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differential equations March 2nd 2008, 09:41 AM #1 Newbie Joined Mar 2008 Posts 15 differential equations Can anyone help with this? x''+9x'+20x=29+20t+6e^(-2t) i) Obtain the solution x(t) as the sum of the solutions obtained when each component is considered individually in turn. ii) Solve...
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Section 17.5 Lecture Notes EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today’s Objectives: Students will be able to analyze the planar kinetics of a rigid In-Class Activities: body undergoing general plan...
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Feynman Kac Formula as appears in Krzysztof Gawedzki's Lectures on conformal field theory up vote 5 down vote favorite 3 The lecture notes appeared in the second volume of "Quantum Fields and Strings, a course for mathematicians". I would like to understand the derivation of (1.3), the 2-point correlation function: $...
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Proofs of the Theorems on Circumscribable Quadrilaterals August 17th 2010, 08:42 PM Vlasev Observe the following illustration. We have the quadrilateral ABCD. The quadrilateral's incircle's center is pt. O. Then there are the two incircles of the triangles formed by the diagonal. P,Q,R and S are the points wh...
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Simple proving the inequalities September 8th 2010, 04:48 PM #1 Member Joined Jan 2010 Posts 88 Simple proving the inequalities |x| ≤ 1 ⇒ |x^2 − x − 2| ≤ 3|x + 1| im guessing you factor it and cancel out the x+1 then im left with this |x-2| ≤ 3 What do i do from there? $|x - 2| = |x + (-...
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How to compute $\mathcal{Ext}^{i}_{X}(\mathcal{O}_{Y_{1}},\mathcal{O}_{Y_{2}})$? up vote 2 down vote favorite 1 Given a smooth variety $X$ and two smooth subvarieties $Y_{1},Y_{2} \subset X$ with smooth intersection $Z=Y_{1} \cap Y_{2}$, I'd like to compute $\mathcal{Ext}^{i}_{X}(\mathcal{O}_{Y_{1}},\mathcal {O}_{Y_{2...
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Continuous function problem November 13th 2006, 01:59 PM #1 Super Member Joined Mar 2006 Posts 705 Thanks 2 Continuous function problem Q: Suppose that f: [0,2] -> [0,4] is continuous. Show that there is an x $\epsilon$[0,2] such that $f(x) = 2x$. Proof: All I know is use the intermediate value ...
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Identifying $T^* Bun_G$ with Higgs bundles up vote 1 down vote favorite 1 Let $G$ be a semisimple algebraic group, $C$ be a smooth projective curve, and $\omega$ be canonical line bundle. The stack $Higgs_{\omega}$ is defined as the stack associating to each $S$ the groupoid consisting of $(E, \phi)$, where $E$ is a ...
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Expected distance between two points with missing coordinates up vote 3 down vote favorite What is the expected distance between two points when one of the points has some unknown (or missing) coordinate values? The two points are in the same finite dimensional real space. Assume that the probability density function...
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Sum of squares of determinants of principal minors up vote 5 down vote favorite 3 I am interested in computing the sum of squares of determinants of principal minors. Let $A$ be an $n\times n$ positive semidefinite matrix and $A_S$ be a principal minor of $A$ indexed by the set $S \subseteq \{1,\ldots,n\}$. The classi...
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[SOLVED] finding surface area using parametric equations March 20th 2010, 06:50 PM #1 Newbie Joined Oct 2009 Posts 10 [SOLVED] finding surface area using parametric equations The question reads Find the surface area generated by rotating x=e^t -t & y=4e^t for 0 to 1 (this is in terms of t) about the ...
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A. Intervals >> << Ndx Usr Pri JfC LJ Phr Dic Rel Voc !: wd Help Phrases 4A. Intervals It is a common need in programming to have to test whether a given number x lies between two other numbers a and b, with a less than b, called the lower boundary and upper boundary. The numbers that lie between the boundaries are c...
