On the Nagumo uniqueness theorem

By a convenient reparametrization of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of a recent generalization of Nagumo’s uniqueness theorem. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities.     

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.     

Geometric invariant theory and Einstein–Weyl geometry

In this article, we give a survey of geometric invariant theory for Toric Varieties, and present an application to the Einstein-Weyl geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space CP_1,1,2. We also find and classify all possible quotients.     

A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments

This article presents a Taylor collocation method for the approximate solution of high‐order linear Volterra‐Fredholm integrodifferential equations with linear functional arguments. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Some numerical examples, which consist of initial and boundary conditions, are given to show the properties of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

On constructing total orders and solving vector optimization problems with total orders

In this paper, we introduce a construction method of total ordering cone on \mathbbRⁿ{\mathbb{R}^n} . It is shown that any total ordering cone on \mathbbRⁿ{\mathbb{R}^n} is isomorphic to the cone \mathbbRⁿ_lex{\mathbb{R}^n_{lex}} . Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented.     

How much do we “pay” for using default parameters?

This paper explores the potential benefit of using tuned parameter settings for integer programming instances. Three metrics are considered for selecting parameters: Time-to-Optimality, Proven-Gap and Best-Integer-Solution. Good parameter settings for each metric are found using the open-source software tool Selection Tool for Optimization Parameters. Computational tests are presented using CPLEX solver (version 9.0) on MIPLIB test instances, showing substantial improvements over the default parameter setting. Although the benefit of a tuned parameter setting on an individual instance is outweighed by the cost of identifying the tuned setting, these results indicate that substantial benefit may be achieved in cases where the cost of tuning parameter settings is justified.     

Manganese(III) Acetate Catalyzed Oxidative Radical Additions of α‐Dicarbonyl Compounds to 1‐ and 2‐Phenylcyclohepta‐1,3,5‐triene

Manganese(III) acetate catalyzed oxidative radical‐addition reactions of α‐dicarbonyl compounds such as methyl acetoacetate ( 6 ), acetylacetone ( 7 ), and dimedone ( 8 ) to the mixture of 1‐ and 2‐phenylcyclohepta‐1,3,5‐triene ( 4 and 5 ) were investigated (Scheme 1). The 1‐phenylcyclohepta‐1,3,5‐triene ( 4 ) formed mainly [2+3] and [4+3] dihydrofuran addition products derived from cycloheptatriene and [2+3] dihydrofuran addition products derived from the norcaradiene structure. The 2‐phenylcyclohepta‐1,3,5‐triene ( 5 ) formed mainly [6+3] dihydrofuran addition products derived from cycloheptatriene and [4+3] dihydrofuran addition products derived from the norcaradiene structure. The structures of isolated products were established by their spectroscopic data (IR, ¹H‐ and ¹³C‐NMR, MS, and elemental analysis) and comparison with literature data. The formation mechanism of the products is discussed.     

Laser induced fluorescence spectroscopy of tetracene with large Ar, Ne, and H2 clusters in superfluid He nanodroplets

Clusters of tetracene molecules with different numbers of attached (Ar)(N), (Ne)(N) and (H(2))(N) particles (N = 1-2000) are assembled inside superfluid He nanodroplets and studied via laser-induced fluorescence. The frequency shift of the fluorescence spectrum of the tetracene molecules is studied as a function of cluster size and pickup order of tetracene and cluster species. For (Ar)(N) and (Ne)(N) clusters, our results indicate that the tetracene molecules reside inside the clusters when tetracene is captured by the He nanodroplet before the cluster species; conversely, the tetracene molecules stay on the surface of the clusters when tetracene is captured after the cluster species. In the case of (H(2))(N) clusters, however, tetracene molecules reside inside the (H(2))(N) clusters irrespective of the pickup order. We conclude that (Ar)(N) and (Ne)(N) clusters are rigid at T = 0.38 K, while (H(2))(N) clusters of up to N = 2000 remain fluxional at the same temperature. The results may also indicate the occurrence of heterogeneous nucleation of the (H(2))(N) clusters, which is induced by the interaction with tetracene chromophore molecules.     

Acetic acid-confined synthesis of uniform three-dimensional (3D) bismuth telluride nanocrystals consisting of few-quintuple-layer nanoplatelets

High-selectivity, uniform three-dimensional (3D) flower-like bismuth telluride (Bi(2)Te(3)) nanocrystals consisting of few-quintuple-layer nanoplatelets with a thickness down to 4.5 nm were synthesized for the first time by a facile, one-pot polyol method with acetic acid as the structure-director. Micrometre-sized 2D films and honeycomb-like spheres can be obtained using the uniform 3D Bi(2)Te(3) nanocrystals as building blocks.