Property Definition and 635 Threads

Hi there...I need ur help on these questions: 1) Can H2O exist as a vapor at -40oc,As a liquid? Why? 2) What would be the general nature of Constant volume lines on Phase (P-T) diagram? Both questions are from Engg. Thermodynamics-Moran,Shaprio(Things engg. think abt section) Also, does anyone...

Hello all, For a monotonic increasing/decreasing function f(x) on x \in \mathbb{R}, we can only have supremum/infimum which is occurred at x = \infty with value \lim_{x\uparrow \infty}f(x) Otherwise, if it was a maximum/minimum, it would violate the assumption of monotonicity. Am I...

I'm having a little trouble distinguishing the line between what the f.i.p implies and what it does not. **EDIT2** Hopefully this will make things more clear What I'm really interested in is a formal definition of the f.i.p regardless of the set in question or the field. Given the sequence...

if A is an n x m matrix where n < m I would like to prove that there exists some \lambda such that rank(A^T A + \lambda I) = m I know that if two of the columns of A^T A are linearly dependent, they are scalar multiples of each other and by adding some \lambda to two different positions, those...

If x_n\geq 0, y_n\geq 0 and \lim \limits_{n \to \infty }x_n exists, we have \limsup\limits_{n\to\infty}(x_n\cdot y_n)=(\lim\limits_{n\to\infty}x_n)\cdot(\limsup\limits_{n\to\infty}y_n). But if \lim\limits_{n\to\infty}x_n<0, do we have analog equation(I guess \limsup\limits_{n\to\infty}(x_n\cdot...

Hi: Is there a relation between k-connectedness ( meaning 1st, 2nd,..,k-th fundamental groups are trivial.) and having the homotopy-lifting property.? . This may be vaguely-related to being able to extend global sections from the j-th skeleton, to the (j+1)-st skeleton (j<=k...

I have a monoid (M,+), and I assume that for any two elements a,b in M it is always possible to find a third element k such that: a + k = b + k Is it possible to prove that M must be a cancellative monoid? In other words, can I prove that a+k=b+k \Rightarrow a=b ?

Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an externally applied magnetic field, thus causing a repulsive effect. This is property of all materials. But can be perceive only for materials which atoms or ions have closed shells. Examples...

1. Prove that for all boolean algebras if x+y=x+z and x'+y = x'+z then y=z. 2. Homework Equations : x+x' = 1, xx'=0, basically we are allowed to use the usual boolean algebra properties. 3.Attempt: This the second part of a problem, in the first part we had to give and example of...

once i was wondering that, how any property of an object describe an object??

Homework Statement Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3? Homework Equations I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then... (x1)^T*x2=0 (x2)^T*x3=0...

Homework Statement Find f:I->I such that each x on I shows up an infinite amount of times on f(I), f continuous Homework Equations Lol , equations? The Attempt at a Solution The weierstrauss function, I want to expand on it's fractal property and say that it crosses a given point...

this problem is from Apostol's Calculus Vol.1, i just started doing proofs so I'm still getting used to it. B - U (A) = ∩ (B-A) the U is the union of sets in a class F and ∩ is the intersection of sets in a class F. written under both the U and the ∩ are A∈F. so i let an element x ∈ B...

In the field of formal rational functions, construct a nest of closed, bounded intervals whose intersection is empty. (That is, show that the Nested Intervals property fails in this field) I know it has to involve radical 2 but because that is the only number we know is irrational but other...

I've encountered this question in some theoretical work I've been doing. Suppose you have two pdfs fH(x) and fL(x) with the same support (bounded or infinite... you can assume whatever you want about it). Suppose that the expected value of a random variable with pdf fL(x) is greater than the...

Homework Statement Prove that \delta(at)=\frac{1}{abs(a)}\delta(t) Hint: Show that \int\phi(t)\delta(at)dt=\frac{1}{abs(a)}\phi(0) (the limits of integration are from -inf to +inf btw, I couldn't find how to put them in..) Homework Equations The Attempt at a Solution Ok. I...

