• East Asian mathematical journal
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• 제26권3호
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• pp.351-363
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• 2010

We introduce a special class of real recurrent polynomials $f_m$$($m{\geq}1$) of degree m+1, with positive roots $s_m$, which are decreasing as m increases. The first root $s_1$, as well as the last one denoted by $s_{\infty}$ are expressed in closed form, and enclose all $s_m$ (m > 1). This technique is also used to find weaker than before [6] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.211-218
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• 2003

Let H be a Hilbert space, X be a real Banach space, A : H \longrightarrow X be an operator with D(A) dense in H, G： H \longrightarrow H be positive definite, $\chi$ $\in$ D(A) and b $\in$ H. Consider the quadratic programming problem: QP： Minimize $\frac{1}{2}$〈p, $\chi$〉 + 〈$\chi$, G$\chi$〉 subject to A$\chi$= b In this paper, we obtain an explicit solution to the above problem using generalized inverses.

• Management Science and Financial Engineering
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• 제13권1호
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• pp.115-119
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• 2007

In [1], robust combinatorial optimization problem is introduced, where a positive integer $\Gamma$ is used to control the degree of robustness. The proposed algorithm needs solutions of n+1 nominal problems. In this paper, we show that the number of problems needed reduces to $n+1-\Gamma$.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1359-1378
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• 2010

The effect of impulse in the ecological models makes them more realistic. Recently, the eco-epidemiological models have become an important field of study from the both mathematical and ecological view points. In this article, we consider some eco-epidemiological systems under the influence of impulsive force. A set of sufficient conditions for the permanence of the system are derived. Stability of the trivial solution and at least one strictly positive periodic solution are obtained. Numerical examples are given in support to our analytical findings. Finally, a short discussion concludes the paper.

• 호남수학학술지
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• 제30권3호
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• pp.411-423
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• 2008

In the field of population dynamics and chemical reaction the possibility or the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study time-dependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

• 대한수학회보
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• 제58권6호
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• pp.1539-1561
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• 2021

We prove Perelman type 𝒲-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.

• 대한수학회지
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• 제56권1호
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• pp.67-80
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• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.613-629
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• 2021

In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on τ-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.

• 충청수학회지
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• 제36권1호
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• pp.39-53
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• 2023

In this paper, we consider a delayed ratio-dependent predator-prey reaction-diffusion system with homogenous Neumann boundary conditions. We study the existence of nonnegative solutions and the stability of the nonnegative equilibria to the system. In particular, we provide a sufficient condition for the positive equilibrium to be globally asymptotically stable.

• 대한수학회지
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• 제60권5호
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• pp.1023-1041
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• 2023

In this paper, motivated by the work of Q. S. Zhang in [25], we derive optimal Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Émery Ricci curvature bounded below.