弱加法范畴的特殊根和Brown—McCoy根

引言 [1]中将象元类是I的加法范畴记作A=∪_αA_β,其中_αA_β表示Hom(α,β)中所有态射之集。据范畴的定义,对于任意α∈I,_αA_α中必有单位元_α|_α,从而对于范畴中规定的加法和乘法来说,_αA_α作成一个有单位元的结合环,今将加法范畴中去掉_αA_α必有单     

关于一般域上的三个对合之积

本文改进了C.S.Ballantine和Kang-Man Liu关于3个对合之积的一些结论。对任意域F，我们证明了，当A∈GL /3（F）时，A是3个对合之积当且仅当对任意α∈F，α^2≠1，有rank(A-αI3)≥1；当A∈GL /4（F）时，A是3个对合之积当且仅当对任意α∈F，α^4≠1，有rank(A-αI4)≥2或A与B=αI3(○ )α^-3相似，当A∈GL /5（F）时，A是3个对合之积当且仅当对任意α∈F，α^4≠1，有rank(A-αI5)≥2且A不与B=αI3(○ )（-det A)I2相似。     

AOR方法的最优因子及效果分析

在[1]中提出了解线性代数方程组 A_x=b (1)的AOR方法: x~(m 1)=L_(α,ω)x~(m) ω(I-αL)~(-1)b, (2 L_(α,ω)=(I-αL)~(-1)[(1-ω)I (ω-α)L ωU], (3)其中A=I-L-U,L,U分别为严格下、上三角矩阵。AOR方法主要用于求解椭圆型离散化方程组,故上面可设diag(A)=I。现记B=L U。 当(2),(3)中两个参数取相同值时,AOR方法退化为相应参数的SOR方法。一个自然的问题是:能否在(2),(3)中选取适当的参数α,ω,使相应的AOR方法比最优参     

BCI—代数的积代数

我们先引入一族BCI-代数的积代数。定理1 设(α∈I)是一族BCI-代数,其中I是指标集。设X=π{X_α:α∈I}是一切映射f:I?U{X_α:α∈I}的集合,使得f(α)∈X_α。对于任意的f,g∈X,定义f*g为     

Existence and multiplicity of normalized solutions for a class of fractional Choquard equations

In this paper, we study the existence and multiplicity of solutions with a prescribed L2-norm for a class of nonlinear fractional Choquard equations in RN:(-△)su-λu =(κα*|u|p)|u|p-2u,where N≥3,s∈(0,1),α∈(0,N),p∈(max{1 +(α+2s)/N,2},(N+α)/(N-2s)) and κα(x)=|x|α-N. To get such solutions,we look for critical points of the energy functional I(u) =1/2∫RN|(-△)s/2u|2-1/(2p)∫RN(κα*|u|p)|u|p on the constraints S(c)={u∈Hs(RN):‖u‖L2(RN)2=c},c >0.For the value p∈(max{1+(α+2s)/N,2},(N+α)/(N-2s)) considered, the functional I is unbounded from below on S(c). By using the constrained minimization method on a suitable submanifold of S(c), we prove that for any c>0, I has a critical point on S(c) with the least energy among all critical points of I restricted on S(c). After that,we describe a limiting behavior of the constrained critical point as c vanishes and tends to infinity. Moreover,by using a minimax procedure, we prove that for any c>0, there are infinitely many radial critical points of I restricted on S(c).     

阻尼层对泡沫铝芯三明治板隔声特性的影响分析

以泡沫铝芯三明治板为研究对象,采用混响室隔声测试研究铺设阻尼层对其隔声量的影响。基于统计能量法理论,用VA One软件对其进行隔声量仿真分析及建模验证。基于验证模型,进一步分析了阻尼材料厚度及材料密度对复合板隔声量的影响。试验结果表明,铺设6 mm阻尼对泡沫铝芯三明治板整体隔声性能提高,尤其是高频区域隔声量有显著提升,高达10 d B。VA One统计能量法仿真预测结果表明,对铺设阻尼的泡沫铝芯三明治板进行隔声量趋势预测计算是可行有效的,且参数调研结果表明,阻尼层厚度对三明治板隔声量有一定程度影响,阻尼厚度每增加1 mm高频区域隔声量提高约2 d B;阻尼材料密度对复合板隔声量影响不大。相关结果为泡沫铝芯三明治板隔声优化提供参考。     

求解奇异摄动转向点问题的一个高阶格式

§1.引言本文考虑以下奇异摄转向点问题: (1.1)这里参数ε是(0,1]中常数,函数α(x)∈C~2[I],b(x),f(x)∈C~3[I],且满足α(x)≥α_*>0,b(x)≥b_*>0,在以上假设下,由[2]可知,方程(1.1)存在唯一解u_ε∈C~4[I],且满足以下不等式     

