• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.465-472
• /
• 2015

In this paper, we study the existence and the stability of equilibria of predator-prey models with Ivlev's functional response. We give a simple proof for the uniqueness of limit cycles of the predator-prey system. The existence and the stability at the origin and a boundary equilibrium point(including the positive equilibrium point) are also investigated.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1305-1319
• /
• 2015

We study the relations between strong isoperimetric inequalities and Gromov hyperbolicity on planar graphs, and give an alternative proof for the following statement: if a planar graph of bounded face degree satisfies a strong isoperimetric inequality, then it is Gromov hyperbolic. This theorem was formerly proved in the author's paper from 2014 [12] using combinatorial methods, while geometric approach is used in the present paper.

• Korean Journal of Mathematics
• /
• v.16 no.2
• /
• pp.165-172
• /
• 2008

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.

• East Asian mathematical journal
• /
• v.28 no.2
• /
• pp.197-213
• /
• 2012

In this paper we study Soltan & Meidman's method that is able to be used in mathematical discovery. We analyze Soltan & Meidman's book "Tozdestva i Neravenstva v Treugolike" that is published in Moldova Republic. In this work we formulate Soltan & Meidman's method related with discovery of triangle's various equalities, and use the method to discovery mathematical equalities. As a result we suggest some new mathematical equalities related with triangle's sides and its proof.

• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.285-297
• /
• 1997

We will study the generalization of theorems on the pe-riodic locally - solvable FC-groups to the theorems on the periodic locally-solvable CC-groups. The main theorem is the Theorem A. For the proof the inverse limit of inverse system and topological ap-proch developed by Dixon is useful.

• The Pure and Applied Mathematics
• /
• v.21 no.4
• /
• pp.307-316
• /
• 2014

We prove the existence of the risk-efficient options proposed by Xu [7]. The proof is given by both indirect and direct ways. Schied [6] showed the existence of the optimal solution of equation (2.1). The one is to use the Schied's result. The other one is to find the sequences converging to the risk-efficient option.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.545-555
• /
• 2004

Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.

• East Asian mathematical journal
• /
• v.24 no.5
• /
• pp.521-526
• /
• 2008

In this study, we'll check the proof of Morley's theorem that calculate the sides XY, YZ and ZX of Morley's triangle. We may now consider calculate area of Morley triangle and observation that, for example, in triangle ABC, length or sides XY, YZ and ZX are $8Rsin{\alpha}sin{\beta}sin{\gamma}$, respectively. Therefore, compare with the area of Morley's triangle XYZ and the area of triangle ABC.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.121-131
• /
• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• The Pure and Applied Mathematics
• /
• v.21 no.2
• /
• pp.141-145
• /
• 2014

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).