Riemann Boundary Value Problem with Square Roots on an Open Arc

The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.     

Isotope effect of the stereodynamics in the reactions F+HCl→HF+Cl and F+DCl→DF+Cl

Using a new ground-state ab initio potential energy surface reported by Deskevich et al., the product polarizations in the reactions F+HCl→HF+Cl and F+DCl→DF+Cl were studied by employing the quasi-classical trajectory method. At a collision energy of 10 kcal/mol, the four generalized polarization-dependent differential cross-sections (2π/σ)(dσ₀₀/dω _t ), (2π/σ)(dσ₂₀/dω _t ), (2π/σ)(dσ₂₂₊/dω _t ) and (2π/σ)(dσ₂₁₋/dω _t ) were calculated in the center-of-mass frame. The distribution of the angle between k and j′, P(θ _r ), the distribution of the dihedral angle denoting the k-k′-j′ correlation, P(φ _r ), and the angular distribution of the product rotational vectors in the form of polar plots P(θ _r , φ _r ) were also calculated. The evident influence of isotope substitution on the product polarization is revealed. This effect may result from the different mass factors of the two reactions.     

Monte Carlo simulations for two-dimensional Ising system far from equilibrium

With a dynamic Monte Carlo simulation, which is free of critical slowing down, the critical behavior of two-dimensional Ising model at non-equilibrium states is investigated. We focus on the two-time autocorrelation function A(t, t' ) to identify the dynamic exponent z in two different evolution stages, quenched from a high temperature state and a completely ordered state to the critical state at TC, re-spectively. By using the heat-bath algorithm, the dynamic critical exponent is estimated as z ≈ 2.16. As a result, the universality of the scaling behavior is verified numerically, and the exponent λC is deter-mined complete by λC = β /ν for the evolutions from an initial completely ordered state.     

Latitudinal shift and tilt of the ring current during magnetic storms

The equatorial ring current (ERC) theory suggested that the distribution of global disturbed horizontal geomagnetic field only depends on the cosine of station’s latitude. However, we always observe a larger ΔH at higher latitude stations than lower ones, implying that the ERC could tilt or/and shift with respect to the equatorial plane during intense storms. In this paper, we analyze 11 intense magnetic storms from 2000 to 2004, and introduce two configurational factors to characterize the topology of storm time ring current. The results show that ERC has occasionally deviated off equatorial plane with both tilt angle δ_t≈13°―25° and latitude shift δ_s≈0°―21.8°. The ground disturbed field distribution should be improved as ΔH_k = ΔH_maxcos(φ_k-δ ), which agree well with the geomagnetic observations.     

A Note on the Prime Spectrums of Character Rings of Finite Groups

0Introduction LetGbeafinitegroupoforder|G|=g,andletR(G)denotethecharacterringofG,whichisgeneratedbyalltheirreduciblecomplexcharactersofG.LetZbetherationalintegerringandNthesetofnatural numbers,andletZ[ω]betheintegralextensiongeneratedbyaprimitiveg throotωofunity.SupposethatSisasubringof thealgebraicnumberfieldsuchthatZ[ω]S.πisasetofra tionalprimenumbersdefinedasfollowsπ={p｜pisarationalprimenumbersuchthatp-1S}.Definition1WecallthataconjugacyclassCofthefinite groupGisaπregularconju…     

Chaos in the sense of Li-Yorke and the order of the inverse limit space

Let I= [0,1] and ω0 be the first limit ordinal number. Assume that f: I→I is continuous , piece-wise monotone and the set of periods of f is { 2': i∈ {0} ∪ N}. It is known that the order of (I, f) is ω0 or ω0 + 1. It is shown that the order of the inverse limit space (I, f) is ω0 (resp. ω0 + 1) if and only if f is not (resp. is) chaotic in the sense of Li-Yorke.     

Investigation of octupole effects in superheavy nuclei with improved potential-energy-surface calculations

It has been found that high-order deformation (e.g.β6) can have important effects on the structures of superheavy nuclei. In the present work, we investigate octupole deformation effects on superheavy nuclei with an improved potential-energy-surface (PES) calculation by including reflection-asymmetric deformations in a space of (β2 ,β3 ,β4 , β5). The calculations give various deformations including highly deformed (β2 ≈ 0.4) and superdeformed (β2 ≈ 0.7) shapes. The octupole-deformation degree of freedom mainly affects the fission barrier beyond the second minimum of PES.     

