scholarly journals On the Borel class of the derived set operator

1982 ◽  
Vol 79 ◽  
pp. 357-380 ◽  
Author(s):  
Douglas Cenzer ◽  
R. Daniel Mauldin
Keyword(s):  
Derived Set ◽  
Borel Class

scholarly journals On the Borel class of the derived set operator. II

1983 ◽  
Vol 79 ◽  
pp. 367-372 ◽  
Author(s):  
Douglas Cenzer ◽  
R. Daniel Mauldin
Keyword(s):  
Derived Set ◽  
Borel Class

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

Iterating the Derived Set Function

1983 ◽  
Vol 90 (10) ◽  
pp. 693
Author(s):  
Denis Higgs
Keyword(s):  
Derived Set ◽  
Set Function

Some Remarks on Extreme Derivates

1969 ◽  
Vol 12 (4) ◽  
pp. 385-388 ◽  
Author(s):  
A. M. Bruckner
Keyword(s):  
Lipschitz Condition ◽  
Real Variable ◽  
Kernel Functions ◽  
Class 1 ◽  
Borel Class ◽  
Borel Measurable ◽  
Class Of Functions

In 1957 Hájek [1] proved that the extreme bilateral derivates of an arbitrary finite real valued function of a real variable, are Borel measurable of class ≦ 2. It was later shown by Staniszewska [3] that Hájek's result is the best possible (even among the class of functions satisfying a Lipschitz condition). Staniszewska exhibited a Eipschitz function whose extreme bilateral derivates are not in Borel class 1. Staniszewska's proof makes use of a result of Zahorski's [4] concerning kernel functions.

scholarly journals Computing Borel's regulator

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Zacky Choo ◽  
Wajid Mannan ◽  
Rubén J. Sánchez-García ◽  
Victor P. Snaith
Keyword(s):  
Infinite Series ◽  
Borel Class

AbstractWe present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on

Iterating the Derived Set Function

1983 ◽  
Vol 90 (10) ◽  
pp. 693-697
Author(s):  
Denis Higgs
Keyword(s):  
Derived Set ◽  
Set Function

Sexual Script Theory: An Integrative Exploration of the Possibilities and Limits of Sexual Self-Definition

2002 ◽  
Vol 30 (2) ◽  
pp. 120-130 ◽  
Author(s):  
Stanton L. Jones ◽  
Heather R. Hostler
Keyword(s):  
Clinical Applications ◽  
Control Beliefs ◽  
Sexual Script ◽  
Script Theory ◽  
Human Community ◽  
Whole Person ◽  
Derived Set ◽  
Sexual Script Theory

Sexual Script Theory (SST) and its clinical applications are premised on the notion that the subjective understandings of individuals of their sexuality determine the persons' choices of sexual actions and the qualitative experiencing of those sexual acts. The key elements of SST and key Christian control beliefs about sexuality are described, and then related in an integrative exploration of SST. The limits of an understanding of psychological scripting grounded in an unfettered Constructivism, and the limits of a purely pragmatic understanding of script legitimacy, are each discussed. We develop the pervasive theme of the necessary connectedness of sexual scripting to the broader processes of self-definition, which for the Christian, are to be rooted in a biblically-derived set of categories that connect sexuality to the character of the whole person, to their union with a spouse in marriage, and to the human community (individually and corporately) in its relationship to God.

Sandwich Beams with Arbitrary Boundary Conditions

1975 ◽  
Vol 97 (3) ◽  
pp. 873-880 ◽  
Author(s):  
Dusan Krajcinovic
Keyword(s):  
Efficient Method ◽  
Present Method ◽  
Sandwich Beams ◽  
Cross Sectional ◽  
Arbitrary Boundary ◽  
Variational Equations ◽  
Material Parameters ◽  
Wide Range ◽  
Derived Set ◽  
Beam Bending

Presented is a practical and efficient method for the analysis of arbitrarily supported sandwich beams. Based on the previously derived set of governing variational equations, the present method utilizes familiar transfer matrix procedure. Final solutions for the displacement and stresses consist of two terms reflecting correspondingly the conventional (solid) beam bending and the cross-sectional distortion. The proposed method is illustrated in a few examples and the results are plotted for a wide range of geometric and material parameters.

scholarly journals Closure System and Its Semantics

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 198
Author(s):  
Yinbin Lei ◽  
Jun Zhang
Keyword(s):  
Closure Operator ◽  
Spatial Relations ◽  
Accumulation Point ◽  
Boundary Operator ◽  
Topological Spaces ◽  
Closure System ◽  
Derived Set ◽  
Topological Closure ◽  
Interior Operator ◽  
Isolated Point

It is well known that topological spaces are axiomatically characterized by the topological closure operator satisfying the Kuratowski Closure Axioms. Equivalently, they can be axiomatized by other set operators encoding primitive semantics of topology, such as interior operator, exterior operator, boundary operator, or derived-set operator (or dually, co-derived-set operator). It is also known that a topological closure operator (and dually, a topological interior operator) can be weakened into generalized closure (interior) systems. What about boundary operator, exterior operator, and derived-set (and co-derived-set) operator in the weakened systems? Our paper completely answers this question by showing that the above six set operators can all be weakened (from their topological counterparts) in an appropriate way such that their inter-relationships remain essentially the same as in topological systems. Moreover, we show that the semantics of an interior point, an exterior point, a boundary point, an accumulation point, a co-accumulation point, an isolated point, a repelling point, etc. with respect to a given set, can be extended to an arbitrary subset system simply by treating the subset system as a base of a generalized interior system (and hence its dual, a generalized closure system). This allows us to extend topological semantics, namely the characterization of points with respect to an arbitrary set, in terms of both its spatial relations (interior, exterior, or boundary) and its dynamic convergence of any sequence (accumulation, co-accumulation, and isolation), to much weakened systems and hence with wider applicability. Examples from the theory of matroid and of Knowledge/Learning Spaces are used as an illustration.

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