scholarly journals Polynomials related to harmonic numbers and evaluation of harmonic number series II

2011 ◽  
Vol 5 (2) ◽  
pp. 212-229 ◽  
Author(s):  
Ayhan Dil ◽  
Veli Kurt
Keyword(s):  
Subject Classification ◽  
Harmonic Number ◽  
Harmonic Numbers ◽  
Number Series ◽  
Exponential Polynomials ◽  
2000 Mathematics Subject Classification

In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers. 2000 Mathematics Subject Classification. 11B73, 11B75, 11B83.

scholarly journals Riordan matrices and sums of harmonic numbers

2011 ◽  
Vol 5 (2) ◽  
pp. 176-200 ◽  
Author(s):  
Emanuele Munarini
Keyword(s):  
Stirling Numbers ◽  
Catalan Numbers ◽  
Subject Classification ◽  
Harmonic Numbers ◽  
Lucas Numbers ◽  
Primary 05A15 ◽  
Secondary 05A10 ◽  
General Identity ◽  
2000 Mathematics Subject Classification ◽  
Fibonacci And Lucas Numbers

We obtain a general identity involving the row-sums of a Riordan matrix and the harmonic numbers. From this identity, we deduce several particular identities involving numbers of combinatorial interest, such as generalized Fibonacci and Lucas numbers, Catalan numbers, binomial and trinomial coefficients, Stirling numbers. 2000 Mathematics Subject Classification: Primary: 05A15; Secondary: 05A10.

scholarly journals Sharp inequalities for the harmonic numbers

2012 ◽  
Vol 28 (2) ◽  
pp. 223-229
Author(s):  
CHAO-PING CHEN ◽  
Keyword(s):  
Harmonic Number ◽  
Harmonic Numbers ◽  
Double Inequality

Let Hn be the nth harmonic number, and let γ be the Euler-Mascheroni constant. We prove that for all integers n ≥ 1, the double-inequality ... holds with the best possible constants ... We also establish inequality for the Euler-Mascheroni constant.

scholarly journals On -Quasi Irresolute Functions

2017 ◽  
Vol 1 (2) ◽  
pp. 72-77
Author(s):  
C. Janaki ◽  
Ganes M. Pandya
Keyword(s):  
Subject Classification ◽  
New Class ◽  
2000 Mathematics Subject Classification ◽  
The Relationship ◽  
Class Of Functions

In this paper we introduce a new class of functions called -quasi irresolute functions. The notion of -quasi graphs are introduced and the relationship between -quasi irresolute functions and -quasi closed graphs is analysed. 2000 Mathematics Subject Classification : 54C08, 54C10.

scholarly journals Some equinumerous pattern-avoiding classes of permutations

2005 ◽  
Vol Vol. 7 ◽  
Author(s):  
M. D. Atkinson
Keyword(s):  
Recurrence Relation ◽  
Subject Classification ◽  
International Audience ◽  
2000 Mathematics Subject Classification

International audience Suppose that p,q,r,s are non-negative integers with m=p+q+r+s. The class X(p,q,r,s) of permutations that contain no pattern of the form α β γ where |α |=r, |γ |=s and β is any arrangement of \1,2,\ldots,p\∪ \m-q+1, m-q+2, \ldots,m\ is considered. A recurrence relation to enumerate the permutations of X(p,q,r,s) is established. The method of proof also shows that X(p,q,r,s)=X(p,q,1,0)X(1,0,r,s) in the sense of permutational composition.\par 2000 MATHEMATICS SUBJECT CLASSIFICATION: 05A05

Some properties of harmonic numbers

2020 ◽  
Vol 57 (2) ◽  
pp. 207-216
Author(s):  
Bing-Ling Wu ◽  
Xiao-Hui Yan
Keyword(s):  
Harmonic Number ◽  
Harmonic Numbers ◽  
Logarithmic Density

