This paper presents a new approach for synthesizing flat-top patterns, based on the least-square error criterion. The cost function is formulated according to the amplitude approximation error without phase constraint. The optimal array weight is obtained by using the Levenberg–Marquardt nonlinear optimization algorithm. Simulations are performed to compare the proposed approach with the Woodwa...

This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the square residual error, the optimal convergence-control parameters ...

-We study the least square regression with data dependent hypothesis and coefficient regularization algorithms based on general kernel. An explicit expression of the solution of this kernel scheme is derived. Then we provide a sample error with a decay of 1 ( ) O m and estimate the approximation error in terms of some kind of K -functional. Index Terms -Least Square Regressions, Data Dependent ...

Recently the so called angel problem was solved independently by four authors. We establish an analogous theorem for triangulations of the plane and derive a solution to the original angel problem from this theorem. Compared to earlier solutions, our approach gives a simpler proof as well as a weaker winning angel. We show that an angel moving from the middle square to any other square of a 3 b...

Heuvers, K.J. and D.S. Moak, The solution of the Binet-Cauchy functional equation for square matrices, Discrete Mathematics 88 (1991) 21-32. It is shown that if f : M,(K)+ K is a nonconstant solution of the Binet-Cauchy functional equation for A, B E M,,(K) and if f(E) = 0 where E is the n x n matrix with all entries l/n then f is given by f(A) = m(det A) where m is a multiplicative function on...

In this paper, based on the properties of almost periodic function and exponential dichotomy of linear system on time scales as well as Krasnoselskii’s fixed point theorem, some sufficient conditions are established for the existence of square-mean almost periodic solutions of neutral stochastic functional differential equations on time scales. Finally, an example is presented to illustrate the...

We provide necessary and sufficient conditions for the uniqueness of solution of the generalized Sylvester and ⋆-Sylvester equations, AXB − CXD = E and AXB+CX ⋆ D = E, respectively, where the matrix coefficients are allowed to be rectangular. These conditions generalize existing results for the same equations with square coefficients. Our characterization reveals unexpected constraints regardin...

a weighted linear regression model with impercise response and p-real explanatory variables is analyzed. the lr fuzzy random variable is introduced and a metric is suggested for coping with this kind of variables. a least square solution for estimating the parameters of the model is derived. the result are illustrated by the means of some case studies.

Combined with an approximation suggested by Taylor and Lipson for the third-order correlation function and the translational invariance approximation, the BGY equation is used to calculate the conformation and thermodynamic properties of a diblock square-well copolymer or a random square-well copolymer. The BGY results for the end-to-end distribution of copolymers are in good agreement with Mon...