• Bulletin of the Korean Chemical Society
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• v.31 no.1
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• pp.59-63
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• 2010

Calculations are presented for the $\gamma$-aminobutyric acid-$(H_2O)_n$ (n = 0-5) clusters in both canonical and zwitterionic forms. We examine the effects of microsolvation on the structures and transformation between the canonical and zwitterionic forms. The canonical forms are predicted to be more stable for n = 0-4. With five microsolvating water molecules, the two forms of $\gamma$-aminobutyric acid become quasidegenerate, with the energies of zwitterionic forms slightly (by 1 - 3 kcal/mol) higher. The lowest energy zwitterionic conformer of $\gamma$-aminobutyric acid-$(H_2O)_5$ cluster is calculated to isomerize to canonical form through a barrier-less proton transfer process and is thus predicted to be kinetically unstable. Therefore, we predict that the canonical conformers of $\gamma$-aminobutyric acid should be observed predominantly in the gas phase at low temperature in presence of up to five water molecules.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.63-82
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• 1997

In experimental situations where n two or three level fac-tors are involoved and n observations are taken then the D-optimal first order saturated design is an $n{\times}n$ matrix with elements $\pm$1 or 0, $\pm$1, with the maximum determinant. Cononical forms are useful for the specification of the non-isomorphic D-optimal designs. In this paper we study canonical forms such as the Smith normal form the first sec-ond and the jordan canonical form of D-optimal designs. Numerical algorithms for the computation of these forms are described and some numerical examples are also given.

• Earthquakes and Structures
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• v.10 no.1
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• pp.25-51
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• 2016

In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.

• Journal of the Korean Institute of Telematics and Electronics
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• v.18 no.3
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• pp.9-14
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• 1981

A nonexhaustive procedure for obtaining minimally testable Reed-Muller Canonical (RMC) forms with minimal 1itera1s of switching functions is presented, And, it is shown that this proced tore allows nonexhaustive and near-optimal handling of functions with Doft Care conditions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.537-542
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• 1998

Logic functions such as fuzzy switching functions and multiple-valued Kleenean functions, that are models of Kleene algebra have been studied as foundation of fuzzy logic. This paper deals with a new kinds of functions-fuzzy switching functions with constants-which have features of both the above two kinds of functions . In this paper, we propose new canonical forms for enumerating them. They are much useful to estimate simply the number of fuzzy switching functions with constants.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.798-804
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• 2014

We present calculations for diglycine - $(H_2O)_n$ (n = 0-3) to examine the effects of microsolvating water on the relative stability of the zwitterionic vs. canonical forms of the dipeptide. We calculate the structures, energies and Gibbs free energies of the conformers at wB97XD/6-311++G** and MP2/aug-cc-pvdz levels of theory level of theory. We predict that microsolvation by up to three water molecules does not give thermodynamic stability of the zwitterion relative to the canonical forms. Our calculations also suggest that zwitterionic diglycine - $(H_2O)_3$ is not stable kinetically in low temperature gas phase environment.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.717-734
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• 1998

In the present paper is presented a new matrix pencil-based numerical approach achieving the computation of the elemen-tary divisors of a given matrix $A \in C^{n\timesn}$ This computation is at-tained without performing similarity transformations and the whole procedure is based on the construction of the Piecewise Arithmetic Progression Sequence(PAPS) of the associated pencil $\lambda I_n$ -A of matrix A for all the appropriate values of $\lambda$ belonging to the set of eigenvalues of A. This technique produces a stable and accurate numerical algorithm working satisfactorily for matrices with a well defined eigenstructure. The whole technique can be applied for the computation of the first second and Jordan canonical form of a given matrix $A \in C^{n\timesn}$. The results are accurate for matrices possessing a well defined canonical form. In case of defective matrices indications of the most appropriately computed canonical form. In case of defective matrices indication of the most appropriately computed canonical form are given.

• Journal of the Korean Mathematical Society
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• v.29 no.1
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• pp.209-223
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• 1992

• Journal of the Korean Mathematical Society
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• v.26 no.1
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• pp.57-65
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• 1989

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.509-514
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• 2016

By constructing a canonical basis for the space $M_k^{\sharp}({\Gamma}_0(N))$ explicitly, we find a basis of the space of cusp forms for ${\Gamma}_0(N)$ consisting of $Poincar{\acute{e}}$ series.