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81.
Galois lattices and formal concept analysis of binary relations have proved useful in the resolution of many problems of theoretical or practical interest. Recent studies of practical applications in data mining and software engineering have put the emphasis on the need for both efficient and flexible algorithms to construct the lattice. Our paper presents a novel approach for lattice construction based on the apposition of binary relation fragments. We extend the existing theory to a complete characterization of the global Galois (concept) lattice as a substructure of the direct product of the lattices related to fragments. The structural properties underlie a procedure for extracting the global lattice from the direct product, which is the basis for a full-scale lattice construction algorithm implementing a divide-and-conquer strategy. The paper provides a complexity analysis of the algorithm together with some results about its practical performance and describes a class of binary relations for which the algorithm outperforms the most efficient lattice-constructing methods. 相似文献
82.
Raymond Turner 《Entropy (Basel, Switzerland)》2021,23(2)
Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems. 相似文献
83.
Morris L. Eaton James P. Hobert Galin L. Jones 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(5):633-653
Consider a parametric statistical model, P(dx|θ), and an improper prior distribution, ν(dθ), that together yield a (proper) formal posterior distribution, Q(dθ|x). The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of θ is admissible under squared error loss. Eaton [M.L. Eaton, A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains, Annals of Statistics 20 (1992) 1147–1179] used the Blyth–Stein Lemma to develop a sufficient condition, call it , for strong admissibility of ν. Our main result says that, under mild regularity conditions, if ν satisfies and g(θ) is a bounded, non-negative function, then the perturbed prior distribution g(θ)ν(dθ) also satisfies and is therefore strongly admissible. Our proof has three basic components: (i) Eaton's [M.L. Eaton, A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains, Annals of Statistics 20 (1992) 1147–1179] result that the condition is equivalent to the local recurrence of the Markov chain whose transition function is R(dθ|η)=∫Q(dθ|x)P(dx|η); (ii) a new result for general state space Markov chains giving conditions under which local recurrence is equivalent to recurrence; and (iii) a new generalization of Hobert and Robert's [J.P. Hobert, C.P. Robert, Eaton's Markov chain, its conjugate partner and -admissibility, Annals of Statistics 27 (1999) 361–373] result that says Eaton's Markov chain is recurrent if and only if the chain with transition function is recurrent. One important application of our results involves the construction of strongly admissible prior distributions for estimation problems with restricted parameter spaces. 相似文献
84.
A new cascade reaction including formal [5?+?2] cycloaddition was developed. Treatment of homocinnamyl alcohol and Co2(CO)6-complexed arylpropynal with BF3·OEt2 resulted in the generation of hydrobenzocycloheptafuran having an alkyne-Co2(CO)6 complex. The reaction consists of 5-membered ring selective Prins cyclization and subsequent Friedel-Crafts cyclization. The cascade reaction was applied to a further multi-step cascade cyclization, which resulted in the formation of more complex polycyclic hydrofurans. 相似文献
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David Jensen 《代数通讯》2013,41(1):347-360
Let (T, M) be a complete local ring such that |T/M| = | T |. Given a finite set of incomparable nonmaximal prime ideals C of T, we provide necessary and sufficient conditions for T to be the completion of a local UFD A, whose generic formal fiber is semilocal with maximal ideals the elements of C. We also show that, given the T above, we can find necessary and sufficient conditions for T to be the completion of a UFD, whose formal fiber over a height one prime ideal is semilocal. Communicated by I. Swanson. 相似文献
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Jinsong Ni 《Central European Journal of Mathematics》2009,7(2):224-229
We will give a condition characterizing spaces X with SNT(X) = {[X]} which generalizes the corresponding result of McGibbon and Moller [8] for rational H-spaces.
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