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101.
Christophe Gallesco Sandro Gallo Daniel Y. Takahashi 《Stochastic Processes and their Applications》2018,128(2):689-706
We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail -algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak- summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are summable. Finally, if we weaken the condition for DU, asking for coincidence on the future -algebra for almost every pair of pasts, we obtain a condition that is equivalent to -mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak- summability condition on the kernel is equivalent to the -mixing of the compatible stationary chain. 相似文献
102.
Sandro Bettin Jonathan W. Bober Andrew R. Booker Brian Conrey Min Lee Giuseppe Molteni Thomas Oliver David J. Platt Raphael S. Steiner 《The Ramanujan Journal》2018,45(3):659-681
By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term \(z^{t^j}\) in their partial numerators, where z is a complex variable and t is a positive integer. This approach is extended to other, sparser, subsequences of Stern polynomials, based on certain Lucas functions; this then leads to further infinite classes of continued fractions. 相似文献
103.
For every and every integer N, let be the minimum of the distance of τ from the sums , where . We prove that , for all sufficiently large positive integers N (depending on C and τ), where C is any positive constant less than . 相似文献
104.
We present a quantitative semiclassical theory for the decay of nondispersive electronic wave packets in driven, ionizing Rydberg systems. Statistically robust quantities are extracted combining resonance-assisted tunneling with subsequent transport across chaotic phase space and a final ionization step. 相似文献
105.
We study the robustness of different sweep protocols for accelerated adiabaticity following in the presence of static errors and of dissipative and dephasing phenomena. While in the noise-free case, counterdiabatic driving is, by definition, insensitive to the form of the original sweep function, this property may be lost when the quantum system is open. We indeed observe that, according to the decay and dephasing channels investigated here, the performance of the system becomes highly dependent on the sweep function. Our findings are relevant for the experimental implementation of robust shortcuts-to-adiabaticity techniques for the control of quantum systems. 相似文献
106.
This paper is concerned with a model of a predator–prey system, where both populations disperse among n patches forming their habitat. Criteria are given tor both survival and extinction of the predator population. In case the predator survives, conditions are derived which guarantee a globally asymptotically stable positive equilibrium 相似文献
107.
Abdulrafiu Tunde Raji Sandro Scandolo Riccardo Mazzarello Schadrack Nsengiyumva Margit Härting David Thomas Britton 《哲学杂志》2013,93(20):1629-1645
By means of an ab initio plane-wave pseudopotential method, monovacancy, divacancy and self-interstitials in hcp titanium are investigated. The calculated monovacancy formation energy is 1.97 eV, which is in excellent agreement with other theoretical calculations, and agrees qualitatively with published experimental results. The relaxation of the atoms around a single vacancy is observed to be small. Two divacancy configurations, the in-plane and the off-plane, have also been shown to be equally stable. With regards to the interstitials, of the eight configurations studied, two (octahedral and basal octahedral) have relatively lower formation energies and are, thus, the most likely stable configurations. We find small energy differences between them, suggesting their possible co-existence. It is also observed that the tetrahedral configuration decays to a split dumbbell configuration, whereas both the basal tetrahedral and the basal pseudocrowdion interstitials decay to the basal octahedral configuration. Using the nudged elastic band method (NEB), we determine a possible minimum energy path (MEP) for the diffusion of self-interstitial titanium atoms from an octahedral site to the nearest octahedral site. The energy barrier for this migration mechanism is shown to be about 0.20 eV. 相似文献
108.
Sandro Sozzo 《Foundations of Physics》2013,43(6):792-804
The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model. 相似文献
109.
Nicolai Haydn Matthew Nicol Sandro Vaienti Licheng Zhang 《Journal of statistical physics》2013,153(5):864-887
Suppose B i :=B(p,r i ) are nested balls of radius r i about a point p in a dynamical system (T,X,μ). The question of whether T i x∈B i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if $E_{n}:=\sum_{i=1}^{n} \mu(B_{i})$ diverges then there is a quantitative rate of entry and $\lim_{n\to\infty} \frac{1}{E_{n}} \sum_{j=1}^{n} 1_{B_{i}} (T^{i} x) \to1$ for μ a.e. x∈X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form $\lim_{ n\to\infty} \frac{1}{a_{n}} \sum_{i=1}^{n} [1_{B_{i}} (T^{i} x)-\mu(B_{i})] \to N(0,1)$ (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are $a^{2}_{n} \sim E [\sum_{i=1}^{n} 1_{B_{i}} (T^{i} x)-\mu(B_{i})]^{2}$ . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability. 相似文献
110.
Sandro Mattarei 《Linear and Multilinear Algebra》2013,61(4):441-449
In a recent study of Engel Lie rings, Serena Cicalò and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of this fact. Our main result generalizes this in the language of tensor algebra, and describes a relatively small generating set for the module generated by all n-th tensor powers of elements of a finitely generated ?-module M, in terms of a generating set for M. 相似文献