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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On cancellation laws in cardinal arithmetic without the axiom of choice
选择公理 基数算术 取消定律
2023/4/17
We survey known results concerning cancellation laws in cardinal arithmetic without the axiom of choice. These results include the cancellation law for Dedekind finite cardinals in cardinal addition a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Low regularity conservation laws for the fifth-order modified KdV equations in Besov spaces
Besov空间 五阶修正KdV方程 低正则性 守恒定律
2023/4/19
We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expa...
From crystal steps to continuum laws:Behavior near large facets in one dimension
Crystal surface Epitaxial relaxation Self-similar solution Burton–Cabrera–Frank (BCF) model Facet Macroscopic limit
2015/10/16
The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by exp...
BOSE-EINSTEIN CONDENSATION AT FINITE TEMPERATURES:MEAN FIELD LAWS WITH PERIODIC MICROSTRUCTURE
quantum dynamics Bose-Einstein condensation periodic homogenization finite temperatures two-scale expansion mean field limit
2015/10/16
At finite temperatures below the phase transition point, the Bose-Einstein condensation, the macroscopic occupation of a single quantum state by particles of integer spin, is not complete. In the lang...
Compact Central WENO Schemes for MultiDimensional Conservation Laws
hyperbolic systems central difference schemes high-order accuracy nonoscillatory schemes WENO reconstruction CWENO reconstruction
2015/10/8
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes, our method is based on r...
On the Behavior of the Total Variation in CWENO Methods for Conservation Laws
Hyperbolic conservation laws Central difference schemes High-order accuracy Non-oscillatory schemes CWENO reconstruction TVB
2015/10/8
We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interest...
Third-order 2D Central Schemes for Hyperbolic Conservation Laws
Two-dimensional framework system the law of conservation of two-dimensional euler equation the high resolution
2015/10/8
We extend a one-dimensional central-scheme first introduced by Liu and Tadmor, to the rather general framework of two-dimensional systems of conservation laws. This scheme is based on a two-dimensiona...
Moderate dispersion in scalar conservation laws
Travelling waves moderate dispersion Korteweg de Vries equation entropy solutions dissipative-dispersive scalar conservation laws
2015/7/14
We consider the weakly dissipative and weakly dispersive Burgers-Hopf-Korteweg-de-Vries equation with the diffusion coefficient ε and the dispersion rate δ in the range δ/ε → 0. We study thetravelling...
POWER LAWS FOR MONKEYS TYPINGS RANDOMLY: THE CASE OF UNEQUAL PROBABILITIES
TYPINGS RANDOMLY UNEQUAL PROBABILITIES
2015/7/6
The case where letters are hit with unequal probability has been the subject of recent confusion, with
some suggesting that in this case the rank-frequency distribution follows a lognormal distributi...
Exact Boundary Conditions for the Initial Value Problem of Convex Conservation Laws
exact boundary conditions artificial boundary conditions convex conservation laws Burgers’ (inviscid) equation
2015/5/4
The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in the-oretical analysis for conservation laws, but also...
Accuracy of Classical Conservation Laws for Hamilton PDES Under Runge-Kutta Discretizations
Accuracy of Classical Conservation Laws Hamilton PDES Runge-Kutta Discretizations
2012/8/7
We investigate conservative properties of Runge-Kutta methods
for Hamiltonian PDEs. It is shown that multi-symplecitic Runge-Kutta meth-
ods preserve precisely norm square conservation law. Based on...
The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws
Two-Component Camassa-Holm Equations CH(2,1) CH(2,2) First-Order Integrating Factors Conservation Laws Exactly Solvable and Integrable Systems
2012/4/26
Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: g...
Some Critical Support for Power Laws and their variations
Some Critical Support Power Laws their variations Adaptation and Self-Organizing Systems
2012/4/26
The paper "Critical Truths About Power Laws" (Science, 335, pp665-666) by MPH Stumpf MPH and MA Porter is commented.
Global classical solutions for partially dissipative hyperbolic system of balance laws
balance laws entropy dissipative classical solutions Chemin-Lerner’s spaces
2012/2/29
This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a gener...
An extension of the modified Sawada-Kotera equation and conservation laws
fundamental mathematics spectralproblem integrable nonlinear evolution equations conservationlaws
2011/10/15
Based onthe modified Sawada-Kotera equation, we introduce a 3×3 matrix spectral problem with two potentials and derive a hierarchyof new nonlinear evolution equations. The second member in thehierarch...