Logarithmic norms and projections applied to linear differential systems

On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems

Logarithmic Derivatives of Solutions to Linear Differential Equations

Given an ordinary differential field K of characteristic zero, it is known that if y and 1/y satisfy linear differential equations with coefficients in K, then y/y is algebraic over K. We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over K that y/y satisfies. Moreover, we provide explicit degree bounds and extend the res...

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Exergy Optimization Applied to Linear Parabolic

A new method of optimization on linear parabolic solar collectors using exergy analysis is presented. A comprehensive mathematical modeling of thermal and optical performance is simulated and geometrical and thermodynamic parameters were assumed as optimization variables. By applying a derived expression for exergy efficiency, exergy losses were generated and the optimum design and operating co...

Norms of Minimal Projections

It is proved that the projection constants of twoand three-dimensional spaces are bounded by 4/3 and (1 + √ 5)/2, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron. In fact, a general inequality for the projection constant of a real or complex n-dimensional space is obtained and the question of equality therein is discussed...