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1.
Material structure of bodies that is usually assumed a-priory in continuum mechanics is constructed on the basis of a balance of a given extensive property on spacetime. Body points are identified with worldlines—the integral lines of the flux of the property. The geometric setting assumes that spacetime has only the structure of a differentiable manifold and no particular frame is assumed to be given. 相似文献
2.
The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely-jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility. In many experimental situations the choice is not clear and a model describing the crossover between these two limiting classes is therefore in high demand. We are proposing a unified chain deformation model which describes the force-deformation curve in terms of the chain bending constant K and bond length b. This model demonstrates that the worm-like and freely-jointed chain models correspond to two different regimes of polymer deformation and the crossover between these two regimes depends on the chain bending rigidity and the magnitude of the applied force. Polymer chains with bending constant K>1 behave as a worm-like chain under tension in the interval of the applied forces f ≤ Kk(B)T/b and as a freely-jointed chain for f ≥ Kk(B)T/b (k(B) is the Boltzmann constant and T is the absolute temperature). The proposed crossover expression for chain deformation is in excellent agreement with the results of the molecular dynamics simulations of chain deformation and single-molecule deformation experiments of biological and synthetic macromolecules. 相似文献
3.
Elizabeth Galati Huachen Tao Moritz Tebbe Rija Ansari Michael Rubinstein Ekaterina B. Zhulina Eugenia Kumacheva 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2019,131(10):3155-3159
Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end‐grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface‐pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish‐kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self‐assembly modes. 相似文献
4.
Reuven Rubinstein 《Methodology and Computing in Applied Probability》2008,10(2):121-178
We present a new generic minimum cross-entropy method, called the semi-iterative MinxEnt, or simply SME, for rare-event probability estimation, counting, and approximation of the optimal solutions of a broad class
of NP-hard linear integer and combinatorial optimization problems (COP’s). The main idea of our approach is to associate with
each original problem an auxiliary single-constrained convex MinxEnt program of a special type, which has a closed-form solution. We prove that the optimal pdf obtained from the
solution of such a specially designed MinxEnt program is a zero variance pdf, provided the “temperature” parameter is set
to minus infinity. In addition we prove that the parametric pdf based on the product of marginals obtained from the optimal
zero variance pdf coincides with the parametric pdf of the standard cross-entropy (CE) method. Thus, originally designed at the end of 1990s as a heuristics for estimation of rare-events and COP’s, CE has
strong connection with MinxEnt, and thus, strong mathematical foundation. The crucial difference between the proposed SME
method and the standard CE counterparts lies in their simulation-based versions: in the latter we always require to generate
(via Monte Carlo) a sequence of tuples including the temperature parameter and the parameter vector in the optimal marginal
pdf’s, while in the former we can fix in advance the temperature parameter (to be set to a large negative number) and then
generate (via Monte Carlo) a sequence of parameter vectors of the optimal marginal pdf’s alone. In addition, in contrast to
CE, neither the elite sample no the rarity parameter is needed in SME. As result, the proposed SME algorithm becomes simpler,
faster and at least as accurate as the standard CE. Motivated by the SME method we introduce a new updating rule for the parameter
vector in the parametric pdf of the CE program. We show that the CE algorithm based on the new updating rule, called the combined CE (CCE), is at least as fast and accurate as its standard CE and SME counterparts. We also found numerically that the variance
minimization (VM)-based algorithms are the most robust ones. We, finally, demonstrate numerically that the proposed algorithms,
and in particular the CCE one, allows accurate estimation of counting quantities up to the order of hundred of decision variables
and hundreds of constraints.
This research was supported by the Israel Science Foundation (grant No 191-565). 相似文献
5.
Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) ?r(2)(t)? ~ t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling ?r(2)(t)? ~ t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log?r(2)(t)?/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales. 相似文献
6.
7.
We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties. 相似文献
8.
9.
Dirk P. Kroese Sergey Porotsky Reuven Y. Rubinstein 《Methodology and Computing in Applied Probability》2006,8(3):383-407
In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In
this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness
of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear
constraints.
相似文献
10.
Zalman Rubinstein 《Aequationes Mathematicae》1981,23(1):108-117
Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered. 相似文献