A method for solving a boundary problem for a nonlinear controlled system

An algorithm is proposed for constructing a control function that transfers a wide class of nonlinear systems of ordinary differential equations from an initial state to an arbitrarily small neighborhood of a given terminal state. The algorithm is convenient for numerical implementation. Taking into account the restrictions on the control and phase coordinates, a constructive criterion is obtained for choosing terminal states for which this transfer is possible. The problem of an interorbital flight is considered and modeled numerically.     

A convergence theorem for the fast multipole method for 2 dimensional scattering problems

The Fast Multipole Method (FMM) designed by V. Rokhlin rapidly computes the field scattered from an obstacle. This computation consists of solving an integral equation on the boundary of the obstacle. The main result of this paper shows the convergence of the FMM for the two dimensional Helmholtz equation. Before giving the theorem, we give an overview of the main ideas of the FMM. This is done following the papers of V. Rokhlin. Nevertheless, the way we present the FMM is slightly different. The FMM is finally applied to an acoustic problem with an impedance boundary condition. The moment method is used to discretize this continuous problem.

     

A hybrid method for inverse cavity scattering problem for shape

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.     

A Practical Algorithm for Computing a Subadditive Dual Function for Set Partitioning

Recently, a new algorithm for computing an optimal subadditive dual function to an integer program has been proposed. In this paper we show how to apply the algorithm to the set partitioning problem. We give several enhancements to the algorithm and we report computational experiments. The results show that it is tractable to obtain an optimal subadditive function for small and medium size problems. To the best of our knowledge this is the first work that reports computational experiments on computing an optimal subadditive dual function.     

Simplified analysis for full-Newton step infeasible interior-point algorithm for semidefinite programming

We present an analysis of the full-Newton step infeasible interior-point algorithm for semidefinite optimization, which is an extension of the algorithm introduced by Roos [C. Roos, A full-Newton step 𝒪(n) infeasible interior-point algorithm for linear optimization, SIAM J. Optim. 16 (2006), pp. 1110–1136] for the linear optimization case. We use the proximity measure σ(V)?=?‖I???V ²‖ to overcome the difficulty of obtaining an upper bound of updated proximity after one full-Newton step, where I is an identity matrix and V is a symmetric positive definite matrix. It turns out that the complexity analysis of the algorithm is simplified and the iteration bound obtained is improved slightly.     

An exact formula for the move-to-front rule for self-organizing lists

A collection of items (e.g., books), each with an associated weight (or popularity), is arranged in a row. At each unit of time an item is removed with probability proportional to its weight and replaced at the left end of the row. Thismove-to-front rule gives a Markov chain on permutations often known as theTsetlin library. We derive an exact and tractable formula for the probability of any permutation after any number of moves. From the formula we read off previously studied quantities of interest associated with the chain, such as the stationary distribution and eigenvalues. Measuring discrepancy from stationarity by separation, we use the formula to find the initial arrangement giving the slowest convergence to stationarity. The time to stationarity in this case is a convolution of geometric random variables which we analyze for three natural choices of weights. We also assess the time required for an important functional, namely, expected search cost, to approach its stationary value.     

Optimal boundedness criteria for extended-real-valued functions

The notion of genuinely bounded below function is introduced and characterized by means of the concept of co-equilibrated function. As an application, we state two boundedness criteria for extended-real-valued functions, both optimal in a clearly defined sense. The first one says that an extended-real-valued function minorized by an affine map and coinciding from some value up with a co-equilibrated function is bounded below. The second criterion states that an extended-real-valued function minorized by an affine map is bounded below provided that one of its sub-level sets is co-equilibrated.     

Estimates for the principal spectrum point for certain time-dependent parabolic operators

Non-autonomous parabolic equations are discussed. The periodic case is considered first and an estimate for the principal periodic-parabolic eigenvalue is obtained by relating the original problem to the elliptic one obtained by time-averaging. It is then shown that an analogous bound may be obtained for the principal spectrum point in the almost periodic case. These results have applications to the stability of nonlinear systems and hence, for example, to permanence for biological systems.     

Invariant Theory for Unipotent Groups and an Algorithm for Computing Invariants

Let X=Spec B be an affine variety over a field of arbitrarycharacteristic, and suppose that there exists an action of aunipotent group (possibly neither smooth nor connected). Thefundamental results are as follows. (1) An algorithm for computinginvariants is given, by means of introducing a degree in thering of functions of the variety, relative to the action. Thereforean algorithmic construction of the quotient, in a certain openset, is obtained. In the case of a Galois extension, k B=K,which is cyclic of degree p=char k (that is, such that the unipotentgroup is G=Z/pZ), an element of minimal degree becomes an Artin–Schreierradical, and the method for computing invariants gives, in particular,the expression for any element of K in terms of these radicals,with an explicit formula. This replaces the well-known formulaof Lagrange (which is valid only when the degree of the extensionand the characteristic are relatively prime) in the case ofan extension of degree p=char k. (2) In this paper we give aneffective construction of a stable open subset where there isa quotient. In this sense we obtain an algebraic local criterionfor the existence of a quotient in a neighbourhood. It is proved(provided the variety is normal) that, in the following cases,such an open set is the greatest one that admits a quotient:

1. when the action is such that the orbits have dimension lessthan or equal to 1 (arbitrary characteristic) and, in particular,for any action of the additive group G_a;
2. in characteristic0, when the action is proper (obtained fromthe results of Fauntleroy)or the group is abelian.

