Impulsive stochastic functional differential inclusions driven by a fractional Brownian motion with infinite delay

In this paper, we prove the existence of mild solutions for a first‐order impulsive semilinear stochastic functional differential inclusions driven by a fractional Brownian motion with infinite delay. We consider the cases in which the right hand side is convex or nonconvex valued. The results are obtained by using two different fixed point theorems for multivalued mappings. Copyright © 2015 John Wiley & Sons, Ltd.     

Dehydration of Magnesium Bromide Hexahydrate Studied by in situ X‐ray Powder Diffraction

Laboratory X‐ray powder diffraction data were used to investigate the dehydration process of magnesium bromide hexahydrate in the temperature range 300 K ≤ T ≤ 420 K. By heating of the as synthesized hexahydrate (MgBr₂ · 6H₂O, observed in the temperature range 300 K ≤ T ≤ 349 K), three lower hydrates can be obtained in overlapped temperature regions: MgBr₂ · 4H₂O (332 K ≤ T ≤ 367 K), MgBr₂ · 2H₂O (361 K ≤ T ≤ 380 K) and MgBr₂ · H₂O (375 K ≤ T ≤ 390 K). Although the crystal structure of the hexahydrate was published almost eighty years ago, there are no data on the structures of the lower hydrates. The crystal structures are reported and are found to be isotypical with the structures of the respective chlorides. The structure of MgBr₂ · 6H₂O is characterized by discrete Mg(H₂O)₆ octahedra and is the only hydrate of this group that contains unbonded Br^– anions. MgBr₂ · 4H₂O is composed of discrete MgBr₂(H₂O)₄ octahedra, and the structure was found to be disordered. The crystal structure of MgBr₂ · 2H₂O is formed by single chains of edge‐sharing MgBr₄(H₂O)₂ octahedra, while in the case of MgBr₂ · H₂O double chains of edge‐shared MgBr₅H₂O are formed. By increasing the temperature, as expected, positive thermal expansion was evidenced. Thermal expansion coefficients, based on the changes of the unit cell parameters, were derived for the following hydrates: MgBr₂ · 6H₂O, MgBr₂ · 4H₂O, and MgBr₂ · 2H₂O.     

Population of the states in collisions of mixed-state (1s21S,1s2s3S) B3+ and C4+ ion beams with He and H2 targets

Auger KLn lines are observed in high-resolution electron spectra obtained in collisions of mixed-state (1s²¹S,1s2s³S) He-like beams of 4 MeV B³⁺ with H₂ and 6 MeV C⁴⁺ with He targets. Supporting atomic structure calculations show these lines to correspond to doubly excited states, which can be readily populated by electron transfer to the component of the mixed-state beam. They thus provide indirect evidence for the existence of the corresponding KLn quartet states, similarly produced, even though their weak Auger decay does not allow for their direct observation in the electron spectra. These KLn quartet states mostly decay in a cascade chain of strong radiative E1 transitions, eventually terminating at the state, which is thus additionally enhanced. An upper limit on the state population due to cascades is obtained by assuming a statistical production of KLn quartet to doublet states followed by a 100% cascade feeding of the state. Our estimated upper limit is supported by our absolute cross section measurements and corresponding three-electron atomic orbital close coupling calculations in progress. Results to date are presented and discussed.     

Optimization of separation in two-dimensional high-performance liquid chromatography by adjusting phase system selectivity and using programmed elution techniques

The overall peak capacity in comprehensive two-dimensional liquid chromatographic (LC x LC) separation can be considerably increased using efficient columns and carefully optimized mobile phases providing large differences in the retention mechanisms and separation selectivity between the first and the second dimension. Gradient-elution operation and fraction-transfer modulation by matching the retention and the elution strength of the mobile phases in the two dimensions are useful means to suppress the band broadening in the second dimension and to increase the number of sample compounds separated in LC x LC. Matching parallel gradients in the first and second dimension eliminate the necessity of second-dimension column re-equilibration after the independent gradient runs for each fraction, increase the use of the available second-dimension separation time and can significantly improve the regularity of the coverage of the available retention space in LC x LC separations, especially with the first- and second-dimension systems showing partial selectivity correlations. Systematic development of an LC x LC method with parallel two-dimensional gradients was applied for separation of phenolic acids and flavone compounds. Several types of bonded C18, amide, phenyl, pentafluorophenyl and poly(ethylene glycol) columns were compared using the linear free energy relationship method to find suitable column combination with low correlation of retention of representative standards. The phase systems were optimized step-by-step to find the mobile phases and gradients providing best separation selectivity for phenolic compounds. The optimization of simultaneous parallel gradients in the first and second dimension resulted in significant improvement in the utilization of the available two-dimensional retention space.     

