We consider the problem of learning on a compact metric space X in a functional analytic framework. For a dense subalgebra of Lip(X), the space of all Lipschitz functions on X, the Representer Theorem is derived. We obtain exact solutions in the case of least square minimization and regularization and suggest an approximate solution for the Lipschitz classifier.

The paper considers a class of nonlinear differential equations which are not solvable in quadratures general case. author’s technology for solving such contains six problems. In this article, the solution to one these problems is given, real area it possible calculate an analytical approximate case value moving singular point obtained. Obtained results based on application elements calculus fi...

The existence, uniqueness approximate solutions of a stochastic fractional differential equation with deviating argument is studied. Analytic semigroup theory and fixed point method is used to prove our results. Then we considered Faedo-Galerkin approximation of solution and proved some convergence results. We also studied an example to illustrate our result.

We utilise the fact that the CCFM equation in the single loop approximation can be diagonalised by the Fourier-Bessel transform. The analytic solution of the CCFM equation for the moments fω(b,Q) of the scale dependent gluon distribution is obtained, where b is the transverse coordinate conjugate to the transverse momentum of the gluon. The unintegrated gluon distributions obtained from this so...