• Honam Mathematical Journal
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• v.39 no.3
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• pp.401-416
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• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.459-479
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• 2007

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.859-893
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• 2009

In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1597-1612
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• 2016

There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.04b
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• pp.262-266
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• 1993

The development of COPS(Computer aided Operation Planning System) needs data mapping paradigm which provides intelligent determonation of cutting conditions from the requirements of process planning side. We proposed the idea of multi-level mapping by the combination of heuristics of domain experts and mathematical abstraction of cutting condition and requirements. Mathematical mathods for the generalization of heuristics were constructed by multi-layer perceptron. DBMS for determination of cutting conditions was constructed by classification and combination of best fitted models. Triangular fuzzy number was used to process the uncertainties in heuristics of experts.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.275-281
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• 2001

The trajectory of a classical dynamics is determined by the least action principle. As soon as we come to quantum dynamics, we have to consider all possible trajectories which are proposed to be a sum of the classical trajectory and Brownian fluctuation. Thus, the action involves the square of the derivative B(t) (white noise) of a Brownian motion B(t). The square is a typical example of a generalized white noise functional. The Feynman propagator should therefore be an average of a certain generalized white noise functional. This idea can be applied to a large class of dynamics with various kinds of Lagrangians.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.865-880
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• 2015

We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence criteria can always be weaker than the corresponding ones in earlier studies. Numerical examples are also provided in this study to solve equations in cases not possible before.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1209-1219
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• 2013

In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it's first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br$\ddot{u}$ck conjecture with the idea of sharing functions.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.281-287
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• 2009

In this paper, we develop the idea of a generalized upper set in a BE-algebra. Furthermore, these sets are considered in the context of transitive and self distributive BE-algebras and their ideals, providing characterizations of one type, the generalized upper sets, in terms of the other type, ideals.