Uniqueness of Solution of the Initial Value Problem for ut=ΔUm-up

The uniqueness of solution of the Cauchy problem u_t = Δu^m - u^p, \qquad S_T = R^n × (0, T) u(x, 0) = Φ(x), \qquad × ∈ R^n is obtained. Where n ≥ 1, m, p > 0, Φ(x) ∈ L^∞(R^n), Φ(x) ≥ 0.     

On the Local Regularity of Solutions for Double Degenerate Nonlinear Parabolic Equations (uq-1)t=div(|ΔU|p-2ΔU) When 1

In this paper, we establish interior Hölder estimates of solutions for double degenerate nonlinear parabolic equations (u^{q-1})_t = div (|∇u|^{p-2}∇u) when 1 < p < 2, p ≤ q.     

关于ut= div(|▽u|p-2▽u)方程解的梯度H?lder连续性的一个注记

对文献［１－３］中的结果：u_t= div(|▽u|^p-2▽u)在ΩＴ＝Ω×（０，Ｔ）上弱解的空间梯度是Ｈ?ｌｄｅｒ连续的做一个补充．在这个注记里，讨论了条件ｐ＞ｍａｘ｛１，２Ｎ/Ｎ＋２｝是怎样由ｕ的性质所决定的．属于L^N_loc(Ω_T)空间解的梯度是Ｈ?ｌｄｅｒ连续的条件仅仅是ｐ＞１．     

On the asymptotic behavior of radial entire solutions for the equation (−Δ)3u = up in Rn

Our main task in this note is to prove the existence and to classify the exact growth at infinity of radial positive $C^6$-solutions of ${(?\mathrm{\Delta })}^{3}u=u^p$ in ${\mathbf{R}}^n$, where $n?15$ and p is bounded from below by the sixth-order Joseph–Lundgren exponent. Following the main work of Winkler, we introduce the sub- and super-solution method and comparison principle to conclude the asymptotic behavior of solutions.     

Search for JPC=even++ glueballs in radiative decay of J/Ψ

Based on the general analysis of decay width and branching ratio of two pseudo scalar meson channels, two sets of discriminants between mesons and glueballs for1 = 0,J ^PC = even⁺⁺ unflavored hadrons with the mass between 1.2 and 2.9 GeV are suggested. Known1 = 0,J ^PC = 2⁺⁺, f₂(1525) particle is discriminated as a typical meson. The way to discriminate new1 = 0,J ^PC = even⁺⁺ unflavored hadrons is discussed.     

关于方程ax+by=cz的Terai-Jesmanowicz猜想

设m是正整数,证明了(A)如果b是奇素数,且a=m3-3m,b=3m2-1,c=m2+1,那么丢番图方程ax+by=cz(1)仅有正整数解(x,y,z)=(2,2,3);(B)如果b是奇素数,且a=m|m4-10m2+5|,b=5m4-10m2+1,c=m2+1,那么丢番图方程(1)仅有正整数解(x,y,z)=(2,2,5).     

Some extremal properties of multivariate polynomial splines in the metric Lp(?d)

We constructed a kind of continuous multivariate spline operators as the approximation tools of the multivariate functions on the (ℝ^d instead of the usual multivariate cardinal interpolation operators of splines, and obtained the approximation error by this kind of spline operators. Meantime, by the results, we also obtained that the spaces of multivariate polynomial splines are weakly asyrnptotically optimal for the Kolrnogorov widths and the linear widths of some anisotropic Sobolev classes of smooth functions on (ℝ^d in the metric L_p((ℝ^d).     

On qualitative analysis of delay systems and xΔ = f(t, x, xσ) on time scales

Here we solve two problems presented in paper [9] (C C Tisdell and A Zaidi, Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal. 68 (2008) 3504–3524). We study existence and uniqueness of solutions for delay systems and first-order dynamic equations of the form x ^Δ = f (t,x,x ^σ ) on time scales by using the Banach’s fixed-point theorem. Some examples are presented to illustrate the efficiency of the proposed results.     

关于Diophantine 方程xn+2kyn=pz2

设p 为奇素数且对任意的整数m, d, p≠(2^m±1)=/d², 则对任意的素数n > p^8p2, 方程xⁿ+2^kyⁿ=pz², k≥2 没有整数解(x, y, z) 使得x, y, z 两两互素且均不为0.     

范畴MΔ中的正合列

本文研究域上矩阵给出的范畴,给出了正合性的等价刻画,提出了将正合列理论应用于矩阵论的途径．     

Anick Resolution and the Minimal Projective Resolution of Uq+(C3)

In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C₃, we compute the minimal projective resolution of the trivial module U_q⁺(C₃)and as an application,we obtain that the global dimension of U_q⁺(C₃) is 9.     

Embedding of Hpω in the class eL

We obtain the necessary conditions for the embedding H _p ^ω ⊂ e ^L (1≤p∞) with convex modulus of continuity ω in terms of this modulus. In the case p=1 these conditions are also sufficient.