Property Definition and 608 Threads

Suppose S\subsetℝn is compact, f: S-->R is continous, and f(x)>0 for every x \inS. Show that there is a number c>0 such that f(x) ≥ c for every x\inS. Attempt: Since S is contained in Rn is compact, then S is closed and bounded. By the extreme value thm there exists values a,b that are an...

Hi guys, I've been playing around with structure generated patterns and have come across one which has caught my attention. I am only just starting to learn about number theory and so I am sure someone might be able to provide an explanation for this. Let me describe what I did then show you the...

Suppose a space X has the intermediate value property (f: X->Y continuous, Y has the order topology), then X is connected. How would you show this? This is just the converse of the intermediate value property.

Homework Statement Let y(t) be the convolution of x(t) with h(t), show that the area under y(t) is the product of the areas under x(t) and h(t) Homework Equations Convolution definition The Attempt at a Solution I found a derivation but it skips a step, uploaded it here: htt...

Doesn't a linear change of coordinates preserve complete intersection for a set of homogeneous polynomials, all of the same degree, in a polynomial ring? That is, apply a change of coordinates to a set of homogeneous polynomials {f_1,... f_k} in C[x_1,...,x_M] to obtain {h_1,..., h_k}. Suppose...

Hello team! I saw the other day in a textbook that the Dirac delta function of the form d(x-a) can be written as d(a-x) but the method was not explained. I was wondering if anyone know where this comes from. I've been googling but can seem to find it out. Any help would be appreciated...

Hi, All: I'm a chemistry ignorant. Please bear a bit. Just curious as to the chemical explanation for why the mixture of bakind soda and (kitchen/cooking) vinegar is an effective disinfectant. Is this a neutralization reaction, with vinegar as the acid and bakind soda as the base? If...

Playing around with logarithms I found an interesting property that "log b^n(a^n) = log b(a)". Then I tried to find some kind of proof that this is right and not only a coincidence. Ι made a gereral formula for any value of both n's (α and β) so that "log b^β(a^α) = x". Therefore "a^α = b^(β*x)"...

Homework Statement use the sifting property of the dirac delta function to evaluate the following integrals. a) integral from -inf to inf sin(t) delta(t-pi/2)dt b) integral from 0 to 2 e^(2t) delta(t-1)dt c) integral from 0 to pi e^tan(theta) delta(theta- 3pi/4)d(theta) d)...

Hi. I have the following sentence: \begin{array}{l} A,B \in {M_{nxn}}\\ A \ne 0\\ B \ne 0\\ {\rm{if }}AB = 0{\rm{ then}}\\ {\rm{|A| = 0 or |B| = 0}} \end{array} I know this is true but how can I realize? Just thinking about an example? Thanks!

Hi, I know that if I have a monomorphism f:X\rightarrow Y then for any arrows g,h:A \rightarrow X we have f \circ g = f \circ h \; \Rightarrow \; g=h However in a topological space, if I have f to be an injection but now have f \circ g \simeq f \circ h (where \simeq denotes homotopic) then...

Homework Statement How can i prove this property of Delta, http://e1204.hizliresim.com/w/d/4bw2j.png Homework Equations This is my homework from John David Jackson's Classical Elektrodynamics book The Attempt at a Solution I can't an attempt. Some properties is proved at wiki and...

Homework Statement Hello friends, i couldn't find a solution for the question below. Can you help me? Thank you very much. Let α-norm and β-norm be two different norms on ℝn. Show that f:ℝn->ℝm is Lipschitz in α-norm if and only if it is Lipschitz in β-norm Homework Equations...

I am reading through Kiselev's Geometry: Book I. It is a plane geometry textbook and in the introduction it says the following "One can superimpose a plane on itself or any other plane in a way that takes one given point to any other given point, and this can also be done after flipping the...

I can't for the life of me figure out why the underlined sentence in red is true: Could someone clarify?

How do I show that Maslov index satisfies the next property (product property). Let \Lambda : \mathbb{R} / \mathbb{Z} \rightarrow \mathcal{L}(n), and \Psi : \mathbb{R}/\mathbb{Z} \rightarrow Sp(2n) be two loops, then if \mu is defined as the Maslov index then \mu(\Psi \Lambda )=...

Homework Statement Prove the following: Let \rho be the correlation coefficient. Prove: \rho(X, Y) = 1 \iff P(Y=aX+b) = 1Homework Equations \rho(X, Y) = cov(X,Y)/\sigma_x\sigma_y The Attempt at a Solution I have no idea how to prove this, I know that rho must lie between 1 and -1 (inclusive)...

