Existence Definition and 602 Threads

What is 'Quantum Domain'? I read something about it being a level of existence... If it is a level of existence, what sort of classification of existence are we talking about?

If counting/positive numbers exist, do they imply the existence of negative numbers? I'd say yes, because there's always a bijection that maps the lowest counting number of the set to the highest, then the second lowest to the second highest, etc. This reversal of order/mirroring is possible...

Investing function fc(x) = (6/x)+(x/2)-c where 0<= c <=3 a) Use alegbra to find the positive fixed point (in terms of c) and identify its exact interval of existence b) Use algebra and calculus to find the exact interval of stability of the fixed point c) Use algebra to find the points of the 2...

Hi to everyone! I'm searching information about evidences of photons existence. It seems like the photoelectric effect isn't for itself a proof of photons existence. Some people tried a semi-classical discussion of this effect (Lamb - "The Photoelectric effect without photons"). I'm...

Homework Statement Given that the divergence of a vector C = 0, show that there exists a vector A such that C = curl A. Homework Equations See above. The Attempt at a Solution No clue. Can this be proved with introductory vector calculus? That's all I know, including many of the...

I am given that a DE with the form x' = f(x) is defined on the interval (c,b) where f has continuous derivative on its domain How do i show that if f(p) = f(q) = 0 and x(t) is between p and q then the maximal interval of existence of x is (-∞, ∞)

i was given that f is a real alued function defined on an open interval I with IVP x'(t) = f(x(t)) where x(s) = b how would I go to prove that if I is continuous on I and b is in I then there exists a postive number say k and a solution x for the initial value problem defined on (s-k,s+k)

Hey! :o I am looking at the following that is related to the existence of the optimal approximation. $H$ is an euclidean space $\widetilde{H}$ is a subspace of $H$ We suppose that $dim \widetilde{H}=n$ and $\{x_1,x_2,...,x_n\}$ is the basis of $\widetilde{H}$. Let $y \in \widetilde{H}$ be...

Homework Statement Prove Existence Unique Real Solution to ## x^{3} + x^{2} -1 =0 ## between ## x= \frac{2}{3} \text{and} x=1## The Attempt at a Solution ## x^{2} ( x+1) =1 ## I know that the solution is x =0.75488, but this came from some website. How do I find this number without a calculator?

Hello, My question is this. Is it possible to prove that there exist an eigenvectors for a symmetric matrix without discussing about what eigenvalues are and going into details with characteristic equations, determinants, and so on? This my short proof for that: (The only assumption is ##A##...

I don't know very much about differential geometry but from the things I know I think that the metric is somehow the quantity which specifies what kind of a geometry we're talking about(Though not sure about this because different coordinate systems on the same manifold can lead to different...

Does Casimir plates prevent photon existence only perpendicular to them? I mean, Casimir attraction arises from the fact that the plates prevent some wavelenghts of photons to exist in between them, so an imbalance arises and pushes the plates together, right? But what about photons in other...

Some sources I have checked define the Hodge dual of a form \omega \in \Omega^p as the object such that \forall \eta \in \Omega^p: \eta \wedge \omega^\star = g(\eta,\omega) \textrm{ Vol} (where "Vol" is a chosen volume form). I can see that there can be only one form with such a solution...

I am reading and trying to follow the notes of Keith Conrad on Tensor products, specifically his notes: Tensor Products I (see attachment ... for the full set of notes see Expository papers by K. Conrad ). I would appreciate some help with Theorem 3.2 which reads as follows: (see attachment...

Hello Everyone. I have a question. Suppose I have a differential equation for which I want to find the values at which \displaystyle f(x,y) and \displaystyle \frac{\partial f}{\partial y} are discontinuous, that I might know the points at which more than one solution exists. Suppose that...

Prove the following Suppose that $f$ is piecewise continuous on [0,\infty) and of exponential order $c$ then \int^\infty_0 e^{-st} f(t)\, dt is analytic in the right half-plane for \mathrm{Re}(s)>c

Hi everyone, :) Here's a question I am stuck on. Hope you can provide some hints. :) Problem: Let \(U\) be a 4-dimensional subspace in the space of \(3\times 3\) matrices. Show that \(U\) contains a symmetric matrix.

