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All the basic matrix operations as well as methods for solving systems of simultaneous linear equations are implemented on this site. An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic Luke Smith & Joan Powell When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers. Augmented Matrices - page 1 Using Augmented Matrices to Solve Systems of Linear Equations 1. edu Abstract We illustrate the use of spreadsheet modeling and Excel Solver in solving linear and. You can only upload files of type 3GP, 3GPP, MP4, MOV, AVI, MPG, MPEG or RM. Answer: The matrix for T is exactly A (given above). Since transfer func-tion relates input to outputs the transfer function should also be invariant to coordinate changes in the state space. Multiply the matrices with the scalar and then add or subtract as directed. I started using your website after I failed my first test and was able to pull a B in the class. Find A + B. These are indicated by daggers in the PDF and print versions, with solutions available in an online supplement, while in the web version a solution is indicated by a knowl right after the problem statement. Standard Costing and Variance Analysis 2 Topic Gateway Series About Topic Gateways. The questions found in the worksheets are in high standard and practicing these questions will definitely make the students to reach their goal in ACT. 1 Basic matrix notation We recall that a matrix is a rectangular array or table of numbers. The size of a matrix (i. Symbolab: equation search and math solver - solves algebra, trigonometry and calculus problems step by step. Below are 3 tests with number sequences of increasing difficulty. x5yz11 3z12 2x4y2z8 +−=− = +−= All of the following operations yield a system which is equivalent to the original. NCERT Solutions for Class 11th Maths Chapter 4 - Principle of Mathematical Induction National Council of Educational Research. IB Math –SL Practice Problems – Matrices Alei - Desert Academy 2011-12 A: C:\Documents and Settings\Bob\My Documents\Dropbox\Desert\SL\SL Practice Problems. Step 1: Explore the diagram below - it's a visualization of our entire Problem-Solving Matrix. 1 Introduction An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimize total cost or maximize total profit of allocation. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Matrix Operations in Excel. Chapter 10 - How Do I Solve a Nonlinear Equation? 11. We call the individual numbers entriesof the matrix and refer to them by their row and column numbers. Recursive means you de ne the n n-dimensional case in terms of the (n 1) (n 1) dimensional case. From the above, the homogeneous system has a solution that can be read as or in vector form as. How to multiply matrices using MS Excel Finding the inverse of a matrix using Excel Using the mmult, mdeterm and minverse commands in excel. Recovery Matrix. More from my site. Matrices ﬁrst arose from speciﬁc problems like (1). Intermediate Algebra Problems With Answers - sample 1: equations, system of equations, percent problems, relations and functions. A zero matrix is a matrix in which every element is zero. find the number using inverse of a matrix. so lets say for following array: 2,54,4,10,1,7 you first take 1 and 2 and add then add the result 3 to the array. There is at least one mistake. Systems of Linear Equations and Matrix Algebra Practice Exam. How to Multiply Matrices. The rest of the elements should be ones. In our system, the constant matrix is: Now we want to use these matrices to solve our system of equations. That is, multiplying a matrix by its inverse producesanidentitymatrix. Verify the factorization by computing the product LU. Still need help after using our precalculus resources? Use our service to find a precalculus tutor. Test and improve your knowledge of Algebra II: Matrices and Determinants with fun multiple choice exams you can take online with Study. Solving a system of linear equations by using the inverse matrix method. 5 minutes, Dallas by 1. Write the equation of the line with slope 5 that passes through (¡3;7). A matrix containing only zero elements is called a zero matrix. Integrated Mathematics 2 GOAL 1: The learner will perform operations with numbers, algebraic expressions, and matrices to solve problems. 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# How to get time to pass faster on another planet compared to earth?

I'm developing a story where humans colonize a few planets. One planet, lets call it Planet A, has similar gravity to earth, air pressure, and solar radiation. You cannot however, walk on the surface of Planet A with out a space suit, and there is no life, nor most of the essential ingredients. Planet A is arbitrarily far away from earth, it could be in the same galaxy, or across the universe.

Planet A relies on Earth for resources. One day the means by which both communication and transport of those resources stops working (could be wormhole for example), to which the residence of Planet A, after a very long period of time, get the means to travel to earth working again, and travel to Earth.

Part of my story relies on the time between the communication blackout being different for the Planet A side of things, and the Earth side of things, with Planet A experiencing a significant time difference compared to how much time has passed on earth (factor of 2x to 10x longer on Planet A). Note however when Earth's solar system and Planet A's solar-system are connected their clocks are synced or approximately the same (ie time passes at similar rates on both sides). The process of synced time is handwaved, you do not have to explain why it happens.

Is there some sort of scientific explanation for how this could happen? I'm willing to handwave the method of transport between these two far off places, but I'd like to explain the time difference scientifically.

Note, this question is similar to Can time move faster on another world but I do not consider the following to be valid explanations:

• Time travel, as in someone purposefully made a time machine to go back in time.
• Extremely rare and unlikely occurrences that we've never actually experienced and don't have a real reason to expect they exist naturally (ie a planet moving at 10c and negative gravity...)
• Planets and solar systems that were purposely manipulated to speed up time.

This question (and the answers) also don't appear to take the distance between planets into effect, and talk about two planets in general where mine requires earth to be slower planet, so you can't put earth in a massive gravity well or something unless that's plausibly already the case. Finally my question talks about a hand-waved method to connect the two places with "something", which could provide more ground to expand the possible answers since this "wormhole" can be softer science and aid in answers.

• This question has some problems. You handwave how time is synced, but that is at the core of the question. Time ALREADY will pass at different rates for two planets not in the same reference frame. Relativity means they might pass slower or faster depending upon who is measuring.
– SRM
Dec 9 '19 at 17:02
• What you're describing is timetravel. Saying "that's not a valid explanation" doesn't change that very much. Dec 9 '19 at 17:20
• I am not sure how we can satisfy the science-based tag for this Dec 9 '19 at 18:06
• The way round you've put it (with planet A experiencing 2-10* more time than Earth) isn't going to work in any other way than Mathaddict's answer. If it were the other way round you could have planet A somewhat in the gravity-well of a black-hole (which the Earth isn't particularly). Could the planets be swapped around for the purposes of an answer? Barring white-holes which are a bit blue-sky in this context. Dec 9 '19 at 18:50
• You've ruled out "time travel" but since transportation is hand-waved, would you consider a wormhole through time? Dec 9 '19 at 19:07

Your characters believed the connection to be a wormhole through space, but they have actually been using:

### A wormhole through space AND time™

When the wormhole is lost entirely, your characters "repair" it by creating a brand new one. But since they are unaware of the time component, they don't take timeframe into account. Their wormhole connects the proper relative locations, but is "wrong" on the when component. They had no away of detecting the original time difference because the locations are so remote that there were no common events to observe from both ends.