Proving the "triangle inequality" property of the distance between sets Here's the problem and how far I've gotten on it: If you are unfamiliar with that notation, S(A, B) = (A \ B) U (B \ A), which is the symmetric difference. And D(A, B) = m^*(S(A, B)), which is the outer measure of...

I feel like I'm missing something obvious, but anyway, in the text it states: lim as n→∞ of an+bn = ( lim as n→∞ of an ) + ( lim as n→∞ of bn ) But say an is 1/n and bn is n. Then the limit of the sum is n/n = 1, but the lim as n→∞ of bn doesn't exist and this property doesn't work...

The definition of 'Bounded above' states that: If E⊂S and S is an ordered set, there exists a β∈S such that x≤β for all x∈E. Then E is bounded above. The 'Least Upper Bound Property' states that: If E⊂S, S be an ordered set, E≠Φ (empty set) and E is bounded above, then supE (Least Upper...

The Order Divisibility Property states that if an = 1 (mod p), then the order ep(a) of a (mod p) divides n. How can I go about proving this? Additionally, if a is relatively prime to p, when does the congruence am = an (mod p) hold? Is there a proof for this as well? Thanks!

Homework Statement If x is a real number, show that there is an integer m such that: m≤x<m+1 Show that m is uniqueHomework Equations Archimedean Property: The set of natural numbers has no upper boundThe Attempt at a Solution I'm having trouble with showing that m is unique. If x is a real...

I have Recently Buyed a new Farm House and Taxes on that is too high according to the actual price of that property, so to get reduction on my property tax. Do I need a Property tax lawyer? Please Help…..

Hi, I have a quick question about certain algebraic properties of convolution. If I have 3 functions x(f), y(f) and z(f), is the following true? [x(f) . g(f)] * z(f) = [x(f) * z(f)].g(f) I looked on Wikipedia but there's only a property like this if one of the terms is a scalar, so most...

Homework Statement two hundred seventy grams of argon at a pressure of 160kpa and a volume of 1.3 m^3. Homework Equations pv=nrt The Attempt at a Solution (160^3)(1.3) = (.27)(8.31)(t) 208=2.2437t t=92.7

Homework Statement a gas in 3-L container at a pressure of 300kpa and a temperature of 700 degrees celsius, and with a mass of .66 g. Homework Equations pv=nrt The Attempt at a Solution (300)(v)= (.00066 kg)(8.31)(191906 k) = 3.51 im not sure what conversion needs to be...

Hey! So when I enter this in Mathematica In[246] = ZTransform[Sum[f[k] g[k - n], {k, 0, n}], n, z] InverseZTransform[%, z, n] I get: Out[246] = ZTransform[f[n], n, z] ZTransform[g[-n], n, z] Out[247] = InverseZTransform[ZTransform[f[n], n, z] ZTransform[g[-n], n, z], z, n]...

Homework Statement As an example, if we find a DFT of x[n]={1,1,0,1} the result will be X(m)={3,1,-1,1} Homework Equations My Question is that as we know DFT holds symmetry property, why this answer does not void for that property?

I'm trying to prove eA eB = eA + B using the power series expansion eXt = \sum_{n=0}^{\infty}Xntn/n! and so eA eB = \sum_{n=0}^{\infty}An/n! \sum_{n=0}^{\infty}Bn/n! I think the binomial theorem is the way to go: (x + y)n = \displaystyle \binom{n}{k} xn - k yk = \displaystyle...

Is color an intrinsic property of a substance? I thought that if a red object is in an enclosed space, so that no light gets in, will no longer be red - and what makes the object "red" is that electrons absorb all colors of light and then reemit (reflect) the red light. Therefore, if no light...

Homework Statement Show: sinh(z + i2(pi)) = sinh(z) using sinh(z) = (ez - e-z)/2 Homework Equations The Attempt at a Solution So far I have (ex + i(2∏+y) - e-(x+i(2∏+y))/2. Need help proceeding from here. My thoughts were to define a z' = x + i(2∏+y) but I don't think that I can then say...

Referring to following video, if I magnetize my screw driver having a magnetic property in this way, I would like to reverse the process, is there any approach to completely remove this magnetic property? so there is no magnetic property from my screw driver. Does anyone have any suggestions...

