• Korean Management Science Review
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• v.10 no.2
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• pp.1-9
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• 1993

This paper shows the application of fuzzy set and nonlinear membership function to linear programming problems in a fuzzy environment. In contrast to typical linear programming problems, the objectives and constraints of the problem in a fuzzy environment are defined imprecisely. This paper describes that fuzzy linear programming models can be formulated using the basic concepts of membership functions and fuzzy sets, and that they can be solved by quadratic programming methods. In a numerical example, a linear programming problem with two constraints and two decision variables is provided to illustrate the solution procedure.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of the Korean Data and Information Science Society
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• v.24 no.2
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• pp.333-339
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• 2013

This paper discusses a method for getting a basis set of estimable functions of less than full rank linear model. Since model parameters are not estimable estimable functions should be identified for making inferences proper about them. So, it suggests a method of using full rank factorization of model matrix to find estimable functions in easy way. Although they might be obtained in many different ways of using model matrix, the suggested full rank factorization technique could be one of much easier methods. It also discusses how to use projection matrix to identify estimable functions.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.183-194
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• 1998

Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.331-347
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• 2017

The aim of the present paper is to introduce a new subclass of meromorphic functions with positive coefficients defined by a certain integral operator and a necessary and sufficient condition for a function f to be in this class. We obtain coefficient inequality, meromorphically radii of close-to-convexity, starlikeness and convexity, convex linear combinations, Hadamard product and integral transformation for the functions f in this class.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1625-1647
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• 2014

By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of p-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1805-1827
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• 2014

Let $\mathcal{K}^{\prime}_M$ be the generalized tempered distributions of $e^{M(t)}$-growth, where the function M(t) grows faster than any linear functions as ${\mid}t{\mid}{\rightarrow}{\infty}$, and let $K^{\prime}_M$ be the Fourier transform spaces of $\mathcal{K}^{\prime}_M$. We obtain the relationship between certain classes of analytic functions in tubes, $\mathcal{K}^{\prime}_M$ and $K^{\prime}_M$.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.465-481
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• 2021

Let f be the function defined on the open unit disk, with f(0) = 0 = f'(0) - 1, satisfying Re (αf'(z) + (1 - α)zf'(z)/f(z)) > 0 or Re (αf'(z) + (1 - α)(1 + zf"(z)/f'(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.

• East Asian mathematical journal
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• v.25 no.2
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• pp.127-140
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• 2009

In this paper a general class of analytic functions involving a convolution structure is introduced. Among the results investigated are the various results depicting useful properties and characteristics of this function class by employing the techniques of differential subordination. Relevances of the main results with some known results are also mentioned briefly.