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1.
Let R be a ring, S a strictly ordered monoid and a monoid homomorphism. In this paper we obtain some necessary conditions for the skew generalized power series ring RS,ω to be right (respectively left) uniserial, and we prove that these conditions are also sufficient when the monoid S is commutative or totally ordered.  相似文献   

2.
We consider linearly ordered, Archimedean dimension groups (G,G+,u) for which the group G/u is torsion-free. It will be shown that if, in addition, G/u is generated by a single element (i.e., ), then (G,G+,u) is isomorphic to for some irrational number τ(0,1). This amounts to an extension of related results where dimension groups for which G/u is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C*-algebra is the Fibonacci C*-algebra.  相似文献   

3.
Let M be a connected compact complex manifold endowed with a strongly pseudoconvex complex Finsler metric F. In this paper, we first define the complex horizontal Laplacian □h and complex vertical Laplacian □v on the holomorphic tangent bundle T1,0M of M, and then we obtain a precise relationship among □h,□v and the Hodge–Laplace operator on (T1,0M,,), where , is the induced Hermitian metric on T1,0M by F. As an application, we prove a vanishing theorem of holomorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M.  相似文献   

4.
Let G be a graph. For u,vV(G) with distG(u,v)=2, denote JG(u,v)={wNG(u)∩NG(v)|NG(w)NG(u)NG(v){u,v}}. A graph G is called quasi claw-free if JG(u,v)≠ for any u,vV(G) with distG(u,v)=2. In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. In this paper we show that every 4-connected line graph of a quasi claw-free graph is hamiltonian connected.  相似文献   

5.
LetXbe a Banach space. GivenMa subspace ofXwe denote withPMthe metric projection ontoM. We defineπ(X) sup{PMMa proximinal subspace ofX}. In this paper we give a bound forπ(X). In particular, whenX=Lp, we obtain the inequality PM2|2/p−1|, for every subspaceMofLp. We also show thatπ(X)=π(X*).  相似文献   

6.
The continuity conditions at the endpoints of interpolation theorems, TaBjMj aAj for j=0, 1, can be written with the help of the approximation functional: E(tTaB1B0)LM0 aA0 and E(tTaB0B1)LM1 aA1. As a special case of the results we present here we show that in the hypotheses of the interpolation theorem the L norms can be replaced by BMO( +) norms. This leads to a strong version of the Stein-Weiss theorem on interpolation with change of measure. Another application of our results is that the condition fL0, i.e., f*L, where f*(γ)=μ{|f|>γ} is the distribution function of f, can be replaced in interpolation with L(pq) spaces by the weaker f*BMO( +).  相似文献   

7.
A hamiltonian cycle C of a graph G is an ordered set u1,u2,…,un(G),u1 of vertices such that uiuj for ij and ui is adjacent to ui+1 for every i{1,2,…,n(G)−1} and un(G) is adjacent to u1, where n(G) is the order of G. The vertex u1 is the starting vertex and ui is the ith vertex of C. Two hamiltonian cycles C1=u1,u2,…,un(G),u1 and C2=v1,v2,…,vn(G),v1 of G are independent if u1=v1 and uivi for every i{2,3,…,n(G)}. A set of hamiltonian cycles {C1,C2,…,Ck} of G is mutually independent if its elements are pairwise independent. The mutually independent hamiltonicity IHC(G) of a graph G is the maximum integer k such that for any vertex u of G there exist k mutually independent hamiltonian cycles of G starting at u.In this paper, the mutually independent hamiltonicity is considered for two families of Cayley graphs, the n-dimensional pancake graphs Pn and the n-dimensional star graphs Sn. It is proven that IHC(P3)=1, IHC(Pn)=n−1 if n≥4, IHC(Sn)=n−2 if n{3,4} and IHC(Sn)=n−1 if n≥5.  相似文献   

