Elements of Small Orders in K2F Ⅱ

In "Elements of small orders in K2(F)" (Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.), the author investigates elements of the form {a, Φn(a)} in the Milnor group K2F of a field F, where Φn(x) is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.     

On copositive approximation in some classical spaces of sequences

In this paper the author writes a simple characterization for the best copositive approximation in c; the space of convergent sequences, by elements of finite dimensional Chebyshev subspaces, and shows that it is unique.     

Orbit configuration spaces of small covers and quasi-toric manifolds

In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifolds;especially for the cases of small covers and quasi-toric manifolds.These kinds of orbit configuration spaces have non-free group actions,and they are all noncompact,but still built via simple convex polytopes.We obtain an explicit formula of the Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope.As a by-product of our method,we also obtain a formula of the Euler characteristic for the classical configuration space,which generalizes the Félix-Thomas formula.In addition,we also study the homotopy type of such orbit configuration spaces.In particular,we determine an equivariant strong deformation retraction of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold,which allows to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence.     

GLOBAL EXISTENCE FOR A CLASS OF SYSTEMSOF NONLINEAR WAVE EQUATIONS INTHREE SPACE DIMENSIONS

Consider a system of nonlinear wave equationsfor i = 1, … , m, where F, (i = 1, … , m) are smooth functions of degree 2 near the origin of their arguments, and u = (u1, … ,um), while u and x u represent the first and second derivatives of u, respectively. In this paper, the author presents a new class of nonlineaxity for which the global existence of small solutions is ensured. For example, global existence of small solutions for arbitrary cubic terms,arbitrary cubic termswill be established, provided that c12 ≠ c22.     

Finite Groups Whose Element Orders Are Consecutive Integers

There are various characterizations of groups by conditions on the orders of itselements.For example,in[2]and[1]the finite group all of whose elements haveprime power order have been classified.In[4—7]some simple groups have beencharacterized by conditions on the orders of its elements and B.H.Neumann[3]has determined all groups whose elements have orders 1,2 and 3.The latter groupsare OC_3 groups in the sense of the following     

On exceptional pq-groups

A finite group G is called exceptional if for a Galois extension F/k of number fields with the Galois group G,in the Brauer-Kuroda relation of the Dedekind zeta functions of fields between k and F,the zeta function of F does not appear.In the present paper we describe effectively all exceptional groups of orders divisible by exactly two prime numbers p and q,which have unique subgroups of orders p and q.     

A conjecture of Abe-Iiyori and the Ree groups ~2F_4(q),Ⅱ

In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'.     

《数学年刊》第35卷B辑第1期(2014)目次和提要

<正>h-P Finite Element Approximation for Full-Potential Electronic Structure Calculations Yvon MADAY The(continuous)finite element approximations of different orders for the computation of the solution to electronic structures were proposed in some papers and the performance of these approaches is becoming appreciable and is now well understood.In this publication,the author     

On Reduced Lantern Relations in Mapping Class Groups

Let S be a hyperbolic Riemann surface with a finite area.Let G be the covering group of S acting on the hyperbolic plane H.In this paper,the author studies some algebraic relations in the mapping class group of(?) for(?) — S\{a point}.The author shows that the only possible relations between products of two Dehn twists and products of mapping classes determined by two parabolic elements of G are the reduced lantern relations.As a consequence,a partial solution to a problem posed by J.D.McCarthy is obtained.     

Characterization of Solid Cones

The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended.     

关于域的K_2群的挠

设F是域,记G_n(F)={{a,Φ_n(a))∈K_2(F)|a,Φ_n(a)∈F_~*},这里Φ_n(x)是n次分圆多项式.首先,使用关于数域上的Mordell猜想的Faltings定理证明了若F是数域,n≠1,4,8,12且含有平方因子,则G_n(F)不是K_2(F)的子群;然后,使用Manin,Grauert,Samuel和李克正关于函数域上的Mordell猜想的结果,对代数闭域上的函数域证明了类似的结果.     

函数域的K_2群的挠元

设F是域,令G_n(F)={{a,φ_n(a)}∈K_2(F)| a,Φ_n(a)∈F~*},这里Φ_n(x)是n次分圆多项式.使用函数域的ABC定理证明了若F是常数域为k函数域,l≠ch(k)是素数,则对n≥3且l>2或n>3且l=2,G_(ln)(F)不是K_2(F)的子群.由此部分地证实了Browkin的猜想.     

ON THE ACCURACY OF THE QUASICONFORMING AND GENERALIZED CONFORMING FINITE ELEMENTS

It is observed in practice that the numerical accuracy of the two unconventional plate elements, i. e., the nine parameter quasi-conforming and generalized conforming elements, is better than that of the usual Zienkiewicz in compatible cubic element and of a new element proposed recently by Specht, although all these elements have the same asymptotical rate of convergence O(h) in the energy norm. In the paper a careful error analysis for the quasi-conforming and generalized conforming elements is given. It is shown that the consistency error due to nonconformity of the two unconventional elements is of order O(h~2), one order high than that of other conventional nonconforming elements with nine parameters.     

The Dissipative Quasi-geostrophic Equation in Weak Morrey Spaces

The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^＊,γ（R^n）, with 1〈p〈∞and A = n-（2α-1）p, and for a small external force in a time-weighted weak Morrey space.     

THE CATASTROPHE MODEL FOR THE ACID-BASE PROPERTY OF THE HYDROXIDES OF ELEMENTS IN AQUEOUS SOLUTION

In this paper the acid-base property of various hydroxides of elements has been studied by applying the catastrophe theory. It is indicated that the topological structure of the plane diagrams formed by bond-parameters may be deduced by using the catastrophe theory.The author considers that the application of catastrophe theory may be open a new way of thinking for the theoretical derivation of plane diagrams of bond-parameters.The discussion in this paper is only an illustration     

Solvable quadratic Lie algebras

A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.     

FINITE ELEMENT METHODS FOR A BI-WAVE EQUATION MODELING D-WAVE SUPERCONDUCTORS

In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.     

The Formual of Generalized Center－Weak Saddle

In his paper,a problem of center-weak focus of a general system of degree n is transformed into a problem of generalized center-weak saddle.It offers:(1) the calculating formula of the saddle values of the former 4 orders in the general system of degree three;(2) some calculating formulae of the saddle values in the general homogeneous system of degree n. The problem of center-focus(saddle)plays an important role in the qualitative theory of ordinary differential equations.However,since the calculations are difficult,the results have not been satisfactory.On the basis of the author‘s work,Northeast.Math.J.,13(4)(1997),487-494,the paper offers some calculating formulae of the saddle values.     

RESEARCH ANNOUNCEMENTS Strong Discreteness of Subgroups of SL(2, Γ_n)

As in [1,6], let Г_n be the n-dimensional Clifford group, i.e., the set of all elements in ndimensional Clifford algebra An, which can be expressed as a finite product of non-zero-vectors and SL(2, Г_n) denote the group of n-dimensional Clifford matrices which satisfy:     

2—Harmonic Curves Isometrially Immersed in a Surfaee

In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.