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The paper suggests constraints on the coefficients ai, bi, ci j of the bilinear continuous-time input-output model that yield generalized state equations with input derivative order lower than that in the input-output equations. In the limiting case when one removes the input derivatives altogether, these conditions provide a solution of the realizability problem. The new state coordinates are found step by step. We first find a coordinate transformation allowing the reduction of the maximal order of the input time derivatives by one and write the corresponding state equations. At the second step we find the next coordinate transformation to lower the maximal order of input time derivative in the new state equations, etc. At each step we check, what condition the coefficients should satisfy to make the next step possible. [ABSTRACT FROM AUTHOR]

The filter generator is an important building block in many stream ciphers. The generator consists of a linear feedback shift register of length n that generates an m-sequence of period 2′ - 1 filtered through a Boolean function of degree d that combines bits from the shift register and creates an output bit zt at any time t. The previous best attacks aimed at reconstructing the initial state from an observed keystream, have essentially reduced the problem to solving a nonlinear system of D = (Multiple line equation(s) cannot be represented in ASCII text) (i) equations in n unknowns using techniques based on linear algebra. This attack needs about D bits of keystream and the system can be solved in complexity O (Dω), where ω can be taken to be Strassen's reduction exponent ω = log2 (7) ≈ 2.807. This paper describes a new algorithm that recovers the initial state of most filter generators after observing O(D) keystream bits with complexity O((D - n)/2) ≈ O(D), after a pre-computation with complexity O(D(log2 D)³). [ABSTRACT FROM AUTHOR]

In this paper we develop techniques for computing elementwise conservative approximations of the flux on element boundaries for the continuous Galerkin method. The technique is based on computing a correction of the average normal flux on an edge or face. The correction is a jump in a piecewise constant or linear function. We derive a basic algorithm which is based on solving a global system of equations and a parallel algorithm based on solving local problems on stars. The methods work on meshes with different element types and hanging nodes. We prove existence, uniqueness, and optimal order error estimates. Lastly, we illustrate our results by a few numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, by means of the concept of the working set, which is an estimate of the active set, we propose a feasible sequential linear equation algorithm for solving inequality constrained optimization problems. At each iteration of the proposed algorithm, we first solve one system of linear equations with a coefficient matrix of size m x m (where m is the number of constraints) to compute the working set; we then solve a subproblem which consists of four reduced systems of linear equations with a common coefficient matrix. Unlike existing QP-free algorithms, the subproblem is concerned with only the constraints corresponding to the working set. The constraints not in the working set are neglected. Consequently, the dimension of each subproblem is not of full dimension. Without assuming the isolatedness of the stationary points, we prove that every accumulation point of the sequence generated by the proposed algorithm is a KKT point, of the problem. Moreover, after finitely many iterations, the working set becomes independent of the iterates and is essentially the same as the active set of the KKT point. In other words, after finitely many steps, only those constraints which are active at the solution will be involved in the subproblem. Under some additional conditions, we show that the convergence rate is two-step superlinear or even Q-superlinear. We also report some preliminary numerical experiments to show that the proposed algorithm is practicable and effective for the test problems. [ABSTRACT FROM AUTHOR]

Multilevel algorithms are a successful class of optimization techniques which addresses the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimization method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan­Lin partition optimization algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of-the-art partitioner and shown to provide improved results. [ABSTRACT FROM AUTHOR]

In this paper, we describe the conditions, providing the existence of splicing of the measures λ , μ and v - finite, finitely additive and integral functions of sets, defined on the algebras of subsets B and C of some set Ω and the algebra U, based on the algebras B and C . Moreover, we show that the measure λ should be a common extension of the measures μ and v , and λ(B∩C)= λ(B)λ(C) for any B ε B, C ε C. [ABSTRACT FROM AUTHOR]

Abstract: Solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application. This paper discusses preconditioning methods based on Block Broyden method. It first introduces the Block Broyden method and preconditioning technique. Then it presents four different preconditioners for the Block Broyden method and discusses the implementation process. It also analyzes the time complexity of the four algorithms. Finally, it solves the nonlinear systems arising from the Bratu problem by the four preconditioning algorithms. Experimental results show that the preconditioning technique is effective for the Block Broyden method and that the preconditioner SSOR has the fastest solving speed and the best performance among the four preconditioners. Therefore, it can be used in the large-scale problems arising from scientific and engineering computing. [Copyright &y& Elsevier]

