On a solution of polynomial grammars and the general algebraic equation

2021 ◽  
pp. 176-178
Author(s):  
O. I. Egorushkin ◽  
I. V. Kolbasina ◽  
K. V. Safonov
Keyword(s):  
Algebraic Equation

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

scholarly journals On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Takashi Uno
Keyword(s):  
Lower Bound ◽  
Algebraic Equation ◽  
Random Variables ◽  
Real Roots ◽  
Number Of Real Roots

We estimate a lower bound for the number of real roots of a random alegebraic equation whose random coeffcients are dependent normal random variables.

Static Analysis of Electrically Actuated Nano to Micron Scale Beams Using Nonlocal Theory

2011 ◽  
Author(s):  
Y. Alizadeh Vaghasloo ◽  
Abdolreza Pasharavesh ◽  
M. T. Ahmadian ◽  
Ali Fallah
Keyword(s):  
Size Effect ◽  
Algebraic Equation ◽  
Bending Moment ◽  
Nonlocal Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Beam Deflection ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Electrically Actuated ◽  
The One

In this paper, size dependent static behavior of micro and nano cantilevers actuated by a static electric field including deflection and pull-in instability, is analyzed implementing nonlocal theory. Euler-bernoulli assumptions are made to model the relation between deflection of the beam and bending moment. Differential form of the constitutive equation of nonlocal theory is used to find the revised equation for bending moment and substituting in the equilibrium equation of electrostatically actuated beams final nonlinear ordinary differential equation is arrived. Also the boundary conditions for solving the equation are revised and to analyze the size effect better governing equation is nondimetionalized. The one parameter Galerkin method is used to transform this equation to a nonlinear algebraic equation. Arrived algebraic equation is solved utilizing Newton-Raphson method. Size effect on the maximum deflection and deflection shape for various applied voltages is studied. Also effect of beam size on the static pull-in voltage is studied. Results indicate that the dimensionless beam deflection decreases as size decreases while the pull-in voltage increases and specially change of deflection and pull-in voltage is significant for nanobeams.

Truss Analyses by DQEM

1999 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Algebraic Equation ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Equation System ◽  
Numerical Approach ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Rigorous Solution ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method

Abstract A new numerical approach for solving generic three-dimensional truss problems having nonprismatic members is developed. This approach employs the differential quadrature (DQ) technique to discretize the element-based governing differential equations, the transition conditions at joints and the boundary conditions on the domain boundary. A global algebraic equation system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the global algebraic equation system. Mathematical formulations for two-dimensional differential quadrature element method (DQEM) truss model are carried out. By using this DQEM model, accurate results of two-dimensional truss problems can efficiently be obtained. Numerical results demonstrate this DQEM model.

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