scholarly journals Functions with sets of points of discontinuity belonging to a fixed ideal

1963 ◽  
Vol 52 (1) ◽  
pp. 25-39 ◽  
Author(s):  
Z. Semadeni
Keyword(s):  
Fixed Ideal ◽  
Points Of Discontinuity

MODEL OF SOCIAL POTENTIAL OF CHILDHOOD IN THE RUSSIAN REGIONS: THE RESULTS OF EXPERIMENTS

2019 ◽  
pp. 152-162
Author(s):  
A.G. Filipova ◽  
A.V. Vysotskaya
Keyword(s):  
Third Wave ◽  
Russian Regions ◽  
The Third ◽  
Control Factors ◽  
Social Potential ◽  
System Input ◽  
Optimal Values ◽  
Fixed Ideal ◽  
And Control ◽  
Selection Of

The article presents the results of mathematical experiments with the system «Social potential of childhood in the Russian regions». In the structure of system divided into three subsystems – the «Reproduction of children in the region», «Children’s health» and «Education of children», for each defined its target factor (output parameter). The groups of infrastructure factors (education, health, culture and sport, transport), socio-economic, territorial-settlement, demographic and en-vironmental factors are designated as the factors that control the system (input parameters). The aim of the study is to build a model îf «Social potential of childhood in the Russian regions», as well as to conduct experiments to find the optimal ratio of the values of target and control factors. Three waves of experiments were conducted. The first wave is related to the analysis of the dynam-ics of indicators for 6 years. The second – with the selection of optimal values of control factors at fixed ideal values of target factors. The third wave allowed us to calculate the values of the target factors based on the selected optimal values of the control factors of the previous wave.

On Rings of Fractions

1970 ◽  
Vol 13 (4) ◽  
pp. 425-430 ◽  
Author(s):  
T. M. K. Davison
Keyword(s):  
Noetherian Ring ◽  
Multiplicative System ◽  
Topological Ring ◽  
Commutative Noetherian Ring ◽  
Image Position ◽  
Fixed Ideal

Let R be a commutative Noetherian ring with identity, and let M be a fixed ideal of R. Then, trivially, ring multiplication is continuous in the ilf-adic topology. Let S be a multiplicative system in R, and let j = js: R → S-1R, be the natural map. One can then ask whether (cf. Warner [3, p. 165]) S-1R is a topological ring in ihe j(M)-adic topology. In Proposition 1, I prove this is the case if and only if M ⊂ p(S), whereHence S-1R is a topological ring for all S if and only if M ⊂ p*(R), where

scholarly journals On the Oscillation Functions derived from a Discontinuous Function

1914 ◽  
Vol 33 ◽  
pp. 139-142
Author(s):  
L. R. Ford
Keyword(s):  
Real Variable ◽  
Continuous Functions ◽  
Discontinuous Function ◽  
Discontinuous Functions ◽  
Word Function ◽  
Points Of Discontinuity

In this paper are introduced what we shall term “successive oscillation functions.” These functions are derived from functions of a real variable. The word “function” as here used has its widest meaning. We say y is a function of x in an interval of the the x-axis, if given any value of x, in the interval one or more values of y are thereby determined. The values of the function may be determined by any arbitrary law whatsoever. We shall deal with discontinuous functions; the theorems will be true for continuous functions, but will be trivial, except in the case of functions which are discontinuous and whose points of discontinuity are infinite in number. We shall assume in what follows that the values of the function lie between finite limits.

End Effect Bending Stresses in Cables

1969 ◽  
Vol 36 (4) ◽  
pp. 750-756 ◽  
Author(s):  
J. A. DeRuntz
Keyword(s):  
Exact Solutions ◽  
Edge Effect ◽  
Shell Theory ◽  
End Effect ◽  
Bending Stresses ◽  
Flexible Cables ◽  
Points Of Discontinuity

An analysis of bending stresses in flexible cables has been carried out. It has been found that stresses which arise due to fixity at the boundaries or other points of discontinuity, decay in an exponential manner from such boundaries, similar to the edge effect solutions of shell theory. Such a phenomenon makes it possible to analyze a finite cable of sufficient length using solutions which are applicable only to infinite or very long cables. In this way the cumbersome but otherwise exact solutions of the elastica are replaced by much simpler ones of sufficient engineering accuracy. The term “sufficient length” is defined as part of the analysis.

scholarly journals Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature

2020 ◽  
Vol 55 ◽  
pp. 93-112
Author(s):  
P.D. Lebedev ◽  
A.A. Uspenskii
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Time Optimal Control ◽  
Dimensional Manifold ◽  
Singular Set ◽  
Time Optimal ◽  
Characteristic Points ◽  
Target Set ◽  
The Right ◽  
Points Of Discontinuity

We consider a time-optimal control problem on the plane with a circular vectogram of velocities and a non-convex target set with a boundary having a finite number of points of discontinuity of curvature. We study the problem of identifying and constructing scattering curves that form a singular set of the optimal result function in the case when the points of discontinuity of curvature have one-sided curvatures of different signs. It is shown that these points belong to pseudo-vertices that are characteristic points of the boundary of the target set, which are responsible for the generation of branches of a singular set. The structure of scattering curves and the optimal trajectories starting from them, which fall in the neighborhood of the pseudo-vertex, is investigated. A characteristic feature of the case under study is revealed, consisting in the fact that one pseudo-vertex can generate two different branches of a singular set. The equation of the tangent to the smoothness points of the scattering curve is derived. A scheme is proposed for constructing a singular set, based on the construction of integral curves for first-order differential equations in normal form, the right-hand sides of which are determined by the geometry of the boundary of the target in neighborhoods of the pseudo-vertices. The results obtained are illustrated by the example of solving the control problem when the target set is a one-dimensional manifold.

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