Property Definition and 608 Threads

Homework Statement If F(k)=TF\{f(x)\},k\neq 0 where TF is the Fourier transform ,and F(0)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(u)du\neq 0 , show that TF\{\int_{-\infty}^{x}f(u)du\}=-i \frac{F(k)}{k} +\pi F(0)\delta(k) Homework Equations The Attempt at a...

I'm having trouble coming to terms with the following: ln x^n = n ln x Which is all nice and well until I tried ln(x + 6) = 2 ln x which is true for x = 3. however, 2 ln x = ln x^2 .. so ln(x + 6) = ln x^2 .. which is true for x = 3 AND x = -2. so the two different ways...

Homework Statement Let (G, °) be a group such that the mapping f from G into G defined by f(a) = a^(-1) is a homomorphism. Show that (G, °) is abelian. The Attempt at a Solution f(a) = a^(-1) f(a^(-1)) = f(a)^(-1) = (a^-1)^-1 = a in order for a group to be abelian it needs to...

Homework Statement Let f be continuous on [a,b] and suppose that f(x) \geq 0 for all x Є [a,b] Prove that if there exists a point c Є [a,b] such that f(c) > 0 , then \int_{a}^{b} f > 0 Homework Equations The Attempt at a Solution Using my books notation, Suppose P =...

Hi all, I have some questions about photons. I'm at the end of the semester of PhysII in the quantum mechanics section and I'm trying to understand how photons determine the property of an electromagnetic wave. The way the textbook describes it the electromagnetic waves are made up of...

Homework Statement Suppose that f:R->Q (reals to rationals) is a ring homomorphism. Prove that f(x)=0 for every x in the reals. Homework Equations Homomorphisms map the zero element to the zero element. f(0) = 0 Homomorphisms preserve additive inverses. f(-a)=-f(a) and finally...

The twin primes 5 and 7 are such that one half their sum is a perfect number. Are there any other twin primes with this property? It works for p=5. I think it should be of the form 1/2*(p+P+2). Is this true? How can I prove it? Thx

Homework Statement Prove that if f(x) satisfies the functional equation f(x+y) = f(x) + f(y) and if f is continuous then f(x) = cx for some constant c. Homework Equations N/A The Attempt at a Solution Assume |f(a)| > |ca| for some a in the domain of f. Since f is continuous at...

Statement to prove: If x > 0, show there exists n in N (the set of all natural numbers) such that 1/(2^n) < x. My work on the proof so far: Let x > 0. By the Archimedian Property, we know if ε > 0, there exists an n in N such that 1/n < ε. Take x = ε . So there exists an n in N such that...

If all subgroups of a group are normal, is the group abelian? I know that the answer is NO... Can you give a counter-example..? Better still can you logically deduce some property the counter-example must have, which will ease our way to finding it...

Homework Statement Hi, I need to prove that if S is a skew-symmetric matrix with NXN dimension and B is any square real-valued matrix, therefore the product of transpose(B), S, and B is also askew symmetric matrix Homework Equations This is what I know so far. 1.Transpose(S) = -S...

Homework Statement V is a linear space over C, finite n-dimensional h: VxV \rightarrow C is an Hermitian Product, POSITIVE DEFINED and so (V,h) Hermitian Space --------------------------------------------------------------- L: V \rightarrow V, is a Linear Endomorphism of V...

I am trying to show that if X is a topological space, ~ an equivalence relation on X and q:X-->X/~ the quotient map (i.e. q(x)=[x]), then the quotient topology on X/~ (U in X/~ open iff q^{-1}(U) open in X) is characterized by the following universal property: "If f:X-->Y is continuous and...

[FONT="Times New Roman"]Do anyone here can thorugh some light on the creep prroperty of Rene-41. I want to know how this material behaves @1400F? Thanks in Advance Sid...

Prove the following? Vectors (v-w)x(v+w)=2(vxw)

Here's something I know there must be a way to easily figure out... but not by me! THE QUESTION... if I have x number of categories to choose from, how many combinations can I get? for example I think that if I had 4 categories there are 15 possible combinations categories A, B, C, D...

From wikipedia: In metaphysics, impenetrability is the name given to that quality of matter whereby two bodies cannot occupy the same space at the same time. The philosopher John Toland argued that impenetrability and extension were sufficient to define matter, a contention strongly disputed by...

A book I was reading advocated that anyone who was interested in buying land in a rural area find out how much the property taxes on the land are before buying any land. How does one find out what the property taxes will be for a given amount of land?

I'm looking for a gas property software which is used for turbine/expander. Below are the basic requirements for the tool: Inputs: Inlet pressure, inlet temperature, discharge pressure, mass flow, process components & compositions. Outputs: Isentropic head, density at inlet...

Homework Statement More of a simple nomenclature question than a physics question: Is there a specific name for the property of gas that says gas will expand to fill the volume and shape of its container? Or is it just called one of the basic properties of gas? Homework Equations N/A The...

Can someone elaborate? Let I = [0,1], A = {0, 1, 1/2, 1/3, 1/4, \cdots}. Show that the homotopy extension property does not hold on the pair (I, A). Thanks in advance, A

i have got 3 questions... What is material property orientation in orthotropic materials...in what way it differs from material distribution with respect to two or three planes?..and how does it affect the material behaviour?

For which property is the value greater for a solution of a nonvolatile solute than for the pure solvent? a.boiling point b.freezing point c.triple point d.vapor pressure Please explain the answer. thanks

Using a small germanium gamma ray detector I have been collecting data on some newly acquired gamma decay sources. The program I have been using gives me a plot of counts vs energy (well channel, but the channels are proportional to the energy) Thus after collecting data I have a bell shaped...

