Safety neighbournoods for the invariants of the matrix similarity

We give safety neighbourhoods for the necessary conditions in the change of the Jordan canonical form of a matrix under small perturbations. We also obtain the minimum distance from an n × n complex matrix which has less than k nonconstant invariant factors (2≤ k≤ n) to the set of matrices which have more or equal to k. When k= 2, we get in particular the distance from a nonderogatory matrix to the set of derogatory matrices.     

An approach formulated in terms of conserved variables for the characterisation of propellant combustion in internal ballistics

A model formulated in terms of conserved variables is proposed for its use in the study of internal ballistic problems of pyrotechnical mixtures and propellants. It is a transient two‐phase flow model adapted from the non‐conservative Gough model. This conversion is mathematically attractive because of the wide range of numerical methods for this kind of systems that may be applied. We propose the use of the AUSM+, AUSM + up and Rusanov schemes as an efficient alternative for this type of two‐phase problem. A splitting technique is applied, which solves the system of equations in several steps. A second‐order approach based on Monotonic Upstream‐Centred Scheme for Conservation Laws (MUSCL) is also used. Some tests are used to validate the code, namely a shock wave test, a contact discontinuity problem and an internal ballistics problem. In this last case, one‐dimensional numerical results are compared with experimental data of 155‐mm gunshots. Copyright © 2015 John Wiley & Sons, Ltd.     

Improved state space relaxation for constrained two-dimensional guillotine cutting problems

Christofides and Hadjiconstantinou (1995) introduced a dynamic programming state space relaxation for obtaining upper bounds for the Constrained Two-dimensional Guillotine Cutting Problem. The quality of those bounds depend on the chosen item weights, they are adjusted using a subgradient-like algorithm. This paper proposes Algorithm X, a new weight adjusting algorithm based on integer programming that provably obtains the optimal weights. In order to obtain even better upper bounds, that algorithm is generalized into Algorithm X2 for obtaining optimal two-dimensional item weights. We also present a full hybrid method, called Algorithm X2D, that computes those strong upper bounds but also provides feasible solutions obtained by: (1) exploring the suboptimal solutions hidden in the dynamic programming matrices; (2) performing a number of iterations of a GRASP based primal heuristic; and (3) executing X2H, an adaptation of Algorithm X2 to transform it into a primal heuristic. Extensive experiments with instances from the literature and on newly proposed instances, for both variants with and without item rotation, show that X2D can consistently deliver high-quality solutions and sharp upper bounds. In many cases the provided solutions are certified to be optimal.     

Analyzing completeness of axiomatic functional systems for temporal × modal logics

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions (being injective, surjective, increasing, etc.) have been considered and axiomatic systems (called functional) which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Big rational surfaces

We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of mathbbP²{mathbb{P}^2} at distinct points lying on a (possibly reducible) cubic.     

Capillary smectization and layering in a confined liquid crystal

Using density-functional theory, we have analyzed the phase behavior of a model liquid crystal confined between two parallel, planar surfaces (i.e., the so-called slit pore). As a result of confinement, a rich phase behavior arises. The complete liquid-crystal phase diagram of the confined fluid is mapped out as a function of wall separation and chemical potential. Strong commensuration effects in the film with respect to wall separation lead to enhanced smectic ordering, which gives capillary smectization (i.e., formation of a smectic phase in the pore), or frustrated smectic ordering, which suppresses capillary smectization. These effects also produce layering transitions. Our nonlocal density-functional-based analysis provides a unified picture of all the above phenomena.     

Ground and excited states of NH4: Electron propagator and quantum defect analysis

Vertical excitation energies of the Rydberg radical NH4 are inferred from ab initio electron propagator calculations on the electron affinities of NH4+. The adiabatic ionization energy of NH4 is evaluated with coupled-cluster calculations. These predictions provide optimal parameters for the molecular-adapted quantum defect orbital method, which is used to determine Einstein emission coefficients and radiative lifetimes. Comparisons with spectroscopic data and previous calculations are discussed.     

Acoustic waves of GaN nitride nanowires

Acoustic waves of GaN nanowires are studied. The materials have a wurtzite structure and thus the elastic anisotropy is included. We use the xyz-algorithm originally employed in the analysis of resonant ultrasound spectroscopy results. We have considered hexagonal cross-section nanowires as those experimentally grown. We have studied also circular cross-section nanowires (nanotubes) for comparison. It was found that the lower frequency modes have a very similar dispersion relation both in shape and frequency value, but higher frequency modes exhibit more important differences. The nanowires are solid or hollow and the influence of the thickness on the dispersion relation and the elastic displacement pattern is considered. Nanowires with a zinc-blende structure have also been considered because of theoretical studies allowing for their existence. We have studied also the squared displacement vectors to see the spatial distribution of the different modes in the nanowires. It was found that there are many modes whose elastic displacement components concentrate around the borders of the nanowire and they do not penetrate almost in the inner part of the nanowire.     

Characterization and reactivity study of non-heme high-valent iron–hydroxo complexes

A terminal Fe^IIIOH complex, [Fe^III(L)(OH)]²⁻ (1), has been synthesized and structurally characterized (H₄L = 1,2-bis(2-hydroxy-2-methylpropanamido)benzene). The oxidation reaction of 1 with one equiv. of tris(4-bromophenyl)ammoniumyl hexachloroantimonate (TBAH) or ceric ammonium nitrate (CAN) in acetonitrile at −45 °C results in the formation of a Fe^IIIOH ligand radical complex, [Fe^III(L˙)(OH)]⁻ (2), which is hereby characterized by UV-visible, ¹H nuclear magnetic resonance, electron paramagnetic resonance, and X-ray absorption spectroscopy techniques. The reaction of 2 with a triphenylcarbon radical further gives triphenylmethanol and mimics the so-called oxygen rebound step of Cpd II of cytochrome P450. Furthermore, the reaction of 2 was explored with different 4-substituted-2,6-di-tert-butylphenols. Based on kinetic analysis, a hydrogen atom transfer (HAT) mechanism has been established. A pK_a value of 19.3 and a BDFE value of 78.2 kcal/mol have been estimated for complex 2.

One-electron oxidation of an Fe^III–OH complex (1) results in the formation of a Fe^III–OH ligand radical complex (2). Its reaction with (C₆H₅)₃C˙ results in the formation of (C₆H₅)₃COH, which is a functional mimic of compound II of cytochrome P450.     

Foaming behavior,cellular structure and physical properties of polybenzoxazine foams

In this paper, polymer foams based on a benzoxazine resin have been successfully prepared using azodicarbonamide (ADC) as a chemical blowing agent and have been characterized regarding their foaming behavior, cellular structure, and physical properties. The effect of the ADC on the curing process of the resin was analyzed using differential scanning calorimetry and blowing agent decomposition was followed by thermogravitmetric analysis (TGA). The characterization of the cellular structure of the foamed samples was done using scanning electron microscopy. The mechanical properties of the foams were determined using compression tests and the thermal conductivity was assessed using the transient plane source method. The results indicated that the curing process and gas release took place in a similar time interval. The foams showed an isotropic cellular structure with relative densities in the range 0.35–0.60, and showed compressive strengths and compressive moduli in the range of 10–70 MPa and 400–1100 MPa, respectively. Thermal conductivities were in the range of 0.06–0.12 W m^?1K^?1. The findings in this paper demonstrate the possibility of producing polybenzoxazine foams using a simple process in which curing and foaming take place simultaneously. In addition, the mechanical characterization of these materials indicates that they are suitable for structural applications. Copyright © 2011 John Wiley & Sons, Ltd.