Bα空间与 Laplace 算子的某些估计

本文共分两部分.第一部分将提供一类新的函数空间,即 Ba 空间,并较详细地研究它们的性质.这类空间包括经典的某些 Orlicz 空间,Orlicz—Sobolev 空间,等等,它们具有某些与 Orlicz 空间类似地性质.但它们包含的内容广泛得多.由于这类空间的研究与应用主要是建立在经典的 Lebesgue 类 L_p 上,所以方法比较自然,结果更加精确.设 B={B_1…,B_m,…)为一串线性赋范函数空间,a={a_1,…,a_m,…}为一串非负实数,φ(z)=Σα_nz~n 为整函数,对于 f∈∩B_m 构成幂级数I(f,α)=Σα_m‖f‖_B_m~mα~m.(I.1)如 I(f,α)具非负收敛半径,我们则称 f∈BL(φ)或记为 B_α,或记为(B_m,α_m,),记 I(f,1)=I(f).空间 BL(φ)的范数定义为‖f‖_Bα=(?){1/α}(I.2)简记为‖f‖.容易证明‖f‖满足范数三条件,如 I(f,α)为α的整函数,则称 f∈BE(φ)或记为 aB,或记为(a_m,B_m),其范数的定义与(I,2)同.aB 构成 Ba 之一子空间.如果取 B_m=L_m,则 Ba≡Orlicz 空间 Lφ,如果取 B_m=W_m~l,则 Ba≡Orlicz— Sobolev 空间 W~lLφ.我们过去实际上是把一些特殊的 Ba 空间应用到差分法的误差估计,强非线性变分问题等等.在本文中,我们探讨这种空间的某些基本性质,诸如完备性,可分性,列紧性,线性泛函,弱收敛,等等.第二部分,实际上是把这种空间用     

The Hausdorf dimension of certain sets in a class of α-Lroth expansions

In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.     

The Hausdorff dimension of certain sets in a class of α-Lüroth expansions

In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.     

Convergence of the Klein-Gordon equation to the wave map equation with magnetic field

This paper is devoted to the proof of the convergence from the modulated cubic nonlinear defocusing Klein-Gordon equation with magnetic field to the wave map equation. More precisely, we discuss the nonrelativistic-semiclassical limit of the modulated cubic nonlinear Klein-Gordon equation with magnetic field where the Planck's constant ?=ε and the speed of light c are related by c=ε−α for some α?1. When α=1 the limit wave function satisfies the wave map with one extra term coming from the magnetic field. However, α>1, the effect of the magnetic filed disappears and the limit is the typical wave map equation only.     

Convergence to the rarefaction wave for a model of radiating gas in one-dimension

In this paper, a sequence of solutions to the one-dimensional motion of a radiating gas are constructed. Furthermore, when the absorption coefficient α tends to ∞, the above solutions converge to the rarefaction wave, which is an elementary wave pattern of gas dynamics, with a convergence rate \(\alpha ^{ - \tfrac{1}{3}} \left| {\ln \alpha } \right|^2\).     

Global stability of traveling wave fronts for non-local delayed lattice differential equations

This paper is concerned with the global stability of traveling wave fronts of a non-local delayed lattice differential equation. By the comparison principle together with the semi-discrete Fourier transform, we prove that, all noncritical traveling wave fronts are globally stable in the form of t^−1/αe^−μt for some constants μ>0 and 0<α≤2, and the critical traveling wave fronts are globally stable in the algebraic form of t^−1/α.     

The scaling window of the 2‐SAT transition

We consider the random 2‐satisfiability (2‐SAT) problem, in which each instance is a formula that is the conjunction of m clauses of the form x∨y, chosen uniformly at random from among all 2‐clauses on n Boolean variables and their negations. As m and n tend to infinity in the ratio m/n→α, the problem is known to have a phase transition at α_c=1, below which the probability that the formula is satisfiable tends to one and above which it tends to zero. We determine the finite‐size scaling about this transition, namely the scaling of the maximal window W(n, δ)=(α_?(n,δ), α₊(n,δ)) such that the probability of satisfiability is greater than 1?δ for α<α_? and is less than δ for α>α₊. We show that W(n,δ)=(1?Θ(n^?1/3), 1+Θ(n^?1/3)), where the constants implicit in Θ depend on δ. We also determine the rates at which the probability of satisfiability approaches one and zero at the boundaries of the window. Namely, for m=(1+ε)n, where ε may depend on n as long as |ε| is sufficiently small and |ε|n^1/3 is sufficiently large, we show that the probability of satisfiability decays like exp(?Θ(nε³)) above the window, and goes to one like 1?Θ(n^?1|ε|^?3 below the window. We prove these results by defining an order parameter for the transition and establishing its scaling behavior in n both inside and outside the window. Using this order parameter, we prove that the 2‐SAT phase transition is continuous with an order parameter critical exponent of 1. We also determine the values of two other critical exponents, showing that the exponents of 2‐SAT are identical to those of the random graph. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 201–256 2001     