8.
Sharp tridiagonal pairs   总被引:1,自引:0,他引:1  
Let denote a field and let V denote a vector space over with finite positive dimension. We consider a pair of -linear transformations A:VV and A*:VV that satisfies the following conditions: (i) each of A,A* is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A*ViVi-1+Vi+Vi+1 for 0id, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A* such that for 0iδ, where and ; (iv) there is no subspace W of V such that AWW, A*WW, W≠0, WV. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0id the dimensions of coincide. We say the pair A,A* is sharp whenever dimV0=1. A conjecture of Tatsuro Ito and the second author states that if is algebraically closed then A,A* is sharp. In order to better understand and eventually prove the conjecture, in this paper we begin a systematic study of the sharp tridiagonal pairs. Our results are summarized as follows. Assuming A,A* is sharp and using the data we define a finite sequence of scalars called the parameter array. We display some equations that show the geometric significance of the parameter array. We show how the parameter array is affected if Φ is replaced by or or . We prove that if the isomorphism class of Φ is determined by the parameter array then there exists a nondegenerate symmetric bilinear form , on V such that Au,v=u,Av and A*u,v=u,A*v for all u,vV.  相似文献   

9.
The generalized nonlinear Schrödinger equation (GNLS) iut + uxx + βu2u + γu4u +  (u2u)x + (u2)xu = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation. Int J Bifucat Chaos 2005:3295–305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.  相似文献   

10.
Given a Newtonian coalgebra we associate to it a chain complex. The homology groups of this Newtonian chain complex are computed for two important Newtonian coalgebras arising in the study of flag vectors of polytopes:R a, b and Rc, d. The homology of Ra, b corresponds to the homology of the boundary of then -crosspolytope. In contrast, the homology of Rc, d depends on the characteristic of the underlying ring R. In the case the ring has characteristic 2, the homology is computed via cubical complexes arising from distributive lattices. This paper ends with a characterization of the integer homology ofZ c, d.  相似文献   

11.
The following reaction-diffusion system in spatially non-homogeneous almost-periodic media is considered in a bounded domain : (1)tu=Auf(u)+g, u|∂Ω=0. Here u=(u1,…,uk) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator A has the following structure: where aijl(y) are given almost-periodic functions. We prove that, under natural assumptions on the nonlinear term f(u), the longtime behavior of solutions of (1) can be described in terms of the global attractor of the associated dynamical system and that the attractors  , 0<<01, converge to the attractor of the homogenized problem (1) as →0. Moreover, in the particular case of periodic media, we give explicit estimates for the distance between the non-homogenized and the homogenized attractors in terms of the parameter .  相似文献   

12.
Let m and n be positive integers with n2 and 1mn−1. We study rearrangement-invariant quasinorms R and D on functions f: (0, 1)→ such that to each bounded domain Ω in n, with Lebesgue measure |Ω|, there corresponds C=C(|Ω|)>0 for which one has the Sobolev imbedding inequality R(u*(|Ωt))CD(|mu|* (|Ωt)), uCm0(Ω), involving the nonincreasing rearrangements of u and a certain mth order gradient of u. When m=1 we deal, in fact, with a closely related imbedding inequality of Talenti, in which D need not be rearrangement-invariant, R(u*(|Ωt))CD((d/dt) ∫{x n : |u(x)|>u*(|Ωt)} |(u)(x)| dx), uC10(Ω). In both cases we are especially interested in when the quasinorms are optimal, in the sense that R cannot be replaced by an essentially larger quasinorm and D cannot be replaced by an essentially smaller one. Our results yield best possible refinements of such (limiting) Sobolev inequalities as those of Trudinger, Strichartz, Hansson, Brézis, and Wainger.  相似文献   

13.
We apply the techniques of monotone and relative rearrangements to the nonrearrangement invariant spaces Lp()(Ω) with variable exponent. In particular, we show that the maps uLp()(Ω)→k(t)u*Lp*()(0,measΩ) and uLp()(Ω)→u*Lp*()(0,measΩ) are locally -Hölderian (u* (resp. p*) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents.  相似文献   

14.
Let σ be an orthogonal representation of a group G on a real Hilbert space. We show that σ is irreducible if and only if its commutant σ(G)' is isomorphic to , or . This result is an analogue of the classical Schur lemma for unitary representations. In both cases (orthogonal and unitary), a representation is irreducible if and only if its commutant is a field. If σ is irreducible, we show that there exists a unitary irreducible representation π of G such that the complexification σ is unitarily equivalent to π if σ(G)' , to π π̄ if σ(G)' , and to π π if σ(G)' (here π̄ denotes the contragredient representation of π). These results are classical for a finite-dimensional σ, but seem to be new in the general case.  相似文献   

