Let f be a binary string and d C 1. Then the generalized Lucas cube Qd(JÐf ) is introduced as the graph obtained from the d-cube Qd by removing all vertices that have a circulation containing f as a substring. The question for which f and d, the generalized Lucas cube Qd(JÐf ) is an isometric subgraph of the d-cube Qd is solved for all binary strings of length at most five. Several isometricall...

we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, thenwe define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix me...

Assume that ? and ? are two independent random variables with distribution functions F? F?, respectively. The of a variable ??, denoted by F??F?, is called the product-convolution F?. It proved F??F? generalized subexponential if belongs to class distributions nonnegative not degenerated at zero.

D denotes the homomorphism poset of finite directed graphs. An antichain duality is a pair 〈F ,D〉 of antichains of D such that (F→) ∪ (→D) = D is a partition. A generalized duality pair in D is an antichain duality 〈F ,D〉 with finite F and D. We give a simplified proof of the Foniok Nešetřil Tardif theorem for the special case D, which gave full description of the generalized duality pairs in D...

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f , that is, f is an entire function satisfying the following growth condition |f(z)| ≤ A exp(σ|y|) for some A, σ > 0 and any z = x + iy ∈ C.

for some positive constant ε depending only on δ. Sometimes we call f a δ-approximate solution of (1.1) and g ε-close to f . Such an idea of stability was given by Ulam [13] for Cauchy equation f(x+y) = f(x)+f(y) and his problem was solved by Hyers [4]. Later, the Hyers-Ulam stability was studied extensively (see, e.g., [6, 8, 10, 11]). Moreover, such a concept is also generalized in [2, 3, 12]...