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71.
Roberto E. Madariaga-Garcia 《Topology and its Applications》2007,154(7):1470-1480
Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size c2 using a forcing model in which CH holds.Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup. In 1996, Robbie and Svetlichny constructed a Wallace semigroup under CH. In the same year, Tomita constructed a Wallace semigroup from MAcountable.In this note, we show that the examples of Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family of selective ultrafilters. As a corollary, the constructions presented here are compatible with the total failure of Martin's Axiom. 相似文献
72.
The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that Cp(X) has the Arkhangel'ski?ˇ property (α1) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, Cp(X) and Arhangel'ski?ˇ's αi-spaces, Topology Appl. 89 (1998) 265-275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of Cp(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S1(Γshr,Γ). Moreover we show that X is a QN-space if and only if Cp(X) has the property (α0), and for perfectly normal spaces, if and only if X has the covering property (β3). 相似文献
73.
M. Frigon 《Journal of Fixed Point Theory and Applications》2007,1(2):189-194
We present results on the global existence of analytic solutions to the Cauchy problem in starshaped or convex complex domains.
No growth conditions are imposed. Our results rely on a notion of solution-tube that we introduce.
à la mémoire de Jean Leray 相似文献
74.
Marilyn Breen 《Journal of Geometry》1989,36(1-2):8-16
LetS be a compact, simply connected set inR
2. If every boundary point ofS is clearly visible viaS from at least one of the three pointsa, b, c, thenS is a union of three starshaped sets whose kernels containa, b, c, respectively. The result fails when the number three is replaced by four.As a partial converse, ifS is a union of three starshaped sets whose kernels containa, b, c, respectively, then the set of points in the boundary ofS clearly visible from at least one ofa, b, orc is dense in the boundary ofS.Supported in part by NSF grant DMS-8705336. 相似文献
75.
This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart. 相似文献
76.
Valery Agoshkov Paola Gervasio Alfio Quarteroni 《Mediterranean Journal of Mathematics》2006,3(2):147-176
New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second
order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence
results are proved for the coupled problem, and the convergence of iterative processes is analyzed.
The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the
first author was visiting the IACS at EPFL. 相似文献
77.
We introduce symmetric Boundary Value Methods for the solution of second order initial and boundary value problems (in particular
Hamiltonian problems). We study the conditioning of the methods and link it to the boundary loci of the roots of the associated
characteristic polynomial. Some numerical tests are provided to assess their reliability.
Dedicated to the memory of Professor Aldo Cossu 相似文献
78.
Igor Chueshov 《Journal of Differential Equations》2007,233(1):42-86
We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation. 相似文献
79.
The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable. 相似文献
80.
We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator. 相似文献