Advances in theoretical and experimental XAFS studies of thermodynamic properties,anharmonic effects and structural determination of fcc crystals

Thermodynamic properties, anharmonic effects and structural determination of fcc crystals have been studied based on the theoretical and experimental Debye–Waller factors presented in terms of cumulant expansion up to the third order, thermal expansion coefficient, X-ray absorption fine structure (XAFS) spectra and their Fourier transform magnitudes. The advances in these studies are performed by the further development of the anharmonic correlated Einstein model primary only for approximating three first XAFS cumulants into the method using that all the considered theoretical and experimental XAFS parameters have been provided based on only the calculated and measured second cumulants. The obtained cumulants describe the anharmonic effects in XAFS contributing to the accurate structural determination. Numerical results for Cu are found to be in good agreement with the experimental values extracted by using the present advanced method and with those obtained by the other measurements.     

Novel methods for synthesizing halide-free alane without the formation of adducts

Many of the current synthesis methods for aluminum hydride (alane—AlH₃) involve reacting AlCl₃ and LiAlH₄ in solvents. The reaction requires the formation of an alane adduct such as AlH₃⋅[(C₂H₅)₂O] prior to obtaining crystallized stable α-AlH₃. This process requires several hours of pumping in a vacuum system to remove the ether and convert the alane etherate into stable α-alane. This crystallization process is both costly and hazardous because a large amount of highly flammable material (e.g. ether) is removed by vacuum pumps over several hours. Conversely, the work presented herein describes novel methods to synthesize adduct-free alane. It is demonstrated here that AlH₃ can form by mixing AlCl₃ and LiAlH₄ in the solid state and heating to 75^∘C; only α-AlH₃ was obtained. The α-AlH₃ product can be washed with minimal solvents leading to zero formation of alane adducts. In addition, the unwanted LiCl by-product is also removed during the solvent wash, resulting in halide-free α-alane. Although simply mixing and heating the reactants led to a 40% yield of alane, having the reactants compacted and mechanically pressed while heating increases the yield to 60% crystalline α-AlH₃.     

Equidistribution of Zeros of Holomorphic Sections in the Non-compact Setting

We consider tensor powers L ^N of a positive Hermitian line bundle (L,h ^L ) over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed as N→∞ with respect to the natural measure coming from the curvature of L. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL ₂(?) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.     

Synthesis and NMR Spectroscopic Characteristics of a Series of Hydrazide‐Hydrazones Containing Furoxan Ring Derived from Isoeugenoxyacetic Acid

A novel hydrazide, 2‐methoxy‐4‐(3‐methyfuroxan‐4‐yl)‐5‐nitrophenoxyacetylhydrazine, was prepared from isoeugenoxyacetic acid. The hydrazide was condensed with aromatic aldehydes to give a series of 20 hydrazide‐hydrazones incorporating the furoxan ring. The structure of obtained compounds was determined by analytical and spectral data. It was demonstrated that the two sets of resonance signals in the ¹H‐NMR and ¹³C‐NMR spectra of the examined hydrazide‐hydrazones are caused by E_N–C(O) and Z_N–C(O) conformers. The energy barriers for the conformation exchange were determined by ¹H‐NMR‐measurement at various temperatures. Among seven tested hydrazide‐hydrazones, four compounds exhibit inhibition activities in vitro on human epidermis carcinoma (KB‐cell) with IC₅₀ = 47, 68, 79, and 103 μg/mL.     

Generalized Cauchy problems involving nonlocal and impulsive conditions

We study the abstract Cauchy problem involving a class of nonlinear differential inclusions, with impulsive and nonlocal conditions. By using MNC estimates, the existence result and continuous dependence on initial data of the solution set are proved.     

To the theory of operator monotone and operator convex functions

We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands in this algebra. We prove that if a function from ℝ⁺ into ℝ⁺ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on the set of positive self-adjoint operators affiliated with this algebra.