Shifting From Ziegler–Natta to Philips‐Type Catalyst? A Simple and Safe Access to Reduced Titanium Systems for Ethylene Polymerization

Silica‐supported titanium(IV) chloride is readily reduced by Mashima and co‐workers' reagent (1‐methyl‐3,6‐bis(trimethylsilyl)‐1,4‐cyclohexadiene) to afford materials active in ethylene polymerisation without need of aluminum alkyl cocatalyst.     

Globally solving nonconvex quadratic programming problems with box constraints via integer programming methods

We present effective linear programming based computational techniques for solving nonconvex quadratic programs with box constraints (BoxQP). We first observe that known cutting planes obtained from the Boolean Quadric Polytope (BQP) are computationally effective at reducing the optimality gap of BoxQP. We next show that the Chvátal–Gomory closure of the BQP is given by the odd-cycle inequalities even when the underlying graph is not complete. By using these cutting planes in a spatial branch-and-cut framework, together with a common integrality-based preprocessing technique and a particular convex quadratic relaxation, we develop a solver that can effectively solve a well-known family of test instances. Our linear programming based solver is competitive with SDP-based state of the art solvers on small instances and sparse instances. Most of our computational techniques have been implemented in the recent version of CPLEX and have led to significant performance improvements on nonconvex quadratic programs with linear constraints.     

Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model

<正>Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.     

Mutually describing multisets and integer partitions

To each finite multiset $A$, with underlying set $S\left(A\right)$, we associate a new multiset $d\left(A\right)$, obtained by adjoining to $S\left(A\right)$ the multiplicities of its elements in $A$. We study the orbits of the map $d$ under iteration, and show that if $A$ consists of nonnegative integers, then its orbit under $d$ converges to a cycle. Moreover, we prove that all cycles of $d$ over $\mathbb{Z}$ are of length at most $3$, and we completely determine them. This amounts to finding all systems of mutually describing multisets. In the process, we are led to introduce and study a related discrete dynamical system on the set of integer partitions of $n$ for each $n\ge 1$.     

On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.     

Realization of Metric Spaces as Inverse Limits, and Bilipschitz Embedding in L 1

We give sufficient conditions for a metric space to bilipschitz embed in L ₁. In particular, if X is a length space and there is a Lipschitz map ${u: X \rightarrow \mathbb R}$ such that for every interval ${I \subset \mathbb R}$ , the connected components of u ^?1(I) have diameter ${\leq {\rm const} \cdot {\rm diam}(I)}$ , then X admits a bilipschitz embedding in L ₁. As a corollary, the Laakso examples, (Geom Funct Anal 10(1):111–123, 2000), bilipschitz embed in L ₁, though they do not embed in any any Banach space with the Radon–Nikodym property (e.g. the space ? ₁ of summable sequences). The spaces appearing the statement of the bilipschitz embedding theorem have an alternate characterization as inverse limits of systems of metric graphs satisfying certain additional conditions. This representation, which may be of independent interest, is the initial part of the proof of the bilipschitz embedding theorem. The rest of the proof uses the combinatorial structure of the inverse system of graphs and a diffusion construction, to produce the embedding in L ₁.     

Integrated optoelectronic circuit forecast

A market research study was conducted, leading to a 10-year forecast of worldwide integrated optoelectronic circuit (IOEC) market and application trends. Four IOEC categories were considered: lightwave, imaging array, digital IC interface optical bus, and other devices. It was concluded that worldwide IOEC production will reach $1.71 billion by 1997. It was also concluded that lightwave IOECs will be the leading device category, with commercial communication the leading application.     

Towards a new framework for evaluating systemic problem structuring methods

Operational researchers and social scientists often make significant claims for the value of systemic problem structuring and other participative methods. However, when they present evidence to support these claims, it is usually based on single case studies of intervention. There have been very few attempts at evaluating across methods and across interventions undertaken by different people. This is because, in any local intervention, contextual factors, the skills of the researcher and the purposes being pursued by stakeholders affect the perceived success or failure of a method. The use of standard criteria for comparing methods is therefore made problematic by the need to consider what is unique in each intervention. So, is it possible to develop a single evaluation approach that can support both locally meaningful evaluations and longer-term comparisons between methods? This paper outlines a methodological framework for the evaluation of systemic problem structuring methods that seeks to do just this.