• The Pure and Applied Mathematics
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• v.20 no.2
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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.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.69-76
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• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.347-350
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• 2000

We present the design of ternary flip-flop which is based on ternary logic so as to process ternary data. These flip-flops are fabricated with ternary voltage mode NOR, NAND, INVERTER gates. These logic gate circuits are designed using CMOS and obtained the characteristics of a lower voltage, a lower power consumption as compared to other gates. These circuits have been simulated with the electrical parameters of a standard 0.25 micron CMOS technology and 2.5 volts supply voltage. The Architecture of proposed ternary flip-flop is highly modular and well suited for VLSI implementation, only using ternary gates.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.10
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• pp.52-62
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• 2003

This paper discusses ternary logic gate, ternary D flip-flop, and ternary four-digit parallel input/output register. The ternary logic gates consist of n-channel pass transistors and neuron MOS(νMOS) threshold inverters on voltage mode. They are designed with a transmission function using threshold inverter that are in turn, designed using Down Literal Circuit(DLC) that has various threshold voltages. The νMOS pass transistor is very suitable gate to the multiple-valued logic(MVL) and has the input signal of the multi-level νMOS threshold inverter. The ternary D flip-flop uses the storage element of the ternary data. The ternary four-digit parallel input/output register consists of four ternary D flip-flops which can temporarily store four-digit ternary data. In this paper, these circuits use 3.3V low power supply voltage and 0.35m process parameter, and also represent HSPICE simulation result.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.6
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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.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.233-245
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• 2013

Let $\mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $\mathcal{X}$ be a ternary Banach $\mathcal{A}$-module. A quartic mapping $D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{\in}\mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.

• International Journal of Highway Engineering
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• v.15 no.5
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• pp.101-110
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• 2013

PURPOSES : The purpose of this study is to evaluate the durability of ternary blended concrete mixtures adding ultra fine admixture. METHODS : From the literature review, crack was considered as the main distress failure criterion on concrete bridge deck pavement. To reduce the initial crack development due to drying shrinkage, CSA expansion agent and shrink reduction agent were used to ternary blended concrete mixtures as a admixture. Laboratory tests including chloride ion penetration test, surface scaling test, rapid freeze & thaw resistance test, non restrained drying shrinkage and restrained drying shrinkage test were conducted to verify the durability of ternary blended concrete mixtures. RESULTS : Based on the test results, proposed mixtures were verified as high qualified durable materials. Expecially initial drying shrinkage crack was not occurred in ternary blended concrete mixtures with CSA expansion agent. CONCLUSIONS : It is concluded that the durability of proposed ternary blend concrete mixture was acceptable to apply for the concrete bridge deck pavement.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.83-90
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• 2009

In this paper, we investigate isomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$$, which was introduced and investigated by Baak in [2].

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.171-178
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• 2017

In this paper, we define $C^*-ternary$ quadratic 3-Jordan homomorphisms associated with the quadratic mapping f(x + y) + f(x - y) = 2f(x) + 2f(y), and prove the Hyers-Ulam stability of $C^*-ternary$ quadratic 3-Jordan homomorphisms.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.357-365
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• 2006

This paper is a sequel of our previous paper [1]. In this paper, we introduce the notions of regular ideal and partial ideal ($p$-ideal) in a ternary semiring and using these two notions we characterize regular ternary semiring.