Oscillation spectra of seed NaCl crystals in aqueous solutions

Using the flicker-noise method (FNM), we investigated the oscillations of clusters in aqueous solutions of NaCl in the range of concentrations from 0.1 to 26.0 mass %. It has been established that in the solutions oscillators whose masses are similar to the masses of the models of aggregates of solvate clusters of ion pairs (SCIP) of salt with a different water content are present. In diluted solutions (<10%), the elementary SCIP has the form NaCl· 40H₂O. For the entire range of concentrations the SCIPs are given by structures based on the cubic system of the sodium chloride system. The base structure for them is a cube formed from 12 SCIPs of salt. The largest cluster revealed by the FNM method for all investigated concentrations of salt had a mass of ≈1.5 million D. The presence of NaCl in water leads to a collapse of its cluster structure, except for the smallest clusters (H₂O)_10…11, whose concentration increases with temperature or solution concentration. The distribution of SCIPs changes dramatically at a temperature above 300 K. The possible structures of SCIPs are given and the mechanism of their formation is discussed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 766–772, November–December, 2005.     

1H, (19)F, and (31)P PGSE NMR diffusion studies on chiral organic salts: ion pairing and the dependence of a diffusion value on diastereomeric structure

1H, (19)F and (31)P pulsed field gradient spin-echo (PGSE) diffusion studies on chiral organic salts that contain hexacoordinate phosphate anions, namely tris(tetrachlorobenzenediolato)phosphate(V) (TRISPHAT) and bis(tetrachlorobenzenediolato)mono([1,1']binaphthalenyl-2,2'diolato)-phosphate(V) (BINPHAT), are reported. The first example of the dependence of a diffusion value on diastereomeric structure is presented. Marked solvent and concentration effects on the diffusion constants (D) of these salts are noted and the question of ion pairing is discussed.     

A complete description of Golay pairs for lengths up to 100

In his 1961 paper, Marcel Golay showed how the search for pairs of binary sequences of length with complementary autocorrelation is at worst a problem. Andres, in his 1977 master's thesis, developed an algorithm which reduced this to a search and investigated lengths up to 58 for existence of pairs. In this paper, we describe refinements to this algorithm, enabling a search at length 82. We find no new pairs at the outstanding lengths 74 and 82. In extending the theory of composition, we are able to obtain a closed formula for the number of pairs of length generated by a primitive pair of length . Combining this with the results of searches at all allowable lengths up to 100, we identify five primitive pairs. All others pairs of lengths less than 100 may be derived using the methods outlined.

     

Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces

We prove that the varieties of complete pairs of zero-dimensional subschemes of lengths d ₁ 2, d ₂ 4 on a smooth irreducible projective algebraic surface are singular.     

Supercuspidal Gelfand pairs

If G is a totally disconnected group and H is a closed subgroup then, according to the Gelfand-Kazhdan Lemma, if the double coset space H?G/H is preserved by an antiautomorphism of G of order two then (G,H) must be a Gelfand pair in the sense that Hom_H(π,1) has dimension at most one for each irreducible, admissible representation π of G. Under certain rather general restrictions, we show that if the symmetry property holds only for almost all double cosets, then (G,H) is a supercuspidal Gelfand pair in the sense that for all irreducible, supercuspidal representations π of G. There exist examples of supercuspidal Gelfand pairs which are not Gelfand pairs.     

Sheaves on Involutive Quantaloids

We extend the well-known notions of a singleton, complete -set, presheaf and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary involutive quantaloids. We show that sheaves on and complete -sets come to the same thing. This paper can be considered as a symmetric version of an earlier work of the author.     

Compact weakly symmetric spaces and spherical pairs

Let be a spherical pair and assume that is a connected compact simple Lie group and a closed subgroup of . We prove in this paper that the homogeneous manifold is weakly symmetric with respect to and possibly an additional fixed isometry . It follows that M. Krämer's classification list of such spherical pairs also becomes a classification list of compact weakly symmetric spaces. In fact, our proof involves a case-by-case study of the isotropy representations of all spherical pairs on Krämer's list.

     

激子自旋弛豫对简并量子点发射光子对纠缠度的影响

利用粒子数运动方程和量子回归理论，计算了单个半导体量子点双激子体系脉冲激发下粒子在各能级间辐射跃迁的二阶交叉相关函数以及系统发射光子对的偏振密度矩阵.分析了激子态能级简并量子点体系发射光子对偏振纠缠特性，讨论了纠缠度随激子态间自旋弛豫的变化关系.研究表明，激子自旋弛豫会破坏该系统发射光子对的纠缠度. 关键词： 纠缠光子对 半导体量子点 二阶相关函数     

Quantum secret sharing between multiparty and multiparty with four states

A protocol of quantum secret sharing between multiparty and multiparty with four states was presented. It was shown that this protocol can nullify the Trojan horse attack with a multi-photon signal, the fake-signal attack with Einstein-Podolsky-Rosen pairs, the attack with single photons, and the attack with invisible photons. In addition, the upper bounds of the average success probabilities were given for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states. Supported by the National Natural Science Foundation of China (Grant No. 10671054), the Key Project of Science and Technology Research of Education Ministry of China (Grant No. 207011) and the Natural Science Foundation of Hebei Province, China (Grant Nos. A2005000140 and 07M006)