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991.
V. F. Murzina 《Algebra and Logic》2005,44(5):313-325
An axiomatization is furnished for a polymodal logic of strictly linearly ordered A-frames: for frames of this kind, we consider
a language of polymodal logic with two modal operators, □< and □≺. In the language, along with the operators, we introduce a constant β, which describes a basis subset. In the language with
the two modal operators and constant β, an Lα-calculus is constructed. It is proved that such is complete w.r.t. the class
of all strictly linearly ordered A-frames. Moreover, it turns out that the calculus in question possesses the finite-model
property and, consequently, is decidable.
__________
Translated from Algebra i Logika, Vol. 44, No. 5, pp. 560–582, September–October, 2005.
Supported by RFBR grant No. 03-06-80178, by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1, and by INTAS grant No. 04-77-7080. 相似文献
992.
More than a decade of research and innovation in using computer-based graphing and simulation environments has encouraged
many of us in the research community to believe important dimensions of calculus-related reasoning can be successfully understood
by young learners. This paper attempts to address what kinds of calculus-related insights seem to typify this early form of
calculus reasoning. The phrase “qualitative calculus” is introduced to frame the analysis of this “other” calculus. The learning
of qualitative calculus is the focus of the synthesis. The central claim is that qualitative calculus is a cognitive structure
in its own right and that qualitative calculus develops or evolves in ways that seem to fit with important general features
of Piaget's analyses of the development of operational thought. In particular, the intensification of rate and two kinds of
reversibility between what are called “how much” (amount) and “how fast” (rate) quantities are what interactively, and collectively,characterize
and help to define understanding qualitative calculus. Although sharing a family resemblance with traditional expectations
of what it might mean to learn calculus, qualitative calculus does not build from ratio- or proportion-based ideas of slope
as they are typically associated with defining rate. The paper does close, however, with a discussion of how understanding
qualitative calculus can support and link to the rate-related literature of slope, ratio and proportion. Additionally, curricular
connections and implications are discussed throughout to help illustrate and explore the significance of learning qualitative
calculus.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
993.
The inverse problem of the calculus of variations for second-order nonlinear and linear systems of differential-difference equations is considered. The relationship between the formal potentiality of a linear system with constant coefficients and the parity of its characteristic function is established. 相似文献
994.
Carlos Simpson 《Letters in Mathematical Physics》2004,69(1-3):287-315
We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This includes the basic reasons why it should be interesting to pure mathematicians, some history, natural desiderata for a useful system, viewpoints on what kind of logic to use, a short explanation of how things work, an overview of different options for encoding sets, and perspectives on future developments. 相似文献
995.
Complex powers of a class of hypoelliptic pseudodifferential operators in Rn, as well as their heat kernels are studied. An application to the Schatten-von Neumann property of pseudodifferential operators is given. 相似文献
996.
Maurice Arrigoni 《Mathematische Nachrichten》1998,192(1):71-89
In this paper, we consider some conditions of finiteness related to the p-class field tower problem over an imaginary quadratic field, where p is an odd prime. 相似文献
997.
998.
The solutions of linear fuzzy stochastic differential systems 总被引:2,自引:0,他引:2
As a completion of previous work of Feng (Fuzzy Sets and Systems 115 (2000) 351) on the general theory of fuzzy stochastic differential systems, the solutions of linear fuzzy stochastic differential systems for general coefficient matrix are discussed. 相似文献
999.
Patrick Cheridito David Nualart 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2005,41(6):1049-1081
We define a stochastic integral with respect to fractional Brownian motion BH with Hurst parameter that extends the divergence integral from Malliavin calculus. For this extended divergence integral we prove a Fubini theorem and establish versions of the formulas of Itô and Tanaka that hold for all . Then we use the extended divergence integral to show that for every and all , the Russo–Vallois symmetric integral exists and is equal to , where G′=g, while for , does not exist. 相似文献
1000.
This paper develops two related fractional trigonometries based on the multi-valued fractional generalization of the exponential function, the R-function. The trigonometries contain the traditional trigonometric functions as proper subsets. Also developed are relationships between the R-function and the new fractional trigonometric functions. Laplace transforms are derived for the new functions and are used to generate solution sets for various classes of fractional differential equations. Because of the fractional character of the R-function, several new trigonometric functions are required to augment the traditional sine, cosine, etc. functions. Fractional generalizations of the Euler equation are derived. As a result of the fractional trigonometry a new set of phase plane functions, the Spiral functions, that contain the circular functions as a subset, is identified. These Spiral functions display many new symmetries. 相似文献