In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...

It is now firmly recognized that although the majority of mammalian genome is transcribed to RNA, protein-coding transcripts occupy only a minor part of mammalian transcriptome. Instead, increasing evidence suggests that the majority of mammalian RNAs is comprised noncoding RNAs (ncRNAs). ncRNAs are a diverse class of RNAs with many subclasses involved in a wide variety of physiological functio...

We introduce a method of searching the k nearest neighbours (k-NN) using PM-tree. The PM-tree is a metric access method for similarity search in large multimedia databases. As an extension of M-tree, the structure of PM-tree exploits local dynamic pivots (like M-tree does it) as well as global static pivots (used by LAESA-like methods). While in M-tree a metric region is represented by a hyper-...

We study the nonequlibrium transport through a quantum dot weakly coupled to Luttinger liquids (LL). A general current expression is derived by using nonequilibrium Green function method. Then a special case of the dot with only a single energy level is discussed. As a function of the dot’s energy level, we find that the current as well as differential conductance is strongly renormalized by th...

Employing the common property E.A , we prove some common fixed point theorems for weakly compatible mappings via an implicit relation in Menger PM spaces. Some results on similar lines satisfying quasicontraction condition as well as ψ-type contraction condition are also proved in Menger PM spaces. Our results substantially improve the corresponding theorems contained in Branciari, 2002 ; Rhoad...

In this paper, we discuss an equation which does not contain the Planck’s constant, but it will turn out the Planck’s constant when we apply the equation to the problems of particle diffraction. PACS numbers: 03.65Bz, 03.65.Ca, 03.65.Pm