浅谈藏语元音多数论

基于藏文文法的研究可窥见,对藏文元音的认定和归类主要有三种学术观点:以文法原典《三十颂》为依据,将元音定为|i||u||e||o|四个;以萨迦索南孜摩和夏鲁译师为代表的学者将藏文三十个字母中的|a|归类为元音,因此,认为元音有五个;后期学者对《三十颂》和《音势论》等经典文法著作作注疏研究,又形成以五个元音为基点和以|a|为零星式元音理论的语法定论。但是依据藏文书面语的语法规则及日常用语的表达习俗,应遵循以|i||u||e||o|四个为元音的语法规则更合乎逻辑。

教师教育的批判与重构

进步论、多数论、功利论不仅不能给教师教育提供坚实可靠的理论根基,而且将导致教师教育走向师道不彰、集体平庸和价值异化的误区。因此,教师教育有必要引入古典目的论的智慧,为自身寻求更加牢固的理论根基,明确教师教育的根本目的,确立正确的发展方向,推崇教师与学生共同追问美好生活的德性,并且以理解为基点,以对话为路径,以制度为保障,从而走出进步论、多数论、功利论带给教师教育的现实困境与发展误区。

The Growth and 1/4-Theorems for Spirallik Maps in l^P, B^P and Inner Product Space

The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.

The Factorization of Adjoint Polynomials of E^G（i）-class Graphs and Chromatically Equivalence Analysis

Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.

A Multi-component Matrix Loop Algebra and Its Application

A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra AM-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.

The Roots of Adjoint Polynomial of the Graphs Contain Triangles

We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.

Effects of Coverage,Water,and Defects on Catechol/TiO2 Interface

Catechol adsorbed on TiO_(2)is one of the simplest models to explore the relevant properties of dye-sensitized solar cells.However,the effects of water and defects on the electronic levels and the excitonic properties of the catechol/TiO_(2)interface have been rarely explored.Here,we investigate four catechol/TiO_(2)interfaces aiming to study the influence of coverage,water,and defects on the electronic levels and the excitonic properties of the catechol/TiO_(2)interface through the first-principles many-body Green’s function theory.We find that the adsorption of catechol on the rutile(110)surface increases the energies of both the TiO_(2)valence band maximum and conduction band minimum by approximately 0.7 eV.The increasing coverage and the presence of water can reduce the optical absorption of charge-transfer excitons with maximum oscillator strength.Regarding the reduced hydroxylated TiO_(2)substrate,the conduction band minimum decreases greatly,resulting in a sub-bandgap of 2.51 eV.The exciton distributions in the four investigated interfaces can spread across several unit cells,especially for the hydroxylated TiO2substrate.Although the hydroxylated TiO_(2)substrate leads to a lower open-circuit voltage,it may increase the separation between photogenerated electrons and holes and may therefore be beneficial for improving the photovoltaic efficiency by controlling its concentration.Our results may provide guidance for the design of highly efficient solar cells in future.

On the multiplicity of binary recurrences

Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, using a new result of Bilu, Hanrot and Voutier on primitive divisors, we proved that N 1(A,B,k)≤1 except N 1(1,-2,1)=5[n=1,2,3,5,13], N 1(1,-3,1)=3, N 1(1,-5,1)=3,N 1(1,B,1)=2(B{-2,-3,-5}), N 1(12,-55,1)=2, N 1(12,-377,1)=2, N 1(A,B,1)=2(A 2+B=±1, A>1), N 1(1,-2,3)=2, N 1(A,B,A)=2(A 2+2B=±1,A>1. For Lehmer sequence, we got a similar result. In addition, we also obtained some applications of the above results to some Diophantime equations.

Brightening of Dark Excitons in Single-Walled Carbon Nanotubes:Investigation by Many-Body Green’s Function Theory

Optical excitations of the hybrids,which are assembled by coupling single-walled carbon nanotubes(SWCNTs)with organic molecules through van der Waals interactions,are studied using ab initio manybody Green’s function theory.We take the semiconducting(7,0)SWCNT,the squarylium and oligothiophene molecules as the example.The E11 and E22 absorption peaks of the(7,0)tube can be redshifted by tens of meV.Most importantly,the lowest dark exciton of the(7,0)tube at the lower-energy side of E11 can be brightened by the interaction between the nanotube and molecules.Position of this new satellite absorption peak is influenced by the type of adsorbed molecule.These findings may be useful for tuning the emission energy and emission efficiency of CNTs.

The Covering Theorems for Normalized Holomorphic Mappings on Bounded Starlike Circular Domains in C^n

In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.