I'm interested in the proper way to give a mathematical definition of a certain geometric property exhibited by certain maps from points to sets. Consider mappings from a n-dimensional space of real numbers P into subsets of an m-dimensional space S of real numbers. For a practical...

Mean Value property (harmonic functions) with a source?? Homework Statement I understand that the heat equation may yield ∂u/∂t=0 on the LHS and on the RHS we may still have Uxx+Q where Uxx is partial with respect to x twice and Q is a heat source. U in our case may be the temperature...

Homework Statement Suppose that f is holomorphic in an open disc U and that Re(f) is constant in U. I have to show that f must be constant in U. Also what is the essential property of the disc U that it used here? Give an example of an open set U for which the conclusion fails.Homework...

Homework Statement proof if f(n) = O(g(n)) then g(n) = O(f(n)) = stands for element of c is some constant Homework Equations if f(n) <= c*g(n) then f(n) = O(g(n)) if g(n) <= c*f(n) then g(n) = O(f(n)) The Attempt at a Solution I tried to go from the left-hand-side(LHS) to the...

My book defines the covariant derivative of a tangent vector field as the directional derivative of each component, and then we subtract out the normal component to the surface. I am a little confused about proving some properties. One of them states: If x(u, v) is an orthogonal patch, x_u...

I'm wondering if there's a term for the property of spheres that makes gravity pull equally on all aspects of the sphere's mass. The wording for what I'm asking is tricky, so I'll give an example of a shape that wouldn't have this property, a long prism. If you drop a long prism on an angle...

Homework Statement Hi, We meet again PF, this time I am little stumped on the following question(link posted down). Homework Equations Link to the question "Question" The Attempt at a SolutionI think I get the gist of it for part (i) my calculated value for equlibirum separation is about...

Homework Statement G=\{x\in R|0\leq x<1\} and for some x,y\in G define x*y=\{x+y\}=x+y-\lfloor x+y \rfloor Homework Equations The Attempt at a Solution I want to proof Associative property: x*(y*z)=(x*y)*z \Leftrightarrow x*(y+z-\lfloor y+z \rfloor)=(x+y-\lfloor x+y \rfloor)*z \Leftrightarrow...

Does anyone know what the physical property measured in seismic surveys is? Seismic surveys used in searching for hydrocarbons to be more specific. I was thinking it would be the rocks density but I'm not sure, can anyone help please? :)

Edit: I answered my own question, I guess this thread serves no purpose so mods, you can delete this. y = x^2 ln y = ln x^2 ln y = 2 ln x Can we do the same thing with: y = x^{2/x} ln y = ln x^{2/x} ln y = \frac{2}{x} x Would that be correct? I just want to make sure because I used this...

Hi. I just saw on wikipedia that natural logarithm has such a property: [x/(1+x)] < ln (1 + x) < x (http://en.wikipedia.org/wiki/Natural_logarithm) Can anyone pls tell me how to prove this? Proving [x/(1+x)] and ln (1 + x) less than 'x' is easy.. But how abt [x/(1+x)] < ln (1 + x)...

Hi, If we have two commuting operators A and B, is true that any function of A will commute with any function of B? I have a result which takes [L_{z},r^{2}]=0 and claims that [L_{z},r]=0. How can this be proved? Thank you

1. The problem I have a problem grasping what the point of the sifting property of the Dirac function is. It isolates the value at a point in a function, right? Doesn't just substituting that point into the function do exactly the same thing? Homework Equations Sifting poperty: if f(t)...

I have a question. I understand that one of the main problems with a theory of everything is the unification of gravity with the other three forces. Could this be due to the fact gravity may not be a force at all but a property of space? If Einstein essentially defined gravity as such, then why...

Hi, this is my first post, and I'm not an expert of any kind or do not believe I am. I have always been fascinated by science, but I some time ask myself some questions, here's one I don't seam to find much info. I found a lot of treads that mentioned the subject but nothing that actually...

Homework Statement N refers to the set of all natural numbers. Part 2: From the previous problem, we have σn : N → N for all n ε N. Show that for any n ε N, σ(n+1)(N) is a subset of σn(N), where we have used n + 1 for σ(n) as we defined in class. 2. The attempt at a solution For Part 2, I...

Homework Statement Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if: e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s)) Is a true statement or not. I've searched...

Why is it that a metric space (X,d) always has two clopen subsets; namely {0}, and X itself? Rudin calls it trivial, and so do about 15 other resources I've perused. What confuses me is that if we define some metric space to be the circle in ℝ2: x2+y2 ≤ r2, then points on the boundary of...