• Korean Journal of Hydrosciences
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• v.5
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• pp.85-97
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• 1994

A hybrid finite difference method for the longitudinal dispersion equation, which is based on combining the Holly-Preissmann scheme with fifth-degree Hermite interpolating polynomial and the generalized Crank-Nicholson scheme, is described and comparatively evaluated with other characteristics-based numerical methods. Longitudinal dispersion of an instantaneously-loaded pollutant source is simulated, and computational results are compared with the exact solution. The present method is free from wiggles regardless of the Courant number, and exactly reproduces the location of the peak concentration. Overall accuracy of the computation increases for smaller value of the weighting factor, $\theta$of the model. Larger values of $\theta$ overestimates the peak concentration. Smaller Courant number yields better accuracy, in general, but the sensitivity is very low, especially when the value of $\theta$ is small. From comparisons with the hybrid method using cubic interpolating polynomial and with splitoperator methods, the present method shows the best performance in reproducing the exact solution as the advection becomes more dominant.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.359-366
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• 2008

Let A(p) be the class of functions $f\;:\;z^p\;+\;\sum\limits_{j=1}^{\infty}a_jz^{p+j}$ analytic in the open unit disc E. Let, for any integer n > -p, $f_{n+p-1}(z)\;=\;z^p+\sum\limits_{j=1}^{\infty}(p+j)^{n+p-1}z^{p+j}$. We define $f_{n+p-1}^{(-1)}(z)$ by using convolution * as $f_{n+p-1}\;*\;f_{n+p-1}^{-1}=\frac{z^p}{(1-z)^{n+p}$. A function p, analytic in E with p(0) = 1, is in the class $P_k(\rho)$ if ${\int}_0^{2\pi}\|\frac{Re\;p(z)-\rho}{p-\rho}\|\;d\theta\;\leq\;k{\pi}$, where $z=re^{i\theta}$, $k\;\geq\;2$ and $0\;{\leq}\;\rho\;{\leq}\;p$. We use the class $P_k(\rho)$ to introduce a new class of multivalent analytic functions and define an integral operator $L_{n+p-1}(f)\;\;=\;f_{n+p-1}^{-1}\;*\;f$ for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.5
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• pp.229-236
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• 2014

Quadrature Amplitude Modulation (QAM) is widely used in contemporary wired and wireless communications systems. In this paper, I propose a generalized triangular quadrature amplitude modulation (gTQAM) that includes the square quadrature amplitude modulation (SQAM), TQAM, and ${\Theta}$-QAM as special cases. Therefore, the proposed gTQAM forming a lattice of arbitrary triangles provides a versatile structure in signal constellations compared to other QAM schemes. For M-ary gTQAM, I derive an exact closed-form expression for the bit error rate (BER), and present the optimal signal constellations for given SNR values from the derived BER expression. Finally, I validate the derived BER results through computer simulations.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.857-868
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• 2016

Let (X, ${\mu}$) be a generalized topological space (GTS) and $\mathcal{H}$ be a hereditary class on X due to $Cs{\acute{a}}sz{\acute{a}}r$ [8]. In this paper, we define an operator $()^{\circ}:\mathcal{P}(X){\rightarrow}\mathcal{P}(X)$. By setting $c^{\circ}(A)=A{\cup}A^{\circ}$ for every subset A of X, we define the family ${\mu}^{\circ}=\{M{\subseteq}X:X-M=c^{\circ}(X-M)\}$ and show that ${\mu}^{\circ}$ is a GT on X such that ${\mu}({\theta}){\subseteq}{\mu}^{\circ}{\subseteq}{\mu}^*$, where ${\mu}^*$ is a GT in [8]. Moreover, we define and investigate ${\mu}^{\circ}$-codense and strongly ${\mu}^{\circ}$-codense hereditary classes.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.369-399
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• 2022

In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced. In this paper, we present the notion of (𝜙, F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.439-447
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• 2003

Let (equation omitted) be a symmetrizable Kac-Moody algebra with the indecomposable generalized Cartan matrix A and W be its Weyl group. Let $\theta$ be the highest root of the corresponding finite dimensional simple Lie algebra ${\gg}$ of g. For the type ${A_N}^{(r)}$, we give an element $\omega_{o}\;\in\;W$ such that ${{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;=\;{\{\Delta\Delta}_{-}}$. And then we prove that the degree of nilpotency of the subalgebra (equation omitted) is greater than or equal to $ht{\theta}+1$.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.179-190
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• 2007

In this paper, we consider the general variational inequality GVI(F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type method $u_{n+l}=(1-{\alpha}+{\theta}_{n+1})Tu_n+{\alpha}u_n-{\theta}_{n+1g}(Tu_n)-{\lambda}_{n+1}{\mu}F(Tu_n),\;n{\geq}0$. for solving the general variational inequalities. The sequence $\{x_n}\$ is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.9
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• pp.1323-1331
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• 1993

In this paper, novel anti-multipath mod/demodulation techniques are introduced, The principal anti-multipath concepts of the double phase shift keying(DSK) system with a differntial detector and the diversity effect to be obtained from the phase shifts at the middle of symbol duration T are described. A generalized form of DSK, referred to as the $\theta$-DSK, is studied, and comparison of bandwidth is mode for various values of $\theta$ and shaping functions.

• Solar Energy
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• v.18 no.3
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• pp.9-14
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• 1998

The present solar energy concentrator is a 2-dimensional system that incorporates with a tubular absorber. A new design theory is developed on the basis of the generalized edge-ray principle. The result shows the increase of concentration ratio for the same acceptance angle as the basic CPC by a factor of $C_{new}=C_{cpc}\{1+(d/{\pi}r)\;sin^2{\theta}_c\}$. For example, if ${\theta}_c=30^{\circ}$, the new design offers the concentration of $2.0{\sim}2.72$, whereas $C_{cpc}=2$. The new system also provide a thin and light-weight design.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.393-400
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• 2008

In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||${\leq}$||f(x+y)+f(z+w)|| in normed modules over a $C^*$-algebra. This is applied to understand homomor-phisms in $C^*$-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||${\leq}$||f(x+y+z+w)||+${\theta}||x||^p||y||^p||z||^p||w||^p$ in real Banach spaces, where ${\theta}$, p are positive real numbers with $4p{\neq}1$.