A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with C boundary which possesses the same property.

Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional mult...

palmprint recognition is a new biometrics system based on physiological characteristics of the palmprint, which includes rich, stable, and unique features such as lines, points, and texture. texture is one of the most important features extracted from low resolution images. in this paper, a new local descriptor, local composition derivative pattern (lcdp) is proposed to extract smartly stronger...

Palmprint recognition is a new biometrics system based on physiological characteristics of the palmprint, which includes rich, stable, and unique features such as lines, points, and texture. Texture is one of the most important features extracted from low resolution images. In this paper, a new local descriptor, Local Composition Derivative Pattern (LCDP) is proposed to extract smartly stronger...

We consider the problem of observation and control of a system of transmission waves. The system is governed by a three-dimensional (respectively two-dimensional) D’ Alembert wave equation in a bounded domain which comprises corners but which is not fissured. On the boundary we have inside an artificial dynamic Wentzell boundary condition coupled with the internal equation by the normal derivat...

We investigate the problem of estimating derivatives of expected steady-state performance measures in parametric systems. Unlike most of the existing work in the area, we allow those functions to be nonsmooth and study the estimation of directional derivatives. For the class of regenerative Markovian systems we provide conditions under which we can obtain consistent estimators of those directio...

The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or −1, then the ...

This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly in a part of the domain) is known; the boundary value and the normal derivative on a part of the boundary of the domain over a finite time interval are known....

For functions from the Sobolev space Hs(Ω), 1 2 < s < 3 2 , definitions of non-unique generalised and unique canonical co-normal derivative are considered, which are related to possible extensions of a partial differential operator and its right hand side from the domain Ω, where they are prescribed, to the domain boundary, where they are not. Revision of the boundary value problem settings, wh...

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest f...