Existence Definition and 543 Threads

Hi all. I'm currently working on a problem that has led me to an integral equation of the form: u(t)=\int_0^t K(t,\tau)f(\tau)\, \mathrm{d}\tau \qquad t\in (0,T) or simply u=Kf. I've managed to prove the following: K :L^2(0,T)\rightarrow L^2 (0,T) K is compact. u\in L^2(0,T)...

ultra sensitive microphone or technique for listening to inner ear A friend has very loud tinnitus. He says it is constantly louder than anything else he can hear. Nothing can be heard by an independant observer such as myself, but it is possible that a sound with a small power level is so...

Hi! Thanks for reading! :) Homework Statement Y(x) is the solution of the next DFQ problem: y' = [(y-1)*sin(xy)]/(1+x^2+y^2), y(0) = 1/2. I need to prove that for all x (in Y(x)'s definition zone), 0<Y(x)<1. Homework Equations I just know that this excercise is under the title of "The...

Fix b >1, \ y >0 , and prove that there is a unique real x such that b^{x} = y . Here is the outline: (a) For any positive integer n , b^{n}-1 \geq n(b-1) . Why do we do this? (b) So b-1 > n(b^{1/n}-1) . (c) If t>1 and n > (b-1)/(t-1) then b^{1/n} < t . etc.. Is...

This is a bit philosophical. What does it mean to say that a mathematical object exists? To add some concrete thoughts, I recently read the following: "The empty set has the property that for all objects x, the statement 'x is in the empty set' is false." But this statement reeks of all...

Let A be a constant. Let f(t) be an integrable function in any interval. Let h(t) be defined on [0, oo[ such that h(0) = 0 and for any other "t", h(t) = (1 - cos(At)) / t It is not difficult to see that h is integrable on [0, b] for any positive "b", so fh is also integrable in...

As I understand it, according to the Copenhagen interpretation of QM, nothing can be said to exist until it is observed. I have also read that it is impossible to observe virtual particles in an experiment. How is it then that virtual particles can be said to exist?

Its my understanding that Bayes' Theorem was presented by a clergyman who used it to answer whether God exists. Does anyone on this forum knows about the conclusion he reached through his research.

Homework Statement y y\prime = 3 y(2) = 0 Homework Equations Solve and find two different solutions. The Attempt at a Solution F = \frac{3}{y} \frac{\partial F}{\partial y} = \frac{-3}{y^2} Where do I go from here?

Homework Statement Hello. My following problem is partially about the maths concept involved but is largely to do with what the question is actually asking? It's from an online quiz and a printscreen of it has been provided as an attachment. Homework Equations See attachments for the...

I ask this because it seems to me there is a striking paradox to a God's existence claim. I do think that what is and what isn't are conceptions that depend on our perception of the universe. So how, then, if we take down this road of thought, can we speak of existence outside the physical...

Homework Statement Prove that for all x there exists and x if it is an element of the positive integers, then there is an integer y and an integer z. Homework Equations The Attempt at a Solution I know that the contrapositive would be "If there is not an element of the positive...

So, I was recently think about something. Don't ask me how I thought of this, but positrons and anti-protons were on my mind all day and I thought of something. I thought about inertia. I thought about it and the more and more I did I figured that there must be something within matter that makes...

Hello! Can anyone help me with the following question about black holes? Let us consider a massive star which at the end of its evolution collapses into a black hole (say a Schwarzschild black hole, for the sake of simplicity). An observer far away, in its coordinate time, will never see the...

How do you prove the existence but not necessarily the value of a limit?

I am familiar with the existence and uniqueness of solutions to the system \dot{x} = f(x) requiring f(x) to be Lipschitz continuous, but I am wondering what the conditions are for the system \dot{q}(x) = f(x) . It seems like I could make the same argument for there existing a...

