Semigroups satisfying (xy)m = xmym

In this paper we characterize Archimedean semigroups with idempotents satisfying (xy)^m = x^my^m as exactly those semigroups which are a retract extension of a completely simple semigroup satisfying (xy)^m = x^my^m by a nil semigroup satisfying (xy)^m = x^my^m. Regular semigroups satisfying (xy)² = x²y² are exactly those semigroups which are a spined product of a band and a semigroup which is a semilattice of Abelian groups. A semigroup which is a nil extension of a regular semigroup satisfies (xy)² = x²y² if and only if it is a retract extension of a regular semigroup satisfying (xy)² = x²y² by a nil semigroup satisfying (xy)² = x²y²     

New β-delayed proton decays in the rare-earth region near the proton drip line

The β-delayed proton precursors 125Nd, 128Pm, 129Sm, 137Gd and 139Dy near the proton drip line were produced by the irradiation of 92Mo, 96Ru and 106Cd with an 36Ar beam, and conclusively identified for the first time by using proton-gamma coincidence in combination with a He-jet tape transport system. Their half-lives were determined to be 0.60(15)s,1.0(3)s,0.55(10)s,2.2(2)s and 0.6(2)s, respectively. The measured energy spectra of β-delayed protons and estimated proton branching ratios to the final states in "daughter" nuclei for the precursors 125Nd, 129Sm, 137Gd and 139Dy, as well as the previously reported ones for the precursors 135Gd and 121Ce, were fitted by a statistical model calculation. The ground-state spins and parities of 121Ce, 125Nd, 129Sm, 135Gd, 137Gd and 139Dy were then assigned as 5/2±,5/2±,1/2±(or 3/2+),5/2+,7/2± and 7/2, respectively. The consistency between the experimental spin-parity assignment and the predicted Nilsson diagrams indirectly indicates that the ground states of 121Ce, 125Nd, 129Sm, 135Gd, 137Gd and 139Dy are highly deformed with β2～0.3.     

Partition relations for uncountable ordinals

Partition relations of the form α→(α,m)², where α is an ordinal andm is a positive integer, are considered. Let κ be a cardinal. The following are proved: If κ is singular and 2^K=K ⁺ then (K⁺)²?((K⁺)²,3)². If κ is a strong limit cardinal, then², iff ((cfκ)²→((cfκ)²,m)². If κ is regular and K²→(K²,3)², then the κ-Souslin hypothesis holds. If K^ω<α+ and cfα=cfκ>ω, then α?(α,3)².     

New class of polynomials

Summary For the simple Bessel polynomials y_n(x), the Rodrigues' formula is y_n(x)==2⁻ⁿe^2/xDⁿ(x²ⁿe^−2/x). The present work generalizes the idea of the simple. Bessel polynomials of Krall-Frink. It is of great interest to investigate the class of polynomials which are closely connected with the Rodrigues' expression e^3/xDⁿ(x³ⁿe^−3/x) or more generally with e^k/xDⁿ(x^kne^−k/x).     

Complex Jordan operators

We prove that an operator J is of the form J = M + N where M is normal, N² = 0, and M commutes with N if and only if J satisfies the three equations J^*nJ³-3JJ^*nJ²+3J²J^*nJ-J³J^*n = 0, n = 1, 2, and 3.     

Lp (?m × ?n) boundedness for the Marcinkiewicz integral on product spaces

L^p(R^m × Rⁿ) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the L^p(R^m × Rⁿ) boundedness of the multiple Marcinkiewicz integral for some fixed 1 > p > ∞ are obtained.     

子流形的测地曲率

该文研究了黎曼齐次空间G/H中子流形M~p和子流形N~q的交M~p∩gN~q的测地曲率,其中g∈G为等距群,并把M~p∩gN~q的第二基本形式表示成M~p和N~q的测地曲率以及它们之间的夹角的组合.     

一类堆垒数论问题(Ⅰ)

§1 引言 堆垒数论中有一个著名的猜测: 设k_1,…,k_s是s个大于1的整数,且k_1≤k_2≤…≤k_s及sum from j=1 to s (k_j~(-1)>1)。又对每个素数p,对大的k,同余方程 X_1~(k_1)+X_2~(k_2)+…+X_s~(k_s)≡n(modp~k) 对某些j,P|x_j都有解,那末当n充分大时,方程     

Uniqueness of mild solutions of the Navier-Stokes equation and maximal Lp-regularity

In this Note, we give a new proof of the uniqueness of mild solutions of the Navier-Stokes equation in C([0,T) ; (L³(ℝ³))³). The main tool of the proof is the maximal L^p-regularity of the Laplacian in (L³ (ℝ³))³.     

Three-dimensional hyperelliptic manifolds

Let X³ = H³, E³, S³, H² × E¹, S² × E¹, T₁(H²), Nil of Solv be one of the eight 3-dimensional geometrics of Thurston [10] and G be a discrete group of isometrics of X³ acting without fixed points. A manifold M³ = X³/G is said to be hyperelliptic if there is an isometric involution on it such that the factor space M³/<> is diffeomorphic to the 3-sphere S³. In analogy with the theory of Riemann surfaces we call involution.In the present paper the existence of hyperelliptic manifolds in each light of the eight 3-dimensional geometrics will be obtained. All the proofs given there will be written in the language of orbifolds whose basic facts can be found in [9].     

