• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권2호
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• pp.129-136
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• 2013

We research properties of ternary numbers with values in ${\Lambda}(2)$. Also, we represent dual ternary numbers in the sense of Clifford algebras of real six dimensional spaces. We give generation theorems in dual ternary number systems in view of Clifford analysis, and obtain Cauchy theorems with respect to dual ternary numbers.

• 호남수학학술지
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• 제38권4호
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• pp.685-692
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• 2016

The aim of this paper is to investigate the differentials of the hypercomplex valued functions in Clifford analysis. Like as the differentials defined by the naïve approach in one complex variable analysis, we define the differentials of functions with values in ternary number functions by same ways. And we survey the properties of each differential with respect to a non-commutativity of the skew field.

• 대한수학회지
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• 제56권1호
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• pp.67-80
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• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• 대한기계학회논문집A
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• 제33권6호
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• pp.568-572
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• 2009

We present a ternary microfluidic multiplexer unit, capable to address three flow channels using a pair of control lines with two different threshold pressure valves. The previous binary multiplexer unit addresses only two flow channels using a pair of control line with identical threshold pressure valves, thus addressing $2^{n/2}$ flow channels using n control lines. The present ternary multiplexer addressing three flow channels using a pair of control lines, however, is capable to address $3^{n/2}$ flow channels using n control lines with two different threshold pressure valves. In the experimental study, we characterized the threshold pressure and the response time of the valves used in the ternary multiplexer. From the experimental observation, we also verified that the present ternary multiplexer unit could be operated by two equivalent valve operating conditions: the different static pressures and dynamic pressures at different duty ratio. And then, $3{\times}3$ well array stacking ternary multiplexers in serial is addressed in cross and plus patterns, thus demonstrating the individual flow channel addressing capability of the ternary multiplexer. Thus, the present ternary multiplexer reduces the number of control lines for addressing flow channels, achieving the high well control efficiency required for simple and compact microfluidic systems.

• East Asian mathematical journal
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• 제29권3호
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• 전자공학회논문지B
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• 제31B권1호
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• pp.57-63
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• 1994

The logic function synthesis using ULM U$_h$ is constructed based on canonic Reed-Muller expansion coefficient for a given function. This paper proposes the fast synthesis algorithm using ULM U$_h$ for ternary function. By using circuit cost and synthesis method of proposed in this paper, order of control input variable minimum number of ULM U$_h$ can be decided in the synthesis of n-variable ternary function. Accordingly, this method enables to optimum circuit realization for ternary function synthesis using ULM ULM U$_h$ and can be applied to ternary function synthesis using ULM U$_h$. The complexity of search for select the order of all control input variables is (n+2)(n-1)/2.

• 전기의세계
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• 제28권1호
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• pp.43-52
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• 1979

Recently, interest in multivalued(MV) logic system has been increased, despites the apparent difficulties for practical application. This is because of the many advantages of the MV compared with the 2-valued logic systems, such as; (a) higher speed of arithmetical operation on account of the smaller number of digits required for a given data, (b) better utilization of data transmission channels on account of the higher information contents per line, (c) potentially higher density of information storage. This paper describes a MV switching theory and experimental MV logic elements based on current-mode logic technique. These elements tried were a 3-stable pulse generator, a ternary AND, a ternary OR, a MT circuit and a ternary inverter. Tristable flops which are indispensable for constituting a ternary shift register are synthesized using these gates. A BCD to TCD decoder, and vice versa, are proposed by using a ternary inverter and some binary gates. Thus, the feasibility of a large scale MV digital system has been demonstrate.

• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.913-927
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• 2024

In this paper, we represent regular functions on ternary theory in the view of quaternion. By expressing quaternions using ternary number theory, a new form of regular function, called E-regular, is defined. From the defined regular function, we investigate the properties of the appropriate hyper-conjugate harmonic functions and corresponding Cauchy-Riemann equations by pseudo-complex forms.

• Macromolecular Research
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• 제11권5호
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• pp.303-310
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• 2003

The phase behavior of binary blends of dimethylpolycarbonate-tetramethyl polycarbonate (DMPCTMPC) copolycarbonates and styrene-acrylonitrile (SAN) copolymers has been examined and then compared with that of DMPC/TMPC/SAN ternary blends having the same chemical components and compositions except that the DMPC and TMPC were present in the form of homopolymers. Both binary and ternary blends were miscible at certain blends compositions, and the miscible blends showed the LCST-type phase behavior or did not phase separated until thermal degradation temperature. The miscible region of binary blends is wider than that of the corresponding ternary blends. Furthermore, the phase-separation temperatures of miscible binary blends are higher than those of miscible ternary blends at the same chemical compositions. To explain the destabilization of polymer mixture with the increase of the number of component, interaction energies of binary pairs involved in these blends were calculated from the phase separation temperatures using lattice-fluid theory and then the phase stability conditions for the polymer mixture was analyzed with volume fluctuation thermodynamics.

• 한국정보통신학회논문지
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• 제11권3호
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• pp.491-499
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• 2007

본 논문에서는 Reed-Muller 전개식에 의한 3치 논리 회로를 설계하는 한 가지 방법을 제시하였다. 제시된 3치 논리 회로의 설계 방법은 Reed-Muller 전개식의 계수에 대하여 모든 변수의 차수를 검사하여 RME 모듈(Reed-Muller Expansions module)의 수를 최소화하는 최적의 제어 입력 변수의 순서를 결정한다. 최적의 제어 입력 변수의 순서는 회로 비용 행렬의 계산에 사용되며, 이 회로 비용 행렬의 계산 결과를 이용하여 Reed-Muller 전개식에 의한 RME 모듈의 나무 구조의 3치 논리 회로를 설계한다. 제시된 방법은 최적 제어 입력 변수를 찾는데 유일하게 단위시간 내에 수행되며, 컴퓨터 프로그램이 가능하고, 프로그래밍 수행 시간이 $3^n$이다.