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1.
Linking, Legendrian Linking and Causality 总被引:1,自引:0,他引:1
The set N of all null geodesics of a globally hyperbolic (d+ 1)-dimensional spacetime (M, g) is naturally a smooth (2d 1)-dimensional contact manifold. The sky of an eventx in M is the subset X of N consisting of all null geodesicsthrough x, and is an embedded Legendrian submanifold of N diffeomorphicto S(d 1). It was conjectured by Low that for d = 2two events x and y are causally related if and only if X andY are linked (in an appropriate sense). We use the contact structureand knot polynomial calculations to prove this conjecture incertain particular cases, and suggest that for d = 3 smoothlinking should be replaced with Legendrian linking. 相似文献
2.
Let A be an order integral over a valuation ring V in a centralsimple F-algebra, where F is the fraction field of V. We showthat (a) if (Vh, Fh) is the Henselization of (V, F), then Ais a semihereditary maximal order if and only if AVVh is a semihereditarymaximal order, generalizing the result by Haile, Morandi andWadsworth, and (b) if J(V) is a principal ideal of V, then asemihereditary V-order is an intersection of finitely many conjugatesemihereditary maximal orders; if not, then there is only onemaximal order containing the V-order. 1991 Mathematics SubjectClassification 16H05. 相似文献
3.
Let X=Spec B be an affine variety over a field of arbitrarycharacteristic, and suppose that there exists an action of aunipotent group (possibly neither smooth nor connected). Thefundamental results are as follows. (1) An algorithm for computinginvariants is given, by means of introducing a degree in thering of functions of the variety, relative to the action. Thereforean algorithmic construction of the quotient, in a certain openset, is obtained. In the case of a Galois extension, k B=K,which is cyclic of degree p=char k (that is, such that the unipotentgroup is G=Z/pZ), an element of minimal degree becomes an ArtinSchreierradical, and the method for computing invariants gives, in particular,the expression for any element of K in terms of these radicals,with an explicit formula. This replaces the well-known formulaof Lagrange (which is valid only when the degree of the extensionand the characteristic are relatively prime) in the case ofan extension of degree p=char k. (2) In this paper we give aneffective construction of a stable open subset where there isa quotient. In this sense we obtain an algebraic local criterionfor the existence of a quotient in a neighbourhood. It is proved(provided the variety is normal) that, in the following cases,such an open set is the greatest one that admits a quotient:
- when the action is such that the orbits have dimension lessthan or equal to 1 (arbitrary characteristic) and, in particular,for any action of the additive group Ga;
- in characteristic0, when the action is proper (obtained fromthe results of Fauntleroy)or the group is abelian.
4.
Noble (1969) has described a method for the solution of N+Mlinear equations in N unknowns, which is based on an initialpartitioning of the matrix A, and which requires only the solutionof square sets of equations. He assumed rank (A) = N. We describehere an efficient implementation of Noble's method, and showthat it generalizes in a simple way to cover also rank deficientproblems. In the common case that the equation is only slightlyoverdetermined (M << N) the resulting algorithm is muchfaster than the standard methods based on M.G.S. or Householderreduction of A, or on the normal equations, and has a very similaroperation count to the algorithm of Cline (1973). Slightly overdetermined systems arise from Galerkin methodsfor non-Hermitian partial differential equations. In these systems,rank (A) = N and advantage can be taken of the structure ofthe matrix A to yield a least squares solution in (N2) operations. 相似文献
5.
Let G be a compact group and C(G) be the C*-algebra of continuouscomplex-valued functions on G. The paper constructs an imbeddingof the Fourier algebra A(G) of G into the algebra V(G) = C(G)hC(G)(Haagerup tensor product) and deduces results about parallelspectral synthesis, generalizing a result of Varopoulos. Itthen characterizes which diagonal sets in G x G are sets ofoperator synthesis with respect to the Haar measure, using thedefinition of operator synthesis due to Arveson. This resultis applied to obtain an analogue of a result of Froelich: atensor formula for the algebras associated with the pre-ordersdefined by closed unital subsemigroups of G. 相似文献
6.