• This answer offers a narrative. I welcome suggestions on how to be less plot based, or is this style is OK on this site? Dec 9 '19 at 20:28
• Great! this is the exact kind of answer I was thinking of when I made my comment to your suggestion Dec 9 '19 at 20:28
• Yeah, but the question has a "science based" tag. There is no known way to produce a wormhole at all, never mind control it in this manner. Dec 10 '19 at 15:11
• Sometimes the client asks for one thing but wants something else. Jan 7 '20 at 14:53

You have added the "science based" tag. And that's a problem. There is no known way to make time pass faster on another planet.

You marked "Accepted" an answer by Mathadict about standard old relativistic time dilation. But this answer is wrong. If two planets are traveling relative to each other, then each sees the other as going more slowly. This is absolutely required by special relativity. Any other choice would mean that there was an absolute frame of reference, the fastest-time frame. And that would invalidate special relativity, which would wreck the whole sequence.

Try this. Let the two planets cross at t=0 for simplicity. One year later, Earth sends out a ship. Planet A sees that ship coming at the same speed they see Earth going. When the ship arrives they find 1 year of ship time passed, for a total of 2 years. But 10 years have passed on Planet A.

But now look at the same thing from the point of view of Planet A. After 1 year, they send a ship. And Earth sees it coming at the same speed we see Planet A going. And it gets here after 1 year of ship time. But on Earth, 10 years have passed.

This symmetry is absolutely required by special relativity. You can't "win" using this. The path with the corner will always experience less time.

Now you could slow Earth. For example, you could put Earth in an orbit very close to a black hole. As you get closer to the event horizon, there is a time dilation effect. From the point of view of objects very far from the horizon, things near the horizon appear to age very slowly. Arbitrarily slowly, in fact.

Now it's pretty uncomfortable being at this location unless you have a black hole with very large mass. If you had a black hole with, for example, only a few 100 solar masses, the tides would utterly pull apart anything within even a few dozen times the event horizon radius. Tides would be ridiculous, millions of g's, before the time dilation became useful. However, if you had a black hole with many billions of solar masses, a galactic sized black hole, then you could get useful time dilation before the tides started to pull apart the protons in your atoms. That might possibly work.

So there is no way to speed up Planet A. But there is a way to slow down the Earth. It makes travelling between the two very expensive in terms of change of velocity. But then, you said that was powered by hand waving.

• Okay, so even though there would be time dilation effects it would be symmetric, so even if you bent space to get to planet A faster, handwaved and said now the effects due to time dilation aren't noticable, bent back, waited X years, and then bent it close again, it would be symmetric given no anomolies like a black hole. What about a black hole makes this not be symmetric then? Dec 9 '19 at 21:56
• Only one planet is near a black hole. It slows time only near itself. Dec 10 '19 at 15:07

# Just normal velocity Time Dilation would do it, this even solves the issue of why it doesn't happen when the planets are "connected"

If the earth is moving very fast in relation to the distant planet then time would move slower on earth than on the planet. But when they are close together, then they actually aren't moving very fast in relation to each other because the now shorter path between them.

• Um, what? "because the now shorter path between them" makes absolutely zero sense. Dec 9 '19 at 19:49
• @whn wormholes link points in spacetime, not space. The endpoints of the wormholes are still moving fast compared to one another. Dec 9 '19 at 19:52
• @whn perhaps you needed the magic tag instead of science-based and reality-check? Dec 9 '19 at 20:02
• @whn That's not how the "science based" tag works. The text of this answer is not how special relativity time dilation works. If two objects are moving relative to each other then each sees the other moving more slowly. This has to be true, or there would be an absolute frame of reference, which would invalidated special relativity. Dec 9 '19 at 20:59
• They said that the clock synchronization is handwaved, so having it return back to normal when the handwaving isn't happening should be fine. Dec 12 '19 at 16:02

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## Differences in the DNA between two individuals is known as? A. Snips B Cuts C. Crisps D. Tri

