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71.
In the early 1930s, Wiener proved that if f(x) is a strictlypositive periodic function whose Fourier series is absolutelyconvergent, then the Fourier series of g(x)=1/f(x) is also absolutelyconvergent [8, pp. 1014]. This phenomenon can be easilyunderstood nowadays using Banach algebra techniques (see, forexample, [4, pp. 202203]). In fact, these techniquesallow us to study the absolute convergence of g(x)=F(f(x)),where F is holomorphic in an open subset of C that containsthe range of f(x) (for xR). In this context, Wiener's originalproblem corresponds to the choice F(z)=1/z. In this work we want to analyse the constraints on the simultaneousrate of vanishing of the Fourier coefficients f(n) and (n) asn. We shall focus on g=1/f, but we shall also study the generalcase g=F(f). In either case, there are obviously no constraintswhen f is a constant function. Although this problem does not seem to be directly related touncertainty inequalities for the Fourier Transform, we observethat there are some analogies, both in the nature of the resultsand in the proof techniques. The general fact with which weare dealing is that f(n) and (n) cannot vanish too quickly atthe same time as n, unless f(x) is constant. The general factthat underlies uncertainty inequalities is that a non-periodicfunction (x) and its Fourier Transform circ;(u) cannot vanishtoo quickly at the same time as x and u, unless (x) is zero(almost everywhere). For a simple introduction to some aspectsof uncertainty inequalities, see [5]; for a thorough and recentintroduction to this vast subject, see [3]. 1991 MathematicsSubject Classification 42A05, 42A16, 42A99. 相似文献
72.
Enrico Schlesinger 《Transactions of the American Mathematical Society》1999,351(7):2731-2743
We prove a version of the Halphen Speciality Theorem for locally Cohen-Macaulay curves in . To prove the theorem, we strengthen some results of Okonek and Spindler on the spectrum of the ideal sheaf of a curve. As an application, we classify curves having index of speciality as large as possible once we fix the degree of and the minimum degree of a surface containing .
73.
Enrico Massa 《General Relativity and Gravitation》1974,5(5):573-591
The general theory of space tensors is applied to the study of a space-time manifoldsV
4 carrying a distinguished time-like congruence Γ. The problem is to determine a physically relevant spatial tensor analysis
over (V
4, Γ), in order to proceed to a correct formulation of Relative Kinematics and Dynamics.
This is achieved by showing that each choice of
gives rise to a corresponding notion of ‘frame of reference’ associated with the congruence Γ. In particular, the frame of
reference (Γ, ∇*) determined by the standard spatial tensor analysis
is shown to provide the most natural generalization of the concept of frame of reference in Classical Physics.
The previous arguments are finally applied to the study of geodesic motion inV
4. As a result, the general structure of the gravitational fields in the frame of reference (Γ, ∇*) is established.
This work was assisted by funds from the C.N.R. under the aegis of the activity of the National Group for Mathematical Physics. 相似文献
74.
Enrico C. Poggio 《Annals of Physics》1973,81(2):481-518
An alternate method of renormalizing a quartic self-interacting boson theory has been developed. We find that one can obtain finite renormalized expressions for the perturbation theory contributions to the Green's function without carrying out limiting procedures. As a consequence of the analysis, one is able to renormalize explicitly the field energy-momentum tensor to all orders. There exists a one-parameter family of renormalized tensors. The method will allow for a simple determination of the asymptotic “zero-mass” theory. 相似文献
75.
Enrico Abignente Paolo De Caprariis Michele Liguori 《Journal of heterocyclic chemistry》1983,20(6):1597-1599
Some new 4,5-dihydro-5-oxoisoxazole derivatives were synthesized as part of a study to prepare potential antiinflammatory agents. The reaction of the diethyl ester of 3-oxopentanedioic acid with hydroxylamine afforded the 3-hydroxyimino derivative, which was then cyclized to the title compound. This reacted with diazomethane to give a couple of isomeric methyl derivatives, namely methyl 2,5-dihydro-2-methyl-5-oxo-3-isoxazoleacetate and methyl 5-methoxy-3-isoxazoleacetate. Reaction of these compounds with ammonia gave the corresponding acetamides. All compounds were characterized by elemental analysis, uv, ir, and 1H-nmr spectra. 相似文献
76.
77.
78.
Thermal conductivities of molecular liquids by reverse nonequilibrium molecular dynamics 总被引:1,自引:0,他引:1
Zhang M Lussetti E de Souza LE Müller-Plathe F 《The journal of physical chemistry. B》2005,109(31):15060-15067
The reverse nonequilibrium molecular dynamics method for thermal conductivities is adapted to the investigation of molecular fluids. The method generates a heat flux through the system by suitably exchanging velocities of particles located in different regions. From the resulting temperature gradient, the thermal conductivity is then calculated. Different variants of the algorithm and their combinations with other system parameters are tested: exchange of atomic velocities versus exchange of molecular center-of-mass velocities, different exchange frequencies, molecular models with bond constraints versus models with flexible bonds, united-atom versus all-atom models, and presence versus absence of a thermostat. To help establish the range of applicability, the algorithm is tested on different models of benzene, cyclohexane, water, and n-hexane. We find that the algorithm is robust and that the calculated thermal conductivities are insensitive to variations in its control parameters. The force field, in contrast, has a major influence on the value of the thermal conductivity. While calculated and experimental thermal conductivities fall into the same order of magnitude, in most cases the calculated values are systematically larger. United-atom force fields seem to do better than all-atom force fields, possibly because they remove high-frequency degrees of freedom from the simulation, which, in nature, are quantum-mechanical oscillators in their ground state and do not contribute to heat conduction. 相似文献
79.
Eckhoff DA Sutin JD Clegg RM Gratton E Rogozhina EV Braun PV 《The journal of physical chemistry. B》2005,109(42):19786-19797
Studying the properties and stability of silicon nanoparticles (Si-np) in aqueous environments may lead to novel applications in biological systems. In this work, we use absorption and photoluminescence (PL) spectroscopy to characterize ultrasmall Si-np prepared through anodic etching and ultrasonic fractionation of a crystalline Si wafer. Their behavior is studied over time in 2-propanol and during treatments with water, NaOH, HCl, and H(2)O(2). The observed population is divided into two types of material: bright species consisting of well-etched Si-np, approximately 1 nm in diameter, and dark species derived from partially etched or aggregated Si structures. The dark material is seen by its scattering in the 2-propanol and water solutions and is largely removed via precipitation with the NaOH or HCl treatment. The bright material includes three distinct species with their respective emissions in the UV-B, UV-A, and hard-blue regions of the spectrum. The hard-blue PL is shown to have a simple pH dependence with a pK(a) approximately 3, providing an important insight into its chemical origin and signaling for possible application of Si-np as environmental probes. Our results offer some potential for tailoring the PL properties of ultrasmall Si-np through control of their surface chemistry. 相似文献
80.
Janulewicz KA Schnürer M Tümmler J Priebe G Risse E Nickles PV Greenberg B Levin M Pukhov A Mandelbaum P Zigler A 《Optics letters》2005,30(12):1572-1574
Investigations of plasma produced by a boron nitride capillary discharge irradiated with a guided 20-TW Ti: sapphire laser pulse at a peak intensity of 4 x 10(18) W/cm2 are presented. The guided laser radiation in the plasma channel generated He-like ions that, subject to suitable plasma temperature, recombined into Li-like nitrogen ions. Intense radiation at a wavelength of 24.77 nm was observed, indicating possible lasing at the 3d(5/2) - 2p(3/2) transition in Li-like nitrogen. 相似文献