• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1729-1735
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• 2015

It is known that the partial sum of the Taylor series of an holomorphic function of one complex variable converges in norm on $H^p(\mathbb{D})$ for 1 < p < ${\infty}$. In this paper, we consider various type of partial sums of a holomorphic function of several variables which also converge in norm on $H^p(\mathbb{B}_n)$ for 1 < p < ${\infty}$. For the partial sums in several variable cases, some variables could be chosen slowly (fastly) relative to other variables. We prove that in any cases the partial sum converges to the original function, regardlessly how slowly (fastly) some variables are taken.

• The Korean Journal of Pharmacology
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• v.14 no.1_2
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• pp.47-54
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• 1978

Recently, a major resection of the pancreas has been carried out not only to treat carcinoma of pancreas but also chronic pancreatitis. But limited and often contradictory reports have been made on the exocrine effects after partial surgical pancreatectomy in mammals. It was suggested that the growth of the residual tissue in pancreatectomized rat is very active, because pancreas has the great power of regeneration after partial pancreatectomy, while others observed that rat pancreas after partial surgical resection revealed a perplexing mixture of atrophy and regeneration of acinar tissue. On the other hand, another results showed that the amount of insulin required to control diabetes after partial resection of pancreas is much greater than that needed after total pancreatectomy. Because the anti-insulin system, such as glucagon secretion and hypophyseoadrenal function, is probably depressed after total pancreatectomy. Furthermore, minimal resection line which will not influence the normal function of pancreas is not agreeable, such 75%, 80% or 95% resection of the total pancreas in rat. So far, studies on the exocrine function other than endocrine function after partial pancreatectomy have been limited. Therefore, the main purpose of this study is to examine the changes of exocrine as well as endocrine function of pancreas at the different time interval after 60% or 80% pancreatectomy in rats. The results summerized as follow: 1) In both 60% and 80% resected groups, a slight decrease of the total body weight was observed at a day after partial pancreatectomy in rats, but the body weight was continued to increase for following 100 days. 2) The weight of residual pancreas was continuously increased during experiment in both 60% and 80% resected groups. But the content of tissue protein in residual pancreas was significantly decreased comparing with those of resected pancreas. 3) The flow rate of pancreatico-biliary juice was significantly decreased immediately after pancreatectomy in both resected groups. But it was recovered to control level after a day in 60% resected group, after 30 days in 80% resected group. 4) The output of amylase and lipase in resected groups were significantly decreased right after pancreatectomy comparing with control group. In the 60% resected group, the output of amylase was recovered during the following 100 days after pancreatectomy, while lipase output in 3 days. However, in the 80% resected group, the output of amylase and lipase were not recovered during 100 days after pancreatectomy. 5) In order to examine the endocrine function, blood sugar level were examined at all experimental periods after partial pancreatectomy. There was no difference between control and 60% resected group in the sugar level. But in the 80% resected group the level was significantly incresed immediately after pancreatectomy, and reached the highest level at 3 days. Then it was decreased to control level during the next 10 days after pancreatectomy. The above results showed that in 60% resected group little changes were observed on pancreatic function, but severe functional impairments were observed in 80% resected group. This results suggested that the endocrine function was recovered within a short period, although the exocrine function was not recovered for a long time after 80% pancreatectomy in rats.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.681-692
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• 2022

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al. [15]. Some examples are also discussed for the sake of better understanding of this article.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.433-444
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• 2023

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w² - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.259-267
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• 2023

The paper presents the introduction of a novel linear derivative operator for meromorphic functions that are linked with q-calculus. Using the linear derivative operator, a new category of meromorphic functions is generated in the paper. We obtain sufficient conditions and show some properties of functions belonging to these subclasses. The partial sums of its sequence and the q-neighborhoods problem are solved.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1753-1757
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• 2015

In this note we obtain a unique continuation result for the differential inequality ${\mid}\bar{\partial}u{\mid}{\leq}{\mid}Vu{\mid}$, where $\bar{\partial}=(i{\partial}_y+{\partial}_x)/2$ denotes the Cauchy-Riemann operator and V (x, y) is a function in $L^2(\mathbb{R}^2)$.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.441-452
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• 2011

The enormous success of the theory of hypergeometric series in a single variable has stimulated the development of a corresponding theory in two and more variables. A wide variety of investigations in the theory of several variable hypergeometric functions have been essentially motivated by the fact that solutions of many applied problems involving partial differential equations are obtainable with the help of such hypergeometric functions. Here, in this trend, we aim at presenting further decomposition formulas for Saran function $F_E$, which are used to give some integral representations of the function $F_E$. We also present a system of partial differential equations for the Saran function $F_E$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.30 no.5
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• pp.795-803
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• 2020

In this paper, we study known-key distinguishing and partial-collision attacks on GFN-2 structures with SP F-functions and various block lengths. Firstly, we show the known-key distinguishing attack is possible up to 15 rounds. Secondly, for the case that the last round function has the shuffle operation, we show that the partial-collision attack is possible up to 14 rounds. Finally, for the case that the last round function has no shuffle operation, we show that the partial-collision attacks are possible up to 11 rounds.