• Journal of the Korean Chemical Society
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• v.9 no.4
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• pp.211-214
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• 1965

The partition function of liquid methyl chloride and methyl bromide are developed by applying the significant structure theory of liquid.$^{(1-3)}$ The parameters therein are determined by the modified significant structure theory of liquid.$^{(4)}$ The molar volume, the vapor pressure, and the entropy of vaporization of the liquids are calculated over a wide temperature range. The critical properties for the liquids are also calculated. The results show good agreement with experimental observations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.254-268
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• 2013

For real-world clustering tasks, the input data is typically not easily separable due to the highly complex data structure or when clusters vary in size, density and shape. Kernel-based clustering has proven to be an effective approach to partition such data. In this paper, we provide an overview of several fuzzy kernel clustering algorithms. We focus on methods that optimize an fuzzy C-mean-type objective function. We highlight the advantages and disadvantages of each method. In addition to the completely unsupervised algorithms, we also provide an overview of some semi-supervised fuzzy kernel clustering algorithms. These algorithms use partial supervision information to guide the optimization process and avoid local minima. We also provide an overview of the different approaches that have been used to extend kernel clustering to handle very large data sets.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.69-76
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• 2002

In this paper, several improved Element-Free Galerkin (EFG) methods containing singular expression in their approximation functions are compared one another through a patch test with near-tip field. Intrinsic enrichments that expand the basis function partially and fully with known near-tip displacement field and a local enrichment using auxiliary supports based on the partition of unity concept are examined by evaluating a relative stress norm error and the stress intensity factor. Some numerical examinations graphically show that how the size of compact support, dilation parameter and the diffraction parameter can affect the accuracy of the improved EFG methods in the error and the stress intensity factor.

• Structural Engineering and Mechanics
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• v.14 no.1
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• pp.57-70
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• 2002

This work presents an iterative mesh partitioning approach to improve the efficiency of parallel substructure finite element computations. The proposed approach employs an iterative strategy with a set of empirical rules derived from the results of numerical experiments on a number of different finite element meshes. The proposed approach also utilizes state-of-the-art partitioning techniques in its iterative partitioning kernel, a cost function to estimate the computational cost of each submesh, and a mechanism that adjusts element weights to redistribute elements among submeshes during iterative partitioning to partition a mesh into submeshes (or substructures) with balanced computational workloads. In addition, actual parallel finite element structural analyses on several test examples are presented to demonstrate the effectiveness of the approach proposed herein. The results show that the proposed approach can effectively improve the efficiency of parallel substructure finite element computations.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.189-212
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• 2006

Let $F^{\alpha}G$ be a twisted group algebra with basis ${{\mu}g|g\;{\in}\;G}$ and $P\;=\;{C_g|g\;{\in}\;G}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $F^{\alpha}G$ generated by all class sums $\sum\limits{_{x{\in}C_g}}\;{\mu}_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^{\alpha}G$ and in $F^{\alpha}H$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $\alpha-spherical$ functions as characters of projective class algebras.

• Bulletin of the Korean Chemical Society
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• v.3 no.1
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• pp.18-23
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• 1982

The molar volumes, the molar heat capacities and the molar entropies of solid argon are calculated from 0 K to the triple point using the vacancies-in-solid model. In the partition function, the central pairwise additive (Mie-Lennard-Jones 12,6) potential is used by introducing numbers, which is obtained by summing powers over all lattice points of a face-centred cubic in terms of the distance between nearest neighbours. A method of iteration is employed to evaluate the potential parameter. The results are compared with experimental values and other theoretical values. The results show a fair agreement with the experimental results.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.969-983
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• 2024

For an integer ℓ ≥ 1, let ${\bar{B}}_{\ell}(n)$ denotes the number of ℓ-regular over partition pairs of n. For certain conditions of ℓ, we study the divisibility of ${\bar{B}}_{\ell}(n)$ and arithmetic properties for ${\bar{B}}_{\ell}(n)$. We further obtain infinite family of congruences modulo 2^t satisfied by ${\bar{B}}_3(n)$ employing a result of Ono and Taguchi (2005) on nilpotency of Hecke operators.

• Journal of Digital Convergence
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• v.12 no.4
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• pp.277-283
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• 2014

Fuzzy modeling is generally using the given data and the fuzzy rules are established by the input variables and the space division by selecting the input variable and dividing the input space for each input variables. The premise part of the fuzzy rule is presented by selection of the input variables, the number of space division and membership functions and in this paper the consequent part of the fuzzy rule is identified by polynomial functions in the form of linear inference and modified quadratic. Parameter identification in the premise part devides input space Min-Max method using the minimum and maximum values of input data set and C-Means clustering algorithm forming input data into the hard clusters. The identification of the consequence parameters, namely polynomial coefficients, of each rule are carried out by the standard least square method. In this paper, membership function of the premise part is dividing input space by using trapezoid-type membership function and by using gas furnace process which is widely used in nonlinear process we evaluate the performance.

• Korean Journal of Environmental Agriculture
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• v.10 no.2
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• pp.149-157
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• 1991

In order to elucidate the possible change in the non-extractable bound residue of TCAB(3,3' 4,4' - tetrachloroazobenzene) in soil as a function of aging period, uniformly ring-labelled $^{14}C-TCAB$ was treated to soil(organic matter : 1.8%), and aged for 3, 6, 9, 12 and 15 months at $21{\pm}1^{\circ}C$, respectively. $^{14}CO_2$ evolution and volatilization loss during the aging were negligible. The amounts of non-extractable bound residue of TCAB increased gradually from 7.55% in 3-month aging to 19.32% in 15-month aging. Partition data suggested no formation of polar groups in the chemical structure of TCAB. Most of $^{14}C-radioactivity$ of bound residues was present in humin in the range of 50.52 to 58.93%. The fact that the number of microorganisms in soil decreased relative to the control suggested no chance of their involvement in the formation of non-extractable bound residues. Accordingly, the increase in the non-extractable bound residue of TCAB in soil with aging period is believed to be due to the transformation of the trans isomer to the cis one which is more polar and more adsorptive than the former.