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991.
Mohammad Gholampour 《Quaestiones Mathematicae》2018,41(2):227-238
We prove that every generalized Jordan derivation D from a JB?-algebra 𝒜 into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C?-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C?-algebra to a Banach bimodule is continuous. 相似文献
992.
Dhanapati Adhikari 《Journal of Differential Equations》2010,249(5):1078-1655
This paper aims at the global regularity of classical solutions to the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. We prove that the Lr-norm of the vertical velocity v for any 1<r<∞ is globally bounded and that the L∞-norm of v controls any possible breakdown of classical solutions. In addition, we show that an extra thermal diffusion given by the fractional Laplace δ(−Δ) for δ>0 would guarantee the global regularity of classical solutions. 相似文献
993.
Kyungkeun Kang 《Journal of Differential Equations》2010,249(11):2643-2493
We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate. Moreover, we prove that such a local boundedness estimate for weak solutions of the system is equivalent to the usual global pointwise bound for the Green's matrix. In the scalar case, such an estimate is a consequence of De Giorgi-Moser-Nash theory and holds for equations with bounded measurable coefficients in arbitrary domains. In the vectorial case, one need to impose certain assumptions on the coefficients of the system as well as on domains to obtain such an estimate. We present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result. 相似文献
994.
Feng-Bin Wang 《Journal of Differential Equations》2010,249(11):2866-2888
This paper examines a system of reaction-diffusion equations arising from a flowing water habitat. In this habitat, one or two microorganisms grow while consuming two growth-limiting, complementary (essential) resources. For the single population model, the existence and uniqueness of a positive steady-state solution is proved. Furthermore, the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values. Mathematical analysis for the two competing populations is carried out. More precisely, the long-time behavior is determined by using the monotone dynamical system theory when the semi-trivial solutions are both unstable. It is also shown that coexistence solutions exist by using the fixed point index theory when the semi-trivial solutions are both (asymptotically) stable. 相似文献
995.
Vesko Valov 《Journal of Mathematical Analysis and Applications》2010,370(1):132-145
The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for 0-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and κ-metrizability, are preserved under Milyutin maps. 相似文献
996.
Pengtao Li 《Journal of Mathematical Analysis and Applications》2010,369(2):595-609
In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Navier-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of . This result applies to the usual incompressible Navier-Stokes equations. 相似文献
997.
The infinite-dimensional special odd contact Lie superalgebras SKO(n,n+1;c) over a field of positive characteristic are studied. In particular, we prove that Lie superalgebras SKO(n,n+1;c) are simple. Besides, the Weisfeiler filtration of SKO(n,n+1;c) is proved to be invariant under automorphisms by characterizing -nilpotent elements. Thereby, we obtain some properties of these Lie superalgebras. 相似文献
998.
Tetsuya Hosaka 《Journal of Pure and Applied Algebra》2010,214(6):919-936
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group G acts geometrically (i.e. properly and cocompactly by isometries) on a proper CAT(0) space X. (Such a group G is called a CAT(0) group.) Then the group G acts by homeomorphisms on the boundary ∂X of X and we can define a metric d∂X on the boundary ∂X. The boundary ∂X is called a scrambled set if, for any α,β∈∂X with α≠β, (1) lim sup{d∂X(gα,gβ)∣g∈G}>0 and (2) lim inf{d∂X(gα,gβ)∣g∈G}=0. We investigate when boundaries of CAT(0) groups (and Coxeter groups) are scrambled sets. 相似文献
999.
Bisubmodular functions are a natural “directed”, or “signed”, extension of submodular functions with several applications.
Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function
minimization (SFM) to bisubmodular function minimization (BSFM). However, they were able to extend only the weakly polynomial
version of IFF to BSFM. Here we investigate the difficulty that prevented them from also extending the strongly polynomial
version of IFF to BSFM, and we show a way around the difficulty. This new method gives a somewhat simpler strongly polynomial
SFM algorithm, as well as the first combinatorial strongly polynomial algorithm for BSFM. This further leads to extending
Iwata’s fully combinatorial version of IFF to BSFM.
The research of S. T. McCormick was supported by an NSERC Operating Grant.
The research of S. Fujishige was supported by a Grant-in-Aid of the Ministry of Education, Culture, Science and Technology
of Japan. 相似文献
1000.
Hedy Attouch 《Journal of Differential Equations》2010,248(6):1315-1344
We study the asymptotic behavior, as time variable t goes to +∞, of nonautonomous dynamical systems involving multiscale features. As a benchmark case, given H a general Hilbert space, and two closed convex functions, and β a function of t which tends to +∞ as t goes to +∞, we consider the differential inclusion