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binomial thm October 8th 2008, 09:00 AM #1 binomial thm Write down the first three terms in the expansion, in descending powers of x, of [ax-(b/x^3)]^8. Hence evaluate the term independent of x of [5x-(1/x^3)]^8. I dunno how to do the Hence part, making use of the terms in the expansion. In this expansi...
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Prove using set algebra Prove using set algebra: A U B = (A ∩ B') U (A' ∩ B) U (A ∩ B) Hello, mathman11! Prove using set algebra: . $A \cup B \;=\; (A \cap B') \cup (A' \cap B) \cup (A \cap B)$ There are two rules for which I do not know the names. I will call them: . $\begin{Bmatrix}S \cup S' \:=\:U && \text{Property...
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Geometric interpretation of the half-derivative? up vote 25 down vote favorite 13 For $f(x)=x$, the half-derivative of $f$ is $$\frac{d^{\frac{1}{2}}}{dx^{\frac{1}{2}}} x = 2 \sqrt{\frac{x}{\pi}} \;.$$ Is there some geometric interpretation of (Q1) this specific derivative, and, ( Q2) of the half-derivative more gener...
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Homework Help Posted by jessica on Saturday, February 16, 2013 at 7:29am. if log x base a,log y base a and log z base a are three consecutive terms of an AP,show that x,y and z are consecutive terms of a GP • math - Reiny, Saturday, February 16, 2013 at 8:03am let A = log[a]x ---> x = a^A let B = log[a]y -...
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Bearing questions - plz help May 23rd 2010, 03:50 AM dee2020 Bearing questions - plz help(SOLVED) 1.A hiker walks due north from A and after 8km reaches B. She then walks a further 8km on a bearing of 120degrees to C. Work out a the distance from A to C and b the bearing of C from A. 2.A helicopter flies on...
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A Proof that the Natural Numbers Form a pca? up vote 5 down vote favorite 1 It is known that the set of natural numbers with the operation ab = {a}b, where {a} represents the index of a recursive function, forms a partial combinatory algebra (pca). All the references I have so far consulted mention the set of natural ...
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Proof of Hartshorne Proposition II 6.8 up vote 5 down vote favorite 1 I would like to ask one question (maybe very simple) about the proof of Proposition II 6.8 in Hartshorne's book Algebraic Geometry page 137. The question is about the proof of the finiteness of non-trivial morphisms between two projective non-singul...
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Sine integral $\int_{-\infty}^{+\infty}\frac{\sin x}x\,dx = \int_{-\infty}^0 \frac{\sin x}x\,dx + \int_0^{+\infty} \frac{\sin x}x\,dx$ $= \lim_{a \rightarrow -\infty} \int_a^0 \frac{\sin x}x\,dx + \lim_{b \ rightarrow +\infty} \int_0^b \frac{\sin x}x\,dx$ now, integrate by parts.. continue.. I don't think sin(x)/x is ...
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Solve by finding an inverse for 7 February 28th 2010, 07:46 PM #1 Super Member Joined Feb 2008 Posts 535 Solve by finding an inverse for 7 Solve 7x = 11 mod 9 by finding an inverse for 7. (= is congruence not equality) I'm trying to do this by using the euclidean algorithm: 9 = 1(7) + 2 7 =...
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jan93 Noesis The Journal of the Mega Society ...
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Aqueeze I dont understand the idea and proof behind Squeeze Theorem Hmm, now let me recall the lecture I had myself :D Lets say we want to know what the limit $\lim_{x \rightarrow 0}$ approaches for the function $x \ \sin(x)$ Now we know $\sin(x)$ oscillates between $1$ and $-1$ So we can say: $-1 < \sin(x) < 1$ (We k...
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Formula for n-th iteration of dx/dt=B(x) up vote 3 down vote favorite 2 Let B(x) be infinitely differentiable with respect to x. Drop the use of parentheses on B to delimit the argument x and use them instead to hold the order of the derivative with respect to x. i.e. $B (0) = B$ $B(1) = dB/dx$, etc. Let parentheses ...