Direct and Indirect Excitons in Two-Dimensional Covalent Organic Frameworks

Highly luminescent bulk two-dimensional covalent organic frameworks(COFs)attract much attention recently.Origin of their luminescence and their large Stokes shift is an open question.After first-principles calculations on two kinds of COFs using the GW method and Bethe-Salpeter equation,we find that monolayer COF has a direct band gap,while bulk COF is an indirect band-gap material.The calculated optical gap and optical absorption spectrum for the direct excitons of bulk COF agree with the experiment.However,the calculated energy of the indirect exciton,in which the photoelectron and the hole locate at the conduction band minimum and the valence band maximum of bulk COF respectively,is too low compared to the fluorescence spectrum in experiment.This may exclude the possible assistance of phonons in the luminescence of bulk COF.Luminescence of bulk COF might result from exciton recombination at the defects sites.The indirect band-gap character of bulk COF originates from its AA-stacked conformation.If the conformation is changed to the AB-stacked one,the band gap of COF becomes direct which may enhance the luminescence.

Stability Analysis for Switching of Discrete Linear Singular Systems

In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.

Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)

In the paper, we prove that the complement of Tm(1,4,m-6)(m> 10) is chromatically unique if and only if m≠5k(k≥2).

Trace Formulae of Characteristic Polynomial and Cayley-HamUton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton＇s theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to ehiral perturbation theory and general relativity.

On Turán type inequality with doubling weights and A weights

Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities under L^p norm for 0〈p≤∞. Our results essentially extend the result of Wang and Zhou （2002）, and the method used in this paper is simpler and more direct than that of Wang and Zhou （2002）. The results and methods have their own values in approximation theory and computation.

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.

Optimal design of structural parameters for shield cutterhead based on fuzzy mathematics and multi-objective genetic algorithm

In order to improve the strength and stiffness of shield cutterhead, the method of fuzzy mathematics theory in combination with the finite element analysis is adopted. An optimal design model of structural parameters for shield cutterhead is formulated,based on the complex engineering technical requirements. In the model, as the objective function of the model is a composite function of the strength and stiffness, the response surface method is applied to formulate the approximate function of objective function in order to reduce the solution scale of optimal problem. A multi-objective genetic algorithm is used to solve the cutterhead structure design problem and the change rule of the stress-strain with various structural parameters as well as their optimal values were researched under specific geological conditions. The results show that compared with original cutterhead structure scheme, the obtained optimal scheme of the cutterhead structure can greatly improve the strength and stiffness of the cutterhead, which can be seen from the reduction of its maximum equivalent stress by 21.2%, that of its maximum deformation by 0.75%, and that of its mass by 1.04%.

Comprehensive G?bner Basis Theory for a Parametric Polynomial Ideal and the Associated Completion Algorithm

Groebner basis theory for parametric polynomial ideals is explored with the main objec- tive of nfinicking the Groebner basis theory for ideals. Given a parametric polynomial ideal, its basis is a comprehensive GrSbner basis if and only if for every specialization of its parameters in a given field, the specialization of the basis is a GrSbnerbasis of the associated specialized polynomial ideal. For various specializations of parameters, structure of specialized ideals becomes qualitatively different even though there are significant relationships as well because of finiteness properties. Key concepts foundational to GrSbner basis theory are reexamined and/or further developed for the parametric case： （i） Definition of a comprehensive Groebner basis, （ii） test for a comprehensive GrSbner basis, （iii） parameterized rewriting, （iv） S-polynomials among parametric polynomials, （v） completion algorithm for directly computing a comprehensive Groebner basis from a given basis of a parametric ideal. Elegant properties of Groebner bases in the classical ideal theory, such as for a fixed admissible term ordering, a unique GrSbner basis can be associated with every polynomial ideal as well as that such a basis can be computed from any Groebner basis of an ideal, turn out to be a major challenge to generalize for parametric ideals; issues related to these investigations are explored. A prototype implementation of the algorithm has been successfully tried on many examples from the literature.

A new many-body potential with the second-moment approximation of tight-binding scheme for Hafnium

In this work,we develop a new many-body potential for alpha-hafnium(α-Hf)based on the second moment approximation of tight-binding(TB-SMA)theory by introducing an additional Heaviside step function into the potential model and a new analytical scheme of density function.All the parameters of the new potential have been systematically evaluated by fitting to ground-state properties including cohesive energy,lattice constants,elastic constants,vacancy formation energy,structure stability and equation of state.By using the present model,the melting point,melt heat,thermal expansion coefficient,point defects,and low-index surface energies ofα-Hf were calculated through molecular dynamics simulations.Comparing with experiment observations from others,it is shown that these properties can be reproduced reasonably by the present model,some results being more consistent to the experimental data than those by previous suggested models.This indicates that this work is sutiable in TB-SMA potential for hexagonal close packed metals.

A New Class of Minimally Spectrally Arbitrary Sign Patterns

If every monic real polynomial of degree n can be achieved as the characteristic polynomial of some matrix B∈Q(A),then sign pattern A of order n is a spectrally arbitrary pattern.A sign pattern A is minimally spectrally arbitrary if it is spectrally arbitrary but is not spectrally arbitrary if any nonzero entry(or entries)of A is replaced by zero.In this article,we give some new sign patterns which are minimally spectrally arbitrary for order n≥9.