• 대한수학회보
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• 제56권5호
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• pp.1327-1340
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• 2019

We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

• East Asian mathematical journal
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• 제25권2호
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• pp.159-169
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• 2009

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

• 대한수학회논문집
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• 제34권4호
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• pp.1223-1228
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• 2019

In the paper, the authors supply complete monotonicity of linear combination of finite psi functions and extend some known results.

• 한국항공우주학회지
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• 제33권10호
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• pp.1-9
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• 2005

단조성 유지 개념을 기반으로, 임의의 격자계에서 적용할 수 있는 새로운 제한자를 개발하였다. 본 논문에서 개발된 제한자는 임의의 계산 격자계에서 정확성과 단조성을 유지할 수 있는 특성을 가졌으며, 이러한 특성으로 인하여 spectral volume 기법으로의 적용이 가능하다. 또한 이 제한자는 smooth extremum에서 물성치의 변화를 허용하여 내삽된 물성치의 정확도를 향상시켜주는 역할을 한다. 일차원, 이차원 수치 해석의 결과를 통하여 본 논문에서 개발된 제한자의 특성을 검증하였다.

• 대한수학회보
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• 제30권2호
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• pp.265-275
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• 1993

In this paper, we study the monotonicity of the Dittert function (abb. MD) on the line segment from A .mem. $K_{n}$ to J$_{n}$ generalizing both the Dittert conjecture and the Monotonicity conjecture for permanent, and obtain a sufficient condition on A .mem. $K_{n}$ for which the MD holds. It is also proved that if A .mem. $K_{n}$ satisfies the Dokovic inequality (1.2) then MD holds for A, and a subclass of $K_{n}$ for which MD holds is found. is found.

• 대한수학회논문집
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• 제26권4호
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• pp.685-693
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• 2011

General framework for proximal point algorithms based on the notion of (A, ${\eta}$)-maximal monotonicity (also referred to as (A, ${\eta}$)-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to (A, ${\eta}$)-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

• 대한수학회논문집
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• 제31권2호
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• pp.355-363
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• 2016

By employing a refined version of the $P{\acute{o}}lya$ type integral inequality and other techniques, the authors establish some inequalities and absolute monotonicity for modified Bessel functions of the first kind with nonnegative integer order.

• 대한수학회논문집
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• 제33권3호
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• pp.985-999
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• 2018

This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권2호
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• pp.141-145
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• 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, ${\infty}$).

• 대한수학회지
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• 제58권4호
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• pp.1001-1017
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• 2021

In this paper, we first apply parabolic inequalities and a maximum principle to give a new proof for symmetry and monotonicity of solutions to fractional elliptic equations with gradient term by the method of moving planes. Under the condition of suitable initial value, by maximum principles for the fractional parabolic equations, we obtain symmetry and monotonicity of positive solutions for each finite time to nonlinear fractional parabolic equations in a bounded domain and the whole space. More generally, if bounded domain is a ball, then we show that the solution is radially symmetric and monotone decreasing about the origin for each finite time. We firmly believe that parabolic inequalities and a maximum principle introduced here can be conveniently applied to study a variety of nonlocal elliptic and parabolic problems with more general operators and more general nonlinearities.