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Very difficult A-level problem from 1971 (UK) October 16th 2011, 09:42 PM #1 Newbie Joined Oct 2011 Posts 3 Very difficult A-level problem from 1971 (UK) Hi. I'm having real trouble answering a question posted online as appearing in a 1971 A level exam (as part of a discussion of whether exams have ...
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Divergence of a series March 20th 2011, 04:01 PM Bruno J. Divergence of a series Here's a challenge problem I just made up: Let $\{a_n\}$ be a sequence of positive real numbers such that $\sum a_n = \infty$. Show that $\frac{a_1}{a_0}+\frac{a_2}{a_0+a_1}+\frac{a_3}{a_0 +a_1+a_2}+ \dots = \infty$. Mar...
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Confidence Interval Review Chapter 7 Inference for Distributions 1 • The previous chapter emphasized the reasoning of tests and confidence intervals • Now we emphasize statistical practice – we no longer assume that population standard...
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how to dolce this?deviative of exponenetial functions February 19th 2006, 07:22 AM #1 Newbie Joined Feb 2006 Posts 2 how to do this?deviative of exponenetial functions $<br /> \frac{x^2 -1}{ e^2^x(x+1)}<br /> <br />$ the outcome supposs to be like this $<br /> \frac{2x-3}{e^2^x}<br /> <br />$ ...
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differential systems April 23rd 2009, 11:39 AM #1 Newbie Joined Feb 2009 Posts 17 differential systems when solving a system of differential equations of the form dy/dt = Ay The constant vector lambda is found with |A - lambda * I| = 0 If lambda is a complex number I have the solution ...
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Statistics Simple regression Statistics for dummies Statistics Gabriel V. Montes-Rojas Gabriel Montes-Rojas Statistics Simple regression Statistics for dummies y = β0 + β1x + u Much of applied e...
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Classification of long exact sequences up vote 12 down vote favorite 3 Let $\mathcal C$ be the category of long exact sequences of finitely generated abelian groups almost all of whose entries vanish. The category $\mathcal C$ is naturally additive as a subcategory of complexes of abelian groups. Question: Can w...
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Posts by Posts by Zach Total # Posts: 303 Social Studies What four influences did Greece had on Roman culture? College Chemistry 1) The concentration of the aluminum ion in a test solution is 0.10M. Using the Ksp for aluminum hydroxide (3. x 10^-34), calculate the concentration of hydroxide needed to precipitate al...
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Dedekind-esque sums up vote 5 down vote favorite Given real numbers $a, b$, let $f(x)$ be the integer nearest to $ax+b$, let $S_n$ be $\sum_{k=0}^{n} (n-2k) f(n-k) = n f(n) + (n-2) f(n-1) + (n-4) f(n-2) + ... - (n-2) f(1) - n f(0)$, and let $s_n = an(n+1)(n+2)/6$ (the value you would get if you replaced each term $f(x...
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One last exponent question~ Can someone check the answer, please? September 27th 2011, 06:44 AM #1 Newbie Joined Sep 2011 Posts 7 One last exponent question~ Can someone check the answer, please? With the help of the forum, I've gone through many more exponent exercises. But I have one more questions. ...
4
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Homework Help Posted by Anonymous on Wednesday, January 19, 2011 at 6:23pm. The price to cover ornaments is a fixed amount plus a percentage of the value of the ornaments. It costs $32 to insure $1000 worth of jewellery or $44.50 to insure $3500 worth of jewellery. What is the fixed amount to insure jewellery? A. $...
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S-unit equation and small sets of places up vote 7 down vote favorite Let $K$ be a number field, and let $S_x$ denote the set of primes of norm at most $x$. Is it possible to find a smaller set of places $T_x\subset S_x$ so that a lot of the solutions of the $S_x$-unit equation $a+b=1$ for $a,b\in S_x$ are solutions o...
