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.     

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).     

Synthesis and Characterization of Polyamide-Containing 2, 6- （Substituded） pyridine Derivatives

0 IntroductionPayrriodminaetiics hoenteer oofc ythcleics m .os tC oambupnoduanndts a cnodn tbaeisntin kgno twhnepyridine ring are widely distributedin nature,principally asenzymes and alkaloids . Pyridine enzymes have been foundintissues of all plants and ani mals examined thus far ,andare derivedfromeither nicotinic acid or Vitamin B6[1].Pyr-idine derivatives are also the building block of many phar-maceuticals with a wide range of functionalities that includeantitubercular compounds ,antivi…     

Some clifford martingale spaces

We study the spaces Hp, Sp, Kp, ∑p and ,p of martingales with measure du=ψdυ,where ψ is a function with Clifford algebra values and satisfies bp+-condition. We proved they are equivalent and isomorphic to the corresponding spaces of martingales with real measure dυ, respectively(1≤p＜∞). In the end,we give a martingale f such that f=(fn) ∞∈1K∞ but f=(E(ψ| n)fn)n≥ ∈1K∞.     

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.     

Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.     

A matrix version of the Wielandt inequality and its application to statistics

Suppose that A is an n × n positive definite Hemitain matrix. Let X and Y be n × p and n × q matrices (p+ q≤n), such that X* Y = 0. The following inequality is proved X*AY( Y* AY)-Y Y*AX≤( (λ1-λn)/(λ1+λn))2 X*AX, where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covari-ance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation.     

The Hàjek-Rènyi inequlity for Banach space valued random variable sequences and its application

In this paper we prove the following Hàjek-Rènyi inequality: Let 0≤p≤1, then for any Banach spaceB, anyL ^p integrableB valued random variable sequence {D _n , n≥1}, any real number sequence {b _n , n≥1} with 0<b _n, ↑ ∞, any integern≥1, there exist a constantC=C _p>0 (only depending onp) such that

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 ≤ ∞.     

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.     

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.     

Molecule modification and mass deposition induced by the implantation of low energy Fe+ ion beams into amino acids

Fe⁺ ion beams with the energy of 110 keV were implanted into films of L(+)-cysteine (HSCH₂CH(NH₂)COOH). One of the single crystals grown in hydrochloric acid solution with the implanted samples through slow evaporation was structurally characterized by the X-ray crystallography. The crystal is monoclinic, space group C2, with a = 1.8534(4) nm, b = 0.5234(1) nm, c = 0.7212(1) nm, β= 103.72°, V = 0.67965(3) nm³, Z = 4, F(000) = 144.0, D{clac} = 1.763 g · cm⁻³, μ(MoK _a = 1.06 mm⁻¹, T = 293(2) K. R = 0.0379, wR = 0.0835 for 660 observed reflections (I > 2σ(I)). The structural formula of the crystal compound is (CH₂CH(NH₂)NO₂)ClFe (M _r = 180.38 u). Products of heavy ion beam irradiation were purified and it was directly confirmed that the implanted Fe⁺ ions had been deposited in the novel molecules. The same doses of Fe⁺ ion beams of the same energy were implanted into films of L(+)-cysteine hydrochloride monohydrate. FTIR spectroscopy of the implanted samples proved that some of the original molecules were seriously damaged and significant modifications were induced.     

Bottom Factors Applied to the Zoning Study of the Risk Levels of Landslides in the Three Gorges Reservoir Area

Without taking inducing factors into consideration, this paper adopts a quantitative analysis of the bottom factors in the Three Gorges Reservoir area, studies the relationship between the bottom factors and the development of landslides, and then zones the area according to risk levels. The bottom factors adopted in this paper include lithological characters（U1 ）, gradient（U2 ）, slope form （U3）, difference of helght（U4 ）, and slope orientation（U5 ）. In 4 650 km^2 of the studied area, the areas of the very high, high, medium and low hazard degree area respectively were 57. 94 km^2 , 2 305.15 km^2, 1 241.6 km^2, 1 045.31 km^2. The methodological steps are （1） inversion statistic analysis, （2） the analysis of contribution ratio and weighing, （3） getting results via fuzzy evaluation of risk levels.     

