1. We consider differential topology to be the study of differentiable manifolds and differentiable maps. Then, naturally, manifolds are considered equivalent if they are diffeomorphic, i.e., there exists a differentiable map from one to the other with a differentiable inverse. For convenience, differentiable means C; in the problems we consider, C' would serve as well. The notions of different...

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

Nature ofphysical problem A lot of problems in physics, chemistry, applied mathematics as well as in engineering and in other fields, are quite often reduced tominimizing a function of several variables. MERLIN is a system designed to minimize a multidimensional function. Method of solution Six algorithms are implemented. Three of them make use of the function’s gradient and hence are suitable ...

We propose a novel variant of the conjugate gradient algorithm, Kernel Conjugate Gradient (KCG), designed to speed up learning for kernel machines with differentiable loss functions. This approach leads to a better conditioned optimization problem during learning. We establish an upper bound on the number of iterations for KCG that indicates it should require less than the square root of the nu...

In this paper we analyze some properties of the principal eigenvalue λ1(Ω) of the nonlocal Dirichlet problem (J∗u)(x)−u(x) = −λu(x) in Ω with u(x) = 0 in R \Ω. Here Ω is a smooth bounded domain of R and the kernel J is assumed to be a C compactly supported, even, nonnegative function with unit integral. Among other properties, we show that λ1(Ω) is continuous (or even differentiable) with respe...

Any sufficiently often differentiable curve in the orbit space of a compact Lie group representation can be lifted to a once differentiable curve into the representation space. Smooth curves can even be lifted to a once differentiable curves which are orthogonal to the orbits.

Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex–differentiable structure on that same space. Complex–differentiable structures on a given real manifold are often not unique. This letter is devoted to analysing the dependence of the notion of a quantum on the complex–differentiable structure chosen on classic...

This paper deals with second-order sensitivity analysis of parameterized vector optimization problems. We prove that the Borwein efficient solution map and perturbation a parametric problem are radial-asymptotic proto-differentiable under some suitable qualification conditions. Some examples also given for illustrating obtained results.

In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an extension of Benson’s outer approximation algorithm for multi-objective linear programming problems...