EAS) events with a shower axis that passes through both IceTop and IceCube, it is possible to distinguish CR from gamma ray EAS by their muon content. CORSIKA Monte Carlo simulations of both EAS types are used to develop and test the best cuts for gamma ray and CR separation. All muon-rich EAS are eliminated by cutting out events that trigger IceCube, suppressing the background to consists of muon-poor CR EAS, while falsely rejecting $\sim$20{\%} of the gamma ray signal. We improve the method by separating the remaining $\sim$20{\%} of gamma ray signal from the CR background by analyzing three types of cuts: rectangular, Fisher Discriminant, and Multilayer perceptron (MLP). With the emaining $\sim$20{\%} of gamma ray EAS, the MLP cut is found to give the best results yielding 33.6{\%} signal efficiency for 99.997{\%} background rejection. Overall, MLP improves signal efficiency to $\sim$86.6{\%}. EA.00037: Investigating the fragmentation of excited nuclear systems Jennifer Erchinger , L.W. May , P. Marini , S. Wuenschel , S.J. Yennello Constraints on the symmetry energy, important in the nuclear equation of state, can be provided by examining the isotopic composition of fragments emitted from excited nuclear systems. These fragments can be studied by isotopic scaling (isoscaling) of fragment yields from two sources with different neutron to proton ratios (N/Z). Traditionally, isoscaling compares isotopically identified fragments from two different reactions, requiring an assumption that the N/Z of the source is that of the reacting system or estimated from a model-based correction. Wuenschel \textit{et al.} used emitted charged particles and neutrons to reconstruct quasiprojectile (QP) N/Z. Bins in QP N/Z were used as the sources for the isoscaling analysis instead of different reaction systems. They showed that comparing bins within a system better defines the source N/Z, giving better constrained symmetry energy. The current research takes an in-depth look at bin-to-bin isoscaling and provides optimal delta and source constraints and shows the effects of excitation energy on isoscaling. EA.00038: The Ursinus College Liquid Hydrogen Target Nicholas Ferrante , Jessica Palardy , Lew Riley , Remco Zegers A liquid hydrogen target has been constructed and tested for use in experiments at the National Superconducting Cyclotron Laboratory at Michigan State University. The design is based upon the Japanese liquid hydrogen and deuterium target at RIKEN in Japan. This target will provide a pure hydrogen target with greater proton density than and without the carbon background of polypropylene targets. Characteristics of the target as well as prospects for its use are discussed. EA.00039: Calibration of CsI Detectors for the NPDG Experiment Charles Fieseler , Septimiu Balascuta , David Bowman , Chris Crawford , Nadia Fomin , Kyle Grammer , Andrew McNamara , Seppo Pentilla The NPDGamma experiment at Oak Ridge National Lab will measure the asymmetry in gamma production in the reaction: neutron + proton -$>$ deuteron + gamma. The parity violating component of this reaction is measured from the correlation of neutron spin and $\gamma$ momentum. In order to detect this asymmetry, 48 cesium iodide scintillators are arranged in a cylinder around a liquid parahydrogen target in a beam of polarized neutrons. The detector efficiency was calibrated using a rotating Cs$^{137}$ source of known intensity. The output voltage output as a function of the rotation angle was fit using a Fourier series expansion plus a linear background term. The amplitude was the ratio of signal to energy deposited in V/MeV/s, essentially an efficiency for each detector. The calibration procedure will be presented, as well as the complete data analysis. Supported by NSF under grant PHY-0855584. EA.00040: Development of an Active Target Time Projection Chamber for Nuclear Reaction Studies with Radioactive Isotope Beams Michael Ford , Daniel Bazin , William Lynch , Wolfgang Mittig , Daisuke Suzuki An Active Target Time Projection Chamber (AT-TPC) is being developed at the NSCL. This new detector uses the gas of a time projection chamber as an active target, providing powerful new capabilities for studying reactions induced by radioactive rare isotope beams. The detector design encompasses a dual gas system, providing one gas optimized for electrical isolation of the field cage and another that serves as the target. For versatile use of targets, the detector should operate with a wide range of target gasses including H$_{2}$, D$_{2}$, $^{3,4}$He and Ne at pressures ranging from .2 to 1.0 atm and electric fields up to 1 kV/cm. Gas amplification and signal detection will be achieved with planar Micromegas structures mounted at the end of the gas detector volume. The Micromegas anode plane will be segmented into approximately 10,000 pads and read out by GET advanced active target electronics that are being developed in collaboration with French and Japanese institutes. I will be presenting the current status of the research and development of the AT-TPC and its prototype. EA.00041: Deuteron Formation for Big Bang Nucleosynthesis Models Jennifer French , Katrina Koehler , June Matthews , Brian Daub , Mark Yuly , Stephen Wender , Vlad Henzl , Mike Kovash A measurement of the H(n, d$\gamma )$ cross section at low energy is being performed at the WNR facility at Los Alamos National Laboratory. This deuteron formation experiment is key to improving calculations of the baryon density in Big Bang Nucleosynthesis models. Incident neutron energies are between 100 keV and 1 MeV. The deuterons are created and detected in a plastic scintillator active target. Gamma rays released by the neutron-proton capture reaction are detected in a BrilLanCe detector. Scattered neutrons from n-p elastic scattering detected in two neutron detectors are used for calibrating the active target ADC spectrum. EA.00042: Improvements to Proton-Carbon Polarimetry at RHIC Kyle Gainey The Relativistic Heavy Ion Collider (RHIC) complex at Brookhaven National Lab provides a beam of up to 70\% polarized protons for study of polarized proton collisions to better understand proton spin structure. The RHIC polarimetry group operates and maintains Proton-Carbon (pC) polarimeters which measure the spin of the protons by running a 10$\mu$m wide carbon strip through the beam, detecting recoiling carbon atoms, and calculating the asymmetry in the carbon recoil. This asymmetry is directly proportional to the beam polarization. The carbon strips are made by evaporating carbon with an electron beam. This method produces targets with very limited lifetimes. An advanced method is being developed to lengthen target lifetimes. The laser plasma ablation (LPA) method offers carbon strip targets whose atoms are more isotropically distributed, resulting in a more durable target. With LPA, a laser is pulsed at a carbon disk, the carbon atoms on the surface of the disk become a plasma, and the atoms condense on a slide, forming strips. This poster will focus on RHIC pC polarimetry and the LPA method of making carbon strip targets. EA.00043: Particle-Induced X-Ray Emission Analysis of Atmospheric Aerosols Colin Gleason , Charles Harrington , Katie Schuff , Maria Battaglia , Robert Moore , Colin Turley , Michael Vineyard , Scott LaBrake We are developing a research program in ion-beam analysis (IBA) of atmospheric aerosols at the Union College Ion-Beam Analysis Laboratory to study the transport, transformation, and effects of airborne pollution in Upstate New York. The simultaneous applications of the IBA techniques of particle-induced X-ray emission (PIXE), Rutherford back-scattering spectrometry (RBS), particle-induced gamma-ray emission (PIGE), and proton elastic scattering analysis (PESA) is a powerful tool for the study of airborne pollution because they are non-destructive and provide quantitative information on nearly all elements of the periodic table. PIXE is the main IBA technique because it is able to detect nearly all elements from Na to U with high sensitivities and low detection limits. The aerosol samples are collected with cascade impactors that allow for the study of particulate matter as a function of particle size and the samples are analyzed using proton beams with energies around 2 MeV from the Union College 1.1-MV Pelletron Accelerator. The emitted X-rays are measured using a silicon drift detector with a resolution of 136 eV. We will describe how the aerosol samples were collected, discuss the PIXE analysis, and present preliminary results. EA.00044: Waiting Points and Bottlenecks in Nova and X-ray Burst Nucleosynthesis Leah Goldberg At Oak Ridge National Laboratory, we are investigating nucleosynthesis in nova explosions and X-ray bursts, specifically at waiting points'' and bottlenecks'' -- unusual phenomenon in which nuclei interrupt the sequence of thermonuclear reactions that form heavier elements from lighter ones, significantly affecting the final abundances and the energy generation rate in stellar explosions. Nuclei identified as waiting points or bottlenecks seem to play a more important role in explosions and need to be singled out for further investigation. Such points are defined by a series of acceptance and rejection tests in a simulation, Computational Infrastructure for Nuclear Astrophysics (CINA), in which a suite of codes visualizes nucleosynthesis over a specified time interval and allows us, for each nucleus, to consider eight surrounding nuclei in the Z=N plane based on possible reaction paths in the rp-process. After considering abundance, lifetime and reaction flux, reaction rate, and reaction Q-value, we accept or reject accordingly, and can then better ascertain the relationship between waiting points and bottlenecks and nuclear flow. EA.00045: Program for Simulating Energy Spectra in Transfer Reaction Studies S.A. Graves , R.L. Kozub , J.L. Wheeler , D.W. Bardayan Studies of exotic nuclei with transfer reactions are important for nuclear structure studies and for many astrophysical applications such as understanding stellar explosions, the nuclear synthesis of lighter elements, and experimentally determining stellar reaction rates. However, the energy spectra from such reactions are sometimes counter intuitive and difficult to interpret. A FORTRAN program has been created to aid in visualizing the expected energy spectra of detected particles for any reaction having two particles in the exit channel. The user provides information about the reaction, the incident beam energy, and the angle of interest. The program produces a visual spectrum using nuclear databases, an existing kinematics code (RELKIN2), and the Xmgrace graphing software. The user is able to display multiple energy spectra so that the effect of various target components can be estimated. An example experimental setup and the output of this program will be presented. EA.00046: Precision Target Mass Monitoring in the Antineutrino Detectors of the Daya Bay Reactor $\theta_{13}$ Experiment Alexander Green The Daya Bay Reactor Neutrino Experiment is designed to measure the neutrino mixing angle $\theta_{13}$ with a sensitivity of $sin^22\theta_{13} < 0.01$. The experiment consists of eight cylindrical antineutrino detectors filled with 20 tons of gadolinium-doped liquid scintillator as the target medium, surrounded by liquid scintillator and mineral oil. One of the dominant systematic errors of the measurement is the uncertainty of the detector target mass. To achieve the experimental sensitivity the detector target mass will be measured to better than 0.1\%. A network of sensors is being developed, which will be mounted in the antineutrino detectors to monitor the liquids inside the detector during data taking with high precision. This instrumentation consists of temperature sensors, inclinometers, capacitance liquid level sensors and ultrasonic liquid level sensors on an RS-485 network. We report on the design, fabrication and testing of this instrumentation system and its integration into the experiment's flow control system. EA.00047: Assembly and Testing of the CUORE Calibration System Ian Guinn The Cryogenic Underground Observatory for Rare Events (CUORE) will search for neutrinoless double beta decay ($0\nu\beta\beta$) of $\rm ^{130}Te$. The observation of this decay would determine that neutrinos are of Majorana type, that is their own anti-particle. An array of natural $\rm Te0_{2}$ bolometers, operated at 10\,mK in order to minimize background radiation, will act as source and detector for this experiment. Since the extraction of the signal is based on energy information only, a precise calibration of the bolometers is extremely important. To calibrate the detectors, twelve strings with radioactive sources will be periodically lowered by motors through guide tubes into precise positions within the cryostat. The sources must be lowered carefully to avoid fricional heating and vibrations that may disrupt the calibration, so encoders, proximity sensors and load cells will be used to constantly monitor the status of each source as they are deployed. Furthermore, the source carriers have to be cooled to 4K to meet heat load requirements of the detector array, using a newly developed thermalization mechanism. This poster will describe testing of a prototype of the calibration system for CUORE and the development of the software control system. EA.00048: Novel Method of Storing and Reconstructing Events at Fermilab E-906/SeaQuest Using a MySQL Database Tyler Hague Fermilab E-906/SeaQuest is a fixed target experiment at Fermi National Accelerator Laboratory. We are investigating the antiquark asymmetry in the nucleon sea. By examining the ratio of the Drell- Yan cross sections of proton-proton and proton-deuterium collisions we can determine the asymmetry ratio. An essential feature in the development of the analysis software is to update the event reconstruction to modern software tools. We are doing this in a unique way by doing a majority of the calculations within an SQL database. Using a MySQL database allows us to take advantage of off-the-shelf software without sacrificing ROOT compatibility and avoid network bottlenecks with server-side data selection. Using our raw data we create stubs, or partial tracks, at each station which are pieced together to create full tracks. Our reconstruction process uses dynamically created SQL statements to analyze the data. These SQL statements create tables that contain the final reconstructed tracks as well as intermediate values. This poster will explain the reconstruction process and how it is being implemented. EA.00049: Study of the Helicity Dependent Parton Densities for the Electron-Ion Collider Caitlin Harper The Electron-Ion Collider (EIC) is currently being designed and one potential location could be Brookhaven National Laboratory through adding an electron beam to the Relativistic Heavy Ion Collider. One of the ultimate goals of the EIC is to look into the inner workings of quantum chromodynamics (QCD), the theory of strong interactions. The force that supplies the internal binding of strongly interacting particles is mediated by the exchange of gluons. Since gluons have colored charge they have the ability to interact among themselves, a unique feature of QCD. Upon completion, the EIC will allow us to study momentum and space-time distribution of gluons in nuclei. One specific key measurement at the EIC is to reveal the individual contributions of quarks and gluons to the spin of the proton at lower momentum fractions than have ever been measured at previous experiments. These factors are represented by the spin-dependent structure function g$_{1}$(x, Q$^{2})$, which covers a wide range in energy-scale, Q$^{2}$, and low momentum fractions, x. Further knowledge is attained through the study of deep inelastic scattering and their asymmetries. EA.00050: Ion-Beam Analysis of Airborne Pollution Charles Harrington , Colin Gleason , Katie Schuff , Maria Battaglia , Robert Moore , Colin Turley , Scott LaBrake , Michael Vineyard An undergraduate laboratory research program in ion-beam analysis (IBA) of atmospheric aerosols is being developed to study pollution in the Capitol District and Adirondack Mountains of New York. The IBA techniques applied in this project include proton induced X-ray emission (PIXE), proton induced gamma-ray emission (PIGE), Rutherford backscattering (RBS), and proton elastic scattering analysis (PESA). These methods are well suited for studying air pollution because they are quick, non-destructive, require little to no sample preparation, and capable of investigating microscopic samples. While PIXE spectrometry is used to analyze most elements from silicon to uranium, the other techniques are being applied to measure some of the remaining elements and complement PIXE in the study of aerosols. The airborne particulate matter is collected using nine-stage cascade impactors that separate the particles according to size and the samples are bombarded with proton beams from the Union College 1.1-MV Pelletron Accelerator. The reaction products are measured with SDD X-ray, Ge gamma-ray, and Si surface barrier charged particle detectors. Here we report on the progress we have made on the PIGE, RBS, and PESA analysis of aerosol samples. EA.00051: Neutron-Gamma Discrimination in Emerging Scintillators via Digital Signal Processing T. Harrington , S. Lakshmi , P. Chowdhury In this research, we report the results of neutron/$\gamma$- ray discrimination performed with two newly developed scintillator crystals provided by Radiation Monitoring Devices Inc. capable of both neutron and $\gamma$-ray detection, $Cs_{2} LiLaBr_{6}$ (CLLB) and $Cs_{2}LiYCl_{6}$ (CLYC). Neutron-gamma discrimination was performed by digitizing the pulse waveforms, from a PuBe source enclosed in paraffin, with a 1 GHz Lecroy Digital Oscilloscope. By exploiting the pulse shape differences between neutron and $\gamma$-ray waveforms in these new crystals, the neutron and $\gamma$-ray signals can be distinguished from one another. The Pulse Shape Discrimination method executed through custom software to discriminate between neutron and $\gamma$-ray waveforms will be discussed. The most recent results obtained using the CLYC and CLLB scintillator crystals coupled to a photomultiplier tube, which includes the optimization of the integration windows, will be presented and discussed. EA.00052: Nuclear Resonance Fluorescence on $^{232}$Th Alexander Hill Nuclear resonance fluorescence (NRF) is a potent tool for isotope identification via $\gamma$-ray interrogation. NRF resonances at several energies were observed while irradiating $^{232}$Th with a 2.95 MeV linearly-polarized, quasi-monoenergetic $\gamma$-ray beam at the High Intensity Gamma Source (HI$\gamma$S) at Triangle Universities Nuclear Laboratory. In- and out-of-plane detectors recorded the emitted gamma rays. Statistical methods such as algorithmic background subtraction and signal variance analysis identified and isolated NRF peaks, revealing asymmetries in the emitted spatial distributions of $\gamma$-rays resulting from E1 and M1 transitions. In addition, a method of spectral unfolding for germanium gamma-ray detectors was developed to determine the energy distribution of the incident beam. EA.00053: Betatron Tunes in the Proposed Medium-Energy Electron-Ion Collider at Jefferson Lab Colin Jarvis , Balsa Terzic The future of Jefferson Lab lies within the construction of a Medium-Energy Electron-Ion Collider (MEIC), which is currently in the proposal stage. In a synchrotron collider storage ring, the orbiting beams oscillate transversely in both the horizontal and vertical directions. The frequency of these oscillations is called the \textit{betatron} \textit{tune}. Depending on the design tune of the collider, non-linear beam-beam effects can cause rapid degradation of the beam quality, thus yielding poor luminosity, which is the figure of merit in the MEIC. The non-linear nature of the beam-beam effects poses a serious obstacle to the efficient analysis of potential design tunes. The goal of this research was to find an X and Y betatron tune, or \textit{working point}, which optimizes luminosity performance. Using code developed at Lawrence Berkeley National Lab, particle interactions were numerically simulated. Beginning with a previously known working point, systematic simulations were run to scan the adjacent tunespace. A subsequent working point was discovered that provides a 33 percent increase in theoretical peak luminosity over the current MEIC design. EA.00054: CASCADE and PACE4 calculations for $\beta$ decay population of low-lying levels in 186Pt En En Jiang , Cen Deng Accurate information on the low-lying levels in the intermediate Pt nuclei, to serve as a basis for structural interpretation, is needed to study the transition from coexisting structures in the lighter Pt nuclei to $\gamma$ -soft structure in the heavier Pt nuclei. CASCADE and PACE4 reaction simulation programs were used to find suitable reactions for the production of unstable 186Au in different neutron channels that would allow the measurement of the energies and decay properties of low-lying levels in 186Pt, populated in the $\beta$-decay. The results of our calculations as well as a discussion on why we determined 175Lu (16O, 5n) to be the most efficient reaction, will be presented. EA.00055: Neutron Elastic and Inelastic Scattering Cross Sections for Light and Heavy Nuclei in the 1$\sim$20 MeV region in Geant4 Michael Jones Neutron interrogation of cargo containers provides a non-intrusive means of identifying Special Nuclear Materials (SNM) through their resulting spectra. However, before a Monte-Carlo analysis of an interrogation system can be performed, it is essential to validate and confirm the code's ability to correctly simulate and produce these spectra. Using Geant4, a simulation toolkit developed by CERN, the neutron elastic and inelastic scattering cross-sections for light and heavy nuclei in the 1$\sim$20 MeV region were calculated. Angle integrated cross-sections were obtained by fitting the angular distributions with Legendre polynomial expansions. The results of these calculations were compared with corresponding experimental data. The analysis showed that the simulations consistently underestimated neutron resulting in large discrepancies in the angle integrated cross-sections for heavier nuclei. EA.00056: Neutron Detector Shielding Using Boron and Water Frederick Jung , Andreas Best , Ani Aprahamian , Michael Wiescher There has always been a need to develop better shielding for particle detectors from background radiation. With the development of DUSEL (Deep Underground Science and Engineering Laboratory at Homestake), new opportunities exist to make measurements away from the surface cosmic radiation. Doing measurements underground, coupled with better shielding, allows measurements of reactions that are too weak to observe otherwise. Underground, we can take advantage of thousands of meters of rock to shield detectors from cosmic background radiation. Even this rock can be insufficient, as a naturally occurring radioisotopes found in the rock can yield many kinds of radiation, such as gamma rays, beta rays, alpha particles, neutrons, and other fission products. We are designing and testing a shield made for our proportional neutron detectors made of boron and water. Water is used to slow down, or thermalize, the neutrons. Boron is in turn used to capture the incoming neutrons, due to its large neutron capture cross section. This shield was tested and the data has been analyzed, showing that we can achieve a factor of 63 reduction in the number of neutrons detected. We will also scale down this design so that it can provide background protection to detectors in the Nuclear Structure Laboratory at the University of Notre Dame. EA.00057: A Statistical Model of the Pure Glueball and Glueball Hybrids Meghann Kennedy , Tyler Matossian Glueballs are predicted by QCD and have been sought for years in many experiments. Although there are several candidates, glueballs are difficult to identify because they can decay into quark-antiquark pairs, mesons or other hybrid states. In this study we used the statistical model of Y-J. Zhang et al. to represent the pure glueball as a Fock state expansion in terms of gluons. Assuming detailed balance between states, we calculated a probability of 45.6\% for the two-gluon state and 30.4\% for the three-gluon state; the probability of subsequent states decreased with each additional gluon. The average number of gluons in a glueball was calculated to be 2.91. We represented the hybrid glueball by adding quark-antiquark pairs to the Fock state expansion. The probabilities of hybrid glueball states were calculated to explore state mixing and predict the relative probabilities with which each state can be observed in