On the Equilibrium Problem of a Soft Network Shell in the Presence of Several Point Loads

2013 ◽  
Vol 392 ◽  
pp. 188-190 ◽  
Author(s):  
Ildar B. Badriev ◽  
Victor V. Banderov ◽  
O.A. Zadvornov
Keyword(s):  
Existence Theorem ◽  
Equilibrium Problem ◽  
Explicit Form ◽  
Integral Identity ◽  
Auxiliary Problem ◽  
Delta Function ◽  
Spatial Equilibrium ◽  
External Point ◽  
The Right ◽  
Generalized Statement

We consider a spatial equilibrium problem of a soft network shell in the presence of several external point loads concentrated at some pairwise distinct points. A generalized statement of the problem is formulated in the form of integral identity. Then we introduce an auxiliary problem with the right-hand side given by the delta function. For the auxiliary problem we are able to find the solution in an explicit form. Due to this, the generalized statement of the problem under consideration is reduced to finding the solution of the operator equation. We establish the properties of the operator of this equation (boundedness, continuity, monotonicity, and coercitivity), which makes it possible to apply known general results from the theory of monotone operatorsfor the proof of the existence theorem. It is proved that the set of solutions of the generalized problem is non-empty, convex, and closed.

scholarly journals Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tao Chen
Keyword(s):  
Saddle Point ◽  
Existence Theorem ◽  
Equilibrium Problem ◽  
Existence Result ◽  
Existence Theorems ◽  
Saddle Points ◽  
Vector Equilibrium Problem ◽  
Saddle Point Theorem ◽  
Vector Equilibrium ◽  
Vector Valued

A new existence result ofε-vector equilibrium problem is first obtained. Then, by using the existence theorem ofε-vector equilibrium problem, a weaklyε-cone saddle point theorem is also obtained for vector-valued mappings.

A method for solving linear programming with interval-valued trapezoidal fuzzy variables

2018 ◽  
Vol 52 (3) ◽  
pp. 955-979 ◽  
Author(s):  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Auxiliary Problem ◽  
Coefficient Matrix ◽  
Uncertain Parameters ◽  
Fuzzy Variables ◽  
Right Hand ◽  
Fuzzy Cost ◽  
The Right ◽  
Interval Valued

An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem. It is demonstrated that study of LP problems with interval-valued trapezoidal fuzzy variables gives rise to the same expected results as those obtained for LP with trapezoidal fuzzy variables.

Echocardiographic determination of valid zero reference levels in supine and lateral positions

1993 ◽  
Vol 2 (1) ◽  
pp. 72-80 ◽  
Author(s):  
LL Kee ◽  
JS Simonson ◽  
NA Stotts ◽  
P Skov ◽  
NB Schiller
Keyword(s):  
Left Atrium ◽  
Supine Position ◽  
Right Atrium ◽  
Reference Point ◽  
Reference Points ◽  
Pressure Measurements ◽  
Proper Position ◽  
External Reference ◽  
External Point ◽  
The Right

BACKGROUND: The phlebostatic axis--the junction of the fourth intercostal space and the midpoint of the anterior-posterior diameter--has been accepted as a reliable external reference point for the mid-right and mid-left atrium. Acceptance of this reference point is based upon research conducted in 1945 that measured venous pressures in the hands of subjects positioned with the head of the bed raised to different levels. The validity of this reference point for intracardiac pressure measurements in supine or laterally positioned patients has not been established. PURPOSE: To determine the validity of the phlebostatic axis in the supine and lateral positions. METHODS: To determine validity in the supine position, we compared the distance from the phlebostatic axis to a fixed external point (the bed surface) and the distance from the right and left atria in the supine position to this same fixed external point. The distances from the right and left atria to the bed surface were determined with echocardiography and were used as the standard for the proper position of external reference points. To determine the validity of the phlebostatic axis in lateral positions, we compared the distances from the right atrium and left atrium to the bed surface in the supine position with those distances in different lateral positions. RESULTS: We analyzed the data of 25 normal, healthy subjects. The study findings show that the phlebostatic axis is a valid reference point for the right atrium, and the phlebostatic axis and midanterior-posterior diameter are valid reference points for the left atrium in the supine position. However, neither is a valid external reference point in the lateral positions. Pressure measurements obtained when patients are in the lateral positions are not accurate. There remains a need to develop valid methods of accurate pressure measurements in various body positions.

