Let D be a list of single digits, and let k be a positive integer. We construct an infinite sequence of positive integers by repeatedly appending, in order, one at a time, the digits from the list D to the integer k, in one of four ways: always on the left, always on the right, alternating and starting on the left, or alternating and starting on the right. In each of these four situations, we i...

In this paper, we introduce the concept of λ-statistically Cauchy sequence of fuzzy numbers and show that it is equivalent to λ-statistically convergent sequence of fuzzy numbers. AMS Subject Classification: 40A05, 40C05, 40D05

The Cauchy problems of Keller-Segel system with logistic source seem much less throughly understood than associated initial-boundary in bounded domains. This paper is concerned the problem generalized given by$ \begin{eqnarray*} \left\{ \begin{array}{llc} \label{188} u_t = \Delta u - \nabla \cdot (u\nabla v)+\lambda u-\mu u^{k}, \\ 0 v+u, \end{array} \right. \end{eqnarray*} $in \begin{document}...

Abstract In this paper, we present the ideal convergence of triple sequences for rough variables. Furthermore, sequence plays an extremely important role in fundamental theory mathematics. This paper presents two types sequence: Convergence trust and mean. Some mathematical properties those new concepts are also given. addition, introduce Cauchy spaces.

a k-nacci sequence in a finite group is a sequence of group elements x0 , x1, x2 ,, xn , forwhich, given an initial (seed) set 0 1 2 1 , , , ,j x x x x  , each element is defined by0 1 11 1for ,for .nnn k n k nxx x j n kxx x x n k        in this paper, we examine the periods of the k-nacci sequences in miller’s generalization of the polyhedralgroups 2,2 2;q , n,2 2;q , 2, n 2;...

Let a 1 < a 2 <. .. be any sequence of integers. Assume that the infinite sequence of condition : To every E > for all n > n and all k o (1) ~u n+-u n I < E a k Obreanu asked (Problem P. 35 Can. Math. Bull .) under what conditions on the sequence a < a 2 <. .. does (1) imply that 1 is convergent. N. G. de Bruijn and P. Erdős the sequence u n proved that a necessary and sufficient the convergenc...

and Applied Analysis 3 where the kernel K t, s is an n × n Cauchy matrix defined in the square a, b × a, b being, for every fixed s ≤ t , a solution of the matrix Cauchy problem LK ·, s t : ∂K t, s ∂t −A t Sh0K ·, s t Θ, K s, s I, 1.8 where K t, s ≡ Θ if a ≤ t < s ≤ b, Θ is n × n null matrix and I is n × n identity matrix. A fundamental n × n matrix X t for the homogeneous φ ≡ θ equation 1.5 ha...

The Cauchy-type product of two arithmetic functions f and g on nonnegative integers is defined by (f • g)(k) := ∑k m=0 ( k m ) f(m)g(k −m). We explore some algebraic properties of the aforementioned convolution, which is a fundamental characteristic of the identities involving the Bernoulli numbers, the Bernoulli polynomials, the power sums, the sums of products, and so forth.

Induction step. Let n 2 and suppose that the lemma holds for all insertion permutations of size strictly less than n. Let π = (π(1), . . . , π(n)) be a permutation drawn uniformly at random from Sn. The rst element π(1) will become the root of the tree Tπ. Since the distribution of π(1) is u.a.r. from [n], the root of the tree is chosen uniformly at random, as required by the construction of ~ ...