• Title/Summary/Keyword: monotonicity

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A MONOTONICITY FORMULA AND A LIOUVILLE TYPE THEOREM OF V-HARMONIC MAPS

  • Zhao, Guangwen
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.5
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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.

ON NONLINEAR VARIATIONAL INCLUSIONS WITH ($A,{\eta}$)-MONOTONE MAPPINGS

  • Hao, Yan
    • East Asian mathematical journal
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    • v.25 no.2
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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.

Monotonicity Preserving Spectral Volume Method (Monotonicity Preserving Spectral Volume 기법)

  • Kim, Sung-Soo;Yoon, Sung-Hwan;Kim, Chong-Am
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.10
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    • pp.1-9
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    • 2005
  • Based on the monotonicity preserving concept, a new limiter, which is applicable to an arbitrary grid system, is developed. This new limiter preserves accuracy and monotonicity on an arbitrary grid system and it is also applicable to spectral volume concept. Numerical experiments for 1-D and 2-D flow show the characteristics of the new limiter.

ON THE MONOTONICITY OF THE DITTERT FUNCTION ON CLASSES OF NONNEGATIVE MATRICES

  • Cheon, Gi-Sang
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.2
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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.

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GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS

  • Verma, Ram U.
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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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.

SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND

  • Guo, Bai-Ni;Qi, Feng
    • Communications of the Korean Mathematical Society
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    • v.31 no.2
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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.

Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

  • Dong, Yongpeng;Fan, Shengjun
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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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.

COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS

  • Qi, Feng;Zhang, Xiao-Jing
    • The Pure and Applied Mathematics
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    • v.21 no.2
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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, ${\infty}$).

SYMMETRY AND MONOTONICITY OF SOLUTIONS TO FRACTIONAL ELLIPTIC AND PARABOLIC EQUATIONS

  • Zeng, Fanqi
    • Journal of the Korean Mathematical Society
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    • v.58 no.4
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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.