In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...

In this paper, various Recursive Mixed L2-Linfty (RML) learning algorithms are developed by choosing different forgetting factor matrix function () for Linear-inthe-Parameters (LIP) models, including Projection, Recursive Mixed L2-Linfty, Recursive Mixed Mean L2-Linfty, weighted Mixed L2-Linfty, instantaneous RML, and Batch RML algorithms. A few models are given to apply the proposed RML alg...

Abstract. The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the BusemannPetty problem, characterizations of intersection bodies, extremal sections of lp-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the resu...

It is proved that if C is a convex body in R" then C has an affine image C (of nonzero volume) so that if P is any 1-codimensional orthogonal projection, \PC\>\C\{tt~l)/n. It is also shown that there is a pathological body, K , all of whose orthogonal projections have volume about \fh~ times as large as |Ä"| . 0. Introduction The problems discussed in this paper concern the areas of shadows (or...

Mixed pixels, which are inevitable in remote sensing images, often result in a lot of limitations in their applications. A novel approach for mixed pixel’s fully constrained unmixing, Fully Constrained Oblique Subspace Projection (FCOBSP) Linear Unmixing algorithm, is proposed to handle this problem. The Oblique Subspace Projection, in which the signal space is oblique to the background space, ...

This paper deals with inequalities for the volume of a convex body and the volume of the projection body, the L-centroid body, and their polars. Examples are the Blaschke-Santaló inequality, the Petty and Zhang projection inequalities, the Busemann-Petty inequality. Other inequalities of the same type are still at the stage of conjectures. The use of special continuous movements of convex bodie...

To screen additives and their mixed ratio suitable for the mycelial growth and fruiting body formation of Oudemansiella radicata in the oak sawdust, additives such as rice bran, fermented soybean powder and wheat bran were used. Generally, the mycelial growth of O. radicata has been stable on oak sawdust mixed with rice bran of 5~20%. In case that O. radicata was cultured for about 30 days at 2...

Rotation intertwining maps from the set of convex bodies in R into itself that are continuous linear operators with respect to Minkowski and Blaschke addition are investigated. The main focus is on Blaschke-Minkowski homomorphisms. We show that such maps are represented by a spherical convolution operator. An application of this representation is a complete classification of all even BlaschkeMi...

We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables $z^2=z$, model rank constraints. By leveraging regularization strong duality, we prove this paradigm yields tractable convex over non-convex set orthogonal matrices. Furthermore, design outer...

This paper gives various (positive and negative) results on the complexity of the problem of computing and approximating mixed volumes of polytopes and more general convex bodies in arbitrary dimension. On the negative side, we present several #P-hardness results that focus on the difference of computing mixed volumes versus computing the volume of polytopes. We show that computing the volume o...