We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)} ∞ n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V-sequences when the product of their discriminants is a perfect square. Moreover, the int...

paris polyphylla smith var. yunnanensis (liliaceae) is an important traditional medicinal plant of the yunnan province in china. however, the genomic information regarding this plant is limited. to further understand its molecular background, we conducted illumina hiseq 2000 second-generation sequencing of this plant species. approximately 30,198,679 reads with an average length of 202 bases we...

bioinformatics, through the sequencing of the full genomes for many species, is increasingly relying on efficient global alignment tools exhibiting both high sensitivity and specificity. many computational algorithms have been applied for solving the sequence alignment problem. dynamic programming, statistical methods, approximation and heuristic algorithms are the most common methods applied t...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

This paper studies combinatorial properties of the complex planar injective words , a chain modules over Temperley-Lieb algebra that arose in our work on homological stability. Despite being linear rather than discrete object, nevertheless exhibits interesting properties. We show Euler characteristic this is n -th Fine number. obtain an alternating sum formula for representation given by its to...