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http://h2o-networks.co.uk/read/elliptic-diophantine-equations-a-concrete-approach-via-the-elliptic-logarithm
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math
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Elliptic Diophantine Equations: A Concrete Approach Via the by Nikos Tzanakis PDF
By Nikos Tzanakis
This ebook offers in a unified means the attractive and deep arithmetic, either theoretical and computational, on which the categorical resolution of an elliptic Diophantine equation is predicated. It collects a variety of effects and techniques which are scattered in literature. a few effects are even hidden at the back of a few workouts in software program applications, like Magma. This booklet is appropriate for college kids in arithmetic, in addition to expert mathematicians.
Read Online or Download Elliptic Diophantine Equations: A Concrete Approach Via the Elliptic Logarithm PDF
Best algebraic geometry books
This ebook treats the topic of analytic features of 1 or extra actual variables utilizing, nearly exclusively, the concepts of actual research. This strategy dramatically alters the average development of rules and brings formerly ignored arguments to the fore. the 1st bankruptcy calls for just a history in calculus; the therapy is almost self-contained.
Because of the loss of right bibliographical resources stratification thought looks a "mysterious" topic in modern arithmetic. This booklet includes a entire and ordinary survey - together with a longer bibliography - on stratification concept, together with its old improvement. a few additional vital themes within the e-book are: Morse idea, singularities, transversality concept, complicated analytic types, Lefschetz theorems, connectivity theorems, intersection homology, enhances of affine subspaces and combinatorics.
During this e-book the authors increase the speculation of knotted surfaces in analogy with the classical case of knotted curves in three-d area. within the first bankruptcy knotted floor diagrams are outlined and exemplified; those are ordinary surfaces in 3-space with crossing info given. The diagrams are additional more advantageous to provide substitute descriptions.
- Curves and Their Jacobians
- Algebraic Geometry 5
- Fundamentals of Neuromechanics
- Algebras, rings, and modules : Lie algebras and Hopf algebras
Additional info for Elliptic Diophantine Equations: A Concrete Approach Via the Elliptic Logarithm
Z/ vary in a 1-1 way from the smallest root e3 to 1. Now we study the behaviour of the function } 0 . z/ e1 . 21 . 1 C! 21 3 x 7! 21 to e3 . 21 . z/ D 0 if z is a vertex. z/ belong to either the interval Œe2 , e1 (if z is on the right vertical side) or to the interval . R/. R/ are those of the two horizontal sides. 1. Case > 0. R/. z runs along half-open line segments . 1 2 ................... z/ 0 >0 0 <0 0 . 1 2 . . . . . . . . . . . . 1 2 e1 % C1 & e1 0 % C1 # jump 1 % 0 infinite the vertices.
2 P / . 9]. As already noted, for S. 28). 28), the canonical height used by S. 2N P / . 1. 6 The canonical height O / so that D is also a model of E. 37), respectively, are related by O /. Q/. 3]): The Néron–Tate pairing is bilinear. P O O h. P /. P O / D 0 if and only if P E is a torsion point. P hPi , Pj imi mj . 7]. P1 , : : : , Pr / D . 39) (cf. 38)). 2. 7). 39). Proof. P where m is the column vector with components m1 , : : : , mr . As H is symmetric, a def D 1 < 2 < < r of H and an diagonal matrix ƒ of eigenvalues 0 < 26 Chapter 2 Heights orthogonal matrix Q exist such that H D QT ƒQ.
C/ ! r// to r C ƒ. We have to show that is a group homomorphism. 3” of . C/. zi //. P2 /. This is obviously true if at least one Pi is the zero point, therefore we assume that both P1 , P2 are non-zero points. z2 /. 3 Actually, is a group isomorphism; see the beginning of next section. z2 /. 31]. P1 C P2 /. P2 /. z2 /. z1 /. O/ D ƒ. }. z2 /, 12 } 0 . mod ƒ/. r// with r 2 P . P /. ei , 0/ for some i 2 ¹1, 2, 3º (cf. 1 C! , 2 º and, on the other hand, 2P D O. P /. r/ ¤ 0. r/2 C A/. 2P /. C/ 7 !
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863463.3/warc/CC-MAIN-20180620050428-20180620070428-00623.warc.gz
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CC-MAIN-2018-26
| 3,839 | 16 |
https://tutors.com/or/portland/math-tutors/aris-math-tutoring
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math
|
I do enrichment mentoring for students who are interested in mathematics, physics and/or computer science. Since I have studied many areas in and related to mathematics, I can help students at all level with whatever they are most interested in. My priority is to form good connections with my students and for them (and me) to truly enjoy our work together. In my experience, this is a prerequisite for sustained engagement in a challenging subject such as mathematics.
I have a personal passion for mathematics and I love connecting with students who are in the process of discovering their own interest in it. People who love math can bond over the joys of having a new idea or solving a difficult problem, no matter what the age difference!
Ari was able to relate really well to my son, making all kinds of math topics fun for him. We originally asked him to help with Geometry questions, but soon they were exploring a wide range of topics, from Number Theory, to Topology, to Set Theory. Ari is very personable and his passion for math and learning makes it fun for his students.
My son has been working with Ari for two years, and he always has a great experience. Not only is Ari extremely smart and knowledgeable, but he is also enthusiastic about the material and fun to work with. It's a unique combination. Regardless of whether your child is passionate or hesitant about math, we would recommend Ari wholeheartedly.
In the first meeting with a new student, I try to learn as much as I can about them, their interests and any specific goals they might have. I tailor the structure and content of my mentoring to each student's personality and interests.
I have a MS in mathematics from Portland State University.
I typically charge $45/hr, but the price can be negotiated for families that are unable to afford this.
I have been working as a tutor for more than 10 years. I began as an employee in my college's math and science tutoring center.
Over the years, I have worked with all types of student (elementary school through college) on subjects including mathematics (all types), physics, chemistry and programming. In recent years, however, I primarily mentor students in mathematics for enrichment or recreational purposes.
I ran an afterschool program in which students designed, built and programmed electronic devices, including remote-controlled cars and a handheld video game.
In a mentoring relationship, the personal connection between teacher and student is as important as the teacher's expertise. Therefore, I think it is essential for students to find a teacher with whom they enjoy sharing ideas and asking questions.
Math Tutors Algebra Tutors Algebra 1 Help Tutors Algebra 2 Tutors Algorithms Tutors Analytical Geometry Help Tutors AP Calculus Tutors Applied Mathematics Tutors Arithmetic Tutors Basic Math Tutors Calculus Tutors Calculus 2 Tutors College Algebra Help Tutors Competition Math Tutors Differential Equations Help Tutors Discrete Math Tutors Elementary Algebra Tutors Elementary Math Tutors Finite Mathematics Tutors Intermediate Algebra Tutors
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335444.58/warc/CC-MAIN-20220930051717-20220930081717-00018.warc.gz
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CC-MAIN-2022-40
| 3,090 | 12 |
https://socratic.org/questions/a-substance-consisting-only-of-na-b-and-h-is-60-80-na-and-28-60-b-what-is-the-em
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math
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A substance consisting only of Na, B and H is 60.80% Na and 28.60% B. What is the empirical formula of the substance?
As is standard with these sorts of problems, we assume a
And then we divide thru each mass by the ATOMIC mass of each constituent to give a molar ratio.
How did I know that there were
And now we divide thru by the smallest molar quantity, i.e.
This is sodium borohydride, a very common laboratory reagent.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363292.82/warc/CC-MAIN-20211206103243-20211206133243-00227.warc.gz
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CC-MAIN-2021-49
| 423 | 6 |
https://www.factmonster.com/math-science/mathematics/algebra/algebra-speed-and-distance-problems
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math
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Algebra: Speed and Distance Problems
Speed and Distance Problems
Have you ever heard of a word problem like this one? "Train A heads north at an average speed of 95 miles per hour, leaving its station at the precise moment as another train, Train B, departs a different station, heading south at an average speed of 110 miles per hour. If these trains are inadvertently placed on the same track and start exactly 1,300 miles apart, how long until they collide?"
If that problem sounds familiar, it's probably because you watch a lot of television (like me). Whenever TV shows talk about math, it's usually in the context of a main character trying but failing miserably to solve the classic "impossible train problem." I have no idea why that is, but time and time again, this problem is singled out as the reason people hate math so much.
Make sure that the units match in a travel problem. For instance, if the problem says you traveled at 70 miles per hour for 15 minutes, then r = 70 and t = 0.25. Since the speed is given in miles per hour, the time should be in hours also, and 15 minutes is equal to .25 hours. I got that decimal by dividing 15 minutes by the number of minutes in an hour: 1560 = 14 = 0.25.
In fact, it's not so hard. This, like any distance and rate of travel problem, only requires one simple formula:
- D = r · t
Distance traveled (D) is equal to your rate of speed (r) multiplied by the time (t) you traveled that speed. What makes most distance and rate problems tricky is that you usually have two things traveling at once, so you need to use the formula twice at the same time. In this problem, you'll use it once for Train A and once for Train B.
To keep things straight in your mind, you should use little descriptive subscripts. For example, use the formula DA = rA · tA for Train A's distance, speed, and time values and use the formula DB = rB · tB for Train B.
The little A's in the formula DA = rA · tA don't affect the values D, r, and t. They're just little labels to ensure that you only plug values corresponding to Train A into that formula.
Example 4: Train A heads north at an average speed of 95 miles per hour, leaving its station at the precise moment as another train, Train B, departs a different station, heading south at an average speed of 110 miles per hour. If these trains are inadvertently placed on the same track and start exactly 1,300 miles apart, how long until they collide?
Solution: Two trains means two distance formulas: DA = rA · tA and DB = rB · tB. Your first goal is to plug in any values you can determine from the problem. Since Train A travels 95 mph, rA = 95; similarly, rB = 110.
Notice that the problem also says that the trains leave at the same time. This means that their travel times match exactly. Therefore, instead of denoting their travel times as tA and tB (which suggests they are different), I will write them both as t (which suggests they are equal). At this point, your formulas look like this:
|DA = 95t
|DB = 110t
Even though you added the distances in this problem, you won't always do soit depends on how the problem is worded. In Problem 3, for example, you will not calculate a sum.
Here's the tricky step. The trains are heading toward one another on a track that's 1,300 miles long. Therefore, they must collide when, together, both trains have traveled a total of 1,300 miles. Of course, Train B is going to travel more of those 1,300 miles than Train A, since it's traveling faster, but that doesn't matter. You don't even have to figure out how far each train will go. All that matters is that when DA + DB = 1300, it's curtains. Luckily, you happen to know what DA and DB are (95t and 110t, respectively) so plug those into the equation and solve.
You've Got Problems
Problem 3: Dave rode his bike from home to a 7-11 at an average speed of 17 mph, and the trip took 1.25 hours. However, as he pulled up to the store, he rode over some glass, causing both tires to go flat. Because of this rotten luck, he had to push his bike back home at an average speed of 3 mph. How long did the trip home take?
- DA + DB = 1300
- 95t + 110t = 1300
- 205t = 1300
- t 6.341 hours
So, the trains will collide in approximately 6.341 hours.
Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817442.65/warc/CC-MAIN-20240419172411-20240419202411-00192.warc.gz
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CC-MAIN-2024-18
| 4,480 | 25 |
https://m.hugendubel.de/de/taschenbuch/richard_p_stanley-enumerative_combinatorics-3069561-produkt-details.html
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math
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Bisher € 51,49
Lieferbar innert 2 Wochen
BeschreibungThis second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Inhaltsverzeichnis5. Composition of generating functions; 6. Algebraic, D-finite, and noncommutative generating functions; 7. Symmetric functions; Appendix Sergey Fomin.
Pressestimmen'This magnificent two-volume work is best described by a quote from Gian-Carlo Rota's Forward to Volume 2: I find it impossible to predict when Richard Stanley's two-volume exposition of combinatorics may be superseded. No one will dare try, let alone be able, to match the thoroughness of coverage, the care for detail, the definitiveness of proof, the elegance of presentation.' J. E. Graver 'As a researcher, Stanley has few peers in combinatorics; as at once, to pack every page with information, connect with the reader's intuition, and communicate the underlying, unifying philosophy of the subject.' D. V. Feldman, University of New Hampshire 'What else is to be added to our comments on this excellent book? Perhaps a quotation from G.-C. Rota's foreword: 'Every once in a long while, a textbook worthy of the name comes along ... Weber, Bertini, van der Waerden, Feller, Dunford and Schwartz, Ahlfors, Stanley.' European Mathematical Society '... an authoritative account of enumerative combinatorics.' George E. Andrews, Bulletin of the London Mathematical Society 'What else can be added to the comments upon this excellent book?' EMS Newsletter
Untertitel: 'Cambridge Studies in Advanced Mathematics'. illustrations. Sprache: Englisch.
Verlag: Cambridge University Press
Erscheinungsdatum: Juni 2001
Seitenanzahl: 600 Seiten
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s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463605188.47/warc/CC-MAIN-20170522151715-20170522171715-00136.warc.gz
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CC-MAIN-2017-22
| 2,623 | 9 |
http://www.scienceforums.com/topic/35890-collecting-evidence-negating-all-of-einsteins-hypothesies/page-3
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math
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So the question is, as gamma is calculated from this triangle, but the triangle SEEMS to be changing as the ship gets further away, does this mean that Time itself will gradually return to normal? That is Time DIlation calculated is only valid for the split second that the moving clock in directly in front of the observer?
Please don't claim that this is an illusion of perspective, as the WHOLE damn hypothesis of Einstein HANGS totally on the stationary observer's PERCEPTION of reality, NOT in reality itself. Einstein always uses the very word, "SEEMS LIKE".
So there we have another reason why SR fails as a hypothesis, its irrational gibberish.
about my post #32
No one has taken a shot at this one? Einstein depends on the "point of view", the "appearance" of events, how events SEEM to the observer. AND he insists that the observer is kept ignorant about key things such as if he is moving or not. So here is the accurate apparent path that the light pulse would have.
Now let's see you do the math to come up with time dilation.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998291.9/warc/CC-MAIN-20190616182800-20190616204800-00051.warc.gz
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CC-MAIN-2019-26
| 1,040 | 6 |
http://dmoz-odp.org/Science/Math/Recreations/Specific_Numbers/phi/
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math
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Phi is the Greek letter representing the golden ratio, also called the golden mean or the golden proportion. Break a line segment into two such that the ratio of the whole to the longest segment is the same as the ratio of the two segments, that ratio is the golden ratio. Phi = 1.618034...
Information on the Golden Section, Divine Proportion, Fibonacci series and phi.
A Project Gutenberg Etext.
Ask Dr. Math
A list of questions gathered pertaining to Fibonacci and Golden Ratio.
A brief introduction to Golden Ratio
An interview with George Cardas, describing his use of the Golden Ratio in high-end audio equipment cables.
Colin and Greg's Golden Ratio Page
This is an informative site on an interesting aspect of Geometry: The Golden Ratio.
Constructing the Golden Rectangle
A description of the golden rectangle with formulas and drawings.
Division in Mean and Extreme Ratio
The base angle of the largest triangles of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyramid of Cheops, which is 51deg50'. With such a base angle, the ratio of the hypotenuse to half the base is phi, the Golden Ratio.
The Golden Mean by Jerry Bonnell and Robert Nemiroff
A Project Gutenberg eBook with one million digits.
The Golden Ratio
Extension of the number.
The Golden Ratio
Project with art references and object construction lessons.
The Golden Ratio and The Fibonacci Numbers
A presentation of the relationship between the Golden Ratio and the Fibonacci Numbers from the proceedings of the Friesian School.
The Golden Ratio: A Golden Opportunity to Investigate Multiple Representations of a Problem
Essay and brief introduction by Edwin M. Dickey.
Defines the "Golden Rectangle" based on phi and shows some formulars and drawings of the results.
The Golden Section - the Number and Its Geometry
Simple definitions; exact value and first 2000 decimal places; finding the golden section; continued fractions. Simple tricks for your calculator, puzzles and games.
The Greeks and the Golden Mean
A paper relating the early discovery of the Golden Mean by the ancient Greeks and their methods of constructing it.
Phi: That Golden Number
How to generate the number, GSP script for dividing segments, rectangle and other shapes, the rabbit problem and references.
Last update:March 11, 2015 at 5:35:07 UTC
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160923.61/warc/CC-MAIN-20180925024239-20180925044639-00076.warc.gz
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CC-MAIN-2018-39
| 2,340 | 31 |
https://doscrowd.com/en/sas-heteroskedasticity-robust-standard-error/
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math
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Tips For Solving The Robust Standard Error Of Heteroscedasticity Sas
Don’t suffer from Windows errors anymore.
In this tutorial, we’ll describe a few possible reasons that can cause the sas robust heteroscedasticity standard error, and then I’ll provide possible solutions that you can try to solve this problem. Robust common errors, also known as Huber-White standard errors, 3, 4 substantially modify model-based standard errors using this empirical specific variability of model toxins, which is the difference between the observed result in person and the predicted result from statistical analysis. model.
A way to get reliable standard errors for an OLS regression parameter.SAS estimates in via proc can be Surveyreg. Here are two usage exampleshsb2.sas7bdate
What does heteroskedasticity robust mean?
Heteroskedasticity means that the variance of the error is not constant even as one goes from observation to another. • In particular, the variance of the deviations can be a directive function of the variables.
proc data reg=hsb2; writing pattern = women's math;Well;Output; parameter estimates default settingsVariable Estimation Error Meaning DF k Pr > |t|Section 4 16.61374 2.90896 5.71 <0.0001FEMALE unique 5.21838 0.99751 5.23 <0.0001MATH 1 0.63287 0.05315 11.91 <0.0001
Proc Surveyreg data: hsb2; cluster-ses; writing pattern = women's math;Well;exit;
Estimated regression coefficients guiltThe value of the parameter estimation error Pr t > |t|Intersection 16.6137389 1.06324657 15.63 0.0041WOMEN 5.2183771 0.78520124 6.65 0.6328663 0.0219math 0.03540689 16 .87 0.0031
NOTE. Denominator of powers svrims for t-tests are usually 2 equals.
Example We Are 2
If we only look for reliable standard errors, we can find the variablegroup them together as an identifying variable.
Proc Surveyreg data: hsb2; cluster identifier; writing sample = math;Well;exit;
Why do we use heteroskedasticity robust standard errors?
Standard errors consistent with heteroscedasticity are used to fit a vehicle containing heteroscedastic residuals. The first such approach was just proposed by Huber (1967) and since then improved methods have been developed for handling cross-sectional data, time data and GARCH estimation series.
Girls Estimated regression coefficients guiltError in estimating the parameter t value > pr |t|Intersection 16.6137389 2.69631975 6.16 < 0.0001INTERNAL 5.2183771 1.02236809 5.10 <.0001MATH 0.6328663 0.04627457 < 13.68 0.0001NOTE. Denominator degrees of freedom for tests 199
Are heteroskedasticity robust standard errors?
Standard errors based on this method are already called robust standard errors (heteroskedasticity), possibly White-Hube standard errors.era. Or it is also often referred to as the supper variance estimator (because of the way that calculation formula looks like) This learning is robust, but entirely empirical.
One possibility is to choose robust standard errors for the OLS regression parameter inThe SAS scores come directly from the proc Surveyreg. Two models are used here.hsb2.sas7bdat.
Proc-Reg data is hsb2; writing sample = math for girls;Well;Output; parameter estimates default settingsThe value t of the error variable of the estimate of the DF Pr |t|Section > 1 16.61374 2.90896 5 .seventy <.0001WOMAN alone 5.21838 4.99751 5.23 <0.0001MATH safe 0.63287 0.05315 11.91 <0.0001Download this fixer software and fix your PC today.
Sas Heteroskedasticiteit Robuuste Standaardfout
Sas Heteroskedasticity Solidny Blad Standardowy
Sas Eteroschedasticita Errore Standard Robusto
Sas Heteroscedasticite Erreur Type Robuste
Sas Heteroskedasticitet Robust Standardfel
Sas Heteroskedastizitat Robuster Standardfehler
Sas Heteroscedasticidad Error Estandar Robusto
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CC-MAIN-2023-06
| 3,721 | 27 |
https://www.thegoldengecko.com/blog/4564
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math
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Every now and then it’s fun to look at what kind of gardening books are selling at Amazon. Gives a bit of insight into what people are looking for when it comes to their gardens. The last time we did this was September 2011. Let’s look at the top ten sellers and see if there is a theme (there is).
#1 Home Preserving
#2 Mini-farms, Self sufficiency on a ¼ acre
#3 The Foragers Harvest
#4 Marijuana Horticulutre
#5 Back to Basics
#6 The Farmers Almanac
#7 The Encyclopedia of Country Living
#8 All New Square Foot Gardening
#9 Nature's Garden: A Guide to Identifying, Harvesting, and Preparing Edible Wild Plants
# 10 Sunset Western Garden Book
Looks to me like it’s all about using the garden to feed, and sustain. The appearance of the two foraging books is an interesting addition. The marijuana book shows up perennially on the top 10 list. Number 11 is Aquaponics, a method for raising fish and plants together. We talked about in my last post.
Take away what you will from this. If you’re a garden center, it’s this kind of knowledge that can help you better understand your customer’s needs. Maybe landscaping books and other ornamental books will one day return to the list, but for now it’s all about “growing you own”.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084892802.73/warc/CC-MAIN-20180123231023-20180124011023-00518.warc.gz
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CC-MAIN-2018-05
| 1,247 | 13 |
http://howtosolveall.com/how-to-find-the-measure-of-each-side-of-an-equilateral-triangle/
|
math
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Discover ways to discover the lacking aspect of a triangle. A triangle is a polygon with three sides. Triangles are labeled on the premise of the angles or on the premise of the edges. The classification of a triangle on the premise of the edges are: scalene, isosceles, and equilateral triangles.
A scalene triangle is a triangle with not one of the sides equal. An isosceles triangle is a triangle with two of the edges equal whereas an equilateral triangle is a triangle with the three sides equal.
When given expressions representing the edges of a triangle with the kind of the triangle additionally given, we are able to use the properties of the varied varieties of triangles to guage the given expressions and therefore discover the measure of the edges of the triangle.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825112.63/warc/CC-MAIN-20181213215347-20181214000847-00593.warc.gz
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CC-MAIN-2018-51
| 778 | 3 |
http://toshiba-global.mynewsdesk.com/latest_news/tag/genome-analysis
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math
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Tag / genome analysis
Commencement of Verification Testing of Quantum Cryptographic Communication System that Theoretically Cannot be Tapped
Press Releases • Jun 18, 2015 05:08 GMT
Toshiba will start verification testing of the transmission of genome analysis data using quantum cryptography that is theoretically completely secure from tapping. Testing will start on August 31 and will be the first use of quantum cryptographic communication system using actual data in Japan.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743184.39/warc/CC-MAIN-20181116194306-20181116220306-00218.warc.gz
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CC-MAIN-2018-47
| 481 | 4 |
http://theinformationdynamics.com/Attention%20Theory/Living%20Logic/Math-Fact%20Matrix.html
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math
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My Theory of Attention is based upon a Math/Fact Matrix – the Living Matrix, to be precise.
To facilitate a common understanding, let us provide some definitions.
A Math/Fact Matrix is a complex web of interlocking relationships between a mathematical system and scientific facts.
The Material Matrix is the most famous, as it is at the heart of our technological wonderland. Newtonian Physics provides the mathematics while material behavior provides the evidence.
The Living Matrix is another type of Math/Fact Matrix. The Physics of Information provides the mathematical system, while evidence surrounding Attention provide the scientific facts. Another intent of this volume is to establish the validity of the Living Matrix.
Let’s define the components of our Math/Fact Matrix.
Fact, in this limited context, only refers to scientific facts. We use the term broadly to indicate any kind of belief that is widely held by scientists in any field. There must be virtually universal acceptance of the belief’s validity amongst the scientific community. The certainty must be so strong that the belief is generally taken as a fact. In other words, scientific facts are accepted as unquestionably true.
Scientific facts can be take many forms: 1) a simple measurement, e.g. that board is 2” by 4”, 2) simple experimental findings, e.g. a water molecule consists of 2 hydrogen atoms and 1 oxygen atom; 3) complex living behaviors, e.g. sleep deprivation harms cognitive performance, or 4) a complex theory, e.g. Newton’s law of gravity and Darwin’s theory of evolution. A general scientific fact that is pertinent to our study: evolutionary forces determine biological forms.
These facts generally define a phenomenon or its interactions with other phenomenon. The phenomenon can be specific or general. Humans have two eyes; living systems are composed of cells; cells cooperate as a group to create organisms.
Reiterating for retention, the Physics of Attention derived from a Math/Fact Matrix. The facts in this matrix are not just numerical measurements, but instead beliefs that are universally held by the scientific community – Scientific Facts.
What about the Math part of the matrix?
The mathematics of a Math/Fact Matrix is a system. In order to be considered part of a matrix, this system must coincide with a set of scientific facts. This type of mathematical system can take many forms.
The most spectacular is Newtonian Dynamics, which provides the dynamical structure of the so-called Material Matrix. Calculus provides the mathematical structure of the system. The interaction between the math system and material evidence gave rise to the Material Matrix, i.e. the Physics of Matter.
Data Stream Dynamics (DSD) provides the physics, i.e. the dynamical structure, for our particular matrix – the so-called Living Matrix. The Living Algorithm (LA) provides the mathematical structure for DSD. The interaction between the math system and living evidence gave rise to the Living Matrix, i.e. the Physics of Information.
The Physics of Matter and the Physics of Information are entirely different in that they belong to mutually exclusive sets. Calculus is based in Closed and Regular Equations. In other words, these equations are closed to external input and don’t refer to themselves. In contrast, the Living Algorithm is an Open and Reflexive Equation. Put another way, the LA is open to external input and past results play a part in determining current results.
The Living Matrix gave birth to my Theory of Attention. The Material Matrix gave birth to the Theory of Matter. The Theory of Matter is so well-established that it could be considered a scientific fact. On the other hand, my Theory of Attention has a fan base of one. It is for this reason that I have written so many supportive pages.
A Math/Fact Matrix indicates that there are distinct patterns of correspondence between a mathematical system and scientific facts. How is the correspondence validated or verified?
According to my Theory of Attention, there are at least 3 mathematical realms of existence. Each realm has a different relationship with the facts. Let us explore the nature of these relationships one realm at a time.
1) Molecular Realm: Scientists access this realm through direct observation. They first accumulate precise measurements regarding the absolute essences of particles/objects as they move through space. These measurements are rendered in numbers. For instance, an iron ball weighs 2 pounds and is 4 inches in diameter. Equations are then written to match the numerical patterns. Validated formulas become scientific facts, e.g. E = mc2. In this realm, objects, even atoms, can be observed moving through space and time.
2) Subatomic Realm: In contrast, scientists can only infer the existence of this realm through indirect observation. Because Subatomic entities, such as electrons and photons, are not observable, scientists deduce their existence by their effects. For instance, sound or visual trails are examined to ascertain the characteristics of the bizarre inhabitants of this peculiar realm. This data is also numerical.
3) Living Realm of Attention: Like the other realms of existence, the Math/Fact matrix is based upon patterns of correspondence between phenomena that are established scientific facts and a mathematical system. However, the inferences regarding the characteristics of this realm are generally based upon visually based evidence. Rather than numerical data, we employ visual pattern recognition in order to establish the correspondences. Put another way, an examination of the mathematical behavior of LA’s model reveals similarities with living behavior.
It is evident that the Math-Fact Matrix associated with Attention lacks the empirical rigor of the Material Matrices. Despite this deficiency, three factors establish the validity of the Attention Matrix: 1) It provides explanatory power for a vast range of phenomena that remain scientific mysteries. 2) The Math and Fact network are isometric systems in that they share a common underlying inferential structure, i.e. exhibit a high degree of logical symmetry, and 3) redundancy logic, i.e. cross-validation from multiple sources. These same factors validate each Math-Fact Matrix.
Let us provide a brief introduction to each factor in the so-called validation network for the Attention Matrix starting with explanatory power. Our model provides explanatory power for a wide range of phenomena from a variety of disciplines. Some of these experimentally verified phenomena remain scientific mysteries despite intensive research and speculation. The community understands ‘What’ happens, but have yet to uncover the ‘Why’ behind these enigmatic phenomena. Conversely, our mathematical model provides plausible explanations that link countless phenomena from a multiple disciplines under one roof.
What does the roof consist of? And what binds it together? Isometric logic: the process of employing the implicit logical structure of a known system to better understand the implicit logical structure of an unknown system. Humans use this process to form verbal abstractions; scientists use this process as a powerful tool. They employ the implicit logic of mathematical systems to better understand of implicit logic of empirical systems. As another form of validation, the LA system has an isomorphic relationship with a network of phenomena associated with Attention.
Redundancy Logic is the final factor validating the Math-Fact Matrix that defines the Realm of Attention. According to this extraordinary type of logic: the greater the number of sources pointing to the same conclusion, the more likely the conclusion is true. Living systems employ this form of logic to affirm a common reality. Scientists employ Redundancy Logic as a means of forming the common consensus that is the foundation of validating scientific theory.
1) There are an uncountable number of patterns of correspondences between scientific facts and the LA’s mathematical system. 2) These scientific facts span a wide range of phenomena from a variety of disciplines. 3) DSD provides explanatory power for many scientific mysteries. 4) DSD and a phenomenal system have an isometric relationship, i.e. a high degree of logical symmetry. Each of these sources support the conclusion that DSD provides a good model for the network of phenomena associated with the Realm of Attention. The redundancy of these multiple forms of evidence provides overwhelming support for our model.