1991 Mathematics Subject Classification:primary 14L30; secondary 14D25, 14D20.     

A plea for octal

It is argued that there are strong practical and pedagogical reasons why some of the traditional units of volume should be preserved. In particular, a working example of an octal system is shown to have many advantages in an otherwise decimal world.     

Bounds for Rounding Errors in the Gaussian Elimination for Band Systems

The results of an error analysis of Gaussian elimination withpartial pivoting for band systems of linear equations are given.These results show an improvement in the bound for the normof the perturbation matrix compared to the known bound in thegeneral case. The maximum pivotal growth is found. It is independentof the order of the matrix. Detailed proofs are given in thereport by Bohte (1974).     

Effective bounds for very ample line bundles

Let be an ample line bundle on a non singular projective -fold . It is first shown that is very ample for . The proof develops an original idea of Y.T. Siu and is based on a combination of the Riemann-Roch theorem together with an improved Noetherian induction technique for the Nadel multiplier ideal sheaves. In the second part, an effective version of the big Matsusaka theorem is obtained, refining an earlier version of Y.T. Siu: there is an explicit polynomial bound of degree in the arguments, such that is very ample for . The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space. Oblatum 30-I-1995 & 18-V-1995     

Evolutionary game model for a marketing cooperative with penalty for unfaithfulness

A game-theoretical model for the behaviour in a marketing cooperative is proposed. For the strategy choice an evolutionary dynamics is introduced. Considering a model with penalty for unfaithfulness and Cournot type market situation, it is shown that, if the penalty is effective then this strategy dynamics drives the players towards an attractive solution, a particular type of Nash equilibrium. A model with redistribution of penalty is also studied. For the symmetric case, on the basis of stability analysis of the strategy dynamics, in terms of the model parameters, sufficient conditions are provided for the strategy choice to converge to a strict Nash equilibrium.     

右型A半群的F-覆盖

A right adequate semigroup of type F is defined as a right adequate semigroup which is an F-rpp semigroup. A right adequate semigroup T of type F is called an F-cover for a right type-A semigroup S if S is the image of T under an L＊-homomorphism. In this paper, we will prove that any right type-A monoid has F-covers and then establish the structure of F-covers for a given right type-A monoid. Our results extend and enrich the related results for inverse semigroups.     

Bayesian policy support for adaptive strategies using computer models for complex physical systems

In this paper, we discuss combining expert knowledge and computer simulators in order to provide decision support for policy makers managing complex physical systems. We allow future states of the complex system to be viewed after initial policy is made, and for those states to influence revision of policy. The potential for future observations and intervention impacts heavily on optimal policy for today and this is handled within our approach. We show how deriving policy dependent system uncertainty using computer models leads to an intractable backwards induction problem for the resulting decision tree. We introduce an algorithm for emulating an upper bound on our expected loss surface for all possible policies and discuss how this might be used in policy support. To illustrate our methodology, we look at choosing an optimal CO₂ abatement strategy, combining an intermediate complexity climate model and an economic utility model with climate data.     

Educating for Good Questioning: a Tool for Intellectual Virtues Education

Questioning is a familiar, everyday practice which we use, often unreflectively, in order to gather information, communicate with each other, and advance our inquiries. Yet, not all questions are equally effective and not all questioners are equally adept. Being a good questioner requires a degree of proficiency and judgment, both in determining what to ask and in deciding who, where, when, and how to ask. Good questioning is an intellectual skill. Given its ubiquity and significance, it is an intellectual skill that, I believe, we should educate for. In this paper, I present a central line of argument in support of educating for good questioning, namely, that it plays an important role in the formation of an individual’s intellectual character and can thereby serve as a valuable pedagogical tool for intellectual character education. I argue that good questioning plays two important roles in the cultivation of intellectual character: good questioning (1) stimulates intellectually virtuous inquiry and (2) contributes to the development of several of the individual intellectual virtues. Insofar as the cultivation of intellectually virtuous character is a desirable educational objective, we should educate for good questioning.     

Optimal Control for an Obstruction Problem

A question of flow around an obstacle leads to an optimal control problem. If an optimum path exists, then it is calculable from the Pontryagin principle. The optimum is verified to be reached, using a discretization of the problem.     

Rounding-based heuristics for nonconvex MINLPs

We propose two primal heuristics for nonconvex mixed-integer nonlinear programs. Both are based on the idea of rounding the solution of a continuous nonlinear program subject to linear constraints. Each rounding step is accomplished through the solution of a mixed-integer linear program. Our heuristics use the same algorithmic scheme, but they differ in the choice of the point to be rounded (which is feasible for nonlinear constraints but possibly fractional) and in the linear constraints. We propose a feasibility heuristic, that aims at finding an initial feasible solution, and an improvement heuristic, whose purpose is to search for an improved solution within the neighborhood of a given point. The neighborhood is defined through local branching cuts or box constraints. Computational results show the effectiveness in practice of these simple ideas, implemented within an open-source solver for nonconvex mixed-integer nonlinear programs.     

A Simple Way for Determining the Normalized Potentials for Harmonic Maps

We give a simple way for determining the normalized potentials in the Weierstrass type representation of the harmonic maps for a Riemann surface to a compact symmetric space. As an application, the normalized potential for an arbitrary constant mean curvature surface in space is obtained.     

A sharp regularization error estimate for bang-bang solutions for an iterative Bregman regularization method for optimal control problems

In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and a regularity condition on the active sets convergence results are presented. Furthermore we show by numerical examples that the provided a-priori estimate is sharp in the bang-bang case. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)