• 호남수학학술지
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• 제44권1호
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• pp.26-35
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• 2022

In this paper we introduce two type of representations of the Pascal matrix via induced transformations of some q-derivatives as well as their some combinatorial applications.

• Kyungpook Mathematical Journal
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• 제10권2호
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• pp.121-131
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• 1970

• 대한수학회지
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• 제38권2호
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• pp.193-226
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• 2001

We study Feynman's Operational Calculus for operator-valued functions of time and for measures which are not necessarily probability measures; we also permit the presence of certain unbounded operators. further, we relate the disentangling map defined within the solutions of evolution equations and, finally, remark on the application of stability results to the present paper.

• 대한수학회논문집
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• 제33권2호
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• pp.473-484
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• 2018

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.237-253
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• 2010

It is shown that an appropriate combination of methods, relevant to operational calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Hermite and Konhauser polynomials and discuss the links with various known polynomials.

• 대한수학회지
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• 제28권1호
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• pp.99-125
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• 1991

• 호남수학학술지
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• 제34권2호
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• pp.289-295
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• 2012

In this note we prove the space (A, ${\parallel}.{\parallel}$) is a Banach space and ${\parallel}ab{\parallel}{\leq}{\parallel}a{\parallel}{\parallel}b{\parallel}$ for $a,b{\in}A$ where $A:=\{a:=(a_t)_{t{\in}G}:{\sum}_{t{\in}G}{\parallel}a_t{\parallel}_t<{\infty}\}$, $G=\mathbb{N}^*$. Also we show some property in (A, ${\parallel}.{\parallel}$).

• 대한수학회논문집
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• 제10권2호
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• pp.443-460
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• 1995

We consider a G/M/1 vacation model where the vacation time has k-stages generalized Erlang distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the limiting probabilities of the queue length at arrival time points and arbitrary time points simultaneously. Operational calculus technique is used for solving non-homogeneous difference equations.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.354-357
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• 2004

According to the computerization of railway signaling systems, the interface link between the signaling systems has been replaced by the digital communication channel. At the same time, the importance of the communication link is more pronounced than in the past. In this paper, new network-based protocol for Korean railway signaling has designed between CTC and SCADA system, and the overview of designed protocol is briefly represented. Using the informal method for specifying the communication protocol, a little ambiguity may be contained in the protocol. To clear the ambiguity contained in the designed protocol, we use LTS model to design the protocol for this interface link between CTC and SCADA, the LTS is an intermediate model for encoding the operational behavior of processes. And then, we verify automatically and formally the safety and the liveness properties through the model checking method. Especially, the modal ${\mu}$-calculus, which is a highly expressive method of temporal logic that has been applied to the model checking method. It will be expected to increase the safety, reliability and efficiency of maintenance of the signaling systems by using the designed protocol for railway signaling in Korea.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.