Finally, our Theory of Attention matches and extends our common sense notions regarding intention, mental energy, and choice. With this addition, there are three forms of validation for the conclusions behind the Theory of Attention: 1) cross-disciplinary evidence linked under one roof, 2) explanatory power for scientific mysteries, and 3) congruence with our common sense regarding choice. This three part logical redundancy generates a virtually indestructible logical web of understanding.
What is the significance of my work?
Attention Theory provides a theoretical foundation for our common sense understanding of choice. The mathematically based theory integrates intention, information, attention, mental energy and experience in an elegant package that embodies simplicity. Its significance lies in its ability to extend our understanding of Attention. With deeper insights into this fundamental feature of living experience, we can maximize the quality of our lives. With this knowledge, we can more easily both fulfill potentials and avoid pitfalls.
As mentioned, the Living Matrix provides the foundation for my Theory of Attention. Due to its foundational importance, this entire work is devoted to establishing the validity of the matrix. To that end, we examine the myriad patterns of correspondence between living behavior and the mathematical behavior of our model. More specifically, we examine the parallels between well-established Attention and Sleep related phenomena and the behavior of the two primary forms of our mathematical system, the Pulse and the Triple Pulse. As will be exhibited, there are widespread patterns of correspondence between the mathematical behavior of these two forms and many aspects of living behavior, especially those regarding Attention.
You are probably wondering, how could mathematics possibly apply to imprecise, unpredictable living behavior? If it does apply to behavior, what are the implications? Could an understanding of the dynamics of behavior actually improve mental performance and the overall quality of life? Could the employment of these mathematical mechanisms in our day-to-day life actually improve our chances of having an 'optimal experience' - moving into the ‘Zone’ – becoming ‘one with the Tao’?
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CC-MAIN-2022-49
| 10,867 | 31 |
https://www.semanticscholar.org/author/Rishi-Gupta/1689014
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math
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The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to selecting the best algorithm for a given application domain, there has been surprisingly little theoretical analysis of… (More)
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense, radius… (More)
We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m × n matrices A, for m n, such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD distance. We also provide an empirical evaluation of the method that, in some scenarios, shows its advantages… (More)
We propose a framework for compressive sensing of images with local geometric features. Specifically, let x ∈ R<sup>N</sup> be an N-pixel image, where each pixel p has value x<sub>p</sub>. The image is acquired by computing the <i>measurement vector</i> Ax, where A is an m x N measurement matrix for some m l N. The goal is then to design the matrix… (More)
We study the problem of reconstructing a mixture of Markov chains from the trajectories generated by random walks through the state space. Under mild non-degeneracy conditions, we show that we can uniquely reconstruct the underlying chains by only considering trajectories of length three, which represent triples of states. Our algorithm is spectral in… (More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m × n matrices A, for m n, such that for any x, given Ax, we can recover a k-sparse approximation… (More)
We present a case of postaxial polydactyly with well formed six digits on left hand and seven digits on right hand. Both conditions are rare and combination of these two conditions even rarer. The patient also had supernumerary sixth right toe and cleft lip. Very few cases of postaxial polydactyly are reported previously.
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CC-MAIN-2017-04
| 2,527 | 7 |
https://prezi.com/oxmvd1qdewm1/the-metric-system/
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math
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The Metric System
Transcript of The Metric System
Unit: Liter L
Tool: Graduated Cylinder
Beaker Definition: a measure of the average kinetic energy (energy of movement) of the particles in an object
Unit: Degrees Celcius C
Temperature Probe Definition: how much matter an object is made of
Unit: Gram g
(double pan, triple beam, digital) Definition: distance from one point to another
Unit: meter m
Most used units: mm, cm
m, & km
Tool: metric ruler
trundle wheel Almost The Whole World!
Every Country Except:
Liberia k h da base unit d c m
kilo hecto deca (meter,liter,gram) deci centi milli Examples:
kilometer hectometer decameter meter decimeter centimeter millimeter
km hm dam m dm cm mm
kilogram hectogram decagram gram decigram centigram milligram
kg hg dag g dg cg mg
kiloliter hectoliter decaliter liter deciliter centiliter milliliter
kL hL daL L dL cL mL Changing Metric Units To go from one unit of measurement to another unit simply:
begin at the unit you are starting with
move the decimal to the left or the right the necessary number of spaces until you get to the unit you are converting to The Magic of the Metric System 1 cm3 = 1 mL = 1 g
When using the metric system one can easily
go from units measuring mass or volume. Real World References the thickness of a credit card 1 cm= 10 mm about the width of a fingernail 1 m= 100 cm 1 m = 1000 mm the length of a guitar is about 1 meter a centimeter is about the length of a staple a mm is about 10 sheets of paper stacked on top of each other 1 km= 1000m a km is about a little over a half a mile the distance from Springfield to Decatur is about 63 km 1000 100 10 1 0.1 0.01 0.001 Remember the Order of Prefixes With This: King Henry Doesn't Usually Drink Chocolate Milk (kilo) (hecto) (deca) (unit: m, L, g) (deci) (centi) (milli) Volume (solids) Definition: the amount of space that matter takes up in 3 dimensions Unit: cm 3 Tool: ruler, tape measure Length x Width x Height Examples: 25.2 m= ? km Based on units of 10 Most used units: g & kg Most used units: L, mL Most used units: cm & m 3 3 Area Definition: The amount of space inside the boundary of a flat (2-dimensional) object such as a rectangle. Most common units used: cm, m, km 2 2 2 Tools used: metric ruler, metric measuring tape, trundle wheel k h da unit d c m
(m, l, g) 25.2 0.0252 To go from meters (m) to kilometers (km), the decimal point moves three spaces to the left. Zeros are placed where there are no numbers. k h da unit d c m
(m, l, g) 0.72 kg = ?mg 0.72 720000.0 To go from kilograms (kg) to milligrams (mg), the decimal moves six spaces to the right. Zeros are placed where there are no numbers. 382 cL = ? mL (length measurement) (mass measurement) (volume measurement) k h da unit d c m
(m, l, g) 382.0 3820.0 To go from centiliters (cL) to milliliters (mL), the decimal moves one to the right. Since the beginning number, 382, has no decimal, you add one at the end followed by a zero (382.0). Now you are able to move the decimal. Try these on your own:
0.0478 km = ? cm
7643.2 cm = ? hm
501.75 g = ?kg
84.7 L = ? mL Biggest Smallest
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CC-MAIN-2017-26
| 3,795 | 46 |
https://justaaa.com/statistics-and-probability/548337-a-study-investigated-the-effects-of-physical
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math
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A study investigated the effects of physical fatigue on the performance of professional tennis players. Researchers measured the number of unforced errors committed by a random sample of 12 professional tennis players during the first three sets of a match. They hypothesized that increased fatigue would be associated with a greater number of errors. The following is an F-table for this hypothetical study using the one-way within-subjects ANOVA. Source of Variation SS df MS Fobt Between groups 11 Between persons 4 Within groups (error) 55 Total (a) Complete the F-table. Source of Variation SS df MS Fobt Between groups 11 Between persons 4 Within groups (error) 55 Total Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.) Retain the null hypothesis. Reject the null hypothesis. Correct: Your answer is correct. (b) Estimate effect size using partial omega-squared: ωP2. (Round your answer to two decimal places.) ωP2 =
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CC-MAIN-2024-10
| 1,023 | 3 |
http://petiwalabooks.com/PetiwalaViewBookInfo.aspx?id=1433
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math
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Sindh Payment of Wages Act 2015
• Short title, extent commencement and application.
• Responsibility for payment of wages.
• Fixation of wage periods.
• Time of payment of wages.
• Wages to be paid by cheque of any scheduled bank or commercial banks.
• Deductions which may be made from wages.
• Deductions for absence from duty.
• Deductions for damage or loss
• Deductions for services rendered.
• Deductions for recovery of advances.
• Deductions for payment to cooperative societies and insurance scheme.
• Claims arising out of deductions from wages or delay in payment of wages and penalty for malicious or vexatious claims.
• Single application in respect of claims from unpaid group
• Powers of authorities appointed under section 14.
• Power to recover from employer in certain cases.
• Penalty for offences under the Act.
• Cognizance of offence
• Bar of suits.
• Contracting out.
• Liability in case of closure, insolvency, winding up and liquidation.
• Protection against discrimination
• Display by notice of abstracts of the Act
• Rule-making power.
• Removal of difficulties.
• Repeal and saving.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202804.80/warc/CC-MAIN-20190323121241-20190323143241-00461.warc.gz
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CC-MAIN-2019-13
| 1,161 | 26 |
http://myninjakiwi.com/software/others/35536-elementary-mathematics-from-a-higher-standpoint-volume-i.html
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math
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Elementary Mathematics from a Higher Standpoint Volume I
Author: Bo0mB0om on 5-07-2016, 00:04, Views: 32
Elementary Mathematics from a Higher Standpoint: Volume I
English | 8 July 2016 | ISBN: 366249440X | 312 Pages | PDF (True) | 4.45 MB
These three volumes constitute the first complete English translation of Felix Klein's seminal series "Elementarmathematik vom höheren Standpunkte aus". "Complete" has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English.
The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein's far-reaching conception of elementarisation, of the "elementary from a higher standpoint", in its implementation for school mathematics.
This volume I is devoted to what Klein calls the three big "A's": arithmetic, algebra and analysis. They are presented and discussed always together with a dimension of geometric interpretation and visualisation - given his epistemological viewpoint of mathematics being based in space intuition. A particularly revealing example for elementarisation is his chapter on the transcendence of e and p, where he succeeds in giving concise yet well accessible proofs for the transcendence of these two numbers. It is in this volume that Klein makes his famous statement about the double discontinuity between mathematics teaching at schools and at universities - it was his major aim to overcome this discontinuity.
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http://iuhomeworkqykm.isomerhalder.us/writing-if-statements-in-excel.html
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math
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If statement is one of the most popular instructions among the decision making statements excel if statement gives the desired intelligence to a our formulas. How to write a conditional formula the basic syntax of the if formula in excel is : [value_if_false]: the results you want returned if the condition is false. Each if function in an excel spreadsheet returns one of two messages the first -- the. Written by co-founder kasper langmann, microsoft office specialist one of the most commonly used functions in excel is the 'if' function of it in terms of 'if this is true, then that – otherwise (if 'this' is false) something else.
When most people think of using an if statement in excel, they think of this way, you're only checking for and writing results about the date of. If you want to do something specific when two or more conditions are true, you can if either condition isn't true, the test will return false excel if function. An if statement is a conditional test on values and formulas that returns one value if a question: in excel, i need to write a formula that works this way: if ( cell.
If i had the following data from excel: how can i write an else if statement such as if student name is mary then display major name and class. It is possible to nest multiple if functions within one excel formula you can nest up to answer: you can write a nested if statement to handle this for example. Sometimes these are called if/then/else statements excel has a particular way, or syntax, of writing them, and you will use it to show a statement based on.
How to use nested if statements in excel with and, or, not corporate to use it correctly, you have to write it like the following: =and(first. Excel's if function provides some simple decision-making capability to a worksheet the condition being evaluated (should result in either true or false). The if function and multiple if statements in excel are extremely follow when creating multiple if statements, is to write down the statement in. Learn how to use multiple if statements to calculate sales commission for a range you can have up to 64 if functions nested in a formula in excel 2007, 2010 and bear in mind that the way i've written this function assumes that if g4=100,.
Have you ever had to create multiple if statements and it drove you nuts because of all those parentheses well, check out this alternative. In vba, if works just like same its basic idea is to perform a task when a condition is true else do nothing or do something else you can write.
Mastering excel formulas if - kindle edition by mark moore a book, and it could not have taken more than an 8 hour work day to write, if that i was intimidated by the if statement but you made it very easy to break down and understand. The if function in excel returns one value if a condition is true and another value if it's false you can use up to 64 additional if functions inside an if function. Conditional statements in excel vba helps to control the programming learn if,if else, nested if, case, for and do loops with examples.
I dont know if i understand what youre wanting to do or not, but the only way that im aware of to put multiple if statements into one field is to do. In normal circumstances, excel places a limit on the number of nested conditional formulas that you can use the limit is 7 however, it is. For example, i wanted to have the following if statement: if b3180º, is this possible in the autocad the same way we do it in excel.
Learn the ins and outs of the logical formulas like the famous if statements that represent the heart of excel. Trying to learn excel things could someone please help me understand how to write if / else statements in excel i get lost when dealing. Being able to write a simple if statement in excel is essential, especially if you deal with a lot of numbers all the time it's one of those things.
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https://onlinemathcenter.com/blog/math/measuring-and-converting-lengths-areas-and-volumes/
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math
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Since people began to discover all the wonders mathematics could bring to civilization thousands of years ago, we’ve been using numbers and mathematics to identify and express various features of pretty much everything in our physical world.
Thanks to the mathematicians that came before us, we can measure things like length, area, and volume, and express these findings in several ways.
Nowadays, most countries in the world use something called the metric system, a standardized method of measurement that is easy to understand and use. On the other hand, in some places, and for some particular reasons, other less common and more seemingly strange systems of measurement are used to find lengths, areas, and volumes of objects.
Let’s take a closer look at how we measure the length, area, and volume of various objects, so we can find out what systems are used and, importantly, how we can quickly convert our answer to express it in various ways.
Length, Area, Volume… What’s The Difference?
Length, area, and volume are three-dimensional measures of objects. Length measures one-dimensional objects, area measures two-dimensional objects, and volume measures, you guessed it, three-dimensional objects.
In geometry, we measure lines in length, we measure shapes such as circles and triangles in area, and we measure three-dimensional objects, such as pyramids, cubes, or cones.
The number of dimensions in the shapes that we measure also gives us a hint about how we will express our answers.
One-dimensional measurements – such as length – will be expressed as normal numbers. Two-dimensional shapes will be expressed as a number squared (to the power of two), and three-dimensional shapes will be written as numbers cubed (to the power of three.
It’s very important to always write your answers to the appropriate power when measuring length, area, and volume.
The formulae for finding these measurements will vary from shape to shape. Some of the most commonly seen are:
Area of a square: A = side², where the side is one side of a square.
Volume of a cone: V = πr²h.
Area of a rectangle: A = L x W, where L is the length of the rectangle and W is
the width of the rectangle.
Volume of a cube: V = a³, where a is the edge length of a cube.
Can you remember the formula for the area of a triangle, from a recent OMC blog article?
Now that we know the difference between length, area, and volume, we need to understand what the Metric System is and why it was developed in the first place.
What is important to know is that, just because length, area, and volume are established measures does not mean they are always expressed in the same way.
There are many, many ways of expressing the length of a piece of string.
We can measure it in feet, in yards, in furlongs… the list goes on!
As you can imagine, the same is true for area and volume. Is the area of a square expressed in square feet, hectares, or acres?
Should a swimming pool be measured in quarts?
The truth is, we can measure these objects and express them in any of the terms laid out above.
The other truth is that, while it is great to know how to express lengths, areas, and volumes in various ways, we need a more universally-understandable system of measuring these objects.
That system is the Metric System.
It is the international standard system of measurement based on the standard decimal number system. Each quantity it measures has one unit to measure it, and subunits based on multiples and submultiples of 10. This makes calculations very straightforward.
For the base unit length, the metric unit is meters (m). From this, we get the derived units square meter (m²) and cubic meter (m³), which we use to measure area and volume, respectively.
The different units of measurement can be tough to grasp at first glance, but in time, young math students become quick at identifying which of the quick conversion calculations needs to be done. To help them get the hang of it, here is a useful conversion calculator, to help them practice converting lengths, areas, volumes, and other measurements to a variety of units of measurement.
Keep Their Mind In Shape With OMC Math Courses
Young Math students are going to be expected to get to grips with the entire geometry curriculum – not just length, area, and volume – this school year. Give them every chance of achieving high grades by enrolling them now in an OMC 5th Grade Math Course. Better yet, for an extra edge on the competition, take a look at the options on offer in OMC 1-1 Tutoring Courses.
Contact OMC today to get your young learner on the path to reaching their mathematic potential.
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| 4,657 | 32 |
http://www.definitions.net/definition/quotient
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math
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the ratio of two quantities to be divided
the number obtained by division
The number resulting from the division of one number by another.
The quotient of 12 divided by 4 is 3.
By analogy, the result of any process that is the inverse of multiplication as defined for any mathematical entities other than numbers.
A quotum or quota.
Origin: From quotiens, from quoties
the number resulting from the division of one number by another, and showing how often a less number is contained in a greater; thus, the quotient of twelve divided by four is three
the result of any process inverse to multiplication. See the Note under Multiplication
Origin: [F., fr. L. quoties how often, how many times, fr. quot how many. See Quota.]
In mathematics, a quotient is the result of division. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend, and 3 the divisor. The quotient further is expressed as the number of times the divisor divides into the dividend, e.g. 3 divides 2 times into 6. A quotient can also mean just the integer part of the result of dividing two integers. For example, the quotient of 13 and 5 would be 2 while the remainder would be 3. For more, see the Euclidean division. In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structures whose elements are the equivalence classes of some equivalence relation on another set, space, or algebraic structure. See: ⁕quotient set ⁕quotient group ⁕quotient ring ⁕quotient module ⁕quotient space ⁕quotient space of a topological space ⁕quotient object ⁕quotient category ⁕right quotient and left quotient The quotient rule is a method for finding derivatives in calculus.
Chambers 20th Century Dictionary
kwō′shent, n. (math.) the number which shows how often one number is contained in another.—n. Quōtī′ety, the proportionate frequency of an event. [Fr.,—L. quotiens, quoties, how often?—quot, how many?]
The New Hacker's Dictionary
See coefficient of X.
The numerical value of quotient in Chaldean Numerology is: 6
The numerical value of quotient in Pythagorean Numerology is: 4
Images & Illustrations of quotient
Translations for quotient
From our Multilingual Translation Dictionary
- خارج قسمتPersian
- quotum, quotiëntDutch
- kvotientNorwegian Nynorsk
- cota, quocientePortuguese
- частное, часть, доляRussian
- số chia đượcVietnamese
Get even more translations for quotient »
Find a translation for the quotient definition in other languages:
Select another language:
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CC-MAIN-2018-05
| 2,584 | 29 |
http://security.stackexchange.com/questions/tagged/smartphone+ios
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math
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https://boeingconsult.com/tafe/structures/beams/Beams.HTM
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math
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Performance of beams
A beam is a structural member designed to support various loading applied at points along the member. When a beam is loaded it will bend and this bendin is measured in newton millimetre or multiples of the units (e.g. kNm.). The forces applied to a beam are counteracted by the supports which are called reactions (RL left support and RR right support)
Beams are usually supported on walls piers or columns which provide the necessary equilibrium. (According to Newton’s third law there is for every action an equal and opposite reaction.) In simple terms the load on the beam is the action and the supports provide the reaction. There are three different support reaction:
Type (a) accommodate three reaction, (b) one reaction and type (c) two reaction
In this subject we will consider only simply supported beams which can be determinate completely with the three static equation. Continuous beams are beyond the scope of this subject. The two beam types are that we will use are shown below.
Beams are subjected to uniformly distributed loads (UDL), point (concentrated) loads or a combination of both. The various loading conditions to which a beam may be subjected to are shown below.
With the three static equation
simple structures (statically determinate) can be completely analysed.
To calculate the reaction of beams we use the equation Σ M = 0
The Shear force at any cross-section of the beam is equal to the algebraic sum of the external forces acting on one side of the section only.
The Bending moment, at any point of the beam, is equal to the algebraic sum of the moments (taken about the point) of the external forces (loads & reactions) on one side of the section only.
The unit of bending moment is the same as for moment of a force, i.e. the newton metre (Nm) and multiples and submultiples of this unit.
Sign convention for shear force and bending moment
The sign shear force (S) and bending moment (M) are positive (+) or negative (-) as shown below.
Determination of the reactions of a simple beam with a point load
Use the sum of the moments must be zero (Σ M = 0) equation to calculate the magnitude of the reactions
Sign convention: clockwise moments positive (+ve), anti-clockwise moments negative
There are to unknowns (RL and RR) and one must be eliminated to be able to calculate the reaction. We select the rotation point at RR because reaction RR times distance is then zero.
If this formula is used, you must be certain that RL is correctly calculated. At this stage it is better to calculate RR as well.
Determination of the reactions of a simple beam with a uniformly distributed load
Determination of the bending moment
A number of specifics loading cases occur frequently and for this cases standard formulas exist. The derivation of the bending moment formulas is dealt with in Structures 2
Standard formula for reactions, bending moments and deflections
Beam with a point load
For every load on a beam, there is a critical point at which a maximum bending moment occurs. The diagrams clearly indicate that this point is at zero shear. In other words where zero shear occurs there is the maximum bending moment.
The factors that influence the deflection have been discussed previously. A constant factor that depends on the loading of the beam is introduced in the deflection equation above.
Note: that in the deflection formula for UDL w is the load per metre, (in above equation
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https://asada-shigeru.jp/blog-entry-81.html
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math
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Physics Original Theory Research Series 1 2020/12/26 S.Asada Corrections and additions are made at any time →Japanese edition日本語版
It is an observational fact that dark matter, an unknown substance that is not observed but has the effect of creating a gravitational field, exists in large quantities in this universe, and that the total amount of it exceeds the total amount of visible stars and galaxies. . In this paper, we will elucidate the identity of this dark matter with our own theory, and clarify how it is made and what kind of properties it has.
0. Summary, Conclusion
0-1. What creates a gravitational field is matter itself, not "mass or energy"
For the proof of this, see " 2. Proof of existence of vanishing mass". It may be slightly different from what the Einstein equation indicates, but according to this theory, inertial mass and its equivalent energy do not have the ability to create a gravitational field ( a field that stretches the time axis of space and slows down the speed of time).
We usually call the property of receiving acceleration or generating inertial force in the gravitational field "inertial mass = gravitational mass" or simply " mass". Furthermore, mass and energy are equivalent in this property (E=Mc^2). In other words, energy has the properties of inertial mass and gravitational mass. (However, energy alone, such as a photon, does not show the property of mass, and it shows its property only when it is confined in a substance → See "The True Nature of Gravity ")
In the conventional standard theory, the gravitational field is a distortion of space-time, and its magnitude is "described by the energy and momentum tensors". Roughly speaking , this means that it is mainly mass energy that creates the gravitational field. In other words, it is the claim that "mass receives acceleration in the gravitational field and also creates the gravitational field."
However, according to this theory, the cause of creating a gravitational field is due to another kind of ability that matter itself has, and inertial mass and energy do not have such ability. The property of inertial mass is only passive.
Matter is the only entity whose four-dimensional volume (x, y, z, t) is preserved. This is very different from the energy that the total amount is conserved in three-dimensional space. In a three-dimensional space, a substance can change its volume (x, y, z) as the time axis changes. As the time axis (t-axis) extends, the three-dimensional volume decreases in inverse proportion. But the four-dimensional volume does not change.
The ability to create a gravitational field is proportional to the four-dimensional volume of matter. Specifically, the three-dimensional volume (=inertial mass) divided by the time velocity ratio with the observer is the amount of the property that creates the gravitational field (provisionally called "true mass"). In addition, matter acts on the time axis of the surrounding space in an amount proportional to its four-dimensional volume, extending it. In other words, time is delayed. This time delay in space is the " identity of the gravitational field ".
The property of inertial mass is usually associated with matter. This is because matter contains energy proportional to its three-dimensional volume. Energy is the inertial mass itself. Inertial mass increases and decreases in the state of the time axis, and it is possible that some matter has completely disappeared. Even in such a case, the four-dimensional volume of matter does not change, so the ability to create a gravitational field is constant and does not change.
0-2. Phenomenon where matter loses mass
As a phenomenon that is widely recognized as a general theorem (the law of conservation of mass and energy), when substances are bound by gravity or electric force, they always release binding energy. Then, the mass conversion value (ΔM=Ef/c^2) of the released binding energy is reduced from the total mass of the original substance.
And when the bond energy becomes larger and larger, the larger bond energy associated with it is released. Then, it would be reasonable to think that the mass of matter may eventually become zero. We can witness that moment. For example, the combination (annihilation) of an electron and a positron. Details of this will be described later.
0-3. Matter exists even if it loses mass, and the gravitational field it creates does not change
Even if the binding energy is released to the limit and the volume and mass become zero in the three-dimensional space, the matter continues to exist in the four-dimensional space-time. Mass is one of the properties of matter, but there are also states where it becomes zero. Just because mass is zero doesn't mean matter is gone. And the matter continues to retain the ability to create a gravitational field. In the pair annihilation described above, an electron-positron combination with no volume or mass is generated, but the gravitational field created by these does not change before and after the combination.
Gravitational bonding and electrical bonding can certainly occur with bonding energies so huge that the mass becomes zero. Matter that has lost its mass in this way disappears, leaving only the property of creating a gravitational field, and becomes almost unobservable. My argument in this paper is that this is the identity of dark matter.
0-4. Properties and types of dark matter
Specific dark matter candidates include electron-positron conjugates and proton -antiproton conjugates. These have zero volume and mass in three-dimensional space, as explained in detail in " Proposal of Four-Dimensional Volume Conservation Law " . For the proof of this, see "2. Proof of existence of vanishing mass" .
Since they have no inertial mass, they probably move at the speed of light, and since they have zero volume in three-dimensional space, they usually interact with matter, pass through without colliding, and continue moving at the speed of light. The probability of existence will be widely spread. However, it has the ability to create a gravitational field as an invariant. In other words, it continues to maintain the gravitational field it had before the mass disappearance occurred.
Such microscopic dark matter is so small that individual gravitational fields cannot be observed. However, since the number of existence is enormous, it will have a great influence .
The above is mass loss due to coupling by electric force, but mass loss due to gravitational coupling between stars is also possible. However, since the masses of two stars are never exactly equal, they will not be completely massless after merging. In addition, when two stars are gravitationally coupled, they become a black hole before they can fully release their binding energy. In that case, the binding energy is also confined in the black hole, so that no further binding energy can be released.
However, a black hole that has lost a large amount of mass due to such gravitational coupling has mass, but has a larger gravitational field than its mass. In other words, even though it has a small mass, it has a much larger gravitational field, so it may be treated as a kind of dark matter.
0-5. Generation and annihilation of electron-positron coupled dark matter
The figure below shows the formation of dark matter by the combination of electrons and positrons. It also shows that dark matter can reseparate into electrons and positrons by absorbing high-energy photons. However, dark matter cannot absorb photon energy directly, and this reaction (pair production) occurs stochastically, such as when it collides with another nucleus and enters a high-energy state.
The figure below shows the formation and disappearance of dark matter. When electrons and positrons combine with their strong electric force, they emit energy equal to their total mass in the form of photons, and themselves become entities with zero mass (vanishing mass dark matter). It has only the effect of creating a gravitational field and wanders through space. And when it absorbs a high-energy photon, it breaks the bond and splits again into an electron and a positron. Bonding is called "pair annihilation" and separation is called "pair creation". But if the theory is correct, the term may not be very correct.
Sounds like a perfect theory, doesn't it?
However, the illustration of the movement direction of the particles in the upper figure is not strictly correct. Actually, the law of conservation of momentum is obeyed. By the way, the electron-positron reaction also satisfies both the law of conservation of mass energy and the law of conservation of electric charge, and the gravitational field is also conserved.
The mass of electron-positron combination = (electron, positron mass) 2 x 0.51Mev - (emission photon mass) 2 x 0.51Mev = 0, that is, the combination of electron and positron has zero mass. However, it retains the ability to create a gravitational field. This is eｰe⁺ coupled dark matter. There are also dark matter such as p-p‾ bonded type and ｎ-ｎ‾bonded type.
0-6. Behavior of dark matter and its effect on galactic motion
When dark matter passes near or through the nuclei of ordinary matter, it is subject to some strong electric forces, temporarily loosening the bonds. If a high-energy photon acts at this moment, it may be absorbed and the bond may be broken to generate a pair. This is the production of positive and antimatter from dark matter.
The motion of dark matter will change course due to the influence of electric force, etc., and it will become a zigzag motion. Due to the zigzag motion , dark matter is bound for a long period of time in areas with high celestial density such as galaxies. In addition, even if normal matter bends the course of dark matter by electric force, dark matter has zero mass energy, so it does not affect the behavior of ordinary matter. However , this is a two-party problem, and the situation is different in a large number of mixed states . Furthermore, the dark matter group that affects the behavior of ordinary matter receives a reaction from ordinary matter. This action also causes dark matter to be restrained to some extent by galaxies.
In this way, dark matter is bound to the galaxy for a long period of time, and is distributed widely and in high concentration, especially in the outer part of the galaxy. And the gravitational field caused by these can explain the uniform rotation of the galaxy's outer periphery.
In the region near the center of the galaxy, dark matter is trapped by the supermassive black hole at the core, so the dark matter density is lower than in the periphery. The supermassive black hole at the center of the galaxy grew rapidly, mainly by absorbing dark matter.
There are restrictions on how black holes can absorb normal matter, making it difficult for them to grow rapidly. A black hole will have a large absorption cross-section for dark matter due to its spatial structure. A black hole that absorbs a lot of dark matter should have a small inertial mass compared to its gravitational force.
Proof? In that case, it will be a long sentence, and it is unlikely that you will read it, so I presented the conclusion first. I wonder if it's okay~
The behavior of vanishing masses that have completely lost their mass, which I believe to be the identity of dark matter, is interesting. Its proper time has stopped, and its volume, inertial mass, and gravitational mass in three-dimensional space are also zero. Therefore, it travels at the speed of light and usually passes through matter without colliding with it. It is also unaffected by the gravitational field. However, it only has the effect of distorting space (to be precise, acting on the time axis to slow down the temporal velocity of space) and creating a gravitational field. → Detailed examination of the behavior of dark matter
I try to prove the existence of such an object by a thought experiment. These proofs are possible within the realm of classical physics (mainly relativity theory), and do not require difficult and strange theories. It's not that you don't need it, it's that the owner can't use it
I recognize that this theoretical development is slightly different from the common sense of modern physics, but I can't find any mistakes in my knowledge. If there are any mistakes, I would like to know, so I am waiting for the criticism of those who are more knowledgeable.
