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The TFR(Tampered Failure Rate) model was proposed by Bhattacharyya and Soejoeti(1989) for step-stress accelerated]ire tests. On step-stress completely accelerated test occasions, the paper gives a method of estimating parameters under a normal stress. 相似文献
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A mathematical model has been developed which aims to give insightinto the transport phenomena in the vicinity of the interfaceof a crystal grown by the Czochralski method in the presenceof an axial magnetic field. The fluid flow, temperature andconcentration fields in this region have a strong effect onthe distribution of impurities and the occurrence of cracks,dislocations and other physical defects in the crystal and soknowledge and ultimately control of these factors is of greatpractical importance. The model incorporates rotation of both the crystal and crucibleby considering the crystal to be an infinite disc rotating ina semi-infinite fluid which may be rotating at infinity. Axialsymmetry is assumed and the magnetic Prandtl number is consideredto be very much less than unity. This means that induced currentscan be neglected and allows a similarity solution to be developed.The system of partial differential equations can then be replacedby an ordinary differential boundary-value problem which issolved numerically. 相似文献
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We develop the immersed interface method (IIM) to simulate a two-fluid flow of two immiscible fluids
with different density and viscosity. Due to the surface tension and the discontinuous fluid properties,
the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interface
separating the two fluids. The IIM computes the flow on a fixed Cartesian grid by incorporating
into numerical schemes the necessary jump conditions induced by the interface.
We present how to compute these necessary jump conditions from the analytical principal jump
conditions derived in [Xu, DCDS, Supplement 2009, pp. 838-845]. We test our method on some canonical
two-fluid flows. The results demonstrate that the method can handle large density and viscosity ratios,
is second-order accurate in the infinity norm, and conserves mass inside a closed interface. 相似文献
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A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors. 相似文献
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The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification. 相似文献
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Hans Smessaert 《Logica Universalis》2009,3(2):303-332
The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition,
namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties
of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions
for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us
to define the Aristotelian relations in Boolean terms and to propose a 3D visualisation by transforming a cube into an octahedron.
In part two, the architecture of the CQA is shown to carry over, both to the classical quantifiers of Predicate Calculus and
to the modal operators—which are given a Generalized Quantifier style re-interpretation. In this way we provide an algebraic
foundation for Blanché’s Aristotelian hexagon as well as a 3D alternative to his 2D star-like visualisation. In a final part,
a richer scalar structure is argued to underly the realm of Modality, thus generalizing the 3D algebra with eight (23) operators to a 4D algebra with sixteen (24) operators. The visual representation of the latter structure involves a transformation of the hypercube to a rhombic dodecahedron.
The resulting 3D visualisation allows a straightforward embedding, not only of the classical Blanché star of Aristotelian
relations or the paracomplete and paraconsistent stars of Béziau (Log Investig 10, 218–232, 2003) but also of three additional
isomorphic Aristotelian constellations. 相似文献
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We reconstruct the stress tensor in the Earth's crust taking perturbations due to the motion of the Earth's hard core into account. In the first-order approximation, the density and pressure are functions of the total potential of all forces under consideration. We estimate the total free-energy balance and calculate the dependence of the free-energy density on latitude. 相似文献
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Guo-jingWang Su-pingQian RongWu 《应用数学学报(英文版)》2003,19(3):521-528
In this paper we consider the risk process described by a piecewise deterministic Markov processes(PDMP). We mainly discuss the distribution of the deficit at ruin for the risk process. We derive the integrodifferential equation satisfied by this distribution. We obtain the explicit expressions for it for certain choices of the claim amount distribution. 相似文献
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本文考虑[1]中所建立的模式,采用约化摄动法及PLK方法,求得了自由面及界面上的二阶椭圆余弦波。在退化情况下与文[3]和[4]的结果符合。 相似文献
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A diffusion equation with nonlinear localized chemical reactions is considered in this paper. As a result of the reactions, although the equation is parabolic, the derivatives of the solution are discontinuous across the interfaces (local sites of reactions). A second-order accurate immersed interface method is constructed for the diffusion equation involving interfaces. The new method is more accurate than the standard approach and it does not require the interfaces to be grid points. Several experiments that confirm second-order accuracy are presented. The efficiency of the proposed algorithm is also demonstrated for solving blow up problems. The proposed technique could be extended for construction of efficient numerical algorithms on uniform grids for the present equations with moving interfaces [9] but more analysis is required. 相似文献
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The purpose of this paper is to study the convergence of finite element approximation to the exact solution of general self-adjoint elliptic equations with discontinuous coefficients. Due to low global regularity of the solution, it is difficult to achieve optimal order of convergence with classical finite element methods [Numer. Math. 1998; 79:175–202]. In this paper, an isoparametric type of discretization is used to prove optimal order error estimates in L 2 and H 1 norms when the global regularity of the solution is low. The interface is assumed to be of arbitrary shape and is smooth for our purpose. Further, for the purpose of numerical computations, we discuss the effect of numerical quadrature on finite element solution, and the related optimal order estimates are also established. 相似文献