[SOLVED] Existence of solution to integral equation Homework Statement There's k:[0,1]²-->R square integrable and the operator T from L²([0,1],R) to L²([0,1],R) defined by T(u)(x)=\int_{0}^{1}k(x,y)u(y)dy (a) Show that T is linear and continuous. (b) If ||k||_2 < 1, show that for any f in...

[SOLVED] Evidence for the existence of neutrinos. [solved]

Homework Statement I was talking with my maths lecturer about how he knew certain special differential equations such as y'' = y has only y = e^x + e^-x as a possible solution. I understand the superposition principle but not why only y = e^x satisfies the DE. Why can't there be some other...

Because of the existence of sterile neutrino, how and why it gives effect on the big bang nucleosynthesis more than active-active neutrino oscillation. Its a question on behalf of my friend. thanks for any help

Homework Statement It is a theorem in my book that if f and g are two Lebesgue integrable complex valued functions on R, then the integral \int_{-\infty}^{+\infty}|f(x-y)g(y)|dy is finite for almost all x in R. Why not all? f is integrable, hence bounded, say, by M. Therefor, whatever x, we...

I have a question. This question, you should know, is based on something that I actually haven't heard in a classroom or anywhere legitimate, so if the assumption that I have that I'm asking my question about is false, just let me know :) Alright, the thing I'm assuming is true is that...

After mulling over special relativity for a while, I have come to some conclusions that seem correct, but I don't know if I'm on the right track. I'd like to know what some of you think. Please keep in mind that I only recently started learning about relativity, so I'm somewhat of a layperson...

I'm reading a proof where there's a conclusion: "Since zW\subset W, there is an eigenvector v\neq 0 of z in W, zv=\lambda v." There W is a subspace of some vector space V, and z is a matrix, in fact a member of some solvable Lie algebra \mathfrak{g}\subset\mathfrak{gl}(V). (Could be irrelevant...

Let w be a 1-form on smooth manifold M. Then is there a vector field X such that locally w(X)=f where f:M-->R continuous? How can I prove it? Thanks.

I have 2 maps f and h such f :\, (\mathcal{X}, \mathbb{E}) \rightarrow (\mathcal{Y}, \mathbb{K}) h :\, (\mathcal{X}, \mathbb{E}) \rightarrow (\mathcal{Z}, \mathbb{G}) where \mathbb{K} and \mathbb{G} are \sigma-algebras on the spaces Y and Z respectively, and \mathbb{E} =...

Could you please explain the theory intuitively and provide a proof to it. I understand how to apply it but i want to understand the logic behind it.

I just don't understand the idea behind it. I hate it when they throw these theories at us without proofs or elaborate explanations and just ask us to accept and applym mthem. Anyone care to enlighten me?

Homework Statement Suppose f(t,x) is a continuous vector valued function on \mathbb{R} \times \mathbb{R}^n. If f is locally Lipschitz with respect to x with the property that \|f(t,x)\| \le C \|x\| for some positive constant C > 0, then prove that the maximum interval of the existence of the...

I have recently been studying Gregory Chaitin's "algorithmic information theory" for a school project. It describes the complexity of mathematical objects by the size of the smallest Turing machine program capable of computing them (in bits). It also defines a "random" object as one with an...

From what I understand, vacuum energy is a form of energy that exists in freespace, even when completely devoid of matter. So, I have two questions: 1. Can vacuum energy exist if there were no matter anywhere in the universe? 2. If so, where does this vacuum energy come from?

Are we sure about the existence of virtual particles?

Hello, I just reading and learning QFT and there is something I've been wondering, hopefully somebody here can help me. Let's say we have an interacting Quantum Field Theory, such as Quantum Electrodynamics if we want to compute an amplitude such as two electrons scattering off each other, then...

What is "existence" and what will it mean to "exist" ? What will it mean that I (eventually) does exist ? What will it mean that something outside me exist as observed by me ? What will it mean that something outside me exist as I does not observe it ? What is then "exisistence" ...

