Closed incompressible surfaces of genus two in 3-bridge knot complements

In this paper, we characterize closed incompressible surfaces of genus two in the complements of 3-bridge knots and links. This characterization includes that of essential 2-string tangle decompositions for 3-bridge knots and links.     

缠绕方程和DNA模型

一般化了DNA重组的缠绕模型的缠绕方程的求解方法, 同时利用有理缠绕和二桥纽结 的关系给出了某些缠绕方程的解.     

Computing the Conway polynomial of several closures of oriented 3-braids

This paper deals with polynomial invariants of a class of oriented 3-string tangles and the knots (or links) obtained by applying six different closures. In Cabrera-Ibarra (2004) [1], expressions were given to compute the Conway polynomials of four different closures of the composition of two such 3-string tangles. By using the expressions and results from that reference, and using an algorithm developed on the basis of Giller?s calculations for 3-string tangles, we provide new results concerning six closures of 3-braids. Surprisingly, for 3-braids two of the closures turn out to be affine functions of the four previously defined. Among the contributions in this paper one finds computational tools to obtain the Conway polynomial of closures of 3-braids in terms of continuous fractions and their expansions. An interesting feature is that our calculations yield explicit, nonrecursive formulas in the case of 3-braids, thereby considerably lowering the time required to compute them. As a byproduct, explicit expressions are also given to obtain both numerators and denominators of continuous fractions in a nonrecursive way.     

Noncritical W-strings and minimal models

We perform a BRST analysis of the physical states described by a general noncriticalW-string. A crucial feature of our analysis is that we introduce a special basis in the Hilbert space of physical states in which the BRST operator splits into a nested sum of nilpotent BRST operators. We argue that the cohomology of each nilpotent BRST operator occurring in the nested sum is closely related to a specificW mimimal model. We discuss in detail the special case of the noncriticalW ₃-string.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 3, pp. 343–357, March, 1994.     

Static and dynamic beam forms of the loss of stability of a long orthotropic cylindrical shell under external pressure

A cylindrical shell with end sections which are closed and supported by hinges, in accordance with the concepts of the rod theory, is considered to be under the action of an omnidirectional external pressure which remains normal to the lateral surface during the deformation process. It is shown that, for such shells, the previously constructed consistent equations of the momentless theory, reduced using the Timoshenko shear model to the one-dimensional equations of the rod theory, describe three forms of loss of stability: (1) static loss of stability, which occures through a bending mode from the action of the total end axial compression force since, under the clamping conditions considered, its non-conservative part cannot perform work on deflections of the axial line; (2) also a static loss of stability but one which occurs through a purely shear mode with the conversion of a cylinder with normal sections into a cylinder with parallel sloping sections and a corresponding critical load which is independent of the length of the shell; (3) dynamic loss of stability which occurs through a bending-shear form and can only be revealed by a dynamic method using an improved shear model.     

The implementation of the finite-volume dynamical core in the community atmosphere model

A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the community atmosphere model (CAM) 3.0 is presented. These 3-D equations can be decoupled into a set of 2-D equations by the introduction of a floating vertical coordinate, resulting in considerable potential parallelism. Subsequent analysis of the data dependencies—in particular those arising from the polar singularity of the latitude-longitude coordinate system—suggests that two separate domain decompositions should be employed, each tailored for a different part of the model. The implementation requires that data be periodically redistributed between these two decompositions. Furthermore, data from nearest neighbors are kept in halo regions, which are updated between iterations. These data movements are optimized through one-sided communication primitives and multithreading. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.     

一类非线性年龄等级结构种群模型的数值解法

假设年轻个体在种群内部竞争中占优,建立一类非线性等级结构种群模型,它是具有全局耦合边界条件的偏微分-积分方程的初边值问题.提出该模型解的数值计算方法,证明算法的收敛性,并给出数值实验结果.     

A mathematical model for enzymatic action on DNA knots and links

This paper deals with some studies pertaining te, nonprocessive recombinase viz. Topoisomerases III, IV. The mathematics of tangles is found to be very useful in studying topoisomerases and recombinases (processive and nonprocessive). It has been seen that the enzyme acts on the DNA if it is in a certain configuration. Electron micrographs of the enzyme-DNA complex show the enzyme as a blob with DNA looping out of it, but they are unable to determine the configuration of the DNA within the blob. By using knot theory and tangle calculus, the configuration of DNA within the enzyme blob as well as the enzyme action has been determined in saine cases.     

Conditions for periodic vibrations in a symmetric <Emphasis Type="Italic">n</Emphasis>-string

A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.      

