• 대한수학회지
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• 제51권5호
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• pp.1045-1073
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• 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].

• 대한수학회지
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• 제54권4호
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• pp.1243-1264
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• 2017

In this paper, we introduce w-Catalan polynomials as a generalization of Catalan polynomials and derive fourteen basic identities of symmetry in three variables related to w-Catalan polynomials and analogues of alternating power sums. In addition, specializations of one of the variables as one give us new and interesting identities of symmetry even for two variables. The derivations of identities are based on the p-adic integral expression for the generating function of the w-Catalan polynomials and the quotient of p-adic integrals for that of the analogues of the alternating power sums.

• 대한수학회보
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• 제52권2호
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• pp.603-618
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• 2015

We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the p-adic integral expression, with respect to a measure introduced by Koblitz, of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.119-130
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• 2013

In this paper, we obtain some generalized symmetry identities involving a unified class of polynomials related to the generalized Bernoulli, Euler and Genocchi polynomials of higher-order attached to a Dirichlet character. In particular, we prove a relation between a generalized X version of the power sum polynomials and this unified class of polynomials.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.869-882
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• 2023

In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.115-120
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• 2018

In this paper, we discover symmetric properties for generalized Carlitz's q-tangent polynomials.

• 호남수학학술지
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• 제41권1호
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• pp.117-133
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• 2019

In the current investigation, we obtain the generating function for Hermite-based degenerate Bernoulli polynomials attached to ${\chi}$ of higher order using p-adic methods over the ring of integers. Useful identities, formulae and relations with well known families of polynomials and numbers including the Bernoulli numbers, Daehee numbers and the Stirling numbers are established. We also give identities of symmetry and additive property for Hermite-based generalized degenerate Bernoulli polynomials attached to ${\chi}$ of higher order. Results are supported by remarks and corollaries.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.597-614
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• 2015

In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between $F_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ and $_HF_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

• 디자인학연구
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• 제18권2호
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• pp.173-188
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• 2005

최근 기업 경영에 있어서 디자인의 중요성이 점차 증가하고 있는 반면 브랜드의 시각적 역할을 담당하는 로고에 대한 연구가 상대적으로 소홀히 다루어져 왔다. 특히 브랜드 로고의 시각적 특성에 대한 소비자 반응 연구는 상대적으로 부족한 실정이다. 이에 본 연구에서는 로고의 시각적인 특성에 대한 실험적인 연구로 제품별 특성에 따라 브랜드 컨셉에 기초하여 선호되는 로고 디자인을 컨조인트 분석방법을 통해 살펴보고 있다. 연구결과 이성적 컨셉의 경우 탐색 재에서는 높은 정교함과 낮은 대칭이, 경험재에서는 높은 연상이, 신뢰재에서는 낮은 정교함과 높은 대칭이 고유특성으로 나타났다. 한편 감성적 컨셉의 경우 탐색 재에서는 높은 정교함과 낮은 연상이, 경험재에서는 낮은 자연스러움이, 신뢰 재에서는 낮은 정교함과 높은 연상이 고유특성으로 나타났다. 이러한 연구결과들과 함께 이론적 실무적 시사점이 논의된다.