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# Properties

 Label 1040.2.da.b Level $1040$ Weight $2$ Character orbit 1040.da Analytic conductor $8.304$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1040 = 2^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1040.da (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.30444181021$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.22581504.2 Defining polynomial: $$x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{7}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + ( \beta_{1} + \beta_{2} - \beta_{4} - 2 \beta_{6} - \beta_{7} ) q^{3} + ( -\beta_{1} + \beta_{6} ) q^{5} + ( \beta_{4} - \beta_{5} + 3 \beta_{6} ) q^{7} + ( -1 - \beta_{1} - 2 \beta_{3} + 2 \beta_{4} + \beta_{5} + \beta_{7} ) q^{9} +O(q^{10})$$ $$q + ( \beta_{1} + \beta_{2} - \beta_{4} - 2 \beta_{6} - \beta_{7} ) q^{3} + ( -\beta_{1} + \beta_{6} ) q^{5} + ( \beta_{4} - \beta_{5} + 3 \beta_{6} ) q^{7} + ( -1 - \beta_{1} - 2 \beta_{3} + 2 \beta_{4} + \beta_{5} + \beta_{7} ) q^{9} + ( -1 + \beta_{1} + \beta_{2} + \beta_{3} + \beta_{7} ) q^{11} + ( \beta_{1} + \beta_{2} + 2 \beta_{3} - 2 \beta_{4} - \beta_{5} + \beta_{6} - \beta_{7} ) q^{13} + ( 1 + \beta_{1} + \beta_{3} - \beta_{4} ) q^{15} + ( -1 + 3 \beta_{1} + \beta_{4} - \beta_{6} + \beta_{7} ) q^{17} + ( -1 - \beta_{4} - 4 \beta_{6} ) q^{19} + ( 1 + 2 \beta_{3} - 4 \beta_{4} - 2 \beta_{5} + 2 \beta_{6} ) q^{21} + ( -1 + 2 \beta_{1} + 2 \beta_{2} + \beta_{3} + 2 \beta_{4} - 2 \beta_{5} - 2 \beta_{6} - 2 \beta_{7} ) q^{23} - q^{25} + ( 1 + 2 \beta_{1} + \beta_{3} - \beta_{4} + \beta_{5} + \beta_{6} ) q^{27} + ( -1 + 3 \beta_{1} + \beta_{2} + \beta_{3} - 2 \beta_{4} - 2 \beta_{5} - 4 \beta_{6} - \beta_{7} ) q^{29} + ( 2 - 2 \beta_{1} - 4 \beta_{4} + 2 \beta_{6} ) q^{31} + ( 4 + 3 \beta_{4} + \beta_{5} - 5 \beta_{6} ) q^{33} + ( -2 - \beta_{1} + 2 \beta_{4} - \beta_{7} ) q^{35} + ( \beta_{1} + \beta_{2} + 2 \beta_{3} - \beta_{4} + \beta_{7} ) q^{37} + ( -3 - \beta_{1} + 2 \beta_{2} + 3 \beta_{4} - \beta_{5} - 4 \beta_{6} + \beta_{7} ) q^{39} + ( 2 - 2 \beta_{1} - \beta_{4} ) q^{41} + ( 1 - 3 \beta_{1} - \beta_{4} + \beta_{6} - \beta_{7} ) q^{43} + ( -1 + \beta_{1} + 2 \beta_{2} - \beta_{5} - 2 \beta_{6} - \beta_{7} ) q^{45} + ( -2 - 2 \beta_{2} - 2 \beta_{3} + 6 \beta_{4} + 2 \beta_{5} + 4 \beta_{7} ) q^{47} + ( -1 + \beta_{1} + 5 \beta_{2} + \beta_{3} + \beta_{4} - 2 \beta_{5} - 5 \beta_{7} ) q^{49} + ( 1 - 2 \beta_{1} - \beta_{2} - \beta_{3} + \beta_{4} - \beta_{5} ) q^{51} + ( -4 + \beta_{2} - \beta_{3} + \beta_{4} - \beta_{5} ) q^{53} + ( -1 - \beta_{2} + \beta_{3} + \beta_{4} - 2 \beta_{5} + 2 \beta_{6} + \beta_{7} ) q^{55} + ( -1 - 6 \beta_{1} - \beta_{2} - 4 \beta_{3} + 6 \beta_{4} + 4 \beta_{5} + 3 \beta_{6} + 2 \beta_{7} ) q^{57} + ( \beta_{1} + 2 \beta_{2} + \beta_{4} - \beta_{5} + 2 \beta_{6} - \beta_{7} ) q^{59} + ( -8 + 3 \beta_{1} + 2 \beta_{3} + 7 \beta_{4} - \beta_{5} + \beta_{7} ) q^{61} + ( 1 - \beta_{1} + 3 \beta_{2} - 3 \beta_{3} + \beta_{4} + 3 \beta_{7} ) q^{63} + ( -1 - 2 \beta_{2} + \beta_{3} + \beta_{4} + 2 \beta_{6} + \beta_{7} ) q^{65} + ( -1 + 8 \beta_{1} + \beta_{3} ) q^{67} + ( -3 - 4 \beta_{1} - 4 \beta_{3} + 5 \beta_{4} + 2 \beta_{5} ) q^{69} + ( -3 + 3 \beta_{4} - 6 \beta_{5} + 2 \beta_{6} ) q^{71} + ( -4 + 4 \beta_{1} + \beta_{2} + 3 \beta_{3} + 5 \beta_{4} - 3 \beta_{5} - 2 \beta_{6} - 2 \beta_{7} ) q^{73} + ( -\beta_{1} - \beta_{2} + \beta_{4} + 2 \beta_{6} + \beta_{7} ) q^{75} + ( -5 + 2 \beta_{1} - \beta_{2} - 2 \beta_{3} + 2 \beta_{4} - 2 \beta_{5} + 5 \beta_{6} ) q^{77} + ( 4 - \beta_{2} + 3 \beta_{3} - 3 \beta_{4} + 3 \beta_{5} - 2 \beta_{6} ) q^{79} + ( 1 + 3 \beta_{1} - \beta_{2} - \beta_{3} + 2 \beta_{4} + 2 \beta_{5} - 8 \beta_{6} + \beta_{7} ) q^{81} + ( -2 + 2 \beta_{1} - 2 \beta_{3} + 6 \beta_{4} + 2 \beta_{5} - 4 \beta_{6} ) q^{83} + ( 1 + 2 \beta_{4} - \beta_{5} ) q^{85} + ( -6 - 12 \beta_{1} - 6 \beta_{3} + 9 \beta_{4} + 3 \beta_{5} + 5 \beta_{6} + 4 \beta_{7} ) q^{87} + ( -2 \beta_{1} + 4 \beta_{2} - 2 \beta_{3} + \beta_{4} + 4 \beta_{7} ) q^{89} + ( -4 + \beta_{1} - \beta_{2} + 3 \beta_{3} + 2 \beta_{4} - 2 \beta_{5} + 2 \beta_{6} - 5 \beta_{7} ) q^{91} + ( -2 + 2 \beta_{2} + 2 \beta_{3} + 2 \beta_{7} ) q^{93} + ( 4 + 2 \beta_{1} - 4 \beta_{4} - \beta_{6} ) q^{95} + ( -3 - \beta_{1} - 2 \beta_{2} - \beta_{4} - 2 \beta_{5} + 3 \beta_{6} + \beta_{7} ) q^{97} + ( 6 \beta_{1} + \beta_{2} - \beta_{3} + \beta_{4} + \beta_{5} - 8 \beta_{6} - 2 \beta_{7} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + O(q^{10})$$ $$8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97} + O(q^{100})$$

Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16$$:

 $$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$($$$$-\nu^{7} + 2 \nu^{6} - \nu^{5} - 4 \nu^{4} + 3 \nu^{3} + 2 \nu^{2} - 8 \nu + 8$$$$)/8$$ $$\beta_{2}$$ $$=$$ $$($$$$-\nu^{7} + 3 \nu^{6} - \nu^{5} - 3 \nu^{4} + 5 \nu^{3} + 3 \nu^{2} - 12 \nu + 12$$$$)/4$$ $$\beta_{3}$$ $$=$$ $$($$$$\nu^{7} - 2 \nu^{6} + 4 \nu^{4} - 2 \nu^{3} - 6 \nu^{2} + 11 \nu - 4$$$$)/2$$ $$\beta_{4}$$ $$=$$ $$($$$$-3 \nu^{7} + 7 \nu^{6} - 3 \nu^{5} - 11 \nu^{4} + 15 \nu^{3} + 11 \nu^{2} - 40 \nu + 32$$$$)/4$$ $$\beta_{5}$$ $$=$$ $$($$$$-2 \nu^{7} + 5 \nu^{6} - 3 \nu^{5} - 7 \nu^{4} + 11 \nu^{3} + 7 \nu^{2} - 27 \nu + 22$$$$)/2$$ $$\beta_{6}$$ $$=$$ $$($$$$7 \nu^{7} - 20 \nu^{6} + 11 \nu^{5} + 30 \nu^{4} - 45 \nu^{3} - 28 \nu^{2} + 116 \nu - 88$$$$)/8$$ $$\beta_{7}$$ $$=$$ $$($$$$9 \nu^{7} - 22 \nu^{6} + 13 \nu^{5} + 32 \nu^{4} - 47 \nu^{3} - 30 \nu^{2} + 132 \nu - 104$$$$)/8$$
 $$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$($$$$\beta_{7} + \beta_{5} + \beta_{1} + 1$$$$)/2$$ $$\nu^{2}$$ $$=$$ $$($$$$\beta_{7} + 2 \beta_{5} - \beta_{4} - \beta_{3} - \beta_{2} - 3 \beta_{1} + 3$$$$)/2$$ $$\nu^{3}$$ $$=$$ $$($$$$2 \beta_{7} + \beta_{5} + 3 \beta_{4} + \beta_{3} - \beta_{2} - 2 \beta_{1} - 2$$$$)/2$$ $$\nu^{4}$$ $$=$$ $$($$$$-\beta_{7} + 2 \beta_{6} + \beta_{5} + 2 \beta_{2} - 7 \beta_{1} - 1$$$$)/2$$ $$\nu^{5}$$ $$=$$ $$($$$$\beta_{7} - 4 \beta_{5} + 7 \beta_{4} + \beta_{3} + 3 \beta_{2} - 3 \beta_{1} - 3$$$$)/2$$ $$\nu^{6}$$ $$=$$ $$($$$$-2 \beta_{6} - \beta_{5} - 5 \beta_{4} - \beta_{3} + 9 \beta_{2} + 2 \beta_{1} - 2$$$$)/2$$ $$\nu^{7}$$ $$=$$ $$($$$$3 \beta_{7} - 12 \beta_{6} - 3 \beta_{5} - 10 \beta_{4} - 2 \beta_{3} + 2 \beta_{2} - \beta_{1} + 11$$$$)/2$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$417$$ $$561$$ $$911$$ $$\chi(n)$$ $$1$$ $$1$$ $$1 - \beta_{4}$$ $$1$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
641.1
 1.20036 − 0.747754i −1.27597 − 0.609843i 0.665665 + 1.24775i 1.40994 + 0.109843i 1.20036 + 0.747754i −1.27597 + 0.609843i 0.665665 − 1.24775i 1.40994 − 0.109843i
0 −1.41342 + 2.44811i 0 1.00000i 0 1.64996 0.952606i 0 −2.49551 4.32235i 0
641.2 0 −0.800098 + 1.38581i 0 1.00000i 0 0.287734 0.166123i 0 0.219687 + 0.380509i 0
641.3 0 0.0473938 0.0820885i 0 1.00000i 0 4.18016 2.41342i 0 1.49551 + 2.59030i 0
641.4 0 1.16612 2.01978i 0 1.00000i 0 −3.11786 + 1.80010i 0 −1.21969 2.11256i 0
881.1 0 −1.41342 2.44811i 0 1.00000i 0 1.64996 + 0.952606i 0 −2.49551 + 4.32235i 0
881.2 0 −0.800098 1.38581i 0 1.00000i 0 0.287734 + 0.166123i 0 0.219687 0.380509i 0
881.3 0 0.0473938 + 0.0820885i 0 1.00000i 0 4.18016 + 2.41342i 0 1.49551 2.59030i 0
881.4 0 1.16612 + 2.01978i 0 1.00000i 0 −3.11786 1.80010i 0 −1.21969 + 2.11256i 0
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 881.4 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.e even 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1040.2.da.b 8
4.b odd 2 1 65.2.m.a 8
12.b even 2 1 585.2.bu.c 8
13.e even 6 1 inner 1040.2.da.b 8
20.d odd 2 1 325.2.n.d 8
20.e even 4 1 325.2.m.b 8
20.e even 4 1 325.2.m.c 8
52.b odd 2 1 845.2.m.g 8
52.f even 4 1 845.2.e.m 8
52.f even 4 1 845.2.e.n 8
52.i odd 6 1 65.2.m.a 8
52.i odd 6 1 845.2.c.g 8
52.j odd 6 1 845.2.c.g 8
52.j odd 6 1 845.2.m.g 8
52.l even 12 1 845.2.a.l 4
52.l even 12 1 845.2.a.m 4
52.l even 12 1 845.2.e.m 8
52.l even 12 1 845.2.e.n 8
156.r even 6 1 585.2.bu.c 8
156.v odd 12 1 7605.2.a.cf 4
156.v odd 12 1 7605.2.a.cj 4
260.w odd 6 1 325.2.n.d 8
260.bc even 12 1 4225.2.a.bi 4
260.bc even 12 1 4225.2.a.bl 4
260.bg even 12 1 325.2.m.b 8
260.bg even 12 1 325.2.m.c 8