experiment. EA.00058: Quasielastic Neutron-Induced Deuteron Breakup. Katrina Koehler , Peter Kroening , Jonathon Slye , Jared Turkewitz , Sho Uemura , Vlad Henzl , June Matthews , Steve Wender , Mark Yuly An experiment to measure the quasielastic d(n,np)n scattering cross-section was conducted at the Los Alamos Neutron Science Center (LANSCE) at intermediate incident neutron energies, ranging up to 800 MeV. Scattered protons from deuteron breakup travel through a magnetic spectrometer on beam right, consisting of a thin $\Delta$E scintillator, three drift chambers, two permanent magnets, and two thin E scintillators. An array of nine two-meter high plastic scintillators detects scattered neutrons on beam left. Analysis of the data from this experiment is underway to determine the scattered angles and energies of the particles, and subsequently the scattering cross-section for the n-d breakup reaction. EA.00059: Maximizing Ion Collider Luminosity Through Genetic Optimization of Beam Tunes Matthew Kramer In designing a particle collider, one goal is to achieve the maximum feasible luminosity, a measure of the rate of collision events. Luminosity depends, in part, on a set of parameters known as the betatron tune working points (oscillation frequencies) of the beam. The relationship is complicated and nonlinear, making optimization extremely difficult. Researchers have long sought viable algorithms for solving this problem. Here, a massively parallel genetic algorithm was developed and used to locate high-luminosity working points for the proposed Medium Energy Ion Collider currently being designed at Jefferson Lab. The algorithm made use of the BeamBeam3D package to perform beam-beam simulations and to then calculate the luminosity of each working point. It was found that after five or more generations, the algorithm successfully located working points with luminosities exceeding the proposed design luminosity of the collider. These results demonstrate that such algorithms provide a feasible solution to this type of problem. Owing to the parallel evaluation of working points, a large subset of tune space can be covered relatively quickly (one or two days). It is hoped that such methods may prove useful for various other difficult optimization problems in accelerator design. EA.00060: Polarization of Target in Crystal Ball Calorimeter Jennifer Kuczynski , William Briscoe , Andreas Thomas A pion photo-production experiment is being conducted at MAMI-lab in Mainz, Germany. In Mainz I was working at the Mainz Microtron (MAMI) using a polarized tagged photon beam, a transversely polarized proton target, and the Crystal Ball calorimeter. The Crystal Ball can measure energy, position energy and timing at many angles. A butanol polarized target was used in the May/June run of the Crystal Ball experiment. Finding an accurate relaxation time for the polarization will be useful in determining a proper time for each experimental run. EA.00061: Using Fiber Optics to Measure Carrier Drift Velocity of Germanium at 40mK Albert Lam The Cryogenic Dark Matter Search (CDMS) uses ultrapure germanium detectors at milliKelvin temperatures to attempt to directly detect weakly interacting massive particles (WIMPs), a candidate for dark matter. When some particle interacts with the crystal structure, ionization and phonon signals are produced. Each particle interaction gives off a unique ratio of ionization signal to phonon signal. In this way, background noise can be separated from events that may involve WIMPs. Current germanium detectors are about the size of a hockey puck. If detectors can be made larger, there would be a greater probability of having a WIMP interaction. To make larger detectors, we need to better understand carrier transport processes in the germanium detectors. So, we measured the carrier drift velocity at 40milliKelvin, the temperature at which detectors operate. The carrier drift velocity gives us insight into how much impurity is present in the germanium detectors. We made this measurement using a fiber optics line. The fiber optics line allowed us to carry light from a 780nm laser diode at room temperature, into our dilution refrigerator and onto a germanium detector at 40milliKelvin. A laser diode allowed us to create electron-hole pairs on the surface of a germanium detector in a much more precise way than a radiation source. EA.00062: Hot Filament Alignment System Edward Lamere The a'' Correlation in Neutron Decay (aCORN) collaboration seeks to measure the electron-antineutrino correlation in free neutron decay to within 1{\%} relative uncertainty as a test of the Standard Model. To accomplish this, two regions of the phase space of the decay must be isolated. The correlation parameter, little a,'' is proportional to the counting asymmetry between these two groups. Before the final measurement can be performed, an in-situ test of the alignment of the magnetic field and the experimental axis, set by a series of tungsten collimators, must be checked. Any misalignment would introduce an asymmetry in the experiment, resulting in an inaccurate little a'' measurement. To test the alignment a filament can be quickly inserted into the aCORN vacuum tube, which produces low energy electrons when heated. These electrons will travel nearly straight along the magnetic field lines due to their minimal cyclotron radius. A misalignment of the field can be determined from the relative currents detected on the final, segmented collimator. A description of the preliminary work on an in-situ alignment system will be presented. EA.00063: The Similarity Renormalization Group with Novel Generators Weishi Li The Similarity Renormalization Group (SRG) uses a series of unitary transformations to decouple high-energy and low-energy physics. Because of the properties of unitary transformations, the SRG automatically preserves physical observables while decoupling allows the truncation of the Hamiltonian, improving convergence. With the relative kinetic energy ($T_{\rm rel}$) as the generator, the SRG has been applied successfully for several years to calculate nuclear structure. However, only a few generators have been explored. Different generators relate to different evolving patterns and parameters. Here some new alternatives, such as an exponential form of $T_{\rm rel}$, are evaluated for the degree of decoupling and improvements in computing speed. EA.00064: Improved Interlock System at the Nuclear Structure Lab at Univ. of Notre Dame Xao Lor , Shelly Lesher , Ed Stech The current interlock system at the Nuclear Structure Lab (NSL) at the University of Notre Dame requires multiple procedures to be performed in order to start up one of the three accelerators. New features and equipment will be added to the current interlock system to allow access into the experimental rooms safely. This change is necessary because the planned addition of experimental equipment will allow beams from two accelerators to enter the same target hall. In order to minimize the impact of one experiment on another, access will be determined by active monitoring of the radiation levels in the rooms instead of the possibility of accelerated beam being present. New equipment planned to be used in the laboratory are personal dosimeter badges, with a monitor reader for a pass-by data exchange and monitor screens to display live radiation levels and access levels in all of the experimental rooms. This poster will present this procedure and explain how personnel can access the NSL rooms safely while the ion beams are on. EA.00065: Production and Quality Tests of Carbon Strip Targets for RHIC Polarimetery William Lynn Spin physics at BNL involves the study of polarized proton-proton collisions in order to better understand proton spin structure. The RHIC accelerator complex is capable of producing a longitudinal or transversely polarized proton beam with a maximum polarization of 70\% and up to a beam energy of 250 GeV. Since research depends heavily on the degree of polarization of the proton beam, it is necessary to check the polarization of the beam after it has left its source by using a polarimeter. There are two polarimeters at RHIC, the Hydrogen-Jet and proton-Carbon (pC) polarimeters. The pC polarimeters measure the polarization of the protons by colliding the beam with a carbon strip target and then measuring the angle of deflection. The targets used in pC polarimeters are manufactured at BNL through an evaporation technique and must have a width of less than 10 $\mu$m. After production, quality checks must be made to ensure that the carbon targets are suitable for use. This poster will focus on the production and quality control of the targets to be used in pC polarimeters. EA.00066: Probing Micro Black Holes and Extra Dimensions through IceCube Sultan Malik If extra space dimensions and low-scale gravity exist, Microscopic Black Holes (MBHs) will be produced in collisions of elementary particles. Ultrahigh-energy cosmic neutrinos, also known as GZK neutrinos, provide a promising window on this phenomenon. For GZK neutrinos above $\sim$10$^{7}$GeV, the MBH production cross section in neutrino-nucleon interactions exceeds the standard model cross section by two or more orders of magnitude increasing the chances of detection by neutrino observatories. The IceCube neutrino observatory, buried 1.4 km under the Antarctic ice near the South Pole, was used to probe production of MBHs in this analysis. One month data from the IceCube detector was searched for events that could be possible MBH events. The expected number of events was also calculated theoretically for both the Standard Model cross section and the MBH model cross section using a standard GZK flux prediction. No significant MBH events were found in the data analysis which is consistent with the low expected number of MBH events. Detecting MBH directly requires large amount of observable data, and so is not an effective method for probing MBHs. Further study is required to come up with indirect ways of detecting MBH production using IceCube. EA.00067: Neutron Detection Improvements for Measurement of Neutron Lifetime Gregory Manus , Chen-Yu Liu , Daniel Salvat , Christopher Cude , Aaron Hanson , Sonya Sawtelle Ultra Cold Neutrons (UCN) have energies low enough to be confined in material and magnetic traps, yet it makes transmission into typical neutron detectors a nontrivial task. The neutron lifetime experiment at LANL may require improvements to a standard ionization chamber detector or an entirely different approach to UCN detection [1]. We compare Si and Zr ionization chamber windows to their Al counterparts. Si's smooth surface and uniform bulk density reduces the total elastic scattering cross-section. Zr's mechanical strength enables thinner, more transparent detector windows than Al. Also, various geometries of electrode grid planes are simulated in Garfield and built. Furthermore, to minimize time and spectrum dependent systematic errors of collection efficiency, we bypass transporting the UCN from trap to detector by detecting UCN directly in the trap. Here we empty BF3 and Ar into the trap where UCN capture in B releases Li and $\alpha$ particles detected by their ionization of Ar. The B capture also emits a gamma which can be detected. Details and progress will be presented at the conference. \\[4pt] [1] Nucl Instrum Meth A 599 (2009) 82-92 EA.00068: New Trigger Logic for the STAR Forward Meson Spectrometer John Calvin Martinez The Forward Meson Spectrometer (FMS) is an electromagnetic calorimeter in the STAR Experiment at RHIC that covers the pseudorapidity region 2.5 $<$ eta $<$ 4 and full azimuth. One of the goals of the FMS is to separate two possible causes of large, previously observed proton transverse single-spin asymmetries, the Sivers effect and the Collins effect. To meet this goal, it will be valuable for the FMS to trigger more efficiently on eta mesons and jet-like events than it does at present. In order to increase the trigger efficiency for non-localized events, like jets and eta decays, a new trigger algorithm has been developed that includes a system of eight overlapping jet-patches, each covering an approximate area of 1.5 x 1.5 in azimuth-pseudorapidity space. The new trigger logic and the expected rates for 200 and 500 GeV p+p collisions will be presented. EA.00069: Magnet Design and Simulation for Neutron Interferometry Robert Milburn , Chris Crawford , Elise Martin The study of neutron interferometry highlights some of the essential components of quantum mechanics allowing us to study the wave-like nature of the neutron. The spin of polarized monochromatic neutrons in an interferometer can be flipped by passing through a static B-field perpendicular to the holding field. Constraints on such a magnet are that the field must be constant within a cylindrical volume, but zero everywhere outside the coil. A double cosine theta coil meets the needs of this particular device. The design, simulation, and plans for construction of this magnet will be presented. EA.00070: Determining the Light Antiquark Asymmetry in the Nucleon Sea with FNAL E-906/SeaQuest Benjamin Miller SeaQuest will use the Drell-Yan process to improve our knowledge of the structure of the nucleon. This experiment will determine the ratio of anti-down to anti-up quarks to larger Bjorken-x than was attained by earlier experiments. SeaQuest's predecessor, Fermilab E-866/NuSea extracted the ratio to x $\approx$ .2 with reasonable precision. SeaQuest will extend the measurements of light antiquark asymmetry to x $\approx$ 0.45. SeaQuest will use the Fermilab 120 GeV/c Main Injector to collide protons with targets of liquid hydrogen, liquid deuterium and, for other measurements, solid nuclear targets. The detector under construction is a two-magnet, focusing spectrometer with four detector stations, similar to the E866/NuSea spectrometer. By comparing the Drell-Yan di-muon cross sections for both proton- proton and proton-deuterium collisions, we can extract $\bar {d}$/$\bar{u}$ for the proton and better understand the properties of the sea of the nucleon. EA.00071: High Energy Pion Photoproduction from Nucleons in the Giessen Bolzmann-Uehling-Uhlenbeck Model Prajwal Mohanmurthy For long, the transitions between perturbative and nonperturbative regimes of QCD have been of interest in nuclear physics. One of the methods used to study these transitions is to look for the onset of predictive QCD laws such as the quark counting rule. Measuring the differential cross section of certain exclusive reactions (such as pion photo production) has been one of the prime methods of investigating quark counting rules. The CEBAF Large Acceptance Spectrometer (CLAS) in Hall B at the Jefferson Lab (JLAB) has been used to measure the cross sections of pion photo production reactions. These measurements can be used to better understand the scaling laws. Although the cross-section does show scaling behavior, the onset of scaling is at unusually low energies and an unexplained sharp drop in the cross-section is observed just before the onset of scaling. There is a lack of theoretical calculations of pion photo production cross-section at these energies. The model known as the Giessen Boltzmann-Uehling-Uhlenback (GiBUU) model has been used to calculate the pion photo-production cross-section and it was compared with the CLAS measurements. The preliminary results shall be presented. EA.00072: Silicon-Strip Detectors for the Array for Nuclear Astrophysics Studies with Exotic Nuclei L.L. Mondello , J.C. Blackmon , L. Linhardt , M. Matos , E.F. Zganjar , E. Johnson , G. Rogachev , I. Wiedenhover The Array for Nuclear Astrophysics Studies with Exotic Nuclei (ANASEN) is a charged-particle detector array that is targeted towards reaction studies with radioactive ion beams at FSU and the NSCL, primarily to help improve understanding of the nuclear reactions important in stellar explosions. New resistive, double-sided silicon-strip detectors were designed and constructed for ANASEN that aim for precise position and energy resolution using a modest number of channels. The first 12 (of 40) detectors for ANASEN were tested at LSU with a 241Am alpha source to characterize the position resolution, energy resolution, and effective length for each detector element, as well as the optimum operating voltage. A custom 72-channel preamplifier unit has also been constructed for silicon-strip detectors, and the performance of the preamplifier as a function of input series resistance was also studied. We will present the results of the source tests and plans for commissioning with ion beams. EA.00073: Simulating the Neutron Detection Efficiency of the CLAS12 Detector M. Moog , G.P. Gilfoyle , J. Carbonneau We have studied the expected performance of the CLAS12 detector that will be built at Jefferson Lab as part of the 12-GeV Upgrade. The Upgrade hopes to further our understanding of the internal structure of nucleons and nuclei by studying properties such as form factors and generalized parton distributions. The initial round of experiments for the Upgrade include ones requiring neutron detection and we are studying the neutron detection efficiency (NDE) in preparation for such experiments. A precise knowledge of the NDE is required to keep systematic uncertainty low. We studied the CLAS12 performance by generating the four-momenta of an electron and neutron after a relativistic, elastic collision and passing this information into the GEANT4-based program gemc. This code uses the four-momenta of these particles and simulates their interaction with the CLAS12 components. Events were reconstructed with the program Socrat. By comparing the number of measured elastically-scattered, electron-neutron coincidences to the number of elastic electrons detected in the simulation we extracted the NDE of the time-of-flight (TOF) scintillators. In previous work we studied one set of TOF panels and have now extended this work to include the full array of TOF scintillators in the simulation and expanded the neutron momentum range. EA.00074: Spectroscopy of Heavy Nuclei with GAMMASPHERE K. Moran , S. Hota , S. Lakshmi , P. Chowdhury We report on analysis of data from a recent experiment carried out using the ATLAS heavy-ion accelerator facility at Argonne National Laboratory. A beam of \hspace{2pt}$^{208}$Pb was incident on a $^{244}$Pu target evaporated on a $^{197}$Au backing. The target and projectile nuclei were mutually excited to high-energy states via inelastic collisions. The GAMMASPHERE detector array, made up of 108 Compton-suppressed germanium detectors positioned in a spherical geometry around the target, was used to detect the resulting gamma radiation as the nuclei decayed to ground state. The data from the experiment was then sorted into a three-dimensional $\gamma$-$\gamma$-$\gamma$ cube,'' which was analyzed using gating techniques in Radware software to investigate the decay structure of the excited nuclei produced by the experiment. A two-dimensional matrix'' was also created using an early-delayed technique, allowing for short-lived isomers produced in-beam to be observed. This data was analyzed using time gates to measure half-lives of observable isomers. Results will be presented and discussed. EA.00075: The influence of eccentricity fluctuations on the extraction of the QGP shear viscosity from elliptic flow data J. Scott Moreland , Ulrich Heinz , Huichao Song In a recent paper [Phys. Rev. C 80 (2009) 061901] we showed that systematic studies of the impact parameter dependence of the eccentricity-scaled elliptic flow $v_2/\epsilon$ can distinguish between different models for the calculation of the initial source eccentricity. These calculations were done with viscous relativistic hydrodynamics in 2+1 space-time dimensions, assuming longitudinal boost-invariance and using the optical versions of the Glauber and fKLN (Color Glass Condensate) models to describe the initial energy density profiles. Here we report on the results on a follow-up study that includes the effects of event-by-event fluctuations in the shape and orientation of the reaction zone that defines the initial fireball density. We explore the effects of eccentricity fluctuations on the collision centrality dependence of the eccentricity-scaled elliptic flow and compare the results with experimentally observed trends in Au+Au collisions at the Relativistic Heavy Ion Collider. EA.00076: LED Monitoring System of the Phenix Muon Piston Calorimeter Steven Motschwiller The Muon Piston Calorimeter in the PHENIX experiment at RHIC has a monitoring system consisting of LEDs and PIN diodes to calibrate out the time dependent changes to the detector. The LEDs track the temperature and radiation-damage changes to the response of the MPC, while the absolute calibration can be done using $\pi^{0}$ decays. To execute this, LEDs flash light through the PbWO4 crystal to the Avalanche Photo Diodes The MPC is made up of 416 independent electromagnetic calorimeter towers. By using the LEDs we can correct for changes in the gains of each tower in the MPC, on a run by run basis. Because the LED value only gives a relative measurement of the gain over time, this method of calibration can only be used in conjunction with absolute calibrations provided by $\pi^{0}$ decays or by minimum ionizing peaks . This work will be used to make a final measurement on Transverse energy at $\sqrt{s_{NN}}$ = 200 GV in Au+Au collisions. EA.00077: Simulation of the CLAS12 Forward Electromagnetic Calorimeter C.J. Musalo , G.P. Gilfoyle , J. Carbonneau The primary mission of Jefferson Lab (JLab) is to reveal the quark and gluon structure of nucleons and nuclei and to deepen our understanding of matter and quark confinement. At JLab there is a need for high-performance computing for data analysis and simulations. The precision of many future experiments will be limited by systematic uncertainties and not statistical ones; making accurate simulations vital. A physics-based simulation of a new detector (CLAS12) is currently being developed called gemc. This new program uses the package Geant4 to calculate the interactions of particles with matter in the components of CLAS12. We have added the electromagnetic calorimeter (EC) detector to the gemc simulation. The EC is a sampling electromagnetic calorimeter made up of alternating layers of lead and plastic scintillator used to detect electrons, photons, and neutrons. The mathematical model of the EC geometry was streamlined to make the code more robust. This geometry is stored in a mysql database on a server at JLab and it was modified using Perl scripts. The new geometry was tested by sending straight tracks (no magnetic field) through the edges of specific layers using the geantino, a Geant4 virtual particle that does not interact with materials. Work supported by US Department of Energy contract DE-FG02-96ER40980. EA.00078: Testing the Large-area multi-Institutional Scintillator Array (LISA) Neutron Detector T.B. Nagi , K.M. Rethman , K.A. Purtell , A.J. Haagsma , C. DeRoo , M. Jacobson , S. Kuhn , A.R. Peters , M. Ndong , S.A. Stewart , Z. Torstrick , R. Anthony , H. Chen , A. Howe , N.S. Badger , M.D. Miller , B.J. Foster , L.C. Rice , C. Vest , A.B. Aulie , A. Grovom , L. Elliot , P. Kasavan The 144 detector modules comprising the Large-area multi-Institutional Scintillator Array (LISA) neutron detector were tested at each of the nine primarily undergraduate institutions. Each module is a 200 cm by 10 cm by 10 cm bar of EJ-200 organic plastic scintillator a with a photomultiplier tube mounted on each end. We used cosmic rays both to ensure that each module was light tight as well as to characterize position and time resolution. In addition, we measured each module's light attenuation using gamma sources. Results will be presented. EA.00079: A MIP-based Energy Calibration of the STAR Endcap Electromagnetic Calorimeter for 2009 Zachary Nault The Endcap Electromagnetic Calorimeter (EEMC) is an integral part of the STAR detector at RHIC. The EEMC is used in detecting forward particles from polarized proton interactions, which aid in understanding the spin structure of the proton. In order to properly use the data collected, the energy and position measurements in the EEMC need to be well-known. To accomplish this, a calibration of the EEMC was done using minimum ionizing particles (MIPs) for the 2009 run. A description of this method and the current status of the energy calibration will be presented. EA.00080: A Database for the Low Background Facility at Lawrence Berkeley National Laboratory Khang Nguyen , James Loach The Low Background Facility (LBF) at Lawrence Berkeley National Laboratory (LBNL) has been serving the worldwide research community since 1962, providing radiopurity measurements of a huge number of different materials. The 100,000 assays that have been performed have contributed to the success of many important experiments, such as SNO and KamLAND, but have mostly remained unavailable to the wider community. A project undertaken by the Neutrino Astrophysics Group at LBNL aims to make the data accessible by creating a comprehensive database of assay results with an accompanying web application. This poster outlines the project. EA.00081: Search for angular anisotropies in neutron emissions of fragmentation reactions with secondary beams Sam Novario , Greg Christian , Jenna Smith , Michael Thoennessen Projectile fragments from the breakup of a secondary beam of $^{29}$Na were measured in coincidence with neutrons expelled in the reaction. A 140 MeV/u $^{48}$Ca beam from the Coupled Cyclotron Facility at Michigan State University was used to produce the secondary $^{29}$Na beam at an energy of 102 MeV/u. This beam impinged on a 987 mg/cm$^{2}$ $^{9}$Be target and the outgoing fragments were deflected by a superconducting 4 T large-gap dipole magnet and analyzed with a set of energy-loss, timing and position sensitive detectors while the outgoing neutrons were measured with the Modular Neutron Array MoNA. The central purpose of the experiment was to study individual neutron unbound resonances in the fragments. In addition, the analysis of the continuum distributions offers the opportunity to investigate reaction dynamical effects. For example, the neutron multiplicity can yield information about the distribution of the initially produced fragments. Also, the angular distributions of the emitted neutrons relative to the fragments may contain information about the fragmentation process. We searched for anisotropies in these angular distributions for several isotopes from Z = 5 through Z = 10 fragments. Initial results will be presented. EA.00082: Discovery of Isotopes A. Nystrom , A. Parker , M. Thoennessen To date, no comprehensive study has been undertaken regarding the initial detection and identification of isotopes. At NSCL, a project has been initiated to catalog and report the initial observation of every isotope. The conditions characterizing the successful discovery of an isotope include a clear and unambiguous mass and element identification through decay curves, mass spectroscopy, $\gamma$-ray spectra, and/or relationships to other isotopes, as well as the publication of such findings in an adjudicated journal. Prior to this work, research on the discovery of isotopes for approximately sixty-five different elements had already been performed within the bounds of this project$^{4}$. Here we present the documentation for nine new elements: rubidium, strontium, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, and rhodium. 