The geometry of Hamilton spaces - An introduction

A short introduction of Hamilton, Cartan and Generalized Hamilton spaces is provided. The Hamilton--Jacobi equations are deduced by variational calculus.     

Measure functions for frames

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful comparison of frames indexed by the same set. We define the ultrafilter measure function, an explicit frame measure function that we show is contained both algebraically and topologically inside all frame measure functions. We explore additional properties of frame measure functions, showing that they are additive on a large class of supersets—those that come from so called non-expansive frames. We apply our results to the Gabor setting, computing the frame measure function of Gabor frames and establishing a new result about supersets of Gabor frames.     

Soft X-ray resonant magnetic scattering studies on Fe/CoO exchange bias system

We have used soft X-ray resonant magnetic scattering (XRMS) to search for the presence of an effective ferromagnetic moment belonging to the antiferromagnetic (AF) layer which is in close contact with a ferromagnetic (F) layer. Taking advantage of the element specificity of the XRMS technique, we have measured hysteresis loops of both Fe and CoO layers of a CoO(40 Å)/Fe (150 Å) exchange bias bilayer. From these measurements we have concluded that the proximity of the F layer induces a magnetic moment in the AF layer. The F moment of the AF layer has two components: one is frozen and does not follow the applied magnetic field and the other one follows in phase the ferromagnetic magnetization of the F layer. The temperature dependence of the F components belonging to the AF layer is shown and discussed.     

The geometry of Ingarden spaces

The Randers spaces RFⁿ were introduced by R. S. Ingarden. They are considered as Finsler spaces Fⁿ = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fⁿ, as Finsler spaces I Fⁿ = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fⁿ and I Fⁿ are completely different. For I Fⁿ we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fⁿ is constructed.     

Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.     

Hydrolysis-condensation of tetraethoxysilane in nonparental solvents studied by GC-MS

Gas-chromatography coupled with mass spectrometry was used to investigate the hydrolysis and condensation of tetra-ethoxysilane (TEOS) in nonparental solvents (MeOH and nPrOH). In the presence of nonparental solvents, the reaction that advanced at highest rate is alkoxy group scrambling, that changes the precursor at the molecular level. Subsequent stages of hydrolysis-polycondensation process are essentially determined by the reactivity of the new molecular species formed.     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Linkage isomerism in nitrite reduction by cytochrome cd1 nitrite reductase

Nitrite reduction by cytochrome cd(1) nitrite reductase (cd(1)NIR) is currently accepted to involve coordination of the nitrite nitrogen atom to the ferrous d(1) heme. Here, density functional theory results are reported on the previously unexplored O-binding of nitrite to ferrous and ferric cd(1)NIR. Although the N-isomer (nitro) is energetically favored over the O-nitrite (nitrito), even one single strong hydrogen bond may provide the energy required to put the two isomers on level terms. When hydrogen bonding existent at the cd(1)NIR active site is accounted for in the computational model, the O-nitrite isomer is found to spontaneously protonate and thus yield a ferric-hydroxo species, liberating nitric oxide. An O-nitrite ferrous cd(1)NIR complex appears to be an energetically feasible intermediate for nitrite reduction. O-Coordination would offer an advantage since the end product of nitrite reduction would be a ferric-hydroxo/water complex, rather than the more kinetically inert iron-nitrosyl complex implied by the N-nitrite mechanism.     

Steric control over hydrogen bonding in crystalline organic solids: a structural study of N,N'-dialkylthioureas

Hydrogen bonding in crystalline N,N'-dialkylthioureas was examined with the help of single-crystal X-ray diffraction, DFT calculations, and Cambridge Structural Database (CSD) analysis. A CSD survey indicated that unlike the related urea derivatives, which persistently self-assemble into one-dimensional hydrogen-bonded chains, the analogous thioureas can form two different hydrogen-bonding motifs in the solid state: chains, structurally similar with those found in ureas, and dimers, that further associate into hydrogen-bonded layers. The formation of one motif or another can be manipulated by the bulkiness of the organic substituents on the thiourea group, which provides a clear example of steric control over the hydrogen bonding arrangement in crystalline organic solids.