Homework Statement . Let ##(M,d)## be a metric space and let ##f:M \to M## be a continuous function such that ##d(f(x),f(y))>d(x,y)## for every ##x, y \in M## with ##x≠y##. Prove that ##f## has a unique fixed point The attempt at a solution. The easy part is always to prove unicity...

Let n be a positive integer, and for each $j = 1,..., n$ define the polynomial $f_j(x)$ by f_j(x) = $\prod_{i=1,i \ne j}^n(x-a_i)$ The factor $x−a_j$ is omitted, so $f_j$ has degree n-1 a) Prove that the set $f_1(x),...,f_n(x)$ is a basis of the vector space of all polynomials of degree ≤ n -...

Hi everyone, :) I am trying to find an approach to solve this but yet could not find a meaningful one. Hope you can give me a hint to solve this problem. Problem: Prove that for any bivector \(\epsilon\in\wedge^2(V)\) there is a basis \(\{e_1,\,\cdots,\,e_n\}\) of \( V \) such that...

Homework Statement Prove that if ##S## is a nonempty closed subset of ##E^n## and ##p_0\in E^n## then ##\min\{d(p_0,p):p\in S\}## exists. 2. The attempt at a solution If ##p_0## was in ##S## why would ##\min\{d(p_0,p):p\in S\} = 0?## Is it just because it is the minimum? How about if ##p_0...

Homework Statement Let ##f## be a continuous map from ##[0,1]## to ##[0,1].## Show that there exists ##x## with ##f(x)=x.## 2. The attempt at a solution I have ##f## being a continuous map from ##[0,1]## to ##[0,1]## thus ##f: [0,1]\to [0,1]##. Then I know from the intermediate value...

A common definition of an inertial frame is that it is a reference frame in which space and time are homogeneous and isotropic; see, for instance, Landau and Lifshitz's Classical Mechanics. L&L also use homogeneity and isotropy to justify the functional form of the Lagrangian. But intuitively...

Iam wondering whether 'infinity' has real physical existence or just a mathematical paradox? If it does have a physical existence why don't we come across any quantity which is physically eternal? Someone please help..

I would like to know how this article applies to the possible existence of FTL particles. Does it point to a possible violation of c as the ultimate speed limit of a particle? In layman's terms what is this paper saying? http://arxiv.org/abs/1309.3713 Thanks

My book has a theorem of the uniqueness of the Lebesgue measure. But my question is: Is it necessarily a good thing that something in mathematics is unique and seems to indicate that this is very important. But my question is? Would the theory of measures fail if there existed another measure...

Hi all, I have a quick question about limits. This is something I should know but shame on me I forgot. If a function is bounded both above and below but isn't monotonic and is not necessarily continuous at all points, how do I go about proving its limit exists? In particular I am thinking...

Hi all, I have my exam in differential equations in one week so I will probably post a lot of question. I hope you won't get tired of me! Homework Statement This is Legendres differential equation of order n. Determine an interval [0 t_0] such that the basic existence theorem guarantees...

Question : suppose space comes into existence (expansion of space) where ever there is a local lack of mass or energy and also suppose things do come in and out of existence (for example virtual particles). If so, could the singularity of the big bang have undergone a cascade of points of...

Prove or disprove for every prime P there is a K such that 10^k=1\text{mod}P. I arrived at this statement while proving something and can't find progress here is the problem which may doesn't matter but if you wan't to find the origin [here]

It seems to me that the question as to whether the universe is infinite or not carries the same validity as the question as to electron, quarks, etc. being infinitesimal or otherwise stated being modeled as point particles. It seems to me that these two quandaries are linked and perhaps can...

in waves and oscillations i read that any bounded medium oscillates in a particular freuency...why is it so?i need a proper reason for this

The "Dark Flow" & the Existence of Other Universes --New Claims of Har I just saw this big news story, "The "Dark Flow" & the Existence of Other Universes --New Claims of Hard Evidence" and thought that others would be interested in hearing this here. Dark Flow isn't new is it? Is this bold...

Hi! I was wondering: is it possible to have a non-orientable surface in 3D which is parametrized by u and v, with u and v periodic (i.e. is it possible to map the torus continuously into a non-orientable surface in 3D?) If so, does anyone have any explicit examples?

