In this paper, we define the β-partial derivative as well β-directional of a multi-variable function based on β-difference operator, Dβ, which is defined by Dβf(t)=f(β(t))−f(t)/β(t)−t, where β strictly increasing continuous function. Some properties are proved. Furthermore, β-gradient vector and directional introduced. Finally, deduce Hahn-partial Hahn-directional derivatives associated with Ha...

Abstract This paper proposes a new method to improve performance of AdaBoost by using a distance weight function to increase the accuracy of its machine learning processes. The proposed distance weight algorithm improves classification in areas where the original binary classifier is weak. This paper derives the new algorithm’s optimal solution, and it demonstrates how classifier accuracy can b...

We consider multifunctions acting between two linear normed spaces and having closed convex images. Approximations are considered which serve as an expansion of it. Generalized delta theorems for random sets in in nite dimensions are shown using those approximations. Furthermore, univalued, resp. Castaing representations of the multifunction are constructed with (higher order) di erentiability ...

Let Σ : M → 2 \ {∅} be a set-valued function defined on a Hausdorff compact topological space M and taking values in the normed space (Y, ‖·‖). We deal with the problem of finding the best Chebyshev type approximation of the set-valued function Σ by a singlevalued function g from a given closed convex set V ⊂ C(M, Y ). In an abstract setting this problem is posed as the extremal problem supt∈M ...

Although the majority of research on spatial sound reproduction has concentrated on the directional components of source location, it is clear that full 3-dimensional rendering also requires an understanding of how to reproduce sound source distance. This article reviews and describes recent psychophysical research on distance perception of sound sources, with emphasis on how various acoustical...

Green economy has been paid more and attention in the information age. Informatization plays an important role development of green by transmission industrial structure rationalization upgrading. Because spatial mobility information, it is necessary to study spillover effect on efficiency economy. In this article, non-radial directional distance function comprehensive index method are used eval...

using the electrostatic capacity of a condenser, the existence of a distance function on a finsler space is discussed. this distance function divides finsler spaces into the two classes, denoted here by i and ii. the topology generated by this distance on the finsler spaces of class ii coincides with its intrinsic topology. this work provides a natural extension of mathematical analysis tools n...

Mobile robots with omni-directional wheels can generate instant omni-directional motion including lateral motion without any extra space for changing the direction of the body. So, they are capable of traveling in every direction under any orientation to approach their destinations even in narrow aisles or tight areas. Especially, if a construction tool is combined to the mobile robot, it can b...