• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제13권4호
• /
• pp.311-318
• /
• 2006

In this paper we establish some new identities involving Stirling numbers of both kinds. These identities are obtained via Riodan arrays with a variable x. Some well-known identities are obtained as special cases of the new identities for the specific number x.

• East Asian mathematical journal
• /
• 제19권1호
• /
• pp.41-48
• /
• 2003

There are many conditions or identities for a lattice to be distributive. In this paper, we study some identities on algebras of type (2,2) and find another set of identities defining distributive lattices. We also study certain identities which define algebras of type (2,2) whose subalgebras generated by two elements are all distributive lattices with at most 4 elements.

• 대한수학회지
• /
• 제51권5호
• /
• pp.1045-1073
• /
• 2014

The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter's classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261] and D. S. Kim's eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350-2359].

• 아동학회지
• /
• 제22권2호
• /
• pp.133-147
• /
• 2001

This study examined whether the ego-identities of institutionalized children and adolescents differ by grade, gender, reason for and length of residence, age at entering the institution, parents' visiting, relationship with parents before entering the institution, and caretakers' emotional support. We assumed that the ego-identities of institutionalized children had an effect on social interactions. The subjects were 121 5th and 6th graders, 135 middle, and 85 high school students who were institutionalized in Seoul. As predicted, the ego-identities of institutionalized children and adolescents differed by grade, and by such social interactions as parents' visiting, relationship with parents before entering the institution, and caretakers' emotional support. Results support the importance of social interactions for understanding the ego-identities of institutionalized children and adolescents.

• Korean Journal of Mathematics
• /
• 제30권1호
• /
• pp.25-42
• /
• 2022

In this paper, we derive analogues of a couple of classes of infinite series identities with the confluent hypergeometric functions involving Dirichlet characters.

• East Asian mathematical journal
• /
• 제39권1호
• /
• pp.23-27
• /
• 2023

In this paper, we derive the some identities which are related to the multifactorial numbers and the Catalan numbers. We utilize the fundamental theorem of Riordan matrix to obtain those identities.

• 대한수학회지
• /
• 제47권3호
• /
• pp.505-521
• /
• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• 대한수학회논문집
• /
• 제32권4호
• /
• pp.885-898
• /
• 2017

The Bailey lemma has been a powerful tool in the discovery of identities of Rogers-Ramanujan type and also ordinary and basic hyper-geometric series identities. The mechanism of Bailey lemma has also led to the concepts of Bailey pair and Bailey chain. In the present work certain new WP-Bailey pairs have been established. We also have deduced a number of basic hypergeometric series identities as an application of new WP-Bailey pairs.

• 대한수학회지
• /
• 제59권5호
• /
• pp.1015-1045
• /
• 2022

Zagier introduced the term "strange identity" to describe an asymptotic relation between a certain q-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.

• 호남수학학술지
• /
• 제38권3호
• /
• pp.479-494
• /
• 2016

In this paper, using a transformation formula for a certain series which comes from the generalized non-analytic Eisenstein series, we obtained some infinite series identities which contain Ramanujan's formula and author's previous results.