On the role of separation in compression wave generation by a train entering a tunnel hood with a window

An approximate analytical theory is proposed for calculatingthe compression wave generated when a train enters a tunnelfitted with an entrance hood with an open window. The pressurerise ahead of the entering train causes air to exhaust fromthe window in the form of a high-speed jet. The profile of thecompression wave transmitted into the tunnel is modified by theinteraction of the train nose with the window, by multiple reflectionsof wave energy between the window and the hood portal priorto transmission into the tunnel, and in addition by the productionof a pressure pulse by the jet. The wave generation problemcan be formulated in a quasi-one-dimensional manner, wherebythe pressure field generated in front of and to the sides ofthe train in the absence of the window is assumed to be scatteredby the window. A self-consistent solution is obtained by evaluatingthe jet flow from the window using a nonlinear empirical quationproposed and validated by Cummings (1984, Amer. Inst. Aeron.Astron. J., 22, 786–792; 1986, J. Acoust. Soc. Amer.,79, 942–951) for the velocity in the window-exit plane.Predictions are found to be in excellent agreement with measurementsof compression wave profiles obtained in model scale experimentsreported by Howe et al. (2003, J. Fluid Mech., 487, 211–243)at train speeds 350 km h^–1.     

分离变量法在变系数(2+1)维方程求解中的应用

分离变量法是求解具有局域相干结构解的有效解析方法.考虑到传播介质的非均匀性和边界的不一致性,变系数(2+1)色散长波方程可以实际地描述宽广的河道或有限深的远海中非线性波的传播.解析研究了变系数(2+1)维色散长波方程.通过分离变量法,得到了该方程组的具有丰富结构的分离变量解.     

推广的KdV方程特征问题解的存在唯一性

推广的KdV方程u_t+αuu_x+μu_x3+εu_x5=0[1]是典型的可积方程.它先后在研究冷等离子体中磁声波的传播[2],传输线中孤立波[3]和分层流体中界面孤立波[4]时导出.本文对推广的KdV方程的特征问题,在Riemann函数的基础上,设计一恰当结构,并由此化待征问题为一与之等价的积分微分方程.而该积分微分方程对应的映射E是列自身的映射[5],依不动点原理,积分微分方程有唯一的正则解,即推广的KdV方程的特征问题有唯一解,且由积分微分方程序列所得的迭代解于Ω上一致收敛.     

Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions

In this paper, the window function, e^−αk2, is applied to regularize the divergent problem which occurs in the Laplace equation with overspecified boundary conditions in an infinite strip region. To deal with this ill-posed problem, the corner of the L-curve is chosen as the compromise point to determine the optimal α of the Gaussian window, e^−αk2, so that the high wave-number (k) content can be suppressed instead of engineering judgement using the concept of a cutoff wave-number. From the examples shown, it is found that a reasonable solution of the unknown boundary potential can be reconstructed, and that both high wave-number content and divergent results can be avoided by using the proposed regularization technique.     

关于虚二次域类数的可除性

设α＞１，ｂ＞１，（α，ｂ）＝１，ｈ（－αｂ）表虚二次域的类数。如果有正整数ｘ，ｙ，ｎ，ｋ满足（１）αｘ￣２＋ｂｙ￣２＝４ｋ￣ｎ，ｂ且；或（２）αｘ￣２＋ｂｙ￣２＝ｋ￣ｎ，ｘ｜α，ｙ｜ｂ且αｂ≡２（ｍｏｄ４），则本文证明了关于ｈ（－αｂ）的可除性的两个定理（见定理１，２），其中符号ｘ｜α表示ｘ的每一个素因子整除α。     

On the strong law of large numbers for delayed sums and random fields

A paper by Chow [3] contains (i.a.) a strong law for delayed sums, such that the length of the edge of the nth window equals n ^α for 0 < α < 1. In this paper we consider the kind of intermediate case when edges grow like n=L(n), where L is slowly varying at infinity, thus at a higher rate than any power less than one, but not quite at a linear rate. The typical example one should have in mind is L(n) = log n. The main focus of the present paper is on random field versions of such strong laws.