Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...

An overview of a family of methods for nding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead.

This survey reviews some of the recent work on semilinear wave equations, in particular the wave map equation. We discuss wellposedness, as well as the construction of special solutions and their stability. Mathematics Subject Classification (2010). 35L05, 35L52, 37K40, 37K45, 53Z05

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

1. Linearity and Continuity 1.1 Continuity 1.2 Linearity 1.3 Perturbation theory and linearity 1.4 Axiomatically linear equations 1.4.1 Fields, Maxwell equations 1.4.2 Densities on phase space in classical physics 1.4.3 Quantum mechanics and Schrödinger equation 2. Examples 2.1 Ordinary differential equations 2.2 The Laplace equation 2.3 The wave equation 2.4 The heat equation and Schrödinger e...

We have discussed general methods for solving arbitrary equations, and looked at the special class of polynomial equations. A subclass of the latter comprises all the systems of linear equations to which the area of linear algebra is devoted. In fact, many a problem in numerical analysis can be reduced to one of solving a system of linear equations. We already witnessed this in the use of Newto...

Let ∇ be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism σ : Γ → Γ is called a symmetry of ∇ if the pull-back bundle and the pull-back connection can be identified with ∇. We study the symmetries by means of what we call the Fano Group; and, under the hypothesis that ∇ has a unimodular reductive Galois group, we relate the differential Galois group,...

For simplicity, we follow the rules: x denotes a set, i, j, k, l, m, n denote natural numbers, K denotes a field, N denotes a without zero finite subset of N, a, b denote elements of K, A, B, B1, B2, X, X1, X2 denote matrices over K, A′ denotes a matrix over K of dimension m × n, B′ denotes a matrix over K of dimension m × k, and M denotes a square matrix over K of dimension n. We now state a n...

UNCERTAIN LINEAR EQUATIONS Mert Pilancı M.S. in Electrical and Electronics Engineering Supervisor: Prof. Dr. Orhan Arıkan July 2010 In this thesis, new theoretical and practical results on linear equations with various types of uncertainties and their applications are presented. In the first part, the case in which there are more equations than unknowns (overdetermined case) is considered. A no...