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991.
We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov
process such that the level of performance of one component can change only for one level lower than the observed one, and
the failures are independent for different components. We derive the probability distribution of the random vector X, representing the state of the system at the moment of failure and use it for testing the hypothesis of equal transition
intensities. Under the assumption that these intensities are equal, we derive the method of moments estimators for probabilities
of failure in a given state vector and the intensity of failure. At the end we calculate the reliability function for such
systems.
Received: May 18, 2007., Revised: July 8, 2008., Accepted: September 29, 2008. 相似文献
992.
Recently a new notion, the so-called boundary relation, has been introduced involving an analytic object, the so-called Weyl family. Weyl families and boundary relations establish a link between the class of Nevanlinna families and unitary relations acting from one Kreĭn space, a basic (state) space, to another Kreĭn space, a parameter space where
the Nevanlinna family or Weyl family is acting. Nevanlinna families are a natural generalization of the class of operator-valued
Nevanlinna functions and they are closely connected with the class of operator-valued Schur functions. This paper establishes
the connection between boundary relations and their Weyl families on the one hand, and unitary colligations and their transfer functions on the other hand. From this connection there are various advances which will benefit the investigations on both sides, including
operator theoretic as well as analytic aspects. As one of the main consequences a functional model for Nevanlinna families is obtained from a variant of the functional model of L. de Branges and J. Rovnyak for Schur functions.
Here the model space is a reproducing kernel Hilbert space in which multiplication by the independent variable defines a closed
simple symmetric operator. This operator gives rise to a boundary relation such that the given Nevanlinna family is realized
as the corresponding Weyl family.
Received: January 21, 2008., Revised: March 31, 2008. 相似文献
993.
Vladimir Ryzhov 《Complex Analysis and Operator Theory》2009,3(1):289-322
The paper defines the Weyl–Titchmarsh function for an abstract boundary value problem and shows that it coincides with the
transfer function of some explicitly described linear boundary control system. On the ground of obtained results we explore
interplay among boundary value problems, operator colligations, and the linear systems theory that suggests an approach to
the study of boundary value problems based on the open systems theory founded in works of M. S. Livšic. Examples of boundary
value problems for partial differential equations and calculations of their Weyl–Titchmarsh functions are offered as illustration.
In particular, we give an independent derivation of the Weyl–Titchmarsh function for the three dimensional Schr?dinger operator
introduced by W.O. Amrein and D.B. Pearson. Relationships to the Schr?dinger operator with singular potential supported by
the unit sphere are clarified and other possible applications of the developed approach in mathematical physics are noted.
Received: May 21, 2007., Revised: October 8, 2007., Accepted: October 11, 2007 相似文献
994.
We study Bernoulli type convolution measures on attractor sets arising from iterated function systems on R. In particular we examine orthogonality for Hankel frequencies in the Hilbert space of square integrable functions on the
attractor coming from a radial multiresolution analysis on R3. A class of fractals emerges from a finite system of contractive affine mappings on the zeros of Bessel functions. We have
then fractal measures on one hand and the geometry of radial wavelets on the other hand. More generally, multiresolutions
serve as an operator theoretic framework for the study of such selfsimilar structures as wavelets, fractals, and recursive
basis algorithms. The purpose of the present paper is to show that this can be done for a certain Bessel–Hankel transform.
Submitted: February 20, 2008., Accepted: March 6, 2008. 相似文献
995.
We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann
transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space.
Received: May 11, 2007. Revised: May 20, 2008. Accepted: May 23, 2008. 相似文献
996.
What is a Logic Translation? 总被引:1,自引:0,他引:1
We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature
of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic
translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes
that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and
logic translation, can be recovered by their abstract properties and are preserved and reflected by translations under suitable
conditions.
In memoriam Joseph Goguen 相似文献
997.
Abbas Bahri 《Journal of Fixed Point Theory and Applications》2009,5(2):265-289
Let v be a nonsingular Morse–Smale vector field in the kernel of a contact form α, with Reeb vector field , defined on M3. We establish that the associated variational problem at infinity defined by the action functional on the stratified space
of curves made of -pieces of orbits alternating with -pieces of orbits satisfies the Palais–Smale condition. This result takes a more special form for the standard contact structure
of S3.
Dedicated to Felix Browder on his eightieth birthday 相似文献
998.
Nikolaos S. Papageorgiou Francesca Papalini 《Journal of Fixed Point Theory and Applications》2009,5(1):157-184
We study a nonlinear periodic problem driven by the scalar p-Laplacian and having a nonsmooth potential (hemivariational inequality). Using a combination of variational techniques and
degree-theoretic methods based on a degree map for certain multivalued perturbations of (S)+operators, we establish the existence of two positive solutions. 相似文献
999.
Existence and Stability Results for Renormalized Solutions to Noncoercive Nonlinear Elliptic Equations with Measure Data 总被引:1,自引:0,他引:1
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is
where is a bounded open subset of , , is the so-called Laplace operator, , is a Radon measure with bounded variation on , , , and belong to the Lorentz spaces , and , respectively. In particular we prove the existence result under the assumption that , is small enough and , with . We also prove a stability result for renormalized solutions to a class of noncoercive equations whose prototype is with . 相似文献
1000.
In this note, we study the non-linear evolution problem $dY_t = -A Y_t dt + B(Y_t) dX_t,$ where $XIn this note, we study the non-linear evolution problem
where is a -H?lder continuous function of the time parameter, with values in a distribution space, and the generator of an analytical semigroup. Then, we will give some sharp conditions on in order to solve the above equation in a function space, first in the linear case (for any value of in ), and then when satisfies some Lipschitz type conditions (for ). The solution of the evolution problem will be understood in the mild sense, and the integrals involved in that definition will be of Young type. 相似文献