Restricted allowable generalized quantum gates

An allowable generalized quantum gate (introduced by Long, Liu and Wang) has the form of U = Σ _k=0 ^d−1 c _k U _k , where U _k’s are unitary operators on a Hilbert space H and |Σ _k=0 ^d−1 c _k |⩽1 and |c _k |⩽1 (0⩽k⩽d−1). In this work we consider a kind of AGQGs, called restricted allowable generalized quantum gates (RAGQGs), satisfying 0 < Σ _k=0 ^d−1|c _k |⩽1. Some properties of the set RAGQG(H) of all RAGQGs on H are established. Especially, we prove that the extreme points of RAGQG(H) are exactly unitary operators on H and that B(H)=R ⁺ RAGQG(H).     

Minus domination number in cubic graph

An upper bound is established on the parameter Γ -(G) for a cubic graph G and two infinite families of 3-connected graphs G k, G * k are constructed to show that the bound is sharp and, moreover, the difference Γ -(G * k)-γ s(G * k) can be arbitrarily large, where Г -(G * k) and γ s(G * k) are the upper minus domination and signed domination numbers of G * k, respectively. Thus two open problems are solved.     

Y_CΩ_(2n)are easy terms

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λx.xx...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini's conjecture: Y CΩ n is an easy term for any natural number n≥2.     

Synthesis and characterization of spinel Li_(1.05)Cr_(0.1)Mn_(1.9)O_(4-z)F_z as cathode materials for lithium-ion batteries

Samples with the nominal stoichiometry Li_1.05Cr_0.1Mn_1.9O_4−z F _z (z=0, 0.05, 0.1, 0.15, and 0.2) were synthesized via the solid-state reaction method and characterized by X-ray powder diffraction (XRD), scanning electron microscopy (SEM), galvanostatic charge/discharge, and slow rate cyclic voltammetry (SSCV) techniques. The results show that the pure spinel phase indexed to Fd3m can be obtained when z=0, 0.05, and 0.1. The substitution of F for O with z≤0.1 contributes to the increase of initial capacity compared with Li_1.05Cr_0.1Mn_1.9O₄ spinels. However, when the F-dopant content is designed to be 0.15 and 0.2, the Li_1.05Cr_0.1Mn_1.9O_4−z F _z samples deliver relatively low capacity and poor cycling properties at 55°C.     

The classification of statistically recursive sets

The main aim of this paper is to make a classification of random setsK _m (ω) constructed in theorem 2. 1 and theorem 2. 1′ in [1]. We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in [2], Graf constructed in [3] and Mauldin constructed in [4] are the special cases ofK _m (ω) constructed in [1], and then these random sets belong to some model respectively according to our classification. Supported by the National Natural Science Fundation and the Doctal Programme Fundation of China Hu Dihe: born in May 1935, Professor     

Organic media enhanced spectrofluorimetric determination of L-ascorbic acid

A novel spectrofluorimetric method for the determination of L-ascorbic acid is proposed. It is based on the inhibition of L-ascorbic acid on the formation of 2,3-diaminophenazine, which is an oxidation product ofo-phenylenediamine catalyzed by laccase. The fluorescence (at λ_cx/λ_cm=464 nm /530 nnm) was enhanced strongly in the presence of organic media. The mechanism ofo-phenylenediamine oxidation reaction catalyzed by laccase in the presence of L-ascorbic acid is discussed. L-ascorbic acid is determined in the ethanol, 1,4-dioxane and acetone over the linear range of 4.0×10⁻⁷≈1.2×10⁻⁴ mol/L, 4.0×10⁻⁷≈8.0×10⁻⁵ mol/L and 4.0×10⁻⁷≈1.0×10⁻⁴ mol/L with a detection limit of 1.20×10⁻⁵ mol/L, 1.19×10⁻⁵ mol/L and 1.24×10⁻⁸ mol/L, respectively. The method has been successfully applied to the simple and rapid determination of L-ascorbic acid in pharmaceuticals and milk powder. Supported by National Natural Science Foundation of China and the Special Funds of State Education Committe for Doctorate Research Huang Zuyun: born in Aug. 1963. Ph.D     

