• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.27-41
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• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Journal of The Korea Institute of Healthcare Architecture
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• v.28 no.1
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• pp.7-21
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• 2022

Purpose: As the pandemic period continues, various attempts are being made to new medical spaces in the medical society. Many hospitals, including existing general hospitals, have been effected by infected patients and are showing limitations in patient care capacity. Mobile-hospitals may be the starting point for the development of new environment in the medical society and healthcare facilities which are not replacing the role of existing hospitals. Mobile-hospitals can possibly respond to situations that require medical services and provide emergency care for various demands in connection with existing healthcare facilities. Methods: Through a total of five investigations/analysis, medical functions that can be inserted into mobile-hospitals based on modular architecture are set. The first is the analysis of domestic legal guidelines, the second is the analysis of previous studies, the analysis of emergency medical facilities and other medical spaces of hospitals to be compared, the fourth is the analysis of medical spaces of actual mobile hospital projects. Results: Through five analyses, medical functions applicable to the modular building platform were finally established. Mobile hospitals can be used not only in disaster sites such as infectious diseases, but also in medical underprivileged areas or general hospitals. Therefore, it is necessary to establish medical functions that meet the specificity of mobile hospitals along with the functions of existing fixed medical facilities. Furthermore, various studies such as use in international aid, use in normal times, and connection with other platform-based medical facilities are considered necessary. Implications: Through 5 strategies of analysis, 41 medical functions which can be applied to UNIT are decided and these functions will be placed where medical services will be required.

• East Asian mathematical journal
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• v.27 no.3
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• pp.339-348
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• 2011

B. C. Berndt [6] has evaluated the transformation formula for a large class of functions that includes and generalizes the classical Dedekind eta-function. In this paper, we consider a twisted version of his formula. Using this transformation formula, we derive modular trans-formation formulas for the generating functions for cranks which were central to deduce K. Mahlburg's results in [11].

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2011.10a
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• pp.793-794
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• 2011

This paper presents a method of the circuit design of the multiple-valued digital logic switching functions based on the modular techniques. Fisr of all, we introduce the necessity, background and concepts of the modular design techniques for the digital logic systems. Next, we discuss the definitions that are used in this paper. For the purpose of the circuit design for the multiple-valued digital logic switching functions, we discuss the extraction of the partition functions. Also we describe the construction method of the building block, that is called the modules, based on each partition functions. And we apply the proposed method to the example, we compare the results with the results of the earlier methods. In result, we decrease the control functions, it means that we obtain the effective cost in the digital logic design for any other earlier methods. In the future research, we require the universal module that traet more partition functions and more compact module.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.7
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• pp.78-91
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• 1998

This paper presents modular design techniques of multiple-valued logic functions about the function decomposition method and input variable management method. The function decomposition method takes avantage of the property of the column multiplicity in a single-column variable partitioning. Due to the increased number of identical modules, we can achieve a simpler circuit design by using a single T-gate, which can eliminate some of the control functions in the module libraty types. The input variable management method is to reduce the complexity of the input variables by proposing the look up table which assign input variables to a code. In this case as the number of sub-functions increase the code-length and the size of the code-assignment table grow. We identify some situations where shard input variables among sub-functions can be further reduced by a simplicication technique. According to the result of adapting this method to a function, we have demonstrated the superiority of the proposed methods which is bing decreased to about 12% of interconnection and about 16% of T-gate numbers compare with th eexisting for th enon-symmetric and irregular function realization.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.987-1028
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• 2014

In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.67-77
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• 2011

We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.73-82
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• 2013

There are some identities between the representations of Hecke operators defined on a subspace of modular forms associated with orders of a Quaternion algebra. In this paper, we find the identities between the zeta functions attached to these representations.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.14-18
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• 1987

In this paper, a system program is introduced for the effective operation of revolute type robot manipulator. The I system program consists of several modes and specific functions. These modes and functions are flexible and easy to use because the structure is modular and conversational. This program had implemented and verified the efficiency together with a five axes robot.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.