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.     

Some polar sets for the generalized Brownian sheet

Let (t)(t ∈ R ₊ ^N ) be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for (t). It is proved that for any a ∈ R ^d , P{ (t) = a, for some t ∈ R _> ^N } = and the probability that (t) has k-multiple points is 1 or 0 according as whether 2kN > d(k − 1)β or 2kN < d(k−1)α. These results contain and extend the results of the Brownian sheet, where R _> ^N = (0,+∞) ^N ,R ₊ ^N =[10,+∞) ^N ,0< α≤1 and β≥1. Biography: LI Huiqiong (1966–), female, Associate professor, research direction: stochastic process and random fractal.     

Local derivation on triangular subalgebras of hyperfinite von Neumann algebras

It is proved that every σ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A (or B) is a derivation. Morevoer, if A is also a σ-Dirichlet subalgebra, each local derivation from A into A is an inner derivation.     

A categorical interpretation of Yetter-Drinfel’d modules

It is known that any strict tensor category (C,⊗,I) can determine a strict braided tensor categoryZ(C), the centre ofC. WhenA is a finite Hopf algebra, Drinfel’d has proved thatZ( _AM) is equivalent to_D(A)M as a braided tensor category, where_AM is the left A-module category, andD(A) is the Drinfel’d double ofA. This is the categorical interpretation ofD(A). Z( _AM) is proved to be equivalent to the Yetter-Drinfel’d module category,_AYD ^A as a braided tensor category for any Hopf algebraA. Furthermore, for right A-comodule categoryM ^A, Z(M^A) is proved to be equivalent to the Yetter-Drinfel’d module category_AY D^A as a braided tensor category. But,in the two cases, the Yetter-Drinfel’d module category_AY D^A has different braided tensor structures.     

The nonwandering set of some Hénon map

For the Hénon mapT _{a, b}(x, y) = (1 −ax ² +y, bx), Benedicks and Carleson proved that for (a,b) near (2, 0) andb > 0, there exists a setE with positive Lebesgue measure, whose corresponding mapT _{a, b} possesses a strange attractor. Viana conjectured that if (a, b) ∈E, then the nonwandering set of the mapT _a, b Ω(T_{a, b}) = ∧_{a, b},Uq _a, b, where ∧_{a, b}, is the strange attractor, q_a,b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E₁ ⊂E.     

Model of Markov Chains in Space-Time Random Environments

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^＊：={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the ＂feedback＂. Some equivalence theorems and law of large numbers are obtained.     

A sufficient condition fork′(z)(k(z)∈H q,q≥1) to be ofH 1

We proved ifk(z)∈H ^q (q≥1),g(z) is analytic on |z|=1, , thenk′(z)∈H ¹, especially, ifq=1, thenk(z) is an analytic function on the closed unit disk |z|≤1. Peng Zhigang: born in June 1970, Ph. D     

Generalized Galerkin approximations for pseudoinverses and operator equations of the first kind

0 IntroductionLeqtuiliHnebaer afo rHimlbaenrtd sap baoceun.dLeedtlianaenardfufnbceti oan baolu onndeHd ,serse--spectively. Our goal is to seekv∈Hsuchthata(u,v) =f(u) , u∈ H (1)As a rule, we call the expression (1) a variational equationandva solutiontothis equation.By virtue of the Riesz repre-sentationtheorem,there exists a uniquely determined boundedlinear operatorA:H→Hsuchthata(u,v) =〈u,Av〉, u,v∈ H,where〈·,·〉is the inner product onH.If the sesquilinearformais also with posit…     

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.     

Existence of single-peaked solution of a semilinear elliptic problem

We discussed the Dirichlet problem of semilinear elliptic equationin (Pβ,α)D;-β△u=uε+εu,u>0,in Ω u=0, on(e),Ω where Ω(∪)RN(N≥4) is smooth and bounded domain,P=N+2/N-2,β,ε>0. We have proved that there exist positive ε0 and ε1 , such that when 0≤ε≤ε0,β>√ε1,(P0,1)has a single-peaked solution uβ, furthermore, |▽μβ|-0in the sense of measure as ε→0 and β→0.     

Julia sets of the random iteration systems and its subsystems

Suppose that P=(p\-1, p\-2, ..., p\-M)\% is a probability vector with p\-i>0 and Y={1, 2, ..., M}. Let (Y, 2\+Y, μ) be a probability space with μ(i)=p\-i, i=1, 2, ..., M, and (∑\-M, B, m)= Π \+∞\-0(Y, 2\+U, μ). It is shown that for any a \%(0≤a ≤1) \%, there exists a set U∈B such that m(U)=a and the Julia set associated with U is equal to the Julia set associated with ∑\-M\%. Moreover repelling fixed points with respect to U are dense in the Julia set associated with U.     