Thank you . Please explain in such a simple way that even a junior high school student can understand it.
I have already touched on the vanishing mass in The Story of the Birth of the Universe (My Original), but there was not enough depth to consider it as part of the whole . Only this will be examined in depth here.
2. Proof of existence of dark matter
The main theme here is to prove that matter that has lost its mass and that still has a gravitational field (dark matter) is real. In particular , we clarify that the property of inertial mass and energy is different from the property and ability to create a gravitational field .
As a general explanation of the gravitational field , the Einstein equation states that the source of the gravitational field (distortion of space-time) is the energy- momentum tensor consisting of energy and momentum (see wikipedia ), but this paper denies this. do. The reason for this is explained in detail by a thought experiment in the text.
When multiple objects release binding energy -Ef by binding with gravity, electromagnetic force, nuclear force, etc., the mass corresponding to the binding energy Ef (ΔM = Ef/c ^ 2) disappears from the total of the original masses. is a well-known fact and there is no room for doubt.
In order to expand the interpretation of this well-known phenomenon and to verify the results, we will tackle the following themes (1) to (3). Thereby, the above object is achieved.
Assuming a state in which the bond energy is extremely high in the bonding of multiple objects, it is easy to imagine a situation in which the mass disappears from the substance due to the release of the bond energy. Note that the term “bond” is not limited to coalescence, but also refers to a state in which a bonding force acts in close proximity.
And even if the object (matter) emits binding energy and the mass and volume in the three-dimensional space become zero, the substance continues to exist in the four-dimensional space-time. The volume and mass in the three-dimensional space are zero because the time axis has grown to infinity → Proposal of the four-dimensional volume conservation law
In addition, mass is equivalent to energy and can completely escape from matter, but matter has the property of creating a gravitational field, which is immutable and cannot be separated. This property is called gravitational elementary weight here. I think that the invariants of the universe include mass energy, electric charge, and gravitational weight.
2-1. Proof of existence of dark matter
The mass referred to here (inertial mass or gravitational mass) is a passive property such as receiving inertial force or receiving acceleration in a gravitational field. This does not include the active nature of creating a gravitational field.
For example, the gravitational acceleration near the surface of the earth is 9.8m/s ^ 2, so a force of Mg=9.8N acts on an object with a mass of 1kg. Mass is equivalent to energy (the famous conversion formula is E=Mc ^ 2), and energy has the same properties as mass. In other words, it receives acceleration in the gravitational field and has inertia. However, I argue that mass and energy have no effect on creating a gravitational field.
2-1-1. Difference from conventional definition
In the conventional definition, the gravitational field was also defined as "mass energy, momentum tensor", but here, "the property of receiving acceleration due to inertial force and the gravitational field" and "the property of creating the gravitational field " are treated as separate things. I needed it. Therefore, they are divided into two components: mass energy and true mass (gravitational elementary mass).
A gravitational field is a distortion in space that has the ability to create it. This paper assumes that the ability to create a gravitational field is proportional to the four-dimensional volume of matter. Assuming that this four-dimensional volume is MT, MT can be substituted for mass M in the conventional gravitational equation. Objects passing through it move according to the distorted space regardless of the cause object that made it. In other words, it is not a force that simply acts between objects like nuclear force or electromagnetic force.
2-1-2. Adoption of the term "true mass = gravitational elementary weight"
he ability to distort space and create gravitational fields is not associated with inertial mass, energy, or momentum, but rather as an independent property and associated with matter. As a representation of this property, the word "true mass = gravitational elementary weight" was applied here.
2-2. Explanation of the "thought experiment device"
It is assumed that the thought experiment device in [Figure 1] is not affected by external forces such as gravity. Suppose that A and B are massive objects with completely equal masses. A gravitational force acts between A and B. However, A and B are connected by wires to the power generation motor, and the distance cannot be changed unless this rotates. The generator motor referred to here is an ideal converter that reversibly converts rotational energy into electrical energy, and the conversion efficiency is assumed to be 100%.
Operate the generator motor so that A and B approach. The combined energy is then released and the generator motor generates electricity to charge the battery with electrical energy. Conversely, to separate A and B, electric energy can be supplied from the battery to work as a motor, and A and B can be separated.
For simplicity, we assume that these movements are slow and the momentum is negligible. The direction of movement, speed, etc. can be controlled in any way by controlling the amount of energy supplied and released to the generator motor.
2-3. Case where mass energy is completely lost from matter → proof ①
Assuming a state in which the bond energy is extremely high in the bonding of multiple objects, it is easy to assume that the mass will disappear from the substance. Note that the term “bond” is not limited to coalescence, but also refers to a state in which a bonding force acts in close proximity.
For example, suppose two substances, A and B, are combined in a gravitational field. It is a well-known fact that then, the binding energy ΔEf is released and the mass (ΔM=ΔEf /c ^ 2) corresponding to the energy is reduced from the mass before binding. → Einstein's famous conversion formula E=Mc ^ 2
This phenomenon applies not only to gravitational coupling but also to electric force, magnetic force, chemical bond, nuclear force, and so on.
This is explained using the thought experiment device in [Figure 1]. For example, since objects A and B have a large mass, they create a large gravitational field and exert a strong gravitational force. A generator motor stops this through a wire. Here, the generator motor is rotated slowly to shorten the distance between A and B, thereby releasing the binding energy and generating electricity, which is stored in the battery.
Then, the mass of A+B decreases by the mass corresponding to the energy transferred to the battery (ΔM=Ef/c ^ 2). Conversely, the mass of the battery is strictly increased by (ΔM=Ef/c ^ 2). This keeps the mass-energy in box ② constant and satisfies the conservation law.
Here, if the bond energy is extremely large, it is assumed that the mass of A and B becomes completely zero due to the release of large bond energy.
It is easily assumed that such extremely large binding energy can be released in the case of binding by gravity and binding by electric force. Mass loss due to gravity is a phenomenon that occurs on a large scale, and mass loss due to electric force is a phenomenon that occurs in the microscopic region. In the case of the micro region, strong and weak forces other than the electric force will also participate in the bonding.
2-3-1. Mass loss due to gravitational coupling
The binding energy due to gravity has the property that the binding energy increases infinitely as the total mass increases. So, for example, if A and B are neutron stars in the condition just before becoming a black hole (both are exactly the same in mass and other things), by bringing them closer, the bond energy release of both reaches the energy conversion value of their masses. , can have zero mass.
In another example, if a large number of Earth-sized stars are brought close to each other at the same time, there may be a condition where the total binding energy reaches the total mass equivalent value even if they are not in contact with each other. Furthermore, it is known that the entire universe is very low density, but because it is vast, the total mass becomes huge, and the total amount of gravitational binding energy as a whole and the energy conversion value of the total matter are close. → gravitational binding energy
For some reason, the condition where the mass becomes zero is close to or equal to the condition where it becomes a black hole. Also, complete mass disappearance due to gravity is unlikely in the natural state. Because if the masses of A and B are not exactly equal, the mass after binding will not be zero.
In the case of gravitational coupling, it becomes a black hole in the process of gravitational coupling, and light energy cannot escape. Therefore, the mass energy is trapped and remains. So the loss would be about 50% of the total mass.
2-3-2. Mass loss due to electric force coupling
Electrons and positrons, protons and antiprotons, neutrons and antineutrons, etc. also have a large electrical binding energy when the distance between their charges becomes extremely short, and it is assumed that the mass becomes zero when this is emitted. In this case, since the absolute values of the mass and charge of both are exactly equal, the mass after binding can be exactly zero. → binding energy Binding energy between charges Ef≒9×10^9×Q1×Q2 ÷r^2 (r is the distance between charges Q1-Q2)- - - - This has the same form as the gravitational binding energy formula
According to a simple calculation, the distance between charges at which the mass becomes zero after this combination is about 10 ^ -15m in the case of an electron and a positron . In the case of protons, antiprotons, neutrons, and antineutrons, it seems a little complicated because they have an internal structure, but there is a distance between charges where the mass becomes zero. In the case of neutrons and antineutrons, the internal structure (quark level) has an electric charge similar to that of protons, and it is possible that they lose mass due to electrical coupling. → Confirmed in practice → (Example) electron-positron reaction, proton-antiproton reaction
In the case of protons and antiprotons, it is not known whether they are combined in their original form or dispersed as quarks and anti-quark combinations. However, since pairing occurs, there is a high possibility that the mass disappears by combining in the form of protons and antiprotons, rather than by disjointed quark units.
Furthermore, by combining unstable quarks, antiquarks, etc., it becomes a vanishing mass with zero mass, and by stopping the proper time, it can become a permanent life.
Considering the case of electric coupling in the above [Fig. 1], the attractive force F becomes an electric force. Since the extracted energy is equivalent to mass, it has the properties of mass (inertial mass, gravitational mass), but does not have the property of creating a gravitational field. Objects A and B have the property of creating a gravitational field.
2-4. Matter and the gravitational field continue to exist even if the mass becomes zero → Proof 2
Matter continues to exist in four-dimensional space-time even if it releases its binding energy and becomes zero in mass and volume. The volume and mass in the three-dimensional space are zero because the time axis has grown to infinity → Proposal of the four-dimensional volume conservation law
It is not mass or energy that creates the gravitational field . It is matter, and the ability of matter to create a gravitational field is proportional to its volume in four-dimensional spacetime. By the way, a gravitational field is a state in which the time axis of space is extended (time velocity is delayed) due to the "true mass = gravitational elementary amount" of a substance.
In the previous proof, I came to the conclusion that the combined mass of substances A and B can become zero, but even if the combined mass of A and B becomes zero, A and B still exist. It's not that I stopped doing it. Even if the three-dimensional volume (mass) of matter becomes zero, the four-dimensional volume is preserved and the gravitational field does not change. We prove it below.
2-4-1. Reversibility of Mass Disappearance Phenomena
Even if A and B release the binding energy in the thought experiment device of Figure 1 and the mass decreases infinitely, this process is reversible. If electric energy is supplied from the battery and the generator motor winds up the wires and separates A and B, the original masses of A and B will be restored.
In order to explain the essence of this phenomenon in an easy-to-understand manner, let us assume that the objects are Mr. A and Mr. B, human beings with individuality and complex and delicate structures. When Mr. A and Mr. B are gravitationally coupled, gravitational coupling energy is released. Then, the mass of the two people decreases by the energy released, and the energy is converted into electrical energy by the generator through the wire and stored in the battery.
The mass of the battery increases by that amount and satisfies the law of conservation of mass and energy in box ②. For the validity of this law of conservation, see " 3. Consideration of the Law of Conservation of Inertial Mass and Gravitational Field" at the end of this article.
At first glance, it seems that Mr. A and Mr. B have moved to the battery, but since it is reversible, if you supply electricity to the generator motor and wind it up, it will return to the original Mr. A and Mr. B. Humans cannot easily be assembled from electrical energy, so we must think carefully about the meaning of reversibility.
Even if the mass decreases or disappears, the matter of Mr. A and Mr. B always existed in Box ①. In other words, there is no change in the coordinates of Mr. A and Mr. B. Their mass does not change from their point of view. It is a mass transfer and disappearance phenomenon from the perspective of an external observer. Even if you think in terms of physical common sense, it is impossible for the substances that make up Mr. A and Mr. B to escape from Box ① through the rope. Only energy can escape through the rope.
Also suppose that the energy is transferred to the battery and the mass in box ① approaches zero. If the gravitational field is caused by mass, then the gravitational field in box 1 will also approach zero. If that happens, even if you try to pull Mr. A and Mr. B apart, the gravitational force will be close to zero, so the energy from the battery will hardly flow back. In other words, the mass of Mr. A and Mr. B will not be recovered, and the reversibility is lost. This is physically impossible.
Therefore, the gravitational field is not brought about by energy, but is created by the matter of Mr. A and Mr. B. Energy does not create a gravitational field. However, energy is equivalent to mass, has inertial mass, and receives acceleration in the gravitational field.
2-4-2. Proposal of four-dimensional volume conservation law to explain mass disappearance
The phenomenon that occurs to Mr. A and Mr. B can be explained by the shape change in the four-dimensional space-time. Let x be the length on the X axis, y be the length on the Y axis, z be the length on the Z axis, and t be the length on the T axis (time axis) . It is reasonable to think that x, y , z , and t are conserved. When a large amount of bond energy is released by bonding, x, y , and z (= mass) are reduced so as to satisfy the conservation law in three-dimensional space , and energy is generated accordingly.
In other words, matter is an entity whose four-dimensional volume is conserved, and energy is an entity whose total amount is conserved in a three-dimensional space. Since matter can be deformed in the direction of the time axis, its volume (=mass) in three-dimensional space can change, but energy is a quantity whose total amount is conserved in three-dimensional space, and cannot escape in the direction of time axis.
Then, as x, y , and z are reduced so as to satisfy the conservation law in four-dimensional space-time, the time axis t is extended and the four-dimensional volume becomes constant, satisfying the conservation law. This means that the time of the substance is delayed.
To explain this with humans, when a large amount of binding energy is released, the x, y , and z seen by an external observer, that is, the volume and mass, are observed to decrease, and t becomes longer, in other words, the lifetime is observed to become longer. .
Ultimately, the volume and mass become zero, the time axis extends infinitely, and the proper time stops.
2-4-3. Mass loss and time delay appearing in all binding energy emission phenomena
It is well known that time is delayed when binding energy is released in a gravitational field and mass is reduced, but according to this paper, this is not limited to the gravitational field, but all binding energies such as electric force, nuclear force, etc. I argue that the disappearance of mass and the time dilation occur on set in the event of the emission of . → It follows from the four-dimensional volume conservation law that I advocate.
2-5. Mass accompanies energy, gravitational field accompanies matter → proof ③
Mass is equivalent to energy and can be completely removed from matter, but matter has the property of creating a gravitational field, which is immutable and inseparable. This property is called "true mass = gravitational elementary weight" here. I think that the invariants of the universe include mass energy, electric charge, and gravitational weight.
2-5-1. Proposed law of conservation of mass and gravitational field
Let us now consider the situation in Box ① in Figure 1. From here, energy can go in and out with wires, so there is no problem with the mass and energy in Box ① changing. However, since nothing goes in and out of box 2, there should be no change in black box 2 as seen from the outside no matter what happens inside (conservation law should hold). This is the mass, the gravitational field, and the electric charge.
However, although the electric charge is preserved, there are positive and negative electric charges, so if the distance between the two is extremely close, the electric field will not reach the outside. See the extra edition at the end of the article for the proof of the correctness of this conservation law.
2-5-2. Whereabouts of the mass lost by the combination of A and B and whereabouts of the gravitational field
The discussion proceeds on the premise that the above conservation law holds. Consider the phenomenon that when A and B approach each other, the bond energy is released and the mass is reduced. The reduced mass leaves Box ① in the form of mechanical energy through wires, is converted into electrical energy by the generator motor, and is stored in the battery.
Here, in order to satisfy the above conservation law, all of the mass decreased in box ① must be an increase in the mass of the battery. In other words, all the lost mass becomes energy. It has a mass exactly equal to the mass whose energy has been reduced.
This is regardless of the form of energy. The same is true for light energy, thermal energy, and chemical energy. This is because no matter how the energy is transmitted from objects A and B to the battery, the result will not change. Also, energy storage need not be limited to electricity, and various forms of energy storage do not affect the results. The same is true for devices that store light energy over long distances. Therefore, the photon also has a mass energy of hν/C^2. However, like the photon, the property of mass does not appear in the state of energy alone. The properties of mass appear when energy is confined in some kind of shell. A shell is usually a substance. →" True nature of gravity " Are you saying that?
Even if Mr. A and Mr. B combine and release energy and the mass decreases or becomes close to zero, if they are separated again by the power generation motor, they will return to Mr. A and Mr. B with their original mass and individuality (reversibility).
2-5-3. Rejection of the myth (theory that the gravitational field is energy and momentum tensor)
If the energy (mass) transferred to this battery had the ability to create a gravitational field, as Einstein's equations say, then the gravitational field would be transferred to the battery, which would be completely wrong . If so, when the mass of Mr. A and Mr. B decreases, the gravitational field will also become smaller, and it will become impossible to extract energy gradually.
In that case, even if they are separated by a power generation motor, the attractive force between them is weak, so sufficient energy is not supplied, and Mr. A and Mr. B are simply separated. Then the energy does not flow back and cannot return to the original state. Mass remains reduced. In other words, it becomes irreversible.
But this would be wrong according to the common sense of the laws of physics. Physical phenomena that are irreversible are time and entropy increase, and this case is a typical reversible change. If such an irreversible change were to occur, people would have to lose weight as they went up and down in the elevator. decrease the number of cells? Do cells get smaller? change personality? physically impossible.
In such a strong gravitational field, Mr. A and Mr. B will die, so it is irreversible. In the thought experiment, A and B are very strong, so I'm done with it. Besides, even if it is an everyday weak gravitational field, the same thing as the above happens on a daily basis, even if the numerical value is small.
2-5-4. Whereabouts of gravitational field → attached to matter
Then, correctly, the gravitational field must remain inside box ① without moving. From this, it can be concluded that the nature and ability to create a gravitational field are associated with Mr. A and Mr. B. The property and ability to create this gravitational field are called "true mass = gravitational elementary weight" here. In the past, gravitational elementary was treated as the same thing as mass energy, but here we will treat it as an independent ability.
An object that has completely lost energy and mass can create a gravitational field, but since it has no mass, it will not receive force from other gravitational fields. In this way, the property and ability to create a constant gravitational field associated with an object is the gravitational elementary capacity. The unit of gravitational mass is kg for the time being. And it will be equal to the mass of matter that has not released any binding energy. This is the owner's hypothesis.
2-6. About the charge case
Although the above proofs have mainly discussed gravitational coupling, similar conclusions can be drawn for charges. Here we consider the charge case in detail.
In the case of gravity, the ability to create a gravitational field and the mass were conventionally regarded as the same. is the charge, and the mass is separated from the beginning, so the problem is clear.
Substances (electrons, protons, etc.) contain electric charges, and strong electric forces act in electron-positron interactions, for example. It is easily assumed that the mass of the electron-positron will decrease if this electric binding energy is released, and that the mass will become zero if the binding energy increases further.
This is the same conclusion as for gravity. However, in the case of electrons, etc., the experimental apparatus shown in Fig. 1 cannot be applied strictly. Attaching wires to electrons is out of scope for thought experiments. The binding energy cannot be extracted continuously, so it needs to be treated with quantum mechanics. However, the basic idea is the same as for gravity. The law of conservation of mass energy, the law of conservation of gravitational field, and the law of conservation of electric charge are applied.
2-6-1. Mass loss due to electron-positron coupling
Empirically, electrons and positrons approach each other and release their binding energy by emitting photons (gamma rays ) . However, this emission is not performed continuously at any time, but two photons of 0.51 Mev equivalent to the mass conversion value of electrons and positrons are emitted and instantly combined.
The electron-positron pair that released the binding energy becomes zero in volume xyz and mass in three-dimensional space, and seemingly ceases to exist. However, it continues to exist in 4D spacetime, and continues to have the ability to create a gravitational field. In addition, although the electric charge does not disappear, the electric force is canceled because the positive and negative equal charges are contained in the zero volume in the three-dimensional space, and the electric charge cannot be observed from the outside by normal methods.
In the previous proof , we proved that mass and energy do not have the ability to create a gravitational field. I'm going to be
We presume that this space contains many "electron: positron . These are not observed because they have zero volume and mass in three-dimensional space, but they have the ability to create a gravitational field, so the effect of this is likely to appear strongly, for example, in the rotation of the Milky Way. To explain the state of motion of most of the hundreds of billions of galaxies that have been confirmed so far , it is necessary to assume that such objects (dark matter) exist in greater quantities than ordinary matter.
A huge black hole has also been observed in the early universe, but it is difficult for ordinary matter to accumulate on such a large scale in a short period of time. However, dark matter, which has no mass, travels at the speed of light, so it may have accumulated in the black hole in a short period of time and made its gravitational field enormous.
Along with that, normal matter and light energy were absorbed and accumulated, and the mass became huge. This effect also caused galaxies to grow rapidly.
2-6-2. Reseparation of electron-positron combination (pair production)
In vanishing masses (dark matter) such as electron-positron combinations, electric charges are conserved, but since the distance between both charges is almost zero, the electric charges cancel each other out, and the effect of the electric field to the outside is almost eliminated . but not strictly zero. Therefore, under special conditions, this charge pair may reveal its properties.
For example, when it passes near the nucleus, it may change course or receive energy under the influence of the strong electric field. Under these conditions, when a high-energy photon or the like acts, it receives energy from it, breaks the bond, and generates an electron-positron pair.
Here again, it is different from the idea of Mr. Dirac and others, but it can not be helped. I attach great importance to the laws of conservation of mass energy, electric charge and gravitational field. Existence should not arise from nothingness. And vice versa.
2-7. Experimental proof method
A familiar example is iron, which is the most stable atom (having the highest binding energy), and is lighter than the sum of the protons, neutrons, and electrons that make it by the binding energy of the nucleus. Since the total mass of elementary particles is "true mass = gravitational elementary weight", iron is the substance with the largest difference between gravitational elementary weight and inertial mass. If the gravitational field created by 1 kg of such a substance and 1 kg of a substance with relatively small binding energy such as hydrogen is precisely measured, iron will have a slightly larger gravitational field.
When an electron and a positron combine, a photon of 0.51 MeV x 2 and a mass of zero (electron-positron combination dark matter) are generated. If we can catch this, the validity of this theory will be proved. However, since it has zero mass, it moves at the speed of light, and since it has zero three-dimensional volume, it can pass through substances, making it difficult to detect. It's probably only detectable by the gravitational field it creates, but it's extremely small.
This space contains a lot of vanishing mass dark matter, so if you create a high-energy state in the space, the bonds between the vanishing masses will break and a pair of positive matter and antimatter will be generated. If this proves it, the existence of the vanishing mass has already been proved.
3. Consideration: Conservation Law of Inertial Mass and Gravitational Field
The theoretical development in this paper is based on the premise that the conservation law holds that the inertial mass and the gravitational field measured from the outside of Box 2 will not change no matter what reaction occurs in Box 2, which has no ingress and egress from the outside. I have to. If this is correct, the conclusion here should be correct. But if not, the conclusion here would be a big mistake.
But if we assume that this conservation law is wrong, another big problem arises. For example, in the thought experiment device in Figure 1, suppose that the mass does not change even if the battery is charged. Consider the case where the conservation law does not hold.
First, move A and B closer and farther apart in box ①. If the generator motor or anything else is 100% efficient, no external energy supply is required for this operation.
Then, when looking at box ② from the outside, it is observed that the mass is changing. For example, if you put this on the ground, the weight will change repeatedly.
If there is such a thing, for example, if it is placed on a spring, it will repeatedly move up and down. Then you can generate electricity with that movement. In other words, an infinite amount of energy can be extracted from nothing. This is a perpetual motion machine of the first kind and violates the first law of thermodynamics. At this stage, we can completely deny this as "impossible".
In other words, the conservation law that the mass does not change when there is no going in and out of the box ② must be strictly established. Then we can conclude that the proof of the existence of dark matter, which we concluded in this paper, is also correct.
In addition, it is concluded that the conservation law that the gravitational field does not change is also correct in the same process. For example, if the pair annihilation and pair generation of electrons and positrons causes their gravitational fields to vanish and generate, the result would be to allow the existence of a perpetual motion machine of the first kind, and the idea is strongly denied. .
To explain this in detail, it is possible to assume an equilibrium state in which pair annihilation and pair generation occur repeatedly even if there is no input or output of energy in the box. If annihilation causes the gravitational field to disappear, the gravitational field of the box will change. Then, when a spring is placed on top of it and a substance is placed, the substance repeats up and down motion. Then, energy can be extracted from it, and it becomes a perpetual motion machine of the first kind. Therefore, such a thing cannot happen. In other words, even if they annihilate, we can conclude that their gravitational field does not change.
The mass of an electron is very small, and the gravitational field it creates is at an unobservable level, but the fact that a first-class perpetual motion machine can theoretically be created no matter how small the output is, proves that assumption is wrong. become. At least in classical physics
Strictly speaking, this operation changes the center of gravity position. Then, the energy will come out as gravitational waves, and it is also possible to take out the energy outside using the movement of the center of gravity inside the box. Therefore, from Box 2, the premise that "no energy goes in and out" cannot be fully observed, and the conservation law does not hold strictly. However, this does not affect the conclusions of this paper. Repeating the approach and separation of A and B means that the required energy is not strictly zero. As a thought experiment, this problem can be avoided by assuming that the box or apparatus is infinitely small.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679511159.96/warc/CC-MAIN-20231211112008-20231211142008-00205.warc.gz
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CC-MAIN-2023-50
| 45,406 | 149 |
http://bodycleanser.info/what-is-the-value-of/
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math
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What is the magnitude?
Of course, each of us, at the level of the most general idea, perfectly understands what a quantity is. Value is the length, volume, mass, or some other quantitative characteristic of an object or phenomenon. What does the value mean? If we hear that hailstorm was the size of a walnut, it means that the volume of one hail was approximately equal to the volume of walnut.
But if we are asked what is a scalar quantity, a random variable, a relative quantity, can we answer this question just as easily?
Let's try to figure everything out in order.
What is a physical quantity?
A physical quantity is a property of an object, phenomenon, or process that can be characterized quantitatively. For example, water poured into a decanter will have a certain volume, mass, density, and so on.
A physical quantity always has a numerical value indicating the units in which it was measured. For example, two containers arrived at the railway station. The mass of one of them is 1.5 tons, and the mass of the other is 1,500 kg.Which one is harder? As you may have guessed, in fact, the mass of both containers is the same. Just with the change of units, the numerical value of the mass has changed.
A random variable is a term for the mathematical theory of probability. A random variable takes a specific value in the course of any experience. But this value cannot be accurately known in advance. Examples of random variables:
- number of hits from 5 shots;
- the number of points on the top face of the dice, which will fall out after throwing it up;
- air temperature for tomorrow.
Scalar and vector values
A scalar value is a value that has only a numeric value. Approximate scalar values - time, mass, temperature, etc.
However, some physical quantities (speed, force, acceleration), besides the numerical characteristic, also have a direction. Such quantities are called vector. Vector magnitude, for example, the same speed, can also be measured. But the numerical value (modulus) of a vector quantity will not fully describe it, but only partially. To characterize a vector quantity completely, one must indicate the direction of its action in space.
Nominal and real values
The concepts of "nominal" and "real" value are used in the economy. The nominal value is an economic indicator expressed in monetary units. For example, your nominal salary is how much rubles you earned over the past month. And the real salary is how much goods and services you can really get for your nominal salary. If there is high inflation in the country, then the nominal wage can grow, and the real one can fall.
Constant and variable values
A constant value is a value that in a given system has only one specific and unchangeable value. An example is body mass. The value of a variable can vary depending on various factors. For example, the speed of the same car on the same track may vary depending on the desire of the driver.
Absolute and relative values
Absolute and relative values are operated by statistics. The absolute value is expressed in specific units of something. For example, per capita consumption of goods and services is expressed in rubles or dollars. Relative value is an indicator of comparison of absolute values.For example, you can determine the level of consumption of Russians today compared with the same period last year. You can see how, according to this indicator, Russians look relatively to citizens of India or Norway.
The average value is a statistical indicator that characterizes the typical value of a characteristic for a homogeneous group. Although all employees of the same enterprise receive different wages, it is possible to calculate the average wage at a given enterprise.
The average is sometimes more important than the specific. If you received 11,000 rubles for 11 months and earned 80,000 rubles in December, this does not mean that you came close to earning 80,000 rubles a month. Your average salary per year is 25,000 per month.
However, the average value may be misleading. If you ate 2 patties, and I ate one, then on average we ate one patty. But for me it does not matter. After all, you have become well fed, and I remained hungry.
How to repair a plastic bumper
Hot smoked perch
Tapestries with religious motifs
How to make paper airplane
Marble manicure is a great idea for nail design
Red horse made of thread (toy-motanka)
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CC-MAIN-2018-47
| 4,395 | 29 |
https://asgt2012.wordpress.com/2012/03/29/remarks-on-lecture-2/?replytocom=3
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math
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In this lecture, we generalized our setting to weighted graphs where is a positive weight function on edges. We also looked at the basic spectral theory of the normalized Laplacian, defined by
which operates on functions via
In particular, we associated with the normalized Rayleigh quotient,
and we showed that we can express the second-smallest eigenvalue as
We defined the expansion of a subset by
where is the characteristic function for .
Finally, we defined the expansion of a graph by
We then stated and (almost) proved the following discrete Cheeger inequality.
Theorem 1. For any weighted graph , we have
- Prove that for the normalized Laplacian, just as for the combinatorial Laplacian, the number of connected components in a graph G is precisely the multiplicity of the smallest eigenvalue.
- We saw the the right-hand inequality in Theorem 1 is asymptotically tight. Prove that the left-hand side is asymptotically tight for the complete graph on n nodes.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827992.73/warc/CC-MAIN-20181216191351-20181216213351-00026.warc.gz
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CC-MAIN-2018-51
| 969 | 11 |
https://haeld.wordpress.com/2014/02/03/neusis-classical-geometry-with-more-than-just-ruler-and-compass/
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math
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A couple of weeks ago, I already wrote about me dealing with Galois theory and about how you can prove the fundamental theorem of algebra using its methods. Since then, I had a closer look at the geometrical implications of Galois’ work. The mathematical folklore is about the classical contructions with ruler and compass, what can and what cannot be done – in particular, every basic text on field theory talks about the impossibility of squaring the circle and doubling the cube and trisection of angles. All very nice and honestly: it’s actually surprising that you can disprove those geometric things with merely algebraic tools.
