The transition matrix between PBW basis and semicanonical basis of U+(sl_n(C))

We prove that the transition matrix between a special Poincaré-Birkhoff-Witt(PBW)basis and the semicanonical basis of U+(sln(C))is upper triangular and unipotent under any order which is compatible with the partial order deg.     

Anti-commutative Grbner-Shirshov basis of a free Lie algebra

The concept of Hall words was first introduced by P. Hall in 1933 in his investigation on groups of prime power order. Then M. Hall in 1950 showed that the Hall words form a basis of a free Lie algebra by using direct construction, that is, first he started with a linear space spanned by Hall words, then defined the Lie product of Hall words and finally checked that the product yields the Lie identities. In this paper, we give a Grbner-Shirshov basis for a free Lie algebra. As an application, by using the ...     

Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor

Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four invariants with degrees two, four, six, and ten, respectively. In this paper, we show that any minimal integrity basis of a third order three-dimensional symmetric and traceless tensor is also an irreducible function basis of that tensor, and there is no syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.     

Unconditional basis recursively generated in L~p on compact sets

We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p > 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algorithm of how to construct an unconditional basis in Lp(Ω,ρ). At the end of this paper, we give the characterization of the functions in Lp (Ω,ρ) by using the wavelet coefficients.     

Semisymmetric graphs of order 6p 2 and prime valency

In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p2 and valency k is semisymmetric if and only if k = 3 and either Γ is the Gray graph, or p ≡ 1 (mod 6) and Γ is isomorphic to one known graph.     

A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRDINGER EQUATION

In this article, a nonconforming quadrilateral element(named modified quasiWilson element) is applied to solve the nonlinear schr¨odinger equation(NLSE). On the basis of a special character of this element, that is, its consistency error is of order O(h~3) for broken H1-norm on arbitrary quadrilateral meshes, which is two order higher than its interpolation error, the optimal order error estimate and superclose property are obtained. Moreover,the global superconvergence result is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.     

$T_{2}(T)$的几乎可裂序列及几乎$\mathcal {D}$-可裂序列

The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and D-split sequences. So in order to study the representations of triangular matrix algebra T2 (T ) = T0TT where T is a finite dimensional algebra over a field, it is important to determine its AR-sequences and D-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and D-split sequences of T2 (T) through the corresponding morphisms and sequences of T. Some interesting results are obtained.     

The Boolean—Valued Model of the Conglomerate Axiom System ACG

The paper[1] constructs the conglomerate axiom system ACG in order to research the base of Category Theory.This paper constructs the model Ω^(B)（where B is a complete Boolean algebra) on the basis of the models △^(B) (see[2])and ∧^(B)(see[5]),and proves:(1)Ω^(B) is Boolean-Valued model of the conglomerate axiom system ACG;(2)The maximum and minimum principles are true in Ω^(B).     

STABLE SOLUTION OF TIME DOMAIN INTEGRAL EQUATION METHODS USING QUADRATIC B-SPLINE TEMPORAL BASIS FUNCTIONS

This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.     

时间序列的AR及ARMA模型的阶数的贝叶斯判据

In this paper, we discuss the problem of determining the orders of AR(k) andARMA(p, q) models of time series on the basis of the Bayesian estimate theory. Ageneral prior distribution for the order and a general family of prior distribution forthe parameters are proposed. With respect to a particular loss-function, the criterionfor the order of AR(k), denoted by η_1(k), and the approximate criterion for theorder of ARMA (p, q) are given. The consistency of the order K estimated by usingη_1(k)is proved.Finally, the simulation comparisons between η_1(k), AIC(k) (Akaike,1976) and φ(k) (Hannan,1979) are made. The results show that η_1(k) is superiorto AIC(k).     

$U({\mathfrak {so}}(7,{\mathbb C}))$的向量表示的范畴化

The aim of this paper is to categorify the n-th tensor power of the vector representation of U (so(7, C)). The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gl n .     

Multi-neighboring grids schemes for solving PDE eigen-problems

Instead of most existing postprocessing schemes,a new preprocessing approach,called multineighboring grids(MNG),is proposed for solving PDE eigen-problems on an existing grid G(Δ).The linear or multi-linear element,based on box-splines,are taken as the frst stage Kh1Uh=λh1Mh1Uh.In this paper,the j-th stage neighboring-grid scheme is defned asKh jUh=λh j Mh jUh,where Kh j:=Mh j 1Kh1and Mh jUh is to be found as a better mass distribution over the j-th stage neighboring-gridG(Δ),and Kh jcan be seen as an expansion of Kh1on the j-th neighboring-grid with respect to the(j 1)-th mass distribution Mh j 1.It is shown that for an ODE model eigen-problem,the j-th stage scheme with 2j-th order B-spline basis can reach2j-th order accuracy and even(2j+2)-th order accuracy by perturbing the mass matrix.The argument can be extended to high dimensions with separable variable cases.For Laplace eigen-problems with some 2-D and 3-D structured uniform grids,some 2j-th order schemes are presented for j 3.     

PARALLEL ALGORITHMS OF ONE-LEG METHOD AND ITERATED DEFECT CORRECTION METHODS

The parallel algorithms of iterated defect correction methods (PIDeCM's) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE'S. As the basis of constructing and discussing PIDeCM's. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.     

THE FINITE DIFFERENCE METHOD FOR DISSIPATIVE KLEIN-GORDON-SCHRDINGER EQUATIONS IN THREE SPACE DIMENSIONS

A fully discrete finite difference scheme for dissipative Klein-Gordon-Schrodinger equationsin three space dimensions is analyzed.On the basis of a series of the time-uniformpriori estimates of the difference solutions and discrete version of Sobolev embedding theorems,the stability of the difference scheme and the error bounds of optimal order for thedifference solutions are obtained in H~2×H~2×H~1 over a finite time interval.Moreover,the existence of a maximal attractor is proved for a discrete dynami...     

Bayesian Estimation for the Order of INAR(q) Mo del

In this paper, we consider the problem of determining the order of INAR(q) model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.     

An orthogonal basis for non-uniform algebraic-trigonometric spline space

Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonal. We construct an orthogonal basis for the n-order(n ≥ 3) algebraic-trigonometric spline space in order to resolve the theoretical problem that there is not an explicit orthogonal basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions,which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.     

ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed.On the basis of a series of the time-uniform priori estimates of the difference solutions,the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L2 × H 1 × H 2 over a finite time interval(0,T ].Finally,the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.     

GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

In this article, we prove the global existence of weak solutions to the nonisothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance.It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.     

无$K_{1,4}$子图的图的路覆盖

For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of G. In this paper, we prove that if G is a K_(1,4)-free graph of order n and σ_(k+1)(G) ≥ n-k, then p(G) ≤ k, where σ_(k+1)(G) = min{∑v∈S d(v) : S is an independent set of G with |S| = k + 1}.     

Analysis of a moving collocation method for one-dimensional partial differential equations

A moving collocation method has been shown to be very efficient for the adaptive solution of second- and fourth-order time-dependent partial differential equations and forms the basis for the two robust codes MOVCOL and MOVCOL4.In this paper,the relations between the method and the traditional collocation and finite volume methods are investigated.It is shown that the moving collocation method inherits desirable properties of both methods: the ease of implementation and high-order convergence of the traditional collocation method and the mass conservation of the finite volume method.Convergence of the method in the maximum norm is proven for general linear two-point boundary value problems.Numerical results are given to demonstrate the convergence order of the method.