Coupled wetting meniscus model for the mechanism of spontaneous capillary action

Capillarity plays a significant role in many natural and artificial processes, but the mechanism responsible for its dynamics is not completely understood. In this study, we consider capillary flow characteristics and propose a coupled wetting meniscus model for the mechanism of spontaneous capillary action. In this model, capillary action is considered as the dynamic coupling of two interfacial forces, i.e., the wall wetting force at the contact line and the meniscus restoring force on the free interface. The wetting force promotes the motion of the contact line directed toward an equilibrium contact angle, whereas the meniscus restoring force promotes a reduction in the interface curvature, which is more consistent with a 90° contact angle. The competing interaction between these two forces is coupled together via the evolution of the interface shape. The model is then incorporated into a finite volume method for a two-fluid flow with an interface. Capillary flow experiments were performed, including vertical and horizontal flows. Phenomena analysis and data comparisons were conducted to verify the proposed model. According to the results of our study, the model can explain the capillary flow process well and it can be also used to accurately guide capillary flow calculations.     

Parallel algorithm for the solutions of PDEs in linux clustered workstations

In this paper we propose parallel algorithm for the solution of partial differential equations over a rectangular domain using the Crank–Nicholson method by cooperation with the DuFort–Frankel method and apply it on a model problem, namely, the heat conduction equation. One of the well known parallel techniques in solving partial differential equations in cluster computing environment is the domain decomposition technique. Using this technique, the whole domain is decomposed into subdomains, each of them has its own boundaries that are called the interface points. Parallelization is realized by approximating interface values using the unconditionally stable DuFort–Frankel explicit scheme, and these values serve as Neumann boundary conditions for the Crank–Nicholson implicit scheme in the subdomains. The numerical results show that our algorithm is more accurate than the algorithm based on the forward explicit method to approximate the values of the interface points, especially, when we use a small number of time steps. Moreover, these numerical results show that increasing the number of processors which are used in the cluster, yields an increase in the algorithm speedup.     

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin–Huxley (HH) mathematical model

In this paper, we have studied the plasmatic membrane behavior using an electric circuit developed by Hodgkin and Huxley in 1952 and have dealt with the variation of the amount of time related to the potassium and sodium conductances in the squid axon. They developed differential equations for the propagation of electric signals; the dynamics of the Hodgkin–Huxley model have been extensively studied both from the view point of its their biological implications and as a test bed for numerical methods, which can be applied to more complex models. Recently, an irregular chaotic movement of the action potential of the membrane was observed for a number of techniques of control with the objective to stabilize the variation of this potential. This paper analyzes the non-linear dynamics of the Hodgkin–Huxley mathematical model, and we present some modifications in the governing equations of the system in order to make it a non-ideal one (taking into account that the energy source has a limited power supply). We also developed an optimal linear control design for the action potential of membranes. Here, we discuss the conditions that allow the use of control linear feedback for this kind of non-linear system.     

基于变分不等式的支持向量机优化算法研究

由于标准支持向量机模型是一个二次规划问题,随着数据规模的增大,求解算法过程会越来越复杂.在K-SVCR算法结构的基础上,构造了严格凸的二次规划新模型,该模型的主要特点是可以将其一阶最优化条件转化为变分不等式问题,利用Fischer-Burmeister(FB)函数将互补问题转化为光滑方程组;建立光滑快速牛顿算法求解,并证明了该算法所产生的序列是全局收敛;利用标准数据集测试提出算法的有效性,在训练正确率和运行时间上与K-SVCR算法相比都有较好的表现,实验结果表明该算法可行且有效.     

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

The dynamic analysis of viscoelastic pipes conveying fluid is investigated by the variable fractional order model in this article. The nonlinear variable fractional order integral-differential equation is established by introducing the model into the governing equation. Then the Shifted Legendre Polynomials algorithm is first presented for dealing with this kind of equations. The convergence analysis and numerical example verify that the algorithm is an effective and accurate technique for addressing this type complicated equation. Numerical results for dynamic analysis of viscoelastic pipes conveying fluid show the effect of parameters on displacement, acceleration, strain and stress. It also indicates that how dynamic properties are affected by the variable fractional order and fluid velocity varying. Most of all, the proposed algorithm has enormous potentials for the problem of high precision dynamics under the variable fractional order model.     

基于代数等价变换下的凸二次规划不可行内点算法

基于代数等价变换和在KMM算法的框架基础上,在原始-对偶内点方法的牛顿方程里嵌入一种自调节功能.从而对凸二次规划提出了一种新的迭代方向的不可行内点算法,并证明了算法的全局收敛性.     

