We show that the maxwellian density f (x, t,v) corresponding to a smooth solution of the Euler equations verifies a kinetic equation in which the interaction part corresponds to the masstransport in v direction along a vector from the subdifferential of the indicator function of the set of maxwillians in the space of regular probability measures with the 2-Wasserstein metric. Our main result sh...

A result on the existence and uniqueness of metric projection for certain sets is proved, by means of a saddle point theorem. A conjecture, based on such a result and aiming for the construction of a nonconvex Chebyshev set in a Hilbert space, is presented.

and Applied Analysis 3 PK is called the metric projection ofH ontoK. It is well known that PK is a nonexpansive mapping ofH onto K and satisfies 〈x − y, PKx − PKy〉 ≥ ∥ PKx − PKy ∥ ∥ 2 , 2.3 for every x, y ∈ H. Moreover, PKx is characterized by the following properties: PKx ∈ K and 〈x − PKx, y − PKx〉 ≤ 0, ∥ ∥x − y∥∥ ≥ ‖x − PKx‖ ∥ ∥y − PKx ∥

In this paper, we consider the strong convergence of the projection type Ishikawa iteration process to a common fixed point of a finite family of I-asymptotically nonexpansive mappings in generalized convex metric spaces. Our results of this paper improve and extend the corresponding results of Temir[4], Thianwan [6].

Metric nearness refers to the problem of optimally restoring metric properties to distance measurements that happen to be non-metric due to measurement errors or otherwise. Metric data can be important in various settings, for example in clustering, classification, metric-based indexing, query processing and graph theoretic approximation algorithms. This paper formulates and solves the metric n...

In this paper, receiver design and performance analysis for coded asynchronous code-division multiple access (CDMA) systems is considered. The receiver front-end consists of the near–far resistant multiuser detector known as the projection receiver (PR). The PR performs multiple-access interference resolution and is followed by error-control decoding. The output of the projection receiver yield...

Distance metric learning (DML), which learns a distance metric from labeled “similar” and “dissimilar” data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the projection vectors in DML to be close to being orthogonal, to achieve three effects: (1) high balancedness – achieving comparable performance on both frequent ...

These notes show how observers can set up a coordinate system and measure the spacetime geometry using clocks and lasers. The approach is similar to that of special relativity, but the reader must not be misled. Spacetime diagrams with rectilinear axes do not imply flat spacetime any more than flat maps imply a flat earth. Cartography provides an excellent starting point for understanding the m...

The differentiability of the metric projection P onto a closed convex set K in Rn is examined. The boundary ãK can have singular points of orders k ̈ −1Ù 0Ù 1ÜÙ n − 1. Here k ̈ −1 corresponds to the interior points of K , k ̈ 0 to regular points of the boundary (i.e., faces), k ̈ 1ÙÜ Ù n − 2 to edges and k ̈ n − 1 to vertices. It is assumed that for every k the set of all singular points forms ...

In this paper, receiver design and performance analysis for coded asynchronous code-division multiple access (CDMA) systems is considered. The receiver front-end consists of the near–far resistant multiuser detector known as the projection receiver (PR). The PR performs multiple-access interference resolution and is followed by error-control decoding. The output of the projection receiver yield...