• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.331-347
• /
• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.11 no.5
• /
• pp.2468-2483
• /
• 2017

The construction of completely random sensing matrices of Compressive Sensing requires a large number of random numbers while that of deterministic sensing operators often needs complex mathematical operations. Thus both of them have difficulty in acquiring large signals efficiently. This paper focuses on the enhancement of the practicability of the structurally random matrices and proposes a semi-deterministic sensing matrix called Partial Kronecker product of Identity and Hadamard (PKIH) matrix. The proposed matrix can be viewed as a sub matrix of a well-structured, sparse, and orthogonal matrix. Only the row index is selected at random and the positions of the entries of each row are determined by a deterministic sequence. Therefore, the PKIH significantly decreases the requirement of random numbers, which has a complex generating algorithm, in matrix construction and further reduces the complexity of sampling. Besides, in order to process large signals, the corresponding fast sampling algorithm is developed, which can be easily parallelized and realized in hardware. Simulation results illustrate that the proposed sensing matrix maintains almost the same performance but with at least 50% less random numbers comparing with the popular sampling matrices. Meanwhile, it saved roughly 15%-35% processing time in comparison to that of the SRM matrices.

• Research in Mathematical Education
• /
• v.9 no.3 s.23
• /
• pp.257-267
• /
• 2005

When notions of numbers are expanded from natural number to complex number, a similar mathematical phenomenon can be observed in each number. As a case study, to complex number, the phenomenon is investigated carefully and teaching materials are created. Then complex number is expressed with matrices and is geometrically treated, so a new number which is an extension of complex number is discovered. Thus, teaching material regarding to complex number and matrices is made for students of ordinary level. Moreover, for talented students, material about an extension of complex number can be added to the previous one.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.557-584
• /
• 2024

An almost complex torus manifold is a 2n-dimensional compact connected almost complex manifold equipped with an effective action of a real n-dimensional torus Tⁿ ≃ (S¹)ⁿ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let M be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for M, and for each type of graph we construct such a manifold M, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch χ_y-genus of M.

• Journal of the Korea Society for Simulation
• /
• v.10 no.4
• /
• pp.41-50
• /
• 2001

When optimizing a complex system by determining the optimum condition of the system parameters of interest, we often employ the process of estimating the unknown objective function, which is assumed to be a second order spline function. In doing so, we normally use common random numbers for different set of the controllable factors resulting in more accurate parameter estimation for the objective function. In this paper, we will show some mathematical result for the analysis of variance when using common random numbers in terms of the regression error, the residual error and the pure error terms. In fact, if we can realize the special structure of the covariance matrix of the error terms, we can use the result of analysis of variance for the uncorrelated experiments only by applying minor changes.

• Communications of the Korean Mathematical Society
• /
• v.27 no.4
• /
• pp.721-732
• /
• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• Industrial Engineering and Management Systems
• /
• v.16 no.1
• /
• pp.141-153
• /
• 2017

A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.

• Clinical and Experimental Reproductive Medicine
• /
• v.17 no.2
• /
• pp.185-196
• /
• 1990

These experiments were performed to know ultrastructural changes of the cumulus expansion in virot. SEM:In expanded oocyte-cumulus complex, the cell surface are characterized by the presence of many evaginations:they are relatively short and round shape. The mucous extracellular material were deposited between cumulus cells. TEM:In compact cumulus cells, golgi apparatus and rough endoplasmic reticulum developed. In expanded cumulus cells, rough endoplasmic reticulum decreased and the smooth endoplasmic reticulum increased. Also, there were numbers of mitochondria. Extracellular mucous material which is presumed to be hyaluronic acid appears when cumulus cell were expanded. In expanded cumulus cell, numbers of smooth endoplasmic reticulum help cumulus cell to develop in steroidogenic cell.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.949-957
• /
• 2005

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.399-405
• /
• 2009

In this paper, we study the Genoochi-zeta functions which are entire functions in whole complex s-plane these zeta functions have the values of the Genocchi numbers and the Genoochi polynomials at negative integers respectively. That is ${\zeta}_G(1-k)={\frac{G_k}{k}}$ and ${\zeta}_G(1-k,x)={\frac{G_k(x)}{k}}$.