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1.
On hearing the shape of a bounded domain with Robin boundary conditions   总被引:2,自引:0,他引:2  
The asymptotic expansions of the trace of the heat kernel (t)= [sum ]j=1 exp(-tj) for small positive t, where {j} j=1 arethe eigenvalues of the negative Laplacian -n = -[sum ]nk=1 (/xk)2in Rn (n = 2 or 3), are studied for a general multiply connectedbounded domain which is surrounded by simply connected boundeddomains i with smooth boundaries i (i = 1,...,m), where smoothfunctions Yi (i = 1,...,m) are assuming the Robin boundary conditions(ni + Yi) = 0 on i. Here /ni denote differentiations along theinward-pointing normals to i (i = 1,...,m). Some applicationsof an ideal gas enclosed in the multiply connected bounded containerwith Neumann or Robin boundary conditions are given.  相似文献
2.
The basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region inR 2 with mixed boundary conditions, from the complete knowledge of the eigenvalues { j } j=1 for the Laplace operator, using the asymptotic expansion of the spectral function (t)= j=1 exp(–t j ) ast0.  相似文献
3.
Summary The trace function where { m} m=1 are the eigenvalues of the Laplacian is studied for a variety of domains. The dependence of(t) on the connectivity of a domain and the boundary conditions is analysed. Particular attention is given to annular domains.
Résumé Pour divers domaines, on étudie la fonction trace , où 1, 2, 3, sont les valeurs propres du laplacien. On analyse comment(t) dépend du domaine et des conditions aux limites. On considère notamment le cas de couronnes circulaires.
  相似文献
4.
The trace function where are the eigenvalues of the three-dimensional Laplacian, is studied for a variety of domains. The dependenceof (t) on the connectivity of domains and the boundary conditionsis analysed. Particular attention is given for a spherical shell.  相似文献
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6.
The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) > 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.  相似文献
7.
Ultrasonic machining (USM) is one of the most effective non-conventional techniques. Its application especially to hard-to-machine material (HTM) is growing rapidly. The main operation condition of USM is at resonance where an exciter derives a tuned blade or a tool. In this paper, the coupling of two non-linear oscillators of the main system and absorber representing ultrasonic cutting process are investigated. This leads to a two-degree-of-freedom Duffing’s oscillator in which such non-linear effects can be neutralized under certain dynamic conditions. The aim of this work is the control of the system behavior at principal parametric resonance condition where the system damage is probable. An approximate solution is derived up to the second order for the coupled system. A threshold value of linear damping has been obtained, where the system vibration can be reduced dramatically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the absorber on system behavior are studied numerically. Comparison with the available published work is reported.  相似文献
8.
In this paper we give an approach for constructing classes of near open and near closed sets which have unusual implication relations. These new classes of subsets are based on the alternative effect of closure and interior operators with respect to two topologies. Also these classes of subsets are applied for constructing several classes of near continuous functions and some types of separation axioms called mildly binormal, almost ij-normal, almost ij-regular, quasi ij-regular and strongly S-ij-regular. Using the introduced functions, we generalize several preservation theorems of normality and regularity to bitopological spaces. Implications between notions are given and counter examples for some reverse directions are obtained. It should be noted that considering the space time as the product of two topologies, the topology of space and that of the space time will open the way for new line of research in the field of quantum gravity initiated by Witten and El-Naschie and many others (cf. [Chaos, Solitons & Fractals 17 (2003) 989; Chaos, Solitons & Fractals 7 (1996) 499; Int. J. Theor. Phys. 37 (1998) 2935; Phys. Today (1996) 24]).  相似文献
9.
We used the technique of the separation of Coulomb and diffraction dissociation of incident heavy ion to select the events due to induced neutron from 16O leaving sub-oxygen nucleus to break-up. The characteristics of these events of neutron emulsion collisions are displayed and compared with that obtained from incident proton at the same energy.

The studied interactions are classified according to the type of target nucleus (H, CNO and AgBr) by using the method of separation. Cascade-evaporation model (CEM) calculations are taken into account and compared with that obtained from the interactions of induced neutron from 16O (4.5 A GeV/c) with emulsion nuclei and with the results of incident proton at the same target and energy. CEM can describe the distributions of proton and neutron interactions. It is conjuctured that it may be possible to develop a similar theoretical model based on the modern methods of nonlinear dynamics, neural network and complexity [Randomness and Undecidability in Physics, World Scientific, Singapore, 1993].  相似文献

10.
In this paper the limit distribution function (d.f.) of general bivariate order statistics (o.s.) (extreme, intermediate and central) is studied by the notion of the exceedances of levels and characteristic function (c.f.) technique. The advantage of this approach is to give a simple and unified method to derive the limit d.f. of any bivariate o.s. The conditions under which the limit d.f. splits into the product of the limit marginals are obtained. Some illustrative examples are given.  相似文献
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