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1.
We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series. 相似文献
2.
We consider the double-scaling limit in the hermitian matrix model for 2D quantum gravity associated with the measure exp
. We show that after the appropriate modification of the contour of integration the Cross-Migdal-Douglas-Shenker limit to the Painlevé I equation (in the generic case of the pure gravity) is valid and calculate the nonperturbative parameters of the corresponding Painlevé function. Our approach is based on the WKB-analysis of the L-A pair corresponding to the discrete string equation in the framework of the Inverse Monodromy Method. Here we extend our results, which were obtained before for the particular casesN=2,3. Our analysis complements the isomonodromy approach proposed by G. Moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself. 相似文献
3.
We introduce a method of solving initial boundary value problems for linear evolution equations in a time-dependent domain, and we apply it to an equation with dispersion relation omega(k), in the domain l(t)相似文献
4.
Demosthenes Kivotides 《Physics letters. A》2018,382(22):1481-1485
It is shown that, as a result of its interactions with superfluid vorticity, a normal-fluid vortex tube in helium-4 becomes unstable and disintegrates. The superfluid vorticity acquires only a small (few percents of normal-fluid tube strength) polarization, whilst expanding in a front-like manner in the intervortex space of the normal-fluid, forming a dense, unstructured tangle in the process. The accompanied energy spectra scalings offer a structural explanation of analogous scalings in fully developed finite-temperature superfluid turbulence. A macroscopic mutual-friction model incorporating these findings is proposed. 相似文献
5.
Sook Voon Yap Robert M. Ranson Wayne M. Cranton Demosthenes C. Koutsogeorgis Gary B. Hix 《Journal of luminescence》2009,129(5):416-422
This research is aimed at developing an optical sensor for remotely measuring human skin temperature in electromagnetically hostile environments, such as within a magnetic resonance imaging (MRI) scanner. In this feasibility study, various concentrations of europium-doped lanthanum oxysulphide (La2O2S: Eu—0.1-15 mol% (m/o)) and terbium-doped lanthanum oxysulphide (La2O2S: Tb—0.005-50 m/o) have been investigated in terms of crystallinity, photoluminescent (PL) spectral and decay time characteristics. For both phosphors, X-ray diffraction (XRD) has shown that as dopancy increases, the (1 0 0) and (0 0 2) reflections merge and there is a reduction in the c-axis parameter as well as the crystallite size. Photoluminescent characterisation (337 nm excitation) has also shown a dependency to dopant concentration through variance of peak intensity. Temperature dependent decay time measurements were carried out over a low temperature range 5-60 °C. Optimum brightness of these temperature dependent lines is achieved at concentrations of 1 and 10 m/o for La2O2S: Eu and La2O2S: Tb respectively. However, optimum temperature dependency is achieved at lower concentration for La2O2S: Eu, specifically at 0.1 m/o. In comparison to conventional phosphor temperature dependent characteristic, La2O2S: Tb showed an increase in decay time with respect to temperature for concentrations above 2 m/o. 相似文献
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Vasilis F. Milas Demosthenes Vouyioukas Nektarios Moraitis Philip Constantinou 《European Journal of Operational Research》2008
A new network has been recently proposed for the provision of fixed broadband services via high altitude platform stations (HAPS) in the 48/47 GHz band. One of the critical issues of this technology is spectrum sharing with the fixed satellite service. This paper examines the effect of Earth-to-stratosphere co-channel interference produced by ground stations of HAPS network to geostationary orbit (GEO) satellite receivers and proposes an interference-to-noise (I/N) calculation model for the evaluation of the current HAPS ground stations power characteristics set by ITU-R. Analytical and simulation results for archetypal systems in realistic scenarios indicate that efficient use of the spectrum shared between heterogeneous HAPS and Fixed Satellite Networks is feasible. Certain consideration is needed prior to the HAPS network development in suburban areas for latitudes from 55° to 65°, and in rural areas for latitudes from 60° to 75°. 相似文献
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The Kadomtsev-Petviashvili equation, a two-spatial-dimensional analogue of the Korteweg-deVries equation, arises in physical situations in two different forms depending on a certain sign appearing in the evolution equation. Here we investigate one of the two cases. The initial-value problem, associated with initial data decaying sufficiently rapidly at infinity, is linearized by a suitable extension of the inverse scattering transform. Essential is the formulation of a nonlocal Riemann-Hilbert problem in terms of scattering data expressible in closed form in terms of given initial data. The lump solutions, algebraically decaying solitons, are given a definite spectral characterization. Pure lump solutions are obtained by solving a linear algebraic system whose coefficients depend linearly on x, y, t. Many of the above results are also relevant to the problem of inverse scattering for the so-called time-dependent Schrödinger equation. 相似文献