Abstract The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework p -vector spaces, in particular, locally -convex spaces $0 < \leq 1$ 0<p≤1 . More precisely, ba...

In this paper, a large-capacity white light source module using high-power blue laser diode and reflective spaced phosphor was designed. The spacing ensured thermal stability. proposed is structure with bi-directional optical system based on rhombus prism lens. can greatly narrow the beam width long-wavelength band-pass filter of 500 nm or more applied to change movement path transmit excited b...

New fixed point results are presented for weakly inward Kakutani condensing maps defined on a Fréchet space E. The proofs rely on the notion of an essential map and viewing E as the projective limit of a sequence of Banach spaces.

in this paper, we first present a new important property for bouligand tangent cone (contingent cone) of a star-shaped set. we then establish optimality conditions for pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

We study the covering dimension of (positive ) solutions to varoius classes of nonlinear equations based on the nontriviality of the fixed point index of a certain condensing map. Applications to semilinear equations and to nonlinear perturbations of the Wiener-Hopf integral equations are given.

The performance of a speech recogniser, or of any other pattern classifier, strongly depends on the input features: to obtain a good performance, the feature set needs to be both highly discriminative and compact. Linear discriminant analysis (LDA) is a common data-driven method used to find linear transformations that map large feature vectors onto smaller ones while retaining most of the disc...

In this paper we study parameterization as a tool for both constructing and smoothing spatial triangulations. Most of the parameterization methods we study are based on convex combination maps, which have the property that the image of each interior vertex is a convex combination of its neighbours. When mapping an existing triangulation, this latter property ensures that whenever the image of t...

Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and convergent variational algorithms, such as dual decomposition, exist. In this work, we generalize dual decomposition to a generic power sum inference task, whic...