A special spatial equilibrium problem

Networks ◽  
1984 ◽  
Vol 14 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Jong-Shi Pang ◽  
Chang-Sung Yu
Keyword(s):  
Equilibrium Problem ◽  
Spatial Equilibrium

Existence and Multiplicity of Solutions for Neumann p-Laplacian-Type Equations

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Existence Theorem ◽  
Multiplicity Result ◽  
Multiplicity Of Solutions ◽  
Neumann Problems ◽  
Strong Resonance ◽  
Existence And Multiplicity ◽  
Right Hand ◽  
The Right ◽  
Nonlinear Neumann Problems

AbstractWe consider nonlinear Neumann problems driven by p-Laplacian-type operators which are not homogeneous in general. We prove an existence and a multiplicity result for such problems. In the existence theorem, we assume that the right hand side nonlinearity is p-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. In the multiplicity result, when specialized to the case of the p-Laplacian, we allow strong resonance at infinity and resonance at 0.

scholarly journals A short remark on an arithmetic function

2021 ◽  
Vol 27 (3) ◽  
pp. 12-15
Author(s):  
Anthony G. Shannon ◽  
◽  
Krassimir T. Atanassov ◽  
◽  
Keyword(s):  
Explicit Form ◽  
Arithmetic Function ◽  
Delta Function ◽  
Arithmetic Functions

An explicit form of A. Shannon’s arithmetic function δ is given. A possible application of it is discussed for representation of the well-known arithmetic functions ω and Kronecker’s delta-function δ_{m,s}.

Steven Weinberg: The Conjectural Sublime

2018 ◽  
Author(s):  
Alan G. Gross
Keyword(s):  
Strong Interaction ◽  
Massless Particle ◽  
Delta Function ◽  
Electroweak Theory ◽  
Interesting Problem ◽  
Wrong Answer ◽  
Heavy Particles ◽  
Strong Force ◽  
Freeman Dyson ◽  
The Right

Steven Weinberg had been working for some time on the problem of the strong force that holds together the components of an atom’s nucleus. He was getting nowhere. “Suddenly,” while driving home in his red Camaro, insight arrived. He did not have the wrong answer to the problem of the strong force but the right answer to a different, equally interesting problem: …And I realized the massless particle in this theory that had given me so much trouble had nothing to do with the heavy particles that feel the strong interaction; it was the photon, the particle of which light was composed, that is responsible for electric and magnetic forces and that indeed has zero mass. I realized that what I had cooked up was an approach not just to understanding the weak interaction but to unifying the theories of the weak and electromagnetic forces into what has since come to be called the electroweak theory… “A Model of Leptons” is a paper of which he is justly proud. It has garnered 4,503 citations; a copy has been offered for sale at $950. This is the physicist at his mathematical best, a language he speaks as if it were his native tongue. Another incident confirms Weinberg’s extraordinary talent. Physicist Rich Muller has a bright idea. After several tries, however, the mathematics continues to defeat him. Despondent, he walks down the hall to an office where Steven Weinberg is chatting with Freeman Dyson. The two agree to help: …Weinberg went to the blackboard, wrote down the first equation. “And then he did some manipulations on it,” said Muller, “and stood back.” Dyson said, “I think if you make a substitution of variables now— .” Weinberg said, “Oh, yes, of course,” and wrote several more lines. “I was taking notes,” Muller said, “but I wasn’t sure what he was doing.” Weinberg paused in his writing, and Dyson said, “Now evaluate the delta function,” and Weinberg said, “Oh, okay.” Weinberg wrote down a few more lines, and Dyson said, “Good. You’ve proven it.”

scholarly journals Preface to the special issue on developments of the concepts of randomness, statistics and probability

2014 ◽  
Vol 24 (3) ◽  
Author(s):  
GIUSEPPE LONGO ◽  
MIOARA MUGUR-SCHÄCHTER
Keyword(s):  
Explicit Form ◽  
Human Beings ◽  
Special Issue ◽  
Statistics And Probability ◽  
The Right ◽  
The Mind

Under a variety of names, and in a more or less explicit form, the concept that we now call ‘probability’ must have taken shape in the mind of human beings since the dawn of thought, as a nuance added to the idea of chance (randomness) or unpredictability, though chance may not be exactly the right word. Some time later, the concepts of what we now describe as ‘statistics’ and ‘statistically stable’, moved away from the idea of ‘chance’ and came closer to something else, which was called ‘probability’ and has been fuzzily conceived as being, in some sense, abstract and ‘ideal’. Throughout history it has been felt that unpredictability can have degrees, and that it can be measured using probabilities.

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