Generalized skew‐Hermitian triangular splitting iteration methods for saddle‐point linear systems

A generalized skew‐Hermitian triangular splitting iteration method is presented for solving non‐Hermitian linear systems with strong skew‐Hermitian parts. We study the convergence of the generalized skew‐Hermitian triangular splitting iteration methods for non‐Hermitian positive definite linear systems, as well as spectrum distribution of the preconditioned matrix with respect to the preconditioner induced from the generalized skew‐Hermitian triangular splitting. Then the generalized skew‐Hermitian triangular splitting iteration method is applied to non‐Hermitian positive semidefinite saddle‐point linear systems, and we prove its convergence under suitable restrictions on the iteration parameters. By specially choosing the values of the iteration parameters, we obtain a few of the existing iteration methods in the literature. Numerical results show that the generalized skew‐Hermitian triangular splitting iteration methods are effective for solving non‐Hermitian saddle‐point linear systems with strong skew‐Hermitian parts. Copyright © 2013 John Wiley & Sons, Ltd.     

A mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints

This study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized. These problems can be modeled as a more general job selection problem. Cases with resumable, non-resumable, and semi-resumable jobs as well as cases without availability constraints are investigated. The proposed efficient mixed integer linear programming approach includes possible improvements to the model, notably specialized lifted knapsack cover cuts. The method proves to be competitive compared with existing dedicated methods: numerical experiments on randomly generated instances show that all 350-job instances of the test bed are closed for the well-known problem 1|_ri|∑_wiUi$1|r_i|\sum w_i{U}_i$. For all investigated problem types, 98.4% of 500-job instances can be solved to optimality within 1 hour.     

Convex equipartitions: the spicy chicken theorem

We show that, for any prime power $n$ and any convex body $K$ (i.e., a compact convex set with interior) in $\mathbb{R }^d$ , there exists a partition of $K$ into $n$ convex sets with equal volumes and equal surface areas. Similar results regarding equipartitions with respect to continuous functionals and absolutely continuous measures on convex bodies are also proven. These include a generalization of the ham-sandwich theorem to arbitrary number of convex pieces confirming a conjecture of Kaneko and Kano, a similar generalization of perfect partitions of a cake and its icing, and a generalization of the Gromov–Borsuk–Ulam theorem for convex sets in the model spaces of constant curvature.     

Exponentially closed fields and the conjecture on intersections with tori

We give an axiomatization of the class ECF of exponentially closed fields, which includes the pseudo-exponential fields previously introduced by the second author, and show that it is superstable over its interpretation of arithmetic. Furthermore, ECF is exactly the elementary class of the pseudo-exponential fields if and only if the Diophantine conjecture CIT on atypical intersections of tori with subvarieties is true.     

A data model for algorithmic multiple criteria decision analysis

Various software tools implementing multiple criteria decision analysis (MCDA) methods have appeared over the last decades. Although MCDA methods share common features, most of the implementing software have been developed independently from scratch. Majority of the tools have a proprietary storage format and exchanging data among software is cumbersome. Common data exchange standard would be useful for an analyst wanting to apply different methods on the same problem. The Decision Deck project has proposed to build components implementing MCDA methods in a reusable and interchangeable manner. A key element in this scheme is the XMCDA standard, a proposal that aims to standardize an XML encoding of common structures appearing in MCDA models, such as criteria and performance evaluations. Although XMCDA allows to present most data structures for MCDA models, it almost completely lacks data integrity checks. In this paper we present a new comprehensive data model for MCDA problems, implemented as an XML schema. The data model includes types that are sufficient to represent multi-attribute value/utility models, ELECTRE III/TRI models, and their stochastic extensions, and AHP. We also discuss use of the data model in algorithmic MCDA.     

Expedient Access to Functionalized Furan/3(2H)-furanone Ensembles via Microwave-Assisted Domino Reactions

A one-pot linkage between furan and 3(2H)-furanone rings has been effected via the microwave-assisted Et₃N-catalyzed domino condensation of the furan and benzofuran carboxylic acids with available cyanopropargylic alcohols (MeCN, 100 °C, 1.2 atm, 2–17 h). Despite involving a number of C-H-forming/breaking steps, the assembly is chemoselective and the final products, 5-(2-furyl)-3(2H)-furanones, are formed in 59–96% yields.     

Early introduction of the amino group to the C27–C35 building block of Eribulin

A new synthetic strategy towards the C27–C35 subunit of Eribulin (1) has been devised to include a protected 1,2-amino alcohol at C34–C35. Early introduction of the C35 amino group in the synthesis of 1 increases the efficiency of the route. This new approach can be accomplished on a multi-gram scale and allows for the successful synthesis of Eribulin.     

Two-state and continuous phase transitions in lipid bilayers A time-resolved X-ray diffraction study

Structural changes associated with transition from one phase to another have been examined in several lipid-water systems using time-resolved X-ray diffraction methods. Two types of transition mechanism can be recognized on the basis of scattering originating from the packing of the hydrocarbon chains. Two-state transitions are characterized by coexistence of the wide-angle scattering patterns of the initial and final phases throughout the transition region. Continuous transitions, on the other hand, take place through a series of intermediate states that are believed to arise from deformation of the hydrocarbon chain lattice as one phase transforms into another. Two-state processes are observed as subgel to liquid crystal transitions, and continuous transformations are typical of subgel to gel phase transitions. Examples of these transition types are presented and other transitions that do not appear to conform to either of these mechanisms are described.     

Sulfur Versus Oxygen in Interaction with the Double Bond: AB Initio Study of Electronic Structure and Prototropic Rearrangement of 1-Methoxy-2-propene and 1-Methylthio-2-propene

The ab initio calculations of 1-methoxy-2-propene ( 1 ), 1-methylthio-2-propene ( 2 ), and their anions are performed using the RHF/6-31+G* geometry optimization followed by MP2/6-31+G* energy calculations. Both 1 and 2 are found to rearrange toward 1-substituted 1-propenes with a comparable exothermic effect. However, the proton abstraction energies of 1 and 2 differ significantly. So, the acidity of propene is just slightly affected by the OCH 3 group while the SCH 3 group decreases its proton abstraction energy by 17.5 kcal/mol. Changes in charge distribution, bond lengths and bond orders suggest the negative hyperconjugation to stabilize anions of 2 but not that of 1 . This divergence is explained with a difference in sulfur and oxygen electronegativity. The d -functions of both sulfur and oxygen act in polarization. The Z -isomer of anion 1 is found to be by 2.9 kcal/mol more stable than its E -isomer, this could provide a predominant kinetic formation of the less stable Z -isomer of 1-methoxy-1-propene under base catalysis.