31 rubidium, 35 strontium, 34 yttrium, 35 zirconium, 34 niobium, 35 molybdenum, 33 technetium, 38 ruthenium, and 38 rhodium isotopes have been discovered so far. The year and author of each initial publication are discussed, along with the location and methods of production and identification. A summary and overview of all $\sim$2000 isotopes documented so far as a function of discovery year, method and place will also be presented. EA.00083: The Ursinus College Liquid Hydrogen Target Jessica Palardy , Nicholas Ferrante , Lewis Riley , Remco Zegers The Ursinus College Liquid Hydrogen Target has been constructed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University, for the purpose of eliminating unwanted gamma-rays from carbon in polyethylene or deuterated polyethylene targets that are commonly used in experiments requiring thick proton targets. Existing geant4 simulations of the Segmented Germanium Array (SeGA) and the CAESium iodide ARray (CAESAR) have been modified to incorporate the liquid hydrogen target. The impact of the target on gamma-ray detection efficiencies and the use of the simulations to plan experiments with the target are discussed. EA.00084: Motor Controls for the NIFFTE Time Projection Chamber Positioning Stand Daniel Pamplin , Nathan Pickle The next generation nuclear power plants will be more efficient and produce smaller amounts of radioactive waste. Design of these new reactors is limited partially by the lack of precise neutron induced fission cross sections at certain incident neutron energies of several isotopes. In order to reduce the uncertainty of the cross sections to less than 1 percent, a Time Projection Chamber (TPC) was built by the Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) collaboration. These improvements in precision will be possible due to the TPC's ability for a full 3-D reconstruction of the fission fragment tracks. The NIFFTE TPC will be installed at Los Alamos National Lab's LANSCE facility. Thin targets will be mounted in the center of the TPC in a pressurized hydrogen gas chamber so that both hemispheres of the reaction will be covered. In this work we will discuss the control of the stepper motors that drive the positioning table of the TPC, which has all of its readout electronics attached, to be lined up with the beam. This includes both the controlling software and its graphical interface to the MIDAS online data acquisition system. EA.00085: Using C++ and SRIM to improve energy resolution using the STARS/LiBerACE arrays Benjamin Pauerstein , Jack Shaw , Danyi Chen , Tim Ross , Richard Hughes , Con Beausang An experiment was conducted at LBNL using the STARS/LiBerACE arrays in which a 25 MeV proton beam was incident on 154, 156, and 158Gd targets to study nuclei around the N=90 shape-change region. STARS uses a delta-E and E silicon detector telescope to identify the type and direction of emitted light, charged particles. Each CD shaped detector is segmented into 24 rings. The data sorting program approximates the angle at which a charged particle was scattered by choosing the angle required to hit the middle of the ring struck in the delta-E detector. This angle is then used to calculate energy losses in the dead layers, and hence the particle's total energy. This method is non-optimal as not all of the particles hit the detector at these angles, and improving the angular resolution should improve the energy resolution. SRIM was used to calculate particle energy loss per unit distance travelled in various materials; a C++ program was then written to obtain detailed energy loss calculations for particles as a function of angle and particle energy measured in the E detector. Preliminary results will be presented. This work is supported by the DOE under grants DE-FG02-52NA26206 and DE-FG02-05ER41379. EA.00086: Sensitivity Study Investigating the Effect of Nuclear Masses on R-process Abundances Nancy Paul , Samuel Brett , Ani Aprahamian Nuclear masses play a critical role in r-process nucleosynthesis, which, though poorly understood, is thought to account for more than 50 percent of the abundances of elements heavier than iron. Using the NGAM nucleosynthesis simulation code and the FRDM mass model, we performed a sensitivity study to identify nuclei whose masses have the greatest impact on the entire r-process abundance distribution. We adjusted the individual FRDM masses by 25 percent and evaluated the overall impact compared to baseline abundances generated from the FRDM masses. We determined the effects of these adjustments by considering both the maximum change and the RMS change in final r-process abundances. We identified several critical nuclei that would be most important to measure in future experiments at radioactive ion-beam facilities although not all nuclei are experimentally accessible at the present time. EA.00087: BECOLA Beam Line Construction and Laser System Eowyn Pedicini , Kei Minamisono , Brad Barquest , Georg Bollen , Andrew Klose , Paul Mantica , Dave Morrissey , Ryan Ringle , Stefan Schwarz , Sophia Vinnikova The BECOLA (BEam COoler and LAser spectroscopy) facility is being installed at NSCL for experiments on radioactive nuclides.\footnote{K. Minamisono \textit{et al}, Proc. Inst. Nucl. Theory \textbf{16}, 180 (2009).} Low energy ion beams will be cooled/bunched in an RFQ ion trap and then extracted to a max of 60 kV. The ion beam will be neutralized through a charge exchange cell (CEC), and remaining ions will be removed by a deflector and collected in a Faraday cup. Collinear laser spectroscopy will be used to measure the atomic hyperfine structure, and nuclear properties will be extracted. The assembly, vacuum testing, and optical alignment of the CEC have been completed and the ion deflector and Faraday cup were also assembled. Stabilization of the Ti:sapphire laser to be used for spectroscopy is achieved through a feedback loop using a precision wavelength meter that is calibrated by a stabilized He-Ne laser. Coupling the He-Ne laser into a single-mode optical fiber was optimized for stable operation of the feedback loop. Finally, a wall chart of nuclear moments was prepared to view trends in $\mu$ and Q for nuclear ground states for planning future measurements. EA.00088: Filtering, Processing, and Analysis of aCORN Project Data Andrew Portuguese The aCORN collaboration seeks to measure the electron-antineutrino correlation in free neutron beta decay characterized by the dimensionless parameter \textit{little a}'' within a 1{\%} relative uncertainty. Cold neutrons decay in the apparatus, and in-coincidence proton and electron detection allows the measurement of the beta electron energy as well as the proton time-of-flight (TOF). The configuration of the apparatus permits coincidence detection in two distinct decay cases, distinguished by the proton TOF, and the experimental asymmetry of these cases enables precise determination of $a$. Since many decays must be used, a data acquisition system with high throughput is necessary to acquire, filter, process, and store all gathered coincidence data in a usable form. aCORN utilizes a Pixie-16 data acquisition system to digitize signals in a 12-bit ADC at a rate of up to 100 MHz. Digitized detector events are time sorted, coincidences are identified, and each fully absorbed electron energy event is stored with its corresponding proton TOF. The analysis code can be adapted to store any other detected data. The principles of the aCORN data handling system will be discussed in this presentation. EA.00089: First Nuclear Self-Absorption Experiment at HI$\gamma$S Relevant to Astrophysics S. Pratt , G. Rusev , E. Kwan , R. Raut , A.P. Tonchev , J.H. Kelley , R. Schwengner In supernovae explosion, about 35 nuclei cannot be produced by $r$ or $s$ processes. These co-called $p$ nuclei can be created by photodisintegration reactions only. Furthermore, network calculations underpredict the abundances of the $p$ nuclei which require more precise measurements of the photo-induced reactions. The accuracy of those measurements rely on the uncertainty of the width of the levels in $^{11}$B used as a calibration standard. These are currently known with a relative uncertainty not better than 5\%. We report the results for the width of the levels at $7.285$ and $8.920$ MeV in $^{11}$B from the first nuclear self-absorption experiment at the High Intensity $\gamma$-Ray Source Facility at Triangle Universities Nuclear Laboratory using monoenergetic photon beams. EA.00090: Performance comparison of MoNA and LISA neutron detectors Kimberly Purtell , Kaitlynne Rethman , Autumn Haagsma , Joseph Finck , Jenna Smith , Jesse Snyder In 2002 eight primarily undergraduate institutions constructed and tested the Modular Neutron Array (MoNA) which has been used to detect high energy neutrons at the National Superconducting Cyclotron Laboratory (NSCL). Nine institutions have now designed, constructed and tested the Large-area multi-Institutional Scintillator Array (LISA) neutron detector which will be used at the NSCL and the future Facility for Rare Isotope Beams (FRIB). Both detectors are comprised of 144 detector modules. Each module is a 200 x 10 x 10 cm$^3$ bar organic plastic scintillator with a photomultiplier tube mounted on each end. Using cosmic rays and a gamma source, we compared the performance of MoNA and LISA by using the same electronics to check light attenuation, position resolution, rise times, and cosmic ray peak widths. Results will be presented. EA.00091: Improving Sr Radioactive Ion Beams at HRIBF Fatima Rafique , Hubert Carter , Carola Jost , Ronald Goans The research conducted at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory (ORNL) utilizes high quality radioactive ion beams (RIBs) to explore the structure of nuclei. This research reviews chemical techniques to improve the intensity and purity of these radioactive ion beams, in particular strontium (Sr) ion beams. A past experiment on $^{92}$Sr showed that the intensity of the Rb contamination was approximately half of the Sr intensity. K$o$ster \textit{et al}. (2008) reported that RbF molecules do not ionize in the ion source, whereas the SrF molecules do. Taking this into account, the data from an old experiment which introduced SF$_{6}$ to the target/ion source was reanalyzed. The yield for $^{93}$SrF was found to be about 4.55 x 10$^{6}$ ions/sec/$\mu$A, while for $^{93}$RbF it was less than 0.2{\%} of $^{93}$SrF. These results are encouraging; therefore, a detailed optimizing experiment using CF$_{4}$ gas is expected to be carried out soon and the results will be presented in the poster. EA.00092: Mass Constraints on Fourth Generation of Standard Model Fermions Enrique Ramirez-Homs , Leo Bellantoni , Jens Erler Current experimental bounds on fourth-generation, standard model fermion masses are revisited. Assuming a fourth generation, we cast uniformly distributed masses for four fermions and determine a probability density function based on consistency with the electroweak oblique parameters, S, T, and U, convoluting over Higgs masses. Recent TeVatron combination limit on Mh in the fourth generation scenario is used and a probability density function for the four fermions is obtained. EA.00093: Construction of the Large-area multi-Institutional Scintillator Array (LISA) Neutron Detector Kaitlynne Rethman , Kimberly Purtell , Autumn Haagsma , Casey DeRoo , Megan Jacobson , Steve Kuhn , Alexander Peters , Tim Nagi , Sam Stewart , Zack Torstrick , Mathieu Ndong , Rob Anthony , Hengzhi Chen , Alex Howe , Nicholas Badger , Matthew Miller , Brad Vest , Ben Foster , Logan Rice , Alegra Aulie , Amanda Grovom , Philip Kasavan , Lewis Elliott The Large-area multi-Institutional Scintillator Array (LISA) will detect high-energy neutrons in experiments with fast rare isotopes. The LISA allows for the study of unbound nuclei as well and many unknown higher-lying unbound states in light neutron-rich nuclei (Z$<$9). Nine primarily undergraduate institutions designed, proposed, and constructed this highly efficient large-area neutron detector that uses an array of 144 individual plastic scintillators to produce a position sensitive system with multi-hit capability. The construction process and characteristics of the detector will be presented. EA.00094: Time resolution tests of Fine Mesh Photo Multipliers for the CLAS12 Central Time-of-Flight Detector A. Reustle , V. Baturin The upcoming CLAS12 Central Time-of-Flight (CTOF) system at Jefferson Lab's Hall B detector will feature a new barrel scintillation detector for identifying particles in that region by TOF-momentum relations. The region will experience a high magnetic field (5T) so the Photo-Multiplier Tubes (PMTs) measuring the scintillations will need to be shielded from this field. New Fine Mesh (FM) PMTs are unaffected by these high Magnetic Fields and would not require the otherwise necessary magnetic shielding of older Linear Focused (LF) PMTs. The question arises whether these FM PMTs produce results refined enough to distinguish between scintillations caused by different species of particles. To distinguish between the Pions, Kaons {\&} Protons expected in the CTOF's given region The PMT's must have a Timing resolution of $\sim$50 ps. To test the Timing resolution of FM PMTs we produced an apparatus consisting of a scintillator and acrylic light guides with one of each type of PMT attached at either end. Directed low level, low frequency light was provided via angled LEDs in perfect optical contact with the scintillator, to reproduce the scintillations caused by ionizing particles as closely as possible. The timing resolution of the Fine Mesh PMT was measured at double that of the Linear Focused PMT, within the margin of acceptability for our detector. EA.00095: Transverse Flow of light clusters in Nuclear Reactions J.A. Rodriguez-Lopez , C.M. Ko , J. Xu Heavy-ion reactions induced by neutron-rich nuclei allow us to study the properties of isospin-asymmetric nuclear matter, specially the density dependence of nuclear symmetry energy. In previous works, light clusters production and their collective flow have been proven to be sensitive to the density dependence of nuclear symmetry energy. By means of a coalescence model based on an isospin-dependent Boltzmann-Uehling-Ulenbeck transport model with a momentum-dependent interaction, we have studied the yield, energy distribution, and transverse flow of light charged particles. We have further used different nuclear symmetry energies in the IBUU model to study their effects on the transverse flow of light charged particles. EA.00096: Feasibility of 238U NRF Detection in Shipping Containers Ben Ryan Sophisticated detection methods are required to efficiently screen the immense volume of containers imported into the United States for the presence of special nuclear materials. The likelihood of detection of characteristic nuclear resonance fluorescence (NRF) lines for the 238U isotope inside a shipping container is examined. Similarly to atoms, nuclei fluoresce when they are excited by incident photons of particular energies unique to each isotope. Detection of the resulting gamma transitions induced by a $\gamma$-source allows for nonintrusive interrogation of materials. The Geant4 Monte Carlo simulation toolkit was modified to support detection of NRF. Simulations of a number of typical cargo container geometries containing natural uranium irradiated by a realistic nearly monoenergetic tunable gamma source were developed. The existence of NRF lines in the resulting spectra of exterior detectors will be described. EA.00097: Monte Carlo Simulations for a Quadrupole Band Pass Filter for LANSCE Protons Salah Salah , Jerry Peterson As we know that protons have a positive charge, which means that if they hit any material, they will ionize it. This issue is a big problem for circuit researchers and indeed it is a problem for NASA and particle accelerator users. Thus, in this research, we have built a conceptual design consisting of two quadrupole magnets to select a band pass'' energy spectrum from the continuous proton spectrum at the LANSCE facility. We have found that we will be able to control and collect the desired protons with adequate rate and energy resolution. Thus, we will be able to create a new facility to measure the effect of 50 -- 700 MeV protons on electronic circuits. EA.00098: Pion Reconstruction for Calibration of the PHENIX Muon Piston Calorimeter in Au+Au Collisions at RHIC Scott Sanowitz The PHENIX Muon Piston Calorimeter (MPC) is a useful tool for analyzing p+p, d+Au, Au+Au collisions at RHIC. Covering forward and backward pseudorapidities (3.1 $< \vert \eta \vert <$ 3.7) the detector has already been used in p+p and d+Au analyses. We are currently calibrating the detector for use in analyzing Au+Au data. Pion reconstruction is one of several methods by which to calibrate the towers of the MPC. Progress on these calibrations will be reported. EA.00099: Mapping of the magnetic field for the NPDGamma Experiment S. Jasmin Schaedler , Stefan Baessler , Septimiu Balascuta , Seppo Pentilla In the NPDGamma-experiment the parity-violating weak meson exchange forces in the reaction $\overrightarrow{n} + p \rightarrow d+ \gamma$ are studied by measuring the angular correlation $A_{\gamma}$ of the emitted photons with respect to the direction of the neutron spin. The experiment is presently being setup at the Fundamental Physics Beam Line of the Spallation Neutron Source in Oak Ridge, TN. From the exit of the polarizer to the liquid Hydrogen target, the cold neutrons are moving in an almost vertical magnetic field. For the field calibration and adjustment a set of four guide coils and four shim coil systems are used. The strength and the direction of the field are measured using two magnetic flux gate sensors. The field magnitude is required to be 98~mT and the vertical field gradient less than 2.2~$\mu$T/cm between the spin flipper and the end of the target. The magnetic field in the target volume has to be vertical better than 2~mrad, to decrease the systematic errors. The measuring procedure and the mapping of the B-field will be presented. EA.00100: Constructing a Radon Scrubber for Air Andrew Schmitz , Xiaoyi Yang , Dongming Mei , Vincente Guiseppe , Chao Zhang , Yongchen Sun , Jason Spaans A recurring problem in low background physics is the presence of the decay products of 222Rn (radon). The particularly treacherous aspect of radon is its gaseous nature and the long half-life of its daughters. Many industrial devices for air radon removal are sold on the market, but none achieve the removal factor required by our experiments in DUSEL. Therefore, we must design our own system to remove the radon from the air. This paper will show a radon removal system that we built at USD using charcoal. We constructed a single charcoal column system to perform a spike'' test, where a chamber is used to gather large amount of radon and then flushed with nitrogen. The radon arrives in the charcoal in the form of a pulse. This technique will allow us to better understand the adsorption and desorption properties of the charcoal under specific flow rates and pressures. A large pressure swing system will be built after the spike test. EA.00101: Proton Induced X-ray Emission Spectroscopy of Red Wine Samples Using the Union College Pelletron Accelerator Katie Schuff , Scott LaBrake A 1-megavolt tandem electrostatic Pelletron particle accelerator housed at Union College was used to measure the elemental composition and concentration of homemade Cabernet and Merlot red wine samples. A beam of 1.8-MeV protons directed at an approximately 12-$\mu$m thin Mylar substrate onto which 8-$\mu$L of concentrated red wine was dried caused inner shell electrons to be ejected from the target nuclei and these vacancies are filled through electronic transitions of higher orbital electrons accompanied by the production of an x-ray photon characteristic of the elemental composition of the target. This is the PIXE Method. Data on the intensity versus energy of the x-rays were collected using an Amptek silicon drift detector and were analyzed to determine the elemental composition and the samples were found to contain P, S, K, Cl, Ca, Sc, Mn, Al, Fe, {\&} Co. Elemental concentrations were determined using the analysis package GUPIX. It is hypothesized that the cobalt seen is a direct result of the uptake by the grapes and as a product of the fermentation process a complex of vitamin B12 is produced. EA.00102: Measuring the Timing Resolution of a Fine-Mesh PMT Under High Magnetic Fields Arun Selvaratnam , Vitaly Baturin The upgraded particle accelerator in Jefferson Lab requires that the detectors in Hall B also be upgraded, so they may cope with its increased power. The CLAS12 Central Time-of-Flight detector will use a new barrel scintillation detector that will be exposed to high magnetic fields ranging up to 5 Tesla. Traditionally, linear focused photomultiplier tubes have been used to determine time-of-flight valuations for charged particles resulting from particle accelerator experiments. However, without heavy shielding, a linear focused PMT will not be able to function in a high magnetic field. A new breed of fine-mesh'' PMTs claim to be unaffected by magnetic fields ranging up to 0.8 to 1.2 T. Our setup consists of a fine-mesh PMT that will receive diffused LED light while different magnetic fields are pointed towards it. The light will travel through wavelength-shifting fiber optic cables to a reference linear focused PMT located outside the magnetic field. Prior studies have only been done with a point-like light source on the PMT within the field. We will find what effects high magnetic fields have on fine-mesh PMTs. EA.00103: Event Reconstruction in a Time Projection Chamber Designed to Make High Precision Fission Cross Section Measurements Sarvagya Sharma The Time Projection Chamber (TPC), being constructed by the NIFFTE (Neutron Induced Fission Fragment Tracking Experiment) collaboration will be used for high-precision fission cross-section measurements. These measurements will aid in the design of future generations of nuclear power plants. The track reconstruction effort in the NIFFTE experiment consists