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排序方式: 共有82条查询结果,搜索用时 15 毫秒
51.
Wagner MM Pinsky PM Malhotra M 《The Journal of the Acoustical Society of America》2003,113(1):313-319
This paper addresses the efficient solution of acoustic problems in which the primary interest is obtaining the solution only on restricted portions of the domain but over a wide range of frequencies. The exterior acoustics boundary value problem is approximated using the finite element method in combination with the Dirichlet-to-Neumann (DtN) map. The restriction domain problem is formally posed in transfer function form based on the finite element solution. In order to obtain the solution over a range of frequencies, a matrix-valued Padé approximation of the transfer function is employed, using a two-sided block Lanczos algorithm. This approach provides a stable and efficient representation of the Padé approximation. In order to apply the algorithm, it is necessary to reformulate the transfer function due to the frequency dependency in the nonreflecting boundary condition. This is illustrated for the case of the DtN boundary condition, but there is no restriction on the approach which can also be applied to other radiation boundary conditions. Numerical tests confirm that the approach offers significant computational speed-up. 相似文献
52.
We resolve the long-standing problem of describing the multidimensional random evolutions by means of the telegraph equations.
This problem was posed by Mark Kac more than 50 years ago and has become the subject of intense discussion among researchers
on whether the multidimensional random flights could be described by the telegraph equations similarly to the one-dimensional
case. We give the exhaustive answer to this question and show that the multidimensional random evolutions are driven by the
hyperparabolic operators composed of the telegraph operators and their integer powers. The only exception is the 2D random
flight whose transition density is the fundamental solution to the two-dimensional telegraph equation. The reason of the exceptionality
of the 2D-case is explained. We also show that, under the standard Kac’s condition, the governing hyperparabolic operator
turns into the generator of the Brownian motion. 相似文献
53.
T.C. Slaba S.R. Blattnig S.K. Aghara L.W. Townsend T. Handler T.A. Gabriel L.S. Pinsky B. Reddell 《Radiation measurements》2010,45(2):173-182
Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward–backward (FB) and directionally coupled forward–backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient. 相似文献
54.
Mark A. Pinsky 《Journal of Theoretical Probability》1993,6(1):187-193
A density functionf(x),xR
n
is said to bepiecewise smooth if for eachxR
n
, the mean value function
is piecewiseC
with compact support. (d is normalized surface measure on the unit sphere). The Fourier transform is
with spherical partial sum
.
Theorem. For suchf, lim
r
f
R
(x)=M
0+f(x) if and only ifrM
r
f(x) hask=[(n–3)/2] continuous derivatives. ([]=integer part). Otherwise we have lim
where 0 is uniquely determined. 相似文献
55.
Functions of the Laplace operator F(− Δ) can be synthesized from the solution operator to the wave equation. When F is the characteristic function of [0, R
2
], this gives a representation for radial Fourier inversion. A number of topics related to pointwise convergence or divergence
of such inversion, as R → ∞, are studied in this article. In some cases, including analysis on Euclidean space, sphers, hyperbolic
space, and certain other symmetric spaces, exact formulas for fundamental solutions to wave equations are available. In other
cases, parametrices and other tools of microlocal analysis are effective. 相似文献
56.
57.
Ross G. Pinsky 《Proceedings of the American Mathematical Society》2002,130(6):1673-1679
Let and let be a continuous, nonincreasing function on satisfying . Consider the heat equation in the exterior of a time-dependent shrinking disk in the plane:
If there exist constants and a constant 0$"> such that , for sufficiently large , then . The same result is also shown to hold when is replaced by , where . Also, a discrepancy is noted between the asymptotics for the above forward heat equation and the corresponding backward one. The method used is probabilistic.
0.\end{split}\end{displaymath}">
If there exist constants and a constant 0$"> such that , for sufficiently large , then . The same result is also shown to hold when is replaced by , where . Also, a discrepancy is noted between the asymptotics for the above forward heat equation and the corresponding backward one. The method used is probabilistic.
58.
Distance functions serve for quantitative evaluation of the degree of similarity, shape content, symmetry, chirality, and so on. We have developed a general methodology and a general computational tool for the estimation of the value of the distance function and of the error in that estimation, which originates in the experimental uncertainty in the location of the set of points of the studied structure (such as that expressed by the atomic displacement factor in X-ray data analysis). 相似文献
59.
60.