Here we develop a technique of computing the invariants of n−ary forms and systems of forms using the discriminants of corresponding multilinear forms buit of their partial derivatives, which should be cosidered as generalizations of classical discriminants and resultants for binary forms. 0 Introduction Let f(y0, y1, ..., yn) = ∑ α1≤...≤αd cα1...αdyα1 ...yαd be an n + 1−ary form of degree d, w...

Eccentric coloring is a new variation of coloring, where higher numbered colors can not be used as freely as lower numbered colors. In addition there is a correspondence between the eccentricity (max distance) of a vertex and the highest legal color for that vertex. In this note we investigate eccentric coloring of trees. We give the eccentric chromatic number or a bound on the eccentric chroma...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

This paper reviews a competent Pittsburgh LCS that automatically mines important substructures of the underlying problems and takes problems that were intractable with firstgeneration Pittsburgh LCS and renders them tractable. Specifically, we propose a χ-ary extended compact classifier system (χeCCS) which uses (1) a competent genetic algorithm (GA) in the form of χ-ary extended compact geneti...

This paper proposes a competent Pittsburgh LCS that automatically mines important substructures of the underlying problems and takes problems that were intractable with first-generation Pittsburgh LCS and renders them tractable. Specifically, we propose a χ-ary extended compact classifier system (χeCCS) which uses (1) a competent genetic algorithm (GA) in the form of χ-ary extended compact gene...

We study the recurrence property of one-per-site frog model FM(d,p) on a d-ary tree with drift parameter p∈[0,1], which determines bias frogs’ random walks. In this model, active frogs move toward root probability p or otherwise to uniformly chosen child vertex. Whenever site is visited for first time, new introduced at site. are interested in minimal pd so that recurrent. Using coupling argume...

The edge-bandwidth problem is an analog of the classical bandwidth problem, in which one has to label the edges of a graph by distinct integers such that the maximum difference of labels of any two incident edges is minimized. We prove tight bounds on the edge-bandwidth of hypercube and butterfly graphs and complete k-ary trees which extend and improve on previous known results. We also provide...