求解对流扩散方程的一类AGE方法

结合Crank-Nicolson格式和第二类Saul’yev非对称格式,设计求解对流扩散方程的交替分组显式方法.得到求解对流扩散方程的交替分组显式方法为该方法是绝对稳定的,且使用方便,适合并行计算,具有较好的精度.     

Banach space valued martingales with respect to complex measure and their inequalities

Let dμ=ϕdν be a complex valued measure where ν is a non-negative measure and ϕ is a complex valued function which satisfiesb _p ⁺ orb _∞ ⁺ ⊂a ₁ condition. We prove some basic martingale inequalities such as B-G inequalities, weak (p, p) and strong (p, p) type inequalities for Banach space valued martingale with respect to complex measure μ. Supported by the National Natural Science Foundation of China Hou Youliang: born in 1956, Ph. D     

Average widths and optimal recovery of multivariate Besov classes inL p (Rd)

Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p<∞) are obtained, and the corresponding weak asymptotic optimal subspaces are identified. Furthermore, the weak asymptotic behavior of optimal recovery is established for the isotropic Besov classes S r pθB(R d) in L p(R d) (1≤p≤∞).     

The Total Irredundance Numbers on Graphs

This paper discusses the total irredundance relations between the graph G and its clone-contraction graph H, that is, let H be the clone-contraction graph of G and v1,v2,...,vk be all contraction vertices ofH. IfS is a maximal total irredundant set of H such that A = S ∩ {V1,V2,…,Vk} contains as few vertices as possible, then S＇= S-A is the maximal total irredundant set of G. Furthermore, we obtain the bound of the total irredundance A（G） number： irt ≤△（G）/2△（G）＋1 n, which n is the order of graph G, and △（G） is maximum degree in G.     

Photocatalytic degradation of trace-level of MicrocystinLR by nano-film of titanium dioxide

The occurrence of toxic water bloom of cyanobacte-ria algae, widely reported in eutrophic freshwater, hasbeen a serious pollution problem in recent years[1]. Mi-crocystins (MCs), the most common cyanobacteriatoxin with a cyclic heptapeptide structure (Fig…     

New method on constructing analytic potential function of diatomic molecules

A new method on constructing analytical potential energy functions is presented, and then a relatively universal analytical potential energy function for precisely calculating the spectra of diatomic molecules and ions is derived. Furthermore, six kinds of common potential energy curves containing three main potential curves i.e. steady state, metastable state and repulsive state are obtained from this potential energy function. Finally, spectroscopic parameters of thirteen diatomic molecules and ions including BeD-X ² Σ ⁺, BeT-X ² Σ ⁺ and Na₂-X ¹ Σ _g ⁺ etc are calculated by using the potential function, as a consequence, all calculation results are in good agreement with experimental data. Biography: YU Changfeng (1962–), male, Associate professor, research direction: theoretical physics.     

Studies on reduced extent method for inhibited thermokinetics of enzyme-catalyzed reaction

The thermokinetic reduced extent equations of reversible inhibitions for Michaiels-Menten enzymatic reaction were deduced, and then the criteria for distinguishing inhibition type was given and the methods for calculating kinetic parameters,K _M,K _i andv _m were suggested. This theory was applied to inverstigate the inhibited thermokinetics of laccase-catalyzed oxidation ofo-dihydroxybenzene bym-dihydroxybenzene. The experimental results show the inhibition belongs to reversible competitive type,K _M=6.224×10⁻³ mol·L⁻¹,K _i=2.363×10⁻² mol·L⁻¹. Xiong Ya: born Sep. 1961, Ph. D. graduate student. Curent research interest is in biothermochemistry research Supported by the National Natural Science Foundation of China