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[SOLVED] tangent sum identity issue October 21st 2009, 03:05 PM #1 Junior Member Joined Sep 2009 Posts 74 [SOLVED] tangent sum identity issue I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mi...
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normal component of accelleration September 22nd 2010, 10:57 PM #1 Member Joined Apr 2009 Posts 87 normal component of accelleration Iam having issues with this one iff anybody can help? Given y^2=3x^3+8x where x and y are in meters and y is positive,what is the normal component of the accellera...
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diophantine problem September 4th 2008, 07:20 AM #1 Junior Member Joined Aug 2008 Posts 42 diophantine problem Suppose $n$ is a fixed integer (positive or negative) $eq 0$ and suppose $x_0^2 - 3y_0^2 = n$ with $x_0 \geq 0,\ y_0 \geq 0$. Let $x_1 = 2x_0 +3y_0,\ y_1=x_0+2y_0$. Show that $x_1...
5
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Quadratic Equation help April 9th 2013, 08:57 PM #1 Newbie Joined Apr 2013 From Sydney Posts 17 Thanks 2 Quadratic Equation help Hi there, I'm having trouble with two of the more challenging problems in my homework. 1) 2x^2 - 3x + 2a = 0 , this needs to be solved using complete the square me...
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Jumping Jack March 22, 2013 We have a fun little programming puzzle today; I found it here, but don’t know the original source of the puzzle: Jack starts at 0 on the number line and jumps one unit in either direction. Each successive jump he makes is longer than the previous by 1 unit, and can be made in either ...
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non-abelian groups of prescribed order up vote 2 down vote favorite 2 Is there a construction that will give a non-abelian group of order $p^mr$ where $p$ is a prime, $r$ and $p$ are relatively prime and $m$ is an arbitrary non-negative integer? I suspect in this generality there is no simple construction so feel free...
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Please need help with direct proof November 9th 2006, 09:24 PM #1 Junior Member Joined Nov 2006 Posts 48 Please need help with direct proof Hi, I have a few problems which i can't solve 1) need to prove (m+dk)mod d = m mod d (where m, d and k are integers and d does not equal to zero) 2) if r i...
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Exponential form - Math Central Hi Kent. "Exponential form" simply means a numeric form involving exponents. One way to write such a number is by recognizing that each position represents a power (exponent) of 10. So you can first break it up into separate pieces. I will use my own number 5 625 702: 5 625 702 = 5 00...
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Question about second/third derivative March 18th 2011, 07:05 AM HAL9000 Question about second/third derivative Hello! I've got a somewhat dumb question. What is the second and third derivative of a composition of two functions in Leibniz notation? March 18th 2011, 07:17 AM HallsofIvy Not a dumb...
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Dimensions of cylinder of a constant surface area but changing volume December 28th 2012, 11:20 AM taursaw62 Dimensions of cylinder of a constant surface area but changing volume Hi there! I'm new around so please feel free to correct me on forum ettiquete here! I am modelling a cylinder that changes volume...
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Solving the Beltrami Equation for a very simple Beltrami Coefficient up vote 7 down vote favorite 3 Let $\mu$ be a function on the complex plane with the property $\mu(z) = \overline{\mu(\bar{z})}$, such that $\mu(z) = \epsilon e^{-2\pi i \bar{z}}$ on the upper-half plane, where $\epsilon$ is a complex number such tha...
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Projective plane conics over Returns True if and only if self has a point defined over \(\QQ\). If point and obstruction are both False (default), then the output is a boolean out saying whether self has a rational point. If point or obstruction is True, then the output is a pair (out, S), where out is a...
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Markov chains Talk0 34,136pages on this wiki Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social | Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology | Statistics: Scientific meth...
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E.W.Dijkstra Archive: Primes once more (re Kac & Ulam) (EWD 1203) The plurals are defined as the integers ≥ 2. The plurals come in two sorts, the composite numbers, i.e. the plurals divisible by a smaller plural, and the prime numbers, i.e. the plurals not divisible by a smaller plural. Lemma 0 Each plural has a prime...