of a variety of statistical estimators to perform track finding and fitting. The Hough Transform is a brute force attempt at finding tracks that isolates features in the TPC volume through data binning. To determine track fit parameters, an iterative Kalman Filter has been implemented that accounts for multiple scattering. Comparing simulated and reconstructed tracks have shown the validity of these track reconstruction methods. In my poster, I will describe these methods in detail and I will also display the results we have achieved using these routines, including the first reconstructed tracks from our prototype TPC. EA.00104: Improving the angular resolution for the silicon detectors of the STARS array John Shaw , Benjamin Pauerstein , Danyi Chen , Timothy Ross , Richard Hughes , Con Beausang The STARS (Silicon Telescope Array for Reaction Studies) array at LBNL is used to measure the emission angles of light charged particles (protons, deuterons and tritons) following transfer reactions. The array consists of two CD-shaped silicon energy detectors: a thin delta E'' detector and a thicker E'' detector, each segmented into twenty-four concentric rings. The angle at which a particle hits the delta E detector is typically approximated in the off-line analysis code as the angle from the beam axis to the center of the ring traversed by the particle. To improve angular resolution, a new method of approximating the angle was investigated. It was thought that energy loss in the delta E could be used to derive angle. SRIM was used to create functions of energy loss per unit distance with respect to particle energy. These functions were used in Fortran codes to create matrices of energy loss for a range of angles and final energies. The matrices were then worked into the off-line analysis code. Preliminary results will be shown. This work is partly supported by the DOE under grant numbers DE-FG02-52NA26206 and DE-FG02-05ER41379. EA.00105: Exploring the Relationship between Intensity and Readout Delay in the WNSL Data Acquisition System Nikolay Shenkov , Tanveer Ahmed , Mirela Fetea , Tan Ahn , Andreas Heinz , Desiree Radeck , Volker Werner While the readout delay as a parameter of the Data Acquisition System (DAQ) is important in the detection of nuclear events and their lifetimes, every aspect of timing in a DAQ needs to be understood in order to get good data. Time correlations of the order of microseconds or more, larger than ones of nano-seconds we mostly used so far, are needed to identify isomers which was motivation for us to experimentally determine timing properties of the Wright Nuclear Structure Laboratory (WNSL) DAQ. Using 137Ba as a standard source of well known intensities, the effect of different delays on intensities of detected peaks was explored for the Data Acquisition System at the WNSL. The resultant data from the Time to Digital Converters (TDC) and Analog to Digital Converters (ADC) was sorted, plotted and analyzed. The results of our test measurement will be presented. EA.00106: Polarized ($\gamma$,n) reaction studies of $^{nat}$Cd, $^{nat}$Sn, and $^{181}$Ta Clarke Smith , Gerald Feldman Asymmetrical ($\gamma$,n) and ($\gamma$,f) neutron yields from polarized photons incident on fissile and non-fissile nuclei make it possible to construct isotopic signature curves useful for cargo interrogation. The High Intensity Gamma-Ray Source (HIGS) provides tunable, nearly mono-energetic $\gamma$ rays with high intensities and circular or linear polarization by colliding electrons with laser photons at the Duke Free Electron Laser Laboratory. HIGS was used to measure asymmetries in neutron emission from linearly polarized $\gamma$ rays incident on $^{nat}$Cd, $^{nat}$Sn, and $^{181}$Ta targets. An array of 18 liquid-scintillator detectors at six angles in the range $\theta$ = 55$^{\circ}$-142$^{\circ}$ was used to detect neutrons both parallel and perpendicular to the plane of polarization at six photon energies between 11.0 and 15.5 MeV. Since $^{nat}$Cd, $^{nat}$Sn, and $^{181}$Ta are non-fissile, any measured asymmetries resulted unambiguously from the ($\gamma$,n) reaction because the ($\gamma$,2n) threshold was above the incident photon energies. Neutrons were distinguished from Compton-scattered photons by pulse-shape discrimination and timing information, and their energies (E$_{n})$ were determined via time-of-flight techniques using a 0.5 meter flight path. The characteristic plots of the parallel/perpendicular ratio of neutron counts as a function of neutron energy E$_{n}$ were constructed and compared to those of previously studied targets at HIGS, including fissile nuclei such as $^{235}$U, $^{239}$Pu, and $^{232}$Th. EA.00107: Assessing the Effects of Magnetic Fields on the Photomultiplier Tubes in the SANE Forrest Smith As nuclear physicists work to understand the behavior of the quarks and gluons that comprise nucleons, polarization has become increasingly important. The Spin Asymmetries of the Nucleon Experiment (SANE) at Jefferson Lab used polarization of both beam and target in electron-proton scattering. While the beam can be produced in a polarized state, the target was polarized by way of a strong magnet. This magnet's field was non-negligible outside of the intended region, and this study examined the field and assessed its effect on photomultiplier tubes (PMTs) used in SANE. The magnetic field was mapped with reference to the location of the PMTs, and a statistical analysis of run data from SANE was done using the physics analysis framework developed ROOT. It was concluded that the magnetic field caused, on average, a 3.3{\%} \underline {+} 1.8{\%} loss in PMT signal due to the bending of electrons. This minor, but statistically significant, effect is consistent with prior, cursory estimates and solidifies the viability of coming results from SANE. These results also provide a good characterization for the PMTs' performance in a magnetic field and will benefit future experiments in which they are used. EA.00108: Modeling of Polarized Electron-Proton Elastic Scattering in Collider Kinematics Caroline Sofiatti The Electron-Ion Collider (EIC) is a proposed new facility designed to collide high-energy polarized electrons with nuclei and polarized protons. The EIC is an essential step towards the next frontier in understanding the fundamental quark-gluon structure of matter. The electron- proton (e-p) program aims at precisely imaging the sea quarks and gluons in the nucleon. The goal of this project is to model the elastic e-p cross section and polarization asymmetry, at the conditions of relevance for the EIC. The concept of cross section is used to express the likelihood of interaction between particles; therefore, it provides important information about the nature of quarks and gluons. The development of the formalism for this reaction makes it necessary to reframe the electron scattering kinematics into the conditions of the EIC. Ultimately, documentation and computer codes regarding the modeling will be made available for future use by the EIC community. EA.00109: Characterization and Resolution of VANDLE Modules Irena Spassova , D.W. Bardayan , J.C. Blackmon , J.A. Cizewski , R.K. Grzywacz , M. Madurga , B. Manning , C. Matei , E. Merino , P.D. O'Malley , S. Paulauskas , W.A. Peters , F. Raiola , F. Sarazin , D. Walter The Versatile Array of Neutron Detectors at Low Energies (VANDLE) is being developed to study the properties of unstable nuclei via (d,n) reactions and beta-delayed neutron emission. It is composed of scintillator bars of two sizes, 60 cm and 2 m, coupled to photomultiplier tubes. Twenty of these bars have been constructed into VANDLE modules and voltages have been gain matched for various energy ranges, and attenuation lengths measured. Measurements were recorded for position and timing resolutions of each module. The results of these characterizations with respect to different assembly parameters will be presented. EA.00110: MCPR -- A Monte Carlo model for studies of Fragmentation Reactions Hannah Staley , Jorge Pereira Fragmentation reactions are nowadays one of the most successful mechanisms to produce new unknown nuclear species. Nuclear reactions have the standard direct and compound-nucleus reactions components. Also there exists abundant evidence of an intermediate process that seems to fall in between these two types, and is more than just a combination of them. This in between state, the so-called pre-equilibrium stage, is less clearly understood. So, there are many models to describe pre- equilibrium reactions. In the present work, a systematic study of fragmentation-reaction data has been carried out, using the new Monte Carlo Pre-equilibrium code MCPR. The model combines a pre-equilibrium stage with the ABLA evaporation model, based on the statistical de-excitation model. Particle spectra; angular distributions; fragment distributions; excitation functions, along with production cross sections, were calculated for a large group of reactions. We particularly are interested in energies and elements studied at the National Superconducting Cyclotron Laboratory, NSCL. Here energies of 80 to 150 MeV/u and masses $\sim$ A=20-200 are typically used. EA.00111: Nuclear Reaction Calculations relevant for p-process nucleosynthesis Benjamin Stefanek , Artemis Spyrou The p-process is an important nucleosynthesis process and essential in the creation of heavy, proton-rich atomic nuclei. The environment where we are investigating the p-process is in core-collapse supernovae. Under such conditions the flux of energetic photons is high, and the p-process can occur through photo-induced reactions on pre-existing s-nuclei. Because of the difficulty of reproducing gamma-alpha and gamma-proton reactions in the lab, we analyze the reactions in reverse. Astrophysical calculations on the abundance of p-nuclei use nuclear input from the Hauser-Feshbach model, which depends on several nuclear parameters. The alpha particle optical model potential and a parameter describing nuclear level densities above the region of discrete levels are two such parameters. In light of these facts, we calculate production cross sections for P-nuclei under various existing parameterizations using the nuclear reaction code Empire. By doing this we hope to understand how production cross sections vary as isotopes further away from stability are considered. The overall goal is to compare the differing predictions to data that will be gathered from future experiments at the NSCL. EA.00112: M1 width of the 2$_{1}^{+}$ state in $^{22}$Na and searches for tensor contributions to beta decays Steven Steininger , Alejandro Garcia , Smarajite Triambak , Devin Short , David Williams A determination of the $\beta \quad - \quad \gamma$ angular correlation from $^{22}$Na beta decay with the GAMMASPHERE array has been used to extract induced-tensor-currents contributions to the weak interaction. The result, together with other available experimental data yielded an unexpectedly large induced tensor (second class) component to the hadronic current, which is at variance with the Standard Model. A weak link in the data used for this analysis is another recoil-order term, the weak magnetism form factor, which was extracted from an independent unpublished determination of the analog isovector magnetic dipole (2$^{+}$ $\to$ 3$^{+})$ gamma-ray transition strength in $^{22}$Na with low statistics and significant backgrounds. We are currently running an experiment to measure the $\Gamma _{M1}$ value from E$_{x}$ = 1952 keV state using a well known 21Ne(p, $\gamma )$ resonance at Ep = 1112 keV. This resonance leads to a gamma cascade in 22Na at E$_{x}$ = 7800 $\to$ 1952 $\to$ 0 keV. We will use a $\gamma -\gamma$ coincidence setup with a 120{\%} HPGe detector and a large 10 $\times$ 10 NaI detector. This method will provide both high detection efficiency and reduced backgrounds. EA.00113: Production of Short-Lived $^{37}$K Heather Stephens , Dan Melconian , Praveen Shidling The purpose of our work during the summer months of 2010 was to produce a beam of $^{37}$K with $\ge$ 99{\%} purity and characterize in detail the remaining contaminants. A projectile beam of $^{38}$Ar at 25 and 29 MeV/nucleon from the K500 cyclotron generated the $^{37}$K by reacting with an H$_{2}$ gas target. The \textit{MARS} spectrometer was then used to separate the reaction products of interest from the primary beam and other unwanted reaction products. From analysis of our production experiment, we were able to successfully produce 807 counts/nC of $^{37}$K with 99.19{\%} purity at 25MeV/u and 1756 counts/nC with 98.93{\%} purity at 29MeV/u. The purity of this beam and rate of production is more than adequate for use in determining the half-life of $^{37}$K, the next step to be done by the team in August 2010. This measurement will be accomplished by implanting the activity into a Mylar tape, placing it between two high-efficiency gas counters and counting the amount of beta decays as a function of time. It is expected the half-life will be measured using the $^{37}$K produced from $^{38}$Ar at 29MeV/u. EA.00114: Construction of Liquid Hydrogen and Deuterium Targets for E906/SeaQuest Michael Stewart E906/SeaQuest at Fermi National Accelerator Laboratory is a fixed target experiment which will examine the sea quark structure of the proton. Specifically, SeaQuest will look at the production of pairs of muons and anti-muons resulting from Drell-Yann interactions in liquid hydrogen and deuterium targets in order to measure the $\bar{d}$ to $\bar{u}$ asymmetry in the proton. In order to perform this experiment, cryogenic targets are used that are 50 cm long and 7.5 cm in diameter. These liquid hydrogen and deuterium targets will be operated at 20 K, with beam heating of 30 J per minute. Cryocoolers have been acquired and condensers designed and fabricated. These have been tested with heat loads similar to those which will be produced by the beam. The design of the SeaQuest cryogenic target system and the performance data collected during the target tests performed in the laboratory will be presented. EA.00115: Modifying the Crystal Ball and Developing Data Acquisition Software Alexey Strakovsky , Baya Oussena This poster describes work done with the A2 Collaboration at the Johannes Gutenberg Universitaet (JGU) in Mainz, Germany. In 2009, we modified the cabling of the Crystal Ball detector, housed at the Mainzer Mikrotron facility (MAMI) at JGU. This reduced the length of the 672 signal cables by approximately 43.68 km to reduce weight on the frame of the detector and make room for a frozen-spin hydrogen target. This involved cutting cables in half and resoldering the ends to new interface cards and photomultiplier tube connectors. More recently in 2010, our focus has been to develop new data acquisition software to replace the one currently in use. The new version, AcquDAQ, is based on C++ rather than the old C programming language. When completed, AcquDAQ will control and read data from the new electronics hardware utilized at MAMI, including the Crystal Ball. EA.00116: Development of a High-Rate Ionization Counter Sabrina Strauss , D.W. Bardayan , K.Y. Chae , J.A. Cizewski , W.A. Peters , K.T. Schmitt , M.S. Smith Ionization counters are useful for the determination of beam composition and beam normalization in many nuclear physics experiments. At the Holifield Radioactive Ion Beam Facility (HRIBF), we have developed and are currently testing a new ionization counter that will count and accurately identify particles at rates up to 10$^{6}$ pps. The new ion counter is based on the tilted electrode gas ion chamber (TEGIC) model developed at RIKEN [1] and consists of alternating anodes and cathodes, effectively creating a stack of ion chambers. Design and results from preliminary testing will be presented. \\[4pt] [1] Kimura \textit{et al.}, Nucl. Instr. And Methods A \textbf{538} 608 (2005). EA.00117: Quality Assurance Testing of RPC Modules for the PHENIX Muon Trigger Upgrade Kyle Sullivan The Relativistic Heavy Ion Collider (RHIC) collides polarized protons to answer fundamental questions regarding the angular momentum of the proton. The PHENIX collaboration is preparing to measure single spin asymmetries of muons from the decay of W bosons in polarized p+p collisions produced by the RHIC collider. An upgrade to the PHENIX muon trigger is necessary to accomplish this goal. Much of this upgrade has already been completed. New front end electronics (FEE) have already been installed on the existing muon tracking system and a station of resistive plate chambers have been installed in the North Arm. This summer, Muhlenberg College contributed to the assembly of a South RPC station. This poster will describe the quality assurance testing of the individual RPC modules as well as the attachment of the FEE boards to the modules. The modules are tested for noise, dark current, gas leaks, efficiency, and cluster size. In addition, the effect of changing the high voltage and thresholds is studied. EA.00118: Analyzing Photoproduction Data at the CB-ELSA Experiment to Establish Missing Hadronic Resonance States Matthew Szmaida The structure and dynamics of the nucleon and its excited states has been the subject of much inquiry since the discovery of the $\Delta$ resonance in the early 1950s. Typically, research into nucleon structure entails acquiring large data sets with input from several experiments using different mechanisms. New resonance states cannot be found by looking at simple spectra. Without precise data from many different nucleon decay channels, it remains difficult or even impossible to accurately determine the properties of well established resonances, or to confirm or rule out the existence of weakly established resonances or new, so-far not observed states. The current challenge is to search for new states and to measure the properties of some of the known higher-lying nucleon states with masses between 1.7 and 2.5 GeV/c$^{2}$. By studying the isospin-selective reaction $\gamma$p$\to \Delta \omega \to$p$\pi ^{0}\omega$, it is possible to isolate contributions from individual excited states and to clarify their importance. In this reaction, only $\Delta$* resonances can contribute in the intermediate state; N* states are excluded due to the zero isospin of the $\omega$ meson. The data for the project were taken with the Crystal-Barrel/TAPS experiment at the Electron Stretcher Accelerator at the University of Bonn, Germany. EA.00119: Development of TReRaC Program for Stellar Explosion Research Kyle Thomsen , Michael Smith Hundreds of different thermonuclear reactions drive a star through its life cycle. If a star's death results in an explosion, elements created by these fusion reactions can be spread throughout the cosmos and ultimately form new stars, planets, and sometimes life. In an effort to further understand what happens when these reactions take place, researchers carry out both lab measurements and simulations to test the most current ideas about the origins of the elements. To better estimate the rates of these reactions, the Thermonuclear Reaction Rate Calculator (TReRaC) program has been written. The strength of this program lies in its acceptance of a wide variety of nuclear physics information as input and its incorporation into the Computational Infrastructure for Nuclear Astrophysics (CINA) -- a suite of tools available to researchers around the world for nuclear astrophysics research. Among the information that TReRaC is capable of handling are each resonance's energy, spin / parity, entrance and exit channel widths, as well as non-resonant capture parameters. Currently, the code is capable of matching test rates to within the accuracy of the input, and we are finalizing the treatment of broad resonances. EA.00120: Slow Control System for the NIFFTE High Precision TPC Remington Thornton The Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) has designed a Time Projection Chamber (TPC) to measure neutron induced fission cross-section measurements of the major actinides to sub-1\% precision over a wide incident neutron energy range. These measurements are necessary to design the next generation of nuclear power plants. In order to achieve our high precision goals, an accurate and efficient slow control system must be implemented. Custom software has been created to control the hardware through Maximum Integration Data Acquisition System (MIDAS). This includes reading room and device temperature, setting the high voltage power supplies, and reading voltages. From hardware to software, an efficient design has been implemented and tested. This poster will present the setup and data from this slow control system. EA.00121: Optimization and Accessibility of the Qweak Database Erik Urban , Damon Spayde The Qweak experiment is a multi-institutional collaborative effort at Thomas Jefferson National Accelerator Facility designed to accurately determine the weak nuclear charge of a proton through measurements of the parity violating asymmetries of electron-proton elastic scattering that result from pulses of electrons with opposite helicities. Through the study of these scattering asymmetries, the Qweak experiment hopes to constrain extensions of the Standard Model or find indications of new physics. Since precision is critical to the success of the Qweak experiment, the collaboration will be taking data for thousands of hours. The Qweak database is responsible for storing the non-binary, processed data of this experiment in a meaningful and organized manner for use at a later date. The goal of this undertaking to not only create a database which can input and output data quickly, but create one which can easily be accessed by those who have minimal knowledge of the database language. Through tests on the system, the speed of retrieval and insert times has been optimized and, in addition, the implementation of summary tables and additional programs should make the majority of commonly sought results readily available to database novices. EA.00122: Monte Carlo Simulation of the DRAGON Recoil Mass Spectrometer End Detectors Laurelle Veloce , J. Fallis , C. Ruiz , S. Reeve DRAGON (Detector of Recoils And Gammas Of Nuclear reactions), located at TRIUMF in Vancouver, BC, is designed to study radiative capture reactions relevant in astrophysical nucleosynthesis processes. These types of reactions help us understand the production of heavy elements in the Universe. An accelerated beam of a given isotope is sent through a gas target where the reactions take place. Magnetic and electrostatic dipoles separate the recoils from the original beam particles, selecting particles according to charge and mass. The products of the nuclear reactions are then detected at the end of DRAGON by heavy ion detectors, which constitute two micro channel plate (MCP) detectors for time of flight measurements, used in conjunction with a Double Sided Silicon Strip Detector (DSSSD) or an ionization chamber (IC). The DSSSD gives information on number of counts, total energy deposited, and position while the IC measures the number of counts and the energy deposited as the particle travels through the chamber. In order to determine which set up is ideal for a given reaction and energy range, we have developed a Monte Carlo simulation of these end detectors. The program simulates both recoil and beam particles, and takes into account effects such as straggling and pulse height defect. Reaction kinematics in the gas target are also considered. Comparisons to recent experimental data will be discussed. EA.00123: Simulation of Photodisintegration Process with Polarized $\gamma$-ray Beams James Walker Large asymmetries were observed in the angular distributions of photo-neutrons produced in the interaction of polarized gamma rays with a variety of targets. In the experiments at high intensity gamma ray source at the Triangle Universities Nuclear Laboratory a survey of physically interesting and/or otherwise important nuclei has been initiated using $\gamma$-ray energy 6-15 MeV In this experiment backgrounds could come from ($\gamma$,n) on nitrogen in the target room, from scattering on the detector mount, or from neutrons scattering from one detector to another. GEANT4 simulations were necessary in order to evaluate the importance of different background sources. GEANT4 applications suitable for simulating the experimental set-up were developed and used to evaluate relevant backgrounds. EA.00124: A New Calibration Technique for the ALICE Electromagnetic Calorimeter at the Large Hadron Collider E. Watkins , M. Perales , M. Cervantes , E. Garcia-Solis , S. Sakai , M. Ploskon , P. Jacobs The Large Hadron Collider at CERN is the world's largest and highest energy, particle and heavy ion collider. The LHC will explore the frontiers of particle physics using high energy proton+proton