The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an kgebralc procedure. A quadratic matrix quation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solu...

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability o...

In this paper, we have obtained and presented new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution and a gravitational potential Z(x) that depends on an adjustable parameter. The quadratic equation of state based on Feroze and Siddiqui viewpoint is used for the matter distribution. The new solutions can be written in terms of elementar...

and Applied Analysis 3 Theorem 1.2 Rassias 18 . Let X be a real normed linear space and Y a real complete normed linear space. Assume that f : X → Y is an approximately additive mapping for which there exist constants θ ≥ 0 and p, q ∈ R such that r p q / 1 and f satisfies the inequality ∥ ∥f ( x y ) − f x − f(y)∥∥ ≤ θ‖x‖p∥∥y∥∥q 1.5 for all x, y ∈ X. Then there exists a unique additive mapping L...

Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique to solve problems which need optimization. Generation of trial solutions have been formed by this method. Many examples have been worked out, and in most ca...

1. Unconstrained finite horizon linear quadratic problem 2 1.1. Critical points of quadratic functionals 2 1.2. Shooting function and Hamiltonian flow 6 1.3. Riccati equation 8 1.4. Expression of the critical value 9 1.5. Legendre forms and minima of quadratic functions 9 1.6. Spectral analysis 12 2. Infinite horizon problems 13 2.1. Setting 13 2.2. Kalman state space theory 13 2.3. The algebra...

where f, g : I × → are given functions, λ ∈ (0, 1]. The study of quadratic integral equation has received much attention over the last thirty years or so. For instance, Cahlon and Eskin [1] prove the existence of positive solutions in the space C[0, 1] and Cα[0, 1] of an integral equation of the Chandrasekhar H-equation with perturbation. Argyros [2] investigates a class of quadratic equations ...

Abstract. A cell-population based model for tumor growth under anti-angiogenic treatment with the tumor volume and its variable carrying capacity as variables is combined with the linear-quadratic model for damage done by radiation ionization. The resulting multi-input system is analyzed as an optimal control problem with the objective of minimizing the tumor volume subject to isoperimetric con...

A convenient and physically sound mathematical model of the external or I − V characteristic of solar cells generators is presented in this paper. This model is compared with the traditional model of p−n junction. The direct analytical calculation of load regime leads to a quadratic equation, which is importantly to simplify the calculations in the real time.