Some mathematical problems in seriation

Some mathematical aspects of seriation are studied in this paper. Certain conditions on an abundance or an incidence matrix have been given in the past which imply that there exists a permutation of its rows so that the resulting matrix is a Q matrix (in which case the original matrix is said to be a pre-Q). These types of results have applications to chronologically ordering archaeological provenances under certain circumstances. Unfortunately these conditions are deficient both theoretically and practically, in that for much archaeological data the conditions are not necessarily true yet the corresponding provenances do have chronological orderings. Here we are able to generalize these results in two ways. First we are able to establish necessary and sufficient conditions on the rows of a matrix for it to be pre-Q. These conditions are local in that they concern only certain triples and quadruples of the rows. Secondly, we are able to interpret seriation in terms of a ternary relation R on a set A and prove the results in this general context. In this form the theorem says that if only certain of the triples and quadruples are R-strings, then the whole set A is an R-string, and so has a linear order consistent with the ternary relation R. This would appear to generalize a theorem of P. C. Fishburn. Both aspects of the generalization mean that the results stated herein have a wider applicability than those given heretofore. Possibly more importantly than this is that they lead to numerical invariants, called the fixing number and the related linear rigidity, of such an R-string on A. The archaeological interpretation of these is given in the paper and data supplied which illustrates this point. Finally various other conditions on products and representations of relations are stated which imply that A is an R-string. One of these generalizes and completes a theorem of D. G. Kendall.     

动力学方程的积分型直接积分法

提出了一个求解动力学问题的新方法(DIM-IM).将动力学方程化成积分方程的形式,借助于该方程构造出了具有显式预测-校正的单步、自起动和四阶精度的积分型直接积分算法.理论分析和算例指出,这一方法较中心差分法、Houbolt法、Newmark法和Wilson-θ法都有较高的精度.本方法适用于强非线性,非保守系统.     

An Efficient Algorithm for Quadratic Sum-of-Ratios Fractional Programs Problem

The quadratic sum-of-ratios fractional program problem has a broad range of applications in practical problems. This article will present an e?cient branch-and-bound algorithm for globally solving the quadratic sum-of-ratios fractional program problem. In this algorithm, lower bounds are computed by solving a series of parametric relaxation linear programming problems, which are established by utilizing new parametric linearizing technique. To enhance the computational speed of the proposed algorithm, a rectangle reducing tactic is used to reject a part of the investigated rectangle or the whole rectangle where there does not contain any global optimal solution of the quadratic sum-of-ratios fractional program problem. Compared with the known approaches, the proposed algorithm does not need to introduce new variables and constraints. Therefore, the proposed algorithm is more suitable for application in engineering.     

The t-analog of the level one string function for twisted affine Kac–Moody algebras

We study Lusztig?s t-analog of weight multiplicities, or affine Kostka–Foulkes polynomials, associated to level one representations of twisted affine Kac–Moody algebras. We obtain an explicit closed form expression for the unique t-string function, using constant term identities of Macdonald and Cherednik. This extends previous work on t-string functions for the untwisted simply-laced affine Kac–Moody algebras.     

Generalized alternating-direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems

The alternating-direction collocation (ADC) method combines the attractive computational features of a collocation spatial approximation and an alternating-direction time marching algorithm. The result is a very efficient solution procedure for parabolic partial differential equations. To date, the methodology has been formulated and demonstrated for second-order parabolic equations with insignificant first-order derivatives. However, when solving transport equations, significant first-order advection components are likely to be present. Therefore, in this paper, the ADC method is formulated and analyzed for the transport equation. The presence of first-order spatial derivatives leads to restrictions that are not present when only second-order derivatives appear in the governing equation. However, the method still appears to be applicable to a wide variety of transport systems. A formulation of the ADC algorithm for the nonlinear system of equations that describes density-dependent fluid flow and solute transport in porous media demonstrates this point. An example of seawater intrusion into coastal aquifers is solved to illustrate the applicability of the method. An alternating-direction collocation solution algorithm has been developed for the general transport equation. The procedure is analogous to that for the model parabolic equations considered by Celia and Pinder [2]. However, the presence of first-order spatial derivatives requires special attention in the ADC formulation and application. With proper implementation, the ADC procedure effectively combines the efficient equation formulation inherent in the collocation method with the efficient equation solving characteristics of alternating-direction time marching algorithms. To demonstrate the viability of the method for problems with complex velocity fields, the procedure was applied to the problem of density-dependent flow and contaminant transport in groundwaters. A standard example of seawater intrusion into coastal aquifers was solved to illustrate the applicability of the method and to demonstrate its potential use in practical problems.