• The Pure and Applied Mathematics
• /
• v.12 no.4 s.30
• /
• pp.253-274
• /
• 2005

An additive regular Semiring S is left inversive if the Set E+ (S) of all additive idempotents is left regular. The set LC(S) of all left inversive semiring congruences on an additive regular semiring S is a lattice. The relations $\theta$ and k (resp.), induced by tr. and ker (resp.), are congruences on LC(S) and each $\theta$-class p$\theta$ (resp. each k-class pk) is a complete modular sublattice with $p_{min}$ and $p_{max}$ (resp. With $p^{min}$ and $p^{max}$), as the least and greatest elements. $p_{min},\;p_{max},\;p^{min}$ and $p^{max}$, in particular ${\epsilon}_{max}$, the maximum additive idempotent separating congruence has been characterized explicitly. A semiring is quasi-inversive if and only if it is a subdirect product of a left inversive and a right inversive semiring.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.575-598
• /
• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1209-1219
• /
• 2018

We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.139-145
• /
• 1996

We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.4
• /
• pp.863-872
• /
• 2023

Let n ⩾ 2 be an integer, we denote the smallest integer b such that gcd {(ⁿ_k) : b < k < n - b} > 1 as b(n). For any prime p, we denote the highest exponent α such that p^α | n as v_p(n). In this paper, we partially answer a question asked by Hong in 2016. For a composite number n and a prime number p with p | n, let n = a_mp^m + r, 0 ⩽ r < p^m, 0 < a_m < p. Then we have $$v_p\(\text{gcd}\{\(n\\k\)\;:\;b(n)1\}\)=\{\array{1,&&a_m=1\text{ and }r=b(n),\\0,&&\text{otherwise.}}$$

• International Journal of Internet, Broadcasting and Communication
• /
• v.7 no.1
• /
• pp.42-48
• /
• 2015

Generally, the current commercial cloud system is hosted by the centralization large datacenter. However, the other clouding forms existed and one of them is the P2P cloud. The P2P Cloud is a distributed systems, is freedom to join and leave and is possible to provide the IaaS. Commonly, P2P Cloud System is based on Pure-P2P System. Since a number of connection paths exist, it has a high reliability and easily scalability of the network. However, there are disadvantages of the slow rate of route because of looking up the all peers in order to search for the peer. In this paper, it proposes the P2P cloud system based on super-peer P2P. Super-peer P2P system has fast routing time, because of searching for cluster unit and it also can has high reliability and high scalability. We designs the super Peer cloud service and proposes the system model and Resource Allocation Algorithm for IaaS in Super peer P2P environment.

• Honam Mathematical Journal
• /
• v.16 no.1
• /
• pp.119-135
• /
• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• ETRI Journal
• /
• v.34 no.4
• /
• pp.591-601
• /
• 2012

Unstructured peer-to-peer (p2p) networks usually employ flooding search algorithms to locate resources. However, these algorithms often require a large storage overhead or generate massive network traffic. To address this issue, previous researchers explored the possibility of building efficient p2p networks by clustering peers into communities based on their social relationships, creating social-like p2p networks. This study proposes a social relationship p2p network that uses a measure based on Hebbian theory to create a social relation weight. The contribution of the study is twofold. First, using the social relation weight, the query peer stores and searches for the appropriate response peers in social-like p2p networks. Second, this study designs a novel knowledge index mechanism that dynamically adapts social relationship p2p networks. The results show that the proposed social relationship p2p network improves search performance significantly, compared with existing approaches.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.41 no.9
• /
• pp.563-570
• /
• 2017

Experimental and numerical studies were performed to investigate the performance and internal flow characteristics of a supersonic second throat exhaust diffuser (STED) with back pressure ($P_a$). An ejector system was used to vary the back pressure ($P_a$) conditions. The operating gas for the STED and the ejector was high pressure nitrogen at room temperature. When the back pressure ($P_a$) at a constant nozzle inlet pressure $P_0$) decreases, the pressure recovery location moves downstream. If the pressure ratio $P_0/P_a$) is the same, even if the nozzle inlet pressures $P_0$) are different, the diffuser's internal flow pattern and starting pressure ratio ($(P_0/P_a)_{st}$) are almost the same.

• Environmental Analysis Health and Toxicology
• /
• v.20 no.1
• /
• pp.23-28
• /
• 2005

PAH 위해성 평가의 생체지표 개발을 위하여, benzo[a]pyrene을 인체 간암 세포주인 HepG2세포에 처리하여 암 억제 단백질인 p53 및 관련 단백질의 발현 양상에 대하여 연구하였다. HepG2 세포의 생존력은 benzo[a]pyrene을 노출시킨 군에서 농도가 증가할수록 감소하였다. p53과 인산화 p53의 발현 양상은 benzo[a]pyrene 농도 의존적으로 증가하는 경향을 보였으며, 반면에 아세틸화 p53은 benzo[a]pyrene의 농도가 증가할수록 감소하는 경향을 나타내었다. 세포 주기 조절에 관련된 p21 단백질은 화학 물질 처리에 의해서 p53과 마찬가지로 증가하였으나, CdK4와 Rb 단백질의 발현에는 변화가 없었다. 상관분석 결과 Benzo[a]pyrene 노출, 세포 생존력, p53, 인산화 p53, p21이 서로 높은 상관성을 보였다. 본 연구의 결과는 p53 단백질의 축적이 benzo[a]pyrene 독성에 있어 매우 중요한 현상이며, 이는 선택적인 지표와 함께 p53 이 benzo[a]pyrene과 같은 PAH 계열의 물질의 위해성 평가를 위한 민감한 생체 지표로써 개발될 수 있음을 시사한다.