scholarly journals Measures of Noncompactness in Regular Spaces

2014 ◽  
Vol 57 (4) ◽  
pp. 780-793 ◽  
Author(s):  
Nina A. Erzakova
Keyword(s):  
Measures Of Noncompactness ◽  
Geometric Characteristics ◽  
Measurable Functions

AbstractPrevious results by the author on the connection between three measures of noncompactness obtained for Lp are extended to regular spaces of measurable functions. An example is given of the advantages of some cases in comparison with others. Geometric characteristics of regular spaces are determined. New theorems for (k,β)-boundedness of partially additive operators are proved.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

Effects of composite geometric characteristics of coarse particles on interface interactions of aggregate-asphalt system

2021 ◽  
Vol 287 ◽  
pp. 122750
Author(s):  
Jinfei Su ◽  
Peilong Li ◽  
Shengfei Sun ◽  
Liuda Cheng ◽  
Jiayu Bi ◽  
...  
Keyword(s):  
Coarse Particles ◽  
Geometric Characteristics

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

scholarly journals METHOD FOR IDENTIFYING SUITABLE COMPONENTS FOR FUNCTIONAL INTEGRATION – FOCUSING ON GEOMETRIC CHARACTERISTICS

2021 ◽  
Vol 1 ◽  
pp. 2047-2056
Author(s):  
Michael P. Voigt ◽  
Dominik Klaiber ◽  
Patrick Hommel ◽  
Daniel Roth ◽  
Hansgeorg Binz ◽  
...  
Keyword(s):  
Lightweight Design ◽  
Functional Integration ◽  
Resource Efficiency ◽  
Installation Space ◽  
Geometric Properties ◽  
Geometric Characteristics ◽  
Step Procedure ◽  
Cad Models ◽  
Selection Of

AbstractThe approach of functional integration has the potential to solve challenges regarding lightweight design and resource efficiency since the number of parts and therefore the weight and needed installation space can be reduced. One important step in developing integrative concepts is the pre-selection of suitable functions or components. Previous methods of pre-selection take various aspects into account. However, pre-selection based on these methods usually requires additional tables and forms, whose preparation and editing quickly becomes time-consuming. At the same time, most of the development engineers are working on CAD models. However, their use in the selection of suitable integration partners is not yet supported sufficiently. The development of more than 80 concepts on five different vehicles has shown that the consideration of geometric properties (position, orientation, size) is effective, as they can be identified with minimal analysis effort while working on CAD. In this paper a four-step procedure is presented how integration partners can be identified directly on the basis of CAD models. A following evaluation with development engineers in practice completes the research.

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

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