Example Definition and 845 Threads

Given a differential equation dy/dt = F(t,y), can anyone give me an example that shows no solution exists if F(t,y) is discontinuous? Thanks

Hi, Does anyone know a fluid with low compressibility? Thanks, H

Hello everybody. I have the following problem: I am given a Speed distribution function, f(v). This distribution is normalized to the total number of particles there are, that's equivalent to: \int_0^\infty f(v) dv = n_0 (particles traveling away from my target are not considered.)Now. I know...

Homework Statement if (an) and (bn) are bounded positive sequences prove that limsup(anbn)<= limsup(an)limsup(bn) and give an example to show there is not equality in general

For any natural number a and b, with b > 1, two natural numbers x and y can always be found such that b^x - b^y is divisible by a. Until now, with many tries of a and b, I have always found corresponding x and y. I would appreciate if somebody could give me a proof or a counter example.

Homework Statement A continuous function g: Q --> R such that g(0)=0 and g(1)=1, but there does not exist any x in Q such that g(x)=1/2Homework Equations Number sets, basic number theory The Attempt at a Solution The function could be f(x) = x^2 since f(0) = 0 f(1) = 1 f(x) = 1/2 here it...

Homework Statement A differentiable function g: R --> R such that f' is unbounded on any interval of length one Homework Equations The Attempt at a Solution It's probably easiest to look at [0,1]...maybe something that goes to infinity as it approaches 1? But not sure if it would...

Homework Statement A continuous function g: Q x Q --> R such that g(0,0)=0 and g(1,1)=1, but there does not exist any x,y\in Q such that g(x,y)=1/2Homework Equations Mean value theorem?The Attempt at a Solution I want to say no, because I'm sure there's something going on because the domain is...

Homework Statement A sequence of Lipschitz functions f_n: [0,1] --> R which converges uniformly to a non-Lipschitz function Homework Equations a function f: A --> R is Lipschitz if there exists a constant M \in R such that |f(x)-f(y)|<=M|x-y| The Attempt at a Solution I don't think...

Give an example to show that if not assuming independence of X1, X2, ..., Xn it is possible to show that Var(1/n * sum from k = 1 to n of Xk) >> \sigma^2/n

Anyone know of an example of an algebra over the field \mathbb{Z}_2 with the following properties? 1. commutative; 2. associative; 3. x^3 = 0 , for all x; and 4. Exists x and y such that x^2y \neq 0 . Grateful!

Homework Statement How to represent function \frac{1}{e^x-x-1} in form of Laurent series around point 0 Homework Equations Laurent series f(z)=\sum^{\infty}_{n=-\infty}a_n(z-z_0)^n Here is z_0=0 The Attempt at a Solution Computer gives \frac{2}{x^2}-\frac{2}{3...

Hi, I'm trying to understand the natural transformation from V to V**, and the book has the theory but I think I'm needing an example. Lets say V=R^2 a vector space over K=R. B={(1,1),(1,-1)} a basis of V B={x/2 + y/2, x/2 - y/2} a basis of V* v = (3,2) a vector of V I want to get a...

Homework Statement A well insulated container of negligible thermal capacity contains 30 kg of water at 90oc. A mixing process then takes place in which 50 kg of liquid water at 17oc is added to the tank. The mixing process is continued until thermal equilibrium is established...

So the general tactic for straight lines: f(x) = 2x Show by epsilon-delta definition of limit, as lim x->2, f(x) tends to 4. let, ε>0, and choose 0<δ<ε/2 (|x - 2|<δ)→ |f(x) - 4| = |2x - 4| = 2|x - 2| < 2δ < ε No problem, but what about for a parabola? g(x) = ax2 for some a in R. Show as lim x...

Attached is a worked problem in the Classical Mech book by Morin. I don't understand how eqn (2.57) is the net moment about the pivot. Isn't it only the moment of the weight of the portion of the stick to the right of the pivot ? What about the moment due to the weight of length 'l' on left...

Spivak: Calculus on Manifolds, p. 42: Assuming "differentiating f(x,g(x)) = 0" means differentiating f \circ h, where h : (-1,1) \rightarrow \mathbb{R}^2 \; | \; x \mapsto (I(x),g(x)), I(x) = x and setting the result identically equal to zero, we have 2x+2g(x) \cdot g'(x) = 0, as...

