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31.
The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at  相似文献   
32.
For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.  相似文献   
33.
The neutron transport equation for a slab geometry with the extremely anisotropic scattering kernel is considered. The albedo and transmission factors are calculated using the variation method. The effect of the extremely anisotropic parameter on the variation of the slab albedo and transmission factor is calculated. The obtained results are compared with the published data.  相似文献   
34.
In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.  相似文献   
35.
Summary Mutual diffusion coefficients of two gases A and B can be determined in an empty gas chromatographic column by letting component B enter at an intermediate position of the column and continuously flow through a part only of it, as a carrier gas. The other component A is injected in a small amount instantaneously at the closed end of the column with the detector placed at the other end. By repeatedly stopping and then restoring after a short time the flow of B, narrow extra peaks are produced on the chromatographic elution curve, owing to diffusion of A into B. An equation is derived giving the area under the curve of each stop-peak as a function of time of the corresponding stop. Plotting the experimental data according to this equation permits the determination of the diffusion coefficient of A into B. Some results obtained by this method show negligible variations with changes in the experimental parameters.  相似文献   
36.
The syntheses of eight [4.3.0] heterobicyclic boronates containing a N → B coordinative bond are described. The monomeric compounds were prepared by reaction of arylboronic acids with a tridentate ligand having the ONO donor set of atoms. It was shown that substituents at the para-position of the B-phenyl moiety transmit electronic effects to the CN bond which in turn is polarized by formation of the N → B coordination bond. At the same time, related tridentate ligands were also reacted with 1,4-benzenediboronic acid in order to prepare benzene diboron complexes. The structure of this type of compounds was confirmed by X-ray analysis for one of the derivatives.  相似文献   
37.
Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures.  相似文献   
38.
In this article, a novel method is proposed for investigating the set controllability of Markov jump switching Boolean control networks (MJSBCNs). Specifically, the switching signal is described as a discrete-time homogeneous Markov chain. By resorting to the expectation and switching indicator function, an expectation system is constructed. Based on the expectation system, a novel verifiable condition is established for solving the set reachability of MJSBCNs. With the newly obtained results on set reachability, a necessary and sufficient condition is further derived for the set controllability of MJSBCNs. The obtained results are applied to Boolean control networks with Markov jump time delays. Examples are demonstrated to justify the theoretical results.  相似文献   
39.
We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° 0,t –1 , whereT(t) is a stochastic process with values in distributions and s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.  相似文献   
40.
Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN 2 of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.
Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN 2 des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.
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