The general rigidity result for bundles of <Emphasis Type="Italic">A</Emphasis>-covelocities and <Emphasis Type="Italic">A</Emphasis>-jets

Let M be an m-dimensional manifold and A = D _k ^r /I = R⊕N _A a Weil algebra of height r. We prove that any A-covelocity T _x ^A f ∈ T _x ^A *M, x ∈ M is determined by its values over arbitrary max{width A,m} regular and under the first jet projection linearly independent elements of T _x ^A M. Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result T ^A *M ? T ^r *M without coordinate computations, which improves and generalizes the partial result obtained in Tomá? (2009) from m ≥ k to all cases of m.We also introduce the space J ^A (M,N) of A-jets and prove its rigidity in the sense of its coincidence with the classical jet space J ^r (M,N).     

Modeling texture evolution during rolling of a Cu–Nb multilayered system

A polycrystal plasticity model is proposed to predict the unique rolling texture of Cu/Nb nanostructured multilayers. At this length scale, the model accounts for the interface between Cu and Nb layers by computing the aggregate response of composite grains using a viscoplastic self–consistent scheme. Each composite grain is divided into Cu and Nb crystals with the interface parallel to the rolling plane, and compatibility and equilibrium are enforced across the interface. A latent hardening effect is introduced to account for the interaction between glide and interface dislocations. The latter are accumulated during slip transmission. This unconventional hardening confines the movement of glide dislocations by promoting symmetry of slip activities. Consequently, it slows development of the rolling texture for Cu/Nb nanolayers, and partially preserves the initial interface orientation defined by the Kurdjumov–Sachs relationship.     

Photoelectron spectroscopy of free multiply charged Keggin anions alpha-[PM12O40]3- (M = Mo, W) in the gas phase

Two polyoxometalate Keggin-type anions, alpha-PM12O40(3-) (M = Mo, W), were transferred to the gas phase by electrospray; their electronic structure and stability were probed by photoelectron spectroscopy. These triply charged anions were found to be highly stable in the gas phase with large adiabatic electron detachment energies of 1.7 and 2.1 eV for M = Mo and W, respectively. The magnitude of the repulsive Coulomb barrier was measured as approximately 3.4 eV for both anions, providing an experimental estimate for the intramolecular Coulomb repulsion present in these highly charged anions. Density functional theory calculations were carried out and compared with the experimental data, providing insight into the electronic structure and valence molecular orbitals of the two Keggin anions. The calculations indicated that the highest occupied molecular orbital and other frontier orbitals for PM12O40(3-) are localized primarily on the mu2-oxo bridging ligands of the polyoxometalate framework, consistent with the reactivity on the mu2-oxo sites observed in solution. It was shown that the HOMO of PW12O40(3-) is stabilized relative to that of PMo12O40(3-) by approximately 0.35 eV. The experimental adiabatic electron detachment energies of PM12O40(3-) (i.e., the electron affinities of PM12O40(2-)) are combined with recent calculations on the proton affinity of PM12O40(3-) to yield O-H bond dissociation energies in PM12O39(OH)2- as approximately 5.1 eV.     

Hyperfinite Lévy Processes

A hyperfinite Lévy process is an infinitesimal random walk (in the sense of nonstandard analysis) which with probability one is finite for all finite times. We develop the basic theory for hyperfinite Lévy processes and find a characterization in terms of transition probabilities. The standard part of a hyperfinite Lévy process is a (standard) Lévy process, and we show that given a generating triplet (γ, C, μ) for standard Lévy processes, we can construct hyperfinite Lévy processes whose standard parts correspond to this triplet. Hence all Lévy laws can be obtained from hyperfinite Lévy processes. The paper ends with a brief look at Malliavin calculus for hyperfinite Lévy processes including a version of the Clark-Haussmann-Ocone formula.