Invariants of Finite Group Schemes 总被引:1,自引:0,他引:1
Let G be a finite group scheme operating on an algebraic varietyX, both defined over an algebraically closed field k. The paperfirst investigates the properties of the quotient morphism X- X/G over the open subset of X consisting of points whose stabilizershave maximal index in G. Given a G-linearized coherent sheafon X, it describes similarly an open subset of X over whichthe invariants in the sheaf behave nicely in some way. The pointsin X with linearly reductive stabilizers are characterized inrepresentation theoretic terms. It is shown that the set ofsuch points is nonempty if and only if the field of rationalfunctions k(X) is an injective G-module. Applications of theseresults to the invariants of a restricted Lie algebra g operatingon the function ring k[X] by derivations are considered in thefinal section. Furthermore, conditions are found ensuring thatthe ring k[X]g is generated over the subring of pth powers ink[X], where p=char,k>0, by a given system of invariant functionsand is a locally complete intersection. 相似文献
7.
It is shown that if a plane of PG(3,q), q even, meets an ovoidin a conic, then the ovoid must be an elliptic quadric. Thisis proved by using the generalized quadrangles T2(C) (C a conic),W(q) and the isomorphism between them to show that every secantplane section of the ovoid must be a conic. The result thenfollows from a well-known theorem of Barlotti. 相似文献
8.
It is proved here that a minimal isometric immersion of a Kähler-Einsteinor homogeneous Kähler-manifold into an Euclidean spacemust be totally geodesic. As an application, it is shown thatan open subset of the real hyperbolic plane RH2 cannot be minimallyimmersed into the Euclidean space. As another application, aproof is given that if an irreducible Kähler manifold isminimally immersed in a Euclidean space, then its restrictedholonomy group must be U(n), where n = dimCM. 2000 MathematicsSubject Classification 53B25 (primary); 53C42 (secondary). 相似文献
9.
Quasi-Permutation Representations of p-Groups of Class 2 总被引:1,自引:0,他引:1
If G is a finite linear group of degree n, that is, a finitegroup of automorphisms of an n-dimensional complex vector space(or, equivalently, a finite group of non-singular matrices oforder n with complex coefficients), we shall say that G is aquasi-permutation group if the trace of every element of G isa non-negative rational integer. The reason for this terminologyis that, if G is a permutation group of degree n, its elements,considered as acting on the elements of a basis of an n-dimensionalcomplex vector space V, induce automorphisms of V forming agroup isomorphic to G. The trace of the automorphism correspondingto an element x of G is equal to the number of letters leftfixed by x, and so is a non-negative integer. Thus, a permutationgroup of degree n has a representation as a quasi-permutationgroup of degree n. See [8]. 相似文献
10.
We consider a nonlinear heat conduction problem for a semi-infinitematerial x > 0, with phase-change temperature T1, an initialtemperature T2 (> T1) and a heat flux of the type q (t) =q0/t imposed on the fixed face x = 0. We assume that the volumetricheat capacity and the thermal conductivity are particular nonlinearfunctions of the temperature in both solid and liquid phases. We determine necessary and/or sufficient conditions on the parametersof the problem in order to obtain the existence of an explicitsolution for an instantaneous nonlinear twophase Stefan problem(solidification process). 相似文献
11.
We introduce a new transform method for solving initial-boundary-valueproblems for linear evolution partial differential equationswith spatial derivatives of arbitrary order. This method isillustrated by solving several such problems on the half-line{t > 0, 0 < x < }, and on the quarter-plane {t >0, 0 < xj < , j = 1, 2}. For equations in one space dimensionthis method constructs q(x, t) as an integral in the complexk-plane involving an x-transform of the initial condition anda t-transform of the boundary conditions. For equations in twospace dimensions it constructs q(x1, x2, t) as an integral inthe complex (k1, k2)-planes involving an (x1, x2)-transformof the initial condition, an (x2, t)-transform of the boundaryconditions at x1 = 0, and an (x1, t)-transform of the boundaryconditions at x2 = 0. This method is simple to implement andyet it yields integral representations which are particularlyconvenient for computing the long time asymptotics of the solution. 相似文献
12.
The StöhrVoloch approach is used to obtain a newbound for the number of solutions in (Fq)2 of an equation f(X,Y) = 0, where f(X, Y) is an absolutely irreducible polynomialwith coefficients in a finite field Fq. 相似文献
13.
The Sharkovskii type of a map of an interval is the Sharkovskii-greatestinteger t such that it has a periodic point of period t. TheSharkovskii type of a cycle (that is, a cyclic permutation)is the Sharkovskii type of the 'connect the dots' map determinedby it. For n 2, let c(n) denote the finite set of integerswhich are Sharkovskil types of n-cycles. We give an internalcharacterization of c(n) and an n4-time algorithm for determiningthe Sharkovskii type of an n-cycle. 相似文献
14.