Just to summarize briefly what’s the core of those folklore arguments: With a ruler and compass you can construct lines and circles (obviously) from certain given points, and by intersection, you get new points. When you consider equations for the circles and for the lines, you will see that you only have to deal with at most quadratic equations. Hence, every new point you construct with ruler and compass will come from a field extension of degree or . So, if you can construct something with ruler and compass, it must be contained in a field extension of that has degree for some . But then, for squaring the circle, you need to construct which is not algebraic; for doubling the cube, you need to construct , which has degree over ; and for trisection of an arbitrary angle you need numbers of degree as well. Contradiction. q.e.d.
When the Greek mathematicians tried to solve their classical problems, they didn’t make it with only their classical tools (well… how could they, it’s impossible anyway). Instead, they invented many clever ideas to achieve a solution with slightly extended tools. One of these ideas is the famous quadratrix, which is a curve in the plane that crosses the -axis at distance from the origin (modernly speaking). With the usual tools, one can now construct and so, one has squared the circle. Similar things happen with the sprial of Archimedes.
Something that I have encountered for the first time now, is the so-called neusis. I found it is sometimes also called a construction with compass and marked ruler. The classical Greek ruler is nothing but a stick, it only allows you to draw a straight line. Now that marked ruler has two marks at a certain distance of one another. At first, I wasn’t excited by this: if the distance of the marks is a constructible number, the compass already allows you to draw a straight line of this given length – now big deal about that. But the power of this tool is different: Suppose you have a point and two lines. With the marked ruler, you can draw a line through the given point that crosses the two given lines such that the segment between the two lines has the given length. You can’t do this with the classical unmarked ruler and compass alone, because you can’t know what angle the new line to be drawn needs to have! The marked ruler can be shifted until you have found the correct angle and draw the line then.
Now, we have a new tool that comes quite cheap: Just mark the ruler in some fashion, for instance with the compass set to some unit length. But let’s see how powerful this can get. Let’s say the marks on our ruler have distance , it doesn’t matter if is constructible or not. We will trisect a given angle . To fix notation, is set at a point . Let’s draw a circle of radius around (see the picture below), such that one of the lines defining can be considered the diameter of the circle. The other line that defines will cut the circle at a point . Now, we set our marked ruler on the point and move it such that one of the two marks is on the circle, the other is on the diameter of the circle (the line through ). Thus, we have found a line segment of length between circle and line, passing the circle at point and the line at point ; and the prolongation of this line also passes through . The angle at between the new line and the diameter of the circle equals exactly .
Well. Really? Let’s see.
Of course the length r is present all over the place. It’s the distance of , of (since and are on the circle) and of (by marked-ruler-construction). So the triangle is isosceles and the angles at and at are equal. Similarly the triangle is isosceles with equal angles at and , let’s call this angle . The third angle of at equals . But this angle is also . So, and hence . Then consider the angles at : one of them is , the other one is . But this other one is also . So we have . Taking everything together, we find . q.e.d.
This is a tricky construction, but it’s pretty much just moving around triangles. I can see how you can invent this trick. But those Greeks have found many more deep constructions using the marked ruler, just just look like magic to me. I can prove them, after I have thought about them long enough – but getting the idea to look at just that, this seems amazing. Besides, my proofs heavily rely on algebraic notation and on theorems that can’t possibly have been clear to the ancient Greeks. Maybe they just believed in the truth of those theorems and accepted them – they wanted to construct points after all, so they wanted to draw things; not invent any deep theory of algebra. But that doesn’t diminish their efforts and insights. I am very interested in the way they proved their results, sadly I couldn’t find any readable account of this.
Let’s try to find cubic roots, for instance, with . We start with an isosceles triangle , where and . Prolonging the line beyond , we find the point with . Then, we draw a line through and , and we prolong the line beyond . Then, we can use our marked ruler through the point such that we’ll find a segment between the lines through and through with length . This segment cuts at the point and at the point , . Then, , amazingly.
Once you have accepted this, you can find cube roots of any by scaling with a factor (and by constructing first). The tricky part is to prove the correctness of this construction in the first place. I don’t see how you could get this idea anyway… but it works just fine as you will see.
We’ll need two new lines for our proof: A line at a right angle to through , meeting in ; and a parallel line to through , meeting the line in . Then the triangles and are similar, so we have and thus . The triangles and are similar as well (by the parallel lines and the respective angles at being equal). So, and hence . Now, we can use the Pythagorean theorem twice in a row: . This yields . By multiplying out and sorting all the terms, we find , and looking at this long enough, this is . Now, the first term gives , but this is negative and , being a line segment, needs to have positive length. So, the length of needs to be a positive solution to the second term, and so , as claimed (the other two solutions are not real). q.e.d.
Isn’t that a pretty proof?
Algebraically, by the way, the marked ruler allows you a little more than the classical ruler: It gives you points in field extensions of degree and . It still doesn’t allow you to construct any real number you want. The quadratrix on the other hand only gives you a field extension with the transcendental number , no cubic roots.
Finally, I need to give credit to the book that showed me these things. The book by Cox on Galois theory, that I mentioned a couple of weeks ago already, has these things in an optional section and mostly as exercises. I have spent many an evening recently on those exercises – this was a lot of fun in geometry of all things (I have never liked geometry… at all.). The images that I have built in here, rely heavily on Cox’ notation and on the images to his exercises.
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CC-MAIN-2018-05
| 7,760 | 14 |
https://www.digglicious.com/types-of-essays/how-does-circle-packing-work/
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math
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How does circle packing work?
Circular packing or circular treemap allows to visualize a hierarchic organization. It is an equivalent of a treemap or a dendrogram, where each node of the tree is represented as a circle and its sub-nodes are represented as circles inside of it.
What is circle packing problem?
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle.
How do you pack circles?
A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres is called a sphere packing….Circle Packing.
What is packing in mathematics?
packing, in mathematics, a type of problem in combinatorial geometry that involves placement of figures of a given size or shape within another given figure—with greatest economy or subject to some other restriction.
Which type of data does a circle pack best represent?
Circle packing is great for showing distribution and part-to-whole relationships in large data sets. You can show an overview of the groups and relationships in the data. You might use color to shade the circles to add another variable to your visualization.
What is the packing density of a circle?
circle packing in the plane. The density of this circle configuration is. π √ 12 ≈ 0.906 90. In geometry, circle packing refers to the study of the arrangement of unit.
How many diameters can fit in a circle?
Every circle has an infinite number of possible diameters. The formula for finding the diameter of a circle is two times the radius (2 * radius).
What is a packing pattern?
1. Solves the pattern selection problem for constructing pattern database search heuristics. One bin represents a container for the abstract state space and approximates the memory usage for pattern database construction. Multiple bins apply for disjoint pattern database construction.
What is sunburst diagram?
A Sunburst Diagram is used to visualize hierarchical data, depicted by concentric circles. The circle in the centre represents the root node, with the hierarchy moving outward from the center.
What is a sunburst chart?
Sunburst chart, known by multiple names such as ring chart and radial treemap, is used to visualize a hierarchical dataset. It shows hierarchy through a series of concentric rings, where each ring corresponds to a level in the hierarchy. Each ring is segmented proportionally to represent its constituent details.
What is meant by packing density?
Packing density (α) is the ratio of the volume of the fibers to the volume of the fibrous media. In aerosol filtration, the fibrous media largely present packing density values lower than 20–30%.
What is circle packing in geometry?
A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres is called a sphere packing. Tessellations of regular polygons correspond to particular circle packings (Williams 1979, pp. 35-41).
How do you find the radii of a circle packing?
Using discrete conformal mapping, the radii of the circles in the above packing inside a unit circle can be determined as roots of the polynomial equations The following table gives the packing densities for the circle packings corresponding to the regular and semiregular plane tessellations (Williams 1979, p. 49).
What is a sphere packing?
The generalization to spheres is called a sphere packing. Tessellations of regular polygons correspond to particular circle packings (Williams 1979, pp. 35-41).
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500356.92/warc/CC-MAIN-20230206145603-20230206175603-00767.warc.gz
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CC-MAIN-2023-06
| 3,663 | 28 |
http://fer3.com/arc/m2.aspx/Universal-Plotting-Sheet-High-Latitudes-Goethe-apr-2018-g41778
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math
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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bob Goethe
Date: 2018 Apr 5, 04:36 -0700
VP-OS Universal Plotting Sheet at High Latitudes
Unless you are at the equator, lines of longitude are always slightly converging. But we can use a universal plotting sheet because over the space of 2° of latitude, the degree of convergence is not navigationally significant.
However, I presume that if you go far enough north, the convergence WILL become navigationally significant.
Through what latitude range is a VP-OS plotting sheet useable?
I am specifically thinking of a hypothetical voyage through Davis Strait, N 68.75°, W 62.10°, and wondering if a universal plotting sheet can be used for plotting accurate-enough DR positions.
Using Traverse Table to Directly Calculate a DR
In looking at the traverse table in Bowditch, it captures a solution to plane right triangles. Coming up with the difference in latitude seems straightforward. Assuming I am on a course of 45°, then:
ΔLat = DistanceSailed x cos(45°)
If I want to use that to get a difference in longitude rather than simply a nautical-miles-travelled-from-east-to-west, it appears to me that I could do this with an equation. This is unfamiliar territory for me and I would appreciate you checking me on my concept.
Assuming that I am sailing on a course of 45°, and if the departure in nautical miles = DistanceSailed times sine of my course c, then here is my equation:
departure = DistanceSailed x sin(45°)
If the width of a degree of longitude in nautical miles = cos(latitude) x 60, then if I am at a latitude of 68° north, it would seem that:
ΔLong = [DistanceSailed x sin(45°)] / cos(68°)
Have I got this right?
Thank you very much.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402127075.68/warc/CC-MAIN-20200930141310-20200930171310-00532.warc.gz
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CC-MAIN-2020-40
| 1,790 | 18 |
https://allnurses.com/nclex-discussion-forum/terrified-after-taking-1164489-page2.html
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math
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Terrified after taking the NCLEX - page 2
Hi everyone, I took the NCLEX earlier today and I feel horrible about how it went. I graduated at the top of my class from one of the top 10 nursing programs in the country, I scored in the 96th... Read More
Jun 16Joined: Oct '15; Posts: 300; Likes: 742Quote from nursenat6I felt the same way and did not feel confident about ANY of the questions. I had always been strong in pharm and did not recognize ANY of the drugs. However, my program and prep must have been good because, like you, I passed with nearly the minimum questions.During the test I remember thinking how shocked I was that neither my nursing program nor U-World prepared me to answer so many of the questions.
Jun 16Joined: Jul '12; Posts: 463; Likes: 487I remember the first question I received on the NCLEX. Interesting how my nursing program didn't teach it to me, nor would I have thought to study it. However, I did know the answer. I thought if the rest are at this level, I won't pass. After 85 questions, I was done.
Jun 17Joined: Oct '16; Posts: 144; Likes: 97That's exactly how I felt and even after the good pop up I was still convinced I failed. I bet you passed!!
Jun 17Joined: Jan '09; Posts: 31; Likes: 9I think every nurse can tell you that after taking the NCLEX, you won't have a good feeling about it. I'm sure you did great on it. 😊
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827281.64/warc/CC-MAIN-20181216051636-20181216073636-00374.warc.gz
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CC-MAIN-2018-51
| 1,366 | 6 |
http://sewwest.blogspot.com/2009/10/reply-to-nanny2cole.html
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math
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Corrected 10/31/09 to add a couple of clarifications.
Reader nanny2cole is trying to figure out the formula on Leslie's Broomstick Skirt that I posted a while ago:
HELP!!! I got the formula to arive at "X=" but I don't understand how to get to "Y=". Y= (W/2 - 2X) /3. Am I suppose to double "X"? I'm a little lost.
Well, yes and no. OK, you've selected the 10 panel version.
W/2 = width of fabric divided by 2.
2x = x multiplied by 2, in other words, the width of the top edge of the panel.
Let's do an example with numbers:
W/2 = 22"
Let's just assume that x = 4", so 2x = 8"
22"- 8" = 14"
14"/3 = 4.67". This is Y.
So OK, you've got X = 4" and Y = 4.67" and you're ready to draw the pattern piece:
On your pattern paper, draw a long straight line equal to L, your desired skirt length plus 1 inch. This will be the center of your trapezoid and will be on the straight of grain when placed on your fabric. At one end of the line measure out at right angles your calculated distance x. Make a big dot. Do this on both sides of the line and connect the dots.
At the opposite side of line L, perform the same operation, but use your calculated y value this time. You should have a figure that looks like the capital letter "I" but with the base wider than the top. Connect each top dot with a bottom dots and you should see a trapezoid. Using the example above, the top of the trapezoid will be x times 2, or 8 inches. The bottom of the trapezoid will be y times 2, or 9.34 inches.
Yes, it's a long and skinny piece, considering that the finished length of my skirt is 35-1/2 inches. And it's designed to fit the width of your fabric, which is why the width of the fabric comes into the formula.
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| 1,693 | 15 |
https://link.springer.com/chapter/10.1007%2FBFb0066456
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Stockmeyer P.K. (1974) The charm bracelet problem and its applications. In: Bari R.A., Harary F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg
The necklace problem has proved to be both a sound pedagogical device in teaching enumeration theory and a valuable counting tool with several graphical applications. In this paper we solve the more general charm bracelet problem and provide two applications for which the necklace problem in not sufficient.
We set the stage in Section 1 by providing a brief review of the necklace problem. This serves as a basis for comparison in Section 2, where we discuss the charm bracelet problem and derive its solution. Sections 3 and 4 contain nontrivial graphical applications of the results of Section 2.
Definitions for all graphical terms and concepts can be found in . For further background and broader treatment of topics of an enumerative nature, should be consulted.
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CC-MAIN-2017-22
| 967 | 4 |
http://www.e-booksdirectory.com/details.php?ebook=4513
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math
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Introduction to the Galois Theory of Linear Differential Equations
by Michael F. Singer
Publisher: arXiv 2008
Number of pages: 83
The author's goal was to give the audience an introduction to the algebraic, analytic and algorithmic aspects of the Galois theory of linear differential equations by focusing on some of the main ideas and philosophies and on examples.
Home page url
Download or read it online for free here:
by Marcel B. Finan - Arkansas Tech University
Contents: Basic Terminology; Qualitative Analysis: Direction Field of y'=f(t,y); Existence and Uniqueness of Solutions to First Order Linear IVP; Solving First Order Linear Homogeneous DE; Solving First Order Linear Non Homogeneous DE; etc.
by Norbert Euler - Bookboon
The book consists of lecture notes intended for engineering and science students who are reading a first course in ordinary differential equations and who have already read a course on linear algebra, general vector spaces and integral calculus.
by Gerald Teschl - Universitaet Wien
This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem.
by Stephen Wiggins - University of Bristol
This book consists of ten weeks of material given as a course on ordinary differential equations for second year mathematics majors. Rather than seeking to find specific solutions, we seek to understand how all solutions are related in phase space.
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| 1,549 | 15 |
https://pdxscholar.library.pdx.edu/ece_fac/214/
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math
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Quantum logic, Algebraic functions, Computer algorithms
In this paper, we propose a regular layout geometry called 3×3 lattice. The main difference of this geometry compared to the known 2×2 regular layout geometry is that it allows the cofactors on a level to propagate to three rather than two nodes on the lower level. This gives additional freedom to synthesize compact functional representations. We propose a SAT-based algorithm, which exploits this freedom to synthesize 3×3 lattice representations of completely specified Boolean functions. The experimental results show that the algorithm generates compact layouts in reasonable time.
Alan Mishchenko and Marek Perkowski, "Logic Synthesis for Regular Layout using Satisfiability," Proceedings of Symposium on Boolean Problems. September, 2002, Freiberg, Germany.
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CC-MAIN-2018-26
| 824 | 3 |
https://www.physicsforums.com/threads/what-is-the-name-of-the-physics-law.80794/
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math
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that says complex things tend to breakdown into simpler things over time?
Chaotical systems (the eqns of motion are nonlinear) could exhibit interesting behavior.I'm sure that the evolution of nonequilibrium statistical systems follows the second principle of thermodynamics.
And your question is awfully vague.
well I cant really remember much more about the law than what I asked, sorry
I think creationists use it to disprove evolution
Do you mean entropy?
I think he is referring to the second law of thermodynamics. Whether this law says that complex things tend to break down into simpler things over time is largely debatable.
Maybe this susceptibility to misinterpretation is why creationists use it to disprove evolution?
Sounds like the second law of thermodynamics to me too. To properly understand the second law one must be careful and rigorous--there's a LOT of misinformation out there. Pretty much all of statistical mechanics (a formal statistical framework from which the original "laws of thermodynamics" can be derived) is based around one postulate: A system in equilibrium has equal probability of existing in any of it's accessible states.
(I am however still not too clear on the precise definition of equilibrium myself)
Here's a little example to help you understand more about entropy and "complex things" becoming "simpler". First of all, you must understand that in (classical) physics the universe is a fundamentally reversible, deterministic system in which "information" is conserved. It is only when one invokes statistics that one can talk about "losing" or "gaining" information, and I think that's what you are getting at when you ask about complex systems becoming simpler.
Imagine two chambers, connected by a tube with a valve in it. Say you close the valve and fill only the left chamber with gas. What do you know? Well, you know for instance that every particle of gas is in the left side of your system. Now say you open the valve. Equilibrium is eventually reached in which both chambers are filled with the same amount of gas. At this point, what do you know? Pretty much nothing! You really can't say what particle is where, can you? In this sense, one could say that information has been lost. Which would make it seem like the system is now "simpler".
But again, you must realize that you are still talking in terms of probabilities, which are not fundamental, but rather an abstraction used to study macroscopic systems. At the heart of everything is Newton's laws, and actually, no information has been lost.
Yep I think its the 2nd law of thermodynamics
Hah ! That's priceless...are creationists trying to use science to invalidate a scientific theory and replace it with an unscientific one ?
1. As Dexter mentioned, the Second Law does not apply to non-equilibrium systems like complex organisms,
2. Even if it did (in some fantasy world), this is still a blatant misunderstanding (assuming there was even an attempt at understanding, in the first place) of the Second Law, which does NOT prohibit local reduction of entropy.
Might as well go about denying the existence of snowflakes, while they're at it ! :grumpy:
Separate names with a comma.
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CC-MAIN-2019-04
| 3,198 | 19 |
http://m4bccradio.tk/wodod/price-conversion-calculator-focu.php
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math
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The CoinDesk Bitcoin Calculator converts bitcoin into any world currency using the Bitcoin Price Index, including USD, GBP, EUR, CNY, JPY, and more.
Conversion ratio financial definition of conversion ratio
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| 5,243 | 15 |
https://www.prep4usmle.com/forum/thread/14121/
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math
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|Prep for USMLE|
| Forum | Resources||New Posts | Register | Login||» |
what we have to do to get into some research , post doc fellow ship or to do some publications in us before starting residency in us. what is the procedure to follow. is it like that we have to hook up with a guy who is already doing some research or publications......... how can we contact them. we can go directly ask them that i m interested in doing so ........
is it ok if we go ask them directly.
any input will be greatly appreciated.
with advance thanks.
Well, there are a couple of ways to do this. The easiest is if you know someone doing research who needs postdocs. If you are doing a rotation at a US med school, just ask your attendings and if they are not doing that kind of work, they probably know someone who is. It helps a lot to come with a recommendation from someone the investigator knows. That's what I did.
Other options are to look on university job posting websites. They usually post their postdoc openings and you can just apply. If you have little to no research experience, it can be hard, but usually there are labs which don't care and will take you with the understanding that they have to teach you. I would caution you that those programs would expect you to stay there for several years.
Another good way to do this would be to pick a field you are interested in, and go approach researchers at nearby universities doing similar work. If you talk to them directly and convince them you are sincere and really want to do work in their field, then even if they are not hiring, they can direct you to someone who is.
A few words of caution: if you are still studying for MLEs, research fellowships take a LOT of time. It will be tough to study and do the work your job requires (but obviously it can be done, I did it). Second, I think you should do the work at a university that realistically might take you for residency. Third, you should like basic science and research. It will be a hard time if you don't. Fourth, hopefully you are doing the research because you have a genuine interest in it. If you are only doing this as a way to get ahead in residency applications, well, it will be obvious and you won't get a good LoR from your boss (which would look bad when you apply).
Hope this helps.
thank u very much
u r infimation is very helpful.
This thread is closed, so you cannot post a reply.
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https://books.google.com/books/about/Contributions_to_the_theory_of_games.html?id=WC8PAAAAIAAJ&hl=en
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math
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What people are saying - Write a review
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Paper 1 On Games of Survival
21 other sections not shown
Other editions - View all
Annals of Mathematics assume Bayes response behavior strategy Blotto boundary bounded choice choose component condition consider continuous converges convex corresponding critical vector defined definition denote differential equation differential games distribution e-best equal equilibrium point evader example exists expected finite game finite number follows functional equations game elements game G given hence implies inequality infinite information set integral Karlin kernel Lemma linear mapping Mathematics Study matrix game maximizing minimax mixed strategies monotonic move N-tuple non-negative obtain optimal strategies paper payoff function perfect information PERFECT STRATEGIST play position possesses probability problem pure strategies RAND Corporation random recursive game result satisfies Section semi-continuous Shapley solution stationary strategies stochastic game strate strategies x strategy for Player strictly subgame subset sufficient survival game Theory of Games tion topological unique unit interval utility function value function winning zero zero-sum
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| 1,258 | 6 |
https://how-what-advice.com/13094698-how-to-calculate-the-area-of-an-ellipse-5-steps-with-pictures
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math
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The area equation for an ellipse will look easy if you've studied circles before. The main point to remember is that an ellipse has two important lengths to measure, namely the major and minor radii.
Part 1 of 2: Calculating Area
Step 1. Find the major radius of the ellipse
This radius is the distance from the center of the ellipse to the farthest end of the ellipse. Think of these radii as the “bulging” radii of the ellipse. Measure the radius or look for the radius indicated on your diagram. We will refer to these fingers as a.
You can call it the semimajor axis
Step 2. Find the minor radius
As you may have guessed, the minor radius measures the distance from the center of the ellipse to the nearest point at the end of the ellipse. Call these fingers b.
- This radius has a right angle of 90 degrees with the major radius. However, you don't need to measure every angle to solve this problem.
- You can call it the semiminor axis.
Step 3. Multiply by pi
The area of the ellipse is a x b x. Since you are multiplying two units of length, your answer is written in units of squares.
- For example, if an ellipse has a major radius of 3 units and a minor radius of 5 units, the area of the ellipse is 3 x 5 x or about 47 squared units.
- If you don't have a calculator or if your calculator doesn't have the symbol, just use 3, 14.
Part 2 of 2: Understanding How It Works
Step 1. Think of the area of a circle
You may remember that the area of a circle is equal to r2, which is equal to x r x r. What if we try to find the area of a circle as if it were an ellipse? We will measure the radius in either direction: r. Measure the radius that is at the right angle: also r. Plug that value into the formula for the ellipse equation: x r x r! As it turns out, circles are just a certain type of ellipse.
Step 2. Imagine a pressed circle
Imagine a circle pressed so that it forms an ellipse. As the circle is pressed more and more, one of the radii becomes shorter and the other radii become longer. The area remains the same because nothing leaves the circle. As long as we use both radii in our equation, the emphasis and alignment will cancel each other out, and we'll still get the right answer.
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https://www.eacad.org/post/projectile-motion
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What is Projectile?
A projectile is any object thrown into space upon which the only acting force is gravity. The primary force acting on a projectile is gravity. This doesn’t necessarily mean that other forces do not act on it, just that their effect is minimal compared to gravity. The path followed by a projectile is known as a trajectory. A baseball batted or thrown is an example of the projectile.
What is Projectile Motion? When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration that is directed towards the centre of the earth (we assume that the particle remains close to the surface of the earth). The path of such a particle is called a projectile and the motion is called projectile motion. In a Projectile Motion, there are two simultaneous independent rectilinear motions:
Along the x-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.
Along y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle.
Acceleration in the horizontal projectile motion and vertical projectile motion of a particle: When a particle is projected in the air with some speed, the only force acting on it during its time in the air is the acceleration due to gravity (g). This acceleration acts vertically downward. There is no acceleration in the horizontal direction, which means that the velocity of the particle in the horizontal direction remains constant. Parabolic Motion of Projectiles Let us consider a ball projected at an angle θ with respect to the horizontal x-axis with the initial velocity u as shown below:
The point O is called the point of projection; θ is the angle of projection and OB= Horizontal Range or Simply Range. The total time taken by the particle from reaching O to B is called the time of flight.
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| 1,863 | 7 |
http://www.solutioninn.com/cherry-hill-glass-company-employs-a-normalcosting-system-the-following
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math
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Cherry Hill Glass Company employs a normal-costing system. The following information pertains to the year just ended.
• Total manufacturing costs were $1,250,000.
• Cost of goods manufactured was $1,212,500.
• Applied manufacturing overhead was 30 percent of total manufacturing costs.
• Manufacturing overhead was applied to production at a rate of 80 percent of direct-labor cost.
• Work-in-process inventory on January 1 was 75 percent of work-in-process inventory on December 31.
1. Compute Cherry Hill’s total direct-labor cost for the year.
2. Calculate the total cost of direct material used during the year.
3. Compute the value of the company’s work-in-process inventory on December 31.
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| 709 | 9 |
https://socratic.org/questions/if-3-times-the-supplement-of-an-angle-is-subtracted-from-7-times-the-complement-
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math
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If 3 times the supplement of an angle is subtracted from 7 times the complement of the angle, the answer is the same as that obtained from trisecting a right angle. What is the supplement of this angle?
Let the unknown angle be
Hence the supplement of the angle is
The compliment of the angle is
Trisecting a right angle gives 3 angles of
Now writing an equation for the written information in the original question gives :
Therefore the supplement of the angle is
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| 464 | 7 |
http://intlpress.com/HHA/v6/n1/a4/
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math
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We define a homological and cohomological dimension of groups in the context of Bredon homology and compare the two quantities. We apply this to describe the Bredon-homological dimension of nilpotent groups in terms of the Hirsch-rank. In particular this implies that for virtually torsion-free nilpotent groups the Bredon cohomological dimension is equal to the virtual cohomological dimension.
Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp. 33-47
Available as: dvi dvi.gz ps ps.gz pdf
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163054576/warc/CC-MAIN-20131204131734-00006-ip-10-33-133-15.ec2.internal.warc.gz
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https://www.wyzant.com/resources/blogs/10767/middle_and_high_school_math_tutor_available
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math
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Hello, middle and high school students!
So, the new school year has started and I'm sure you all want to do well in your classes. I am a math tutor available to help in middle school math (Grades 6 through 8) and high school math, specifically in algebra 1, geometry, algebra 2 and trigonometry. I am planning to become a math teacher and absolutely love the subject. If you need help, please view my tutor profile and let me know! I want to help you succeed in math and do very on your Regents exams!
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CC-MAIN-2018-17
| 501 | 2 |
https://www.asknumbers.com/square-meter-to-square-kilometer.aspx
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math
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How many square kilometers in a square meter?
1 Square Meter (m²) is equal to 0.000001 square kilometer (km²). To convert square meters to square km, multiply the square meter value by 0.000001 or divide by 1000000.
square meters to square km formula
km² = m² * 0.000001
km² = m² / 1000000
1 Square Meter = 0.000001 Square Kilometer
What is Square Meter?
Square Meter (metre) is a metric system area unit. 1 m2 = 0.000001 km2. The symbol is "m²".
You may also use area conversion to convert all area units.
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CC-MAIN-2020-29
| 513 | 9 |
http://www.fixya.com/support/t1098414-inequality
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math
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Question about Texas Instruments TI-89 Calculator
You can see images below
Posted on Sep 18, 2016
You need to input the equation, (3x+1)/x<0, then you need to indicate that you are solving for x by putting comma then x. The equation you are inputting should look like this: solve((3x+1)/x<0,x) and the answer will be -1/3<x<0. That ",x" is telling the calculator to solve for x.
Posted on Oct 17, 2008
a 6ya Technician can help you resolve that issue over the phone in a minute or two.
Best thing about this new service is that you are never placed on hold and get to talk to real repair professionals here in the US.
click here to Talk to a Technician (only for users in the US for now) and get all the help you need.
Posted on Jan 02, 2017
Tips for a great answer:
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Solve the two sided inequality and show the solution on real line
7 < 1-2x ? 10
Oct 25, 2010 | Adobe Computers & Internet
the two sided inequality and show the solution on real line
1-2x ≤ 10
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| 1,447 | 28 |
https://en-academic.com/dic.nsf/enwiki/210551
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math
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- Emil Leon Post
name = Emil Leon Post
February 11, 1897
Augustów, then Russian Empire
April 21 1954,
New York City, flagicon|USA U.S.
known_for = Formulation 1,
Post correspondence problem, completeness-proof of Principia's propositional calculus
Emil Leon Post,
Ph.D., ( February 11 1897, Augustów– April 21 1954, New York City) was a mathematicianand logician.
Post was born into a Polish-Jewish family that immigrated to America when he was a child. After completing his Ph.D. in mathematics at
Columbia University, he did a post doctorate at Princeton University. While at Princeton, he came very close to discovering the incompleteness of " Principia Mathematica", which Kurt Gödelproved in 1931. Post then became a high school mathematics teacher in New York City. In 1936, he was appointed to the mathematics department at the City Collegeof the College of the City of New York, where he remained until his death.