collisions and the properties of the Quark-Gluon Plasma through the collision of heavy nuclei at high energy. ALICE is one of the four LHC experiments, specialized for the study of heavy ion collisions. This study presents a new technique for the calibration of an essential detector of ALICE - the EMCal. We utilize various computational techniques and analyze proton-proton collision data recorded at 900 GeV. The ALICE TPC is used to isolate the tracks of e+e- pairs that originate from the decay of j/psi particle and that fall within the EMCal's acceptance. The TPC measures the momentum of these electron tracks, which is compared to the energy deposited by them in the EMCal. We therefore use the precise measurement of TPC momentum as the reference to calibrate the EMCal energy measurement. In this presentation we will show the steps taken to analyze the data from the TPC, how we performed the matching of electron tracks from the j/psi decay with the energy deposited in the EMCal, and some preliminary results of this calibration technique. Research funded by NSF and DoE. EA.00125: High-Purity Germanium Characterization Nick Weinandt , Yongchen Sun , Dongming Mei Underground germanium crystal growth is a main focus of the CUBED 2010 research in the state of South Dakota where the DUSEL will be hosted. High-purity germanium is essential to the construction of germanium detectors for neutrioless double-beta decay and dark matter experiments planned for DUSEL. The characterization of germanium ingots and crystals is an important part of the high-purity germanium crystal growth process. Through the characterization process, we can learn important information such as net impurity concentration and crystal structure. The information can be fed back to the zone refining and crystal growth processes. Resistivity measurements and Hall Effect experiments were used to understand the impurity concentration of the germanium bars. Both experiments were run at 77K to avoid thermal conductivity. When resistivity and Hall Effect experiments are coupled with future research into and Spectroscopies, we can begin to understand exactly what impurities are present in the sample. With resistivity, the Hall Effect, Photo-Thermal Ionization Spectroscopy, and Deep-Level Transit Spectroscopy, we can gain a more complete understanding of the characterization techniques and the growing of the crystal. At the conference I would be able to show the results obtained from our experiments EA.00126: Tagging the Decay of Neutron Unbound States near the Dripline Alissa Wersal , Greg Christian , Michael Thoennessen , Artemis Spyrou Near the neutron dripline the study of neutron-unbound states is a valuable spectroscopic tool. Neutron-decay spectroscopy experiments, however, only determine the relative energy of the resonances. If the neutron decays to a bound excited state, it is necessary to measure the $\gamma$-decay in order to determine the absolute excitation energy of the initial state. The CAESium iodide ARray (CAESAR) was used for the first time in coincidence with the MoNA/Sweeper setup at the NSCL to perform this type of experiment. A secondary 70 MeV/u $^{32}$Mg beam produced at the Coupled Cyclotron Facility bombarded a 288 mg/cm$^{2}$ beryllium target. After the reaction, any charged particles were deflected by a superconducting 4T large-gap dipole magnet, and their positions, time of flight, and energy loss were measured. Neutrons were detected in coincidence with the Modular Neutron Array (MoNA) while CAESAR recorded any possible gamma rays. The Doppler shifted calibration of CAESAR was performed with gamma rays from Coulomb excited $^{32}$Mg and from $^{30}$Na fragments. Preliminary results will be presented. EA.00127: Implanted $^3$He Targets for Inverse Reaction Studies with Radioactive Ion Beams J.L. Wheeler , R.L. Kozub , S.A. Graves , D.J. Sissom , D.W. Stracener , D.W. Bardayan , C. Jost , P.D. O'Malley Proton transfer reactions, such as ($^3$He,d), are extremely important for measuring the properties of single particle states and resonances. Many such resonances are important in the rp process of explosive nucleosynthesis, but cannot be measured via resonance scattering directly. For the ($^3$He,d) reaction, it is necessary to use localized $^3$He targets, and gas jet targets are expensive and difficult to construct. An alternative approach is to implant $^3$He into thin aluminum foils. We are continuing our project\footnote{D.J. Sissom \emph{et al.} http://meetings.aps.org/link/BAPS.2008.DNP.DA.92}$^,$\footnote{J.L. Wheeler \emph{et al.} http://meetings.aps.org/link/BAPS.2009.HAW.GB.133} of implanting $^3$He into 0.65 ${\mu}$m thick aluminum foils at the Holifield Radioactive Ion Beam Facility at ORNL. Target profiles are analyzed using Rutherford backscattering to determine the concentration and distribution of the implanted $^3$He. An update of these results and a detailed description of the procedures will be presented. This research is supported by the U.S. Department of Energy. EA.00128: Production and Separation of Exotic Beams via Fragmentation Reactions Using MARS Kenneth Whitmore , R.E. Tribble , B.T. Roeder , L. Trache Radioactive nuclei away from the valley of stability are important in the study of nuclear astrophysical reactions. Because such nuclei cannot be found in nature, they must be produced in the lab in order to be studied. The Momentum Achromat Recoil Spectrometer (MARS) at Texas A\&M University is able to produce beams of radioactive nuclei and separate them from other products based on their charge, mass, and energy. Fragmentation reactions can produce a wider range of exotic beams at higher energies than other reaction mechanisms at lower energies. Reaction products from three different fragmentation reactions are studied, and production rates for various nuclei are determined and compared to predictions made by the simulation program LISE++. Production rate is related to the cross section, the kinematics and other particulars of a given reaction, and it is important to know how well the simulation can predict these rates. Work presented includes data from reactions with $^{36}$Ar at 45 MeV/u, $^{40}$Ar at 40 MeV/u, and $^{24}$Mg at 48 MeV/u, all on a $^{9}$Be target. These are the first fragmentation reactions to be studied with MARS. EA.00129: Evaluation of the KATRIN Detector Kevin Wierman The KArlsruhe TRItium Neutrino experiment, (KATRIN), is designed to make a direct, model independent measurement of the electron neutrino mass with a sensitivity of .2 eV. A neutrino mass measurement will guide theory beyond the current Standard Model, which considers neutrinos to be massless, as well as modern cosmological models. KATRIN determines the neutrino mass by using magnetic adiabatic collimation and an electrostatic retarding spectrometer coupled to a 148 pixel PIN diode array to analyze the spectrum of electrons emitted during tritium beta decay. In addition to basic counting, the energy, spatial and temporal resolutions of the detector will be used to reduce systematic error. The detector performance was characterized using an $^{241}Am$ gamma source and a mono-energetic photoelectron source. The response to the electron source was used to monitor the thickness of the non-reactive dead-layer of the detector. The absolute detector efficiency is monitored to the 1\% level by comparing a femto amp photocurrent source to the electron rate in the detector. By March 2011, the system will be available for use in commissioning the rest of the KATRIN hardware in Karlsruhe, Germany. EA.00130: Development of an Organic Liquid Scintillation Detector to be Used for Measuring Muon-Induced Processes at Homestake Brian Woltman , Patrick Davis , Dongming Mei , Chao Zhang Understanding the backgrounds produced by muon-induced processes is important to the success of experiments searching for rare event physics such as neutrinoless double-beta decay, dark matter, or neutrino oscillations, which require extremely low backgrounds. Measuring these muon-induced processes is vital for the low background experiments planned for Sanford Lab/DUSEL at the Homestake Mine in Lead, SD. We have constructed and calibrated a 12 liter liquid scintillation detector joined with two photomultiplier tubes (PMTs). We will present the construction and calibration of the detector, including its efficiency and neutron/gamma discrimination. We will also discuss the capabilities of our detector for use in low-background underground laboratories. EA.00131: Extraction of Beam Spin Asymmetry in the $\vec {\gamma }d\to pp\pi ^-$ Reaction Weizhi Xiong , Yordanka Ilieva Here we present a new method to estimate the polarization observable beam spin asymmetry (Sigma) from experimental data on nuclear reactions initiated by linearly polarized photon beam. We use the Maximum Log-Likelihood (LL) method to determine the estimator for Sigma and its uncertainty. We construct the probability density function (p.d.f.) of the azimuthal angle ($\phi )$ according to the physics dependence of the cross section of a nuclear reaction on $\phi$, in which Sigma is a parameter. In order to test our estimator, we applied it to randomly generated events similar to real data from the $\vec {\gamma }d\to pp\pi ^-$ reaction occurring when a photon strikes a deuterium target. We analyzed samples generated with, and without, detector acceptance folded in the p.d.f., where we extract the functional dependence of the detector acceptance from data taken with the CLAS detector at Jefferson Lab. We find that the value of Sigma estimated from the LL method is consistent with the true value and our estimator is unbiased. We show that the LL method yields an estimate for Sigma that has a smaller uncertainty than estimates obtained from fits to azimuthal distributions. Ours is a new and original study which supports the rich N* physics program based on polarization observables that is currently being run in Hall B at JLab.
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• We report results from the first search for $\nu_\mu\to\nu_e$ transitions by the NOvA experiment. In an exposure equivalent to $2.74\times10^{20}$ protons-on-target in the upgraded NuMI beam at Fermilab, we observe 6 events in the Far Detector, compared to a background expectation of $0.99\pm0.11$ (syst.) events based on the Near Detector measurement. A secondary analysis observes 11 events with a background of $1.07\pm0.14$ (syst.). The $3.3\sigma$ excess of events observed in the primary analysis disfavors $0.1\pi < \delta_{CP} < 0.5\pi$ in the inverted mass hierarchy at the 90% C.L.
• This paper reports the first measurement using the NOvA detectors of $\nu_\mu$ disappearance in a $\nu_\mu$ beam. The analysis uses a 14 kton-equivalent exposure of $2.74 \times 10^{20}$ protons-on-target from the Fermilab NuMI beam. Assuming the normal neutrino mass hierarchy, we measure $\Delta m^{2}_{32}=(2.52^{+0.20}_{-0.18})\times 10^{-3}$ eV$^{2}$ and $\sin^2\theta_{23}$ in the range 0.38-0.65, both at the 68% confidence level, with two statistically-degenerate best fit points at $\sin^2\theta_{23} =$ 0.43 and 0.60. Results for the inverted mass hierarchy are also presented.
• ### Strain driven charge-ordered state in La$_{0.67}$Ca$_{0.33}$MnO$_3$(cond-mat/0102321)
Feb. 19, 2001 cond-mat.str-el
We present evidence for the coexistence of ferromagnetic metallic and charge ordered insulating phases in strained thin films of La$_{0.67}$Ca$_{0.33}$MnO$_3$ at low temperatures. Such a phase separated state is confirmed using low temperature magnetic force microscopy and magnetotransport measurements. This phase separated state is not observed in the bulk form of this compound and is caused by the structural inhomogeneities due to the non-uniform distribution of strain in the film. The strain weakens the low temperature ferromagnetic metallic state and a charge ordered insulator is formed at the high strain regions. The slow dynamics of the transport properties of the mixed phase is illustrated by measurements of the long time scale relaxation of the electrical resistance.
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HIGHLIGHTS OF 2019
# The expansion of the Universe is faster than expected
### Subjects
The present rate of the expansion of our Universe, the Hubble constant, can be predicted from the cosmological model using measurements of the early Universe, or more directly measured from the late Universe. But as these measurements improved, a surprising disagreement between the two appeared. In 2019, a number of independent measurements of the late Universe using different methods and data provided consistent results, making the discrepancy with the early Universe predictions increasingly hard to ignore.
• The local or late Universe measurement of the Hubble constant improved from 10% uncertainty 20 years ago to less than 2% by 2019.
• In 2019, multiple independent teams presented measurements with different methods and different calibrations to produce consistent results.
• These late Universe estimations disagree at 4$$\sigma$$ to 6$$\sigma$$ with predictions made from the cosmic microwave background in conjunction with the standard cosmological model, a disagreement that is hard to explain or ignore.
The goal of modern cosmology is to explain the evolution of the Universe from its inception to the present time using our limited understanding of its composition and physical laws. This is even harder than it sounds! The first difficulty materialized in 1929 when initial estimates of the present expansion rate — known as the Hubble constant or H0 — rewound to the Big Bang singularity implied that the Universe was younger than the age estimated for the Earth and Sun. In retrospect, both figures were well off the mark, but there has been tremendous progress in the meantime. The measurement of H0 improved from 10% uncertainty at the start of the 2000s to less than 2% by 2019. In the past few years, reduced uncertainties from both the cosmic microwave background (CMB) — the afterglow of the Big Bang — and local Universe measurements have revealed an underlying discrepancy that is growing harder to ignore.
Scientists now have a ‘standard model of cosmology’, called ΛCDM (lambda cold dark matter), economically crafted from six free parameters and a number of well-tested ansatzes. The model characterizes a wide range of phenomena including the accelerating expansion, structure formation, primordial nucleosynthesis, flat geometry of spacetime, fluctuations of the Big Bang afterglow and the first combination of baryons into atoms. Remarkably, dark components (matter and energy) account for 95% of the Universe, as described by ΛCDM, their presence robustly inferred from their gravitational effects. Yet despite the success in better understanding our Universe confirmed by a wealth of precise measurements, in the past few years there has been growing evidence that the expansion of the Universe is still exceeding our predictions.
Observations of the CMB from the ESA Planck satellite provide the best present calibration of the parameters in ΛCDM, which are used together to provide the most precise estimate of two contemporary quantities: the present age of the Universe of 13.8 ± 0.02 billion years and today’s Hubble constant of H0 = 67.4 ± 0.5 km s−1 Mpc−1. The use of other measurements from the primordial epoch of the Universe yield a very similar figure. But this estimation from the early Universe is based on the simplest guesses about the nature of dark matter and dark energy and an uncertain roster of relativistic particles (such as neutrinos). A powerful, end-to-end test of ΛCDM and these assumptions is to measure the Hubble constant in the local or late Universe to a comparable, 1% precision.
The best-established local method is to build a ‘distance ladder’ using simple geometry to calibrate the luminosities of specific star types, pulsating (Cepheid variables) and exploding (type Ia supernovae or SNe Ia), which can be seen at great distances where their redshifts measure the cosmic expansion. A ladder is necessary because even with the most luminous tools, SNe Ia are too rare to be seen within the range of techniques such as parallax that are purely geometric. The trigonometric parallax can be measured to any visible object, but usefully within only a fraction of the Milky Way. Discovered by Henrietta Leavitt Swan in 1912, Cepheids are supergiant stars whose period of variation strongly correlates with their luminosity. They reach luminosities of 100,000 times that of the Sun, which makes them visible with the Hubble Space Telescope (HST) in most galaxies to a distance of 40 Mpc. Supernovae reach 10 billion solar luminosities, but only occur once a century in a typical galaxy. Two decades of measurements with these tools have consistently yielded values for H0 in the low 70s.
Then the SH0ES (supernovae H0 for the equation of state) project advanced this method by expanding the sample of high-quality calibrations of SNe Ia by Cepheids, increasing the number of independent geometric calibrations of Cepheids and measuring the fluxes of all Cepheids along the distance ladder with the same instrument to negate calibration errors1. Improved geometric distance estimates to the Large Magellanic Cloud using detached eclipsing binaries2 and to galaxy NGC 4258 using water masers (sources of microwave stimulated emission)3 have greatly aided this work. The best value of the SH0ES project H0 = 73.5 ± 1.4 km s−1 Mpc−1 is in 4.2σ tension with the early Universe prediction.
An independent, local measurement of H0 comes from the H0LiCOW (H0 lenses in COSMOGRAIL’s Wellspring) team, which has been measuring the time delays between multiple images of background quasars to constrain the different image path lengths caused by the strong gravitational lensing from a foreground galaxy. Six such systems have been measured to yield H0 = 73.3 ± 1.8 km s−1 Mpc−1 (ref.4) with a seventh from a different team, STRIDES (strong-lensing insights into dark energy survey), yielding H0 = 74.2 ± 3.0 km s−1 Mpc−1 (ref.5). Lensing analyses have markedly improved in the past two decades, and these have demonstrated internal consistency from systems with different numbers of quasar images, mean time delays, telescopes and methods used to estimate the lens mass.
Alternative distance ladders have recently been constructed substituting other types of stars in the role usually played by Cepheids. The tip of the red giant branch (TRGB) is the peak brightness reached by red giant stars after they stop fusing hydrogen and begin fusing helium in their core, a valuable discontinuity that can be observed in SNe Ia hosts at distances up to ~20 Mpc with the HST. Because the TRGB is not a type of star, but rather a feature of the distribution of thousands, its luminosity cannot be easily calibrated with the limited quality of parallax measurements in the Milky Way, nor readily seen directly with HST in our nearest neighbour, the Large Magellanic Cloud, limiting the precision of its calibration. Nevertheless, recent results from TRGB have yielded 69.8 ± 1.9 km s−1 Mpc−1 (ref.6) and 72.4 ± 1.9 km s−1 Mpc−1 (ref.7) with the primary difference between these resulting from different estimates of the extinction of TRGB by dust in the Large Magellanic Cloud and of the calibration between HST and ground-based photometry.
Miras are variable, red giant stars recently pressed into service to measure H0 as a check on both Cepheids and TRGB and yield H0 = 73.3 ± 3.9 km s−1 Mpc−1 using new HST observations and the previously discussed geometric distances8. Two other updates to the local measurement of H0 come from water masers in four galaxies at great distances (H0 = 74.8 ± 3.1 km s−1 Mpc−1) and the use of a method called Surface Brightness Fluctuations (H0 = 76.5 ± 4.0 km s−1 Mpc−1)(ref.9). See Fig. 1 for a summary of results.
Eleven unique averages provide a comprehensive picture of these recent H0 measurements (see Supplementary information). These were constructed to each exclude a different method (Cepheids, TRGB, Miras, SNe Ia, lensing) or geometric calibration (parallaxes, DEBs, masers in NGC 4258) or team to allow for ‘peremptory challenges’ to the results while using only measurements without overlapping data. They range from 72.8 ± 1.1 km s−1 Mpc−1 to 74.3 ± 1.0 km s−1 Mpc−1 and 4.5σ to 6.3σ tension with the Planck estimate. Indeed, it is telling that all recent local measurements exceed the early Universe prediction. Thus, it is hard to avoid the conclusion that the tension with the early Universe prediction is both highly significant and not easily attributed to an error in any one tool, team or method. New measurements from the local Universe using gravitational lensing and from the early Universe using ground-based CMB polarization are highly anticipated to weigh in over the next few years and may provide new insights.
If the Universe fails this crucial end-to-end test (it surely hasn’t yet passed), what might this tell us? It is tempting to think we may be seeing evidence of some ‘new physics’ in the cosmos. Indeed, a large number of theoretical solutions have been proposed and are reviewed in ref.10. For example, if we lived near the middle of a vast and deep void in the large-scale structure of the Universe, this could cause excessive, local expansion. However, the odds of a void this large occurring by chance is incredibly low. Calculations show that it exceeds 10σ (ref.11) and is also strongly ruled out empirically by the lack of evidence of any end to the void from SNe Ia at greater distances12. Dark energy with an equation of state lower than vacuum energy could produce stronger acceleration and explain the discrepancy, but this possibility is disfavoured by other intermediate-redshift measurements.
Greater success in explaining the H0 measurement discrepancies has been achieved by altering the composition of the Universe shortly before the emergence of the CMB. An additional component in ΛCDM, such as a new neutrino or scalar field (the latter called early dark energy or EDE), could have increased the early expansion, decreased the sound horizon of primordial fluctuations and raised the predicted value of H0 depending on the approach used, to 70–73 km s−1 Mpc−1 (ref.10) in plausible agreement with the local value. New particles tend to create new conflicts with the CMB, whereas EDE is claimed to improve agreement with the CMB. A criticism of EDE is that its scales must be finely tuned, although the same may be said of the other two episodes of dark energy (inflation and present acceleration). This raises the question of whether apparent episodes of such anomalous expansion are common or even related. Further, if the true expansion rate is the higher, local value, the Universe may actually be up to a billion years younger than expected. More work on the theoretical side and new data are badly needed before we may hope to reach the long sought end-to-end understanding of the Universe.
## Change history
• ### 10 January 2020
The Competing interest statement is added as it was missing from the previous version.
## References
1. 1.
Riess, A. G. et al. Large Magellanic Cloud Cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond ΛCDM. Astrophys. J. 876, 85 (2019).
2. 2.
Pietrzyn´ski, G. et al. A distance to the Large Magellanic Cloud that is precise to one per cent. Nature 567, 200–203 (2019).
3. 3.
Reid, M. J., Pesce, D. W. & Riess A. G. An improved distance to NGC 4258 and its implications for the Hubble constant. Astrophys. J. Lett. 886, L27 (2019).
4. 4.
Wong K. C. et al. H0LiCOW XIII. A 2.4% measurement of H0 from lensed quasars: 5.3σ tension between early and late-Universe probes. Preprint at: https://arxiv.org/abs/1907.04869 (2019).
5. 5.
Shajib, A. J. et al. STRIDES: A 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354. Preprint at: https://arxiv.org/pdf/1910.06306 (2019).
6. 6.
Freedman, W. L. et al. The Carnegie-Chicago Hubble Program. VIII. An independent determination of the Hubble constant based on the tip of the red giant branch. Astrophys. J. 882, 34 (2019).
7. 7.
Yuan, W. et al. Consistent calibration of the tip of the red giant branch in the Large Magellanic Cloud on the Hubble Space Telescope photometric system and a re-determination of the Hubble constant. https://10.3847/1538-4357/ab4bc9 (2019).
8. 8.
Huang, C. D. et al. Hubble Space Telescope observations of Mira variables in the type Ia supernova host NGC 1559: an alternative candle to measure the Hubble constant. Astrophys. J. in the press.
9. 9.
Verde, L., Treu, T. & Riess, A. G. Tensions between the early and the late Universe. Nat. Astron. 3, 891–895 (2019).
10. 10.
Knox, L & Millea, M. The Hubble hunter’s guide. Preprint at: https://arxiv.org/abs/1908.03663 (2019).
11. 11.
Wu, H. Y. & Huterer, D. Sample variance in the local measurements of the Hubble constant. Mon. Not. R. Astron. Soc. 471, 4946–4955 (2017).
