scholarly journals On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

2020 ◽  
Vol 15 (2) ◽  
pp. 99-112
Author(s):  
Fabrizio Durante ◽  
Juan Fernández-Sánchez ◽  
Claudio Ignazzi ◽  
Wolfgang Trutschnig
Keyword(s):  
Integrable Function ◽  
Average Distance ◽  
Extremal Problems ◽  
Riemann Integrable Function ◽  
Limit Points ◽  
Maximal Average ◽  
Uniformly Distributed Sequences

AbstractMotivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type {\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,} where µC is a copula measure and F is a Riemann integrable function on [0, 1]2 of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.

A Convergence Theorem for Certain Riemann Sums

1969 ◽  
Vol 12 (4) ◽  
pp. 523-525 ◽  
Author(s):  
Charles K. Chui
Keyword(s):  
Convergence Theorem ◽  
Integrable Function ◽  
Riemann Sums ◽  
Riemann Integrable Function ◽  
Image Position

For a Riemann integrable function f on the interval [0,1], letand consider the Riemann sums

Mean Value Theorem for the m-Integral of Dinculeanu

1972 ◽  
Vol 15 (2) ◽  
pp. 243-251 ◽  
Author(s):  
Pedro Morales
Keyword(s):  
Convex Hull ◽  
Integrable Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Real Interval ◽  
Riemann Sums ◽  
Differentiable Functions ◽  
Riemann Integrable Function ◽  
Dominated Convergence ◽  
M Integral

The classical mean value theorem asserts that if f is a real, bounded, Riemann integrable function defined on a finite real interval a≤t≤b, then , where infa≤t≤bf(t)≤y0supa≤t≤bf(t). The extensions of Choquet [3], Price [15], and of this paper generalize the fact that y0 belongs to the closure of the convex hull of f([a, b]). The version of Choquet ([3, p. 38]) applies to a continuous function on a compact interval with values in a Banach space; that of Price ([15, p. 24]) applies to a bilinear integral of a special type containing the Birkhoff integral [2]. The m-integral of Dinculeanu [6] (specialization of Bartle's *- integral [1]) leaves intact the Lebesgue dominated convergence theorem and is strong enough to support an extended development. The paper is organized as follows: the object of §2 is to express the integral of a bounded m-integrable function as a limit of Riemann sums; §3 gives Price's generalization of "convex hull" [15]; the theorem of the paper is established in §4; §5 gives applications to vector differentiation which, for continuously differentiable functions, contain results of Dieudonné [5] and McLeod [13].

scholarly journals ALMOST RIEMANN INTEGRABLE FUNCTIONS

1995 ◽  
Vol 26 (3) ◽  
pp. 231-233
Author(s):  
MOUSTAFA DAMLAKHI
Keyword(s):  
Arbitrary Function ◽  
Integrable Function ◽  
Bounded Interval ◽  
Integrable Functions ◽  
Riemann Integrable Function ◽  
Riemann Integrable Functions

An arbitrary function $f$ on a bounded interval $[a,b]$ is  termed an almost $R$-integrable function if there exists a Riemann integrable function $g$ such that $f =g$ a.e. In this note a characterization of the class of almost $R$-integrable functions is obtained.

On the Location of Quiescent Prominences with Respect to Coronal Holes

1979 ◽  
Vol 44 ◽  
pp. 209-213
Author(s):  
B. Rompolt
Keyword(s):  
Coronal Hole ◽  
Average Distance ◽  
Coronal Holes

The aim of this contribution is to turn attention to a peculiarity of location of the filaments (quiescent prominences) with respect to the boundaries of the coronal holes. It is generally known that quiescent prominences are located at some distance from the boundary of coronal holes. My intention was to check whether the average distance between the nearest border of a coronal hole and the prominence is comparable to the average horizontal extension of a helmet structure overlying the prominence. As well as, whether this average distance depends upon the orientation of the long axis of the prominence with respect to the nearest boundary of the coronal hole.

Mobile network synthesis strategy

2019 ◽  
pp. 98-101
Author(s):  
V. Lyandres
Keyword(s):  
Average Distance ◽  
Mobile Network ◽  
Base Station ◽  
Service Area ◽  
Base Stations ◽  
Frequency Assignment ◽  
Network Synthesis ◽  
Universal Method ◽  
Synthesis Strategy ◽  
Adaptive Vector Quantization

Introduction:Effective synthesis of а mobile communication network includes joint optimisation of two processes: placement of base stations and frequency assignment. In real environments, the well-known cellular concept fails due to some reasons, such as not homogeneous traffic and non-isotropic wave propagation in the service area.Purpose:Looking for the universal method of finding a network structure close to the optimal.Results:The proposed approach is based on the idea of adaptive vector quantization of the network service area. As a result, it is reduced to a 2D discrete map split into zones with approximately equal number of service requests. In each zone, the algorithm finds such coordinates of its base station that provide the shortest average distance to all subscribers. This method takes into account the shortage of the a priory information about the current traffic, ensures maximum coverage of the service area, and what is not less important, significantly simplifies the process of frequency assignment.

Investigation of Limit Points and Separation Axioms Using Supra $\beta$-Open Sets

2020 ◽  
Vol 32 (2) ◽  
pp. 171-187
Author(s):  
T. M. Al-Shami ◽  
E. A. Abo-Tabl ◽  
B. A. Asaad
Keyword(s):  
Separation Axioms ◽  
Limit Points
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