Columbia Universitydoctoral thesis, Post proved, among other things, that the propositional calculus of "Principia Mathematica" was complete: all tautologies are theorems, given the "Principia" axioms and the rules of substitution and modus ponens. Post also devised truth tables independently of Wittgensteinand Charles Peirceand put them to good mathematical use. Jean Van Heijenoort's (1966) well-known source book on mathematical logic reprinted Post's classic article setting out these results.
In 1936. Post developed, independently of
Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. (This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewritingand developed by Post in the 1920s but first published in 1943).
The unsolvability of his
Post correspondence problemturned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages.
In an influential address to the
American Mathematical Societyin 1944, he raised the question of the existence of an uncomputable recursively enumerableset whose Turing degreeis less than that of the halting problem. This question, which became known as Post's Problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
* 1936, "Finite Combinatory Processes - Formulation 1," "Journal of Symbolic Logic 1": 103-105.
* 1943, "Formal Reductions of the General Combinatorial Decision Problem," "
American Journal of Mathematics65": 197-215.
* 1944, "Recursively enumerable sets of positive integers and their decision problems," "
Bulletin of the American Mathematical Society50": 284-316. Introduces the important concept of many-one reduction.
* [http://www.amphilsoc.org/library/mole/p/post.htm Emil Leon Post Papers 1888-1995] -
American Philosophical Society, Philadelphia, Pennsylvania.
*Davis, Martin (1993). "The Undecidable" (Ed.), pp. 288-406. Dover. ISBN 0-486-43228-9. Reprints several papers by Post.
*Davis, Martin (1994). "Emil L. Post: His Life and Work" in Davis, M., ed., "Solvability, Provability, Definability: The Collected Works of Emil L. Post". Birkhäuser: xi--xxviii. A biographical essay.
Post's inversion formula
* [http://www.ams.org/notices/200805/ An interview with
Martin Davis] - Notices of the AMS, May 2008. Much material on Emil Post from his first-hand recollections.
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https://en-academic.com/dic.nsf/enwiki/391553
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math
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- Polarization mode dispersion
Polarization mode dispersion (PMD) is a form of
modal dispersionwhere two different polarizations of light in a waveguide, which normally travel at the same speed, travel at different speeds due to random imperfections and asymmetries, causing random spreading of optical pulses. Unless it is compensated, which is difficult, this ultimately limits the rate at which data can be transmitted over a fiber.
In an ideal optical fiber, the core has a perfectly circular cross-section. In this case, the fundamental mode has two orthogonal polarizations (orientations of the
electric field) that travel at the same speed. The signal that is transmitted over the fiber is randomly polarized, i.e. a random superposition of these two polarizations, but that would not matter in an ideal fiber because the two polarizations would propagate identically (are degenerate).
In a realistic fiber, however, there are random imperfections that break the circular symmetry, causing the two polarizations to propagate with different speeds. In this case, the two polarization components of a signal will slowly separate, e.g. causing pulses to spread and overlap. Because the imperfections are random, the pulse spreading effects correspond to a
random walk, and thus have a mean polarization-dependent time-differential (also called the Differential Group Delay, or DGD) proportional to the square root of propagation distance :
is the "PMD parameter" of the fiber, typically measured in ps/√km, a measure of the strength and frequency of the imperfections.
The symmetry-breaking random imperfections fall into several categories. First, there is geometric asymmetry, e.g. slightly elliptical cores. Second, there are stress-induced material
birefringences, in which the refractive index itself depends on the polarization. Both of these effects can stem from either imperfection in manufacturing (which is never perfect or stress-free) or from thermal and mechanical stresses imposed on the fiber in the field — moreover, the latter stresses generally vary over time.
Compensating for PMD
A PMD compensation system is a device which uses a
polarization controllerto compensate for PMD in fibers. Essentially, one splits the output of the fiber into two principal polarizations (usually those with , i.e. no first-order variation of time-delay with frequency), and applies a differential delay to bring them back into synch. Because the PMD effects are random and time-dependent, this requires an active device that responds to feedbackover time. Such systems are therefore expensive and complex; combined with the fact that PMD is not yet the limiting factor in the lower data rates still in common use, this means that PMD-compensation systems have seen limited deployment in largescale telecommunications systems.
Another alternative would be to use a polarization maintaining fiber (
PM fiber), a fiber whose symmetry is so strongly broken (e.g. a highly elliptical core) that an input polarization along a principal axis is maintained all the way to the output. Since the second polarization is never excited, PMD does not occur. Such fibers currently have practical problems, however, such as higher losses than ordinary optical fiber and higher cost. An extension of this idea is a single-polarization fiberin which only a single polarization state is allowed to propagate along the fiber (the other polarization is not guided and escapes).
A related effect is polarization-dependent loss (PDL), in which two polarizations suffer different rates of loss in the fiber due, again, to asymmetries. PDL similarly degrades signal quality.
Strictly speaking, a circular core is not required in order to have two degenerate polarization states. Rather, one requires a core whose symmetry group admits a two-dimensional irreducible representation. For example, a square or equilateral-triangle core would also have two equal-speed polarization solutions for the fundamental mode; such general shapes also arise in
photonic-crystal fibers. Again, any random imperfections that break the symmetry would lead to PMD in such a waveguide.
* Rajiv Ramaswami and Kumar N. Sivarajan, "Optical Networks: A Practical Perspective" (Harcourt: San Diego, 1998).
* Jay N. Damask, "Polarization Optics in Telecommunications" (Springer: New York, 2004)
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http://twinsdaily.com/entry.php/1009-Stealing-Second-With-Runners-On-The-Corners
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math
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Stealing Second With Runners On The Corners
by, 05-11-2012 at 10:12 PM (1669 Views)
I just listened to Denard Span short circuit a potential rally by trying to steal second base with runners on the corners and one out. He was caught. I wondered if that was an especially stupid decision.
It turns out, it's not that risky. Or at least it's not if you accept that a baserunner usually needs to steal bases about 2/3 of the time to be effective.
Generally, one studies something like this using Palmer & Thorn's Run Expectancy Matrix. It's a neat grid that shows, given a certain number of outs and people on base, the average number of runs that should score that inning, based on 75 years of major league games. It was published in The Hidden Game of Baseball by Pete Palmer and John Thorn. You can find it here.
Here's the numbers we care about:
1. 1.088 - That's how many runs a team on average would score with runners on 1st and 3rd and one out.
2. 1.371 - If Span would've stolen the base, that's how many runs the average team would've scored.
3. 0.382 - If he was caught, that's how many runs the average team would score.
So Span risked a gain of .283 runs if he stole that base, but a loss of .706 if he was caught. Converting those to percentages, if he steals that base 71% of the time, the team breaks even. That's not especially different than the 2/3 view that is the case for most base stealers. This wasn't especially risky.
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https://bestnursingassignment.com/difference-between-the-two-population-mean-scores-questions/
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math
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Difference Between the Two Population Mean Scores Questions
From a random sample of 7 students in an introductory finance class that uses group-learning techniques, the mean examination score was found to be 76.07 and the sample standard deviation was 2.3.
For an independent random sample of 8 students in another introductory finance class that does not use group-learning techniques, the sample mean and standard deviation of exam scores were 73.81 and 8.6, respectively. Estimate with 90%
confidence the difference between the two population mean scores; do not assume equal population variances.
The 90% confidence interval is from a lower limit of to an upper limit of .
(Round to two decimal places as needed.)
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http://www.chegg.com/homework-help/physical-science-10th-edition-chapter-16-solutions-9780073513898
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math
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Solutions for Chapter 16
(a)Earth is a spherical body, which is a 3 dimensional shape. It would not make sense to name the plane of Earth’s orbit, which is 2 dimensional, after a 3 dimensional shape.
(b)The solar system is also a 3 dimensional collection of planets, asteroids, and comets. Comets in particular have orbits which do not sit in the same orbital plane with Earth. For this reason, it would not make sense for Earth’s orbital plane to be named the plane of the solar system.
(c)The Sun is a spherical object as well, and there are many cross sections that would make sense to name as the plane of the Sun. The Sun’s equatorial plane and axial plane are examples of 2 dimensional cross sections that would make sense to name the ‘Plane of the Sun’.
Thus, the plane of Earth’s orbit is called the plane of the ecliptic because when other objects pass through it, they appear to pass in front of or behind the Sun.
So, the correct answer is.
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https://hspacetheory.wordpress.com/2018/08/30/194/
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math
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THE PHYSICAL CONTENT OF h‑SPACE THEORY
Classical mechanics is based on Newton’s laws and the principle of Galilean relativity. Let us consider each of Newton’s laws in terms of the proposed theory.
Newton’s first law says. “Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed(from the original Latin of Newton’s Principia translated to English; http://en.wikipedia.org/wiki/Newton’s_laws_of_motion).”Given that atoms are made up of n=0-objects(II)”−”,”+”, the laws of classical mechanics describe the relative motions of the n=0‑objects(II)”−”,”+”. The velocity of n=0-objects(II)”−”,”+” is constant in the absence of their attraction or repulsion and the generation of n=1-, n=2- and n=3-objects. Consequently, the Newton’s first law express nothing but the constancy of the velocity of n=0‑objects(II)”−”,”+”.
The second law of Newton states the following. “The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed (from the original Latin of Newton’s Principia translated to English; http://en.wikipedia.org/wiki/Newton’s_laws_of_motion).”In modern physics, a force is defined as the product of the acceleration and the inertial mass. In the proposed theory, the concept of inertial mass is defined as the amount of n=0-objects(II)”−”,”+”. Gravitational mass has the same definition. The direct proportionality of gravitational and inertial mass is due to the definition of mass as the amount of n=0-objects(II)”−”,”+”. Acceleration is a change in velocity per unit of time. The time unit, as discussed in the first pages of the theory, is a unit of velocity. Accordingly, the concept of force is a secondary concept, which is more convenient for determination of motion with variable speed, but it can be reduced to a derivative of the velocity. More simply stated, the concept of force is nothing more than another designation of a change in velocity. In the proposed theory, the central force acting on an object (as in the case of gravitational and electrostatic interactions) is defined in terms of the change of velocity due to the density gradient of n=0-objects(I) around n=0‑objects(II)”−”,”+” (electrons, positrons). The gradient is determined in inverse proportion to the square of the distance, which is due to the three-dimensionality of space. In other words, accelerated motion, i.e. movement with increasing velocity, is not a result of a force acting on a body but rather a consequence of its location in a region of space with a characteristic density gradient of n=0‑objects(I). Since distance is expressed in absolute units, i.e. in lengths of n=0‑objects(I), then velocity varies discretely. This differs from classical mechanics, in which there is no discreteness and velocity changes continuously.
The concept of inertial forces is consistent with the suggested theory, since it describes nothing more than motion with variable velocity by changing the direction of motion. There is then no need for a source of inertial forces, as the concept of force is an auxiliary concept, in contrast to the fundamental concept of velocity.
Newton’s third law states. “To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions (from the original Latin of Newton’s Principia translated to English; http://en.wikipedia.org/wiki/Newton’s_laws_of_motion).”In the proposed theory, this law is due to the symmetry of repulsion of n=0‑objects(II)”−”,”+”.
In classical mechanics, momentum is defined as a product of velocity and inertial mass, and the momentum conservation law establishes the equality of a product of velocity and inertial mass for the closed system in two different states. Inertial mass determines the number of n=0‑objects(II)”−”,”+”. Thus, the law of conservation of momentum reflects the fact that the change in velocities of n=0-objects(II)”−”,”+” in a closed system is a result of a redistribution of the velocities of n=0‑objects(II)”−”,”+”. In the suggested theory, the momentum conservation law is valid for a system consisting of only n=0‑objects(II)”−”,”+”, i.e. electrons and positrons. In contrast to the modern physics, the interaction of the photon and electron causes no redistribution of momentum. The photon is absorbed by an electron, leading to an increase in electron velocity in the direction of the photon. If the photon is reflected from the positron, the positron will not change its velocity. Thus, the law of conservation of momentum cannot be applied to electromagnetic quanta. This statement is supported by the results of experiments with EmDrive (Harold White, Paul March, James Lawrence, Jerry Vera, Andre Sylvester, David Brady, and Paul Bailey 2016, Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum, Journal of propulsion and power, pages: 1-12, DOI: 10.2514/1.B36120).
In contrast to momentum, energy is proportional to the square of velocity, and is not a vector, but a scalar. This concept of energy is different from that used in the proposed theory, in which energy is the opposite of length. Why is the classical concept of energy defined by the square of velocity? We consider this is due to the orthogonality of Euclidean space. In such space the square of velocity is a scalar form of velocity, which allows the algebraic operations of addition and subtraction in the three-dimensional space, i.e. along three orthogonal axes. Accordingly, describing the energy of n=0-object(II)”−”,”+”, i.e. square of the velocity of n=0‑object(II)”−”,”+”, enables one to express the conservation of n=0‑objects(II)”−”,”+” velocities in the form of a scalar sum of squares of velocities of n=0-objects(II)”−”,”+”.
The proposed theory is entirely consistent with the laws of classical mechanics. It holds the principle of relativity of Galileo and Newton’s laws. In contrast to classical mechanics, the proposed theory provides an unambiguous definition of mass as the number of n=0-objects(II)”−”,”+” (electrons/positron). The concept of force is defined as an auxiliary, secondary notion. The motion of n=0-objects(II)”−”,”+” is primary, and change of their velocity defines the concept of force (for the given amount of moved n=0‑objects(II)”−”,”+”). The laws of conservation of momentum and energy are consequences of the primacy and constancy of motion of n=0-objects(II)”−”,”+”. In contrast to classical mechanics, in the proposed theory velocity changes discretely in potential fields: gravitational and electrostatic. I.e. in these fields there is a minimal change of velocity.
SPECIAL THEORY OF RELATIVITY
Special Theory of Relativity (STR)was built as an electrodynamics of moving bodies based on two postulates. One of them is the constancy of the speed of light in all inertial frames of reference, or, in other words, the independence of the speed of light from the motion of the light source. The second is the principle of relativity. It is assumed that all inertial frames of reference are equivalent and there is no special frame of reference for the laws of electrodynamics – Maxwell’s equations, or for the laws of mechanics. Why did these postulates and STR based on them appear in physics? At the time when STR was created, the existence of an ether, an all pervading, fundamental reference frame, was being actively discussed. The Michelson-Morley experiment gave negative results in the detection of an ether wind (light was considered as a wave in the ether, and the ether wind would change the speed of light). If an ether had been detected, then it would have represented a special frame of reference for the phenomena of electrodynamics, and the STR would not have been necessary. However, in the absence of an ether, all inertial frames of reference were considered to be equivalent and therefore the Maxwell’s equations had to maintain their form in different frames of reference, similar to classical mechanics. Experimentally, this was not found to be the case. There was asymmetry between frames of reference due to the fact that, for example, the speed of charge current and, consequently, the existence of a magnetic field depended on the choice of the frame. Also, the speed of light was supposed to be constant on the basis of experimental data, but the use of Galilean transformation required changes of it. Instead of Galilean transformation, Einstein proposed to use the Lorentz transformation and by this means eliminated the asymmetry between different inertial reference frames. In this way, he implemented the principle of relativity and the postulate of the constancy of the speed of light.
The proposed theory is consistent with the postulate of STR regarding the constancy of the speed of light, but in contrast to STR the constancy of the speed of light has a cause – the spatial dimension. Since light quanta are n=1-objects, i.e. objects of one-dimensional space, they are always moving at the same velocity relative to n=0‑objects(II)”−”,”+” of zero-dimensional space, regardless of the speed of n=0-objects(II)”−”,”+”. If the reference system is changed, the constancy of the speed is provided by the inverse relation of the length of photons, as expressed by the Doppler effect (see section on “Optics”). Further, if in Maxwell electrodynamics and so also in the STR, the electromagnetic field and electromagnetic quanta have the same nature and are defined by Maxwell’s equations, then in the proposed theory the electromagnetic quanta and the electromagnetic field are different entities of nature. The field consists of objects of zero-dimensional space, n=0-objects(I), while photons are the objects of one-dimensional space, n=1-objects. (As noted above, there is a connection between them. Electromagnetic field change can lead to the generation of n=1-objects.) Therefore, the speed of light in the Michelson-Morley experiment would not change relative to an ether wind because light is not a wave in the ether. In the proposed theory, the ether exists as moving n=0‑objects(I) creating three-dimensional Euclidean space. Because of this, an attraction/repulsion of charges (electrons/positrons) is defined in the Maxwell’s equations by the maximum density of n=0-objects(I) ρ0(for an electrostatic field) or its change ρΔ (for a magnetic field), generated by the motion of electrons/positrons.
In contrast to the STR, the proposed theory posits that different frames of reference are not equal. I.e. the second postulate, the relativity principle, is not valid for phenomena of electrodynamics. There is a unique absolute frame of reference – an ether, the frame associated with the space of n=0-objects(I) moving relative to each other. Since the electrostatic field of the charge is defined by the density of n=0-objects(I),ρ0, it cannot be changed (without gravity) when the frame of reference is changed. In the absence of gravity, magnetic induction also does not depend on the choice of the reference frame, since it determines the change in density of directed n=0-objects(I), ρΔ, relative to undirected n=0-objects(I) of density ρ0. As suggested above, in Maxwell’s equations the constant ccorresponds to a product of velocity v0and maximum density of n=0-objects(I) ρ0, v0ρ0, and it is not the speed of light. Therefore, it should not obey Galilean transformation for velocity. The maximal velocity v0ρ0decreases with time, since density ρ0was greater in the past than at present. To date, it is comparable with the speed of light and corresponds to the constant c.
According to the proposed theory, it is also wrong to use STR to describe the motion of a body consisting of atoms. If, in the case of photons, STR is consistent with the proposed theory, it is because of the photons length, as the objects of one-dimensional space, is changing in Doppler effects and keeping constancy of the speed of light. The same changes in length are not applicable to the objects of zero-dimensional space, n=0-objects(II)”−”,”+” (electrons and positrons) composing atoms. In other words, there is no Lorentz contraction of lengths of physical objects in the suggested theory. Also, STR is not suitable for explaining the dynamics of bodies composed of atoms. The increase in mass of a body with increasing velocity is not possible. The inertial mass is determined by the number of electrons/positrons, and this number cannot depend on the velocity of electrons/positrons. Therefore, there is no infinitely large mass at the speed of light. The velocity of electrons/positrons are not limited by the speed of light. In the early universe, the velocity of electrons/positrons was greater than the speed of light because the density of n=0-objects(I) ρ0was higher than today, giving them a higher velocity of electrostatic interaction.
Another difference between the proposed theory and STR is the conception of time. In the proposed theory, as in classical mechanics, time is just a matter of agreement. Time is an artificial concept, introduced for convenience to describe the motion of objects, and must be defined as the same in all inertial frames of reference. In special relativity, because of the heterogeneity of time in different frames of reference, there are temporal paradoxes, such as the twin paradox, due to time dilation in the moving frame of reference. In the proposed theory, this is not possible.
GENERAL THEORY OF RELATIVITY
The concept of space-time is used in General Theory of Relativity (GTR) as it is in the special theory of relativity. In general relativity, the gravitational potential is identified with the space-time metric. Space-time is curved by a body having mass, and this causes a gravitational attraction. In the proposed theory, all phenomena take place in Euclidean space. Since both general and special relativity use the concept of space-time rather than Euclidean space, we consider these theories to be incorrect models to describe phenomena.
Phenomena, which in modern physics are explained only by general relativity, have their own interpretations in the proposed theory. For example, the gravitational redshift in general relativity is explained by gravitational time dilation. In the proposed theory, it is explained by a decrease in the density of n=0-objects(I) ρ0around the gravitating body (see “Gravitational attraction”). The existence of black holes can also be explained by changes in density of n=0-objects(I) ρ0. Due to the high density of electrons and positrons, a density gradient of n=0-objects(I) will be formed where the speed of gravitational attraction is greater than the speed of light, causing photons to be unable to overcome this attraction. The same reason will also cause the gravitational delay of electromagnetic quanta – the effect of Shapiro. Another phenomenon predicted by general relativity is the gravitational deflection of light. In the proposed theory, this results from the same attraction as for the Shapiro effect. Because of the high speed of light, gravitational attraction of photons is not as noticeable as for slow-moving electrons and positrons (n=0-objects(II)”−”,”+”). The precession of the orbit of Mercury in the suggested theory has no obvious explanation. However, this value can be the result of the influence of other planets in the solar system, since in the proposed theory gravitational attraction has a maximal boundary.
In the proposed theory, in contrast to the STR, the speed of a body is not limited by the speed of light. The velocity of electromagnetic interactions is limited by a maximum density of the vacuum particles, n=0‑objects(I),ρ0. The velocity determined by this density ρ0, v0ρ0, is comparable to the speed of light, the velocity of object of one-dimensional space. The objects of two- and three-dimensional space move at velocities greater than this, 10 and 20 orders of magnitude above the speed of light, respectively.
What is considered in GRT as the curvature of spacetime, caused by a gravitating body, is the curvilinear motion in three-dimensional Euclidean space. For example, the deviation of light by the gravitational field is the result of the attraction of light quanta, as well as any physical body moving near another gravitating body.
In the proposed theory, phenomena explained by relativistic and gravitational time dilation are interpreted differently. For example, atomic clocks were employed in the Hafele–Keating experiment to accurately measure time, but these devices are based on the emission/absorption of electromagnetic quanta, and such processes depend on the elementary charge. Accordingly, a change of elementary charge caused by a change in gravitational potential will affect electromagnetic emission/absorption in the atomic clock and so “change” the time. Because of this, the atomic clocks of GPS satellites must be calibrated. Similarly, the change of the elementary charge is responsible for the observed effect in an experiment with masers – in the Gravity Probe A experiment.
Quantum mechanics was created to explain the atom, since a classical planetary model was not satisfactory and was valid only as the Bohr model. Without the Bohr postulates, the atom would have to die as a result of energy loss by electrons (in the form of electromagnetic radiation) and their collapse into the nucleus. This paradox was formally resolved by quantum mechanics, where electrons were not allowed to have trajectories. Quantum mechanics has parameters related only to the initial and final stationary states of the electrons in atom, but not to any trajectories. Instead of the coordinates and velocities of the electron, probability values were used to describe these stationary states.
The proposed theory of the atom returns to the classical description of electron motion as having a trajectory. Electrons can move closer to the nucleus from more remote positions. At the closer distance, a photon can be generated if it complies with the integer value of the energy of the emitted photon. In this case, emission of a photon reduces the velocity of the electron. Ultimately, the electron can occupy the minimum distance at which its velocity becomes equal to zero relative to the nucleus. This distance is ≈ 10−10 m. If there is no such compliance, then the electron will not radiate, and will continue to move to the other side of the nucleus, and away from it until its attraction to the nucleus leads to a complete stop and subsequent reversal back to the nucleus at a speed corresponding to a given distance from the nucleus. In contrast to the planetary model, the proposed theory predicts that electrons do not have strictly defined orbits, but rather changing trajectories. This distinguishes also the proposed theory from quantum mechanics, where there is no concept of electron trajectories in the atom. One can say that the electron oscillates around the nucleus, with a maximum distance from the nucleus of ≈10−5 m. At the distance ≈10−10 m, the electron is at rest relative to the nucleus. The absorption of a photon by an electron will increase electron velocity and distance from the nucleus.
Another problem that was solved by quantum mechanics is the wave-particle duality. When particles pass through a thin metal film, diffraction rings are formed on a screen behind the film. A similar pattern is observed in the case of X-rays. Since X-radiation is believed to be a wave, it was suggested that particles can act in a similar manner, like waves. This phenomenon was termed the wave-particle duality. To explain this in quantum mechanics, it was decided to replace the notion of a trajectory with the concept of a superposition of states, more precisely, the superposition of probability of alternative states, i.e. probability for a particle to be at the same time in alternative states. In this context, the particle in each experiment can be detected with a certain probability, in one of these states. In the suggested theory, there is no wave-particle duality. Wave feature of particles in such phenomena as diffraction and interference are not due to the wave nature of the particles, but because of the generation of waves in the vacuum, which consists of n=0-objects(I) (see “Optics”). The cause of waves of the n=0‑objects(I) is the motion of photons or other particles, since they displace the n=0-objects(I). The displaced n=0-objects(I) move like a wave and the velocity of these waves is close to the speed of light (slightly higher). Waves of n=0‑objects(I) create waves of particles, moving relative to the n=0‑objects(I). This mechanism can explain the interference in the double-slit experiment, where the intensity of particles was set so low that only one particle could pass through the slits at any time. The same interference pattern is observed at both high and low particle fluxes. Quantum mechanics argues that this result is the inherent property of the particles, their nondeterministic, probabilistic behavior, according to the uncertainty principle. In the proposed theory, this interference pattern arises from the interference of waves of n=0-objects(I), displaced by moving particles. In this way, the interpretation of the two-slit experiment is returned to the deterministic view.
The proposed theory also explains the discreteness of atomic spectra. Space, in the proposed theory, is composed a finite number of n=0-objects(I), so space is not infinitely divisible, i.e. matter is discrete. Since the number of n=0-objects(I), defining their density in the certain area of the space, is finite, then the difference of densities for different electron positions are also integers that determines the length of the generated n=1-object, as a multiple of an integer unit (see “Atoms and spectra”).
In the proposed theory, explanation of the phenomenon of quantum tunneling does not require the uncertainty principle. As presented above (see “Superconductivity”), the tunneling of the electron has the same nature as superconductivity. It is due to the lack of interaction of the tunneling electron with the nucleus and electrons between 10−15 m and 10−10 m from the nucleus of atom.
THE CASIMIR EFFECT
The Casimir effect is the attraction of electrically neutral conductors and insulators. The distance, from which the effect becomes detectable, is a few micrometers. With decreasing distance the attractive force increases in inverse proportion to the distance in power of four. In modern physics, the effect is explained by quantum fluctuations of virtual particles of the electromagnetic field. In the proposed theory, the effect can be due to density fluctuations of n=0-objects(I). The fact that the length of a n=0‑object(I), ≈ 10−5 m, is comparable with the distance at which the Casimir effect begins to appear (several micrometers) fits with the proposed interpretation.
The main difference between the proposed theory and the quantum theory is the deterministic character of physical phenomena and the rejection of their probabilistic nature. The uncertainty principle is not a principle of nature; at best it is a statistical description, at worst – it is a delusion. Quantization of physical quantities is a manifestation of the discreteness and finiteness of matter of our universe.
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https://k21st.wordpress.com/2013/12/17/sentient-code-an-inside-look-at-stephen-wolframs-utterly-new-insanely-ambitious-computational-paradigm/
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Wolfram gave me a glimpse under the hood in an hour-long conversation. And I have to say, what I saw was amazing.
Google wants to understand objects and things and their relationships so it can give answers, not just results. But Wolfram wants to make the world computable, so that our computers can answer questions like “where is the International Space Station right now.” That requires a level of machine intelligence that knows what the ISS is, that it’s in space, that it is orbiting the Earth, what its speed is, and where in its orbit it is right now.
See on venturebeat.com
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https://www.studysmarter.us/textbooks/physics/physics-for-scientists-and-engineers-a-strategic-approach-with-modern-physics-4th/the-micromacro-connection/q-53-a-gas-of-atoms-or-molecules-has-of-thermal-energy-its-m/
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A gas of atoms or molecules has of thermal energy. Its molar specific heat at constant pressure is . What is the temperature of the gas?
The molecular temperature is
The temperature of a gas determines the average translational kinetic energy of the molecules.
The molecules in a hot gas move faster than those in a cold gas; the mass is constant, but the kinetic energy, and hence the temperature, is higher due to the molecules' increased velocity.
If the weather changes, by , then the thermoelectric power for a gas changes by the equation in the form
Where is the molecule initial temperature at constant volume, and it has a relationship with the molar specific heat at constant pressure. by
We solve equation for to be in the form
is the number of moles there are. Knowing how many molecules there are , we can get the number of moles by using Avogadro's number as next
Now substitute we get,
A cylinder of nitrogen gas has a volume of and a pressure of atm.
a. What is the thermal energy of this gas at room temperature ?b. What is the mean free path in the gas?c. The valve is opened and the gas is allowed to expand slowly and isothermally until it reaches a pressure of atm . What is the change in the thermal energy of the gas?
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http://www.ask.com/web?q=Instrument+to+Find+Mass&o=2603&l=dir&qsrc=3139&gc=1
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Doppler spectroscopy is an indirect method for finding extrasolar planets and
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Instrument used to find mass. _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _. 2. Metric unit for
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The other name of the mass flow meter is Coriolis flow meter. By the means of
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please help me guys!
well think what is the formula to find the perimeter?
i dont remember
so now do the math with the formula
can you give me the answer then we discuss it?
perimeter of rectangle is : P = 2L + 2W start subbing in : P = 64 L = 20 W = 11 if it comes out correct, then it can be a solution if it comes out incorrect, then it cannot
here are my options
No, the rectangle cannot have x = 20 and y = 11 because x + y ≠ 64 No, the rectangle cannot have x = 20 and y = 11 because x + y ≠ 32 Yes, the rectangle can have x = 20 and y = 11 because x + y is less than 64 Yes, the rectangle can have x = 20 and y = 11 because x + y is less than 32
no option has 62 as an answer
ok...lets sub P = 2L + 2W 64 = 2(20) + 2(11) 64 = 40 + 22 64 = 62....it cannot be true
the= with a line through it means not = to. get it?
so whats the final answer from the options?
I would say A
no problem do you need more help?
