Calculating the directional derivative of a class of the set-valued mappings G(x) = {z |Az ≤ h(x)}, in the sense of Tyurin (1965) and Banks & Jacobs (1970) is presented that can be viewed as an extension to the one given by Pecherskaya. Results obtained in this paper are used to get a bound of the Lipschitz constant for the solution sets of the perturbed Linear Programming. This new bound is sm...

First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the g...

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

Received Jul 5, 2012 Revised Aug 8, 2012 Accepted Aug 15, 2012 In this paper, a new one-stage nonlinear directional derivative scheme has been proposed for edge detection. The directional edge detection method was applied to gray and color images. The results were compared to three wellknown conventional edge detectors namely Canny, Prewitt, and Sobel. According to results, the directional deri...

Here, ∆ is the Laplacian, μ ∈ R is a fixed parameter, ν is the outward unit normal to Ω, and Ω+ := Ω, Ω− := Rn \ Ω̄. For 1 < p < ∞, L̇p1(∂Ω) is the classical homogeneous Lp-based Sobolev spaces of order one on ∂Ω, M denotes the non-tangential maximal operator, ∂ν is the normal derivative and all restrictions to the boundary are taken in the non-tangential limit sense; detailed definitions are giv...

Generalized second–order directional derivatives for nonsmooth real–valued functions are studied and their connections with second–order variational sets are investigated. A necessary second–order optimality condition for problems with inequality constraints is obtained.

A novel boundary integral equation (BIE) is developed for eddy-current nondestructive evaluation problems with surface crack under a uniform applied magnetic field. Once the field and its normal derivative are obtained for the structure in the absence of cracks, normal derivative of scattered field on the conductor surface can be calculated by solving this equation with the aid of method of mom...

The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The trans-membrane potential is determined implicitly as part of the algorithm. The method is compared to an analytic solution ba...

The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free boundary. We establish a global-in-tim...

In the present paper a morphological approach for segmenting orientation fields is proposed. This approach is based on the concept of the line-segment and orientation functions. The line-segment function is computed from the supremum of directional erosions. This function contains the sizes of the longest lines that can be included in the structure. To determine the directions of the line segme...