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71.
We consider some inequalities in such classical Banach Function Spaces as Lorentz, Marcinkiewicz, and Orlicz spaces. Our aim is to explore connections between the norm of a function of two variables on the product space and the mixed norm of the same function, where mixed norm is calculated in function spaces on coordinate spaces, first in one variable, then in the other. This issue is motivated by various problems of functional analysis and theory of functions. We will currently mention just geometry of spaces of vector-valued functions and embedding theorems for Sobolev and Besov spaces generated by metrics which differ from L
p. Our main results are actually counterexamples for Lorentz spaces versus the natural intuition that arises from the easier case of Orlicz spaces (Section 2). In the Appendix we give a proof for the Kolmogorov–Nagumo theorem on change of order of mixed norm calculation in its most general form. This result shows that L
p is the only space where it is possible to change this order. 相似文献
72.
Let W and Z be Banach spaces, and let and be closed subspaces. Let be a subspace of , the Banach space of bounded linear operators from W* to Z**, containing . We describe, for and , all norm-preserving extensions of to the space in terms of convergence of convex combinations. We also characterize denting points of bounded convex subsets of Banach spaces
in similar terms. Various applications are presented.
Supported by Estonian Science Foundation Grant 5704. 相似文献
73.
We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact, we define and study the notions of the L-double quotient spaces and the sum of L-double fuzzy closure spaces. Finally, we study the additivity of two kinds of L-double fuzzy closure spaces. 相似文献
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77.
Marco Fuhrman Gianmario Tessitore 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):429-464
We consider a forward-backward system of stochastic evolution equations in a Hilbert space. Under nondegeneracy assumptions on the diffusion coefficient (that may be nonconstant) we prove an analogue of the well-known Bismut-Elworthy formula. Next, we consider a nonlinear version of the Kolmogorov equation, i.e. a deterministic quasilinear equation associated to the system according to Pardoux, E and Peng, S. (1992). "Backward stochastic differential equations and quasilinear parabolic partial differential equations". In: Rozowskii, B.L., Sowers, R.B. (Eds.), Stochastic Partial Differential Equations and Their Applications , Lecture Notes in Control Inf. Sci., Vol. 176, pp. 200-217. Springer: Berlin. The Bismut-Elworthy formula is applied to prove smoothing effect, i.e. to prove existence and uniqueness of a solution which is differentiable with respect to the space variable, even if the initial datum and (some) coefficients of the equation are not. The results are then applied to the Hamilton-Jacobi-Bellman equation of stochastic optimal control. This way we are able to characterize optimal controls by feedback laws for a class of infinite-dimensional control systems, including in particular the stochastic heat equation with state-dependent diffusion coefficient. 相似文献
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《Optimization》2012,61(5-6):407-411
We present a class of functionals on a real Banach space for which every local minimum point with respect to the norm topology is so also with respect to the weak topology 相似文献
80.
In this paper,we introduce the notion of intuitionistic fuzzy slightly continuity as a generalizing fuzzy continuity.Basic properties and preservation theorems of intuitionistic fuzzy slightly continuous functions are obtained. 相似文献