Adaptive preconditioning for a stream of SLAEs

The paper considers the way of reducing the time consumed to solve SLAEs with iterative methods by reusing the data structures obtained in the solution of a previous SLAE, or selecting a preconditioner from the available set of preconditioners to minimize the time of solving the next SLAEs. Such adaptive preconditioning is used to solve time-dependent nonlinear problems. SLAEs generated at the Newton iteration n-1 of every computation step are solved using the SLAE structure of the first Newton iteration and the selection of a preconditioner from the given set allows reducing the time of solving SLAEs of a varying complexity at different time steps. The adaptive preconditioning idea and its application are demonstrated for a stream of SLAEs in some RFNC-VNIIEF’s codes.

On the Complexity of Concurrent Multiset Rewriting

In this paper, we are interested in the runtime complexity of programs based on multiset rewriting. The motivation behind this work is the study of the complexity of chemistry-inspired programming models, which recently regained momentum due to their adequacy to large autonomous systems. In these models, data are most of the time left unstructured in a container, formally, a multiset. The program to be applied to this multiset is specified as a set of conditioned rules rewriting the multiset. At run time, these rewrite operations are applied concurrently, until no rule can be applied anymore (the set of elements they need cannot be found in the multiset anymore). A limitation of these models stand in their complexity: each computation step may require a complexity in [Formula: see text] where n denotes the number of elements in the multiset, and k is the size of the subset of elements needed to trigger a given rule. By analogy with chemistry, such elements can be called reactants. In this paper, we explore the possibility of improving the complexity of searching reactants through a static analysis of the rules' condition. In particular, we give a characterisation of this complexity, by analogy to the subgraph isomorphism problem. Given a rule R, we define its rank rk(R) and its calibre C(R), allowing us to exhibit an algorithm with a complexity in [Formula: see text] for searching reactants, while showing that [Formula: see text] and that [Formula: see text] most of the time.

Research on Numerical Computation of Natural Frequency of Transverse Vibration for Simply Supported Beam of Non-Uniform

Recursive and inexplicit differential equation of the second order with variable coefficients is derived from the fourth order linear homogeneous differential equation with variable coefficients of transverse vibration of non-uniform beam, which is about deflection and bending moment according to boundary conditions and order reduction. By finite difference method, numerical computation and accuracy are studied for natural frequency of transverse vibration for simply supported beam of non-uniform. Theoretical analysis and orthogonal computation examples show that numerical computation algorithm is very simple, and accuracy of computation depends on variety rate of gradually changed cross section in vertical direction and numbers of computation step, which is independent of width and length of beam; numerical accuracy of computation is estimable for given length or numbers of computation step; and reasonable length or numbers of computation step is determinable for given accuracy demand.

A FINITELY PRESENTED GROUP WITH ALMOST SOLVABLE CONJUGACY PROBLEM

The algorithmic unsolvability of the conjugacy problem for finitely presented groups was demonstrated by Novikov in the early 1950s. Various simplifications and alternative proofs were found by later researchers and further questions raised. Recent work by Borovik, Myasnikov and Remeslennikov has considered the question of what proportion of the number of elements of a group (obtained by standard constructions) falls into the realm of unsolvability. In this paper we provide a straightforward construction, as a Britton tower, of a finitely presented group with solvable word problem but unsolvable conjugacy problem of any r.e. (recursively enumerable) Turing degree a. The question of whether two elements are conjugate is bounded truth-table reducible to the question of whether the elements are both conjugate to a single generator of the group. We also define computable normal forms, based on the method of Bokut', that are suitable for the conjugacy problem. We consider (ordered) pairs of normal words U, V for the conjugacy problem whose lengths add to l and show that the proportion of such pairs for which conjugacy is undecidable (in the case a ≠ 0) is strictly less than l2/(2λ - 1)l where λ > 4. The construction is based on modular machines, introduced by Aanderaa and Cohen. For the purposes of this construction it was helpful to extend the notion of configuration to include pairs of m-adic integers. The notion of computation step was also extended and is referred to as s-fold computation where s ∈ ℤ (the usual notion coresponds to s = 1). If gcd (m, s) = 1 then determinism is preserved, i.e., if the modular machine is deterministic then it remains so under the extended notion. Furthermore there is a simple correspondence between s-fold and standard computation in this case. Otherwise computation is non-deterministic and there does not seem to be any straightforward correspondence between s-fold and standard computation.

Operational interpretations of an extension of Fω with control operators

We study the operational semantics of an extension of Girard's System Fω with two control operators: an abort operation that abandons the current control context, and a callcc operation that captures the current control context. Two classes of operational semantics are considered, each with a call-by-value and a call-by-name variant, differing in their treatment of polymorphic abstraction and instantiation. Under the standard semantics, polymorphic abstractions are values and polymorphic instantiation is a significant computation step; under the ML-like semantics evaluation proceeds beneath polymorphic abstractions and polymorphic instantiation is computationally insignificant. Compositional, type-preserving continuation-passing style (cps) transformation algorithms are given for the standard semantics, resulting in terms on which all four evaluation strategies coincide. This has as a corollary the soundness and termination of well-typed programs under the standard evaluation strategies. In contrast, such results are obtained for the call-by-value ML-like strategy only for a restricted sub-language in which constructor abstractions are limited to values. The ML-like call-by-name semantics is indistinguishable from the standard call-by-name semantics when attention is limited to complete programs.

The Algebra of Synchronous Processes

An algebraical theory called ASP is presented, describing synchronous cooperation of processes. The theory ASP was first mentioned in BERGSTRA & KLOP [4] as an alternative for the theory ACP, which works with asynchronous cooperation (see also in [5]). One of the main differences between ASP, as it is presented here, and the algebraic theory SCCS of MILNER [9] is the representation of parallelism, which is done by considering a computation step as a vector, each component of which represents an atomic action on a corresponding channel. This paper concludes with an example, to give an idea how to work with ASP.

A numerical method for integrating the unsteady boundary-layer equations when there are regions of backflow

A numerical method for integrating the unsteady twodimensional boundarylayer equations using a second-order-accurate implicit method, which allows for arbitrary mesh spacing in the space and time variables, is developed. A unique feature of the method is the use of an asymptotic solution valid at the downstream end of the integration mesh which permits backflow to be taken into account. Newton's iterative technique is used to solve the nonlinear finite-difference equations a t each computation step, using a rapid algorithm for solving the resulting linearized equations. The method is applied to a flow which is periodic in time and contains regions of backflow. The numerical computations are compared with known numerical and asymptotic solutions and the agreement is excellent.