• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.521-538
• /
• 2024

In this paper, using the notion of the imprecise set, the idea of an imprecise group is introduced including some examples. The two key rules of classical set theory are obeyed by this extended version of fuzzy sets, which the existing complement definition of a fuzzy set failed to do. With the support from general group theory, the paper also provides some fundamental properties of an imprecise group here. Additionally, it includes a few characteristics of imprecise subgroups, and abelian imprecise group.

• Journal of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.763-780
• /
• 2001

The use and development of of computer technology by algebraists over the last forty years has revolutionised the way in which algebraists think about algebra, and the way they teach it and conduct their research. This paper is a personal reflection on these changes by a somewhat unwilling computer user.

• Bulletin of the Korean Chemical Society
• /
• v.32 no.4
• /
• pp.1187-1194
• /
• 2011

The hydrogen abstraction reaction of $CF_3CH_2CHO$ + OH has been studied theoretically by dual-level direct dynamics method. Two stable conformers, trans- and cis-$CF_3CH_2CHO$, have been located, and there are four distinct OH hydrogen-abstraction channels from t-$CF_3CH_2CHO$ and two channels from c-$CF_3CH_2CHO$. The required potential energy surface information for the kinetic calculation was obtained at the MCG3-MPWB//M06-2X/aug-cc-pVDZ level. The rate constants, which were calculated using improved canonical transitionstate theory with small-curvature tunneling correction (ICVT/SCT) were fitted by a four-parameter Arrhenius equation. It is shown that the reaction proceeds predominantly via the H-abstraction from the -CHO group over the temperature range 200-2000 K. The calculated rate constants were in good agreement with the experimental data between 263 and 358 K.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.289-303
• /
• 2004

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We study the full non-rigid group (f-NRG) of tetraammineplatinum(II) with two separate symmetry groups C2v and C4v. We prove that they are groups of order 216 and 5184 with 27 and 45 conjugacy classes, respectively. Also, we will compute the character tables of these groups.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.657-663
• /
• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.915-931
• /
• 2009

The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of 2,3,5,6-Tetramethylpyrazine The f-NRG of this molecule is seen to be isomorphic to the group $\mathbb{Z}_3{\wr}(\mathbb{Z}_2{\times}\mathbb{Z}_2)$, where $\mathbb{Z}_n$ is the cyclic group of order n, of order 324 which has 45 conjugacy classes. We determine the some properties and relations between characters of the group. Also, we examine the symmetry group of this molecule and show that its symmetry group is $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

• Journal of applied mathematics & informatics
• /
• v.7 no.3
• /
• pp.875-886
• /
• 2000

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. Then ${\theta}$:G -> G given by ${\theta}(A)$ = ${(A^t)}^{-l}$, where $A^t$ denotes the transpose of the matrix A, is an automorphism of G. Therefore we may form the group G.$<{\theta}>$ which is the split extension of the group G by the cyclic group $<{\theta}>$ of order 2. Our aim in this paper is to find the complex irreducible character table of G.$<{\theta}>$.

• Nuclear Engineering and Technology
• /
• v.56 no.10
• /
• pp.4207-4218
• /
• 2024

One of the essential requirements for molten salt reactor (MSR) design is methodology for analyzing multiphysics phenomena, such as the behavior of liquid fuel. In the research of Molten Salt Fast Reactors (MSFRs), the Neutron Diffusion Equation (NDE) is widely employed. This study introduces a method to enhance the accuracy of neutronic analysis of MSFR using the NDE. Using the simple structure of MSFR and the characteristics of liquid nuclear fuel, it is intended to enable the application of the simple equivalence method, which is difficult to perform on the existing fast reactor. A straightforward yet effective approach named the simplified Generalized Equivalence Theory (simplified GET) is proposed for applying flux-volume-weighted homogenized cross-sections and representative Discontinuity Factor (DF) values obtained at material. This approach, while similar to the General Equivalence Theory (GET) method, significantly simplifies the enhancement of accuracy in reactor analysis, minimizing computational efforts. Our investigation spans from the initial core to the burned core, ensuring the applicability of this simple method throughout the reactor's operational life. The proposed method demonstrates promising results, offering a viable solution to improve the accuracy of NDE-based calculations in MSFRs.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.1_2
• /
• pp.71-77
• /
• 2022

This work considers the existence and uniqueness of fuzzy solutions for impulsive abstract partial neutral functional differential systems. To establish the existence and uniqueness, we apply the concept of impulse, semi group theory and suitable fixed point theorem.

• Structural Engineering and Mechanics
• /
• v.3 no.2
• /
• pp.135-144
• /
• 1995

Since structural systems may fail in any one of several failure modes, computation of system reliability is always difficult. A method using numerical quadrature for computing structural system reliability with either one or more than one failure mode is presented in this paper. Statistically correlated safety margin equations are transformed into a group of uncorrelated variables and the joint density function of these uncorrelated variables can be generated by using the Maximum Entropy Method. Structural system reliability is then obtained by integrating the joint density function with the transformed safety domain enclosed within a set of linear equations. The Gaussian numerical integration method is introduced in order to improve computational accuracy. This method can be used to evaluate structural system reliability for Gaussian or non-Gaussian variables with either linear or nonlinear safety boundaries. It is also valid for implicit safety margins such as computer programs. Both the theory and the examples show that this method is simple in concept and easy to implement.