N(2,2,0)代数的E-反演半群

本文研究了N(2,2,0)代数(S,*,△,0)的E-反演半群.利用N(2,2,0)代数的幂等元,弱逆元,中间单位元的性质和同宇关系,得到了N(2,2,0)代数的半群(S,*)构成E-反演半群的条件及元素α的右伴随非零零因子唯一,且为α的弱逆元等结论,这些结果进一步刻画了N(2,2,0)代数的结构.     

Cauchy problem F(t, x(t), x′(t)) = 0, x(0) = 0: solvability and asymptotics of solutions

For the singular Cauchy problem, the authors find some sufficient conditions for the existence of continuously differentiable solutions x: (0, ρ] → ℝ (ρ > 0 is sufficiently small) of the form

Lie Symmetries of the Equation ut(x, t)?+?g(u)ux(x, t) = 0

In this paper the invariance criterion is applied for the nonlinear equation

On solutions of functional-differential equations f ′( x ) = a ( x ) f ( g ( x )) + b ( x ) f ( x ) + c ( x ) in the large

We consider solutions of functional-differential equations

Rn+1上self-shrinkers的谱特征

本文研究了self-shrinkers谱与几何的关系.利用渐进展开式系数相等的方法,获得了如下结果:设M是R~(n+1)上的n(n≥2)维闭self-shrinkers,且M和s~n(2n~(1/2))有相同的平均曲率,如果spec~p(M)=spec~p(s~n(2n~(1/2)),则M是s~n(2n~(1/2),并推广了R~(n+1)上self-shrinkers的特征.     

Complete description of invariant Einstein metrics on the generalized flag manifold SO(2n)/U(p)?× U(n ? p)

We find the precise number of non-K?hler SO(2n)-invariant Einstein metrics on the generalized flag manifold M = SO(2n)/U(p)×U(n−p) with n ≥ 4 and 2 ≤ p ≤ n−2. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems. We also examine the isometric problem for these Einstein metrics.     

Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L2((a, b) × (c, d); p(x)q(y))

Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials in some classes of functions and for the Kolmogorov N-widths of these classes. These results find applications in numerical analysis. Original Russian Text ? V.A. Abilov, M.K. Kerimov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 8, pp. 1364–1368.     

矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解

本文研究了矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解问题.利用矩阵的Kronecker积和Moore-Penrose广义逆方法,得到了矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解的表达式.     

Connected subgroups of SO(2, n) acting irreducibly on ?2,n

We classify all connected subgroups of SO(2, n) that act irreducibly on ℝ^{2, n} . Apart from SO ₀(2, n) itself these are U(1, n/2), SU(1, n/2), if n even, S ¹ · SO(1, n/2) if n even and n ≥ 2, and SO ₀(1, 2) for n = 3. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian conformal structures, namely SO ₀(2, n), SU(1, n), and SO ₀(1, 2).     

Controlled algebraic K-theory of integral group ring of SL(3, ?)

We calculate the lower Controlled Algebraic K-theory of any finitely generated infinite subgroup of SL(3,Z), the group of 3×3 integral matrices of determinant 1.     

On the Diophantine Equation G n ( x )?= G m ( P ( x ))

 Let K be a field of characteristic 0 and let p, q, G ₀ , G ₁ , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G _n (x)) _n=0 ^∞ be defined by the second order linear recurring sequence

On the Diophantine Equation G n ( x )?= G m ( P ( x ))

 Let K be a field of characteristic 0 and let p, q, G ₀ , G ₁ , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G _n (x)) _n=0 ^∞ be defined by the second order linear recurring sequence

Weyl’s theorem for algebraically wF(p, r, q) operators with p, r?>?0 and q?≥?1

If T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting in an infinite-dimensional separable Hilbert space, then we prove that Weyl’s theorem holds for f(T) for any f ∈ Hol(σ(T)), where Hol(σ(T)) is the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl’s theorem holds for f(T). In addition, if T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1, then we establish the spectral mapping theorems for the Weyl spectrum and for the essential approximate point spectrum of T for any f ∈ Hol(σ(T)), respectively. Finally, we examine the stability of Weyl’s theorem and the a-Weyl’s theorem under commutative perturbations by finite-rank operators.     

A(α)-Acceptability of Rational Approximations to Function exp(z)

In this paper, two necessary and sufficient conditions, and a sufficient condition of A()-acceptability for (n, m) rationa approximation to function exp(z) are given, where a (0, x/2). A necesary and sufficient condition of A-acceptability for (n, m) rational approximation to exp(z) of order p is obtained, where nmp.     

Complete ( q 2?+ q +?8)/2-caps in the spaces PG (3, q ), q ≡ 2 (mod 3) an odd prime, and a complete 20-cap in PG (3, 5)

An infinite family of complete (q ² + q + 8)/2-caps is constructed in PG(3, q) where q is an odd prime ≡ 2 (mod 3), q ≥ 11. This yields a new lower bound on the second largest size of complete caps. A variant of our construction also produces one of the two previously known complete 20-caps in PG(3, 5). The associated code weight distribution and other combinatorial properties of the new (q ² + q + 8)/2-caps and the 20-cap in PG(3, 5) are investigated. The updated table of the known sizes of the complete caps in PG(3, q) is given. As a byproduct, we have found that the unique complete 14-arc in PG(2, 17) contains 10 points on a conic. Actually, this shows that an earlier general result dating back to the Seventies fails for q = 17.      

Gaussian Estimates of Order α and L p -Spectral Independence of Generators of C 0-Semigroups

We prove L^p-spectral independence for generators of C₀-semigroups estimated by the positive C₀-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C₀-semigroup .     

The Rν-generalized solution of a boundary value problem with a singularity belongs to the space W2,ν+β2+κ+1/κ+2 (Ω, δ)

In the present paper, for a boundary value problem with noncoordinated degeneration of the data and a singularity in the solution, we show that the R _ν -generalized solution belongs to the weighted space W _2,ν+gb ^2+κ+1/κ+2 (Ω, δ)(κ > 0). Original Russian Text ? V.A. Rukavishnikov, E.V. Kuznetsova, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 6, pp. 894–898.     

Linearizability of d-webs, d?≥?4, on two-dimensional manifolds

We find d – 2 relative differential invariants for a d-web, d 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g₄(x, y),..., g_d(x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g₄, and d – 4 PDEs of the second order with respect to f and g₄,..., g_d. For d = 4, this result confirms Blaschkes conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give the Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage.     

方程x'(t)=ax(t)+bx(3[(t+1)/3])的数值稳定性分析

本文研究了分段连续型微分方程x''(t)=ax(t)+bx(3[(t+1)/3]) Euler-Maclaurin方法的数值稳定性问题.利用特征分析的方法,获得了数值解稳定的充分条件,进而证明了Euler-Maclaurin方法保持了精确解的稳定性.最后给出了一些数值例子.     

唯一g(x)-clean环

本文研究了唯一g(x)-clean环的性质与结构.利用g(x)-clean环的方法,得到了唯一g(x)-clean环与g(x)-clean环的关系,唯一g(x)-clean环与一类特殊的生成环的等价条件,以及斜Hurwitz级数环的g(x)-clean性,推广了g(x)-clean环的研究结果.