On the limiting behavior of weighted partial sums for<Emphasis Type="Italic">B</Emphasis> valued martingale difference sequences

Let {X_n, n≥1} be a martingale difference sequence and {a _nk , 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ _k=1 ⁿ a _nk X _k is investigated and some new results are obtained. Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019) Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

Almost sure convergence of weighted sums of NA sequences

For double arrays of constants {a _ni, 1≤i≤k _n, n≥1} and NA r.v. 's {X _n, n≥1}, conditions for almost sure convergence of are given. Both casesk _n ↑ ∞ andk _n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. Supported by the National Natural Science Foundation of China Cheng Riyan: born in 1968, MS student     

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

Letm, n andk be positive integers, m> 1 andk≤ n. Let ‰ _m =‰m‰ denote the residue class ring modulom. Let ‰ _m denote the group of additive characters of ‰ _m denote the identity of ‰ _m . A necessary and sufficient condition for the systemf ₁,...,f _k ∈ ‰ _m [x ₁, ...,x _m ] to be orthogonal is given: for all additive characters ψ₁, ..., ψ _k ∈ ‰ _m with ψ_i,≠x₀ forsomei, . As corollaries, the result of Shiue-Sun-Zhang and the result of Sun are obtained.     

Theoretical characterization of single-electron iodine-bond weak interactions in CH3…I-Y（Y=BH2,H,CH3,C2H3,C2H,CN,NC）systems

Iodine-involved single-electron halogen bonds (SEXBs) weak interactions in the systems of CH3···I-Y(Y = BH2, H, CH3, CH==CH2, C≡CH, CN, NC) were investigated for the first time using B3LYP/6-311++G(d,p) and MP2/aug-cc-pVTZ computational levels (the relativistic effective core potential basis set of Lanl2dz was used on iodine atom). The interaction energies between two moieties with basis set super-position error corrections for the seven complexes are -0.57, -1.36, -3.80, -2.17, -4.49,-6.33 and -8.64 kJ mol-1 (MP2/aug-cc-pVTZ ), respectively, which shows that SEXBs interactions are all weak. Natural bond orbital theory analysis revealed that charges flow from CH3 to the I-Y moiety. The total amount of natural bond orbital charge transfer (ΔNC) from the CH3 radical to I-Y increases in the order CH3…IBH2 < CH3…IH ≈ CH3…ICH3 ≈ CH3···IC2H3 < CH3…ICCH< CH3…ICN< CH3…INC. Atoms-in-molecules theory was used to investigate the topological properties of the bond critical points in the seven SEXB structures.     

Almost sure convergence of weighted sums of NA sequences

For double arrays of constants {a _ni, 1≤i≤k _n, n≥1} and NA r.v. 's {X _n, n≥1}, conditions for almost sure convergence of are given. Both casesk _n ↑ ∞ andk _n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. Supported by the National Natural Science Foundation of China Cheng Riyan: born in 1968, MS student     

Tree decomposition

A tree decomposition of graph G=(V, E) is referred to as a partition of edge set E into edge-disjoint trees. Given (not necessarily distinct) vertices u-1, u-2...u-k∈V with k≥2, a sufficient and necessary condition is given for a connected graph G=(V,E) to have a tree decomposition {T-1, T-2...T-k} such that V(T-i)=V{u-i}, i=1,2,... k.     

A note on characteristic generators of a free cyclic code and its dual

Let C be a free cyclic code over Z _n ^α and dim _p C = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα − k characteristic generators of C ^⊥ are p-linearly independent. We then show that to any trellis that can be constructed from k p-linearly independent characteristic generators of C, there exists a trellis for C ^⊥ with the same state-complexity profile, which generalizes the conjecture of Koetter and Vardy to a free cyclic code over Z _n ^α. Foundation item: Supported by the National Natural Science Foundation of China(60673071)