It doesn't make much sense....x and y do not have to equal 64.....2x + 2y have to equal 64
so whats the answer? texaschic
yes buttons i could use some more help.
k what do ya need
I think it is B
64 = 2x + 2(11) 64 = 2x + 22 64 - 22 = 2x 42 = 2x 21 = x the width would have to be 21 for this to be true so I guess it is A
you guess?? thats not to reliable
to match the answer choices p = 64 = 2(x + y) 32 = x + y when x = 20 and y = 11 x + y not = 31 so B
correction not = 32 so B
thanks triciaal.....my mind was going blank....it is B, I see that now....because x + y would not have to equal 64 for it to be true
I agree with triciaal
so its b?
@texaschic101 welcome @david821 yes but do you see why?
x + y has to equal 32 for it to be correct....and if you do 20 + 11...that is 31, so it is not true
its because x+y=31 not 32
I need a job as an online tutor so I wouldn't have to leave now.
i need more help on one more quest
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https://forsaljningavaktierlqjm.firebaseapp.com/52658/12899.html
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Physical unit . 146 high-quality, full-color pages; Printed single-sided on 80-lb coated paper ; Science units are not spiral-bound because so many pages need to be cut, removed, or copied; Complete PDF download. Digital copy of full unit for optional printing of consumable pages or copies for multiple children in the same household
Our videos will help you understand concepts, solve your homework, and do great on your exams. Important Questions for CBSE Class 12 Chemistry – Kinetics PREVIOUS YEARS’ QUESTIONS 2015 Short Answer Type Questions [I] [2 Marks] Question 1: Write two differences between order of a reaction and molecuiarity of a reaction. Answer : Question 2: Define rate constant (k). Write the unit of rate constant for the following: (i) First […] Home AP Chemistry Unit #9: Applications of Thermodynamics ENE-5.A Explain whether a process is thermodynamically favored using the relationships between K, Chemistry primarily uses five of the base units: the mole for amount, the kilogram for mass, the meter for length, the second for time, and the kelvin for temperature. The degree Celsius (o C) is also commonly used for temperature. The numerical relationship between kelvins and degrees Celsius is as follows.
A cumulative constant can always be expressed as the product of stepwise constants. There is no agreed notation for stepwise constants, though a symbol such as K L Formula in Hill system is K: Computing molar mass (molar weight) To calculate molar mass of a chemical compound enter its formula and click 'Compute'. In chemical formula you may use: Any chemical element. Capitalize the first letter in chemical symbol and use lower case for the remaining letters: Ca, Fe, Mg, Mn, S, O, H, C, N, Na, K, Cl, Al. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Unit consistency in rate T is the temperature, T TPW = 273.16 K by definition of the kelvin; A r (Ar) is the relative atomic mass of argon and M u = 10 −3 kg⋅mol −1 .
2SO 2 (g) + O 2 (g) ↔ 2SO 3 (g) After the reactants and the product reach equilibrium and the initial temperature is restored, the flask is found to contain 0.30 mole of SO 3. Based on these results, the equilibrium Year outline of the new NGSS 3-course model "Chemistry in the Earth System" embedded with earth science standards. Links to lesson segment bundles being uploaded.
K_\text c K c. K, start subscript, start text, c, end text, end subscript. and. Q. Q Q. Q. can be used to determine if a reaction is at equilibrium, to calculate concentrations at equilibrium, and to estimate whether a reaction favors products or reactants at equilibrium.
Symbol. K. SO4. Charge. 1+ 2–.
Unit 3 - Area of Study 2: How can the yield of a chemical product be optimised? a spreadsheet to manipulate data to illustrate the constancy of Kc at constant
If you are absent, or missed part of the notes, or lost a worksheet or handout, this is the place to come. When 0.40 mole of SO 2 and 0.60 mole of O 2 are placed in an evacuated 1.00–liter flask, the reaction represented below occurs. 2SO 2 (g) + O 2 (g) ↔ 2SO 3 (g) After the reactants and the product reach equilibrium and the initial temperature is restored, the flask is found to contain 0.30 mole of SO 3. Based on these results, the equilibrium Having said all of that, it is still not uncommon for many chemistry applications at this level, to totally ignore the concept of activities altogether, and to still quote units for K. This can be problematic when one tries to justify units for ∆G° in the equation ∆G° = -RT lnK, for example, but it still goes on. The numerical value of K depends on the particular reaction, the temperature, and the units used to describe concentration. For liquid solutions, the concentrations are usually expressed as molarity.
If you are absent, or missed part of the notes, or lost a worksheet or handout, this is the place to come. 2017-02-01
Entropy increases when matter becomes more dispersed. For example, the phase change from solid to liquid or from liquid to gas results in a dispersal of matter as the individual particles become freer to move and generally occupy a larger volume.Similarly, for a gas, the entropy increases when there is an increase in volume (at constant temperature), and the gas molecules are able to move
UNIT V FUELS Rev.Ed. 2013-14 Engineering Chemistry Page 109 3. British Thermal Unit (B.Th.U.) : The amount of heat required to raise the temperature of one pound of water (454g) by one degree fahrenheit.
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Kelvin UNIT I. PHYSICAL CHEMISTRY:- a) Gas law and Kinetic Theory:- Ideal gas equation thermodynamic quantities of cell reactions (DG, DH, DS and K) - Over 27 Jun 2016 11 Rate = k[A][B]0 units of k = mol L−1 s−1 /(mol L−1 )1+0 = s−1 For the reaction aA + bB → cC + dD A.K.GUPTA, PGT CHEMISTRY, KVS going to C plus D, the rate law could be expressed, rate equals rate constant k times the concentration of A to the m and B to the n, where m and n are the order of Macromolecular Science Turns 100 by Christine K. Luscombe and Gregory T. Russell En. Chemistry and Environment Chemistry Applied to World Needs The unit is also cofounder and partener of the Institut Curie chemical Library Jennemann R, Dransart# D, Podsypanina K, Lombard B, Loew D, Lamaze C, 12 Apr 2010 The temperature 0 K is commonly referred to as "absolute zero." On the widely used Celsius temperature scale, water freezes at 0 °C and boils at RIKEN Center for Computational Science Medicinal Chemistry Applied AI Unit. Unit Leader: Watanabe C, Okiyama Y, Tanaka S, Fukuzawa K, Honma T.: 7 Mar 2019 We constructed a unit plan using AACT resources that is designed to teach the Describe how temperature affects the rate of a chemical reaction. between the equilibrium constant (K) and the reaction quotient (Q), as R = gas constant (dependent on the units of pressure, temperature and volume) R = 0.0821 L atm K-1 mol-1, if, (a) Pressure is in atmospheres (atm) The equilibrium constant, capital K, is a thermodynamic quantity.
Having said all of that, it is still not uncommon for many chemistry applications at this level, to totally ignore the concept of activities altogether, and to still quote units for K. This can be problematic when one tries to justify units for ∆G° in the equation ∆G° = …
The Seven SI Units: This figure displays the fundamental SI units and the combinations that lead to more complex units of measurement. It should be apparent that the move into modern times has greatly refined the conditions of measurement for each basic unit …
An Atomic Assault: A "Nuclear Chemistry" Unit (PBL) for High School ChemistrySummary: A father is accused of assault with a radioactive substance. To go forward with a criminal case, investigators need to know what substance was used.
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P=pressure of the gas (atm) K=Henry's Law Constant (atm/M) ***Watch the units some chemist use the equation S=KP (solubility= Henrys constant x pressure).
101.3 kPa = 1 atm. There are 1,000 pascals in 1 kilopascal.
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The Curie temperature was increased from 430 K for x=0 to 443 K for x=0.4. 0.1, 0.2) crystallize in the tetragonal symmetry in the range 10–400 K and converts to cubic symmetry above 450 K. The unit cell Journal of Solid State Chemistry.
Reaction. Another property of a In order to understand how the concentrations of the species in a chemical reaction change with time it is necessary We can write the rate expression as rate = -d[B]/dt and the rate law as rate = k[B]b . Then simply solve for Ea i 2 Jan 2021 Get the definition of the reaction rate constant in chemistry and learn about the factors or reaction rate coefficient and is indicated in an equation by the letter k. The units of the rate constant depend on the or The rate constant, k, for the reaction or enough information to determine it. In some cases, we need to know the initial concentration, [Ao]. Substitute this information 9 Nov 2017 Andselisk correctly identified the law of dilution and the name Ostwald is often connected with it. Kdissociation=α21−α⋅c.
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https://casualnavigation.com/what-is-a-sextant-used-for/
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A sextant is a highly accurate scientific instrument, used for measuring the angle between two objects. Its best-known use is in celestial navigation when you measure the altitude of a celestial body. Celestial navigation is not the only situation where you can use a sextant though.
A sextant can be used for:
- Measuring the altitude of celestial bodies
- Finding a vertical sextant angle of a charted object
- Measuring horizontal sextant angles of multiple charted objects
- Using vertical sextant angles to find a clearing range
- Using horizontal sextant angles to find a danger angle
Sextants are simply a tool used for measuring angles. When used for navigation, you can apply those angles in any number of different ways to find your position and keep yourself safe.
Finding a line of position by measuring the altitude of a celestial body
The best-known use for a sextant is to find the altitude of a celestial body as part of a celestial fix.
You use the sextant to measure the angles between the horizon and any celestial body. Any celestial body will work. You can use the sun; the moon; planets; or stars. As long as the body you choose in is the nautical almanac, you will be able to perform the calculations you require.
A celestial fix is a complicated procedure, best explained with a video demonstration. I made the video below to cover the whole process, so you can watch that if you would like to know in detail how to find a line of position with a sextant.
If you don’t want to watch, then we can summarise the method instead. The principle of a celestial line of position is that you measure the altitude of a celestial body using a sextant, and compare it to the altitude that you expect the body to be, according to your almanac.
The difference between the observed altitude and the calculated altitude gives you a line of position that you can plot on the chart. Taking three observations gives you three lines of position, which can be used for a three-point fix.
The precision of the sextant is needed because each degree of error would give you an error of 60 nautical miles in your position.
Why is it useful to find a line of position from a celestial body?
In navigation, you need to be able to find a line of position from a celestial body because it is the only non-electronic way of fixing your position when out of sight of land.
The sextant is by no means as accurate as a GPS, but it is accurate enough to use as a backup if your GPS should fail.
Using the sextant to measure the altitude of celestial bodies gives you the most accurate measurement that it is possible to get with a handheld instrument. Nothing else is able to give you the same accuracy.
Finding a range by measuring the vertical sextant angle of a charted object
Branching away from celestial navigation, you can use the sextant for terrestrial navigation as well.
When you have a charted object with a known height, you can use the sextant and trigonometry to calculate your distance from the object, giving you a line of position.
A good example is a lighthouse, where a nautical chart will tell you the height of the focal plane of the light.
In the diagram above, you can use your sextant to measure the angle, θ.
The height of the lighthouse can found from the chart. You’ll need to apply the height of the tide to the charted height depending on how your chart references heights. For example, if heights are referenced to HAT, you will need to use the following formula:
Height = Charted Height + HAT – Current Height of Tide
Once you have found the current height of the lighthouse above the water level, and have measured the angle, θ, with your sextant, you can use trigonometry to calculate the distance to the lighthouse.
Range = Height of Lighthouse / Tan θ
With the range, you can then plot a line of position using normal chartwork techniques. You have a range, and a charted object, so you know you are somewhere along an arc of constant range from the charted object.
Using the sextant gives you precision when measuring a vertical angle that just wouldn’t be possible with other instruments. This is especially important when the height is small compared to the range.
You can measure the angle of a lighthouse that it 10s of meters tall, even when you are a few miles away. The sensitivity and precision of the sextant are essential when measuring such small angles.
Why are vertical sextant angles useful?
Using a sextant to measure vertical sextant angles allows you to get two lines of position off a single charted object.
You can calculate the range, and you can take a compass bearing.
With two lines of position, you can get a reasonable idea of your location. It isn’t yet enough to confirm your position because for that you would need a third line of position.
The only other way to get a range to use as a line of position is with radar. Radars are electronic equipment, that cost a lot of money to install. They are also subject to the same failures as all electronic equipment.
Once you have the skills to use a sextant to get a vertical sextant angle, you give yourself even more tools in your arsenal for coastal navigation.
Using horizontal sextant angles to find a line of position from two charted objects
Turning your sextant on its side, you can use it to find horizontal sextant angles. These are exactly what they sound like. They are the horizontal angle between two charted features.
You can use a horizontal sextant angle to plot a line of position.
Horizontal sextant angles use circle theorems to plot lines of position. Specifically, the “angle at the centre theory”.
In the image above, circle theory tells us that the angle, “a”, will be twice the size of angle, “b”. You have used your sextant to measure angle “b”, so you can use mathematics to calculate the size of angle “a”.
Once you have found angle “a” you can use triangle theory to calculate the size of both angles “c”.
You can then use angle “c” to plot onto your chart and find the centre of the circle. Using the centre, and one of the charted features, as the radius, you can plot the entire circle. The circle is your line of position.
The horizontal sextant angle between two charted objects gives you a single line of position. You can use a third object to get three lines of position and a full three-point fix.
You take the angles between:
- Object 1 & object 2
- Object 2 & object 3
- Object 3 & object 1
An alternative to using three objects is to use the two objects as we did in the example. You can then use the bearings of both objects as well to give yourself a three-point fix.
Why are horizontal sextant angles useful?
Horizontal sextant angles are particularly useful because they give you the ability to fix your position independently of any other equipment.
Using three charted objects, you can fix your position using your sextant on its own. This is especially useful because it will give you an accurate position fix even when your boat’s compass is not working.
The sextant does not rely on any external inputs. It is purely a scientific instrument used to measure angles. Using the accuracy of a sextant allows you to plot extremely accurate lines of position using horizontal sextant angles.
Finding a clearing range using a vertical sextant angle of a charted object
While you can use a sextant to plot a line of position using vertical sextant angles, you can extend that use to find a clearing angle.
The principle of clearing angles is that as you get closer to a charted object, the angle that you measure will get bigger.
You can calculate the maximum angle that you want to keep yourself a safe distance away from a hazard.
We already found a line of position using the angle, θ. As you are navigating closer to the coast, a clearing angle tells you the maximum that you can let θ get to while keeping yourself safe. We call that θ(max).
If I am on my sailing yacht, I can periodically check the angle between the top of the lighthouse and the surface of the water. As long as it is less than my pre-determined θ(max), I know that I am in safe water.
Why is it useful to work with vertical clearing angles?
Using a sextant to find a vertical clearing angle is especially useful for coastal navigation. If you know that you need to keep 0.25 nautical miles from a lighthouse to keep yourself safe, you can just calculate the angle that you are looking for.
It is then incredibly fast to measure the angle with your sextant and check it is less than your clearing angle.
The major advantage is that you do not need to constantly go back and complete trigonometry to find your distance from the lighthouse.
Again, the sextant is independent of all electronic navigational equipment making it an ideal backup for keeping yourself safe.
Assuming you have planned clearing angles during your passage planning stage, you can very quickly cross-check the safety margin that your GPS is giving you.
Using a horizontal sextant angle to find a danger angle with charted objects
In the same way that we worked backwards to find a vertical clearing angle, you can do the same thing with horizontal sextant angles.
The principles are the same as they were for calculating lines of position, but we work backwards to find a danger angle instead.
In the image above, I have plotted a 0.5 nautical mile ring around a danger. I then plotted a circle which runs through the two charted objects and the very edge of the danger area. The angle, “a” is found by measuring between the lines joining the edge of the danger area and the charted objects.
You then set your sextant the same as angle “a”.
As you approach the danger, you can observe the two charted objects, measuring the angle between them. The further away you are, the smaller the angle will be.
As you get close, the angle between the charted objects will get bigger. You know you are safe as long as the angle you measure stays smaller than angle “a”.
Why is it useful to use horizontal danger angles?
Horizontal danger angles are useful for coastal navigation in the same way vertical sextant angles are. They can keep you a safe distance away from dangerous water.
Again, they are completely independent of all electronics. If you lose your GPS and your radar, horizontal danger angles keep you safe using only your sextant.
With horizontal danger angles, the sextant isn’t the only tool that can accomplish it. You can simply set some dividers or anything else that can hold an angle to be the correct amount. Using a sextant will be one of the most accurate ways of doing it though.
The thing with danger angles is that they do not need to be measured accurately. You only need to know when you have crossed the danger angle. The advantage of using a sextant, however, is that whenever you take a measurement less than the danger angle, you can use the accurate measurement to complete a horizontal sextant angle plot and get an accurate line of position.
What else can you use a sextant for?
Sextants are useful any time you need to measure angles.
We have already discussed a few situations that make the most of the fine accuracy that a sextant can achieve. When accuracy isn’t too important, while you can use a sextant, other methods will be plenty accurate enough and allow you to get the job done quicker.
For example, doubling the angle on the bow. This is a method for finding your range from a fixed object using triangle theorems. You can use a sextant to measure the angle from the bow to the charted object, but the precision given by a sextant would be considered overkill.
When doubling the angle on the bow, you only need enough accuracy to know when the angle is doubled, to the nearest degree. The ship’s compass is usually accurate enough for this purpose.
Likewise, you could use a sextant to measure the relative bearing of different vessels to determine if a risk of collision exists. Again, using a sextant is overkill in this sort of situation. While it will give you a very precise answer, if you are relying on the sort of level of precision that a sextant will give you, it is safe to assume the risk of collision does exist.
Overall, the sextant is a precision instrument, used for measuring angles. When you need a high level of precision, it can be the ideal tool to use. When precision is not too important, other methods may be more efficient than the sextant.
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http://www.discuss.wmie.uz.zgora.pl/php/discuss3.php?ip=&url=plik&nIdA=13067&sTyp=HTML&nIdSesji=-1
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Mathematicae General Algebra and Applications 22(2) (2002)
Ivan Chajda and Kamil Dusek
Department of Algebra and Geometry
Palacký University of Olomouc
Tomkova 40, CZ-77900 Olomouc, Czech Republic
A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of
propositional logic having non-involutory negation (e.g. intuitionistic logic). We show that every
pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a
more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence
between this algebra and a quasi-implication algebra is shown.
Keywords: implication, non-involutory negation, quasi-implication algebra, implitcation algebra,
pseudocomplemented semilattice, q-semilattice.
2000 Mathematics Subject Classification: 03G25, 06A12, 06D15.
J.C. Abbott, Semi-boolean algebras , Mat. Vesnik 4 (1967), 177-198.
R. Balbes, On free pseudo-complemented and relatively pseudo-complemented semi-lattices , Fund.
Math. 78 (1973), 119-131.
I. Chajda, Semi-implication algebra , Tatra Mt. Math. Publ. 5 (1995), 13-24.
I. Chajda, An extension of relative pseudocomplementation to non-distributive lattices , Acta Sci.
Math. (Szeged), to appear.
A. Diego, Sur les algèbres de Hilbert , Gauthier-Villars, Paris 1966 (viii+55pp.).
O. Frink, Pseudo-complements in semi-lattices , Duke Math. J. 29 (1962), 505-514.
Received 10 October 2002
Revised 23 January 2003
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CC-MAIN-2021-10
| 1,490 | 23 |
http://www.shonscience.com/announcements--homework/category/pangaea
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math
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- Pick and research any 2 of the below pieces of evidence that support the theory that the continents were once connected as the super-continent "Pangaea". You may use the provided links, textbooks, and video below.
- Complete a graphic organizer for each piece of evidence.
Evidence of Pangaea
3. Glacial Deposits
Additional research sites:
Use the evidence provided to recreate Pangaea.
If you have trouble, refer to the following sites for guidance:
Complete the activity, "Plate Boundaries".
1. How many tectonic plates are there?
2. How are continental and oceanic crust different?
3. What is a "boundary"?
4. What is a convergent boundary?
5. What is one example of a convergent boundary?
6. What is a divergent boundary?
7. What is one example of a divergent boundary?
8. What is a transform boundary?
9. What is one example of a transform boundary?
Read, "Slip, Slide, and Collide".
1. How does the density of an oceanic plate compare to the density of a continental plate?
2. Roll your mouse over the graphic to define the following terms: subduction zone, lithosphere, asthenosphere, magma, trench, volcano, volcanic arc
3. What causes Earthquakes and tsunamis?
4. What is created when two continental plates collide?
5. What is a rift? **watch the animation on the formation of a rift**
Bonus 1: Try the "Plate & Boundaries Challenge".
Bonus 2: Try the "Plate Interactions Challenge".
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CC-MAIN-2022-05
| 1,395 | 25 |
http://mathhelpforum.com/calculus/3546-integration-problems-urgent.html
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math
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1/cot(x) is simply tan(x), so this integral is really
Use this identity and it should be easy.
Attached document contain question rearding indefinite integrals.
Can someone help to provide solution for all three questions ASAP.
Apologise for improper way of defining the question as i don't have the software in which we can draw maths problem nicely.
Thanks in advance.
_____________Originally Posted by Jameson
for this problem, i think just rewrite the function in term tanx = sinx/cosx
then, you will flip cosx into the denominator. It will come out like this, intergal of (sinx/cos^2x)dx
next step, using the sub methods
let u = cosx, du = - sinxdx
-du = sinxdx
then just jam that into the integral.
u will get something like du/u^2
bring u^2 on top : u-2
take the integral. u^-1/-1 or
1/-cosx + c will become your answer
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542520.47/warc/CC-MAIN-20161202170902-00433-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 826 | 17 |
http://ir.lib.sdu.edu.cn/widgets/sdjgk/?h=gain&job=detail&a_id=JQd7vWUBFjIhTVEbs7se
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math
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标题：Maximum Principle for Nonzero-Sum Stochastic Differential Game With Delays
作者：Chen, Li;Yu, Zhiyong
作者机构：[Chen, L] Department of Mathematics, China University of Mining and Technology, Beijing, 100083, China;[ Yu, Z] School of Mathematics, Shandong Univer 更多
通讯作者地址：[Chen, L]China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China.
来源：IEEE Transactions on Automatic Control
关键词：Anticipated backward stochastic differential equation (ABSDE);maximum principle;nonzero-sum stochastic differential game;open-loop equilibrium point;stochastic differential delay equation (SDDE)
摘要：In this technical note, we discuss a nonzero-sum stochastic differential game with delays. Not only the state variable, but also control variables of players involve delays. This kind of games are motivated by some interesting problems arising from economics and finance. Using anticipated backward stochastic differential equations, we establish a necessary condition and a sufficient condition of maximum principle for the delayed game problem. To explain theoretical results, we apply them to an economic problem.
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CC-MAIN-2021-17
| 1,167 | 7 |
https://research.tue.nl/en/publications/upper-and-lower-bounding-techniques-for-frequency-assignment-prob
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math
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We consider two variants of the radio link frequency assignment problem??. These problems arise in practice when a network of radio links has to be established??. Each radio link has to be assigned a particular frequency??. The interference level between the frequencies assigned to the di??erent links has to be acceptable??, since otherwise communication will be distorted.?? The frequency assignments have to comply with certain regulations and physical characteristics of the transmitters.?? Moreover??, the number of frequencies is to be minimized, because each frequency used in the network has to be reserved at a certain cost??.
We develop several approximation algorithms for the problems??, which are based on local search,?? and we compare their performance on some practical instances.?? Lower bounding techniques based on nonlinear programming and the chromatic number of a graph are used to estimate the quality of the approximate solutions for these instances??.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572163.61/warc/CC-MAIN-20220815085006-20220815115006-00588.warc.gz
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CC-MAIN-2022-33
| 977 | 2 |
https://panel.waset.org/author/karim-hamidi-machekposhti
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math
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Floods have huge environmental and economic impact. Therefore, flood prediction is given a lot of attention due to its importance. This study analysed the annual maximum streamflow (discharge) (AMS or AMD) of Karkheh River in Karkheh River Basin for flood predicting using ARIMA model. For this purpose, we use the Box-Jenkins approach, which contains four-stage method model identification, parameter estimation, diagnostic checking and forecasting (predicting). The main tool used in ARIMA modelling was the SAS and SPSS software. Model identification was done by visual inspection on the ACF and PACF. SAS software computed the model parameters using the ML, CLS and ULS methods. The diagnostic checking tests, AIC criterion, RACF graph and RPACF graphs, were used for selected model verification. In this study, the best ARIMA models for Annual Maximum Discharge (AMD) time series was (4,1,1) with their AIC value of 88.87. The RACF and RPACF showed residuals’ independence. To forecast AMD for 10 future years, this model showed the ability of the model to predict floods of the river under study in the Karkheh River Basin. Model accuracy was checked by comparing the predicted and observation series by using coefficient of determination (R2).
Rainfall and runoff phenomenon is a chaotic and complex outcome of nature which requires sophisticated modelling and simulation methods for explanation and use. Time Series modelling allows runoff data analysis and can be used as forecasting tool. In the paper attempt is made to model river runoff data and predict the future behavioural pattern of river based on annual past observations of annual river runoff. The river runoff analysis and predict are done using ARIMA model. For evaluating the efficiency of prediction to hydrological events such as rainfall, runoff and etc., we use the statistical formulae applicable. The good agreement between predicted and observation river runoff coefficient of determination (R2) display that the ARIMA (4,1,1) is the suitable model for predicting Karkheh River runoff at Iran.
The probability distributions are the best method for forecasting of extreme hydrologic phenomena such as rainfall and flood flows. In this research, in order to determine suitable probability distribution for estimating of annual extreme rainfall and flood flows (discharge) series with different return periods, precipitation with 40 and discharge with 58 years time period had been collected from Karkheh River at Iran. After homogeneity and adequacy tests, data have been analyzed by Stormwater Management and Design Aid (SMADA) software and residual sum of squares (R.S.S). The best probability distribution was Log Pearson Type III with R.S.S value (145.91) and value (13.67) for peak discharge and Log Pearson Type III with R.S.S values (141.08) and (8.95) for maximum discharge in Jelogir Majin and Pole Zal stations, respectively. The best distribution for maximum precipitation in Jelogir Majin and Pole Zal stations was Log Pearson Type III distribution with R.S.S values (1.74&1.90) and then Pearson Type III distribution with R.S.S values (1.53&1.69). Overall, the Log Pearson Type III distributions are acceptable distribution types for representing statistics of extreme hydrologic phenomena in Karkheh River at Iran with the Pearson Type III distribution as a potential alternative.
This study was designed to find the best-fit probability distribution of annual rainfall based on 50 years sample (1966-2015) in the Karkheh river basin at Iran using six probability distributions: Normal, 2-Parameter Log Normal, 3-Parameter Log Normal, Pearson Type 3, Log Pearson Type 3 and Gumbel distribution. The best fit probability distribution was selected using Stormwater Management and Design Aid (SMADA) software and based on the Residual Sum of Squares (R.S.S) between observed and estimated values Based on the R.S.S values of fit tests, the Log Pearson Type 3 and then Pearson Type 3 distributions were found to be the best-fit probability distribution at the Jelogir Majin and Pole Zal rainfall gauging station. The annual values of expected rainfall were calculated using the best fit probability distributions and can be used by hydrologists and design engineers in future research at studied region and other region in the world.
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CC-MAIN-2021-10
| 4,324 | 4 |
https://ocsef.org/voting-fraud-detector/
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math
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By: Ben A.
School: McPherson Magnet
Science Teacher: Elizabeth Conrad
Ben’s project is titled “Fraud Detector,” and based on the research question, “Can Benford’s Law detect voting fraud?” Benford’s Law is a theory that the first digit in every number of certain data sets will follow a pattern. The pattern is that about 30% of all the first digits of every number in the data set will be a 1. About 18% will be a 2, 12% a 3 and so on, with the smallest percentage of numbers in the data set being a 9. This will be explained in more detail later on, but the question is if Benford’s Law applies to vote counts in elections and if it can detect voting fraud.
To conduct this project, Ben used a computer, 10 federal election results, a random number generator, and Benford’s Law percentages. To perform this experiment, Ben extracted the first digit of numbers in a data set of just random numbers 1 – 99,999. He then organized them into groups with the same first digit. Once Ben finished counting how many 1s, 2s, 3s, etc. there were, he took that data and created a graph, comparing it against a Benford’s Law graph. Ben performed this action nine more times to get a total of ten random number data sets. Upon completion, he repeated the process using numbers from 10 different U.S. Presidential and House of Representatives elections.
Ben hypothesized that the random numbers would not follow Benford’s Law, but the election results would and because of this, you could detect voting fraud using Benford’s Law. When he finished testing, Ben noticed that all of the random data sets did not follow Benford’s Law, but all of the election data sets did, thus proving that Ben’s hypothesis was correct and you can use Benford’s Law to detect voting fraud.
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CC-MAIN-2023-50
| 1,789 | 6 |
https://rwer.wordpress.com/2016/04/07/utility-theory-an-empty-tautology/
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math
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Utility theory — an empty tautology
from Lars Syll
In 1938 Paul Samuelson offered a replacement for the then accepted theory of utility. The cardinal utility theory had been discarded a couple of years earlier, but according to Samuelson, the ordinalist revision of utility theory was not drastic enough. One ought to analyze the consumer’s behaviour without having recourse to the concept of utility at all, since this did not correspond to directly observable phenomena.
The new theory’s main feature was a consistency postulate which said ‘if an individual selects batch one over batch two, he does not at the same time select two over one.’ From this ‘perfectly clear’ postulate and the assumptions of given demand functions and that all income is spent, Samuelson could derive all the main results of ordinal utility theory (single-valuedness and homogeneity of degree zero of demand functions, and negative semi-definiteness of the substitution matrix).
In 1950 Hendrik Houthakker made an amendment to the theory assuring integrability, and by that the theory had according to Samuelson been ‘brought to a close.’ According to Houthakker, the aim of the revealed preference approach was ‘to formulate equivalent systems of axioms on preferences and on demand functions.’
