• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.389-397
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• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.3
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• pp.27-38
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• 1999

We study on the security for the block ciphers with 20block structure which have provable security against DC and LC on the view point of higher order DC, 2-block structures are classified three types according to the location of round function such as C(Center)-type R(Right)-type and L(Left)-type We prove that in the case of 4 rounds encryption function these three types provide the equal strength against higher order DC and that in the case of 5 or more rounds R-type is weaker than C-type and L-type.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.759-771
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• 2020

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.573-583
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• 2019

This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Some properties for the ratio of the modified Lommel functions with the Lommel function, sinh and cosh are also discussed. As a consequence, $Tur{\acute{a}}n$ type and reverse $Tur{\acute{a}}n$ type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.243-268
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• 2019

The main aim of this paper is to study some growth properties of composite entire functions on the basis of relative $(p,q)-{\varphi}$ type and relative $(p,q)-{\varphi}$ weak type where p and q are any two positive integers and ${\varphi}(r):[0,+{\infty}){\rightarrow}(0,+{\infty})$ be a non-decreasing unbounded function.

• Journal of Mechanical Science and Technology
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• v.14 no.11
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• pp.1187-1197
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• 2000

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.19-29
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• 2006

In this paper, we obtain some inequalities similar to Hilbert type. Some new inequalities are also given.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.10
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• pp.1469-1478
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• 2015

In this paper, The methodology of Type-2 fuzzy set-based Radial Basis Function Neural Network(T2RBFNN) is proposed for Sewage Treatment Process and the simulator is developed for application to the real-world sewage treatment plant by using the proposed model. The proposed model has robust characteristic than conventional RBFNN. architecture of network consist of three layers such as input layer, hidden layer and output layer of RBFNN, and Type-2 fuzzy set is applied to receptive field in contrast with conventional radial basis function. In addition, the connection weights of the proposed model are defined as linear polynomial function, and then are learned through Back-Propagation(BP). Type reduction is carried out by using Karnik and Mendel(KM) algorithm between hidden layer and output layer. Sewage treatment data obtained from real-world sewage treatment plant is employed to evaluate performance of the proposed model, and their results are analyzed as well as compared with those of conventional RBFNN.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.43-49
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• 2010

Aerodynamic design of the vane type multi-function probe was tried by using CFD and wind tunnel test for the MALE UAV and small business jets. The present multi-function probe can measure total pressure, static pressure and angle of attack by using rotating vane. Therefore major performances are determined by aerodynamic characteristics of vane. In oder to design the sensor compatible to the requirement, aerodynamic characteristics of sensors was investigated by using CFD and dynamic response analysis was also performed for trasient performance. The final aerodynamic performance was measured by the wind tunnel test at Aeorsonic and the results successfully used for the design of vane type multi-function air data sensor.