An extrapolation theorem on martingale spaces with Ap weights

In this paper, we prove an extrapolation theorem of operators in martingale spaces with A _p weights, which shows that for operators T defined on martingale space L _u ¹ , if T is bounded on martingale space L ^p0(w) for some 1 < p ₀ < ∞ and every, w∈ A _∞, so it is on L ^p,s (w) for every 1 < p, s < ∞, and w ∈ A _∞. We also get some properties of A _p weights and prove that if w ∈ A ₁, then the maximal operator M is bounded on L ^p,q (w) with 1 < p < ∞, 1 < q ≤ ∞.     

柴油机SCR尿素喷射方式研究

鉴于柴油机选择性催化还原系统尿素喷射特性与氮氧（NO_x）转化效率密切相关,本文搭建SCR系统小样试验台,NO和NH₃作为主要试验用气,研究了不同氨氮比和不同温度条件下V₂O₅-WO₃/TiO₂催化剂的氨存储、氨泄漏以及NO_x转化效率的影响.结果表明:氨氮比越大,氨存储量的建立时间越短,NO_x转化效率的提升就越快;氨氮比为0.22时,15 s内NO_x转化效率从0增大到4.3%;当氨氮比为0.30时,15 s内NO_x转化效率从0增大到8.7%;随着氨氮比的增大氨泄漏会提前出现;氨氮比先大后小的喷射方法有利于改善NO_x转化效率.采用氨氮比先大后小的喷射方法,进行ETC标准循环测试,NO_x比排放从8.26 g/（kW·h）减少到1.91 g/（kW·h）,NH₃泄漏均值为5×10-6,峰值为18×10-6,满足国V排放法规要求.      

The Distribution of a CP-asymmetric quantity in the decay channel J / Ψ → π + π ? π 0

The distribution of a CP-asymmetric quantityA in the decay channelJ/ψ→π ⁺ π ⁻ π ⁰ is investigated. This dimensionless quantityA is constructed from the momenta of the π-meson final states, namely A=P _x ^{π +} P _y ^{π −} -P _x ^{π −} P _y ^{π −}, whereP _h,P _x ^h andP _y ^h are the module of the momentum of a hadron h, the x- and y-components of that momentum respectively, theJ/ψ particle is produced by e⁺ e⁻ collision, and the direction of the momentum of e⁺ is taken to be the positive direction ofz axis. There would exists the violation under the combined transformation of charge conjugation and space reflection (CP violation) when the average ofA among a lot of events, 〈A〉, be examined to be nonzero clearly from data. In this way, 748 events are selected from the BES experimental data, and analyzed. The corresponding averageA-value is measured to be 〈A〉 = 0.010 39 ± 0.014 61 ± 0.015 2. Further, some discussion of our result, the size of the data sample being need for further attempt and a possible perspective are given.     

Walsh spectrum properties of rotation symmetric boolean function

Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.     

On the boundary value problem for harmonic maps of the Poincaré disc

The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfying where ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with norms It is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B .     

NMR and IR investigations of ternary inclusion complexes among β-cyclodextrin, rare earth metal ions, and naphthalenediamines

Ternary inclusion complexes β-cyclodextrin (β-CD), rare earth metal ions (YbCl₃, YCl₃), and 1,8-naphthalene- diamine/1,5-naphthalenediamine are synthesized in basic aqueous media, which are characterized via ¹H NMR and IR spectroscopy. The stoichiometric proportion of β-CD:YbCl₃:1,5-naphthalenediamine is 2:1:2, that of β-CD:YCl₃:1,8-naphthalenediamine is 2:1:1, and that of β-CD:YbCl₃:1,8-naphthalenediamine is 2:1:1. The IR spectroscopy of the ternary inclusion complexes in the range of 935–1 000 cm⁻¹ reveals the existence of the coordinate bond M—O or M—N. The possible conformations of the ternary inclusion complexes are depicted. Biography: JIANG Huiming(1972–), male, Associate professor, research direction: molecular complex chemistry, supramolecular chemistry.     

Preparation,crystal structure and quantum chemical investigation of [Li(NTO) (H2O)]

[Li(NTO)(H₂O)₂] was prepared by mixing the aqueous solution of 3-nitro-1,2,4-triazol-5-one (NTO) and lithium hydroxide. The crystal structure of [Li(NTO)(H₂O)₂] was determined by single crystal diffraction analysis. The crystal is monoclinic, space group P2₁/n with crystal parameters of a = 0.742 0(2) nm, b = 0.344 9(1) nm,c = 2.490 6(3) nm, β= 94.89(1)°, Z = 4,D _c , = 1.799 g cm⁻³,V = 0.635 nm³, μ = 1.591 cm⁻¹, F(000) = 392. The finalR is 0.051. The MNDO MO calculation shows that the coordinate bonds of title compound possess certain extent of covalent character. O₂ atom of NTO anion is bonded to Li atom; the nitro group will be lost first when NTO is decomposed.