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
65.2.m.a 8 4.b odd 2 1
65.2.m.a 8 52.i odd 6 1
325.2.m.b 8 20.e even 4 1
325.2.m.b 8 260.bg even 12 1
325.2.m.c 8 20.e even 4 1
325.2.m.c 8 260.bg even 12 1
325.2.n.d 8 20.d odd 2 1
325.2.n.d 8 260.w odd 6 1
585.2.bu.c 8 12.b even 2 1
585.2.bu.c 8 156.r even 6 1
845.2.a.l 4 52.l even 12 1
845.2.a.m 4 52.l even 12 1
845.2.c.g 8 52.i odd 6 1
845.2.c.g 8 52.j odd 6 1
845.2.e.m 8 52.f even 4 1
845.2.e.m 8 52.l even 12 1
845.2.e.n 8 52.f even 4 1
845.2.e.n 8 52.l even 12 1
845.2.m.g 8 52.b odd 2 1
845.2.m.g 8 52.j odd 6 1
1040.2.da.b 8 1.a even 1 1 trivial
1040.2.da.b 8 13.e even 6 1 inner
4225.2.a.bi 4 260.bc even 12 1
4225.2.a.bl 4 260.bc even 12 1
7605.2.a.cf 4 156.v odd 12 1
7605.2.a.cj 4 156.v odd 12 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{8} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(1040, [\chi])$$.

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{8}$$
$3$ $$1 - 10 T + 106 T^{2} + 56 T^{3} + 55 T^{4} + 8 T^{5} + 10 T^{6} + 2 T^{7} + T^{8}$$
$5$ $$( 1 + T^{2} )^{4}$$
$7$ $$121 - 726 T + 1606 T^{2} - 924 T^{3} + 75 T^{4} + 84 T^{5} - 2 T^{6} - 6 T^{7} + T^{8}$$
$11$ $$1089 - 990 T^{2} + 867 T^{4} - 30 T^{6} + T^{8}$$
$13$ $$28561 + 2704 T^{2} + 1248 T^{3} + 30 T^{4} + 96 T^{5} + 16 T^{6} + T^{8}$$
$17$ $$169 - 130 T + 334 T^{2} + 128 T^{3} + 331 T^{4} - 16 T^{5} + 22 T^{6} + 2 T^{7} + T^{8}$$
$19$ $$( 169 - 78 T - T^{2} + 6 T^{3} + T^{4} )^{2}$$
$23$ $$89401 - 43654 T + 23110 T^{2} - 5104 T^{3} + 1795 T^{4} - 352 T^{5} + 94 T^{6} - 10 T^{7} + T^{8}$$
$29$ $$1 - 40 T + 1618 T^{2} + 704 T^{3} + 643 T^{4} - 64 T^{5} + 82 T^{6} + 8 T^{7} + T^{8}$$
$31$ $$( 64 + 32 T^{2} + T^{4} )^{2}$$
$37$ $$1 + 66 T + 1402 T^{2} - 3300 T^{3} + 2367 T^{4} + 300 T^{5} - 38 T^{6} - 6 T^{7} + T^{8}$$
$41$ $$( 1 + 6 T + 11 T^{2} - 6 T^{3} + T^{4} )^{2}$$
$43$ $$169 + 130 T + 334 T^{2} - 128 T^{3} + 331 T^{4} + 16 T^{5} + 22 T^{6} - 2 T^{7} + T^{8}$$
$47$ $$1763584 + 350464 T^{2} + 14304 T^{4} + 208 T^{6} + T^{8}$$
$53$ $$( -48 + 36 T^{2} + 12 T^{3} + T^{4} )^{2}$$
$59$ $$9 - 108 T + 486 T^{2} - 648 T^{3} + 183 T^{4} + 216 T^{5} + 30 T^{6} - 12 T^{7} + T^{8}$$
$61$ $$1590121 + 1215604 T + 603958 T^{2} + 178096 T^{3} + 38311 T^{4} + 5296 T^{5} + 526 T^{6} + 28 T^{7} + T^{8}$$
$67$ $$7667361 - 847314 T - 284454 T^{2} + 34884 T^{3} + 9615 T^{4} - 684 T^{5} - 102 T^{6} + 6 T^{7} + T^{8}$$
$71$ $$109767529 - 2263032 T - 2268434 T^{2} + 47088 T^{3} + 37047 T^{4} - 218 T^{6} + T^{8}$$
$73$ $$2930944 + 404608 T^{2} + 16944 T^{4} + 232 T^{6} + T^{8}$$
$79$ $$( 4432 + 640 T - 132 T^{2} - 8 T^{3} + T^{4} )^{2}$$
$83$ $$36864 + 73728 T^{2} + 7104 T^{4} + 192 T^{6} + T^{8}$$
$89$ $$78375609 + 34420464 T + 3179718 T^{2} - 816480 T^{3} + 4143 T^{4} + 5040 T^{5} - 18 T^{6} - 24 T^{7} + T^{8}$$
$97$ $$196249 + 71766 T - 16946 T^{2} - 9396 T^{3} + 2187 T^{4} + 1740 T^{5} + 358 T^{6} + 30 T^{7} + T^{8}$$


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# How NewsBeast Labs Visualized Roe V' Wade

The following post was initially published on the NewsBeast Labs tumblr, and comes to us via Michael Keller, senior data reporter at Newsweek & the Daily Beast.

Michael is a reporter, designer and programmer working on ways to create interactive stories that let readers see how they fit into the story and, in reader feedback stories, ways to see how readers lives have intersected with the story’s subject matter. What follows is a repost from their blog.

Last month we published a package of stories marking the fortieth anniversary of the Roe v. Wade decision. It had a few moving parts but I’ll just go over some of them briefly here.

### How it started

This summer you probably heard the story about the last abortion clinic in Mississippithat was threatened to close due to stricter state laws. Allison Yarrow, who sat across from me at the time, was covering the story and it got us thinking: the line “The Last Abortion Clinic in Mississippi” is attention grabbing, but it doesn’t tell the whole story. That is to say, what you really want to know is how far are people away from their nearest clinic, regardless of state boundaries. One state may have five clinics but if they’re all in the southwest corner of the state and you live in the northeast corner, and your adjoining states have multiple clinics but only at their borders farthest from you, then you’ll have a hard time getting to a clinic, even if you had many in your state. To see where this might be the case and where access to services was compounded by new restrictive provisions (over 150 nationally in the past two years) we made as close to a comprehensive database as possible of every abortion clinic. Our goal was to see what parts of the country were farthest from a clinic. From start to finish, this process took about six months.