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Math Help June 28th 2011, 07:23 AM #1 MHF Contributor Joined Mar 2010 From Florida Posts 3,093 Thanks 5 Subsequences Suppose $\{x_n\}\to x_0$ and $\{y_n\}\to x_0$. Define a sequence $\{z_n\}$ as follows: $z_{2n}=x_n$ and $z_{2n-1}=y_n$. Prove that $\{z_n\}$ converges to $x_0$. Let $\epsilon...
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Solving of Trigonometry equation January 2nd 2011, 06:10 PM #1 Junior Member Joined Aug 2010 Posts 37 Solving of Trigonometry equation Hi Guys ! Am Currently stuck with this question : If sin(x+y) = 1 and if tanx = 9tany , find the value of tanx. Need help guys thanks ! have you playe...
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M. L. BAKER GG. An angel came down for a meeting of the American Philosophical Association. Greeting the assembled philosophers, the angel offered to answer a single question for them. Immediately the philosophers set to arguing about what they should ask. So the angel said, “Alright, you figure out what you want to a...
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[SOLVED] Equivalence Relations October 22nd 2008, 08:54 AM #1 Junior Member Joined Sep 2008 From Indiana Posts 26 [SOLVED] Equivalence Relations Prove that if R is a symmetric, transitive relation on A and the domain of R is A, then R is reflexive on A. I'm not really sure where to start. I...
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Trivial canonical bundle up vote 1 down vote favorite Let $X$ be a complex compact Kähler minimal surface with zero algebraic dimension and $H^2(X,\mathcal{O}_X) \ne 0$. We know that according to Enriques–Kodaira classification, $X$ is either a torus or a K3 surface. In particular, its canonical bundle is trivial. My...
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ISDA® - PDF ISDA® Alternative compounding methods for over-the-counter derivative transactions David Mengle, ISDA Head of Research February 5, 2009 Summary • There are two methods for compou...
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Help with this Calculus Problem May 30th 2006, 01:42 PM Susie38 Help with this Calculus Problem This is a piecewise function Let f(x) = 2/pi*x when [0,pi/2] 2sinx when (pi/2, 3pi/2] 1 when (3pi/2, 2pi] a. find a continuous function, F(x), satisfying F(x) = the integral f(t) dt from 0 to x, on [...
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Statistics Question February 21st 2008, 07:47 AM #1 Member Joined Dec 2006 Posts 79 Statistics Question I'm given this problem. σ²(t) = V((1-t)X + tY) = at² + 2bt+c where a=? b=? c=? E(X) = 2 E(Y) = 3 E(X^2) = 53 E(Y^2) = 45 E(XY) = -21 Can someone please explain what σ²(t...
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The mathematics of blackjack: Probabilities We first present the probabilities attached to card dealing and initial predictions. In making this calculus, circumstantial information such as fraudulent dealing is not taken into account (as in all situations corresponding to card games). All probabilities are calculated ...
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Cutting Elbows Let's cut one of these 90° elbows into smaller 45° elbows. A quick division of 90° /45° shows that two 45° elbows can be created from one 90° elbow. Below you will find three different ways to calculate measurements to mark 45° elbows. The first method is: Measuring or calculating the insid...
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Formulas and Missing Quantities Date: 10/09/2004 at 04:45:34 From: Pilar Subject: Drinking a swimming pool Could you drink enough water in a life time to empty a pool? My math teacher told us to solve this problem and I understand it but I really don't get how we have to solve it! I thought of using a pool that is ...
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Pascal Triangle If the computational board fields are used for the numbers from the above binomial expressions, the following number triangle is formed : There are some proofs that this number triangle was familiar to the Arab astronomer, poet and mathematician Omar Khayyam as early as the XI century. Most probably th...
