• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.321-325
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• 2012

In this paper, we consider twisted $q$-Euler polynomials and define a $p$-adic $q$-transfer operator (see [6]). From this operator, we investigate the eigenvalues of the $p$-adic $q$-transfer operator on the space of twisted $q$-Euler polynomials.

• Journal of Korean Neurosurgical Society
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• 제48권1호
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• pp.14-19
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• 2010

Objective : Allelic losses or loss of heterozygosity (LOH) at many chromosomal loci have been found in the cells of meningiomas. The objective of this study was to evaluate LOH at several loci of different chromosomes (1p32, 17p13, 7q21, 7q31, and 22q13) in different grades of meningiomas. Methods : Forty surgical specimens were obtained and classified as benign, atypical, and anaplastic meningiomas. After DNA extraction, ten polymorphic microsatellite markers were used to detect LOH. Medical and surgical records, as well as pathologic findings, were reviewed retrospectively. Results : LOH at 1p32 was detected in 24%, 60%, and 60% in benign, atypical, and anaplastic meningiomas, respectively. Whereas LOH at 7q21 was found in only one atypical meningioma. LOH at 7q31 was found in one benign meningioma and one atypical meningioma. LOH at 17p13 was detected in 4%, 40%, and 80% in benign, atypical, and anaplastic meningiomas, respectively. LOH at 22q13 was seen in 48%, 60%, and 60% in benign, atypical, and anaplastic meningiomas, respectively. LOH results at 1p32 and 17p13 showed statistically significant differences between benign and non-benign meningiomas. Conclusion : LOH at 1p32 and 17p13 showed a strong correlation with tumor progression. On the other hand, LOH at 7q21 and 7q31 may not contribute to the development of the meningiomas.

• East Asian mathematical journal
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• 제36권1호
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• pp.13-24
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• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.221-229
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• 1998

Let $k$ be a real abelian field and $k_{\infty}$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension. By using the main conjecture of Iwasawa theory, we have the following: If $p$ does not divide $\prod_{{{\chi}{\in}\hat{\Delta}_k},{\chi}{\neq}1}B_{1,{\chi}{\omega}^{-1}$, then $A_n$ = {0} for all $n{\geq}0$, where ${\Delta}_k=Gal(k/\mathbb{Q})$ and ${\omega}$ is the Teichm$\ddot{u}$ller character for $p$. The converse of this statement does not hold in general. However, we have the following when $k$ is of prime conductor $q$: Let $q$ be an odd prime different from $p$. and let $k$ be a real subfield of $\mathbb{Q}({\zeta}_q)$. If $p{\mid}{\prod}_{{\chi}{\in}\hat{\Delta}_{k,p},{\chi}{\neq}1}B_{1,{\chi}{\omega}}-1$, then $A_n{\neq}\{0\}$ for all $n{\geq}1$, where ${\Delta}_{k,p}$ is the $Gal(k_{(p)}/\mathbb{Q})$ and $k_{(p)}$ is the decomposition field of $k$ for $p$.

• 충청수학회지
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• 제33권1호
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• pp.147-156
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• 2020

The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σ_i is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.

• 한국정보처리학회논문지
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• 제6권8호
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• pp.2098-2115
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• 1999

신경망 회로의 해석에서 아직 해결하지 못하는 부분이 은닉층(hidden layer)의 해석이다. 본 논문에서는 신경망 회로의 기본적인 구성회로로써 하나의 입력(p levels)과 하나의 출력(q levels)을 갖는 2-layer Core-Net를 정의하고, 이 Core-Net의 처리 가능 용량(the capacity)은 2차원 무게값 공간(weight space)을 나눌 수 있는 영역의 수로, {{{{ {a}_{p,q} = {{q}^{2}} over {2}p(p-1)- { q} over {2 } (3 { p}^{2 } -7p+2)+ { p}^{2 }-3p+2}}}}임을 수학적 귀납법으로 증명하였다. 이 Core-Net로 신경망 회로의 중간층 해석이 가능함을 시뮬레이션 예제를 통하여 보였다.

• East Asian mathematical journal
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• 제35권3호
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• pp.285-288
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• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• 대한수학회지
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• 제34권4호
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• pp.1049-1064
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• 1997

We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

• 대한수학회보
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• 제53권5호
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• pp.1291-1308
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• 2016

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids {$z{\in}\mathbb{C}^3:{\mid}z_1{\mid}^p+{\mid}z_2{\mid}^q$ < 1, ${\mid}z_1{\mid}^p+{\mid}z_3{\mid}^r$ < 1}. We consider cases p = 6, q = r = 2 and p = q = r = 2. We also investigate the Lu Qi-Keng problem for p = q = r = 2.

• 충청수학회지
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• 제27권3호
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• pp.427-431
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• 2014

In this paper, we show that groups of order $2^npq$, where p, q are primes of the from $p=2^n-1$, $q=2^{n-1}+p$ with $n{\geq}3$, are not simple and groups of order $2^npq^t$ for $t{\geq}2$, where p, q are odd primes of the form $p=2^m-1$, $q=2^n-1$ with m < n, are not simple.