But if this is all, what has revealed preference theory then achieved? In 1997 Reinhard Sippel performed experiments that he argued showed ‘a considerable number of violations of the revealed preference axioms’ and that from a descriptive point of view – as a theory of consumer behaviour – the revealed preference theory was of a very limited value.
Today it seems as though the proponents of revealed preference theory have given up the original 1938-attempt at building a theory on nothing else but observable facts, and settled instead on the 1950-version of establishing ‘logical equivalences.’
When talking of determining people’s preferences through observation, Hal Varian, for example, has ‘to assume that the preferences will remain unchanged’ and adopts ‘the convention that … the underlying preferences … are known to be strictly convex.’ He further postulates that the ‘consumer is an optimizing consumer.’ If we are ‘willing to add more assumptions about consumer preferences, we get more precise estimates about the shape of indifference curves.’ Given these assumptions, and that the observed choices satisfy the consistency postulate as amended by Houthakker, one can always construct preferences that ‘could have generated the observed choices.’ This does not, however, prove that the constructed preferences really generated the observed choices, ‘we can only show that observed behavior is not inconsistent with the statement. We can’t prove that the economic model is correct.’
Revealed preference theory tried to build a new theory and to put it in operational terms, but ended up with just giving a theory logically equivalent to the old one. As such it also shares its shortcomings of being empirically nonfalsifiable and of being based on unrestricted universal statements.
As Janos Kornai once remarked — ‘the theory is empty, tautological. The theory reduces to the statement that in period t the decision-maker chooses what he prefers … The task is to explain why he chose precisely this alternative rather than another one.’
Mainstream (neoclassical) economics doesn’t want to get involved in psychological discourse, so it basically assumes that the aims and ends of people are exogenously ‘given’ and that a fortiori preferences also are ‘given’ and that people behave as if they were maximizing a utility function based on these ‘given’ preferences. However — what people usually do, is to base their choices on aims and ends, while their preferences are not given, but rather something that comes out of people’s deliberations on these aims and ends in specific spatio-temporal contexts. We all make choices, but they certainly aren’t based on ‘preference rankings’ or their equivalent utility representations!
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123632.58/warc/CC-MAIN-20170423031203-00385-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 4,118 | 11 |
https://trackbarn.com/products/essx-pole-tip
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math
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1. Tape 0 end of the scale to pole.
2. Measure pole circumference above existing tip by wrapping ruler around the pole.
3. Read measurement where ruler crossed 0 point of scale
4. Shaded measurement values below may require additional wraps of athletic tape to insure a snug fit.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100568.68/warc/CC-MAIN-20231205204654-20231205234654-00391.warc.gz
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CC-MAIN-2023-50
| 279 | 4 |
https://search.ieice.org/bin/summary.php?id=e94-a_4_1144&category=A&lang=&year=2011&abst=/
|
math
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For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
A Study on Weighting Scheme for Rational Remez Algorithm
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2011/04/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
IIR digital filter, the rational Remez algorithm, ripple ratio,
Full Text: PDF>>
In this paper, we present a numerical method for the equiripple approximation of IIR digital filters. The conventional rational Remez algorithm quickly finds the squared magnitude response of the optimal IIR digital filters, and then by factorizing it the equiripple filter is obtained. Unlike the original Remez algorithm for FIR filters, it is difficult for the rational Remez algorithm to explicitly control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by manually changing the weights in order to achieve the ratio of the weights exactly. To address this problem, we modify the conventional algorithm and make it possible to directly control the ripple ratio. The method iteratively solves eigenvalue problems with controlling the ripple ratio. Using this method, the equiripple solutions with desired weights are obtained automatically.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337415.12/warc/CC-MAIN-20221003101805-20221003131805-00498.warc.gz
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| 1,501 | 12 |
http://k4tsis.tk/wukef/probability-tree-homework-help-1756.php
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math
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I created this for a lesson observation - the PP and worksheet are adaptations of other resources I found.The Prince, help tree probability homework wandering the lands in search of another Hancock concludes, As at Giza, therefore, a huge sum.The purpose of this task is to help students discover the Fundamental Counting Principle through the.
Math(Probability) need help - page 3 - jiskha.com
Enter your e-mail and subscribe to our newsletter for special discount offers on homework.The best we can say is how likely they are to happen, using the.The authors of prior mentees including their preliminary studies in the section Trying out to-do lists probability tree homework help (with all those whove supported.
Maths help sheets - School A to Z
Lesson Topic: Tree Diagrams Grade: 7 Subject: Math 7 Student Teacher: Jordan Hunt Virginia Standards of Learning Objective Standard 7.10 Strand: Probability and.Make a probability tree of all of the possible combinations of draws that Marcus and his brother could make.
PROBABILITY HELP? - Tutorhelpdesk.com Free Homework Help
Primary maths help sheets. 2D space and 3D objects. 2D shapes (PDF).We at My Homework help have decided to help out a student learning about this subject with our Tree Diagrams homework and assignment help team.These printable math worksheets will help students learn about probability of random events.As an Example.support that an arena has two hockey and two basketballs games scheduled for a Weekend.But to make time for repair, only two games can be played these games are to selected at random,the problem out come are representative on the random tree Diagram.How to use a tree diagram to calculate combined probabilities of two independent events.
self study - Probability Homework Help - Cross Validated
Resources Jobs News Community Courses Log out Help. Home feed. Probability Worksheet. 4.5 (8) Prepared by Created by.
3 Probability Questions, Statistic Assignment Homework Help
Activity for assignment practices Kindergarten through 6th grade students find probability diagrams.Most of the worksheets on this page align with the Common Core Standards.
GCSE Maths Probability, Tree Diagrams help please?
Help with probability homework. up vote 2 down vote favorite. 2. Help with homework proof Probability-2.Homework Assignments questions on Statistics for Probability - Tree Diagrams are listed below.
probability - Why do we multiply in tree diagrams
Probability Homework Help - My Geeky Tutor
For the first question, if you know how to draw the probability tree than you should be able to get the other answers.
High school statistics | Math | Khan Academy
Tree Diagram Stats Homework, assignment and Project Help, Tree Diagram Tree Diagrams often aid in understanding and solving probability problems.
These dynamically created Probability Worksheets are great for learning and practicing the concept of probability.Please can someone help me with this question, I am really stuck.Charts and diagrams to organize your implications on a one-word help homework probability negative response in the country, check over diagrams.Calculating probabilities can be hard, sometimes we add them, sometimes we multiply them, and often it is hard to figure out what to do.
Determining Probabilities Using Tree Diagrams and Tables
This high school probability and statistics class is aligned with the Common Core State Standards.
Java Normal Probability Calculator - Math.com
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Download "Probability Based on Tree Diagram" by Homework
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Probability Worksheets - Super Teacher Worksheets
We offer probability assignment help and homework help.Tree diagrams can organize problems having more than two stages.
Finite Math Examples | Probability | Finding the
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s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948609934.85/warc/CC-MAIN-20171218063927-20171218085927-00393.warc.gz
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CC-MAIN-2017-51
| 4,064 | 31 |
https://stromcv.com/precalculus-questions-solver-with-steps-16
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math
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Solve the integral. v=\int\cos\left (x\right)dx v = ∫ cos(x)dx. Apply the integral of the cosine function: \int\cos (x)dx=\sin (x) ∫ cos(x)dx = sin(x) \sin\left (x\right) sin(x) Now replace the
Genuinely helps students to learn difficult subjects with thorough breakdowns of solution, including alternative methods of solving. Again thanksâ¤ï¸â¤ï¸â¤ï¸.
Thank you for making such a helpful app. I totally recommend 👌 it's really good and it helped with my school work keep up the good work. I just love, this app help me to prevent facing problem on mathematics.
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Solve pre-calculus problems step-by-step Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic
Expert instructors will give you an answer in real-time
Mathematics is a way of dealing with tasks that require e#xact and precise solutions.
Improve your academic performance
You can get an expert answer to your question in real-time on JustAsk.
Mathematics is the study of numbers, shapes, and patterns. It is used in everyday life, from counting and measuring to more complex problems.
Obtain Help with Homework
You can improve your academic performance by studying regularly and attending class.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00642.warc.gz
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CC-MAIN-2023-06
| 1,527 | 12 |
https://payhip.com/b/6lsy
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math
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YOU GET WORD DOCUMENT SOLUTION
The Solo Hotel opened for business on May 1, 2014. Here is its trial balance before adjustment on May 31.
1. Insurance expires at the rate of $360 per month.
2. A count of supplies shows $1,157 of unused supplies on May 31.
3. (a) Annual depreciation is $3,840 on the building.
(b) Annual depreciation is $3,720 on equipment.
4. The mortgage interest rate is 6%. (The mortgage was taken out on May 1.)
5. Unearned rent of $2,522 has been earned.
6. Salaries of $805 are accrued and unpaid at May 31.
Journalize the adjusting entries on May 31. (Credit account titles are automatically indented when the amount is entered. Do not indent manually.)
Prepare a ledger using T-accounts. Enter the trial balance amounts and post the adjusting entries. (Post entries in the order of journal entries presented in the previous question.)
Prepare an adjusted trial balance on May 31.
Prepare an income statement for the month of May.
Prepare a retained earnings statement for the month of May.
Prepare a classified balance sheet at May 31. (List current assets in order of liquidity. List Property, Plant and Equipment in order of Land, Buildings and Equipment .)
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738552.17/warc/CC-MAIN-20200809102845-20200809132845-00422.warc.gz
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CC-MAIN-2020-34
| 1,184 | 15 |
http://ideas.repec.org/p/ecm/wc2000/0830.html
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math
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Breaking the Curse of Dimensionality
AbstractThis paper proposes a new nonparametric estimator for general regression functions with multiple regressors. The method used here is motivated by a remarkable result derived by Kolmogorov (1957) and later tightened by Lorentz (1966). In short, any continuous function f(x_1,...,x_d) has the representation G[a_1 P_1(x_1) + ... + a_d P_1(x_d)] + ... + G[a_1 P_m(x_1) + ... + a_d P_m(x_d)], m = 2d+1, where G(.) is a continuous function, P_k(.), k=1,...,2d+1, is Lipschitz of order one and strictly increasing, and a_j, j=1,...,d, is some constant. Generalizing this result, we propose the following estimator, g_1[a_1,1 p_1(x_1) + ... + a_d,1 p_1(x_d)] + ... + g_m[a_1,d P_m(x_1) + ... + a_d,d p_m(x_d)], where both g_k(.) and p_k(.) are twice continuously differentiable. These functions are estimated using regression cubic B-splines, which have excellent numerical properties. This problem has been previously intractable because there existed no method for imposing monotonicity on the p_k(.)'s, a priori, such that the estimator is dense in the set of all monotonic cubic B-splines. We derive a method that only requires 2(r+1)+1 restrictions, where r is the number of interior knots. Rates of convergence in L_2 are the same as the optimal rate for the one-dimensional case. A simulation experiment shows that the estimator works well when optimization is performed by using the back-fitting algorithm. The monotonic restriction has many other applications besides the one presented here, such as estimating a demand function. With only r+2 more constraints, it is also possible to impose concavity.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0830.
Date of creation: 01 Aug 2000
Date of revision:
Contact details of provider:
Phone: 1 212 998 3820
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
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- David E. A. Giles & Robert Draeseke, 2001. "Econometric Modelling based on Pattern recognition via the Fuzzy c-Means Clustering Algorithm," Econometrics Working Papers 0101, Department of Economics, University of Victoria.
- Mark Coppejans, Mico Mrkaic & Holger Sieg, 2000. "Experimentation And Learning In Rational Addiction Models With Multiple Addictive Goods," Computing in Economics and Finance 2000 81, Society for Computational Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If references are entirely missing, you can add them using this form.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657133132.72/warc/CC-MAIN-20140914011213-00294-ip-10-196-40-205.us-west-1.compute.internal.warc.gz
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CC-MAIN-2014-41
| 3,056 | 17 |
https://www.rcsb.org/structure/4WZJ
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math
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Structure of the spliceosomal U4 snRNP core domain and its implication for snRNP biogenesis.Leung, A.K., Nagai, K., Li, J.
(2011) Nature 473: 536-539
- PubMed: 21516107
- DOI: 10.1038/nature09956
- Primary Citation of Related Structures:
- PubMed Abstract:
- Crystal structures of two Sm protein complexes and their implications for the assembly of the spliceosomal snRNPs.
Kambach, C., Walke, S., Young, R., Avis, J.M., de la Fortelle, E., Raker, V.A., Luhrmann, R., Li, J., Nagai, K.
(1999) Cell 96: 375
- RNA binding in an Sm core domain: X-ray structure and functional analysis of an archaeal Sm protein complex.
Toro, I., Thore, S., Mayer, C., Basquin, J., Seraphin, B., Suck, D.
(2001) EMBO J 20: 2293
- Crystal structure of human U1 snRNP, a small nuclear ribonucleoprotein particle, reveals the mechanism of 5' splice site recognition.
Kondo, Y., Oubridge, C., van Roon, A.M., Nagai, K.
(2015) Elife 4: --
- Re-refinement of the spliceosomal U4 snRNP core-domain structure
Li, J., Leung, A.K., Kondo, Y., Oubridge, C., Nagai, K.
(2016) Acta Crystallogr D Biol Crystallogr 72: 131
The spliceosome is a dynamic macromolecular machine that assembles on pre-messenger RNA substrates and catalyses the excision of non-coding intervening sequences (introns). Four of the five major components of the spliceosome, U1, U2, U4 and U5 small nuclear ribonucleoproteins (snRNPs), contain seven Sm proteins (SmB/B', SmD1, SmD2, SmD3, SmE, SmF and SmG) in common ...
The spliceosome is a dynamic macromolecular machine that assembles on pre-messenger RNA substrates and catalyses the excision of non-coding intervening sequences (introns). Four of the five major components of the spliceosome, U1, U2, U4 and U5 small nuclear ribonucleoproteins (snRNPs), contain seven Sm proteins (SmB/B', SmD1, SmD2, SmD3, SmE, SmF and SmG) in common. Following export of the U1, U2, U4 and U5 snRNAs to the cytoplasm, the seven Sm proteins, chaperoned by the survival of motor neurons (SMN) complex, assemble around a single-stranded, U-rich sequence called the Sm site in each small nuclear RNA (snRNA), to form the core domain of the respective snRNP particle. Core domain formation is a prerequisite for re-import into the nucleus, where these snRNPs mature via addition of their particle-specific proteins. Here we present a crystal structure of the U4 snRNP core domain at 3.6 Å resolution, detailing how the Sm site heptad (AUUUUUG) binds inside the central hole of the heptameric ring of Sm proteins, interacting one-to-one with SmE-SmG-SmD3-SmB-SmD1-SmD2-SmF. An irregular backbone conformation of the Sm site sequence combined with the asymmetric structure of the heteromeric protein ring allows each base to interact in a distinct manner with four key residues at equivalent positions in the L3 and L5 loops of the Sm fold. A comparison of this structure with the U1 snRNP at 5.5 Å resolution reveals snRNA-dependent structural changes outside the Sm fold, which may facilitate the binding of particle-specific proteins that are crucial to biogenesis of spliceosomal snRNPs.
MRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 0QH, UK.
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http://popstoptv.com/tag/arrest/
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math
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Rick Springfield was arrested this morning for failure to appear in court! TMZ learned that deputies arrived at singer’s house in Los Angeles early this morning to execute a warrant,
The infamous rapper 2 Chainz was arrested last night on charge of possession of weed. 2 Chainz claims that he didn##Q##t even had weed on him just a grinder. He
Salwa Amin, a cast member from MTV’s newest reality show, is facing a drug charge in West Virginia. I guess the “Buckwild” star’s motto, “whatever happens, happens,” didn’t take into account
Lindsay Lohan’s dad is speaking out about her arrest following a fight in a New York City club on Thursday. Michael Lohan is pleading with his daughter to check into
Jay McGuiness of “The Wanted” wears his own DIY T-Shirt that says “Free Lindsay” just one night after Lindsay Lohan##Q##s most recent arrest. The night before the boy band hotties
Lindsay Lohan was arrested early this morning for punching a woman in the face, and TMZ has just learned that the troubled actress may have thrown a “racial slur” at her victim.
Lindsay Lohan may be having the worst week ever! Not only was Lindsay Lohan##Q##s big “comeback” film (ahem) made-for-tv movie- Liz & Dick a universal flop, but she was charged today
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702019913/warc/CC-MAIN-20130516110019-00057-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
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https://core.ac.uk/display/22694113
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math
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We prove two results about generically stable types p in arbitrary theories. The first, on existence of strong germs, generalizes results from on stably dominated types. The second is an equivalence of forking and dividing, assuming generic stability of p (m) for all m. We use the latter result to answer in full generality a question posed by Hasson and Onshuus: If p(x) ∈ S(B) is stable and does not fork over A then p ↾ A is stable. (They had solved some special cases.) 1 Stable and generically stable types Our notation is standard. We work with an arbitrary complete theory T in language L. C denotes a ‘monster model’. M denotes a small elementary submodel, and A, B,... denote small subsets. L(C) denotes the collection of formulas with parameters from C, likewise L(A) etc. We sometimes say A-invariant for Aut(C/A)-invariant. By a global type we mean a complete type over C. We assume familiarity with notions from model theory such as heir, coheir, definable type, forking. The book is a good reference, but see also . Stable types Definition 1.1 Let π(x) be a partial type over a set A of parameters. π is stable if all complete extensions p(x) ∈ S(B) of π over any set B ⊇ A are definable. The definition of stable partial type goes back to Lascar and Poizat. Many other equivalent formulations of this notion are known, which we now mention. These should be considered well known, but Section 10 of contains proofs and/or references for the next three Remarks/Facts. Remark 1.2 The following are equivalent for any partial type π(x) over A: 1. π(x) is stable. 2. For every B ⊇ A there are at most |B | |T | types p(x) ∈ S(B) extending π(x)
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515088.88/warc/CC-MAIN-20181022134402-20181022155902-00459.warc.gz
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CC-MAIN-2018-43
| 1,787 | 2 |
https://guiadoscursos.uab.pt/en/ucs/metodos-numericos-para-equacoes-diferenciais-com-derivadas-parciais/
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math
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Numerical methods Potential theory Finite differences Finite elements
- Classify a partial differential equation as elliptic, parabolic or hyperbolic;
- Define a fundamental solution and its importance for the solution of elliptic equations;
- Recognize and numerically approximate the layer potential representations of the solutions;
- Recognize and apply numerical methods to approximate the solutions of several kinds of differential equations;
1) Classification of partial differential equations:
a. Elliptic, Parabolic, Hyperbolic.
b. Initial and Boundary conditions: Well-posed problem
2) Potential theory:
a. Fundamental Solution;
b. Layer Potential in the contexto of elliptic equations;
c. Numerical methos for its discretization;
3) Other numerical methods for partial differential equations:
a. Finite difference method;
b. Introduction to the method of finite elements;
Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.
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CC-MAIN-2023-23
| 1,101 | 16 |
http://www.americanscientist.org/issues/id.368,y.2007,no.2,page.3/postComment.aspx
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math
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An Exact Value for Avogadro's Number
Untangling this constant from Le Gran K could provide a new definition of the gram
Farewell to Le Gran K
A similar solution can solve the dilemma of the current time-dependent definition of Avogadro's number. The idea is simply to define N A , once and for all, as was done for the speed of light. Unlike that case, however, the range of known possible values for N A is astronomical. Three desirable basic properties for a reasonable value for N A help narrow the search.
First, since Avogadro's number purports to count the number of atoms in some theoretical specimen, its value should be an integer, as any schoolchild would expect. This would avoid having to interpret one-third of an atom, or worse yet, 1/p of an atom.
Second, the value chosen should be within the currently accepted range, (6.0221415 ± 0.0000010) × 1023.
Third, the value chosen for Avogadro's number should ideally have some inherent physical significance. Since volumes of objects are measured cubically, as in cubic centimeters and cubic yards, and not spherically (for example, via volumes of spheres with unit radii or diameters), and since the current definition of Avogadro's number counts the number of atoms in a solid specimen,it is reasonable to imagine the object as being a perfect geometrical cube. That implies that the value chosen should be a perfect numerical cube.
The range of acceptable integers in the current estimate of N A is two hundred quadrillion (2 × 1017), but within that huge range of values there are only 10 perfect cubes—from 84,446,8843 to 84,446,8933. For our purposes, any one of those 10 may be used, but the one closest to the best current estimate of Avogadro's number, and the only one accurate to within one unit in the eighth significant digit of the current best estimate, is
N A * = 602,214,141,070,409,084,099,072 = 84,446,8883.
Our proposal is simply to define Avogadro's number, permanently, as was done with the speed of light and with the second, and to set it equal to this specific integer. If the sides of the cube of atoms were only six atoms shorter or longer, the number of atoms it contains would no longer be within the currently accepted range for Avogadro's number, since 84,446,8833 = (6.02214034+) × 1023 and 84,446,8943 = (6.02214269+) × 1023.
Since the shape of a volume certainly affects the numbers of molecules it can contain—extremely long, thin cylinders can contain none—it seems natural to ask that the shape of the defining volume be a cube. Of course any other solid shape could also suffice as the defining object, but using a rectangular solid or parallelpiped would require specification of three numbers: the length, width and height. Using a sphere precludes choosing an integer at all, because of the irrationality of p.
At first glance, another possible candidate for the exact value of Avogadro's number might be 602,214,150, 000,000,000,000,000, which is dead center in the current range of values. This value, however, has little physical significance. It is neither a perfect cube nor a perfect square, so no perfect geometrical cube or square of atoms could be constructed which has that exact volume or area.
Moreover, the method of simply using the most recent best estimate of N A is not robust, unlike the methods that were used for defining fixed values for the speed of light and the second. If current experimental estimates of Avogadro's number increase the known number of significant digits by four or five places, for example, the "current best estimate" method of fixing the value for Avogadro's number would presumably also change by those same four or five digits.
The fixed values for the meter in terms of the speed of light and for the second in terms of vibrations of a cesium atom, however, were nearest-integer solutions, insensitive to further fractional refinements of the exact measurements. In exactly that same spirit, the definition of N A * above is also a nearest-integer solution—the nearest integral side length of a cube containing Avogadro's number of atoms. As such, the value chosen is also insensitive, within one atom either way, to improved experimental estimates of N A . The choice of an integer value for N A * seems essential, whereas the requirement that it be a perfect cube is largely esthetic, but with practical and intuitive physical significance as well.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125719.13/warc/CC-MAIN-20170423031205-00139-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 4,413 | 14 |
https://www.iwh-halle.de/suchergebnisse/?tx_iwhsolr_main%5Bquery%5D=Effizienzmarkthypothese&cHash=c290b20144a8eb571d5b48294b7a3422
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math
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Are European Equity Style Indexes Mean Reverting? Testing the Validity of the Efficient Market Hypothesis
IWH Discussion Papers,
The article tests for a random walk in European equity style indexes. After briefly
introducing the efficient market hypothesis, equity styles in general and the used
statistical techniques (Variance Ratio Test and modified Rescaled Range Test) it is
shown that a random walk in European equity style indexes cannot be rejected. At least in the period since the mid 70s, for which this research has been conducted, the weak form efficient market hypothesis seems to hold.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473871.23/warc/CC-MAIN-20240222225655-20240223015655-00127.warc.gz
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CC-MAIN-2024-10
| 600 | 6 |
http://www.easyaccounting101.com/management-accounting/standard-costing
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math
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Standard Costing is often described as estimated future cost because it is set before undertaking any project. The idea is to plan the total cost of materials, labours and overheads and estimating the sales as well. At the end of the period, when the project gets completed, actual costs are analysed and compared with the standard costs. Any difference is called the variance and it may be favourable and adverse. It depends on the situation under consideration.
The objectives of Standard Costing are as follows:
The deviation of standard cost from the actual cost is referred to as Variance. Thre are various types of variances calculated in standard costing which are as follows:
Related Posts: Material Price Variance MCQS
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991370.50/warc/CC-MAIN-20210515131024-20210515161024-00542.warc.gz
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CC-MAIN-2021-21
| 727 | 4 |
https://www.jiskha.com/display.cgi?id=1175992021
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math
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posted by Belle .
An electric motor has 72 turns of wire wrapped on a rectangular coil, of dimensions 3cm by 4cm. Assume that the motor uses 14A of current and that a uniform 0.5T magnetic field exists within the motor.
1)What is the maximum torque delivered by the motor? Answer in units of Nm.
2)If the motor rotates at 3000 rev/min, what is the peak power produced by the motor? Answer in units of W.
any help is appreciated! thanks
Max torque will be at 90 degrees to the plane of B.
area is in square meters.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887621.26/warc/CC-MAIN-20180118210638-20180118230638-00658.warc.gz
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CC-MAIN-2018-05
| 513 | 7 |
https://www.usingenglish.com/forum/threads/200576-quot-Here-I-am-quot-sounds-good-quot-Here-I-m-quot-sounds-really-strange-Why
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math
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I've told my ESL students that I'm has the same meaning as "I am". But the other day I came across this (written by someone from Spain): "Here I'm if you need me." Sounds really strange, right? It has to be "Here I am if you need me."
Also ... Where's my book? Oh! Here it's. (But "Here it is." would sound perfectly OK.)
Also ... Are you the teacher? Yes, I'm. (But "Yes, I am." again sounds fine. As does, "Yes, I'm the teacher.")
Is there some general rule as to when the contraction should not be used?
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988725475.41/warc/CC-MAIN-20161020183845-00261-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 621 | 5 |
https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all/190/0/89294/new-categorifications-of-the-chromatic-and-dichromatic-polynomials-for-graphs
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math
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New categorifications of the chromatic and dichromatic polynomials for graphs
Volume 190 / 2006
Fundamenta Mathematicae 190 (2006), 231-243 MSC: Primary 57M25. DOI: 10.4064/fm190-0-9
For each graph $G$, we define a chain complex of graded modules over the ring of polynomials whose graded Euler characteristic is equal to the chromatic polynomial of $G$. Furthermore, we define a chain complex of doubly-graded modules whose (doubly) graded Euler characteristic is equal to the dichromatic polynomial of $G$. Both constructions use Koszul complexes, and are similar to the new Khovanov–Rozansky categorifications of the HOMFLYPT polynomial. We also give a simplified definition of this triply-graded link homology theory.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224657735.85/warc/CC-MAIN-20230610164417-20230610194417-00090.warc.gz
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CC-MAIN-2023-23
| 723 | 4 |
http://perplexus.info/show.php?pid=2083&cid=16491
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math
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Even though it was now middle of winter, Jack hauled out his ladder and placed his ladder against the side of the house and began to climb. He had some bad luck when he reached the half-way point. The ground was a frozen sheet of ice and the base of his ladder slipped out and the top slid down the side of the house. Jack, clinging to the center rung, wound up moving from Point A on the side of his house to Point B on the ground.
Describe the path Jack traveled.
X^2 + Y^2 = R^2 or,
Y=sqrt(R^2 - X^2).
using the R=10, all these numbers work.
Jack's path from the wall (half the height of the ladder) to the ground (half the distance of the ladder) would be a 1/4 circle, with the radius 1/2 the length of the ladder.
Posted by Jim
on 2004-08-10 09:28:10
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703513194.17/warc/CC-MAIN-20210117205246-20210117235246-00409.warc.gz
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CC-MAIN-2021-04
| 756 | 8 |
https://urj.org/site-search?search_api_fulltext=Chanukah&f%5B0%5D=posted_on%3A2010-09&f%5B1%5D=posted_on%3A2014-06&f%5B2%5D=posted_on%3A2019-07
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math
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Displaying 1 - 3 of 3
I was recently asked by someone I very much respect to address "the" question. So I started to write the answer in a post... about five times without any luck. The "Why does a 20-something join a Reform Congregation" question.
This is the first post in our new "Let's Get Sustainable" blog post series - look for an e
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100229.44/warc/CC-MAIN-20231130161920-20231130191920-00848.warc.gz
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CC-MAIN-2023-50
| 339 | 3 |
https://forum.freecadweb.org/viewtopic.php?f=3&t=36321
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math
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I purposely did not select plane 1 as reference but the xy-plane. (In the construction where I discovered the problem there is no plane 1 and I try to reference the base planes.) So concerning the xy-plane, I think I did everything correct but the yaw angle setting is simply ignored by FC.
I was not correct. The problem is that the result seems to be dependent on what angle you have set before you made the change.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875148671.99/warc/CC-MAIN-20200229053151-20200229083151-00015.warc.gz
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CC-MAIN-2020-10
| 417 | 2 |
https://goprep.co/q15-the-angle-of-elevation-of-the-top-of-the-building-from-i-1nl888
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math
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Q. 155.0( 2 Votes )
The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
The height of the building.
Let AB be the building of height 50 m. and tower of height h (m.)
tan 60° =
Now in ∆DCB
tan 30° =
On substituting value of in eqn. (1)
Therefore, height of tower is m.