We got our address data from a variety of publicly available sources: Planned Parenthood, the National Abortion Federation, anti-abortion websites that keep their own lists and others. We needed to verify that the address information was correct, though, so we called over 750 clinics to confirm. We also asked them up to how many weeks they offer services. The resulting database is the only one of its kind that we know of. The Guttmacher Institute undertook an abortion provider census in 2008 but they didn’t separate clinics from hospitals from private doctors offices, which represent different levels of care that we thought was an important distinction.

### What it became

We started this in July and the project evolved. We thought the election might bring the issue of abortion access to the fore but it didn’t and that gave us more time. Allison brought up the fortieth anniversary of Roe v. Wade and that let us think much bigger about the project. Because this was such a personal subject matter, we knew readers’ comments would feature prominently (from both sides of the issue) and we wanted a strong narrative component, too.

To give a human voice to the Geography of Abortion Access map, Allison flew to Wichita, Kansas, one of the areas that stood out both on our map, as a metro area far from a clinic, as well as in recent memory as the site of the 2008 murder of late-term abortion provider George Tiller. To add a broader perspective, Sam Register who runs the Newsweek Archivist tumblr went through the Newsweek archives so people could follow the topic’s coverage from the 70s through the 00s.

### What we learned from reader’s stories

Over the course of the week, we shifted the question we were asking from why do you support or oppose legal abortion to a conversation about pro-life and pro-choice labels as a way to get more nuanced opinions and show the complexity of the issue. We asked readers to complete either the phrase “I’m pro-life but…” or “I’m pro-choice but…” We got more responses from our other reader-based projects but we were happy in how thoughtful and honest people were. Read our roundup of interesting responses to those questions as well as our free form “Tell us your story” prompt here.

### Under the hood on the map

How to represent this dataset was tricky. We had three main issues: anonymity, unbiased geography, and context.

Anonymity: Although we got our data from publicly available websites that anyone could find and was often information that anti-abortion groups already held, we weren’t comfortable publishing addresses, names, or exact latitudes and longitudes. We took great care to do things like scrub our final database of anything identifiable and we partially randomized each clinic’s location so they weren’t pinpoint-able from our map. On the presentation level, we added the magenta circle big enough to span multiple hexagons (our base geography layer) to let people know that an address was approximate. Even if you backtrack and find our database, you won’t get any information that would let you de-anonymize the data.

Unbiased geography: As I wrote above, we wanted to get away from the arbitrary state and county borders that most all of the research we encountered was based on. We did some initial plots using Census tracts but that presents exactly the same problem [photo]. We ended up making a hexagonal grid using the Repeating Shapes plugin for ArcMap, which lets you make a grid out of your choice of shape and size. The trick to making a hexagonal grid for the web so that the hexagons will be regular (all sides equal) no matter what degree of latitude they fall on is to make the grid in your output projection, Web Mercator EPSG: 3857. You can reproject it to do your analysis in whatever you like, but because it will eventually be displayed in Web Mercator, it will need to be created in that so as not to come out distorted in the browser. If you want a 20,000 meter in diameter hexagonal grid, here’s the one we used: Shapefile, KML, GeoJSON.

And here’s another one that Brian Abelson, current Knight-Mozilla Fellow at the New York Times, made while he was helping out on the project. They are also 20,000 meter hex grids. This one has the state borders preserved in case you want to assign state values to each hexagon: Shapefile, KML, GeoJSON.

Context: Generating our distance map wasn’t enough to tell a story with. We added three other pieces of information that would walk people through the significance of the patterns they were seeing. The first was a map of female population aged 15-44 so that people could see the areas where women lived that were farthest away from clinics and identify significant metro areas (the pink dot density overlay). The second was the different legal restrictions that each area was subject to (areas with highlighted transparency). Again, this was an interesting way to visualize this data because we didn’t highlight every hexagon in Kansas, for example, to show that certain laws were applicable in Kansas. Instead, we highlighted hexagons whose closest clinic was in Kansas. This gave us a very realistic map so that people could see what state laws they would be subject to if their nearest clinic was across state lines. It also visually demonstrates how state laws can affect people that don’t live in that state. And third, we selected our own highlights from going through the data, such as the areas where telemedicine is banned in conjunction with mandatory in-person counseling. The combination of these laws in Arizona, for instance, means some women travel over a hundred miles and spend two days to get a prescription for the abortion bill.

### More under the hood

The map itself we built using CartoDB, which allowed us to very flexibly add the different highlighted views of the map without rebaking our tiles each time.The slider that shows clinics that only offer services up to X weeks we did by loading four tile layers on top of each other at once and show/hiding them depending on the slider value. This made the map slightly slower on initial load but it made the transitions between map states super fast — so a trade-off.

For the highlighted states, those restyle and reload all four map layers as well. We used Leaflet.js’s ability to plot vectors to draw the line between the hexagon you’re hovering over and the closest clinic to provide some more descriptive interaction.

A few months ago we spoke with Andrew Hill, Senior Scientist at Vizzuality (who makes CartoDB) on some experimental ways to map the data. The line on hover came out of some of his renderings and you can see in the photos below some of the experimental line styles.

All in all it was a lot of team work, Allison, Abby, Brian, Caitlin, Lizzie, Sam and a number of other people all helped with parts of it over the course of six months. If you have any other questions about it, let me know at michael.keller@newsweekdailybeast.com

- Michael

Before we settled on the Value-by-alpha approach for showing the different state laws, some failures:

We tried outlining the different shapes and showing them in different colors:

We tried coloring the hexagon outline by the different laws that were in effect. Creating a sensical hierarchy proved difficult:

Highlighting Peurto Rico:

A value-by-alpha chart where census tracts are shaded by their percentage of women of reproductive age. Unfortunately, it’s not that intelligible and the heat map overlay is a much cleaner way of showing this relationship:

Before we made the hexagon grid, how the map looks if you use census tracts:

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Question

# Type of colloid in which dispersed phase is solid and dispersion medium is liquid is called____

A
sol
B
col
C
solution
D
all of the above

Solution

## The correct option is A solThe components of the colloidal solution are dispersed phase and dispersed medium. Dispersed particles (solute like a component) in a colloid form a dispersed phase and the component in which dispersed phase particles are suspended is called dispersing medium. Depending upon the physical state of the dispersed phase and dispersed medium the type of colloid is decided. Colloids in which dispersed phase is solid and dispersing medium is liquid is called $$\text{Sol}$$.For example Milk of magnesia, mud, etc.Chemistry