12. 12.
Kenworthy, W. D., Scolnic, D. & Riess, A. G. The local perspective on the Hubble tension: local structure does not impact measurement of the Hubble constant. https://10.3847/1538-4357/ab0ebf (2019).
Authors
## Ethics declarations
### Competing interests
The author declares no competing interests.
## Rights and permissions
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Riess, A.G. The expansion of the Universe is faster than expected. Nat Rev Phys 2, 10–12 (2020). https://doi.org/10.1038/s42254-019-0137-0
• Published:
• Issue Date:
• ### Direct geometrical measurement of the Hubble constant from galaxy parallax: predictions for the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope
• Rupert A C Croft
Monthly Notices of the Royal Astronomical Society (2021)
• ### Determining the Hubble constant without the sound horizon: Measurements from galaxy surveys
• Oliver H. E. Philcox
• , Blake D. Sherwin
• , Gerrit S. Farren
• & Eric J. Baxter
Physical Review D (2021)
• ### Cosmological constraints on late-Universe decaying dark matter as a solution to the H0 tension
• Steven J. Clark
• , Kyriakos Vattis
• & Savvas M. Koushiappas
Physical Review D (2021)
• ### A combined analysis of the H0 late time direct measurements and the impact on the Dark Energy sector
• Eleonora Di Valentino
Monthly Notices of the Royal Astronomical Society (2021)
• ### Distribution of Si ii λ6355 velocities of Type Ia supernovae and implications for asymmetric explosions
• Keto D Zhang
• , WeiKang Zheng
• , Thomas de Jaeger
• , Benjamin E Stahl
• , Thomas G Brink
• , Xuhui Han
• , Daniel Kasen
• , Ken J Shen
• , Kevin Tang
• & Alexei V Filippenko
Monthly Notices of the Royal Astronomical Society (2020)
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## Student Loans
The government's recent takeover of student loans has been overshadowed by the rest of the health-insurance bill of which it was a part. On the one hand, Obama is right that the current system amounted to an absurd giveaway to banks. On the other hand, Obama's claim that this new legislation will somehow reduce the cost of college is absurd. Perhaps I've said it before, but when he makes claims like this, I find myself trying to decide if he really believes it or if he is lying as a means to an end. I'm tending toward the latter conclusion.
This post at The Corner sums up the situation well. Not surprising is that it was written by a guy at CATO.
I saw in a blog comment somewhere that people with student loans who work for the government will have their loans waived after 10 years. I am not sure if that made it to the final law. If so, I find it pretty disgusting. We seem more and more to have two classes of citizens.
## A tiny glimpse of silver
Lots of people have pointed out that for many employers, it will be cheaper for them to dump their employee's health insurance and pay the fines instead. Which means the link between your employer and your health insurance is about to be broken for a large number of people across the country.
Isn't that a good thing? Isn't making individuals responsible for purchasing their own insurance something conservatives and market experts have been hoping for for a long time?
Anyway, it's a tiny glimpse of silver lining.
Google should have done this long ago. Still, I salute them for doing the right thing now. Via the Corner
Two months after a series of suspicious China-based cyber-attacks, Google has stopped censoring Chinese search results, and google.com.cn now redirects to a Hong-Kong based site, google.com.hk.
Like they say, don't be evil.
## Words of Wisdom
It might be a good time to remember that the ends never justify the means. It was one of Nixon's mistakes. There are no ends, only means.
-Penn Jillette
## Never Paying the Piper
KJL writes in the Corner:
Congratulations, Democrats. Beginning now, you own the health-care system in America. Every hiccup. Every complaint. Every long line. All yours.
I don't think that it will hurt them. The Democrats have owned public education in urban areas for many decades. Have they been held accountable? Has it hurt them? No.
## Welcome!
Looks like National Healthcare has landed. I believe Kent Brockman said it best...
"Ladies and gentlemen, uh, we've just lost the picture, but what we've seen speaks for itself. The Corvair spacecraft has apparently been taken over- 'conquered' if you will- by a master race of giant space ants. It's difficult to tell from this vantage point whether they will consume the captive Earthman or merely enslave them. One thing is for certain: there is no stopping them; the ants will soon be here. And I, for one, welcome our new insect overlords. I'd like to remind them as a trusted TV personality, I can be helpful in rounding up others to toil in their underground sugar caves."
## Sorcery?
I understand AI's position...
Amnesty International is calling on Saudi Arabia's King Abdullah to stop the execution of a Lebanese man sentenced to death for "sorcery."
In a statement released Thursday, the international rights group condemned the verdict and demanded the immediate release of Ali Hussain Sibat, former host of a popular call-in show that aired on Sheherazade, a Beirut based satellite TV channel.
According to his lawyer, Sibat, who is 48 and has five children, would predict the future on his show and give out advice to his audience.
but if they let him go, and he turns someone into a toad, is AI going to take responsibility?
## Hypothesis Testing - II
A comment I posted on a blog:
[previous commenter] has a good point, and I see this sort of thing all the time in medical research. Do you think the life expectancy of people who drink Coke is *exactly* equal to the life expectancy of people who drink Pepsi? Exactly equal? Of course not. If you sample enough people, eventually you will detect a "statistically significant" difference. Then you can publish your paper saying e.g. "we found that people who drink Coke live significantly shorter lives than people who drink Pepsi!" Or, as it would appear in the newspaper and on tv: "Coke Kills!!"
## Hypothesis Testing
I think the way hypothesis testing is presented to students and justified makes no sense. Suppose we know that x has been drawn from a normal distribution with unit variance, and we want to test H_0: mu=0. Suppose x=2. Then they say “given H_0, the chance of seeing |x|>1.96 is less than 5%, so since x=2>1.96 we reject H_0.” Why does this make sense? Given H_0, the chance of seeing |x|<.01 is less than 5% too. Would you reject the null if our sample were x=0? No! So then they talk about x being “extreme,” i.e. far from the mean. What exactly does distance from the mean have to do with it? Suppose we knew that x was drawn from a uniform distribution on some interval [mu-1/2,mu+1/2], and again we wanted to test H0: mu=0. If x=.4999 would you reject? No, that makes no sense, because given H0, x=.4999 is no less likely than x=0. You could reject if x=.5001, but not if x is in the interval (-1/2,1/2). You could easily find an example of a bimodal distribution where the pdf at the mean is zero. Then you should reject if the sample is near the mean! Distance from the mean is not in general relevant.
I am being pedantic, but hypothesis testing works e.g. for the standard normal distribution f because if x>1.96, then f(x) is much less than values of f near x=0, not because of areas at the tails or distance from the mean.
## Corner Filter
I was just thinking... wouldn't it be nice to have a browser extention that allowed you to read NRO's "The Corner" without having to wade through KJL's endless abortion and Catholic-related posts?
## California Energy
Interesting article on California's energy policy.
In many countries, electric utilities struggle to keep up with demand, and often fail. The World Bank estimates that almost 1.5 billion men, women, and children lack reliable access to electricity. They want it, but they can't have it. In new-agey California, it's the other way around. The centerpiece of California's energy policy is really the absence of energy.
The state is in serious trouble. Its leadership doesn't seem to understand that.
## Fess Parker
Fess Parker has died. His tv-star days were a bit before my time, but I remember we had a Disney album of his, "Pecos Bill," that I enjoyed a lot as a kid.
One of the songs "Hunter's Return" is a lullaby that I like and remember. I sang it about 1,000,000 times to soothe my daughter when she was a baby. So thanks to him for that.
Rest in Peace.
## Woulda Coulda Shoulda
Saw this last night...
"Gee, that's a bit high!" I thought.
The lastest...
What a difference a day makes. Coulda made some easy money. No guts no glory.
Why is everyone suddenly re-evaluating this?
## 3000 percent!
President Obama yesterday:
Now, so let me talk about the third thing, which is my proposal would bring down the cost of health care for families, for businesses, and for the federal government. So Americans buying comparable coverage to what they have today -- I already said this -- would see premiums fall by 14 to 20 percent -- that’s not my numbers, that’s what the nonpartisan Congressional Budget Office says -- for Americans who get their insurance through the workplace. How many people are getting insurance through their jobs right now? Raise your hands. All right. Well, a lot of those folks, your employer it’s estimated would see premiums fall by as much as 3,000 percent [sic], which means they could give you a raise. (Applause.)
## So, how deep is the state of California's problems?
My license tags on my car expired in January, but we only realized it today. As a result, I just had to spend 2 hours at the DMV and pay a 60% late penalty for my new tags.
According to a person at the DMV, they sent me two notices, one in mid-November, and another about two weeks ago. Neither my sister nor myself ever saw either of those notices. Now, I can see misplacing one of them, but not two of them.
So here's the question: is California in enough financial do-do, that they secretly stopped sending out the renewal notices in hopes that there will be lots of people like me who have to pay the 60% penalty?
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# Does the sun have angular momentum?
The sun was formed like this: Clouds of dust and gas were moving and so this cloud of gas and dust pulled together its particles by the gravity of these particles. Since this cloud used to move in order to conserve momentum the sun should rotate. Does the law of conservation of angular momentum hold true? The distance to the center is reduced compare to the radius of the original cloud so the velocity of the sun should increase. So does the sun revolve around its own axis? Also does the sun revolve around any other object like the earth revolves around the sun?
• yes, it takes about a month. 25 days in some parts, 38 days in others....universetoday.com/60192/does-the-sun-rotate – user146020 Mar 10 '17 at 14:15
• Did you try looking at, say, Wikipedia, which has a handy sidebar with things like rotational periods and so on? – Emilio Pisanty Mar 10 '17 at 14:32
• Angular momentum about which point/axis? – xasthor Mar 10 '17 at 14:36
• @xasthor - it can reasonably be assumed that OP means "is there no axis about which the Sun has no angular momentum" which is the more precise way of formulating what I think is intended. – Floris Mar 10 '17 at 14:54
• Jupiter has more angular momentum than the sun. – aliential Jan 3 '18 at 4:28
The Sun certainly has angular momentum. You are correct that if two objects are of the same mass, the speed of rotation of the smaller denser object must be greater than the speed of the larger more diffuse object if both are to have the same angular momentum. The Sun is estimated to contain 99.86% of the total mass of the original nebula from which it formed, packed into a much smaller diameter.
Helioseismology has been used to probe the density, composition, and motion of the interior of the Sun. It's estimated that the Sun's angular momentum of rotation about its axis is $S = 1.92\times 10^{41}\ kg\cdot m^2\cdot s^{-1}$.
In addition to rotating on its axis, the Sun (and the entire Solar System) revolve around the center of the Milky Way Galaxy. One revolution takes one galactic year, which equals about 225 to 250 million terrestrial years. It's estimated that the speed of galactic revolution at our Sun's distance from the center of the galaxy is 1/1,300 the speed of light, c.
So the Sun has angular momentum from revolving around the galactic center, as well as from rotating around its own axis. The Sun's angular momentum of revolution around galactic center is part of the entire angular momentum of the Milky Way, just as angular momentum of the planets is part of the entire angular momentum of the Solar System.
• @Nick Your edit removed the last part of the answer, too. I fixed it, but next time please be more careful. – peterh - Reinstate Monica Mar 10 '17 at 17:35
I think I have the answer. Lets look at it intuitively. Lets say the nebula that formed the sun had a mass of 100kg and had a velocity of 10 km/sec. So the momentum was say 1000 kg m/s. Now when the sun formed it had the same mass (Roughly 99.8 % of solar mass) as that of the nebula. So in order to conserve momentum it should have a speed of 10 km/s. Lets substitute 10 km/s with 27 days needed for one rotation.
In other words I am saying that the nebula that formed the sun would have been moving very slowly, so slow that it takes 27 days for the sun to revolve on its axis and complete a rotation. This is so because of the law of conservation of momentum.
Correct me if I am wrong.
• Hmmm .. while the sun makes up more than 99% of the mass of the solar system that does not imply that material now in the sun was the same fraction of the material in the collapsing protostellar nebula. A non-trivial amount of dust and gas is lost to radiation pressure as the forming star first grows hot from compression. – dmckee --- ex-moderator kitten Mar 18 '17 at 15:14
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# Equations and Identities
You have probably come across many equations by now. However, what do we actually mean by the term 'equation'? You may have also heard of an identity. Sometimes it can be difficult to distinguish between equations and identities. In this article, we will be looking at equations, identities as well as their differences. However, we will first outline what we mean when talking about equations and identities. We will do so in the below section, and then discuss the differences between them.
## Expressions, equations, identities, and formulae
This section will consist of lots of definitions and examples. However, it is important that you understand each of the key terms as you may be given a particular example in your GCSE exam and asked to determine whether it is an expression, equation, identity, or formula. Here we go...
### Definition of expressions
An expression is a collection of mathematical terms, related by mathematical operations. A mathematical term is a single mathematical number or letter, for example, x or 3. We could also have 3x2, where 3 is known as the coefficient of x.
The following are examples of mathematical expressions:
### Definition of equations
Once we have a firm grasp on what mathematical expressions are we can start to build connections between them, in order to compare them.
If we break down the word equation we get ‘equa-tion’. Now ’equa’ sounds very similar to ‘equal’, which is no coincidence: an equation is a statement that two mathematical expressions shall be the same.
An equation is a statement that two mathematical expressions shall be the same.
An equation is expressed with an equal sign between two mathematical expressions. The fancy word for the equal sign is the equality symbol.
In a few words, anything with an equal sign is an equation. Sounds simple, right? Here are some examples of equations:
#### Solution of an equation
It is important to note here that two expressions may only be equal under specific conditions. For example, if we are told , we know this is an equation because there is an equality symbol. However, using the basic rules of addition, we know that the equation can only be true if . This is called the solution of the equation.
The solution of an equation is the set of all values that, when substituted for the variables in the equation, make the equation true.
### Definition of identities
Some expressions are always equal to each other, regardless of the values of the variables they contain. In this case one speaks of a mathematical identity:
A mathematical identity is where two mathematical expressions are always identical. An identity is expressed using the identity symbol , which looks a bit like an equals sign with an extra line.
## Differences between identities and equations
Often, one of the biggest challenges is determining whether something is an equation or identity. In this section, we will discuss how to establish whether something is an equation or an identity and note the key difference between them.
As established, an equation shows that two expressions are equal. However, they may only be equal for a specific value. For example, if we have, this equation is only true when . Identities on the other hand show that two expressions are always identical. For example, we could say that , since, no matter what the value of is, the two expressions are always the same.
If we asserted the identity , we know that the left-hand side is equal to the right-hand side for all values of because we have an identity symbol. However, the only way for this to be possible is if and . In this case, we would have which we know is true for all values of .
We could say that since identities show equality between expressions, all identities are equations. However, not all equations are identities so it is important that you are aware of the key difference between the two.
Here is again the main point: Equations show equality under at least one condition, identities show equality under all conditions.
## Definition of formulae
We have a fourth thing to consider, and that is a formula. While we are here, it is worth mentioning that the plural of formula is formulae. Now, onto some more definitions and examples...
A formula is a special type of equation representing a general fact or rule one can work with.
A mathematical formula is a type of equation as all formulae have an equal sign. However, they are equations with a specific purpose. They give us a way of working something out. For example, if we wanted to convert degrees Fahrenheit to degrees Celsius, we could use a formula. There are many formulae that are specifically useful for GCSE mathematics, including the quadratic formula, the trigonometric formulae, and also the speed, distance, and time formula. In the example below we will look at some specific formulae.
This is quite possibly one of the most iconic formulae in GCSE mathematics – the quadratic formula. This article is not about the quadratic formula specifically, so we will not talk about it in too much depth. However, this is just a friendly reminder that you probably should learn it.
Again, this article is not specifically about volume, mass, and density so we do not need to talk about it in too much depth. However, you do need to learn this formula at some point! It means that if you have the density of an object and volume, you can work out the mass. It is very handy.
This is another classic. Speed, distance, and time. You do need to know this formula, not just for GCSE mathematics, but for physics too. But once you know it, you can work out the speed of any moving object given the distance and time.
This is Pythagoras's Theorem. However, by definition, it is also a formula, as it enables us to work out an unknown quantity which in this case, is the missing side of a right-angled triangle. You need to know this for your GCSE exams.
This is a formula that relates the final velocity of a moving object, with the initial velocity, time, and acceleration. It is one of the SUVAT formulae which you may come across if you study A-level Mathematics. You don't specifically need to know this formula, you just need to be able to know that it is a formula, as it enables us to work out something specific (eg, the initial velocity, final velocity, acceleration, or time)
You may have seen this formula before. It is one of Einstein's most famous formulae relating mass to energy and the speed of light. It is quite famous, but you do not need to know this formula for GCSE mathematics. You simply need to know that it is a formula as it enables us to work something out.
Above are just a few examples of some formulae that you may or may not need to know for your GCSE maths exams. There are others, however, this article is not about going over every single one. Instead, it is about being able to see a formula, and subsequently being able to state that it is a formula, as opposed to an equation, identity, or expression.
Below we will cover some relevant examples to this topic. You will need to know the differences between an expression, identity, equation, and formula so let's just quickly recap the differences between these four things.
• An expression is a collection of mathematical terms.
• An equation is anything with an equal sign, hence 'equa' 'tion'.
• An identity is where two mathematical expressions are identical, denoted with an identity symbol, .
• A formula is a type of equation where we are working out something specific, for example, the mass of an object.
## Examples of identities and equations
Now that we have thoroughly defined some mathematical terms, we will go through some questions that you may come across in your GCSE exam.
Label the following either an identity, equation, expression, or formula:
Solution:
1. is the formula for the area of a circle. It enables us to work out the area given the radius. Thus the first one is a formula.
2. has no equality sign, and is simply a collection of mathematical terms connected with an addition symbol. Thus it is an expression.
3. has an equals sign, and thus it is an equation. It is only true for specific values of , (), thus it is not an identity.
4. has an equals sign and thus is an equation. However, this equation is true for all values of and so it is an identity and can be expressed using the identity symbol .
For the below identity, work out the values of and :
Solution:
We know that it is an identity, and so the left-hand side must be equal to the right-hand side. The coefficient of on the right-hand side is and so the coefficient on the left-hand side must also be . Thus, .
On the left-hand side, we could group up the coefficients of as follows:
. Therefore, we could say that since the coefficient of on both sides must be the same. Since we already know that , we can say that and so . Thus, and .
## Equations and Identities - Key takeaways
• An expression is a collection of mathematical terms, related by mathematical operations.
• An equation is any mathematical relation expressed with an equal sign.
• An identity is where two mathematical expressions are always identical.
• A formula is an equation that enables us to work out something specific.
• Identities are expressed using the symbol which is like an equal sign with an extra line.
• The difference between an equation and an identity is that equations state equality under a specific condition, identities show that two expressions are always equal.
An equation is true for certain values, an identity is true for all values.
Identities are equations where two expressions are always equal, as oppose to just under certain conditions.
An expression is a collection of mathematical terms. An equation is where two expressions are equal for some values. An identity is where two expressions are always equal, regardless of the values. A formula is a rule for working something specific out.
An equation is any mathematical relation expressed with an equality sign.
An identity is where two expressions are always true.
## Final Equations and Identities Quiz
Question
What is the process of writing equations?
Writing equations is the process of writing a mathematical statement that does contain equal signs.
Show question
Question
Familiarising yourself with the problem is the first step to writing words in mathematic symbols.
True
Show question
Question
What can be used to express problems in a short and concise way?
Math symbols
Show question
Question
When examining the problem, we need to realise that the variable is what?
The unknown quantity
Show question
Question
What is the standard form?
The standard form is a way of representing mathematical concepts such as equations in specific rules such that they appear in a common way.
Show question
Question
What is the process of writing the equation of a line from a graph?
• First by finding the slope of the line
• Then by finding the y-intercept.
Show question
Question
Which equation has the highest exponent of the variable as 2?
Show question
Question
What does 'm' represent in the slope-intercept form of writing equations?
The slope
Show question
Question
What is an equation?
Where two expressions are connected with an equality sign.
Show question
Question
What is an identity?
When two expressions are always true
Show question
Question
What is a formula?
A rule for working something specific out
Show question
Question
What is an expression?
A collection of mathematical terms.
Show question
Question
What is the difference between an identity and equation?
An identity is where two expressions are always true, an equation is when two expressions are only true under specific conditions
Show question
Question
Is 2x+1 an expression, equation, identity or formula?
expression
Show question
Question
Is 2x+1=2 an expression, equation, identity or formula?
equation
Show question
Question
Is 2x+4x=6x an expression, equation, identity or formula?
identity
Show question
Question
Is speed=distance/time an expression, equation, identity or formula?
formula
Show question
Question
Is y=x+1 an expression, equation, identity or formula?
formula
Show question
Question
What is the meaning of solving equations?
Solving equations is the process of finding the values for variables in these equations.
Show question
Question
What is the golden rule of solving equations?
The golden rule that states that any kind of arithmetic operations done to either side of the equation should be done to the other side as well.
Show question
Question
Equations that require just one step to get done solving them are known as
One-step equations
Show question
Question
What are two-step equations?
Two-step equations require two steps to solve
Show question
Question
In the process of solving equations, we isolate the variable to find its solution
True
Show question
Question
The last step in solving equations involve verifying your solution.
True
Show question
60%
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# How do you evaluate the integral int sinx/(cosx + cos^2x) dx?
Feb 17, 2017
The integral equals $\ln | \sec x + 1 | + C$
#### Explanation:
Call the integral $I$. Note that the expression $\cos x + {\cos}^{2} x = \cos x \left(1 + \cos x\right)$. For partial fractions to work, expressions need to be factored the most possible.