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Monotone sequences and Cauchy sequences March 19th 2009, 11:35 AM #1 Member Joined Oct 2008 Posts 124 Monotone sequences and Cauchy sequences Suppose that x>0. Define a sequence (s_n) by s_1=k, and s_(n+1) = (((s_n)^2)+x)/(2s_n) for n elements in N. Prove that for any k>0, lim s_n = sqrt(x). I've go...
5
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Differential equation with switched parameters and boundary conditions in integral form up vote 0 down vote favorite 1 Sorry for the title, I didn't find a better description (showing that I have no idea for the solution). Feel free to put in a better title and change the tags if you can grasp a view on the problem. ...
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A direct proof that minimal primes are associated up vote 0 down vote favorite 2 It is a well-known theorem that, for a Noetherian ring $A$, the minimal primes of $A$ are among the associated primes of $A$; i.e., for every minimal prime $\mathfrak{p}$ of $A$, there is an element $f \in A$ such that $Ann(f) = \mathfrak...
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Is the evaluation of polynomial functors appropriately continuous? up vote 7 down vote favorite 1 I'd like a nice proof of the following fact. Let $C$ and $D$ be categories, and let $\mathbf{Cat}/(C\times D)$ be the usual (1-categorical) slice category whose objects are triples $(X,F\colon X\to C, G\colon X\to D)$, $...
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What is the lower bound for highly composite numbers? Take the 2-minute tour × MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required. I will start off with the simplest type, $$ d(n) \leq \sqrt{3 n} $$ and $$ d(n) \leq 24 \left(\frac{n}{315}\right)^{1/3}...
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How to solve this System of Second Order Differential Equations (DE) with Initial Value Problem (IVP) up vote 3 down vote favorite 1 Hello, I'm trying to figure out how solve the below for varying time and/or corresponding theta. I'm stumped.. any insight is greatly appreciated. Thank you $\ddot{R} = −\alpha|v|\dot{R...
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Torsors and the fpqc topology up vote 4 down vote favorite Fix a scheme $S$, a group scheme $G/S$ (let us say smooth, maybe even affine with some finiteness conditions if you like), and suppose I have some other $S$-scheme $P$ with a right $G$-action. We want to investigate the question of whether $P$ is a $G$-torsor ...
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Preduals of B(E) up vote 7 down vote favorite 1 For a Hilbert space $H$ it is well known that the algebra $B(H)$ has a unique predual; the Banach space of trace class operators. If $E$ is a Banach space then is it known whether 1. $B(E)$ is always a dual Banach algebra? 2. The predual is always unique? I'm aware...
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Irrationality of pi: the unpossible function Recall from my last post what we are trying to accomplish: by assuming that $\pi$ is a rational number, we are going to define an unpossible function! So, without further ado: Suppose $\pi = \frac{a}{b}$, where $a$ and $b$ are positive integers. Define the function $f$ lik...
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Symmetries of a Cube Date: 10/09/2003 at 02:27:34 From: Johny Subject: symmetries of cube Prove that the group of symmetries of a cube is isomorphic to S_4. Date: 10/09/2003 at 07:10:14 From: Doctor Jacques Subject: Re: symmetries of cube Hi Johny, Note that we must consider the group of rotations of the cube (i....
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Question about the Hardy-Littlewood method (quite basic) up vote 7 down vote favorite 3 Hi, I have a question about the Hardy-Littlewood method. Writing $R_s(n)$ for the number of ways to write $n$ as a sum of $s$ $k$-th powers and $f(\alpha )$ for the sum $\sum _{m=1}^Ne(\alpha m^k)$, we have $R_s(n)=\int _\mathfra...
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Is displacement controled by stable norm? up vote 4 down vote favorite 1 Let $T^n$ be the $n$-dimensional torus and $g$ be a Riemannian metric on $T^n$. Let $\tilde g$ be the induced metric on the universal covering; using suitable coordinates, $\tilde g$ is therefore a $ \mathbb{Z}^n$-periodic metric on $\mathbb{R}^n...