Homework Statement A function f: R -> R such that f is continuous at a point c if and only if c is not an element of the set: { m\2^n: m,n in Z, n>=0) Homework Equations Definition of continuity/discontinuity? The Attempt at a Solution Is it enough to say that we can define a...

Homework Statement An open set A contained in R (reals) such that the closure of A = R, but R \ A is uncountable Homework Equations I guess knowing that for the closure of a set A to be equal to R means that A is dense in R? The Attempt at a Solution Every thing I try seems to...

Hello, I found http://omlc.ogi.edu/classroom/ece532/class1/radiance_flashlight.html" an example of calculation of radiance. I found this example quite confusing, and now I am not sure whether it's me who didn't understand some concepts, or the author who silently made a bunch of simplifying...

Hi, Can somebody give me an example of a rank 4 tensor in physics? Thanks.

I’m studying GR and am curious about manifold, atlas and charts. I have an idea for building a simple example, in one dimension, and wanted to ask if what I’m doing below is “legal”/correct. Imagine a space flight that can be divided into three segments: A-B: velocity starts at zero and...

This is an example shown in "Introduction to Electrodynamics" by Griffiths. Page 226 example 5.8. Given a sheet of current K on the xy-plane where current traveling in +ve x direction. Find the magnetic field. I am confused on the way the book justify the z direction of B is zero. The...

Homework Statement In Example 3 under Theorem 2.5 of Apostol's Calculus Volume 1, I don't understand how the final formula on the right is obtained.Homework Equations The identity cos 2x = 1 - 2 sin2 x implies sin2x = 1/2(1 - cos 2x) so, from Example 2, we obtain: \int^a_0\,sin^2\,x\,dx =...

Homework Statement [PLAIN]http://hh7.net/Apr1/hh7.net_13016941501.gif Homework Equations these statement are false and i need counter example for each one The Attempt at a Solution for(ii) i can say that f(x)=x2-4 on [-6,6] for others i need help

On page 60 of his 3rd edition of Classical Electrodynamics, he discusses the method of images applied to a grounded conducting sphere with a single charge q outside it. Near the end of the problem, he calculates the force on a small patch of area da as (sigma^2/2epsilon_nought)da. Now, it...

Can you provide one to show a separable complete boundd metr. space X is not always seq. compact.

I'm looking for a good example for a freshman mechanics class to demonstrate how one can integrate the equations of motion numerically when there is no closed-form solution. The problem below is the best I've been able to come up with yet, but I'm not totally happy with it, and I'm wondering if...

Hello, I'm reading through John Conway's A Course in Functional Analysis and I'm having trouble understanding example 1.5 on page 168 (2nd edition): Let (X, \Omega, \mu) and M_\phi : L^p(\mu) \to L^p(\mu) be as in Example III.2.2 (i.e., sigma-finite measure space and M_\phi f = \phi f is a...

molecular: Pb(NO3)2 (aq) + 2 KI (aq) ----->2KNO3 (aq) + Pbl2 (s) Ionic equation Pb2+ (aq) + 2NO3- (aq) + 2 K (aq) + 2 I- (aq)----->2K+ (aq)+ 2NO3- (aq) + PbI2 (s) I know why they break apart in the ionic part, its because ionic things aer broken up, but how would you know that they join...

Hi everyone, I'm wondering why Mathematica (8.0) can't bring this to the obvious form -1, and leaves the expression as is: Simplify[(b^8 + c^4) /a^8, a^8 + b^8 + c^4 == 0] Is there any nice and elegant way how to achieve that? (I know, that I could take e.g. /.c->(-a^8-b^8)^(1/4), but...

The is example 10.1 in page 417. The example is the find the current density from given condition: V=0,\;\;\hbox{ and } \;\;\vec A=\frac{\mu_0 k}{4c}(ct-|x|)^2 \hat z \;\hbox { for x = +ve and }\;\; \vec A=0 \;\;\hbox { for x = -ve.} c=\frac 1 {\sqrt{\mu_0 \epsilon_0}} From this...

Homework Statement Give an example of a continuous, non-negative function f: [1, infinity) --> R such that if an = f(n) for each positive integer n, the series \sum an diverges, while the improper integral from 1 to infinity of f converges. Justify your answer. Homework Equations N/A...