$I = \int \sin \frac{x}{\cos x \left(1 + \cos x\right)}$
To perform a partial fraction decomposition, we want to get rid of the trigonometric functions if possible. We can do this through a u-substitution. Let $u = \cos x$. Then $\mathrm{du} = - \sin x \mathrm{dx}$ and $\mathrm{dx} = \frac{\mathrm{du}}{- \sin x}$.
$I = \int \sin \frac{x}{u \left(1 + u\right)} \cdot \frac{\mathrm{du}}{- \sin x}$
$I = - \int \frac{1}{u \left(1 + u\right)} \mathrm{du}$
We're now going to use partial fraction decomposition to seperate integrals.
$\frac{A}{u} + \frac{B}{u + 1} = \frac{1}{u \left(u + 1\right)}$
$A \left(u + 1\right) + B u = 1$
$A u + A + B u = 1$
$\left(A + B\right) u + A = 1$
Now write a system of equations.
$\left\{\begin{matrix}A + B = 0 \\ A = 1\end{matrix}\right.$
This means that $A = 1$ and $B = - 1$.
The integral becomes.
$I = - \int \frac{1}{u} - \frac{1}{u + 1} \mathrm{du}$
$I = - \int \frac{1}{u} + \int \frac{1}{u + 1} \mathrm{du}$
$I = \ln | u + 1 | - \ln | u | + C$
$I = \ln | \cos x + 1 | - \ln | \cos x | + C$
This can be simplified using $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$.
$I = \ln | \frac{\cos x + 1}{\cos} x |$
We can rewrite $\frac{1}{\cos} x$ as $\sec x$.
$I = \ln | \sec x \left(\cos x + 1\right) |$
$I = \ln | 1 + \sec x |$, since $\sec x$ and $\cos x$ are reciprocals.
Hopefully this helps!
Feb 17, 2017
$\ln | 1 + \sec x | + C .$
#### Explanation:
Let $I = \int \sin \frac{x}{\cos x + {\cos}^{2} x} \mathrm{dx} .$
$\text{Subst. "u=cosx rArr du=-sinxdx,} s o , I = - \int \frac{1}{u + {u}^{2}} \mathrm{du} .$
We can integrate using Partial Factions, but, it is much simpler
without that.
$I = - \int \frac{1}{u \left(1 + u\right)} \mathrm{du} = - \int \frac{\left(u + 1\right) - u}{u \left(u + 1\right)} \mathrm{du}$
$= - \int \left\{\frac{u + 1}{u \left(u + 1\right)} - \frac{u}{u \left(u + 1\right)}\right\} \mathrm{du}$
$= \int \frac{1}{u + 1} \mathrm{du} - \int \frac{1}{u} \mathrm{du}$
$= \ln | u + 1 | - \ln | u |$
$= \ln | \frac{u + 1}{u} | = \ln | \frac{u}{u} + \frac{1}{u} |$
Since, $u = \cos x$, we have,
$I = \ln | 1 + \sec x | + C .$
Enjoy Maths.!
|
## Electronic Journal of Statistics
### Minimax Euclidean separation rates for testing convex hypotheses in $\mathbb{R}^{d}$
#### Abstract
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a closed convex subset $\mathcal{C}$ of $\mathbb{R}^{d}$. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension $d$ and variance $\frac{1}{n}$ giving rise to the minimax separation rate. In this paper we discuss lower and upper bounds on this rate for different smooth and non-smooth choices for $\mathcal{C}$.
#### Article information
Source
Electron. J. Statist., Volume 12, Number 2 (2018), 3713-3735.
Dates
First available in Project Euclid: 7 November 2018
https://projecteuclid.org/euclid.ejs/1541559861
Digital Object Identifier
doi:10.1214/18-EJS1472
#### Citation
Blanchard, Gilles; Carpentier, Alexandra; Gutzeit, Maurilio. Minimax Euclidean separation rates for testing convex hypotheses in $\mathbb{R}^{d}$. Electron. J. Statist. 12 (2018), no. 2, 3713--3735. doi:10.1214/18-EJS1472. https://projecteuclid.org/euclid.ejs/1541559861
#### References
• [1] Arias-Castro, E., and Casal, A. R. On estimating the perimeter using the alpha-shape., Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 53, 3 (2017), 1051–1068.
• [2] Baraud, Y. Non-asymptotic minimax rates of testing in signal detection., Bernoulli 8, 5 (2002), 577–606.
• [3] Baraud, Y., Huet, S., and Laurent, B. Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function., The Annals of Statistics (2005), 214–257.
• [4] Birgé, L. An alternative point of view on Lepski’s method., Lecture Notes-Monograph Series (2001), 113–133.
• [5] Bull, A., and Nickl, R. Adaptive confidence sets in $l_2$., Probability Theory and Related Fields 156, 3-4 (2013), 889–919.
• [6] Burnashev, M. On the minimax detection of an imperfectly known signal in a white noise background., Theory Probab. Appl. 24 (1979), 107–119.
• [7] Cai, T. T., and Low, M. Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional., The Annals of Statistics 39, 2 (2011), 1012–1041.
• [8] Carpentier, A. Testing the regularity of a smooth signal., Bernoulli 21, 1 (2015), 465–488.
• [9] Casey, J. E xploring Curvature., Vieweg Wiesbaden, 1996.
• [10] Chernoff, H. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations., The Annals of Mathematical Statistics 23 (1952), 493–507.
• [11] Comminges, L., and Dalalyan, A. Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression., Electronic Journal of Statistics 7 (2013), 146–190.
• [12] Gayraud, G., and Pouet, C. Adaptive minimax testing in the discrete regression scheme., Probability Theory and Related Fields 133, 4 (2005), 531–558.
• [13] Ingster, Y. On testing a hypothesis which is close to a simple hypothesis., Theory Prob. Appl. 45 (2000), 310–323.
• [14] Ingster, Y., and Suslina, I. Minimax detection of a signal for Besov bodies and balls., Problems of Information Transmission 34, 1 (1998), 48–59.
• [15] Ingster, Y., and Suslina, I., Nonparametric goodness-of-fit testing under Gaussian models. Springer-Verlag New York, Inc., 2003.
• [16] Juditsky, A., and Nemirovski, A. On nonparametric tests of positivity/monotonicity/convexity., The Annals of Statistics (2002), 498–527.
• [17] Lepski, O., Nemirovski, A., and Spokoiny, V. On estimation of the $l_r$ norm of a regression function., Probability Theory and Related Fields 113, 2 (1999), 221–253.
|
## 3.5 Julia Standard Library
Julia has a rich standard library that is available with every Julia installation. Contrary to everything that we have seen so far, e.g. types, data structures and filesystem; you must load standard library modules into your environment to use a particular module or function.
This is done via using or import. In this book, we will load code via using:
using ModuleName
After doing this, you can access all functions and types inside ModuleName.
### 3.5.1 Dates
Knowing how to handle dates and timestamps is important in data science. As we said in Why Julia? (Section 2) section, Python’s pandas uses its own datetime type to handle dates. The same is true in the R tidyverse’s lubridate package, which also defines its own datetime type to handle dates. In Julia packages don’t need to write their own dates logic, because Julia has a dates module in its standard library called Dates.
To begin, let’s load the Dates module:
using Dates
#### 3.5.1.1Date and DateTime Types
The Dates standard library module has two types for working with dates:
1. Date: representing time in days and
2. DateTime: representing time in millisecond precision.
We can construct Date and DateTime with the default constructor either by specifying an integer to represent year, month, day, hours and so on:
Date(1987) # year
1987-01-01
Date(1987, 9) # year, month
1987-09-01
Date(1987, 9, 13) # year, month, day
1987-09-13
DateTime(1987, 9, 13, 21) # year, month, day, hour
1987-09-13T21:00:00
DateTime(1987, 9, 13, 21, 21) # year, month, day, hour, minute
1987-09-13T21:21:00
For the curious, September 13th 1987, 21:21 is the official time of birth of the first author, Jose.
We can also pass Period types to the default constructor. Period types are the human-equivalent representation of time for the computer. Julia’s Dates have the following Period abstract subtypes:
subtypes(Period)
DatePeriod
TimePeriod
which divide into the following concrete types, and they are pretty much self-explanatory:
subtypes(DatePeriod)
Day
Month
Quarter
Week
Year
subtypes(TimePeriod)
Hour
Microsecond
Millisecond
Minute
Nanosecond
Second
So, we could alternatively construct Jose’s official time of birth as:
DateTime(Year(1987), Month(9), Day(13), Hour(21), Minute(21))
1987-09-13T21:21:00
#### 3.5.1.2 Parsing Dates
Most of the time, we won’t be constructing Date or DateTime instances from scratch. Actually, we will probably be parsing strings as Date or DateTime types.
The Date and DateTime constructors can be fed a string and a format string. For example, the string "19870913" representing September 13th 1987 can be parsed with:
Date("19870913", "yyyymmdd")
1987-09-13
Notice that the second argument is a string representation of the format. We have the first four digits representing year y, followed by two digits for month m and finally two digits for day d.
It also works for timestamps with DateTime:
DateTime("1987-09-13T21:21:00", "yyyy-mm-ddTHH:MM:SS")
1987-09-13T21:21:00
You can find more on how to specify different date formats in the Julia Dates’ documentation. Don’t worry if you have to revisit it all the time, we ourselves do that too when working with dates and timestamps.
According to Julia Dates’ documentation, using the Date(date_string, format_string) method is fine if it’s only called a few times. If there are many similarly formatted date strings to parse, however, it is much more efficient to first create a DateFormat type, and then pass it instead of a raw format string. Then, our previous example becomes:
format = DateFormat("yyyymmdd")
Date("19870913", format)
1987-09-13
Alternatively, without loss of performance, you can use the string literal prefix dateformat"...":
Date("19870913", dateformat"yyyymmdd")
1987-09-13
#### 3.5.1.3 Extracting Date Information
It is easy to extract desired information from Date and DateTime objects. First, let’s create an instance of a very special date:
my_birthday = Date("1987-09-13")
1987-09-13
We can extract anything we want from my_birthday:
year(my_birthday)
1987
month(my_birthday)
9
day(my_birthday)
13
Julia’s Dates module also has compound functions that return a tuple of values:
yearmonth(my_birthday)
(1987, 9)
monthday(my_birthday)
(9, 13)
yearmonthday(my_birthday)
(1987, 9, 13)
We can also see the day of the week and other handy stuff:
dayofweek(my_birthday)
7
dayname(my_birthday)
Sunday
dayofweekofmonth(my_birthday)
2
Yep, Jose was born on the second Sunday of September.
NOTE: Here’s a handy tip to just recover weekdays from Dates instances. Just use a filter on dayofweek(your_date) <= 5. For business day you can checkout the BusinessDays.jl package.
#### 3.5.1.4 Date Operations
We can perform operations in Dates instances. For example, we can add days to a Date or DateTime instance. Notice that Julia’s Dates will automatically perform the adjustments necessary for leap years, and for months with 30 or 31 days (this is known as calendrical arithmetic).
my_birthday + Day(90)
1987-12-12
We can add as many as we like:
my_birthday + Day(90) + Month(2) + Year(1)
1989-02-11
In case you’re ever wondering: “What can I do with dates again? What is available?” then you can use methodswith to check it out. We show only the first 20 results here:
first(methodswith(Date), 20)
[1] show(io::IO, dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/io.jl:736
[2] show(io::IO, ::MIME{Symbol("text/plain")}, dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/io.jl:734
[3] DateTime(dt::Date, t::Time) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/types.jl:403
[4] Day(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/periods.jl:36
[5] Month(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/periods.jl:36
[6] Quarter(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/periods.jl:36
[7] Week(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/periods.jl:36
[8] Year(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/periods.jl:36
[9] firstdayofmonth(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:84
[10] firstdayofquarter(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:157
[11] firstdayofweek(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:52
[12] firstdayofyear(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:119
[13] lastdayofmonth(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:100
[14] lastdayofquarter(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:180
[15] lastdayofweek(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:68
[16] lastdayofyear(dt::Date) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/adjusters.jl:135
[17] +(dt::Date, t::Time) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/arithmetic.jl:19
[18] +(dt::Date, y::Year) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/arithmetic.jl:27
[19] +(dt::Date, z::Month) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/arithmetic.jl:54
[20] +(x::Date, y::Quarter) in Dates at /opt/hostedtoolcache/julia/1.7.3/x64/share/julia/stdlib/v1.7/Dates/src/arithmetic.jl:73
From this, we can conclude that we can also use the plus + and minus - operator. Let’s see how old Jose is, in days:
today() - my_birthday
12687 days
The default duration of Date types is a Day instance. For the DateTime, the default duration is Millisecond instance:
DateTime(today()) - DateTime(my_birthday)
1096156800000 milliseconds
#### 3.5.1.5 Date Intervals
One nice thing about Dates module is that we can also easily construct date and time intervals. Julia is clever enough to not have to define the whole interval types and operations that we covered in Section 3.3.6. It just extends the functions and operations defined for range to Date’s types. This is known as multiple dispatch and we already covered this in Why Julia? (Section 2).
For example, suppose that you want to create a Day interval. This is easy done with the colon : operator:
Date("2021-01-01"):Day(1):Date("2021-01-07")
2021-01-01
2021-01-02
2021-01-03
2021-01-04
2021-01-05
2021-01-06
2021-01-07
There is nothing special in using Day(1) as the interval, we can use whatever Period type as interval. For example, using 3 days as the interval:
Date("2021-01-01"):Day(3):Date("2021-01-07")
2021-01-01
2021-01-04
2021-01-07
Or even months:
Date("2021-01-01"):Month(1):Date("2021-03-01")
2021-01-01
2021-02-01
2021-03-01
Note that the type of this interval is a StepRange with the Date and concrete Period type we used as interval inside the colon : operator:
date_interval = Date("2021-01-01"):Month(1):Date("2021-03-01")
typeof(date_interval)
StepRange{Date, Month}
We can convert this to a vector with the collect function:
collected_date_interval = collect(date_interval)
2021-01-01
2021-02-01
2021-03-01
And have all the array functionalities available, like, for example, indexing:
collected_date_interval[end]
2021-03-01
We can also broadcast date operations to our vector of Dates:
collected_date_interval .+ Day(10)
2021-01-11
2021-02-11
2021-03-11
Similarly, these examples work for DateTime types too.
### 3.5.2 Random Numbers
Another important module in Julia’s standard library is the Random module. This module deals with random number generation. Random is a rich library and, if you’re interested, you should consult Julia’s Random documentation. We will cover only three functions: rand, randn and seed!.
To begin, we first load the Random module. Since we know exactly what we want to load, we can just as well do that explicitly:
using Random: seed!
We have two main functions that generate random numbers:
• rand: samples a random element of a data structure or type.
• randn: samples a random number from a standard normal distribution (mean 0 and standard deviation 1).
#### 3.5.2.1rand
By default, if you call rand without arguments it will return a Float64 in the interval $$[0, 1)$$, which means between 0 inclusive to 1 exclusive:
rand()
0.18600655050915005
You can modify rand arguments in several ways. For example, suppose you want more than 1 random number:
rand(3)
[0.6348331348677316, 0.7644789964575275, 0.6930821877797426]
Or, you want a different interval:
rand(1.0:10.0)
4.0
You can also specify a different step size inside the interval and a different type. Here we are using numbers without the dot . so Julia will interpret them as Int64 and not as Float64:
rand(2:2:20)
6
You can also mix and match arguments:
rand(2:2:20, 3)
[14, 12, 8]
It also supports a collection of elements as a tuple:
rand((42, "Julia", 3.14))
42
And also arrays:
rand([1, 2, 3])
2
Dicts:
rand(Dict(:one => 1, :two => 2))
:two => 2
For all the rand arguments options, you can specify the desired random number dimensions in a tuple. If you do this, the returned type will be an array. For example, here’s a 2x2 matrix of Float64 numbers between 1.0 and 3.0:
rand(1.0:3.0, (2, 2))
2×2 Matrix{Float64}:
3.0 1.0
3.0 1.0
#### 3.5.2.2randn
randn follows the same general principle from rand but now it only returns numbers generated from the standard normal distribution. The standard normal distribution is the normal distribution with mean 0 and standard deviation 1. The default type is Float64 and it only allows for subtypes of AbstractFloat or Complex:
randn()
-0.616456676630725
We can only specify the size:
randn((2, 2))
2×2 Matrix{Float64}:
-2.72294 2.18743
0.462197 0.251399
#### 3.5.2.3seed!
To finish off the Random overview, let’s talk about reproducibility. Often, we want to make something replicable. Meaning that, we want the random number generator to generate the same random sequence of numbers. We can do so with the seed! function:
seed!(123)
rand(3)
[0.521213795535383, 0.5868067574533484, 0.8908786980927811]
seed!(123)
rand(3)
[0.521213795535383, 0.5868067574533484, 0.8908786980927811]
In some cases, calling seed! at the beginning of your script is not good enough. To avoid rand or randn to depend on a global variable, we can instead define an instance of a seed! and pass it as a first argument of either rand or randn.
my_seed = seed!(123)
Random.TaskLocalRNG()
rand(my_seed, 3)
[0.521213795535383, 0.5868067574533484, 0.8908786980927811]
rand(my_seed, 3)
[0.19090669902576285, 0.5256623915420473, 0.3905882754313441]
NOTE: Note that these numbers might differ for different Julia versions. To have stable streams across Julia versions use the StableRNGs.jl package.
One last thing from Julia’s standard library for us to cover is the Downloads module. It will be really brief because we will only be covering a single function named download.
Suppose you want to download a file from the internet to your local storage. You can accomplish this with the download function. The first and only required argument is the file’s url. You can also specify as a second argument the desired output path for the downloaded file (don’t forget the filesystem best practices!). If you don’t specify a second argument, Julia will, by default, create a temporary file with the tempfile function.
Let’s load the Downloads module:
using Downloads
For example, let’s download our JuliaDataScience GitHub repository Project.toml file. Note that download function is not exported by Downloads module, so we have to use the Module.function syntax. By default, it returns a string that holds the file path for the downloaded file:
url = "https://raw.githubusercontent.com/JuliaDataScience/JuliaDataScience/main/Project.toml"
my_file = Downloads.download(url) # tempfile() being created
/tmp/jl_DfJiF3
With readlines, we can look at the first 4 lines of our downloaded file:
readlines(my_file)[1:4]
4-element Vector{String}:
"name = \"JDS\""
"uuid = \"6c596d62-2771-44f8-8373-3ec4b616ee9d\""
"authors = [\"Jose Storopoli\", \"Rik Huijzer\", \"Lazaro Alonso\"]"
"version = \"0.1.0\""
NOTE: For more complex HTTP interactions such as interacting with web APIs, see the HTTP.jl package.
CC BY-NC-SA 4.0 Jose Storopoli, Rik Huijzer, Lazaro Alonso
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# Exporting to HTML with LaTeX Environments (amsthm)
I have been using org-mode to keep a personal maths notes wiki for the past several weeks. I chose HTML for this project as I wanted to be able to
1. Format the entries without having to worry about loading PDFs or how things would look on a page
2. Navigate between entries seamlessly
3. Edit all of the entries from within org-mode with support for org-publish
4. Share individual entries if need be
5. View these files on a wide range of devices
However, I am unable to figure out a way to get theorem, proof, and other environments to export to my .html wiki files. As was addressed in this Stack Exchange post mathjax doesn't seem to be the right tool for the job here.
With #+LaTeX_HEADER: \usepackage{amsthm} in the relevant org-files and attempted to use latexml to process the LaTeX in my .org file using.
(setq org-latex-to-mathml-convert-command
"latexmlmath \"%i\" --presentationmathml=%o")
However, this still doesn't provide the required result. I am able to use hevea outside of emacs on tex files, which yields the required result with theorem and proof environments rendering as intended when defined using \newtheorem{theorem}[]. However, I don't know how I would export using hevea and org-publish without creating a new export backend.
Any ideas on how to get either hevea to work with org-publish or get amsthm environment support in HTML (preferably with numbering)? Thank you!
EDIT: Thanks to Nick for the suggestion to add example inputs and outputs!
Say I was working with a file projectfile.org with the content
#+ LaTeX_HEADER: \usepackage{amsthm}
#+BEGIN_theorem
The statement of a theorem.
#+BEGIN_proof
Proof of a theorem
#+END_proof
#+END_theorem
If I run C-c C-e h h on the file I get an projectfile.html that looks like this
If I run C-c C-e l l' (which producesprojectfile.tex) and then runhevea projectfile.texmyprojectfile.html looks like this
I have a dozen or so org files in my wiki folder and so when I run org-publish-project I would like to get html output that is similar to the the second result (theorem numbering, proof formatting, and so on).
• I suggest you provide an example of the input and output that you want. Some people know about org, some people know about latex, some people know about \newtheorem, some people know about hevea, but as you add more and more of these, the intersection gets smaller and smaller: you may be the only one left in it :-) – NickD Sep 19 '17 at 1:53
• @Nick Thank you! I have added some more information. – Ryan J.C. Sep 19 '17 at 12:22
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# Conditional probability?
Let's consider this hypothetical game, in which there are 10 cards, and one of the cards is marked as a winning card. We put the cards in a stack and pass them around in a circle, each person choosing one card at random and passing the remaining stack on, until none are left.
