In this work we study the set of leader codewords of a non-binary linear code. This set has some nice properties related to the monotonicity of the weight compatible order on the generalized support of a vector in Fnq . This allows us to describe a test set, a trial set and the set zero neighbours in terms of the leader codewords.

This informal note presents generalized versions of the higherorder frame and anti-frame rules. The main insights reside in two successive generalizations of the “tensor” operator ⊗. In the first step, a form of “local invariant”, which allows implicit reasoning about “well-bracketed state changes”, is introduced. In the second step, a form of “local monotonicity” is added.

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals [Formula: see text] and [Formula: see text] depending on a parameter [Formula: see text], which contains an earlier result in the particular case [Formula: see text].

Complete monotonicity properties of some functions involving the psi function are studied and some known results are extended and generalized. Moreover, a necessary and sufficient conditions for some functions to be completely monotonic are presented and proved. Mathematics subject classification (2010): 33B15, 26D15.

In this paper, we consider and study a class of vector variational-like inequalities in Banach space without any generalized monotonicity by exploiting vector version of minimax inequality and obtain the existence results of solutions to the class of vector variational-like inequalities. The results presented here are different from [1, 5, 11], and extend and generalize the corresponding result...

Some monotonicity results for the function f( )x ) n;k , where x ( ) n;k is the kth zero of generalized Laguerre polynomial L ) n (x) and f( ) is a suitable function of , are derived by means of the classical method of Stiltjes. c © 2002 Published by Elsevier Science B.V.

A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and Born-Infeld systems. 2000 MSC: 58E15.