SOLUTIONS TO A CLASS OF PARABOLIC INHOMOGENEOUS NORMALIZED p-LAPLACE EQUATIONS

In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.

Normalized fatigue properties of asphalt mixture at various temperatures

This study normalized the mixture's fatigue behavior at various temperatures,and the strength and fatigue tests of the mixture were conducted.The stress state of the asphalt mixture includes direct tensile,uniaxial compression,and indirect tensile.The Desai yield surface and fatigue path were proposed.And a normalized fatigue characteristics model of the mixture was established.The following conclusions were obtained.With the increases in the loading rate,the strength of the asphalt mixture increased.As the temperature increases,the strength of the mixture is reduced.At various temperatures and rates,the strength forms a closed curved surface.The Desai strength yield surface was established,which forms a closed curved surface.When the loading rate and temperature are below a certain critical line,the asphalt mixture will not undergo strength damage.At a fixed stress state,the fatigue damage path of the mixture was determined.The stress ratio was determined considering the influence of the loading rate.In this way,a normalized model can be described to express the asphalt mixture fatigue properties at various temperatures and stress levels.For the asphalt mixture in an indirect tensile state,the normalized fatigue equation parameter is 4.09.This model is more suitable for reflecting the viscous-elastic behavior of the mixtures than the fatigue equation determined by the notional stress ratio.

STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY

We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation language M ATHEMATICA,and extending the matrix representation method.This method can be used to calculate the focal value of any high order terms.This method has been verified by an example.The advantage of this method is simple and more readily applicable.the result is directly obtained by substitution.

On the nonlocal stabilization by starting control of the normal equation generated from the Helmholtz system

We consider the problem of stabilization near zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum.This problem was previously studied in Fursikov and Shatina(2018).As it was recently revealed,the control function suggested in that work contains a term impeding transferring the stabilization construction on the 3D Helmholtz system.The main concern of this paper is to prove that this term is not necessary for the stabilization result,and therefore the control function can be changed by a proper way.

SOME PROPERTIES OF LSQR FOR LARGE SPARSE LINEAR LEAST SQUARES PROBLEMS

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.

A priori, de novo mathematical exploration of gene expression mechanism via regression viewpoint with briefly cataloged modeling antiquity

Various algorithms have been devised to mathematically model the dynamic mecha- nism of the gene expression data. Gillespie＇s stochastic simulation （GSSA） has been exceptionally primal for chemical reaction synthesis with future ameliorations. Several other mathematical techniques such as differential equations, thermodynamic models and Boolean models have been implemented to optimally and effectively represent the gene functioning. We present a novel mathematical framework of gene expression, under~ taking the mathematical modeling of the transcription and translation phases, which is a detour from conventional modeling approaches. These subprocesses are inherent to every gene expression, which is implicitly an experimental outcome. As we foresee, there can be modeled a generality about some basal translation or transcription values that correspond to a particular assay.