Bivariate fibonacci like p-polynomials

In this article, we study the bivariate Fibonacci and Lucas p-polynomials (p ? 0 is integer) from which, specifying x, y and p, bivariate Fibonacci and Lucas polynomials, bivariate Pell and Pell-Lucas polynomials, Jacobsthal and Jacobsthal-Lucas polynomials, Fibonacci and Lucas p-polynomials, Fibonacci and Lucas p-numbers, Pell and Pell-Lucas p-numbers and Chebyshev polynomials of the first and second kind, are obtained. Afterwards, we obtain some properties of the bivariate Fibonacci and Lucas p-polynomials.     

Pell graphs

In this paper, we introduce the Pell graphs, a new family of graphs similar to the Fibonacci cubes. They are defined on certain ternary strings (Pell strings) and turn out to be subgraphs of Fibonacci cubes of odd index. Moreover, as well as ordinary hypercubes and Fibonacci cubes, Pell graphs have several interesting structural and enumerative properties. Here, we determine some of them. Specifically, we obtain a canonical decomposition giving a recursive structure, some basic properties (bipartiteness and existence of maximal matchings), some metric properties (radius, diameter, center, periphery, medianicity), some properties on subhypercubes (cube coefficients and polynomials, cube indices, decomposition in subhypercubes), and, finally, the distribution of the degrees.     

两路关联光纤激光器互注入锁相实验

基于角锥互注入锁相相干合成方案,利用光纤Bragg光栅（R=85％@1064nm）作为两路光纤激光器的共用腔镜,实现了两路光纤激光器相关联,进一步提高了激光的互注入能量。采用外腔结构,较容易实现了两路光纤激光器的能量互注入锁相。在实验上观察到了远场清晰稳定的干涉条纹（可见度超过0．8）,获得了功率合成效率约为80％的线偏振相干激光输出。