scholarly journals Some advances on essential spectra of one sided operator matrix with application

2021 ◽  
Author(s):  
Marwa Belghith ◽  
Nedra Moalla ◽  
Ines Walha
Keyword(s):  
Differential Equations ◽  
Unbounded Operator ◽  
Matrix Form ◽  
Operator Matrix ◽  
Essential Spectra ◽  
The One

This paper deals with a new description of the one sided operator matrix form, as a generalization of the case of the unbounded operator matrix with the non diagonal domain, to investigate some advances in the analysis of some essential spectra under weaker hypotheses then the one provided in the works of [17, 33]. An example of differential equations is tested to ensure the validity of the abstract results.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

Comparison Theorem for any Solutions of Backward Stochastic Differential Equations and its Application

2012 ◽  
Vol 524-527 ◽  
pp. 3801-3804
Author(s):  
Shi Yu Li ◽  
Wu Jun Gao ◽  
Jin Hui Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Local Martingale ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
The One ◽  
Uniformly Lipschitz

ƒIn this paper, we study the one-dimensional backward stochastic equations driven by continuous local martingale. We establish a generalized the comparison theorem for any solutions where the coefficient is uniformly Lipschitz continuous in z and is equi-continuous in y.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 101-102
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Variation Of Parameters ◽  
First Approximation ◽  
The One ◽  
Equivalent Method

For the solution of mechanical problems, two methods in general present themselves: the one furnished by the variation of parameters, or constants, which complete the integral obtained by the first approximation,—the other furnished by the integration of the differential equations by means of indeterminate coefficients, or some equivalent method. Each of these methods is applicable to the theory of the perturbations of the heavenly bodies, and they lead to expressions which are of course substantially identical, but which do not appear in the same shape except after certain transformations. The object of the author in the present paper is to effect transformations, by which their identity is established, making use of the developments given in his former papers, published in the Philosophical Transactions. The identity of the results obtained by either methods affords a confirmation of the exactness of those expressions.

scholarly journals RADIATIVE DAMPING AND FUNCTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2627-2638 ◽  
Author(s):  
SUVRAT RAJU ◽  
C. K. RAJU
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
General Technique ◽  
Covariant Model ◽  
Maxwell Electrodynamics ◽  
Functional Differential ◽  
The One ◽  
Radiative Damping

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

A Novel Method for Solving Consistency-Order Initial Value of Ordinary Differential Equations

2014 ◽  
Vol 543-547 ◽  
pp. 1844-1847
Author(s):  
Si Min Zhu ◽  
Hai Yun Deng ◽  
Kai Zheng ◽  
Hua Mei Li ◽  
Xiao Zhou Chen
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Integral Formula ◽  
Absolute Error ◽  
The Other ◽  
It Use ◽  
Initial Value ◽  
Novel Method ◽  
The One ◽  
Legendre Quadrature

It is known that the level of the consistency-order of initial value problem is an important standard to determine whether the constructed methods for solving initial value problem of ODEs is suitable or not. There are two methods to solve the consistency-order of initial value problem in general. The one is using the remainder of integral formula as local truncated error, and the other one is using absolute error as local truncated error. In the paper, we propose a novel method based on Gauss-Legendre quadrature formula. It use the method of the remainder of integral formula as local truncated error exists in most of the literatures, and it will be solved once again for the consistency-order of the constructed methods that exist in currently literatures by using absolute error as local truncated error, and then draw a conclusion that is differ from what has been proved correspondingly.

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