P(x) = "x is Provable" axiom 1 : P(x)→x "Statement x can be proven true." 1. (x∧¬x) consider a contradiction 2. x simplification(1) 3. ¬x simplification (1) 4. x∨∀sP(s) addition (2) 5. ∀sP(s) disjunctive syllogism (3,4) 6. (x∧¬x)→∀sP(s) conditional proof (1,5) "Anything is provable if it follows...

Homework Statement Hello, I have a following problem. For a three-qubit state i need to trace subsystem. For this subsystem AB I calculate eigenvalues and eigenvectors. The task is now to determine according the eigenvalues and eigenvectors whether quantum discord in this system is non-zero...

Are systems ever in a pure quantum mechanical state? If they are, is it possible to know the precise pure QM state? The example I am thinking of is the spin of an electron. If we measure the spin about the "z-axis" and find the result to be "up" then we say the electron is in the pure state...

Hello MHB, Integrate \int_0^4 \frac{dx}{(x-2)^3} We are suposed to integrate when x goes from zero to 4 but when x is 2 the integration does not exist so the integrate does not exist as well? Regards, |\pi\rangle

How does it work, exactly? Assume I have a vector field function and I take the curl of it. If I get a curl of zero, then does that guarantee that there is no potential function? And if I get a curl of non-zero, does that guarantee that there is a potential function? I googled this...

Here is the question: Here is a link to the question: Maths: Caluclus > Functions? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Suppose you have an ODE y' = F(x,y) that is undefined at x=c but defined and continuous everywhere else. Now suppose you have an IVP at the point (c,y(c)). Then is it impossible for there to be a solution to this IVP on any interval containing c, given that the derivative of the function, i.e...

The vector potential in classical electrodynamics can be introduced due to the fact that the magnetic field is the vortex: div \vec B = 0 → \vec B = rot \vec A In the four-dimensional form (including gauge) Maxwell's equations look particularly beautiful: \partial_{\mu}\partial^{\mu} A^{\nu} = j...

Greetings, My questions below could be categorized into a mixture of “history of chemistry” and “experimental basis for chemistry”. I’m having difficulty phrasing the questions that I have, so I’m going to start by stating them as directly as I can, and then spend the rest of this post...

[b]1. Let a != 0 and b be elements of the integers mod n. If the equation ax=b has no solution in Zn then a is a zero divisor in Zn The Attempt at a Solution Not sure where to start on this proof, I keep trying to find something using the properties of modular arithmetic but am coming up empty

Homework Statement y''-4y=12x Homework Equations I don't know The Attempt at a Solution http://imageshack.us/a/img7/944/20130207102820.jpg I'm not sure if I did this right, I'm putting this here to make sure. Please respond within 3 hours if you can because it will be due.

Homework Statement Find a solution of the IVP \frac{dy}{dt} = t(1-y2)\frac{1}{2} and y(0)=0 (*) other than y(t) = 1. Does this violate the uniqueness part of the Existence/Uniqueness Theorem. Explain. Homework Equations Initial Value Problem \frac{dy}{dt}=f(t,y) y(t0)=y0 has a...

according to special relativity theory, any object that has relative velocity also has lorenz- contraction L' = L0 *sqrt (1-(v/c^2)) it sounds odd that this is only kind of length contraction known to exist. why there are no other kind of length expansions or contractions, or are them...

Homework Statement Prove or disprove: \exists a binary operation *:\mathbb{N}\times\mathbb{N}\to\mathbb{N} that is injective. Homework EquationsThe Attempt at a Solution At first, I was under the impression that I could prove this using the following operation. I define * to be...

Hello! This question may seem silly. I'm a first year engineering and computer science student, not a mathematics student. I have only recently become interested in prime numbers, factorization algorithms, and prime number finding algorithms. I know only extremely elementary number theory...

Homework Statement given ##A \subset \mathbb{R}## ##f:A \subset \mathbb{R} \to \mathbb{R}^+## considering the function g such that: ##g(x):=\sqrt{f(x)} x \in A## with ##x_0## limit point in A. Prove that if ##\displaystyle \lim_{x \to x_0} f(x)## exists, then ##\displaystyle \lim_{x \to...