Finite Aperture Stereo

International Journal of Computer Vision - Multi-view stereo remains a popular choice when recovering 3D geometry, despite performance varying dramatically according to the scene content. Moreover,...     

Finite Boltzmann schemes

In the special case of relaxation parameter ω = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the Maxwell–Boltzmann constraints for the equilibrium distribution, and the constraints for finite difference stencils as derived from Taylor series expansion. For convection–diffusion we analyse the equivalence between FB and the Lax–Wendroff FD scheme in detail. It follows that the Lax–Wendroff procedure is performed automatically in the finite Boltzmann schemes via the imposed Maxwell–Boltzmann constraints. Furthermore, we make some remarks on FB schemes for fluid flows, and show that an earlier related study can be extended to rectangular grids. Finally, our findings are briefly checked with simulations of natural convection in a differentially heated square cavity.     

Finite element costs

This paper describes an extension to the classical finite element analysis methods. Using the same data inherent in the stiffness matrix, and adding cost parameters as input, a finite element structural analysis program is shown to output cost data. The basic concept is that the material costs are only a fraction of the total costs, which include labor and overhead. It is theorized that the labor and overhead costs may be dominant, and are related to structural complexity and numbers of joints.Two examples are given: a simple four-member truss illustrates the method, and a transmission tower example is offered to demonstrate the principle.     

Finite element analysis

Current use of the finite element method in engineering practice is considered. The increasing use of finite element analysis in a CAD environment and factors influencing it are discussed.The technological state of the art is briefly reviewed. Special consideration is given to shell elements and solution methods, illustrating the progress being made in these and other areas of finite element technology. Future trends are predicted.     

Interval-Valued Finite Markov Chains

The requirement that precise state and transition probabilities be available is often not realistic because of cost, technical difficulties or the uniqueness of the situation under study. Expert judgements, generic data, heterogeneous and partial information on the occurrences of events may be sources of the probability assessments. All this source information cannot produce precise probabilities of interest without having to introduce drastic assumptions often of quite an arbitrary nature. in this paper the theory of interval-valued coherent previsions is employed to generalise discrete Markov chains to interval-valued probabilities. A general procedure of interval-valued probability elicitation is analysed as well. In addition, examples are provided.     

Finite Difference/Finite Element Methods for Distributed-Order Time Fractional Diffusion Equations

In this paper, a class of distributed-order time fractional diffusion equations (DOFDEs) on bounded domains is considered. By L1 method in temporal direction, a semi-discrete variational formulation of DOFDEs is obtained firstly. The stability and convergence of this semi-discrete scheme are discussed, and the corresponding fully discrete finite element scheme is investigated. To improve the convergence rate in time, the weighted and shifted Grünwald difference method is used. By this method, another finite element scheme for DOFDEs is obtained, and the corresponding stability and convergence are considered. And then, as a supplement, a higher order finite difference scheme of the Caputo fractional derivative is developed. By this scheme, an approach is suggested to improve the time convergence rate of our methods. Finally, some numerical examples are given for verification of our theoretical analysis.     

Computing in Finite Time

If a message can have n different values and all values are equally probable, then the entropy of the message is log(n). In the present paper, we discuss the expectation value of the entropy, for an arbitrary probability distribution. We introduce a mixture of all possible probability distributions. We assume that the mixing function is uniform

Construction of Finite Groups

We1999 Academic Pressintroduce three practical algorithms to construct certain finite groups up to isomorphism. The first one can be used to construct all soluble groups of a given order. This method can be restricted to compute the soluble groups with certain properties such as nilpotent, non-nilpotent or supersoluble groups. The second algorithm can be used to determine the groups of orderCopyright pⁿ ·  qwith a normal Sylow subgroup for distinct primespandq. The third method is a general method to construct finite groups which we use to compute insoluble groups.     