I have a question regarding the radius of convergence and hopely someone can help me with it. Suppose \SigmaNANZN-1 is given and if its primitive exists, will these two polynomials have the same radius of convergence?

I have so many fundamental questions about physics, i hope they are not considered "speculative" and deleted... Physics convolutes things so much, i wonder what does physics define as a physical property. For instance - an electron has a property (quality) of charge. Hopefully - this means...

What kind of sets exhibit the wada property? I know R2 does but does it extend to R3 or R itself?

Homework Statement Find three disjoint open sets in the real line that have the same nonempty boundary. Homework Equations Connectedness on open intervals of \mathbb{R}. The Attempt at a Solution If this is it all possible, the closest thing I could come up with to 3 disjoint...

Homework Statement Prove: If A is an invertible matrix and k is a positive integer, then (A^k)^-1 = (A^-1)(A^-1) ...A^-1=(A^-1)^k Homework Equations none The Attempt at a Solution I have a hard time proving this. How do I go about doing this? Any help would be great. I really...

tell me about colligative property?

It is said on wiki* that "Maximal compact subgroups are not unique unless the group G is a semidirect product of a compact group and a contractible group, but they are unique up to conjugation, meaning that given two maximal compact subgroups K and L, there is an element g in G such that...

Homework Statement We are supposed to prove that sin(x+y) = cos(x)sin(y) + sin(x)cos(y) Homework Equations cos(A-pi/2) - sin(A) sin(pi/2 - A) = Cos(A) sin(A-pi/2) = -cos(A) The Attempt at a Solution We had to prove all of the relevant equations but were allowed to work in groups...

[for all of the following, "lim" means the limit as n->∞] Let an be a sequence of real numbers. Theorem: if lim an = L and lim an = M, then L=M. (Incorrect) "Proof": lim an = L and lim an = M Thus, L = lim an = lim an = M (transitive property) Therefore, L=M. To me, every step in...

Hello, Saw this expression: ^{inf}_{-inf} \int e^{x^{2}} = 2 \times ^{inf}_{+0} \int e^{x^{2}} I am unable to understand this change of base. You can change from -inf to 0 and 0 to +inf but do not see how that equals to 2 * the integral from 0 to infinity. I hope someone will help me...

Homework Statement Warren Siegel, Fields, ex. IA2.3(b) Define the eigenstate of the fermionic annihilation operator as a|\zeta\rangle=\zeta |\zeta\rangle. \zeta is a Grassmann (anti-commuting) number. Show that a^\dag|\zeta\rangle=-\frac{\partial}{\partial\zeta}|\zeta\rangle. Homework...

Hi, I am actually not really concerned about what the whole details are but more whether my approach is correct to show the following statement: Let f be continuous on a closed bounded region \Omega and let (x_0 ,y_0) be a point in the interior of \D_r. Let D_r be the closed disk with center...

What is the essence of space? Is it a property of matter? If not, is it an entirely new stuff distinct from matter? If the former is true, why does space seem so homogeneous to us while the distribution of matter seems so uneven. If the latter is the case, what does it mean by the matter without...

Can anyone do a very comprehensive breakdown of the Laplace translation property for me? I don't understand how to apply it: L[eat f(t)] = L[f(t)] s-> s-a Here is a specific problem that applies it: Homework Statement Y(s) = 4/(s+1)3 + 1/(s+1)2 + 2/(s+1) I need to perform an inverse Laplace...

Homework Statement Hello. I am relatively new to this subject please forgive my incompetence. Please correct me if I have misunderstandings. I understand that the cross product of two vectors (say A and B) in R3 is a vector that is orthogonal to both A and B. But how A x B be...

Use determinant property to evaluate matrice determinant Homework Statement 3x3: A = 12 27 12 28 18 24 70 15 40 What determinant property can I use to find the determinate of this matrix? I cannot see any relationship between the rows or columns. Apparently 720 comes into it somehow, but I...

Homework Statement Let X have a geometric distribution. Show that P(x>or= k+j|x>or=k) = P(X>or=j) where k and j are nonnegative integers. The Attempt at a Solution P(x>or= k+j|x>or=k) = P(x>or= k+j intersect x>or=k)/P(x>or=k) = P(x>or=k+j)/P(x>or=k) for j>or= 0 =...

