• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.19-27
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• 2004

We define an additive (n, 2)-mapping, and prove the stability of additive (n, 2)-mappings.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.515-527
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• 2009

Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${\cup}${$A{\in}M_n(R)\;{\mid}\;detA{\neq}0$ and det $A{\neq}U(R)$}${\cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.31-36
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• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

• Proceedings of the KIEE Conference
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• 2005.04a
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• pp.203-206
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• 2005

본 연구에서는 카오스 2중 Tent 사상에 의한 랜덤 주파수 캐리어 발생기를 제안하고 있다. 제안된 방법은 2중 텐트사상의 분기트리(Bifurcation Tree)에서 카오스 발생 영역인 $\lambda$=0.99을 이용하여 랜덤 수글 발생시키고 있다. 제안된 방법과 종전의 LCG(Linear Congruential Generator)에 의한 방법의 고조파 스펙트럼을 실험에 의하여 비교 검토하였다.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.4
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• pp.127-135
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• 1994

In this paper we propose an EWLD(Enhanced Weighted Levenshtein Distance) algorithm to organize code-string pattern matching linear array processor based on the mappting to an one-dimensional array from a two-dimensional matching matrix, and design a processing element(PE) of the processor, N PEs are required instead of NS02T in the processor because of the mapping. Data input and output between PEs and all internal operations of each PE are performed in bit-serial fashion. The bit-serial operation consists of the computing of word distance (WD) by comparison and the selection of optimal code transformation path, and takes 22 clocks as a cycle. The layout of a PE is designed based on the double metal $1.5\mu$m CMOS rule. About 1,800 transistors consistute a processing element and 2 PEs are integrated on a 3mm$\times$3mm sized chip.

• Journal of Communications and Networks
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• v.16 no.3
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• pp.270-279
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• 2014

The Viterbi decoding algorithm, which provides maximum - likelihood decoding, is currently considered the most widely used technique for the decoding of codes having a state description, including the class of linear error-correcting convolutional codes. Two classes of nonbinary convolutional codes are presented. Distance preserving mapping convolutional codes and M-ary convolutional codes are designed, respectively, from the distance-preserving mappings technique and the implementation of the conventional convolutional codes in Galois fields of order higher than two. We also investigated the performance of these codes when combined with a multiple frequency-shift keying (M-FSK) modulation scheme to correct narrowband interference (NBI) in power-line communications channel. Themodification of certain detectors of the M-FSK demodulator to refine the selection and the detection at the decoder is also presented. M-FSK detectors used in our simulations are discussed, and their chosen values are justified. Interesting and promising obtained results have shown a very strong link between the designed codes and the selected detector for M-FSK modulation. An important improvement in gain for certain values of the modified detectors was also observed. The paper also shows that the newly designed codes outperform the conventional convolutional codes in a NBI environment.

• Smart Structures and Systems
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• v.9 no.6
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• pp.535-547
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• 2012

Controlling the balance of motion in a context involving a biped robot navigating a rugged surface or a step is a difficult task. In the present study, a $3{\times}5$ flexible piezoelectric tactile sensor array is developed to provide a foot pressure map and zero moment point for a biped robot. We introduce an innovative concept involving structural electrodes on a piezoelectric film in order to improve the sensitivity. The tactile sensor consists of a polymer piezoelectric film, PVDF, between two patterned flexible print circuit substrates (FPC). Additionally, a silicon rubber bump-like structure is attached to the FPC and covered by a polydimethylsiloxane (PDMS) layer. Experimental results show that the output signal of the sensor exhibits a linear behavior within 0.2 N ~ 9 N, while its sensitivity is approximately 42 mV/N. According to the characteristic of the tactile sensor, the readout module is designed for an in-situ display of the pressure magnitudes and distribution within $3{\times}5$ taxels. Furthermore, the trajectory of the zero moment point (ZMP) can also be calculated by this program. Consequently, our tactile sensor module can provide the pressure map and ZMP information to the in-situ feedback to control the balance of moment for a biped robot.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.433-446
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• 1999

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. The mapping $theta$ sending a matrix to its transpose-inverse is an auto-mophism of G and therefore we can form the group $G^+$ = G.<$theta$>. In this paper conjugacy classes of elements in $G^+$ -G are found. These classes are closely related to the congruence classes of invert-ible matrices in G.

• Nuclear Engineering and Technology
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• v.55 no.9
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• pp.3268-3276
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• 2023

The practice of identifying the potential zones for mineral exploration in a speedy and low-cost method includes the use of satellite imagery analysis as a part of remote sensing techniques. It is challenging to explore the iron mineralization of a region through conventional methods which are a time-consuming process. The current study utilizes the Hyperion satellite imagery for mapping the iron mineralization and associated geological features in the Irikkur region, Kannur, Kerala. Along with the remote sensing results, the field study and laboratory-based analysis were conducted to retrieve the ground truth point and geochemical proportion to verify the iron ore mineralization. The MC simulation showed for shielding properties indicate an increase in the linear attenuation coefficient with raising the Fe₂O₃+SiO₂ concentrations in the investigated rocks where it is varied at 0.662 MeV in the range 0.190 cm^-1 - 0.222 cm^-1 with rising the Fe₂O₃+SiO₂ content from 57.86 wt% to 71.15 wt%. The analysis also revealed that when the γ-ray energy increased from 0.221 MeV to 2.506 MeV, sample 1 had the largest linear attenuation coefficient, ranging from 9.33 cm1 to 0.12 cm^-1. Charnockite rocks were found to have exceptional shielding qualities, making them an excellent natural choice for radiation shielding applications.