Finite Reasons for Safety

In this paper we investigate to what extent a very simple and natural “reachability as deducibility” approach, originating in research on formal methods for security, is applicable to the automated verification of large classes of infinite state and parameterized systems. In this approach the verification of a safety property is reduced to the purely logical problem of finding a countermodel for a first-order formula. This task is delegated then to generic automated finite model building procedures. A finite countermodel, if found, provides with a concise representation for a system invariant sufficient to establish the safety. In this paper we first present a detailed case study on the verification of a parameterized mutual exclusion protocol. Further we establish the relative completeness of the finite countermodel finding method (FCM) for a class of parameterized linear arrays of finite automata with respect to known methods based on monotonic abstraction and symbolic backward reachability. The practical efficiency of the method is illustrated on a set of verification problems taken from the literature using Mace4 model finding procedure.     

Parameterization in Finite Precision

Certain classes of algebraic curves and surfaces admit both parametric and implicit representations. Such dual forms are highly useful in geometric modeling since they combine the strengths of the two representations. We consider the problem of computing the rational parameterization of an implicit curve or surface in a finite precision domain. Known algorithms for this problem are based on classical algebraic geometry, and assume exact arithmetic involving algebraic numbers. In this work we investigate the behavior of published parameterization algorithms in a finite precision domain and derive succinct algebraic and geometric error characterizations. We then indicate numerically robust methods for parameterizing curves and surfaces which yield no error in extended finite precision arithmetic and, alternatively, minimize the output error under fixed finite precision calculations. Received January 8, 1997; revised August 27, 1998.     

Finite element mesh generation

The capabilities of a geometric modeller are extended towards finite element analysis by a mesh generator which extracts all its geometric and topological information from the model. A coarse mesh is created and subsequently refined to a suitable finite element mesh, which accomodates material properties, loadcase and analysis requirements. The mesh may be optimized by adaptive refinement, ie according to estimates of the discretization errors.A survey of research and development in geometric modelling and finite element analysis is presented, then an implementation of a mesh generator for 3D curvilinear and solid objects is described in detail.     

Finite automata with multiplication

A finite automaton with multiplication (FAM) is a finite automaton with a register which is capable of holding any positive rational number. The register can be multiplied by any of a fixed number of rationals and can be tested for value 1. Closure properties and decision problems for various types of FAM's (e.g. two-way, one-way, nondeterministic, deterministic) are investigated. In particular, it is shown that the languages recognized by two-way deterministic FAM's are of tape complexity log n and time complexity n³. Some decision problems related to vector addition systems are also studied.     

Automata over Finite T-Quasigroups

This paper investigates families of automata without outputs and also families of reversible Mealy and Moore automata specified by recurrence relations over finite T-quasigroups. Based on the decomposition of an Abelian group into the direct sum of primary cyclic groups, a unified approach is proposed to the hardware and software synthesis of such automata. Estimates are found for the time and space complexities of computations executed by these automata during one clock cycle.     

High Order Finite Difference and Finite Volume Methods for Advection on the Sphere

Numerical schemes used for computational climate modeling and weather prediction are often of second order accuracy. It is well-known that methods of formal order higher than two offer a significant potential gain in computational efficiency. We here present two classes of high order methods for discretization on the surface of a sphere, first finite difference schemes satisfying the summation-by-parts property on the cube sphere grid, secondly finite volume discretizations on unstructured grids with polygonal cells. Furthermore, we also implement the seventh order accurate weighted essentially non-oscillatory (WENO7) scheme for the cube sphere grid. For the finite difference approximation, we prove a stability estimate, derived from projection boundary conditions. For the finite volume method, we develop the implementational details by working in a local coordinate system at each cell. We apply the schemes to compute advection on a sphere, which is a well established test problem. We compare the performance of the methods with respect to accuracy, computational efficiency, and ability to capture discontinuities.     

一类有限半格的自同态半环

研究两条有限链直积上自同态半环的性质。利用有限链直积上的两种二元运算，给出了两条有限链直积的子集构成自同态像集的充要条件，证明了自同态半环的乘法半群是正则半群。通过对有限链直积上的自同态进行分解，得到了自同态半环可由其乘法半群的幂等元集生成；推广了有限链上自同态半群的一些结果。