• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• 한국생산제조학회지
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• 제24권5호
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• pp.535-540
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• 2015

We propose an enhanced Green's function approach to predict thermal stresses by considering temperature-dependent material properties. We introduce three correction factors for the maximum stress, the time taken to reach maximum stress, and the time required to attain steady state based on the Green's function results for each temperature. The proposed approach considers temperature-dependent material properties using correction factors, which are defined as polynomial expressions with respect to temperatures based on Green's functions, that we obtain from finite-element (FE) analyses at each temperature. We verify the proposed approach by performing detailed FE analyses on thermal transients. The Green's functions predicted by the proposed approach are in good agreement with those obtained from FE analyses for all temperatures. Moreover, the thermal stresses predicted using the proposed approach are also in good agreement with the FE results, and the proposed approach provides better predictions than the conventional Green's function approach using constant, time-independent material properties.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.745-763
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• 2021

For a value s ∈ ℂ∪ {∞}, two meromorphic functions f and g are said to share the value s, CM, (or IM), provided that f(z)-s and g(z)-s have the same set of zeros, counting multiplicities, (respectively, ignoring multiplicities). We say that a meromorphic function f shares s ∈ Ŝ partially with a meromorphic function g if E(s, f) ⊆ E(s, g). It is easy to see that "partially shared values CM" are more general than "shared values CM". With the help of partially shared values, in this paper, we prove some uniqueness results between a non-constant meromorphic function and its generalized differences or shifts. We exhibit some examples to show that the result of Charak et al. [8] is not true for k = 2 or k = 3. We find some gaps in proof of the result of Lin et al. [24]. We not only correct these resuts, but also generalize them in a more convenient way. We give a number of examples to validate certain claims of the main results of this paper and also to show that some of conditions are sharp. Finally, we pose some open questions for further investigation.

• 호남수학학술지
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• 제34권4호
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• pp.473-482
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeo-metric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_C$.

• 호남수학학술지
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• 제34권1호
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• pp.113-124
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_A$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.137-145
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$.

• 대한수학회보
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• 제51권5호
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• pp.1425-1432
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• 2014

The Euler zeta function is defined by ${\zeta}_E(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^8}$. The purpose of this paper is to find formulas of the Euler zeta function's values. In this paper, for $s{\in}\mathbb{N}$ we find the recurrence formula of ${\zeta}_E(2s)$ using the Fourier series. Also we find the recurrence formula of $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{(2_{n-1})^{2s-1}}$, where $s{\geq}2({\in}\mathbb{N})$.

• 대한수학회논문집
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• 제30권4호
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• pp.403-414
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• 2015

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

• BMB Reports
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• 제55권10호
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• pp.481-487
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• 2022

Over the past few years, hydrogen sulfide (H₂S) has been shown to exert several biological functions in mammalian. The endogenous production of H₂S is mainly mediated by cystathione β-synthase, cystathione γ-lyase and 3-mercaptopyruvate sulfur transferase. These enzymes are broadly expressed in liver tissue and regulates liver function by working on a variety of molecular targets. As an important regulator of liver function, H₂S is critically involved in the pathogenesis of various liver diseases, such as non-alcoholic steatohepatitis and liver cancer. Targeting H₂S-generating enzymes may be a therapeutic strategy for controlling liver diseases. This review described the function of H₂S in liver disease and summarized recent characterized role of H₂S in several cellular process of the liver.

• 대한산업공학회지
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• 제15권2호
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• pp.33-44
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• 1989

This paper presents stochastic-statistical dominance rules which eliminate dominated alternatives thereby reduce the number of satisficing alternatives to a manageable size so that the decision maker can choose the best alternative among them when neither the utility function nor the probability distribution of outcomes is exactly known. Specifically, it is assumed that only the characteristics of the utility function and the value function are known. Also, it is assumed that prior probabilities of the mutually exclusive states of nature are not known, but their relative bounds are known. First, the notion of relative risk aversion is used to describe the decision maker's attitude toward risk, which is defined with the acknowledgement that the utility function of the decision maker is a composite function of a cardinal value function and a utility function with-respect to the value function. Then, stochastic-statistical dominance rules are developed to screen out dominated alternatives according to the decision maker's attitude toward risk represented in the form of the measure of relative risk aversion.