AbstractLet Hn be the n-th harmonic number and let vn be its denominator. It is known that vn is even for every integer . In this paper, we study the properties of Hn and prove that for any integer n, vn = en(1+o(1)). In addition, we obtain some results of the logarithmic density of harmonic numbers.

scholarly journals FINITE CONJUGACY IN ALGEBRAS AND ORDERS

2001 ◽  
Vol 44 (1) ◽  
pp. 201-213 ◽  
Author(s):  
M. A. Dokuchaev ◽  
S. O. Juriaans ◽  
C. Polcino Milies ◽  
M. L. Sobral Singer
Keyword(s):  
Conjugacy Class ◽  
Division Ring ◽  
Multiplicative Group ◽  
Central Element ◽  
Subject Classification ◽  
Group Rings ◽  
2000 Mathematics Subject Classification ◽  
Primary 16U60 ◽  
Finite Conjugacy

AbstractHerstein showed that the conjugacy class of a non-central element in the multiplicative group of a division ring is infinite. We prove similar results for units in algebras and orders and give applications to group rings.AMS 2000 Mathematics subject classification: Primary 16U60. Secondary 16H05; 16S34; 20F24; 20C05

scholarly journals An Extension of a Congruence by Tauraso

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Romeo Meštrović
Keyword(s):  
Positive Integer ◽  
Elementary Proof ◽  
Harmonic Number ◽  
Combinatorial Identity ◽  
Harmonic Numbers

For a positive integer let be the th harmonic number. In this paper we prove that, for any prime ,  . Notice that the first part of this congruence is proposed in 2008 by Tauraso. In our elementary proof of the second part of the above congruence we use certain classical congruences modulo a prime and the square of a prime, some congruences involving harmonic numbers, and a combinatorial identity due to Hernández. Our auxiliary results contain many interesting combinatorial congruences involving harmonic numbers.

scholarly journals Ideal convergence in n-normal spaces and some new sequence spaces via n-norm

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Mehmet Gürdal ◽  
Ahmet Sahiner
Keyword(s):  
Sequence Spaces ◽  
Subject Classification ◽  
Matrix Transformations ◽  
Normed Spaces ◽  
Primary 40A05 ◽  
Ideal Convergence ◽  
Secondary 46A70 ◽  
2000 Mathematics Subject Classification

In this paper we introduced some new sequence spaces using n-normed spaces and gave some preliminary result for matrix transformations between some sequence spaces. 2000 Mathematics Subject Classification. Primary 40A05, 40A45; Secondary 46A70.

scholarly journals Fractional derivatives of Colombeau generalized stochastic processes defined on R+

2011 ◽  
Vol 5 (2) ◽  
pp. 283-297 ◽  
Author(s):  
Danijela Rajter-Ciric
Keyword(s):  
Stochastic Process ◽  
Cauchy Problem ◽  
Stochastic Processes ◽  
Fractional Derivatives ◽  
Subject Classification ◽  
2000 Mathematics Subject Classification ◽  
Derivatives Of

We consider Caputo and Riemann-Liouville fractional derivatives of a Colombeau generalized stochastic process G defined on R+. We give proper definitions and prove that both are Colombeau generalized stochastic processes themselves. We also give a solution to a certain Cauchy problem illustrating the application of the theory. 2000 Mathematics Subject Classification: 46F30, 60G20, 60H10, 26A33

The Proof of Strong Markov Property Based on one Definition

2015 ◽  
Vol 742 ◽  
pp. 419-428
Author(s):  
Rong Tang ◽  
Yi Xuan Dong
Keyword(s):  
Markov Process ◽  
Markov Property ◽  
Subject Classification ◽  
Strong Markov Property ◽  
Homogeneous Markov Process ◽  
Primary 60J25 ◽  
Strong Markov Process ◽  
2000 Mathematics Subject Classification ◽  
Strong Markov

In this paper, for countable homogeneous Markov process, we prove strong Markov property defining by [2] are valid. So for an arbitrary countable homogeneous Markov process is a strong Markov process.2000 Mathematics Subject Classification. Primary 60J25, 60J27.

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