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.     

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.     

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.     

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.)     

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     

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.     

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.     

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 ^#.     

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     

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.