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Expected value and variance March 9th 2010, 12:52 AM #1 Member Joined Oct 2009 Posts 195 Thanks 1 Expected value and variance An electronic system has two components X and Y, and works if just one or both components are functioning. Their lifespan function is written as: f(x,y) = 2^e−(x+2y), x >...
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Question about WHY something must be done September 16th 2010, 04:35 PM #1 Junior Member Joined Aug 2008 Posts 40 Question about WHY something must be done Hi, I've been away from math for a few years now and coming back to it with an algebra review I've run into a problem. I was answering a questio...
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Laplace Transforms January 28th 2009, 07:03 PM #1 Member Joined Jan 2009 Posts 91 Laplace Transforms find the laplace transform F(s) of f(t) = sin wt the w is actually supposed to be omega what i got was integeral from 0 to infinity of: (sin wt)*(e^-st) dt then i integrated by parts a...
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Volume of body obtained by rotating around the x axis and y axis. May 3rd 2012, 03:14 PM #1 Newbie Joined Feb 2011 Posts 18 Volume of body obtained by rotating around the x axis and y axis. Hi, If y= 4x^3+3x^2-4x-3, calculate the volume of the body obtained by rotating y around 1) the x axis 2) the ...
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Math Forum Discussions - Re: Definitions missing Date: Jun 4, 2013 5:58 AM Author: Andrzej Kozlowski Subject: Re: Definitions missing In most cases exact definitions can be found in the various relevant tutorials. For example, StandardDeviation for discrete data (list) is defined in tutorial/BasicStatistics: The vari...
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COnverting rectangular equations to polar (and vice versa) April 27th 2008, 11:28 PM #1 Junior Member Joined Oct 2007 Posts 31 COnverting rectangular equations to polar (and vice versa) i understand the concepts of converting single coordinates, however im confused on how and why on some these parts.... ...
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Does the tangent bundle of this fiber product split? up vote 1 down vote favorite 1 Let $\mathcal X \to S$ be the local universal family of an elliptic curve, and let $E \to S$ be a vector bundle over $S$. Then we can form the fiber product $\mathcal Y = \mathcal X \times_S E$, which will be a smooth complex manifold ...
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dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: 9 Group Title Suppose a forest fire spread...
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how many distinguishable words December 23rd 2010, 12:09 PM bigwave how many distinguishable words How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? answer is 90,720 December 23rd 2010, 12:16 PM Plato If the same question were asked ...
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Inverse Functions: Arcsec(x) Date: 02/11/99 at 20:15:09 From: Knote Subject: Calculus If y = arcsec(x) then what does x equal? Date: 02/22/99 at 15:53:11 From: Doctor Elizabeth Subject: Re: Calculus Hi, Knote. Good question! Let's take a closer look at that. First, what does the notation "arcsec()" stand for? W...
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Software Sales Date: 02/01/97 at 11:07:47 From: frank kreager Subject: Software Sales Hi, I am doing word problems and am having a lot of trouble putting them into mathematical equations. Once I get the mathematical equation, I don't have any difficulties. For instance: The three best selling software applications...
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When does "splits" imply "cosplits"? up vote 7 down vote favorite 4 In the category of groups, there are lots of "exact sequences", e.g. 4 → H → 2, that neither split nor cosplit, where H is the eight-element group of quaternions, and lots of sequences like 4 → D → 2 that split but do not cosplit, where D is the eight...
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Prove an inequality Hello, could someone help with proving this inequality: $a^2+b^2+1 \ge ab + a + b$ Thanks in advance One way is to consider a line b = k * a for some number k and to prove that the inequality holds for all points (a, b) on this line. (For completeness, one should consider the line a = 0, but the in...