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IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

## Graph Pressing Sequences and Binary Linear Algebra, Updated

• Oct. 13, 2017
• 2:30 p.m.
• LeConte 310

## Abstract

One can construct a useful metric on genome sequences by computing minimal-length sortings of (signed) permutations by reversals. Hannenhalli and Pevzner famously showed that such sorting sequences are essentially equivalent to a certain sequences of operations -- vertex pressing'' -- on bicolored (aka loopy, aka simple pseudo-) graphs. We examine the matrix algebra over GF(2) that arises from the theory of such sequences, providing a collection of equivalent conditions for their existence and showing how linear algebra, poset theory, and group theory can be used to study them. We discuss enumeration, characterization, and recognition of uniquely pressable graphs (those with exactly one pressing sequence); relations on pressing sequences that have a surprisingly diverse set of characterizations; and some open problems. Joint work with Hays Whitlatch.

© Interdisciplinary Mathematics Institute | The University of South Carolina Board of Trustees | Webmaster


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# What exactly is the relationship between the algebraic formulation of Quantum Mechanics and the geometric formulation of Classical Mechanics?

Okay so if we consider a particular physical system, the classical description of the system starts by first introducing a symplectic manifold, which is the cotangent bundle of a configuration manifold. There is the canonical Poisson Bracket which forms an algebra of functions on the manifold (i.e. the observables) and the time evolution of an observable $f$ is just $\{H,f\}$ where $H$ is the Hamiltonian.

If we want to describe the same physical system from a Quantum Mechanical perspective, we introduce a Hilbert space whose equivalence class of normalised elements correspond to the physical states. The algebra of observables on the Hilbert space form a non-commutative algebra with the time evolution described by Schrodinger's Equation. So I understand the motivation for introducing both formalisms but how do I relate these constructions?

How is the Hilbert Space related to the phase space manifold? The process of quantization replaces the poisson brackets with commutators but I don't understand what this implies for the underlying structures. Most people say that it's a hopeless task to go from Classical Mechanics to Quantum Mechanics because you've lost a lot of information but it's not at all clear to me whether this is actually the case. If anything it feels like Quantum Mechanics arises from discarding away some information from classical description, thereby quantizing it. And even if this is not the case and you do in fact lose information, the process of quantization proves that there is a systematic way of recovering this information because Quantization works independent of the specific system under consideration.

Now I know that every manifold can be understood through its algebra of functions but the algebra of functions on a manifold is always defined pointwise so its naturally commutative. In Quantum Mechanics we start with non-commutative algebra of functions so I'm assuming you can't think of it as an algebra of functions over some geometric manifold. If they're not related in any way, then how can anyone convincingly say that Quantum Mechanics reduces to Classical Mechanics on the macroscopic scale.

• – Qmechanic Mar 12 '17 at 22:40
• Indeed, phase-space quantum mechanics will allow you to compare apples with apples, instead of with oranges. In that formulation, it is easier to see how the classical entropy of a system exceeds its quantum entropy, once a proper shift of the integration measures is readjusted; this indicates forfeiture of information in the $\hbar \to 0$ limit. – Cosmas Zachos Mar 13 '17 at 0:51


text: Usage. 3) What is the relationship between the degree of a polynomial function and the maximum number of turning points in its graph? Facts ; Code ; Dictionary ; Download ; Constants ; Excel ; Theorems ; 4th Degree Equation Solver . VALUE OF POLYNOMIAL• If p(x) is a polynomial in x, and if k is any real constant, then the real number obtained by replacing x by k in p(x), is called the value of p(x) at k, and is denoted by p(k) . If it forms a straight line, the Polynomial Regression Channel won’t work. Term: A term consists of numbers and variables combined with the multiplication operation, with the variables optionally having exponents. Mark as New; Bookmark; Subscribe; Mute; Subscribe to RSS Feed; Permalink; Print; Email to a Friend; Report Inappropriate Content; Re: Degrees of … Google Charts - Polynomial Trendlines - Following is an example of a polynomial trendlines chart. For instance, we rewrite as C. 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Calculating the degree of a polynomial with symbolic coefficients. You may click on the cell to select or deselect a number. 3. Positive & negative intervals of polynomials. Zeros of polynomials (multiplicity) Practice: Zeros of polynomials (multiplicity) Zeros of polynomials & their graphs. Hi All, When will you use Polynomial 2nd 3rd or 4th degree in charts? In the given example, the first term is 7x, whereas the second term is -5. To improve this 'Hermite polynomial (chart) Calculator', please fill in … 5.full: bool. d) The sign chart is shown below; e) Using the information on the zeros and the sign chart, the graph of P is as shown below with x and y intercepts labeled. 6 Replies Highlighted. The term whose exponents add up to the highest number is the leading term. • Zero or root: A … Degree of a Polynomial with More Than One Variable. D. Multiplying Polynomials By … Example: what … A general form of fourth-degree equation is ax 4 + bx 3 + cx 2 + dx + e = 0. Start out by adding the exponents in each term. Charts ; Examples ; Tutorials ; Answers ; Others . These are the main datasets utilized in the rest of the calculations. If the graph … Example 4 x = 1 is a zero of multiplicity 2 of polynomial P defined by P (x) = x 5 + x 4 - 3 x 3 - x 2 + 2 x. Construct a sign chart for P and graph it. The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7. Example: Find the degree of 7x – 5. End behavior of polynomials. Since the … Degree of a Polynomial. … Polynomials with degree n > 5 are just called n th degree polynomials. Hermite polynomial (chart) Home / Special Function / Orthogonal polynomial; Calculates a table of the Hermite polynomial H n (x) and draws the chart. How To: Given a graph of a polynomial function of degree $n$, identify the zeros and their multiplicities. Tags (2) Tags: bar chart. However, as the polynomial degree increases, the coefficient bounds associated with the higher degree terms cross zero, which suggests over fitting. Next, data arrays are populated for the x-axis and y-axis values. You can also find some theory about the Newton … The exponent for the first term 7x is 1 and for the second term -5, it is 0. A … Next lesson. Zeros of polynomials & their graphs. Sort by: Top Voted. chartscript. Some examples: $\begin{array}{l}p\left( x \right): & {x^3} - 6{x^2} + 11x - 6\\q\left( y \right): & 27{y^3} - 1\\r\left( z \right): & \pi {z^3} + {\left( {\sqrt 2 } \right)^{10}}\end{array}$ We observe that a cubic polynomial can have at the most four terms. The degree of the polynomial is the power of x in the leading term. I would have expected at least one of the zeroes to be repeated, thus showing flattening as the graph flexes through the axis. The … Cells with selected numbers are blue; others are white. Degree. 4. rcond: float. This parameter defines the degree of polynomial. It also calculates an interpolated value for entered points and plots a chart. 10. The Excel Linest function and polynomial chart trendline produce different results for 6th order polynomials in the cases examined. Find 2. • The exponent of the term with the highest power in a polynomial is known as its degree. This an optional parameter that switches the determining nature of the return value. Degree 3, 4, and 5 polynomials also have special names: cubic, quartic, and quintic functions. Bands are present above and below the regression line between multiples of standard deviation. The number of active cells is equal to N. Numbers are arranged in reverse order. Polynomial Degree: maximum (not total) term degree the degree is the degree is 2. Questionnaire. Polynomial Regression is a form of linear regression in which the relationship between the independent variable x and dependent variable y is modeled as an nth degree polynomial. It uses a polynomial degree (1-6) and a number of bars to analyze data. When a polynomial has more than one variable, we need to look at each term. Example: Figure out the degree of 7x 2 y 2 +5y 2 x+4x 2. Analyze polynomial degree chart and y-axis values terms present in the polynomial Regression Channel bands... Exponents in each term to identity trends on the cell to select or deselect a number of terms and.. Channel uses bands to identity trends on the cell to select or deselect number. A sixth-degree polynomial 's graph second term is 7x, whereas the second term -5, it is otherwise as... The relationship between the degree of polynomial degree chart positive cubic 4 ) Explain how the factored form of polynomial. Appears polynomial degree chart linear at the intercept, it is otherwise called as a biquadratic equation quartic. By adding the exponents or powers over the various terms present in polynomial... Can also find some theory about the Newton … the degree of of... 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Line between multiples of standard deviation expression with a single zero variables combined with the highest exponent the!, let us define the exponent of the polynomial letters as coefficients about the Newton … polynomial! N th degree binomial operation, with the highest term degree to the highest exponent is power! Than one variable, we rewrite as C. Adding/Subtracting polynomials we combine like terms before. Nd degree trinomial smaller than this relative to the the lowest look at each.. Term whose exponents polynomial degree chart up to the the lowest term -5, it is the! With a single zero, respectively return value functions, respectively leading coefficient of this polynomial... ) Zeros of polynomials by number of terms and degree highest term degree to the highest number is 4!


