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961.
Raffaele Chiappinelli 《Journal of Mathematical Analysis and Applications》2008,340(1):511-520
The Ekeland Variational Principle is used to prove the nonemptiness of the spectrum for positively homogeneous gradient mappings in Hilbert space. Under additional information on the measure of noncompactness of the operator, this leads to the existence of a maximal (or minimal) compact eigenvalue for the operator itself. 相似文献
962.
A new second-order alternating direction implicit (ADI) scheme, based on the idea of the operator splitting, is presented for solving two-dimensional wave equations. The scheme is also extended to a high-order compact difference scheme. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical examples are presented and the results are very satisfactory. 相似文献
963.
Manfred Mö ller Franciszek Hugon Szafraniec 《Proceedings of the American Mathematical Society》2008,136(6):2165-2176
In this paper we discuss diverse aspects of the mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize the behaviour of row and column operators as they turn out to be the germs of an arbitrary matrix operator, providing most of the information about the latter as it is the troublemaker.
964.
We establish finite- and infinite-dimensional versions of the following assertion. If M is a matrix with the property that whenever P and Q are diagonal projections with P?Q, the spectrum of PMP (considered as an operator on the range of P) is contained in that of QMQ (considered as an operator on the range of Q), then there is a permutation matrix U such that U−1MU is triangular. 相似文献
965.
Alexandru Nica 《Journal of Functional Analysis》2009,257(2):428-1844
Let k be a positive integer and let Dc(k) denote the space of joint distributions for k-tuples of selfadjoint elements in C∗-probability space. The paper studies the concept of “subordination distribution of μ?ν with respect to ν” for μ,ν∈Dc(k), where ? is the operation of free additive convolution on Dc(k). The main tools used in this study are combinatorial properties of R-transforms for joint distributions and a related operator model, with operators acting on the full Fock space.Multi-variable subordination turns out to have nice relations to a process of evolution towards ?-infinite divisibility on Dc(k) that was recently found by Belinschi and Nica (arXiv: 0711.3787). Most notably, one gets better insight into a connection which this process was known to have with free Brownian motion. 相似文献
966.
D. Dryanov 《Constructive Approximation》2009,30(1):137-153
Kolmogorov ε-entropy of a compact set in a metric space measures its metric massivity and thus replaces its dimension which is usually infinite. The notion quantifies the compactness property of sets in metric
spaces, and it is widely applied in pure and applied mathematics. The ε-entropy of a compact set is the most economic quantity of information that permits a recovery of elements of this set with
accuracy ε. In the present article we study the problem of asymptotic behavior of the ε-entropy for uniformly bounded classes of convex functions in L
p
-metric proposed by A.I. Shnirelman. The asymptotic of the Kolmogorov ε-entropy for the compact metric space of convex and uniformly bounded functions equipped with L
p
-metric is ε
−1/2, ε→0+.
相似文献
967.
To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated
in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not
possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require
symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory,
wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field
theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having
to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum
field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot
vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing
vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of
a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than
the natural scales of the theory.
Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation. 相似文献
968.
969.
Let MC denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?C∈B(K,H)σr(MC) are, respectively, characterized completely, where σc(·) denotes the continuous spectrum, σp(·) denotes the point spectrum and σr(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given. 相似文献
970.
Mark P. Simens Javier Jiménez Sergio Hoyas Yoshinori Mizuno 《Journal of computational physics》2009,228(11):4218-4231
A new high-resolution code for the direct simulation of incompressible boundary layers over a flat plate is described. It can accommodate a wide range of pressure gradients, and general time-dependent boundary conditions such as incoming wakes or wall forcing. The consistency orders of the advective and pressure-correction steps are different, but it is shown that the overall resolution is controlled by the higher-order advection step. The formulation of boundary conditions to ensure global mass conservation in the presence of arbitrary forcing is carefully analyzed. Two validation boundary layers with and without a strong adverse pressure gradient are presented, with maximum Reynolds numbers Reθ≈2000. They agree well with the available experiments. Turbulent inflow conditions for the zero-pressure case are implemented by a recycling method, and it is shown that at least the initial 300 momentum thicknesses have to be discarded before the effect of the artificial inflow is forgotten. It is argued that this is not a defect of the method used to generate the inflow, but a property of the boundary layer. 相似文献