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1.
Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.  相似文献
2.
This text is a report of an international conference about mathematics education in French-speaking countries in the XXth century and prospects for the beginning of the XXIth century which was organised by the CFEM in Grenoble from 15 to 17 July 2000.  相似文献
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4.
We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the delta-convex structure of the function. The new definition extends to a more general class of functions, which includes Lipschitz functions definable on o-minimal structure and quasidifferentiable functions.  相似文献
5.
Let \(\eta : C_{f,N}\rightarrow \mathbb {P}^1\) be a cyclic cover of \(\mathbb {P}^1\) of degree \(N\) which is totally and tamely ramified for all the ramification points. We determine the group of fixed points of the cyclic covering group \({{\mathrm{Aut}}}(\eta )\simeq \mathbb {Z}/ N \mathbb {Z}\) acting on the Jacobian \(J_N:={{\mathrm{Jac}}}(C_{f,N})\) . For each prime \(\ell \) distinct from the characteristic of the base field, the Tate module \(T_\ell J_N\) is shown to be a free module over the ring \(\mathbb {Z}_\ell [T]/(\sum _{i=0}^{N-1}T^i)\) . We also study the subvarieties of \(J_N\) and calculate the degree of the induced polarization on the new part \(J_N^\mathrm {new}\) of the Jacobian.  相似文献
6.
A theory of the shock wave structure in a rarefied polyatomic gas is developed on the basis of the recent new approach to extended thermodynamics. We summarize the following points (i) and (ii) based on the previous study on this subject and also show the new point (iii): (i) The theory can explain the change of types of the shock wave structure observed experimentally with the increase of the Mach number from unity; the nearly symmetric shock wave structure (Type A, small Mach number), the asymmetric structure (Type B, moderate Mach number), and the structure composed of thin and thick layers (Type C, large Mach number). (ii) The theoretical prediction of the mass density profile agrees well with experimental data. (iii) The points (i) and (ii) are not strongly affected by the details of the temperature dependence of the bulk viscosity.  相似文献
7.
It is well recognized that using the hot standby redundancy provides fast restoration in the case of failures. However the redundant elements are exposed to working stresses before they are used, which reduces the overall system reliability. Moreover, the cost of maintaining the hot redundant elements in the operational state is usually much greater than the cost of keeping them in the cold standby mode. Therefore, there exists a tradeoff between the cost of losses associated with the restoration delays and the operation cost of standby elements. Such a trade-off can be obtained by designing both hot and cold redundancy types into the same system. Thus a new optimization problem arises for the standby system design. The problem, referred to in this work as optimal standby element distributing and sequencing problem (SE-DSP) is to distribute a fixed set of elements between cold and hot standby groups and select the element initiation sequence so as to minimize the expected mission operation cost of the system while providing a desired level of system reliability. This paper first formulates and solves the SE-DSP problem for 1-out-of-N: G heterogeneous non-repairable standby systems. A numerical method is proposed for evaluating the system reliability and expected mission cost simultaneously. This method is based on discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated optimization problem. Examples are given to illustrate the considered problem and the proposed solution methodology.  相似文献
8.
We show that a combination of two simple preprocessing steps would generally improve the conditioning of a homogeneous system of linear inequalities. Our approach is based on a comparison among three different but related notions of conditioning for linear inequalities.  相似文献
9.
A topic of recent interest in the retail financial sector has been the growth of credit unions or “pure cooperatives”. Past credit union researchers built mathematical models of credit union operations. These models identified important operating characteristics but were modeled under assumptions of static operating environments. The model presented in this paper departs from the traditional static models and examines dynamic operation for a United States credit union. Its inter-temporal structure clarifies a number of issues—such as optimal equity retention and inter-temporal rate policy—not addressed by earlier studies. Given initial conditions, the model specifies equity retention and inter-temporal deposit and loan rate policies until an equilibrium state is reached.  相似文献
10.
Self-diffusion, or the flux of mass of a single species within itself, is viewed as an independent phenomenon amenable to treatment by the introduction of an auxiliary field of diffusion velocities. The theory is shown to be heuristically derivable as a limiting case of that of an ordinary binary mixture.  相似文献
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