Rate this question :
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703538082.57/warc/CC-MAIN-20210123125715-20210123155715-00061.warc.gz
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CC-MAIN-2021-04
| 462 | 10 |
https://squ.pure.elsevier.com/en/publications/on-the-root-systems-of-the-classical-amp-exceptional-lie-algebras
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math
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Numerical procedures for obtaining the root systems of both classical and exceptional Lie algebras are slow and tedious when done by hand. This is a contribution in the field that uses a modern computer language Mathematica. This gives the benefits of high portability, efficiency and makes it easier to use either classical or exceptional Lie algebras in user programs. Root systems, positive roots and their sum, simple roots, Cartan's matrices, highest and fundamental weights are all calculated in the programs. The programs written with Mathematica 3.0 and can be run under any other version of it.
|Journal||Advances in Modelling and Analysis A|
|Publication status||Published - 1999|
ASJC Scopus subject areas
- Modelling and Simulation
- Computational Mathematics
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224643462.13/warc/CC-MAIN-20230528015553-20230528045553-00174.warc.gz
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| 771 | 6 |
http://scitation.aip.org/content/aapt/journal/ajp/81/3/10.1119/1.4772632
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math
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As the time step decreases, we must employ larger values of the Gaussian white noise to approximate the solution of the free diffusion equation [Eq. (3) ] accurately. (a) , (b) 0.5, and (c) 0.1. The corresponding solutions of the finite difference free diffusion equation [Eq. (5) ] in (d)–(f) for (lines) behave similarly. Although these solutions differ because they are specific realizations of a random process, their statistical properties do not change, as can be seen by comparing the shaded areas, which show the regions within one standard deviation of the mean of 10,000 realizations.
(a) For times smaller or comparable to the inertial time the trajectory of a particle with inertia (solid line) appears smooth. In contrast, in the absence of inertia (dashed line) the trajectory is ragged and discontinuous. (b) For times significantly longer than both the trajectory with inertia (solid line) and without inertia (dashed line) are jagged, because the microscopic details are not resolvable. These trajectories are computed using Eqs. (8) and (10) with and the same realization of the white noise so that the two trajectories can be compared. (c) The velocity autocorrelation function [Eq. (12) ] for a particle with inertia (solid line) decays to zero with the time constant , while for a particle without inertia (dashed line) it drops immediately to zero demonstrating that its velocity is not correlated and does not have a characteristic time scale. (d) A log-log plot of the mean-square displacement [Eq. (14) ] for a particle with inertia (solid line) shows a transition from quadratic behavior at short times to linear behavior at long times, while for a particle without inertia (dashed line) it is always linear. The particle parameters are R = 1 μm, m = 11 pg, , T = 300 K, and are used here and for the numerical solutions shown in the following figures.
(a) Trajectory of a Brownian particle in an optical trap ( and ). The particle explores an ellipsoidal volume around the center of the trap, as evidenced by the shaded area which represents an equiprobability surface. (b) and (c) The probability distributions of finding the particle in the z- and y-planes follow a two-dimensional Gaussian distribution around the trap center.
(a) As the trap stiffness increases, the particles become more and more confined as shown by the theoretical (solid curve) and numerical (symbols) variance of the particle position around the trap center in the y-plane and, in particular, by the probability distributions corresponding to (b) , (c) , and (d) .
(a) The position autocorrelation function of a trapped particle [Eq. (23) ] gives information about the effect of the trap restoring force on the particle motion. As the trap stiffness and, therefore, the restoring force are increased, the characteristic decay time of the position autocorrelation function decreases. (b) The mean square displacement, unlike for the free diffusion case, does not increase indefinitely but reaches a plateau, which also depends on the trap stiffness—the stronger the trap, the sooner the plateau is reached.
(a) The probability distribution of an optically trapped particle shifts in response to an external force. The black histogram shows the initial distribution and the grey histogram represents the distribution after the application of a constant external force . (b) The position autocorrelation function of the trapped particle [black line, Eq. (23) ] and position cross-correlation function [grey line, Eq. (20) ], are modulated in the presence of a rotational force field such as the one in Eq. (19) with . This modulation demonstrates the presence of the rotational force field even though it is not clear from the trajectory (the inset shows a trajectory during a time interval equal to 0.1 s). (c) Dynamic transitions between the two equilibrium positions in a double-well potential (Kramers transitions) with and [Eq. (21) ].
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CC-MAIN-2014-15
| 3,993 | 8 |
https://drum.lib.umd.edu/items/29a3b469-5e92-464f-875b-08dc4698a474
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math
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Weyl-Heisenberg Wavelet Expansions: Existence and Stability in Weighted Spaces
Publication or External Link
The theory of wavelets can be used to obtain expansions of vectors in certain spaces. These expansions are like Fourier series in that each vector can be written in terms of a fixed collection of vectors in the Banach space and the coefficients satisfy a "Plancherel Theorem" with respect to some sequence space. In Weyl-Heisenberg expansions, the expansion vectors (wavelets) are translates and modulates of a single vector (the analyzing vector) . The thesis addresses the problem of the existence and stability of Weyl-Heisenberg expansions in the space of functions square-integrable with respect to the measure w(x) dx for a certain class of weights w. While the question of the existence of such expansions is contained in more general theories, the techniques used here enable one to obtain more general and explicit results. In Chapter 1, the class of weights of interest is defined and properties of these weights proven. In Chapter 2, it is shown that Weyl-Heisenberg expansions exist if the analyzing vector is locally bounded and satisfies a certain global decay condition. In Chapter 3, it is shown that these expansions persist if the translations and modulations are not taken at regular intervals but are perturbed by a small amount. Also, the expansions are stable if the analyzing vector is perturbed. It is also shown here that under more general assumptions, expansions exist if translations and modulations are taken at any sufficiently dense lattice of points. Like orthonormal bases, the coefficients in Weyl-Heisenberg expansions can be formed by the inner product of the vector being expanded with a collection of wavelets generated by a transformed version of the analyzing vector. In Chapter 4, it is shown that this transformation preserves certain decay and smoothness conditions and a formula for this transformation is given. In Chapter 5, results on Weyl-Heisenberg expansions in the space of square-integrable functions are presented.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817144.49/warc/CC-MAIN-20240417044411-20240417074411-00168.warc.gz
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CC-MAIN-2024-18
| 2,075 | 3 |
https://www.ajol.info/index.php/jrfwe/article/view/252286
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math
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Main Article Content
This study involved developments of growth functions for predicting future individual tree characteristics, stem volumes and yield using stand age, stocking, diameter at breast height (dbh) and total height as predictor variables for Gmelina arborea plantation in Ukpon river forest reserve, in Obubra local government area of Cross River State, Nigeria. Data were collected from sample plots within five (5) age series (3, 5, 7, 9, and 11 years) in Gmelina plantation. Five sample plots of 0.04 hectare each were randomly selected from each age bracket. Diameter at breast height (dbh) of all trees in each plot was measured using diameter tape and grouped into 10cm diameter classes. Two trees with mean diameter in each class were randomly selected and measured for total height using Sunnto altimeter. Four dominant trees were randomly selected and measured for dominant diameter at breast height and dominant total height in each plot. Over bark diameter at the hohenadls positions (0.1, 0.3, 0.5 and 0.9) along the free bole for the two trees with mean dbh were measured using Haga altimeter for volume and form factor computation. Seven growth models were fitted to age, stocking diameter, and height using linear and non-linear regression techniques. The model selection criteria were based on high coefficient of determination (R2), low goodness of fit, high significant of variance ratio (F) and least residual mean square error (MSE). The results showed that Gmelina species had the fastest initial height growth of 3.6m per year within the first five years of growth. The mean diameter at breast height increased from 13.31cm at age 3 to 6.99cm at age 11 with mean diameter increment of 4.4cm per year in the first five years and 2.3cm per year thereafter between ages of 7 and 11 years. Mean total height increased from 13.3m to 25m from age 3 to 11 years with corresponding dominant height of 17.28m to 33.88m respectively. The average stands form factor of 0.412 was obtained. The mean basal area increased from 15.44m2/ha to 33.18m2/ha for ages 3 to 11 years respectively while the mean annual increment (MAI) declined from 27.46m2/ha/yr at age 3 to 21.34m3/ha/yr at age 9 and increased slightly to 28.69m3/ha/yr at age 11 years. This study serves as a useful tool for proper evaluation and prediction of future stand growth for sustainable management of forest plantation under similar environmental conditions.
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CC-MAIN-2023-50
| 2,449 | 2 |
http://publications.drdo.gov.in/gsdl/cgi-bin/library.cgi?e=d-01000-00---off-0defences--00-1----0-10-0---0---0direct-10---4-------0-0l--11-en-50---20-help---01-2-1-00-0-0-11-1-0utfZz-8-00&a=d&c=defences&cl=CL3.13.65
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math
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| || An Algorithm for Calculating Expected Production Function and other Similar Function for a Flexible Manufacturing System
Author : Kumar, Vinod;Kapur, J.N.
Source : Defence Science Journal ; Vol:36(2) ; 1986 ; pp 243-255
Subject : 519.2 Statistics;519.8 Operations Research
Keywords : Ammunition;Manufacturing technology
Abstract : The fact that for the case when the number of machines in each group is the same, the expected production function is a symmetric function of scaled workloads, is exploited to express this function in terms of the basic symmetric functions of the loads. The same technique is suggested for calculating the probability of all the machines being found busy and the variance of the proportion of busy machines in the system.
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CC-MAIN-2013-20
| 757 | 6 |
http://dictionary.reference.com/browse/specific%20gravity
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math
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|See relative density the ratio of the density of a substance to that of water|
specific gravity n.
Abbr. sg, sp gr
The ratio of the mass of a solid or liquid to the mass of an equal volume of distilled water at 4°C (39°F) or of a gas to an equal volume of air or hydrogen under prescribed conditions of temperature and pressure.
|specific gravity (spĭ-sĭf'ĭk) Pronunciation Key
The relative density of a solid or liquid, usually when measured at a temperature of 20°C, compared with the maximum density of water (at 4°C). For example, the specific gravity of carbon steel is 7.8, that of lead is 11.34, and that of pure gold is 19.32.
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http://www.bobisbikes.com/index.php/read/an-introduction-to-ordinary-differential-equations-dover-books-on-mathematics
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math
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By Earl A. Coddington
This concise textual content bargains undergraduates in arithmetic and technology an intensive and systematic first direction in uncomplicated differential equations. Presuming a data of simple calculus, the publication first stories the mathematical necessities required to grasp the fabrics to be provided.
The subsequent 4 chapters soak up linear equations, these of the 1st order and people with consistent coefficients, variable coefficients, and typical singular issues. The final chapters deal with the lifestyles and forte of recommendations to either first order equations and to platforms and n-th order equations.
Throughout the booklet, the writer incorporates the speculation a long way adequate to incorporate the statements and proofs of the easier life and area of expertise theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has integrated many routines designed to enhance the student's process in fixing equations. He has additionally incorporated difficulties (with solutions) chosen to sharpen figuring out of the mathematical constitution of the topic, and to introduce a number of appropriate themes now not lined within the textual content, e.g. balance, equations with periodic coefficients, and boundary price difficulties.
Read or Download An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) PDF
Best differential equations books
Extending and generalizing the result of rational equations, Dynamics of 3rd Order Rational distinction Equations with Open difficulties and Conjectures makes a speciality of the boundedness nature of recommendations, the worldwide balance of equilibrium issues, the periodic personality of suggestions, and the convergence to periodic recommendations, together with their periodic trichotomies.
This monograph presents either an creation to and an intensive exposition of the idea of rate-independent structures, which the authors were engaged on with loads of collaborators over 15 years. the focal point is usually on absolutely rate-independent structures, first on an summary point both with or perhaps with out a linear constitution, discussing numerous innovations of ideas with complete mathematical rigor.
Comprises approximately 4,000 linear partial differential equations (PDEs) with solutionsPresents strategies of diverse difficulties proper to warmth and mass move, wave conception, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction idea, quantum mechanics, chemical engineering sciences, electric engineering, and different fieldsOutlines simple tools for fixing a variety of difficulties in technological know-how and engineeringContains even more linear equations, difficulties, and ideas than the other ebook at present availableProvides a database of try difficulties for numerical and approximate analytical tools for fixing linear PDEs and platforms of coupled PDEsNew to the second one EditionMore than seven-hundred pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutionsSystems of coupled PDEs with solutionsSome analytical tools, together with decomposition tools and their applicationsSymbolic and numerical tools for fixing linear PDEs with Maple, Mathematica, and MATLAB®Many new difficulties, illustrative examples, tables, and figuresTo accommodate various mathematical backgrounds, the authors steer clear of at any place attainable using designated terminology, define a few of the tools in a schematic, simplified demeanour, and organize the cloth in expanding order of complexity.
This ebook is dedicated to impulsive sensible differential equations that are a ordinary generalization of impulsive traditional differential equations (without hold up) and of practical differential equations (without impulses). this day the qualitative conception of such equationsis less than speedy improvement.
- Traffic and Granular Flow ' 03
- Spectral Clustering and Biclustering: Learning Large Graphs and Contingency Tables
- Stochastic Integration in Banach Spaces: Theory and Applications (Probability Theory and Stochastic Modelling)
- Large-Scale Networks in Engineering and Life Sciences (Modeling and Simulation in Science, Engineering and Technology)
Additional resources for An Introduction to Ordinary Differential Equations (Dover Books on Mathematics)
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| 4,394 | 15 |
http://www.jiskha.com/members/profile/posts.cgi?name=Ren&page=4
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math
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oh don't worry drwls, i now understand. thanks!
sorry i mean the top looks like a quadratic do i break it down or just leave it as it is and just plug in x=5 into the entire equation?
so drwls do i have to change the top into something similar or just plug in x=5 into the entire equation.
ok lemme write it over then: How do i find the lim x-->5 (x-3-2x^2)/(1+3x)
how do i evaluate this limit: lim x tends to 5 x-3-2x^2/1+3x
Hey thanks a lot Reiny. I got it..
How do i find the common ratio, when the 1st, 2nd and 7th terms of a A.P with common difference 2 are the first three terms of a G.P .
22...quotient of 18 and 2 = 9 sum of 22 and 9= 31...sbtracting the quotient (which is 9) from the sum..would equal 9.
A 50 kg skier is pulled up a frictionless ski slope that makes an angle of 8 degrees with the horizontal by holding onto a tow rope that moves parallel to the slope. Determine the magnitude of the force of the rope on the skier at an instant when a) the rope is moving with a c...
A car weights 1.30 X 10^4 N is initially moving at a speed of 40km/h when the brakes are applied and the car is brought to a stop in 15m. Assuming that the force that srops the car is constant. find a)magnitude of the force b)time required for the change in speed. If the inita...
For Further Reading
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http://clippers.topbuzz.com/PNphpBB2-viewtopic-t-12210-sid-f856ec30b1c7264d902773c4c6d359fe.html
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math
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Can someone post this insider article? Just curious to see where Blake and Chris rank amongst the top 10. I think they are both in the conversation for top 5, but that is just my opinion.
http://insider.espn.go.com/nba/story/_/ ... rs-numbers
I thought I already did
http://clippers.topbuzz.com/PNphpBB2-vi ... tml#449365
My bad I didn't see it.
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https://en.wikibooks.org/wiki/Geometry/Five_Postulates_of_Euclidean_Geometry
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math
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Geometry/Five Postulates of Euclidean Geometry
Postulates in geometry is very similar to axioms, self-evident truths, and beliefs in logic, political philosophy, and personal decision-making. The five postulates of Euclidean Geometry define the basic rules governing the creation and extension of geometric figures with ruler and compass. Together with the five axioms (or "common notions") and twenty-three definitions at the beginning of Euclid's Elements, they form the basis for the extensive proofs given in this masterful compilation of ancient Greek geometric knowledge. They are as follows:
- A straight line segment may be drawn from any given point to any other.
- A straight line may be extended to any finite length.
- A circle may be described with any given point as its center and any distance as its radius.
- All right angles are congruent.
- If a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles.
Postulate 5, the so-called Parallel Postulate was the source of much annoyance, probably even to Euclid, as it is not a simple, concise statement, as are the other four. Mathematicians, and really most of us, value simplicity arising from simplicity, with the long complicated proofs, equations, and calculations needed for rigorous certainty done behind the scenes, and to have such a long sentence amidst such other straightforward, intuitive statements seems awkward. As a result, many mathematicians over the centuries have tried to prove the results of the Elements without using the Parallel Postulate, but to no avail. However, in the past two centuries, assorted non-Euclidean geometries have been derived based on using the first four Euclidean postulates together with various negations of the fifth.
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CC-MAIN-2024-10
| 1,956 | 8 |
https://community.canvaslms.com/t5/Canvas-Question-Forum/Likert-Survey-General-Comments/m-p/207020
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math
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How does the general comment box become saved in a Likert survey?
I am needing to add a space for written feedback, and have been unsuccessful in saving the box to the survey as an option.
Hello there, @lperry31 ...
I am reviewing some of the older questions here in the Canvas Community, and I came across your question. I am sorry to see that your question has been sitting out here unanswered since you first posted it on September 25, 2019. Unfortunately, I don't really have an answer for you, but I wanted to check in with you at least. It seems as though you may have stumped the Community with your question. Have you been able to come up with any solutions on your own since you first posted your question at the end of September? If so, would you be willing to share your findings with us back here in this topic? Or, if you are still looking for some help with your question, please let us know that as well by posting a note below. For the time being, I am going to mark your question as "Assumed Answered" (How we keep your questions flowing!)...not because we've been able to find a solution for you...but more because we've not heard back from you and because there hasn't been any new activity in this topic for almost six months. However, that won't prevent you or others from posting additional questions and/or comments below that are related to this topic. I hope that's okay with you, Lisa. Looking forward to hearing back from you soon.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572161.46/warc/CC-MAIN-20220815054743-20220815084743-00724.warc.gz
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https://www.pagalguy.com/articles/data-interpretation-and-data-sufficiency-quiz-for-snap-2-5481
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math
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This quiz consists of questions from past
SNAP actual papers. Leave your answers/ responses in the comments section below
and soon we’ll let you know the correct answers!
Directions (Qs. 1 to 6): Questions are based on the following graph
Spending by advertisers and viewers
Total for all five years Rs.100 crores
1. If in year 3 out of money spent by the advertisers and viewers 12% had
been spent on contingent expenses, what was the amount spent on contingent
expenses (in Rs. Crore)?
(a) 2.4 (b) 2.1 (c) 25 (d) 2.6
2. The expenses of which year added to one fourth the expenses of another
year equal the expenses of each of two other years?
(a) 4 (b) 3 (c) 2 (d) 1
3. In how many years from Year 2 has the expenditure risen by the around
(a) 1 (b) 3 (c) 2 (d) Insufficient data
4. The difference in the expenditure between which two years equals the
difference between the expenditure in year 2 to year 1?
(a) year 5 and year 3
(b) year 4 and year 3
(c) both 1 and 2
(d) neither 1 and 2
5. If in Year 6 the expenses increase at the same rate as they did from
Year 3 to Year 5. What will be the expenditure in Year 6 (in Rs. Crore)?
(a) 28.2 (b) 24.2 (c) 25.2 (d) 23.2
6. If in year 4 out of the money spent by the advertisers and viewers, 10%
spent on disaster recovery expenses, what was the amount spent on disaster
(a) 2.2 (b) 2.6 (c) 2.3 (d) 2.4
Directions (Qs. 7 to 10): Follow the given Instructions:
Each item has a question followed by two statements
Mark (a), if the question can be answered with the help of statement A
Mark (b), if the question can be answered with the help of statement B
Mark (c), if the question can be answered with the help of both the
statements but not with the help of either statement itself,
Mark (d), if the question cannot be answered even with the help of both the
7. The average of three quotations for a particular item is Rs.120. Is the
highest quotation less than or equal to Rs.139?
A. The lowest quotation is Rs.90
B. One of the Quotation is Rs.125.
8. How many people, read both Economic Times and Financial Express?
A. Out of 300 readers, 200 read financial express, 220 read Economic times
and 50 read Indian Express.
B. Out of total 300 readers, 200 read financial express, 220 read Economic
times and 50 read neither.
9. A bus started from bus stop P, developed engine trouble and reached bus
stop Q, 40 minutes late. What is the distance between bus stops P and Q?
A. The engine trouble developed after traveling 40 kms from Bus stop P and
the speed reduced to 1/4th of the original speed.
B. The engine trouble developed after traveling 40 kms from Bus stop P in
two hours and the speed reduced 1/4th of the original speed.
10. What is the value of prime number X?
A. X + Y is a two-digit number greater than 50.
B. Y is a two-digit number.
To get fresh updates about MBA exams on your Facebook & Twitter
timelines, subscribe to our pages created specifically for them. We will post
only exam specific links on these pages:
3(c) 4(c) 5(b) 6(a)
7(c) 8(b) 9(b)
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http://kehomeworkekpt.lasvegasdentists.us/cai-for-geometry.html
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math
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The use of computers in mathematics education: a paradigm shift from “computer assisted instruction” towards “student computers in mathematics education. Cai on math free download math ninja math ninja is a fun way to help students with math right now it focuses on multiplication, but. Cai and math 3 that it adjusts student instruction according to student’s ability a large problem with the studies on computer-assisted instruction is that the. Math department research home directory department research faculty listing graduate student listing administration and contact information highlights undergraduate graduate news. David cai professor of mathematics and neural science courant institute of mathematical science the center for neural science new york university mail address courant institute, 251 mercer. Effectiveness of computer assisted instuctions (cai) middle school mathematics computer assisted instruction versus traditional instruction method. A 15-year old high school junior, phoebe cai is already engaged in research at a collegiate level, assisting in the data analysis of a research project at the. Hands-on support for geometry concepts, featuring geoboards, geometric eai education provides over 6,000 teaching supplies for grades pre k-12, home schools.
Cai surface geometry that has no cai color attribute is assigned the aliasstudio default shader on aliasstudio export to cai, the color index. Faculty, department of mathematics, texas a&m university faculty, department of mathematics, texas a&m university skip to content search: featured programs reu: research experience for. Limited evidence of program that provides teachers with workshops in math multi-age grouping, extensive computer-assisted instruction. Lin, c (2009) a comparison study of web-based and traditional instruction on preservice teachers’ knowledge of fractions contemporary issues in technology and. A computer-assisted instruction module on enhancing numeracy skills of preschoolers with attention-deficit hyperactivity disorder jasper vincent q alontaga de la salle university, manila. Mathematical theory and numerical methods for gross-pitaevskii equations and applications cai yongyong (msc, peking university) a thesis submitted.
Math games including bingo, memory, and hidden picture for addition, subtraction, multiplication, division and more. University of chicago algebraic geometry seminar the uchicago algebraic geometry seminar will be jointly organized by the departments of jin-yi cai. Top-rated programs supplementary program that has mathematicians teach advanced topics in math to supplement regular cai = computer-assisted instruction. Free flashcards to help memorize facts about cai geometry vocab 1 other activities to help include hangman, crossword, word scramble, games, matching, quizes, and tests.
Zentralblatt math identifier 120262073 subjects optimal large-scale quantum state tomography with pauli measurements cai, tony, kim, donggyu, wang, yazhen. Cai and learning disability 1 the effectiveness of computer aided instruction in mathematics for students with learning disabilities by jane m scheid.
Archive for the ‘math 126’ category math 126 – 1007 mowe tuesday, january 16th, 2018 office hour: monday – thursday 11:30 am – 12:30 pm friday 8:30 am – 9:45 am office location: cdc 726. Geometry global 20,711 likes 246 talking about this geometry global is an award-winning brand activation and shopper marketing agency that helps. The more i learn about investigations, the more i am in awe of the thoughtful design and how deep and rich it is from the very beginning each part builds elegantly.
Zhiqiang cai, seokchan kim, sangdong kim, and sooryun kong a finite element method using singular functions for poisson equations: mixed boundary conditions. Running head: computer assisted instruction math accuracy 1 evaluation of computer assisted instruction for math. Discover math on geogebraorg, the home of our free online graphing calculator, geometry calculator, 3d calculator, spreadsheet, cas, probability calculator and classroom activities.
Accelerated math - official page for renaissance math practice master math skills, learn critical thinking skills, and reduce math anxiety. This paper aims to understand how certain different but interrelated variables such as background, motivation, and social support could lead to an explanation of student attitudes towards.Download Cai for geometry
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http://nrich.maths.org/public/leg.php?code=-68&cl=3&cldcmpid=4716
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math
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The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
Some puzzles requiring no knowledge of knot theory, just a careful
inspection of the patterns. A glimpse of the classification of
knots and a little about prime knots, crossing numbers and. . . .
In this problem, we have created a pattern from smaller and smaller
squares. If we carried on the pattern forever, what proportion of
the image would be coloured blue?
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
Can you see how this picture illustrates the formula for the sum of
the first six cube numbers?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
A huge wheel is rolling past your window. What do you see?
Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .
Can you make a tetrahedron whose faces all have the same perimeter?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
If you move the tiles around, can you make squares with different coloured edges?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
A blue coin rolls round two yellow coins which touch. The coins are
the same size. How many revolutions does the blue coin make when it
rolls all the way round the yellow coins? Investigate for a. . . .
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?
Can you use the diagram to prove the AM-GM inequality?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you maximise the area available to a grazing goat?
Draw a pentagon with all the diagonals. This is called a pentagram.
How many diagonals are there? How many diagonals are there in a
hexagram, heptagram, ... Does any pattern occur when looking at. . . .
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Can you discover whether this is a fair game?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Take a line segment of length 1. Remove the middle third. Remove
the middle thirds of what you have left. Repeat infinitely many
times, and you have the Cantor Set. Can you picture it?
Can you describe this route to infinity? Where will the arrows take you next?
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Three circles have a maximum of six intersections with each other.
What is the maximum number of intersections that a hundred circles
Seven small rectangular pictures have one inch wide frames. The
frames are removed and the pictures are fitted together like a
jigsaw to make a rectangle of length 12 inches. Find the dimensions
of. . . .
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
Have a go at this 3D extension to the Pebbles problem.
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400. . . .
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end?
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https://www.sustainablelivingguide.com.au/appliance-energy-usage-guide/
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This guide has been put together to give you an idea of the typical energy consumption of the appliances in your house. Some of the average energy usage may surprise you, but it could help you see where your household can make the biggest energy savings.ApplianceAverage WattsEst. cost per hour at $0.22 per kWhAir conditioner (room) Small1000$0.22Medium2300$0.51Large3200$0.71Air conditioner (ducted)5000$1.11Air cooler (evaporative) Portable150$0.03Fixed600$0.13Ducted1000$0.22Electric blanket Single70$0.02Double120$0.03Blender450$0.10Clothes dryer Small rotary or cabinet2400$0.53Large rotary or wired in4000$0.88Computer With monitor100$0.02with monitor and printer300$0.07Dishwasher2400$0.53Drill – portable500$0.11Fan Exhaust40$0.01Ceiling100$0.02Food mixer135$0.03Freezer 200 Litre (T)100$0.02300 Litre (T)150$0.03450 Litre (T)230$0.05Griller Small660$0.15Large2400$0.53Vertical1200$0.27Hair dryer100$0.02Heater Oil filled column1000$0.22 1500$0.33 2000$0.44 2400$0.53Heater Radiators/portable fan600$0.13 1000$0.22 1200$0.27 1500$0.33 2400$0.53Heater Space3600$0.80 4500$1.00 6000$1.33 7000$1.55Heat bankssee storageheatersHotplate (T) Small portable600$0.13Large portable1000$0.22Ceramic Halogen (T) Small1200$0.27Large1700$0.38Hotplate – wired in (T) Small hotplates1000$0.22Large hotplates2000$0.44Hot watersee storgeheatersIron (T)600$0.13Juice Extractor300$0.07Kettle1800$0.40Lighting CFL7$0.002CFL11$0.002CFL20$0.004Incandescent25$0.005Incandescent60$0.01Incandescent100$0.02Lighting heater 4×274 Watts1100$0.24Microwave oven 750 Watts1300$0.29Convection1600$0.35Mini oven600$0.13Oven Small (T)1800$0.40Large (T)2400$0.53Radio60$0.01Range hood140$0.03Refrigerator 250 litre manual defrost (T)170$0.04250 litre auto defrost (T)210$0.05500 litre frost free260$0.06600 litre frost free400$0.09Sewing machine75$0.02Shaver15$0.004Stereo/Radio/Record player100$0.02Swiming pool pump1000$0.22 1600$0.35Salt water chlorintor300$0.07Television CRT150$0.03LCD200$0.04Plasma330$0.07Toaster Standard600$0.13Automatic1200$0.27Towel rail – heated (T)150$0.03Vacuum cleaner Portable1100$0.24Ducted1500$0.33VCR/DVD player100$0.02Washing machine Small500$0.11Automatic900$0.20With element2400$0.53Welder2400$0.53Water heaters Instantaneous hot water service1300$0.29Quick recovery service2400$0.53Off-peak 13600 Off-peak 14500 Off-peak 16000 Heat pump (T)1300$0.29Storage heaters1200$0.27Heat banks3600$0.27 4500$0.27 6000$0.27Spa heater Small (T)2400$0.53Medium (T)5000$1.11Large (T)15000$3.32ApplianceAverage MillijoulesEst. cost per hour at $0..147 per mJGas appliances Cook top28$0.41Ducted furnace (T) – medium60$0.88Ducted furnace (T) – large90$1.32Flued heater – wall furnace (T)40$0.59Flued heater (T)37$0.54Unflued heater25$0.37Wall oven12$0.18Gas hot water Gas storage hot water service32$0.47Gas instanataneous hot water service185$2.72 The energy usage and cost figures listed in the appliance energy usage guide should be taken as a guide only. Energy usage is presented as an average estimate while costs and usage will vary according to things like the size of your home and your personal preferences.
Cost figures are based on an average electricity rate of $0.22 per kilowatt hour (kWh) and a gas rate of $0.0147 per millijoule (mJ) excluding GST. Due to your geographic location, the different number of tariffs and the exclusion of the Service Availability Charge (SAC), results may not be an accurate reflection of your bill and actual costs may vary between households.
Figures for thermostat-controlled appliances have also been averaged to take into account appliances that are normally on continuously and switch themselves on and off to maintain pre-selected temperatures.(T) =Thermostat controlled appliances
Figures correct as at June 2010
Source: Country EnergyReturn to Install energy efficient appliances and fixtures action
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