Elementary characterizations of generalized weighted Morrey-Campanato spaces

Let α∈ (0,∞), p, q ∈ [1,∞), s be a nonnegative integer, and ω∈ A1(Rn) (the class of Muckenhoupt's weights). In this paper, we introduce the generalized weighted Morrey-Campanato space L(α, p, q, s, ω; Rn) and obtain its equivalence on different p ∈ [1,β) and integers s ≥ nα (the integer part of nα), where β = (1q - α)-1 when α 1q or β = ∞ when α≥ 1q. We then introduce the generalized weighted Lipschitz space ∧(α, q, ω; Rn) and prove that L(α, p, q, s, ω; Rn)  ∧(α, q, ω; Rn) when α∈ (0,∞), s ≥ nα , and p ∈ [1,β).     

The Blow-up Rate of Positive Solution of a Parabolic System

This paper deals with the blow-up properties of solutions to a system of semilinear heat equations with the boundary conditions u(x,t)=v(x,t)=0 on SR×[0,T).The exact estimates on blow-up rate of solutions are established.     

Large time behavior and pointwise estimates for compressible Euler equations with damping

The Cauchy problem of the compressible Euler equations with damping in multi-dimensions is considered when the initial perturbation in H3-norm is small. First, by using two new energy functionals together with the Green's function and iteration method, we improve the L2-decay rate in Tan and Wang(2013)and Tan and Wu(2012)when(ρ0-ˉρ,m)˙B-s1,∞×˙B-s+11,∞with s∈[0,2]is bounded.In particular,it holds that the density converges to its equilibrium state at the rate(1+t)-34-s2 in L2-norm and the momentum decays at the rate(1+t)-54-s2 in L2-norm.Moreover,under a weaker and more general condition on the initial data,we show that the density and the momentum have different pointwise estimates in dimension d with d 3on both space variable x and time variable t as|Dαx(ρ-ˉρ)|C(1+t)-d2-|α|2(1+|x|21+t)-rwith rd2and|Dαxm|C(1+t)-d2-|α|+12(1+|x|21+t)-d2 by a more elaborate analysis on the Green’s function.These results improve those in Wang and Yang(2001),where the density and the velocity(the momentum)have the same pointwise estimates.     

本刊英文版2015年58卷第5期摘要（英文）

<正>Wellposedness of some quasi-linear Schrodinger equations CHEMIN Jean-YvesSALORT Delphine Abstract This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g.We first prove that,in this context,the propagation of regularity holds which ensures local wellposedness for initial data small enough in H~(1/2)and belonging to the Besov space B_(2,1)~(3/2).In a second step,we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence     

The Inviscid Limit for the Steady Incompressible Navier-Stokes Equations in the Three Dimension*

In this paper, the authors consider the zero-viscosity limit of the three dimensional incompressible steady Navier-Stokes equations in a half space R⁺×R². The result shows that the solution of three dimensional incompressible steady Navier-Stokes equations converges to the solution of three dimensional incompressible steady Euler equations in Sobolev space as the viscosity coefficient going to zero. The method is based on a new weighted energy estimates and Nash-Moser itera...     

QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Let Xt(x) be the solution of stochastic dierential equations with smooth and bounded derivatives coeffcients. Let Xnt(x) be the Euler discretization scheme of SDEs with step 2-n. In this note, we prove that for any R 0 and γ∈(0, 1/2), supt∈[0,1],|x|≤R |Xnt(x, ω)- Xt(x, ω)|≤ξR,γ(ω)2-nγ, n≥1, q.e., where ξR,γ(ω) is quasi-everywhere finite.     

Convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations

We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method.     

RETRACTED ARTICLE: A uniqueness lemma with applications to regularization and incompressible fluid mechanics

In this paper,we extend our previous result from Lévy(2016).We prove that transport equations with rough coefficients do possess a uniqueness property,even in the presence of viscosity.Our method relies strongly on duality and bears a strong resemblance to the well-known DiPerna-Lions theory first developed by DiPerna and Lions(1989).This uniqueness result allows us to reprove the celebrated theorem of Serrin(1962)in a novel way.As a byproduct of the techniques,we derive an L¹ bound for the vorticity in terms of a critical Lebesgue norm of the velocity field.We also show that the zero solution is unique for the 2D Euler equations on the torus under a mild integrability assumption.     

Parameterized Littlewood-Paley Operators on Weighted Herz Spaces

The strong type and weak type estimates of parameterized Littlewood-Paley operators on the weighted Herz spaces K_q~(α,p) (ω_1, ω_2) are considered. The boundedness of the commutators generated by BMO functions and parameterized Littlewood-Paley operators are also obtained.     

Zero dissipation limit of the compressible heat-conducting navier-stokes equations in the presence of the shock

The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ = O（ε）, κ/ε≥ c 〉 0, as ε→ 0 （see （1.3））, if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier–Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.