A cell-centered finite volume method is proposed to approximate numerically the solution to the steady convection-diffusion equation on unstructured meshes of $d$-simplexes, where $d\geq 2$ is the spatial dimension. The method is formally second-order accurate by means of a piecewise linear reconstruction within each cell and at mesh vertices. An algorithm is provided to calculate nonnegative and bounded weights. Face gradients, required to discretize the diffusive fluxes, are defined by a nonlinear strategy that allows us to demonstrate the existence of a maximum principle. Finally, a set of numerical results documents the performance of the method in treating problems with internal layers and solutions with strong gradients. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, some new oscillation criteria are obtained for the first-order delay difference equation , where k,l1,l2,, ls are positive integer numbers, f is a function. Our results improve the known results in the literature. And some examples are given to demonstrate the advantage of our results. [Copyright &y& Elsevier]

Many characterizations of semipreconnected (=β-connected) spaces are obtained by Aho and Nieminen [2]. In this paper, we obtain further characterizations of semipreconnected spaces. We introduce β-separated and βs-connected sets and by using these sets we obtain several properties of β-connected subspaces. [ABSTRACT FROM AUTHOR]

We use a version of the Fair-Luke algorithm to find the Padé approximate solutions of the Painlevé I and II equations. We find the distributions of poles for the well-known Ablowitz-Segur and Hastings-McLeod solutions of the Painlevé II equation. We show that the Boutroux tritronquée solution of the Painleé I equation has poles only in the critical sector of the complex plane. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behavior at infinity in the complex plane. [ABSTRACT FROM AUTHOR]

For two given projections p and q in a C*-algebra, we investigate how to express the Drazin inverses of the product pq and the difference p - q, and give applications. As a special case, we obtain the results of [C. Y. Deng, 'The Drazin inverses of products and differences of orthogonal projections', J. Math. Anal. Appl. 335 (2007) 64-71], with considerably simpler proofs. [ABSTRACT FROM AUTHOR]

A BDDC (balancing domain decomposition by constraints) method is developed for elliptic equations, with discontinuous coefficients, discretized by mortar finite element methods for geometrically nonconforming partitions in both two and three space dimensions. The coarse component of the preconditioner is defined in terms of one mortar constraint for each edge/face, which is the intersection of the boundaries of a pair of subdomains. A condition number bound of the form C maxi{(1 + log(Hi/hi))2} is established under certain assumptions on the geometrically nonconforming subdomain partition in the three-dimensional case. Here Hi and hi are the subdomain diameters and the mesh sizes, respectively. In the geometrically conforming case and the geometrically nonconforming cases in two dimensions, no assumptions on the subdomain partition are required. This BDDC preconditioner is also shown to be closely related to the Neumann-Dirichlet version of the FETI-DP algorithm. The results are illustrated by numerical experiments which confirm the theoretical results. [ABSTRACT FROM AUTHOR]

We construct an algorithm that tests a system of recurrence equations on a tree for the existence of a nontrivial solution and computes it. [ABSTRACT FROM AUTHOR]

We calculate the Hochschild cohomology of the algebra of smooth functions on a finite-dimensional real torus with coefficients in the adjoint representation, generalizing the previously developed technique to the discrete case for this. [ABSTRACT FROM AUTHOR]

We deal with periodic groups saturated with dihedral groups. In particular, it is proved that periodic groups of bounded period, and also periodic Shunkov groups, saturated with dihedral groups, are locally finite. [ABSTRACT FROM AUTHOR]

The structure of a clone of functions respecting an amalgam is described. Also, for clones RA and RB of relations, conditions are specified under which the amalgam of RA and RB, restricted to the domains of RA and RB, coincides with these. [ABSTRACT FROM AUTHOR]

We settle Question 10.61 in the Kourovka Notebook for the case where the order of an element a is even. [ABSTRACT FROM AUTHOR]