Local parabolic and elliptic gradient estimates for a generalized heat-type equation under the Yamabe flow

2020 ◽  
Vol 485 (1) ◽  
pp. 123770
Author(s):  
Liangdi Zhang
Keyword(s):  
Type Equation ◽  
Gradient Estimates ◽  
Yamabe Flow

Gradient estimates for Neumann boundary value problem of Monge–Ampère type equations

2016 ◽  
Vol 19 (04) ◽  
pp. 1650041 ◽  
Author(s):  
Feida Jiang ◽  
Ni Xiang ◽  
Jinju Xu
Keyword(s):  
Matrix Function ◽  
Symmetric Matrix ◽  
Type Equation ◽  
Neumann Boundary ◽  
Gradient Estimates ◽  
Neumann Boundary Value Problem ◽  
The Matrix ◽  
Elliptic Solutions ◽  
Monge Ampere ◽  
Gradient Bound

This paper concerns the gradient estimates for Neumann problem of a certain Monge–Ampère type equation with a lower order symmetric matrix function in the determinant. Under a one-sided quadratic structure condition on the matrix function, we present two alternative full discussions of the global gradient bound for the elliptic solutions.

scholarly journals Logarithmic gradient estimates to a Monge-Ampere Type equation on \(S^n\)

2015 ◽  
Vol 3 (3) ◽  
pp. 126
Author(s):  
Yunhua Ye
Keyword(s):  
Type Equation ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
Dimensional Sphere ◽  
Geometric Problems ◽  
Monge Ampere

<p>Monge-Ampere type equations arise naturally from many geometric problems. In this paper, we are concerned with one of these Monge-Ampere type equations on  dimensional sphere \(S^n\) and obtain logarithmic gradient estimate by using Bernstein technique.</p>

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

A class of monotonic quantities along the Yamabe flow

2020 ◽  
Vol 27 (1) ◽  
pp. 17-27
Author(s):  
Farzad Daneshvar ◽  
Asadollah Razavi
Keyword(s):  
Yamabe Flow

β Grain Growth Kinetics of a New Metastable β Titanium Alloy

2013 ◽  
Vol 747-748 ◽  
pp. 844-849 ◽  
Author(s):  
Yue Fei ◽  
Xin Nan Wang ◽  
Zhi Shou Zhu ◽  
Jun Li ◽  
Guo Qiang Shang ◽  
...  
Keyword(s):  
Titanium Alloy ◽  
Grain Growth ◽  
Kinetic Equations ◽  
Type Equation ◽  
Growth Exponent ◽  
Solution Treated ◽  
Growth Activation ◽  
Grain Growth Kinetics ◽  
Kinetics Of ◽  
Strength And Ductility

Ti-Mo-Nb-Cr-Al-Fe-Si alloy is a new metastable β titanium alloy with excellent combination of strength and ductility. The β grain-growth exponent and the activation energies for β grain growth for the investigated alloy at specified temperature were computed by the kinetic equations and the Arrhenius-type equation. The rate of β grain growth decreases with elongating solution treated time and increases with the increasing solution-treated temperature. The β grain-growth exponents, n, are 0.461, 0.464 and 0.469 at 1113, 1133 and 1153K, respectively. The β grain growth activation energy is determined to be 274 KJ/mol.

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