The General Solution of the Planar Laplace Problem

2005 ◽  
pp. 123-134
Author(s):  
C. Marchal
Keyword(s):  
General Solution ◽  
Laplace Problem

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

Catalytic, Enantioselective Syn-Diamination of Alkenes

2019 ◽  
Author(s):  
Zhonglin Tao ◽  
Brad Gilbert ◽  
Scott Denmark
Keyword(s):  
General Solution ◽  
Organic Synthesis ◽  
Medicinal Chemistry ◽  
Catalytic Cycle ◽  
Bifunctional Nucleophile

The enantioselective, vicinal diamination of alkenes represents one of the stereocontrolled additions that remains an outstanding challenge in organic synthesis. A general solution to this problem would enable the efficient and selective preparation of widely useful, enantioenriched diamines for applications in medicinal chemistry and catalysis. In this Article we describe the first enantioselective, <i>syn-</i>diamination of simple alkenes mediated by a chiral, enantioenriched organoselenium catalyst together with a <i>N,N’-</i>bistosyl urea as the bifunctional nucleophile and <i>N-</i>fluorocollidinium tetrafluoroborate as the stoichiometric oxidant. Diaryl, aryl-alkyl, and alkyl-alkyl olefins bearing a variety of substituents are all diaminated in consistently high enantioselectivities selectivities but variable yields. The reaction likely proceeds through a Se(II)/Se(IV) redox catalytic cycle reminiscent of the <i>syn-</i>dichlorination reported previously. Furthermore, the <i>syn</i>-stereospecificity of the transformation shows promise for highly enantioselective diaminations of alkenes with no strong steric or electronic bias.

Insider's Dilemma: A General Solution in a Repeated Game

2015 ◽  
Author(s):  
Cesi Berardino ◽  
Walter Ferrarese
Keyword(s):  
General Solution ◽  
Repeated Game
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