What is the probability that I pick the winning card? Initially, for the first person choosing, the probability is 1/10. Does the probability increase with successive turns, because the chances that the winning card is picked is smaller at the beginning? Or is the probability the same 1/10 throughout the whole game? Is it more beneficial to go later than to go first? I tried to think about this through an expected value lens and got all confused.
• A bit confusing in the sense that it depends on how many friends are participating. For example if there are five friends, then each has 2 cards. Also, it depends on whether or not the cards are face up or face down. If the cards are face up, the odds must account for the additional information of not getting the winning card at each step. If the cards are hidden, for five friends, and are not looked at until all the cards are dealt, then the odds are one in five for each player. So, in effect, the conditional probability depends on the conditions of the game. – Carl Aug 23 at 7:30
The probability that the first player wins is $$1/10$$.
The probability that the second player wins is the probability to have the winning card still in the stack (i.e. the probability that the first player did not win - $$1-1/10=9/10$$) times the probability that the second player will draw the winning card from the stack of 9 cards (i.e. $$1/9$$). Multiply those and you see that you end up with $$9/10 \cdot 1/9 = 1/10$$, same as the first player.
Similarly, the third player has a probability of $$9/10 \cdot 8/9 = 8/10$$ to get a stack with the winning card in it, but if they get it, they have a probability of $$1/8$$ to draw the winning card; again, it multiplies to $$1/10$$.
This holds on all the way until the 10th player (of course, the 11th player has no probability to draw the winning card).
For your intuition, consider this: The later players have a lower probability to have the winning card still in the stack (because more players drew from it), but if it's there - they have a higher probability to draw it (because the stack is smaller).
For another bit of intuition, consider that this process is no different than assigning cards at random... would you expect any other probability than $$1/10$$?
The probability is always 1/10 unless the players look at the card and then you know that it's not a winning card (or is). This is not really a conditional probability problem because you don't condition on anything and no new information is made available until all 10 player, presumably reveal their cards after everyone has drawn.
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Question
A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km. The trip took 18.0 min. (a) What was her average speed? (b) If the straight-line distance from her home to the university is 10.3 km in a direction $25.0^\circ$ south of east, what was her average velocity? (c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity for the entire trip?
a) $40.0 \textrm{ km/h}$
b) $34.3 \textrm{ km/h}$
c) average speed = $3.20 \textrm{ km/h}$, average velocity = $0$
Solution Video
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International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier
International Tables for Crystallography (2013). Vol. D, ch. 1.2, pp. 67-68
## Section 1.2.7.4.3. Diagonalization of the action matrix and determination of the invariant tensor
M. Ephraïm,b T. Janssen,a A. Jannerc and A. Thiersd
#### 1.2.7.4.3. Diagonalization of the action matrix and determination of the invariant tensor
| top | pdf |
An invariant element of the tensor space under the group G is a vector v that is left invariant under each generator: If the number of generators is one, . This equation is solved by diagonalization: where . The dimension of the solution space is the number of elements that are equal to zero. The corresponding rows of Q form a basis for the solution space. (See example further on.)
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# expcdf
Cumulative distribution function for exponential distribution
### expcdf(x, mu)
• The input arrays mu and x should have the same sizes. They contain, respectively, mean values of the CDFs being evaluated, and x values at which the CDFs are evaluated.
• If one of the inputs is a scalar, it would be expanded to match the size of the other input.
• It returns NaN for negative elements of mu.
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• V S Rawat
Articles written in Pramana – Journal of Physics
• Physics and technology of tunable pulsed single longitudinal mode dye laser
Design and technology demonstration of compact, narrow bandwidth, high repetition rate, tunable SLM dye lasers in two different configurations, namely Littrow and grazing incidence grating (GIG), were carried out in our lab at BARC, India. The single longitudinal mode (SLM) dye laser generates single-mode laser beams of $\sim 400$ MHz (GIG configuration) and $\sim 600$ MHz (Littrow configuration) bandwidth. Detailed performance studies of the Littrow and GIG dye laser resonators showed that GIG dye laser results in narrower linewidth and broad mode hop free wavelength scanning over 70 GHz. In this paper we present experimental studies carried out on the high repetition rate SLM dye laser system.
• Measurement of flow fluctuations in single longitudinal mode pulsed dye laser
A simple technique had been demonstrated for measuring flow-induced fluctuations in the single longitudinal mode (SLM) pulsed dye laser. Two prominent frequency components of 10.74 Hz and 48.83 Hz were present in the output of the Nd:YAG-pumped SLM dye laser. The flow-induced frequency component of 48.83 Hz was present due to the revolution per minute of the motor attached to the magnetically coupled gear pump. The time average bandwidth of 180 MHz has been obtained for this SLM dye laser. The effect of pump pulse energy on the bandwidth of the SLM dye laser was studied. The bandwidth of the SLM dye laser was increased to 285 MHz from 180 MHz, when the pump pulse energy was increased to 0.75 mJ from 0.15 mJ for a constant dye flow velocity of 0.5 m/s.
• # Pramana – Journal of Physics
Volume 96, 2022
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019
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# What are high frequencies and low frequencies in a signal?
I'm new to signal processing. I'm plotting a signal in the time-domain in matlab. I don't understand which parts of the signal are high frequencies and low frequencies, can someone explain what a high and low frequency is, and how to see high frequencies and low frequencies on a graph?
-
Read about FFT in MATLAB. You cannot always "see" the high and low frequencies by plotting the signal in the time domain, though in a few toy examples, the results would be obvious enough. – Dilip Sarwate Dec 27 '11 at 14:21
so if i plot using fft i would be able to easily see what frequencies occur more often and the ones that occur the most are the ones that have a higher frequency, right? – user1117262 Dec 27 '11 at 14:32
Broadly speaking, yes, the FFT will reveal the frequency content, but be aware that there are many niggling details that can trip up the neophyte. It is quite easy to get answers that are misleading by not applying the FFT properly. – Dilip Sarwate Dec 27 '11 at 14:55
The high frequencies contribute to the fast varying parts of the signal(the sharp transitions), while the low frequencies contribute to the slow variations of the signal in the time domain.
You might want to take a look over here: http://cns-alumni.bu.edu/~slehar/fourier/fourier.html
Also, if you have the time you might want to take a look at this online course: http://academicearth.org/courses/the-fourier-transform-and-its-applications You won't regret it.
-
High and low frequencies are dependent on the application. A low frequency for wifi would be 2.4GHz, while a high frequency would be 5GHz. For human speech a low frequency is 300Hz, while a high frequency is 3000Hz.
A graph of a fft (Fast Fourier Transform) allows us to visualize different frequencies. This example is adapted from Matlab's fft help. The following figure shows the first 100 out of $2^{20}$ samples of a time signal with two frequencies. Note how it is difficult to see the 1Hz component in this figure.
To see the frequency content we plot the spectrum as show in the following figure. Here we can clearly see the two frequencies - one at 1Hz and the other at 50Hz.
Here is the code I used to generate these plots.
fs = 2^10; %sample frequency in Hz
T = 1/fs; %sample period in s
L = 2^20; %signal length
t = (0:L-1) * T; %time vector
A1 = 0.2; %amplitude of x1 (first signal)
A2 = 1.0; %amplitude of x2 (second signal)
f1 = 1; %frequency of x1
f2 = 50; %frequency of x2
x1 = A1*sin(2*pi*f1 * t); %sinusoid 1
x2 = A2*sin(2*pi*f2 * t); %sinusoid 2
y = x1 + x2;
%Plot signal
figure;
set(gcf,'Color','w'); %Make the figure background white
plot(fs*t(1:100), y(1:100));
set(gca,'Box','off'); %Axes on left and bottom only
str = sprintf('Signal with %dHz and %dHz components',f1,f2);
title(str);
xlabel('time (milliseconds)');
ylabel('Amplitude');
%Calculate spectrum
Y = fft(y)/L;
ampY = 2*abs(Y(1:L/2+1));
f = fs/2*linspace(0,1,L/2+1);
i = L/fs * (max(f1,f2)) + 1; %show only part of the spectrum
%Plot spectrum.
figure;
set(gcf,'Color','w'); %Make the figure background white
plot(f(1:i), ampY(1:i));
set(gca,'Box','off'); %Axes on left and bottom only
title('Single-Sided Amplitude Spectrum of y(t)');
xlabel('Frequency (Hz)');
ylabel('|Y(f)|');
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Good explanation, but I feel it's a little unfair to say that you can observe the 1 Hz component in the transform but not in the time domain. If you looked at a few seconds (or even 1 second) of y in the time domain the wander would show up. I'd also recommend a window on the FFT, just so others who come across this example don't get the wrong idea. – mtrw Dec 27 '11 at 23:17
@mtrw: I agree. If I show more of the signal in the time domain, seeing that there is more than one frequency would be easier. As far as windowing, I'm not sure I understand of which wrong idea you are thinking. There are lots :-) – Richard Povinelli Dec 27 '11 at 23:28
How about the wrong idea that it's ok to look at a spectrum of a signal that's not periodic in the transform frame if you didn't apply a window first? – mtrw Dec 27 '11 at 23:33
It is OK to "look" at the spectrum of a signal not periodic in the transform aperture. Windowing is information lossy. There are sometimes other ways of dealing with the various artifacts. – hotpaw2 Dec 28 '11 at 1:43
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# How does Env.shapeNumber work?
I expected these two lines to produce similar envelopes, but they differ…significantly. Perhaps someone can help me understand why?
Env([0,1,0],[0.01,1],Env.shapeNumber(\cubed)).plot;
Env([0,1,0],[0.01,1],\cubed).plot;
I’d like to be able to pass an integer to a Synth arg in order to get the curves normally accessed by key (\sine, \welch, etc.)…if possible!
Hello!
They cannot be identical because
Env.shapeNumber(\cubed)
returns a number 7 as an integer. The third argument of Env.new is the curve which accepts a Symbol, Float, or an Array of those. Since the number 7 is an integer, it will internally be interpreted as a float, i.e. as a curvature value for all segments. 0 means linear, positive and negative numbers curve the segment up and down.
Thus, the first code
Env([0,1,0],[0.01,1],Env.shapeNumber(\cubed)).plot;
is same as the following code:
Env([0, 1, 0], [0.01, 1], 7).plot;
In the help document of VarLag, there are some examples with Env.shapeNumber.
https://doc.sccode.org/Classes/VarLag.html
prko is correct that you can’t use the shape number in an Env definition directly, because it will be interpreted as a curvature value.
The shape number is embedded into the envelope’s array representation (to which it’s converted when it’s used in an EnvGen).
To pass in the shape number, then, AFAIK you have to hack the array representation. The array starts with four values: initial level, number of segments, release node, loop node. You don’t want to touch these. Starting with index 4, then you have four values for each segment: target level, time, shape number, curvature. Overwrite these with synth controls.
This example assumes the same shape for all segments.
(
SynthDef(\envtest, { |out, shape = 0, curve = 0, time = 1, amp = 0.1|
// \lin is a dummy curvature -- it will be replaced
var env = Env([0, 1, 0], [0.5, 0.5], \lin);
var eg;
var envArray = env.asArray;
envArray[6, 10 ..] = shape;
envArray[7, 11 ..] = curve;
eg = EnvGen.kr(envArray, timeScale: time, doneAction: 2);
Out.ar(out, (SinOsc.ar(440) * (eg * amp)).dup);
)
Synth(\envtest, [shape: Env.shapeNumber(\lin)]);
Synth(\envtest, [shape: Env.shapeNumber(\sin)]);
Synth(\envtest, [shape: Env.shapeNumber(-4), curve: -4]);
hjh
3 Likes
Thanks @prko and @jamshark70 for your replies - accessing the envArray should work for my purposes.
Just to clarify, what’s the distinction between shape and curvature?
1 Like
Yes, the distinction between shape and curvature is difficult to grasp.
Here’s some of the code from Env.sc:
prAsArray {
var contents, size;
var levelArray = levels.asUGenInput;
var timeArray = times.asUGenInput;
var curvesArray = curves.asArray.asUGenInput;
size = times.size;
contents = Array.new((size + 1) * 4);
size.do { arg i;
};
^contents.flop;
}
The last two lines make the distinction, though rather vaguely.
curveValue was written for & only used in .asArray above:
curveValue { arg curve;
^if(curve.isSequenceableCollection) {
curve.collect { |x|
if(x.isValidUGenInput) { x } { 0 }
}
} {
if(curve.isValidUGenInput) { curve } { 0 }
}
}
It’s only purpose is to replace invalid Ugen arguments with zero values.
It’s unclear how .curveValue fits into the bigger picture of the envelope, and how it differs from typical .curves (shapes) such as \linear, \exponential, \welch, etc.
Shape is \lin, \exp, \sin etc. (or one other shape which isn’t named, for a curved line).
Curvature is a parameter of that unnamed shape, which specifies how far away from a straight line to bend.
hjh
1 Like
Can you send an example?
Different segment shapes and curve values are plotted here – see the last 3 in the first section for curvature.
http://doc.sccode.org/Classes/Env.html#examples
hjh
So, a major element of the distinction is when float or integer values (or an array of them) are used instead of the traditional values found in Env.shapeNames?
\sine would be a shape, and -4 would be a curve
Thank you as always for answering where no one else can.
I’ve come to the understanding that either a shape value such as \sine or \welch can be used, or a curve value which is an instance of magnitude, and they can’t be used simultaneously in the same envelope segment, though they can be used in the same envelope.
Also rather strange, on my end running Env.shapeNumber with any number returns an integer 5.
For .asArray, when the contents are being made, the last two lines are still a source of slight confusion.
size.do { arg i;
};
If these values are treated so distinctly, then why is .shapeNumber & curveValue used on every value in the curvesArray?
And why are both added to contents for each envelope segment, when they can never be used simultaneously?
To use one of the examples from the documentation:
Env.new([0, 1, 0.3, 0.8, 0], [2, 3, 1, 4], 2).asArray
Returns:
// [ 0, 4, -99, -99, 1, 2, 5, 2, 0.3, 3, 5, 2, 0.8, 1, 5, 2, 0, 4, 5, 2 ]
The values can be followed just as seen in the source code:
contents.add(levelArray.at(0));
size.do { arg i;
};
The values 5 and 2 can be seen representing each segment for the curvesArray
Env.shapeNumber will return 5 when given any number, and the segments have a true curve value of 2.
-5 to 5 is the full range of effective curve values, with the exception of 0, which has the same effect on curve as the default value, \lin.
@jamshark70’s original example works because he’s passing the envelope’s array representation to the EnvGen's envelope argument.
This can be seen in the source for EnvGen:
EnvGen : UGen { // envelope generator
*ar { arg envelope, gate = 1.0, levelScale = 1.0, levelBias = 0.0, timeScale = 1.0, doneAction = 0;
envelope = this.convertEnv(envelope);
^this.multiNewList(['audio', gate, levelScale, levelBias, timeScale, doneAction, envelope])
}
EnvGen first calls convertEnv on it’s envelope:
*convertEnv { arg env;
if(env.isSequenceableCollection) {
if (env.shape.size == 1) {
^env.reference
} {
// multi-channel envelope
^env.collect(_.reference)
};
};
^env.asMultichannelArray.collect(_.reference).unbubble
}
The following both return the same result:
EnvGen.convertEnv([ 0, 2, -99, -99, 1.0, 0.01, 5, -4.0, 0, 1.0, 5, -4.0 ]);
EnvGen.convertEnv(Env.perc);
As a final note:
##### A shapeNumber of 5 is the true missing or unnamed shape.
(step -> 0)
(linear -> 1)
(exponential -> 2)
(sine -> 3)
(wel -> 4)
(sqr -> 6)
(cubed -> 7)
(hold -> 8)
##### In the array passed to EnvGen, the shape number must be 5 for the curve # to have an effect.
AppClock.sched(0, r{
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 5, -4, 0.3, 3, 5, -1, 0.8, 1, 5, 1, 0, 4, 5, 4 ])}.plot(10);
// ~ # ~ # ~ # ~ #
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 0, -4, 0.3, 3, 0, -1, 0.8, 1, 0, 1, 0, 4, 0, 4 ])}.plot(10);
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 1, -4, 0.3, 3, 1, -1, 0.8, 1, 1, 1, 0, 4, 1, 4 ])}.plot(10);
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 2, -4, 0.3, 3, 2, -1, 0.8, 1, 2, 1, 0, 4, 2, 4 ])}.plot(10);
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 3, -4, 0.3, 3, 3, -1, 0.8, 1, 3, 1, 0, 4, 3, 4 ])}.plot(10);
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 4, -4, 0.3, 3, 4, -1, 0.8, 1, 4, 1, 0, 4, 4, 4 ])}.plot(10);
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 6, -4, 0.3, 3, 6, -1, 0.8, 1, 6, 1, 0, 4, 6, 4 ])}.plot(10);
{EnvGen.ar([ 0, 4, -99, -99, 1, 2, 7, -4, 0.3, 3, 7, -1, 0.8, 1, 7, 1, 0, 4, 7, 4 ])}.plot(10);
})
The following lines are useful for printing Env.shapeNames:
Env.shapeNames.keys(SortedList).printAll
cub
cubed
exp
exponential
hold
lin
linear
sin
sine
sqr
squared
step
wel
welch
Env.shapeNames.keys(SortedList).collect{ |n| n -> shapeNumber(Env, n) }.printAll
(cub -> 7)
(cubed -> 7)
(exp -> 2)
(exponential -> 2)
(hold -> 8)
(lin -> 1)
(linear -> 1)
(sin -> 3)
(sine -> 3)
(sqr -> 6)
(squared -> 6)
(step -> 0)
(wel -> 4)
(welch -> 4)
Env.shapeNames.invert.keys(SortedList).collect{ |n| Env.shapeNames.findKeyForValue(n) -> n }.printAll
(step -> 0)
(linear -> 1)
(exponential -> 2)
(sine -> 3)
(wel -> 4)
(sqr -> 6)
(cubed -> 7)
(hold -> 8)
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Math Help - differential equation working
1. differential equation working
Hello, I am looking at the differential equation:
dR/DΘ + R = e^-Θ * sec^2Θ
I understand how to use e^(integral of e^(1dΘ) to multiply both sides which gives me:
(looking at left hand side of equation only)
e^Θ * dR/dΘ + e^Θ * R
However I am not sure how to further simplify the left hand side of the equation before integrating.
Can someone please show me the process for doing that.
Thanks kindly for any help.
2. Re: differential equation working
now you can use the property -
$\frac{du}{d\theta}v+\frac{dv}{d\theta}u=\frac{duv} {d\theta}$
where $u=e^\theta$ and $v=R$
eventually you'll get
$\frac{d(e^\theta R)}{d\theta}=\sec^2\theta$
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# Uniform Circular Motion: Centripital Acceleration vs. Acceleration
by Chele
Tags: acceleration, centripital, circular, motion, uniform
P: 17 I am very new to physics and am taking a my first University Physics class. This is not a call for a problem to be solved, but a clarification on terminology. In solving problems for uniform circular motion, some problems call for the acceleration of the object (a=v^2/r) and others the centripital or instantanious acceleration (a=4pi^2r/T^2). Can you please attempt to explain, in layman's terms, the difference between the two references to acceleration? Thanks for your assistance.
Mentor
P: 40,280
Quote by Chele In solving problems for uniform circular motion, some problems call for the acceleration of the object (a=v^2/r) and others the centripital or instantanious acceleration (a=4pi^2r/T^2).
The two formulas are equivalent. (Express the speed in terms of circumference over period and you'll see for yourself.)
For uniform circular motion, the acceleration is centripetal. (Centripetal just means "towards the center".)
P: 17 Wow- I'll need to look at that in further detail.... Thanks for your help!
HW Helper
P: 2,882
## Uniform Circular Motion: Centripital Acceleration vs. Acceleration
Quote by Chele Wow- I'll need to look at that in further detail.... Thanks for your help!
Indeed, the two are equivalent for UCM. This can be seen easily if you recall that for constant speed, you may use v= distance/time. If you wait for the particle to go through a full circle, it will have covered a distance 2 Pi r, and the time elapsed will be the period T.
So
$v_{ucm} = \frac{2 \pi r}{T}$
Using this formula it is simple to prove that the two equations for acceleration you gave are equal.
P: 17 Okay, thanks. I worked it out and it is exactly the same. Not sure why I didn't see it before. Thanks guys!
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# Semidefinite relaxations of quadratic constraint
#1
Hello,
I am trying to solve an optimization problem with 174 quadratic constraints of the form
x_{1,2}(k)^TQx_{1,2}(k) +c^Tx_3(k) \leq 0, where Q is symmetric positive definite and the subscripts 1,2 are meant to indicate that at each time step k only variables 1 and 2 are included in this constraint. Currently I enforce these constraints by looping over all time steps.
I would like to try a semidefinite relaxation of these constraints which is defined as: \text{Tr}\ QX(k) + c^Tx_3(k) \leq 0, where the condition X(k) = x_{1,2}(k)x_{1,2}(k)^T is relaxed to an inequality and written as \begin{pmatrix}1& x_{1,2}(k)^T \\ x_{1,2}(k)& X(k) \end{pmatrix} \succeq 0 using the Schur complement.
My question is: is it possible to declare a variable X(k) for every timestep k within a loop so that the matrix inequality stated above can be enforced within a loop?
Multiple matrix variables definition
(Michael C. Grant) #2
Sure, you can create a 3-D array variable:
variable X(N,N,M) symmetric
Each 2-D slice X(:,:,k) will be symmetric.
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