Even permutations as a product of two elements of order five

Let A_n denote the alternating group on n symbols. If n = 5, 6, 7, 10, 11, 12, 13 or n ⩾ 15, every permutation in A_n is the product of two elements of order 5 in A_n. The same is true for n ⩽ 14, except for thirteen types of permutations, namely 3¹, 2², 2⁴, 3³, 2¹3¹4¹, 2²5¹, 2⁵4¹, 1¹, 1², 1³, 1⁴, 3¹1¹, 2⁴1¹. (For example, the permutation (12)(34)(56)(78)(9) is not the product of two elements of order 5 in A₉.)     

The translation planes admitting a nonsolvable doubly transitive line-sized orbit

The finite translation planes of ordern not in {3⁴,3⁶,11²,19²,29²,59² that admit a non-solvable doubly transitive line-sized orbit are completely classified.     

Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H<Superscript>1</Superscript>

Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H¹(Rⁿ), we shall show the asymptotic behavior for its solutions in C(0, ∖;H¹(Rⁿ)) ∩ L²(0, ∖;H^1,2n/(n-2)(R²)), n≥3. Analogous results also hold in the case that the nonlinearity has the subcritical power in H¹(Rⁿ), n≥1. Dedicated to Professor Zhou Yulin for his 80th birthday.     

On a family of relative quartic Thue inequalities

We consider the relative Thue inequalities

|X⁴−t²X²Y²+s²Y⁴|?²|t|−²|s|−2,     

关于复射影空间的三维全实极小子流形

本文给出复射影空间中三维紧致全实极小子流形的Ricci曲率和数量曲率的鞭些拼挤定理.特别是证得:若M³是CP³的紧致全实极小子流形且它的Ricci曲率大于1/6,则M³是全测地的.     

On the well-definedness of the order of an ordinary differential equation

It is proved that if the differential equations y ^{( n )}=f(x, y, y′, …, y ^{( n ?1 )}) and y ^{( m )}=g(x, y, y′, …, y ^{( n ?1 )}) have the same particular solutions in a suitable region where f and g are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical Lipschitz condition), then n?=?m and the functions f and g are equal. This note could find classroom use in a course on differential equations as enrichment material for the unit on the existence and uniqueness theorems for solutions of initial value problems.     

广义逆多项式模的Attached素理想

设R是有单位元1的结合环,(S,≤)是严格全序Artin幺半群,M_R是右R-模,Att(M_R)与Att([M~(S,≤)]_([[R~(S,≤)]]))分别表示模M_R与广义逆多项式模[M~(S,≤)]_([[R~(S,≤)]])的所有Attached素理想组成的集合.该文主要讨论了广义幂级数环[[R~(S;≤)]]广义逆多项式模[[R~(S;≤)]]的Attached素理想的相关性质,证明了在一定条件下,有Att([M~(S,≤)]_([[R~(S,≤)]])={[[PR~(S;≤)]]P∈Att(M_R)}.这一结论表明广义逆多项式模([M~(S,≤)]_([[R~(S,≤)]])的Attached素理想在一定条件下可以用模M_R的Attached素理想来刻画,推广了Annin S在文献[1]中关于斜多项式环上逆多项式模的Attached素理想的相关结论.     

Reverse Order Law for the Group Inverse in Semigroups and Rings

In this paper, we provide equivalent conditions for the two-sided reverse order law for the group inverse (ab)^# = b ^# a ^# and (ba)^# = a ^# b ^#, in semigroups and rings. Moreover, we prove that, under finiteness conditions, these conditions are also equivalent with the one-sided reverse order law (ab)^# = b ^# a ^#.     

Separability and entanglement in tripartite states

While classical correlations can be freely distributed among many systems, this is not true for entanglement and quantum correlations. If a quantum system S^a is entangled with another quantum system S^b, then its entanglement with any third quantum system S^c cannot be arbitrary. This is the celebrated monogamy of entanglement. Implicit in this general statement is the plausible belief that only entanglement between the systems S^a and S^b constrains the entanglement between S^a and the third system S^c. We demonstrate that even classical correlations between S^a and S^b may impose surprisingly stringent restrictions on the possible entanglement between S^a and S^c. In particular, perfect bipartite classical correlations and full entanglement cannot coexist in any tripartite state. An intuitive explanation of this monogamy of hybrid classical and quantum correlations might be that the system S^a has a correlating capability, which cannot be used to establish any entanglement with a third system (but can still be used to establish classical correlations) if it is exhausted when correlated with S^b (in either a classical or quantum fashion). This may be interpreted as an alternate version of monogamy.     

Further results on the reverse-order law

An explicit expression is obtained for a pair of generalized inverses (B^?,A^?) such that B^?A^?=(AB)⁺_MN, and a class of pairs (B^?,A^? of this property is shown. A necessary and sufficient condition for (AB)^? to have the expression B^?A^? is also given.