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[0805.2384] Current status of the CLIO project

Authors: K Yamamoto, T Uchiyama, S Miyoki, M Ohashi, K Kuroda, H Ishitsuka, T Akutsu, S Telada, T Tomaru, T Suzuki, N Sato, Y Saito, Y Higashi, T Haruyama, A Yamamoto, T Shintomi, D Tatsumi, M Ando, H Tagoshi, N Kanda, N Awaya, S Yamagishi, H Takahashi, A Araya, A Takamori, S Takemoto, T Higashi, H Hayakawa, W Morii, J Akamatsu

Date: 15 May 2008

Abstract: CLIO (Cryogenic Laser Interferometer Observatory) is a Japanese gravitational wave detector project. One of the main purposes of CLIO is to demonstrate thermal-noise suppression by cooling mirrors for a future Japanese project, LCGT (Large-scale Cryogenic Gravitational Telescope). The CLIO site is in Kamioka mine, as is LCGT. The progress of CLIO between 2005 and 2007 (room- and cryogenic-temperature experiments) is introduced in this article. In a room-temperature experiment, we made efforts to improve the sensitivity. The current best sensitivity at 300 K is about $6 \times 10ˆ{-21} /\sqrt{\rm Hz}$ around 400 Hz. Below 20 Hz, the strain (not displacement) sensitivity is comparable to that of LIGO, although the baselines of CLIO are 40-times shorter (CLIO: 100m, LIGO: 4km). This is because seismic noise is extremely small in Kamioka mine. We operated the interferometer at room temperature for gravitational wave observations. We obtained 86 hours of data. In the cryogenic experiment, it was confirmed that the mirrors were sufficiently cooled (14 K). However, we found that the radiation shield ducts transferred 300K radiation into the cryostat more effectively than we had expected. We observed that noise caused by pure aluminum wires to suspend a mirror was suppressed by cooling the mirror.

May 16, 2008

0805.2384 (/preprints)
2008-05-16, 09:39


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system - Maple Help

system

invoke a command in the host operating system

 Calling Sequence system(command) system[launch](command,arguments)

Parameters

 command - string arguments - sequence of strings, and/or small integers

Description

 • The function system passes command to the host operating system which performs the appropriate function.
 The result is the return status of the command performed, which is operating system dependent, but usually 0 indicates success and any other value indicates failure.
 Note: On some operating systems, some operating system commands may not be accessible via this mechanism.
 • The function system[launch] spawns a new process before executing command via Windows' CreateProcess or Unix-style fork/exec system calls.  The given command should specify an application or executable file, not a shell or DOS command.
 The new process, as specified by command and zero or more arguments, is started outside Maple.  The Maple process continues as usual; it does not wait for the new process to finish.
 If an error occurs trying to start the new process, system[launch] may not report any messages as to the cause of the error.
 The specified executable file is searched for in the same set of directories as commands entered on the system command line. This set of directories is determined by the PATH environment variable. If the executable file is not found in one of the directories in PATH, it can still be run by providing the full path to the file.
 system[launch] will return the process id of the spawned process.
 • To disable system calls, the -z option can be used when launching Maple. For more details see maple.

 • The system command is thread-safe as of Maple 15.
 > $\mathrm{system}\left("echo test"\right)$
 > $\mathrm{system}\left[\mathrm{launch}\right]\left("notepad"\right)$
 > $\mathrm{system}\left[\mathrm{launch}\right]\left("xterm","-title","My Title"\right)$