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O-Level Questions O-Level Practice Question 2: A helium balloon has a volume of 621 cm3 at ground level where the atmospheric pressure is 101,000 Pa. The balloon rises and expands to 636 cm3. At this point, what is the height of the balloon above ground ? Take the density of air to be 1.25 kg/m3 and constant over the h...
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Folding a piece of paper in half A few weeks ago, I asked the following question: “If you fold a (humungous) piece of paper in half 50 times, how thick would the pile be? 1cm, 1m, 1km, 1,000km, 1,000,000km…?” Here I discuss the possibilities of folding paper in half 50, 25, 15 and then 9 times. 50 folds How thick?...
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Does Weyl's Inequality prove equidistribution? up vote 10 down vote favorite 3 Let $f(n) = \theta n^d + a_{d-1} n^{d-1} + \cdots a_1 n + a_0$ be a polynomial with real coefficients, and $\theta$ irrational. Let $S_N = \sum_{n=1}^N e^{2 \pi i f(n)}$. Weyl's Equidistribution theorem for polynomials is equivalent to the ...
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Discounted Cash Flow Questions & Answers - Basic 1. Walk me through a DCF. &quot;A DCF values a company based on the Present Value of its Cash Flows and the Present Value of its Terminal Value. First, you project out a company&#039;s financials using assumptions for revenue growth, expenses and Working Capital; then y...
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Intersection of 2 Planes help July 20th 2008, 08:12 AM #1 Junior Member Joined Sep 2007 Posts 55 Intersection of 2 Planes help Hello everyone! I truly hope someone can explain this question out to help me out! It's been 2 hours and still no luck! Any help is truly appreciated! ----------------------...
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Integration Question May 21st 2008, 06:21 AM looi76 Integration Question Question A curve is such that $\frac{dy}{dx} = \frac{4}{\sqrt(6 - 2x)}$, and $P(1,8)$ is a point on the curve. Find the equation of the curve. Attempt: $\frac{dy}{dx} = \frac{4}{\sqrt(6 - 2x)}$ $\int 4(6-2x)^{-\frac{1}{2}...
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Given 2 towers of fields, when are these fields isomorphic? up vote 5 down vote favorite Let $F_0 \subset F_1 \subset F_2 \subset \cdots$ and $K_0 \subset K_1 \subset K_2 \subset \cdots$ be two towers of fields. Also, let $F = \cup_{i=0}^\infty F_i$ and $K = \cup_{i=0}^\infty K_i$. Now suppose for each $i$ we have in...
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dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: agentx5 Group Title Check my work on this ...
5
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Confusion with respect to a general angle September 14th 2012, 01:38 AM #1 Confusion with respect to a general angle Hello, I shall post the problem with the answer (s) as a given, but it's more of an explanation on what's just happened from which I'm after. Anyway: $-540 < 3x < 540$ $tan\ 3x ...
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A problem about Determinant of sum of permutation matrices up vote 3 down vote favorite Let $w_1$ and $w_2$ be two permutations of $\{1, \cdots , k\}$ such that for all $1\leq i \leq k$, $w_1(i)\neq w_2(i)$. Let $m$ and $n$ be two relatively prime integers. Then is there exist two diagonal matrices $D_1, D_2 \in M_k(\...
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Modeling April 9th 2007, 07:17 PM pakman Modeling The problem states that a tank originally contains 100 gal of fresh water. Then water containg 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped,...
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Equivalence Relations April 29th 2010, 02:44 PM #1 MHF Contributor Joined Mar 2010 From Florida Posts 3,093 Thanks 5 Equivalence Relations $x,y,z\in\mathbb{R}$ $x\sim y$ iff. $x-y\in\mathbb{Q}$ Prove this is an equivalence relation. Reflexive: $a\sim a$ $a-a=0$; however, doe...
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Very tricky and interesting modular question July 9th 2010, 12:29 PM elemental Very tricky and interesting modular question This is a very tricky question: Find the last three digits of 2008^2007^2006^2005^...^1 If you're having trouble thinking about how the exponents are arranged, just imagine eve...
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