Functional Definition and 419 Threads

what are the requirements of a functional J[y] to exist in the form that its minimum will yield to a differential equation?..i mean let be the functional with condition: J[y]=\int_{a}^{b}dx(p(x)(y`)^{2}+V(x)y^{2}) \int_{a}^{b}y^{2}dx=C with c a constant... then what conditions should...

let be the functional equation f(x,y)=g(r(x)+h(y)) my question is..does this equation have a solution?..thanks...

Im having some difficulties proving some basic properties of the adjoint operator. I want to prove the following things: 1) There exists a unique map T^*:K\rightarrow H 2) That T^* is bounded and linear. 3) That T:H\rightarrow K is isometric if and only if T^*T = I. 4) Deduce that if T is...

Question 1 Prove that if (V, \|\cdot\|) is a normed vector space, then \left| \|x\| - \|y\| \right| \leq \|x-y\| for every x,y \in V. Then deduce that the norm is a continuous function from V to \mathbb{R}.

I saw this video today and I believe it is a presentation from SUN's "Project Looking Glass". Now this is the desktop of my dreams! http://abum.com/files/Movies/3d_desktop.wmv http://www.sun.com/software/looking_glass/

Given a set of m real functions of n variables, what is a necessary and sufficient condition for the functions to be functionally independent ? A set a functions f_i(x_1,...x_n)\quad i=1,...m are functionally independent, if the only function \phi(u_1,...u_m) such that \phi(f_1,...f_m)=0 is...

Let be F the functional given by J(y)=J(x,y,dy/dx) my question is,apart from the usual definition of functional derivative and Lagrange equation,..does a numerical method exist to calculate it,i mean am looking for a recursive method,you introduce an initial function y0(x) from this you...

Find f(x) if f(x) + f(\frac{x-1}{x}) = 1 + x

Hi, Does anyone of you have some links or references to books on Functional Density Theory ? I know the basics but i would like to learn a whole lot more. Thanks in advance marlon

This is about amines: The functional groups present are: C=O and NH2 Why does the N get protonated always but not C=O, since the oxygen has more lone pairs and more electronegative than N so shouldn't the oxygen be protonated more easily? I can't think of any good reasons... please help...

Lets say for example a hydrocarbon skeleton has two diff functional groups branched to the skeleton.. Let's say one of the functional groups pH is less than 9 to 10, and the other functional group's pH is greater than 2 to 4 that means that molecule to be electrically charged, the pH of the...

Does anyone know good online references about functional derivatives? Most of the documents contain only the definition, but I would like some more complete material containing, for example, rules for differentiate composite functionals and other details.

I'm trying to learn density functional theory by myself, but I'm a bit confused as to how to use it. Is the following methodology correct (I think it'd take forever to use LaTex to write the equations, so I have a link to small webpage that already has the equations laid out and numbered)...

Hi All, I have a problem, and it is so confusing to me. I put it here in the hope of getting some helps to make it clear. Thank you, the problem is given below. What is the greatest value of b for which any real valued function f that satisfies the following properties mus also...

schröder's equation is a functional equation. let's assume A is a subset of the real numbers and g maps A to itself. the goal is to find a nonzero (invertible, if possible) function f and a real number r such that f\circ g=rf. motivation: if there is an invertible f, then the nth iterate...

hi! there is a good functional analysis book by Erwin Kreyzig...which has hilbert spaces and banach spaces and stuff!

Is it possible for us to make a functional model of the human brain? I'm not interested in the phylosophical implications, but more in the resources, techonolgies we can use (that's why I posted here... )

where could i find in internet a course of functinal derivation and integration for physicist?... a explanation or introduction to functional integration

let be the equation f(g(t))=g(t) where f is known but g(t) not... i think that perhaps we could solve it by iteration so g(t) would be g(t)=fofofofofofofo... where fof means the composition of f with itself...is that solution right? i do not even konw if my process to solve the functional...