• 대한수학회보
• /
• 제44권1호
• /
• pp.1-12
• /
• 2007

In this paper, we consider the q-Volkenborn integral of uniformly differentiable functions on the p-adic integer ring. By using this integral, we obtain the generating functions of twisted q-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.

• Journal of Oral Medicine and Pain
• /
• 제24권1호
• /
• pp.9-24
• /
• 1999

Pumping into the upper joint cavity of the TMJ was done on patients who had reducible disc displacement with pain. This article discusses the change in TMJ sounds before and after the Pumping treatment. 20subjects(mean age of $32.1{\pm}10.2yr$)were selected among those who visited the department of Oral Medicine of Yonsei University for the treatment of craniomandibular dysfunctions. Through a thorough history taking, clinical exam and X-ray taking these subjects were diagnosed as reducible disc displacement patients, and they were subdivided into two groups as acute and chronic according to the time the TMJ sound was made. Sonopak was used to measure the TMJ sound before, right after and one-week after the Pumping treatment. VAS was used to measure the degree of subjective TMJ complaints(sounds and pain) before and one-week after the Pumping treatment. Vibration related items included total integral, high integral, low integral, ratio of high integral to low integral, peak amplitude, peak frequency and median frquency. 1. It was not statistically significant between the acute and chronic groups before the treatment. However, total integral, high integral, low integral, peak amplitude, peak frequency, median frequency showed to be greater in the chronic group. 2. In all the subjects, just after the Pumping treatment was done, total integral, high and low integral, peak amplitude and peak frequency significantly decreased (p<0.05). Even after one week, low integral, peak frequency and median frequency significantly decreased (p<0,05), and the TMJ sound diminished accordingly. 3. Comparing the two groups(before and right after the Pumping treatment), there was the following difference ; in the acute group, high integral, high amplitude, high frequency and median frequency significantly decreased(p<0.05). In the chronic group, total integral, high integral, low integral, ratio, peak amplitude and peak frequency significantly decreased(p<0,05). It was not statistically significant between the acute and chronic group. 4. Comparing the two groups(right after and one week after the Pumping treatment), there was the following difference : in the acute group, high integral, high amplitude, high frequency and median frequency significantly decreased(p<0.05), In the chronic group, low integral significantly decreased(p<0.05). However, although it was not statistically significant, after one week, there was an increase in total integral, ratio, peak amplitude and peak frequency compared to right after the treatment group. 5. In the VAS of before and one week after the Pumping treatment of the TMJ pain and sound, the TMJ pain significantly decreased(p<0.05) in both the acute and chronic group. However, it was not statistically significant between the two groups. There was a statistically significant decrease(p<0.05) in the TMJ sound in the acute group after one week of Pumping treatment, but no change was notable in the chronic group and it was not statistically significant between the two groups. From the above results, we can conclude that Pumping into the upper joint cavity of patients having reducible disc displacement is effective in reducing clicking and pain. Therefore, it can be applied in diverse clinical fields.

• 대한수학회논문집
• /
• 제38권2호
• /
• pp.401-430
• /
• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• 대한수학회보
• /
• 제34권3호
• /
• pp.335-350
• /
• 1997

In this article, a scattering problem in a nonhomogeneous medium is formulated as an integral equation which contains boundary and volume integrals. The integral equation is solved for sufficiently small $$\mid$$\mid$1-p$\mid$$\mid$,$\mid$$\mid${k_i}^2-k^2$\mid$$\mid$\;and\;$\mid$$\mid${\nabla}p$\mid$$\mid$$ where $k,\;k_i$ and p the wave numbers and the density respectively.

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.651-669
• /
• 2018

The article is themed to classify new (fully) degenerate Hermite-Bernoulli polynomials with formulation in terms of p-adic fermionic integrals on $\mathbb{Z}_p$. The entire paper is designed to illustrate new properties in association with Daehee polynomials in a consolidated and generalized form.

• East Asian mathematical journal
• /
• 제19권1호
• /
• pp.27-39
• /
• 2003

Integral inequalities of Gruss type obtained via $P\acute{o}lya-Szeg\ddot{o}$ and Shisha-Mond results are given. Some applications for Taylor's generalized expansion are also provided.

• Journal of the Korean Statistical Society
• /
• 제17권1호
• /
• pp.24-29
• /
• 1988

The asymptotic distribution of the sample partial autocorrelation terms after lag p of an AR(p) model has been shown by Dixon(1944). The derivation is based on multivariate analysis and looks tedious. In this paper we present an interesting contour-integral derivation.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1994년도 가을 학술발표회 논문집
• /
• pp.38-45
• /
• 1994

P-version finite element model for the computation of stress intensity factors in two dimensional cracked panels by J-integral method is presented. The proposed model is based on high order theory and hierarchical shape function. The displacements fields are defined by integrals of Legendre polynomials which can be classified into three part such as basic mode, side mode, integral mode. The stress intensity factors are computed by J-integral method. The example models for validating the proposed p-version model are centrally cracked panel, single and double edged crack in a rectangular panel under pure Mode I. And the analysis results are compared with those by the h-version of FEM and empirical solutions in literatures. Very good agreement with the existing solution are shown.

• Journal of applied mathematics & informatics
• /
• 제37권3_4호
• /
• pp.295-305
• /
• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.

• 대한수학회지
• /
• 제38권1호
• /
• pp.163-176
• /
• 2001

We examine Orlicz-type integral inequalities for operators and obtain as a corollary a characterization of such inequalities for the Hardy-Littlewood maximal operator extending the well-known L(sup)p-norm inequalities.