in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes’ frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters ar...

The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the null space of the measurement procedure and as such, any two matrices which have the same null space will have NSP if either one of them does. On the other h...

This paper describes ILP-PLAN, a framework for solving AI planning problems represented as integer linear programs. ILP-PLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand-bound IP solvers and efficient new integer...

For the mean curvature vector field H and the Laplace operator ∆ of a submanifold in the Minkowski space, a submanifold satisfying the condition ∆H = f H + gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper...

We present a branch-and-bound algorithm for minimizing multiple convex quadratic objective functions over integer variables. Our method looks efficient points by fixing subsets of variables to values and using lower bounds in the form hyperplanes image space derived from continuous relaxations restricted functions. show that stops after finitely many fixings with detecting both full nondominate...

Fermat’s well-known factorization algorithm is based on finding a representation of natural numbers $N$ as the difference squares. In 1895, Lawrence generalized this idea and applied it to multiples $kN$ original number. A systematic approach choose suitable values for $k$ was introduced by Lehman in 1974, which resulted first deterministic considerably faster than trial division. paper, we c...

In this paper, we study different types of non-additive set multifunctions (such as: uniformly autocontinuous, null-additive, null-null-additive), presenting relationships among them and some of their properties regarding atoms and pseudo-atoms. We also study non-atomicity and non-pseudo-atomicity of regular null-additive set multifunctions defined on the Baire (Borel respectively) δ-ring of a ...