First order spectral perturbation theory of square singular matrix polynomials

We develop first order eigenvalue expansions of one-parametric perturbations of square singular matrix polynomials. Although the eigenvalues of a singular matrix polynomial P(λ) are not continuous functions of the entries of the coefficients of the polynomial, we show that for most perturbations they are indeed continuous. Given an eigenvalue λ₀ of P(λ) we prove that, for generic perturbations M(λ) of degree at most the degree of P(λ), the eigenvalues of P(λ)+?M(λ) admit covergent series expansions near λ₀ and we describe the first order term of these expansions in terms of M(λ₀) and certain particular bases of the left and right null spaces of P(λ₀). In the important case of λ₀ being a semisimple eigenvalue of P(λ) any bases of the left and right null spaces of P(λ₀) can be used, and the first order term of the eigenvalue expansions takes a simple form. In this situation we also obtain the limit vector of the associated eigenvector expansions.     

Analysis of multiple scattering iterations for high-frequency scattering problems. II: The three-dimensional scalar case

In this paper, we continue our analysis of the treatment of multiple scattering effects within a recently proposed methodology, based on integral-equations, for the numerical solution of scattering problems at high frequencies. In more detail, here we extend the two-dimensional results in part I of this work to fully three-dimensional geometries. As in the former case, our concern here is the determination of the rate of convergence of the multiple-scattering iterations for a collection of three-dimensional convex obstacles that are inherent in the aforementioned high-frequency schemes. To this end, we follow a similar strategy to that we devised in part I: first, we recast the (iterated, Neumann) multiple-scattering series in the form of a sum of periodic orbits (of increasing period) corresponding to multiple reflections that periodically bounce off a series of scattering sub-structures; then, we proceed to derive a high-frequency recurrence that relates the normal derivatives of the fields induced on these structures as the waves reflect periodically; and, finally, we analyze this recurrence to provide an explicit rate of convergence associated with each orbit. While the procedure is analogous to its two-dimensional counterpart, the actual analysis is significantly more involved and, perhaps more interestingly, it uncovers new phenomena that cannot be distinguished in two-dimensional configurations (e.g. the further dependence of the convergence rate on the relative orientation of interacting structures). As in the two-dimensional case, and beyond their intrinsic interest, we also explain here how the results of our analysis can be used to accelerate the convergence of the multiple-scattering series and, thus, to provide significant savings in computational times.     

Eigenfunction Expansions and Transformation Theory

Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space Φ^× in a convenient Gelfand triplet Φ⊆ℋ⊆Φ^×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized bases of eigenfunctions in both frameworks direct integrals and Gelfand triplets. Transformation formulas look like usual in Physics literature, as limits of integral functionals but with well defined kernels. Several approaches are feasible. Vitali approach is used.     

Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean

Strongly absolute bases are, roughly speaking, purely nonlocally convex bases in quasi-Banach spaces. When, in addition, they are unconditional then the discrete lattice structure they induce in the space is lattice anti-Euclidean. In this brief note we characterize the complemented unconditional basic sequences in those quasi-Banach spaces with strongly absolute unconditional basis, and use this result to derive the uniqueness of unconditional basis in many classical quasi-Banach spaces.     

Fujita exponents for evolution problems with nonlocal diffusion

We prove the existence of a critical exponent of Fujita type for the nonlocal diffusion problem

The dual geometry of Boolean semirings

It is well known that the variety of Boolean semirings, which is generated by the three element semiring ${\mathbb{S}}$ , is dual to the category of partially Stone spaces. We place this duality in the context of natural dualities. We begin by introducing a topological structure S? and obtain an optimal natural duality between the quasi-variety ISP( ${\mathbb{S}}$ ) and the category IS _c P+(S?). Then we construct an optimal and very small structure S? _os that yields a strong duality. The geometry of some of the partially Stone spaces that take part in these dualities is presented, and we call them “hairy cubes”, as they are n-dimensional cubes with unique incomparable covers for each element of the cube. We also obtain a polynomial representation for the elements of the hairy cube.     

Developing a market-based approach to managing the US strategic petroleum reserve

The Strategic Petroleum Reserve has not been used effectively to manage the consequences of oil shocks in the United States. The main reason is that political decision makers tend to hoard the reserves during crises and bureaucratic processes delay the sale of the reserves. Also, the enabling legislation focused on ameliorating shortages whereas disruptions result price spikes rather than shortages. We develop a Markov game of the buildup and drawdown of the reserve in which a public player aims to maximize consumer welfare at the same time private holders of inventory maximize their profit. The methodological contribution in this paper is the development of financial options to implement the public player’s optimal policy. We use the solution of this game to calculate the number and value of options necessary for the private marketplace to trigger the optimal buildup and drawdown of the reserve.     

Properties of alkali-halide salt solutions about polarizable nanoparticle solutes for different ion models

We investigate the distributions of various salts about large hydrophobic polarizable solutes in aqueous electrolyte solutions. The solutes are modeled as nanometer-sized cylindrical objects, a scale relevant to biomolecules and nanomaterials, and particularly high aspect ratio nanoparticles. Interactions, including image charge forces arising from the finite polarizability of the solute, between explicit solvent/ions and the solute are computed explicitly using a molecular dynamics simulation methodology we have recently introduced. Comparisons are made between several salt species and different models of the force fields for each ionic component of the salt. We find evidence that both small cations, Li(+), and large anions, I(-), adsorb at hydrophobic interfaces. Our results indicate that the ion structure about the solute is strongly dependent on the force field investigated, suggesting that ion selectivity is quite sensitive to the respective parameters defining the ion's size and binding energy as well as to the polarizability of the solute.     

Rapid direct analysis in real time (DART) mass spectrometric detection of juvenile hormone III and its terpene precursors

Direct analysis in real time (DART) is a plasma-based ambient ionization technique that enables rapid ionization of small molecules with high sample throughput. In this work, DART was coupled to an orthogonal (oa) time-of-flight (TOF) mass spectrometer and the system was optimized for analyzing a vital hormonal regulator in insects, juvenile hormone (JH) III and its terpene precursors, namely, farnesol, farnesoic acid, and methyl farnesoate. Optimization experiments were planned using design of experiments (DOE) full factorial models to identify the most significant DART variables contributing to JH III analysis sensitivity by DART-TOF mass spectrometry (MS). The optimized DART-TOF MS method had femtomole to sub-picomole detection limits for terpene standards, along with mass accuracies below 5 ppm. Finally, the possibility of distinguishing between two farnesol isomers by in-source-collision-induced dissociation (CID) in the first differentially pumped region of the oaTOF mass spectrometer was investigated. DART-MS enabled high-throughput, sensitive analysis with acquisition times ranging from 30 s to a minute. To the best of our knowledge, this is the first report on the application of DART-MS to the detection and identification of volatile or semi-volatile insect terpenoids, and on the use of DOE approaches to optimize DART-MS analytical procedures.     

1‐(2‐Aminophenyl)‐3‐(4‐pyridyl)prop‐2‐en‐1‐one: a three‐dimensional framework structure built from N—H...N,C—H...O and C—H...π(arene) hydrogen bonds

The intramolecular dimensions of the title compound, C₁₄H₁₂N₂O, provide evidence for a polarized electronic structure. The molecule, which is almost completely planar, contains an intramolecular N—H...O hydrogen bond, and the molecules are linked by a combination of N—H...N, C—H...O and C—H...π(arene) hydrogen bonds to form a three‐dimensional framework structure.