Given a_{0} = 0, a_{1} = 1, and a_n = Ba_{n-1} - a_{n-2}; prove that \sum_{i=1}^{m} a_{2i-1} = (a_{m})^2

Let D = [d11 d12] [d21 d22] be a 2x2 matrix. Prove that D commutes with all other 2x2 matrices if and only if d12 = d21 = 0 and d11 = d22. I know if we can prove for every A, AD=DA should be true, but I really don't know how to proceed from there. I tried equating elements of AD with...

well i tried the CRC handbook and online search of 2-methoxyethyl-2-methylpropanoate

Given a constant one-form k_1 \ dx + k_2 \ dy + k_3 \ dz in \bold{R}^{3} , and three points \vec{a}, \ \vec{b}, \ \vec{c} in \bold{R}^3 , prove that \int_{\vec{a}}^{\vec{c}} k_1 \ dx + k_2 \ dy + k_3 \ dz = \int_{\vec{a}}^{\vec{b}} k_1 \ dx + k_2 \ dy + k_3 \dz + \int_{\vec{b}}^{\vec{c}}...

What property of the magnet determines which side of it is North and which side is South? I know that we are unable to separate the poles of a magnet (ie cut a magnet in halves and we get two magnets). How come?

Hi, I am just wondering if the zero product property (ab=0 implies a=0 or b=0) can be proven on the integers, or is it directly axiomatic to the defining of the integers? Also, where might I find a definition of the integer axioms? Thanks a lot,

Homework Statement a system has the following property: Its response to a sum of inputs is the sum of its responses to the inputs. (a) Prove that the scaling property holds for any integer scaling factor (b) Prove that the scaling property holds for any rational scaling factor...

My question is stated in the title. I wonder is it that scientists are not able to explain the origin of magnetic moment of elementary particles and say that it's an intrinsic property just like mass.

Let \left\{x_{n}\right\} be a nonempty sequence of monotonically increasing rational numbers bounded from above. Prove that \left\{x_{n}\right\} has a least upper bound in \mathbb{R}. If we choose a monotonically decreasing sequence of upper bounds \left\{b_{n}\right\} with the property that...

hello! i am quite new to material engineering and so my question might seem a bit too obvious. her it is: i have a metal ring-(picture1(304 stainless steel)) i need to know what property of the metal defines the ring's resistance to "opening"- like shown in the second picture thank you very...

I read that a single electron, when passing two slits, would exhibit wave like distribution on target screen. This makes me wonder about the following. 1) Would this have anything to do with the interference by the slots? I understand that my question may be moot because such interference...

So I am looking at the proof for this in a linear algebra book and I half way get it: Theorem: If the all elements of the jth column of a determinate D are linear combinations of two columns of numbers, i.e., if D=\lambda b_{i}+uc{i} where lambda and mu are fixed numbers, then D is...

Given a positive whole number n, \exists N with the following property: if A is a subgroup of {1,2,...,N} with at least N/2 elements, then there is a positive whole number m<= N - n such that |A \cap{m+1, m+2,..., m+k}|>=k/2 \forall k = 1, 2, …, n.

Homework Statement The theorem about the closest point property says: If A is a convex, closed subspace of a hilbert space H, then \forall x \in H\,\, \exists y \in A:\,\,\,\, \| x-y\| = \inf_{a\in A}\|x-a\| I have to show that it is enough to show this theorem for x = 0 only, by...

Can anybody tell me what are Residual property and Excess property in thermodynamics for?

Prove that if the functions g:[a,b] --> R and h:[a,b] --> R are continuous, with h(x)\geq0 for all x in [a,b] then there is a point c in (a,b) such that \int h(x)g(x)dx = g(c) \int h(x)dx when the integrals go from a to b --- My immediate thought was Integral MVT, so I said \int...

So, I know the proof for a non-decreasing set using the continuity property, and I'm wondering if I have to use the intersection of all pairwise disjoint sets rather than the union, as seen in the non-decreasing proof. Any help would be greatly appreciated!

Someone please help me with this qiestion: Prove that for all integers a, b, and c, if a divides b but not c then a does not divide b + c, but the converse is false. Thanks.

What property of light does the photoelectric effect display?

I know this is elementary but I'm having trouble with proofs of some of the convolution properties: 1. f * (g * h) = (f * g) * h 2. (cf) * g = c(f * g) = f * (cg) Please show me the proofs step by step or lead me to a link where the detailed proofs are displayed. Sorry for such...

Is it possible for atoms of the same chemical element to have different chemical properties? My attempt Isotopes of an element differ from one another by the number of neutrons in the nucleus. They have same number of proton in the nuclei so they have the same chemical properties but not...

If gravity is a "property" of Mass, and mass is a "property" of matter, and matter is known to be composed of highly integral infinitessimal Force Fields, why jump to the conclusion of Gravitons, when one has not thoroughly defined Force Field. Of what are these force fields composed? Is the...

The adjoint of an operator A is defined as an operator A* s.t. <\phi|A\psi> = <A^{*}\phi|\psi>. How would you use the properties of inner products (skew-symmetry, positive semi-definiteness, and linearity in ket) to show that (cA)* = c*P* Note that I am using the conjugate and the...

Homework Statement Given x<y for some real numbers x and y. Prove that there is at least one real z satisfying x<z<y Homework Equations This is an exercise from Apostol's Calculus Vol. 1. The usual laws of algebra, inequalities, a brief discussion on supremum, infimum and the...

Homework Statement The nested set property: "If {F_k} is a decreasing sequence of non empty compact sets in a metric space (M,d), then their intersection is non empty." First I cooked up a proof of my own and then I read the one provided by the book. It seemed to me that they were perfectly...

If I put some kind of alcohol, can it destroy the property of vitamin C?