Wiltshire casts doubt on existence of "dark energy" Wiltshire is a minority voice in cosmology, but one worth listening to. Speculation about a "dark energy particle" would be in vain if the appearance of acceleration can be traced to classic GR effects, which is what he tries to do. Wiltshire...

I would like to find a proof for the existence of the instantaneous center, and show that it only exists for velocity and not acceleartion. Anyone know where I could find this proof.

Hi everyone I'm currently readig Bruce Rosenblum & Fred Kuttner's book Quantum Enigma: Physics Encounters Consciousness and studying to be an NLP practitioner as well as practising tai chi. There are lot more parallels in these three areas than I imagined there would be. I have a few...

According to Klein Kaluza theory of fifth dimension (followed by string theory), there is an elecromagnetic dimension in which every particle of Universe (in Dirac Vacuum) perform translatory and rotational motion due to which they drag the e-m dimension. Thus if any two particles are placed...

I have been recently introduced to the idea of Jordan form of a matrix, and I have attempted to prove it. However, there is one step that I cannot prove. If I can prove the step, then everything else is done. Let A be a m by m matrix with characteristic polynomial ch(x)=(x-\lambda)^{m} I want...

Homework Statement A plane is colored blue and red in any way . Prove that there exists a rectangle with vertices of the same color Homework Equations Its obviously true. The Attempt at a Solution I was thinking proofy by pig hole, but haven't quite figured it out.

i need to prove diprove that there exist matrices A1,A2,...,As such that rank Ai=1 for every i=1,...,s and A=A1+A2+...+As with rankA=10. my feeling this is not true, i thought trying to prove this by ad absrudum, let us assume that they exist, then the rows of Ai are scalar multiple of one row...

I'm reteaching electrodynamics to myself on a more rigorous footing, and I'm trying to prove to myself that setting the divergence of the vector potential is justified using a gauge shift. I could use the Helmholtz theorem to do this, but the problem with this from my perspective is that I...

RE: Thoughts on existence (& happiness) Sorry I'm not sure if its o.k. to continue a thread, I just find this an interesting subject because it's such a basic question. What are peoples reasons for living from one day to another? Not only as individual humans but as a whole specie. I'm not...

This poll presents these options "I experience life as a physical phenomenon" and "I experience life as a non - physical phenomenon" and will include the obligatory third option of "all of the above" and the 4th choice "I experience life in a way other than physical, non-physical and not...

There are certain possibilities for the form of existence from my point of view but one of these possibilities seems to be really logical and sounds very likely to be true which is given as follows I'd be glad to receive your comments on this subject; Let’s imagine two astronomers traveled...

Greating my friends, I have just returned home today from heart surgery. I still feeling the effects of the operation, because I'm affried the hospital send me home a bit to early. But I have to have these questions finished before tomorrow. So therefore I would very much appreciate...

Hi, For a first order Diff Equa. x'=f(x,t) and the IC: x(0)=x_0. with t from [0 to infinity) If f(x,t) doesn't satisfy the Lipschitz condition, can I say for sure that there doesn't exist a global unique solution? I think the answer is "no" but I am not sure. Can you all confirm...

Prove that if b is greater than or equal to zero (b in R), there exists a non-negative real number x such that x2=b. I really don't know where to go. I think I need to modify a proof done in a class that I missed, so if someone could just give me a few hints I'll fill in the rest. Thanks Josh

Let be the integrals: \int_{-\infty}^{\infty}dx Cos(uf(x)) (or the same but a sine) and \int_{-\infty}^{\infty}dxe^{-ag(x)} Where "a" is a a>0 positive constant, u can be either positive or negative.. and g(x)>0 for every real x.. my question is will these integrals "always2 exist...

Hello, I would be glad to know your point of view on the following idea of mine :smile: , I'll be happy to have links for or against this idea. Thankyou for giving the time ________________________________________________________ Whenever I start thinking about the existence of the...