• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.87-98
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• 2001

In this paper, we study hash function, which will take a message of arbitrary length and produce a massage digest of a specified size. The message digest will then be signed. We have to be careful that the use of a hash function h does not weaken the security of the signature scheme, for it is the message digest that is signed, not the message. It will be necessary for h to satisfy certain properties in order to prevent various forgeries. In order to prevent various type of attack, we require that hash function satisfy collision-free property. In section 1, we introduce some definitions and collision-free properties of hash function. In section 2, we study a discrete log hash function and introduce the main theorem as follows : Theorem Suppose $h:X{\rightarrow}Z$ is a hash function. For any $z{\in}Z$, let $$h^{-1}(z)={\lbrace}x:h(x)=z{\rbrace}$$ and denote $s_z={\mid}h^{-1}(z){\mid}$. Define $$N={\mid}{\lbrace}{\lbrace}x_1,x_2{\rbrace}:h(x_1)=h(x_2){\rbrace}{\mid}$$. Then (1) $\sum\limits_{z{\in}Z}s_z={\mid}x{\mid}$ and the mean of the $s_z$'s is $\bar{s}=\frac{{\mid}X{\mid}}{{\mid}Z{\mid}}$ (2) $N=\sum\limits_{z{\in}Z}{\small{s_z}}C_2=\frac{1}{2}\sum\limits_{z{\in}Z}S_z{^2}-\frac{{\mid}X{\mid}}{2}$. (2) $\sum\limits_{z{\in}Z}(S_z-\bar{s})^2=2N+{\mid}X{\mid}-\frac{{\mid}X{\mid}^2}{{\mid}Z{\mid}}$.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.371-379
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• 2012

Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.585-590
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• 2016

Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• Journal of the Korean Society of Marine Environment & Safety
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• v.21 no.2
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• pp.179-187
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• 2015

The purpose of this study is to identify the aspect that the traffic distribution function changes, according to the direction of the datum line and the horizontal and vertical positions of the datum point applied when it is calculated. Targeting routes at the entrance of Mokpo Harbor, this study tested using AIS survey data of January 2013 the effects of the three variables-direction of the datum line(${\theta}$), horizontal position($\mathfrak{L}_H$) and vertical position($\mathfrak{L}_V$) on mean ($\bar{x}$) and standard deviation (${\delta}$). The test result showed that $\bar{x}$ and ${\delta}$ were changed according to the change of ${\theta}$, because the extracted sample data were changed according to ${\theta}$; and the changes of $\bar{x}$ and ${\delta}$ according to ${\theta}$ were drawn as the relation of the sine function' sum. In addition, it was found that setting up ${\theta}$ that the change value of ${\delta}$ becomes the least as the direction of the datum line was valid, to determine the optimum passage distribution function on complex waters with multiple branches of route. The result of this study is expected to be used as basic data to understand maritime traffic flow based on more quantified data of normal distribution and make decisions related to maritime traffic safety management.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.563-569
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• 2005

In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.946-952
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• 2010

A method for the identification of structural characteristic parameters of a steel bar in the matrices form such as stiffness matrices and mass matrices from frequency response function(FRF) by genetic algorithm is proposed. As the method is based on the finite element method(FEM), the obtained matrices have perfect physical meanings if the FRFs got from the analysis and the FRFs from the experiments were well coincident each other. The identified characteristic matrices from the FRFs with maximun 40 % of random errors by the genetic algorithm are coincident with the characteristic matrices from exact FEM FRFs well each other. The fitted element diameters by using only 2 points experimental FRFs are similar to the actual diameters of the bar. The fitted FRFs are good accordance with the experimental FRFs on the graphs. FRFs of the rest 9 points not used for calculating could be fitted even well.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.511-521
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• 2007

Let S($z_1$, $z_2$) be a power series with operator coefficients such that multiplication by 5($z_1$, $z_2$) is a contractive transformation in the Hilbert space $\mathbf{H}_2$($\mathbb{D}^2$, C). In this paper we show that there exists a Hilbert space D($\mathbb{D}$,$\bar{S}$) which is the state space of extended canonical linear system with a transfer fucntion $\bar{S}$(z).

• Transactions of Materials Processing
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• v.27 no.5
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• pp.296-300
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• 2018

T-type and H-type section steels were generally used in shipbuilding and offshore plants and were produced by welding technology. These section steels were produced by handwork, and the supplying amounts can't satisfy the demand amounts of the fabrication companies. In case of fillet welding, there are some gaps in weld-joint region due to no groove preparation processing and it can occur crack initiation in the welded region. It is important to evaluate the microstructural and mechanical properties of welded zone to solve these problems. To satisfy the demand amounts of T-bar parts, automatic welding technology was introduced and several conditions as a function of welding speeds were carried out to improve the manufacturing speed. Heat-affected zone may be affected by variation of heat input and cooling rate through automatic welding speed and welding speed is necessary to be optimized. In this study, fusion zone and heat-affected zone were investigated by microstructural and mechanical analysis and were evaluated whether the welded parts were sound or not.