Why exactly is it so important to know about the models of the universe(flat/open/closed)? Why is it so important to know that the universe is expanding? What do we benefit from it? what is the relevance of it? Even if we know the "truth", what does it mean to "us"? I don't really mean these...

In my textbook there is an example with the following reaction and rate: C6H6 + 3H2 -> C6H12 Rf = kf[C6H6][H2] Then the the example claims that the ratio of the rate constants is: kf / kr = [C6H12] / ( [H2]3 [C6H6] ) How is the denominator of that ratio possible if the forward...

I'm teaching Calculus and am looking for an example of a first order differential equation application that is reasonably easy to explain in terms of where the equation comes from, but difficult or impossible to solve. I'm trying to show when you would need to use approximation techniques...

In special relativity the relativity of simultaneity is explained with the following example. We have one frame of reference - a train moving from left to right with constant speed v relatively to the embankment, and second frame of reference - the embankment itself. On the embankment there are...

Homework Statement Homework Equations The Attempt at a Solution I don't know how to start a proof for this. Intuitively I would think think that C = f^(-1)(f(c)), which would imply that C is a subset of f^(-1)(f(c)), however that is not the case and the problem asks for an...

Homework Statement Prove or give a counterexample: for all x > 0 we have x2+1< (x+1)2\leq 2(x2+1)Homework Equations The Attempt at a Solution I used my calculator to do the graph of all 3 functions and saw that the statement was always true (at least for x>0). So I couldn't see another proof...

Homework Statement I need a example of a continuous function f:(X, d) -> Y(Y, p) does NOT map a Cauchy sequence [xn in X] to a Cauchy sequence of its images [f(xn) in Y] in the complex plane between metric spaces. Homework Equations If a function f is continuous in metric space (X, d), then...

[b]1. Let M(2,R) be the set of all 2 x 2 matrics over R. Give an example of matrices A,B,C in M(2,R) such that AB=AC, but B is not equal to C. [b]3.

Suppose the function f has the following four properties: 1. f is continuous for x >=0; 2. f'(x) exists for x > 0; 3. f(0) = 0; 4. f'is monotonically increasing. I'm just looking for functions that have these 4 properties to better understand what f represents. So far, I came...

I have a question about covariant and contravariant vectors. I tried making concrete examples and in one example I succeed, in another I fail. It is said that displacement vectors transform contravariantly, and gradients of a scalar transform covariantly. I can get the whole story working in...

I have to find two planes z=f_1(x,y)=a1*x+b1*y+c1 z=f_2(x,y)=a2*x+b2*y+c2 That satisfy: 1. both planes go through (-5,9,8) 2. the intersection line between the planes is located outside of the Cylinder x^2+y^2=4 3. the surface area of x^2+y^2=4 that is bounded between f1 and f2 is...

I am looking for an example of a 4 dimensional compact smooth manifold that has the following properties - it is orientable - it can be smoothly embedded in R^8 - its Euler characteristic is odd - its second Stiefel-Whitney class is zero

I'm missing something here on the light clock example from http://en.wikipedia.org/wiki/Time_dilation. I understand the math on the picture, but I'm missing how that applies to time dilation. Why does the light pulse take on a diagonal path for the moving observer? Is the light pulse still...

I know that in QM, one observation like position will alter the wavefunction so that momentum changes. But how do we see this mathematically when we include time dependence, whether in matrix mechanics or wave mechanics? Is it as simple as writing PQx where x is the state, Q position matrix, P...

Homework Statement [PLAIN]http://img12.imageshack.us/img12/6109/17007711.jpg The attempt at a solution For part (a), I can only find a normal compressive stress. It is as follows: \sigma_{c} = \frac{F}{A} \sigma_{c} = \frac{100*9.81}{\pi(0.013)^{2}} \sigma_{c} = 1847704 Pa...

Hello physicsforums community. I have recently learned about Lagrange multipliers and have been given three problems to solve. Could you guys please go over my work and see if I have the gist of it? One question, a theoretical one, I have no idea how to begin. Any advice regarding this would be...

Hi, Everybody: I am trying to understand torsion and relative cycles in a more geometric way; I think I understand some of the machinery behind relative cycles (i.e., the LES, and the induced maps.), and I understand that by ,e .g., Poincare duality, in order to have torsion in...