Suppose a sequence (Sn)n, converges to a limit S. In this paperwe construct, from a good estimate (Dn)n of (|SnS|),an acceleration method for (Sn)n based on: (a) an automaticselection between two transformations if (Dn)n converges logarithmically;(b) composite sequence transformations if (Dn)n converges linearly. 相似文献
15.
Let X and Y be reflexive Banach spaces with strictly convexduals, and let T be a compact linear map from X to Y. It isshown that a certain nonlinear equation, involving T and itsadjoint, has a normalised solution (an eigenvector)corresponding to an eigenvalue, and that the sameis true for each member of a countable family of similar equationsinvolving the restrictions of T to certain subspaces of X. Theaction of T can be described in terms of these eigenvectors.There are applications to the p-Laplacian, the p-biharmonicoperator and integral operators of Hardy type. 相似文献
16.
The combined effect of diffusion, and of convection by Poiseuilleflow, on the distribution of a small quantity of miscible additiveinjected into a tube of radius a, is to spread it longitudinallywith a Taylor "effective diffusion coefficient", to an approximationthat is good at times greater than about 0.5a2/D (Bailey &Gogarty, 1962), where D is the molecular diffusion coefficient.The present theory, complementary to the Taylor theory, determinesthe initial action of diffusion on the front of the concentrationdistribution, to an approximation that is good at times t lessthan about 0.1a2/D. The theory is exact wherever the added substancedoes not yet interact with the tube wall, and predicts thatthe spread in the front due to diffusion extends (Fig. 2) overa distance of order DUt2/a2, where U is the velocity on theaxis of the tube. The transition between distributions characteristicof the two theories is illustrated (Fig. 4); and the introductionindicates the relevance of the new theory to work (Caro, 1966)on tracers used in study of the blood circulation. 相似文献
17.
If two operator algebras A and B are strongly Morita equivalent(in the sense of [5]), then their C*-envelopes C*(A) and C*(B)are strongly Morita equivalent (in the usual C*-algebraic sensedue to Rieffel). Moreover, if Y is an equivalence bimodule fora (strong) Morita equivalence of A and B, then the operation,YhA, of tensoring with Y, gives a bijection between theboundary representations of C*(A) for A and the boundary representationsof C*(B) for B. Thus the noncommutative Choquet boundariesof Morita equivalent A and B are the same. Other important objectsassociated with an operator algebra are also shown to be preservedby Morita equivalence, such as boundary ideals, the Shilov boundaryideal, Arveson's property of admissability, and the latticeof C*-algebras generated by an operator algebra. 1991 MathematicsSubject Classification 47D25, 46L05, 46M99, 16D90. 相似文献
18.
Let G denote the p-adic group GL(n), and let S(G) denote theSchwartz algebra of G. We construct a Chern character from theK-theory of the reduced C*-algebra of G to the periodic cyclichomology of S(G) which becomes an isomorphism after tensoringover Z with C. 相似文献
19.
The Finite Dimensional Approximation Property and the AR-Property in Needle Point Spaces 总被引:1,自引:0,他引:1
We introduce the notion of the finite dimensional approximationproperty (the FDAP) and prove that if a subset X of a linearmetric space has the FDAP, then every non-empty convex subsetof X is an AR. As an application we show that every needle point space X containsa dense linear subspace E with the following properties: (i) E contains a non-empty compact convex set with no extremepoints; (ii) all non-empty convex subsets of E are AR. 相似文献
20.
A linear projection R on a Jordan*-triple A is said to be structuralprovided that, for all elements a, b and c in A, the equality{Rab Rc} = R{a Rbc} holds. A subtriple B of A is said to becomplemented if A = B + Ker(B), where Ker(B) = {aA: {B a B}= 0}. It is shown that a subtriple of a JBW*-triple is complementedif and only if it is the range of a structural projection. A weak* closed subspace B of the dual E* of a Banach space Eis said to be an N*-ideal if every weak* continuous linear functionalon B has a norm preserving extension to a weak* continuous linearfunctional on E* and the set of elements in E which attain theirnorm on the unit ball in B is a subspace of E. It is shown thata subtriple of a JBW*-triple A is complemented if and only ifit is an N*-ideal, from which it follows that complemented subtriplesof A are weak* closed, and structural projections on A are weak*continuous and norm non-increasing. It is also shown that everyN*-ideal in A possesses a triple product with respect to whichit is a JBW*-triple which is isomorphic to a complemented subtripleof A. 相似文献