Homework Statement For the construction of a thermometer, one of the essential requirements is a thermometric substance which a. remains liquid over the entire range of temperature to be measured b. has a property that varies linearly with temperature c. has a property that varies with...

Homework Statement Find the eigenfunctions and eigenvalues of the translation operator \widehat{T_{a}} Translation operator is defined as \widehat{T_{a}}\psi(x)=\psi(x+a) (you all know that, probably you just call it differently) Homework Equations The eigenvalue/eigenfunction equation is...

What is the \int(u)-1 where u is a fonction of x , forming a quadratic equation. As in: \int(u)-1 where u = x2+2ax+a2 for example. Is there a basic property for this... or do I have to play around with the fonction u , in order to integrate? ---- I know that \int(x)...

Homework Statement A characteristic property is a property that can be used to help identify a substance since it is the same for all samples of the substance. We have now studied mass, volume and density. Which of these is a characteristic property of substances? Explain. Homework...

I am confused regarding the heat properties of electromagnetic radiation. Wiki states "Any electromagnetic radiation can heat a material when it is absorbed.". Does this imply radiation with wavelengths in the visible light region can also heat a material, that is, increase its temperature? From...

I'm considering the problem: Given c \in \bold{F}, v \in V where F is a field and V a vector space, show that cv = 0, v \neq 0 \ \Rightarrow \ c = 0 I've been wrapping my head around this one for a while now but I can't seem to get it. Proving that if cv = 0 and v \neq 0 implies v = 0 is...

Hi, I am looking for a nonlinear equation capable of approximating a sigmoid curve that can be multiplied by another equation of the same type with different parameters and this product can be made linear in the parameters. I am an ecologist, so I hope I am using the right terms. I...

A set X is *this* iff whenever x is a subset of X, then x is also an element of X. Note that this is not transitivity.

d1 and d2 are metrics on a space X. Does min(d1,d2) satisfy the triangle inequality. I think it does not but I am having a hard time finding a counter example.

I want to show the triangle inequality, d(x,x)=0, d(x,y)\neq0 for x\neqy implies that d(x,y)=d(y,x). Note that I do not have d(x,y)>0. But I know how to show this if I can get the transitive property. I have been trying to use the triangle ineq. to establish d(x,y)>=d(y,x) and...

Does there exist an uncountable set of positive reals such that every countable decreasing sequence from that set sums to a finite number?

Hi, I am reading Baby Rudin on my own to get prepared for the analysis class that I will be taking in the fall. I got up to this theorem, and I was wondering if someone can clarify me the proof of this (i.e. Thm 1.11, the first theorem). 1.11 Theorem: Suppose S is an ordered set with the lub...

Statement: 37. Let G be a group and suppose that a * b * c = e for a, b, c \in G. Problem: Show that b * c * a = e. Thought Process Can we assume that our binary operator * is abelian. Thus, a * b * c = a * (b * c) = (b * c) * a = b * c * a. Thanks, JL

I haven't been taking math for 3 years so I have a question about the following: is 14m6n2 the same as 2mn x 7m5n basically asking this because I am not sure whether or not I can factor the terms out like this if this information is insufficient I can post the whole problem. Thanks in advance.

Hello, I'm trying to prove the time differentiation property of Laplace transform. dx(t)/dt = sX(s) http://img10.imageshack.us/img10/290/tlaplace.jpg http://g.imageshack.us/img10/tlaplace.jpg/1/ how do i continue from here ?

I saw the technique of using a mathematical system called the "Four minute clock". Basically, the clock has 4 numbers, 0, 1, 2 and 3, and only one hand. We can make a summation table which will look like the image attached. According to the text, if there is symmetry (reflection) across the...

There are certain properties of lines of force, I know they are not real, but following these 'properties', given position and intensity of magnetic/electric field sources we will be able to reconstruct these lines without any practicals. So I have a problem with lines of forces. Sources...