Linear equations

In this paper "Some new identities in combinatoric", the binomial numbers m n are very important in several applications and satisfy several number of identities. The purpose of this paper is to introduce a new combinatorial integer m,n j and obtain some algebraic identities by means of double combinatorial argument.

14p runordie3 27-06-2022 15 3   Download

This study develops unconditionally monotone finite-difference scheme of second-order of local approximation on uniform grids for the initial boundary problem value for the Gamma equation through the establishment of two-side estimates for the scheme’s solution.

8p tamynhan6 14-09-2020 19 2   Download

In this paper, we study the solvability analysis of arbitrarily high-order linear differential-algebraic equations (DAEs) with time-varying coefficients, using the algebraic-behavior approach. We propose a concept of strangeness-index and construct condensed forms for high-order linear DAEs.

14p vibenya 31-12-2024 5 2   Download

Lecture Control system design: Mathematical models of systems presents the following content: Differential equations of physical systems, linear approximations of physical systems, the laplace transform, the transfer function of linear systems, block diagram models, signal – flow graph models, the simulation of systems using control design software.

62p youcanletgo_04 17-01-2016 59 4   Download

Lecture "Fundamentals of control systems - Chapter 2: Mathematical models of continuous control systems" presentation of content: Presentation of content, transfer function, block diagram algebra, signal flow diagram, state space equation, linearized models of nonlinear systems.

120p doinhugiobay_17 04-03-2016 104 8   Download

The dissertation is divided into four chapters: Chapter 1 - Preliminaries; Chapter 2 - Lyapunov exponents for dynamic equations; Chapter 3 - Bohl exponents for implicit dynamic equations; Chapter 4 - Stability radius for implicit dynamic equations.

117p monsterhunterer 20-06-2021 21 3   Download

Purpose: Study the existence of inertial manifolds and the asymptotic behavior of solutions to certain classes of evolution equations in an infinite-dimensional Banach space. The evolution equations considered with the linear parts is the generator of a semigroup and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to admissible function spaces which contain wide classes of function spaces like Lp-spaces, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory.

27p tunelove 10-06-2021 26 3   Download

The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the half-space of the medium.

6p tohitohi 19-05-2020 14 1   Download

Semi-submersible drilling platforms are huge bulk structures for extracting the oil products from great depth of seas. For such bulk structures, the Morrison’s equations are no longer valid for determining the loads applied to the semi-submersible drilling platforms.

8p tohitohi 19-05-2020 15 1   Download

The objective of the thesis: Establishing thermal models of single-node, two-node and many-node associated with different thermal loading models acting on a small satellite in Low Earth Orbit. Finding analytical solutions of equations of thermal balance for small satellites by the dual criterion equivalent linearization method.

27p xacxuoc4321 08-07-2019 40 7   Download

The process of finding an optimum outcome from a set of constrained resources, where the objective function and the constraints can be expressed as linear equations. The process of finding an optimum outcome from a set of constrained resources, where the objective function and the constraints can be expressed as linear equations.

15p muaxuan102 21-02-2013 52 6   Download

Annals of Mathematics This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1...

51p noel_noel 17-01-2013 49 8   Download

We introduce and study “isomonodromy” transformations of the matrix linear difference equation Y (z + 1) = A(z)Y (z) with polynomial A(z). Our main result is construction of an isomonodromy action of Zm(n+1)−1 on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)). The (birational) action of certain rank n subgroups can be described by difference analogs of the classical Schlesinger equations, and we prove that for generic initial conditions these difference Schlesinger equations have a unique solution. ...

43p tuanloccuoi 04-01-2013 67 8   Download

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric Γ-function over Fq [T ] are explained by the standard functional equations. Contents 1. Introduction 2. Notation and terminology 3. A linear independence criterion 4. Tools from (non)commutative algebra

78p tuanloccuoi 04-01-2013 60 7   Download

TWO-POINT BOUNDARY VALUE PROBLEMS FOR HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH STRONG SINGULARITIES R. P. AGARWAL AND I. KIGURADZE Received 4 April 2004; Revised 11 December 2004; Accepted 14 December 2004 For strongly singular higher-order linear differential equations together with two-point conjugate and right-focal boundary conditions, we provide easily verifiable best possible conditions which guarantee the existence of a unique solution. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. Statement of the main results 1.1.

32p sting12 10-03-2012 57 7   Download

ON A PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND-ORDER LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS S. MUKHIGULASHVILI Received 26 October 2004 and in revised form 7 March 2005 Unimprovable efficient sufficient conditions are established for the unique solvability of the periodic problem u (t) = (u)(t) + q(t) for 0 ≤ t ≤ ω, u(i) (0) = u(i) (ω) (i = 0,1), where ω 0, : C([0,ω]) → L([0,ω]) is a linear bounded operator, and q ∈ L([0,ω]). 1. Introduction Consider the equation u (t) = (u)(t) + q(t) for 0 ≤ t ≤ ω with the periodic boundary conditions u(i) (0) = u(i)...

15p sting12 10-03-2012 65 5   Download

SEMILINEAR PROBLEMS WITH BOUNDED NONLINEAR TERM MARTIN SCHECHTER Received 17 August 2004 We solve boundary value problems for elliptic semilinear equations in which no asymptotic behavior is prescribed for the nonlinear term. 1. Introduction Many authors (beginning with Landesman and Lazer [1]) have studied resonance problems for semilinear elliptic partial differential equations of the form −∆u − λ u = f (x,u) in Ω, u = 0 on ∂Ω, (1.1) where Ω is a smooth bounded domain in Rn , λ is an eigenvalue of the linear problem −∆u = λu in Ω, u = 0 on ∂Ω, (1.

8p sting12 10-03-2012 38 3   Download

ON STABILITY ZONES FOR DISCRETE-TIME PERIODIC LINEAR HAMILTONIAN SYSTEMS ˘ VLADIMIR RASVAN Received 18 June 2004; Revised 8 September 2004; Accepted 13 September 2004 The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems.

13p sting12 10-03-2012 39 5   Download

ON THIRD-ORDER LINEAR DIFFERENCE EQUATIONS INVOLVING QUASI-DIFFERENCES ˇ ´ ˇ ZUZANA DOSLA AND ALES KOBZA Received 30 June 2004; Revised 20 September 2004; Accepted 12 October 2004 We study the third-order linear difference equation with quasi-differences and its adjoint equation. The main results of the paper describe relationships between the oscillatory and nonoscillatory solutions of both equations. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1.

13p sting12 10-03-2012 32 4   Download

ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL SOLUTION OF ODEs L. ACETO, R. PANDOLFI, AND D. TRIGIANTE Received 21 July 2004; Accepted 4 October 2004 The study of the stability properties of numerical methods leads to considering linear difference equations depending on a complex parameter q. Essentially, the associated characteristic polynomial must have constant type for q ∈ C− . Usually such request is proved with the help of computers.

14p sting12 10-03-2012 50 7   Download