15.
16.
Let d≥3. Let H be a d+1-dimensional vector space over GF(2) and {e0,…,ed} be a specified basis of H. We define Supp(t){et1,…,etl}, a subset of a specified base for a non-zero vector t=et1++etl of H, and Supp(0)0/. We also define J(t)Supp(t) if |Supp(t)| is odd, and J(t)Supp(t){0} if |Supp(t)| is even.For s,tH, let {a(s,t)} be elements of H(HH) which satisfy the following conditions: (1) a(s,s)=(0,0), (2) a(s,t)=a(t,s), (3) a(s,t)≠(0,0) if st, (4) a(s,t)=a(s,t) if and only if {s,t}={s,t}, (5) {a(s,t)|tH} is a vector space over GF(2), (6) {a(s,t)|s,tH} generate H(HH). Then, it is known that S{X(s)|sH}, where X(s){a(s,t)|tH{s}}, is a dual hyperoval in PG(d(d+3)/2,2)=(H(HH)){(0,0)}.In this note, we assume that, for s,tH, there exists some xs,t in GF(2) such that a(s,t) satisfies the following equation: Then, we prove that the dual hyperoval constructed by {a(s,t)} is isomorphic to either the Huybrechts’ dual hyperoval, or the Buratti and Del Fra’s dual hyperoval.  相似文献   

17.
Letμbe a Gaussian measure (say, onRn) and letK,LRnbe such thatKis convex,Lis a “layer” (i.e.,L={xaxub} for someabRanduRn), and the centers of mass (with respect toμ) ofKandLcoincide. Thenμ(KL)μ(Kμ(L). This is motivated by the well-known “positive correlation conjecture” for symmetric sets and a related inequality of Sidak concerning confidence regions for means of multivariate normal distributions. The proof uses the estimateΦ(x)> 1−((8/π)1/2/(3x+(x2+8)1/2))ex2/2,x>−1, for the (standard) Gaussian cumulative distribution function, which is sharper than the classical inequality of Komatsu.  相似文献   

18.
P.M. Cohn has proved the remarkable theorem, that every invertible n × n matrix over a free algebra is the product of elementary n × n matrices, see [C1], [C2]. In this note we prove the analogue for symplectic 2 × 2 matrices over free algebras relative to a homogeneous involution: every symplectic 2 × 2 matrix is the product of elementary symplectic 2 × 2 matrices.In Section 1 we define the group Sp2(R) of symplectic 2 × 2 matrices over an involutive ring R. The group ESp2(R) generated by elementary symplectic matrices is introduced in Section 3.In Section 2 we prove a reducibility criterion for homogeneous polynomials in a free algebra KX over a commutative field K. It leads to a special form in the factorization of symmetric homogeneous polynomials, see Corollary to Proposition 2.2.We prove in Section 4 that ESp2(KX) = Sp2(KX), if the involution on KX is homogeneous.In a subsequent article we will show that the main result is also true for 2g × 2g symplectic matrices over free algebras relative to homogeneous involutions, g ≥ 1. It seems that a proof of this result will be much more complicated than the case g = 1.  相似文献   

19.
A one-dimensional singularly perturbed problem with a boundary turning point is considered in this paper. Let Vh be the linear finite element space on a suitable grid . A variant of streamline diffusion finite element method is proved to be almost uniform stable in the sense that the numerical approximation uh satisfies u-uhC|lnε| infvhVhu-vh, where C is independent with the small diffusion coefficient ε and the mesh . Such stability result is applied to layer-adapted grids to obtain almost ε-uniform second order scheme for turning point problems.  相似文献   

20.
We show that a sequentially (τ)-complete topological vector lattice Xτ is isomorphic to some L1(μ), if and only if the positive cone can be written as X+ = +B for some convex, (τ)-bounded, and (τ)-closed set B X+ {0}. The same result holds under weaker hypotheses, namely the Riesz decomposition property for X (not assumed to be a vector lattice) and the monotonic σ-completeness (monotonic Cauchy sequences converge). The isometric part of the main result implies the well-known representation theorem of Kakutani for (AL)-spaces. As an application we show that on a normed space Y of infinite dimension, the “ball-generated” ordering induced by the cone Y+ = + (for u >) cannot have the Riesz decomposition property. A second application deals with a pointwise ordering on a space of multivariate polynomials.  相似文献   

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