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     

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).     

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.     

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.     

A new upper bound on the cyclic chromatic number

A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number χ^c. Let Δ^* be the maximum face degree of a graph. There exist plane graphs with χ^c = ?3/2 Δ^*?. Ore and Plummer [ 5 ] proved that χ^c ≤ 2, Δ^*, which bound was improved to ?9/5, Δ^*? by Borodin, Sanders, and Zhao [ 1 ], and to ?5/3,Δ^*? by Sanders and Zhao [ 7 ]. We introduce a new parameter k^*, which is the maximum number of vertices that two faces of a graph can have in common, and prove that χ^c ≤ max {Δ^* + 3,k^* + 2, Δ^* + 14, 3, k^* + 6, 18}, and if Δ^* ≥ 4 and k^* ≥ 4, then χ^c ≤ Δ^* + 3,k^* + 2. © 2006 Wiley Periodicals, Inc. J Graph Theory     

Final state interactions in the decay of light hypernuclei

The excited states of Li⁴, Li⁵ and Be⁸ have been investigated by studying the final state interactions in the π^?-mesic decays of_ΛHe⁴,_ΛHe⁵ and_ΛLi⁸ respectively. The experimental results indicate the existence of final states like Li^5* at 1·8 MeV and Be^8* at 0 and 2·9 MeV to be dominant in the decay of_ΛHe^5* and_ΛLi⁸ respectively; the results on the decay of_ΛHe⁴ suggest the presence of a Li^4* state at about 4 MeV to dominate.     

β-delayed proton decays of81Zr and85Mo

β-delayed proton decays of T_z = 1/2 series nuclei⁸¹Zr and⁸⁵Mo have been studied in detail by using p-γ coincidence measurement. The β-delayed proton spectra populating the first excited states of the daughter nuclei have been obtained. Half-life of⁸¹Zr has been measured tobe5.3s ± 0.5 s and that of⁸⁵Mo 3.2 s ± 0.2 S. By using statistical model calculations and systematic analyses, spins and parities for the ground states of⁸¹Zr and⁸⁵Mo have been tentatively assigned to be 3/2^? and 1/2^?, respectively. Mass excess of⁸¹Zris -58.3 MeV± 0.2 MeV and that of⁸⁵Mo-59.1 MeV ± 0.4 MeV. Combining the measured half-lives with the calculated partial ones yields the branches of β-de-layed proton decay for⁸¹zr and⁸⁵Mo of (1.2 ± 0.2) × 10^-3 and (1.4 ± 0.2) × 10^-3, respectively.     

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.     

Asymptotic Properties and Hausdorff Dimensions of Fractional Brownian Sheets

Let B^H = {B^H(t ), t ∈ ℝ^N} be an (N, d)-fractional Brownian sheet with index H = (H₁, . . . , H_N) ∈ (0, 1)^N. The uniform and local asymptotic properties of B^H are proved by using wavelet methods. The Hausdorff and packing dimensions of the range B^H ([0, 1]^N), the graph Gr B^H ([0, 1]^N) and the level set are determined.     

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.     

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].     

On the Riemann Summability of Fourier Integrals and Real Hardy Spaces

We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L¹ or the real Hardy spaces defined on ℝⁿ, where n ≥ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H¹(ℝ) into L¹(ℝ) and from L¹(ℝ) into weak –L¹(ℝ). We also prove that the double maximal Riemann operator is bounded from the hybrid Hardy spaces H^(1,0)(ℝIsup2), H^(0,1)(ℝ²⁾ into weak –L¹(ℝ²). Hence pointwise Riemann summability of Fourier integrals of functions in H^(1,0) ∪ H^(0,1)(ℝ²) follows almost everywhere.The maximal conjugate Riemann operators as well as the pointwise convergence of the conjugate Riemann means are also dealt with.     

Boundedness of Marcinkiewicz integrals and their commutators in H 1 (ℝ n × ℝ m )

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H ¹ (? ⁿ × ? ^m ) to the Lebesgue space L ¹(? ⁿ × ? ^m ) and their commutators with Lipschitz functions from the Hardy space H ¹ (? ⁿ × ? ^m ) to the Lebesgue space L ^q (? ⁿ × ? ^m ) for some q > 1.     

乘子算子及其交换子在Morrey空间上的有界性

证明了乘子算子(M_p~q(R~n),Lip(β-n/q))的有界性和(M_p~q(R~n),BMO(R~n))的有界性.还得到乘子算子及其交换子在广义Morrey空问Lp,L_(p,φ)(R~n)上的有界性.     

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.     

Minimal triangulations of Kummer varieties

By an (abstract) Kummer variety K^d we mean the d-dimensiona1 torus T^d modulo the involution ? ? — ?. The 2^d elements in T^d of order two are fixed points of the involution and therefore K^d has 2^d isolated singularities (for d ≧ 3). Any simplicial decomposition of K^d must have at least as many vertices. In this paper we describe a highly symmetrical simplicial decomposition of K^d with 2^d vertices such that the link of each vertex is a combinatorial real projective space ?P^d-1 with 2^d—1 vertices. The automorphism group of order (d + 1)! 2^d admits a natural representation in the affine group of dimension d over the field with two elements. A particular case is the classical Kummer surface with 16 nodes (d=4). In this case our 16-vertex triangulation has a close relationship with the abstract Kummer configuration 16₆.     

On the Cardinalities of the Row spaces of Non-full Rank Boolean Matrices

n -2 integers 2 ^{n -2}+2 ^{n -3}+2 ^s, where s=0,1,2,..., n-3, in the interval (2 ^{n -2}+2 ^{n -3},2 ^{n -1}] such that these integers are the cardinalities of row spaces R(A) of non-full rank Boolean matrices A of order n. We also show that for each s, where s=0,1,2,..., n-3, there exists A epsilon B _n such that A is non-full rank and the cardinality of R(A) equals 2 ^{n -2}+2 ^{n -3}+2 ^s.     

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     

On existence and nonexistence of some harmonic maps

LetS ^1.1 denote the submanifold of Lorentz spaceR ^2.1, which is composed of all pointsl withl ²=1 and letT ^1.1=R ^1.1/Z×Z. In this paper we study the existence of nontrivial harmonic maps fromT ^1.1 toS ^1.1 andH ², and construct a harmonic map for any homotopy class of maps fromT ² toS ^1.1.