Goodness-of-fit tests based on the empirical characteristic function

The paper is devoted to the supremum-type multivariate goodness-of-fit tests based on the empirical characteristic function. Particular attention is devoted to the composite hypothesis of normality and Gaussian distribution mixture model. An analytical way to approximate the null asymptotic distributions of the considered test statistics is discussed applying the theory of large excursions of differentiable Gaussian random fields. The produced comparative Monte Carlo power study shows that the considered tests are powerful competitors to the existing classical criteria, clearly dominating in verification of the goodness-of-fit hypotheses against the specific types of alternatives.     

Sanctolide A, a 14-membered PK-NRP hybrid macrolide from the cultured cyanobacterium Oscillatoria sancta (SAG 74.79)

Sanctolide A (1), a 14-membered polyketide-nonribosomal peptide (PK-NRP) hybrid macrolide, was isolated from the cultured cyanobacterium Oscillatoria sancta (SAG 74.79). The planar structure was determined using various spectroscopic techniques including HRESIMS, and 1D and 2D NMR analyses. The relative configuration was assigned by J-based configurational analysis in combination with NOE correlations. The absolute configuration was determined by Mosher ester and enantioselective HPLC analyses. The structure of sanctolide A (1) features a rare N-methyl enamide and a 2-hydroxyisovaleric acid, which are incorporated to form a 14-membered macrolide ring structure, comprising a new type of cyanobacterial macrolides derived from a PKS-NRPS hybrid biosynthetic pathway.     

Cycles of Spatial Discretizations of Shadowing Dynamical Systems

Let H(B,α) be the JBW^*-algebra of elements of a continuous W^*-algebra B invariant under the ^*-anti-automorphism α of B of order two. Then the mapping I → I ∩ H(B, α) is an order isomorphism from the complete lattice of α-invariant weak^* closed inner ideals in B onto the complete lattice of weak^* closed inner ideals in H(B, α), every one of which is of the form eH(B, α) α(e) for some unique projection e in B with α-invariant central support. A corollary of this result completely characterizes the weak^* closed inner ideals in any continuous JBW^*-triple.     

Investigations of the mega-ampere multiwire X pinch

The results of experimental investigations into the dynamics of a plasma produced in the multiwire X pinch at currents up to 2.3 MA are presented. The materials, diameters, and the number of wires are varied. At such currents, the power of the soft x-ray radiation with the photon energy from 1 to 2 keV increases to 120 GW, and, since the size of a hot spot is less than 20 μm, it corresponds to a source brightness of ～10¹⁵ W/(cm² sr). The energy recorded in lines of neon-like molybdenum (in the range of 2.5–3 keV) is higher than 10 J. Hard x-ray radiation detected in experiments with tungsten and molybdenum X pinches has the photon energy ≥800 keV.     

Fano line shape and anti-crossing of Raman active E2g peaks in the charge density wave state of NbSe2

Low energy Raman scattering from the ab-plane of the 2H polytype single crystal NbSe₂ has been investigated in the normal (N), incommensurate charge density wave (ICDW) and superconducting (SC) phases. The temperature dependence of the polarization resolved Raman response has been obtained for the excitation wavelength of 647 nm and fitted to phenomenological models for the E_2g and A_1g symmetry channels. The A_1g response can be fitted by a simple damped oscillator peak superimposed on continuous background. The E_2g response displays an anti-resonance interference pattern between the inter-layer phonon and the CDW-induced mode such that a hybridized configuration (Fano line shape [1]) is required for modelling. The polarization specific peak maxima positions and line widths as a function of temperature, deduced in this manner, are presented. Partial suppression of the electronic continuum scattering in the Raman shift range up to 110 cm⁻¹ in the A_1g symmetry channel and beyond 300 cm⁻¹ in the E_2g symmetry channel is indicative of high energy electronic states far away from the Fermi surface participating in the ICDW formation.     

A Noble‐Metal‐Free System for Photocatalytic Hydrogen Production from Water

A series of heteroleptic copper(I) complexes with bidentate $\widehat{PP}$ and $\widehat{NN}$ chelate ligands was prepared and successfully applied as photosensitizers in the light‐driven production of hydrogen, by using [Fe₃(CO)₁₂] as a water‐reduction catalyst (WRC). These systems efficiently reduces protons from water/THF/triethylamine mixtures, in which the amine serves as a sacrificial electron donor (SR). Turnover numbers (for H) up to 1330 were obtained with these fully noble‐metal‐free systems. The new complexes were electrochemically and photophysically characterized. They exhibited a correlation between the lifetimes of the MLCT excited state and their efficiency as photosensitizers in proton‐reduction systems. Within these experiments, considerably long excited‐state lifetimes of up to 54 μs were observed. Quenching studies with the SR, in the presence and absence of the WRC, showed that intramolecular deactivation was more efficient in the former case, thus suggesting the predominance of an oxidative quenching pathway.     

The nature of the chemical bond in UO2

The nature of the chemical bond in UO₂ was analyzed taking into account the X-ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO₈ (D_4h) cluster, reflecting uranium's close environment in UO₂, and the U₁₃O₅₆ and U₆₃O₂₁₆ clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO₂ single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO₂ are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO₂ was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO₈ and by 25% in U₆₃O₂₁₆.     

General theorems on large deviations for random vectors

In the paper, we present some general theorems on large deviations of random vectors with cumulants satisfying the generalized Statulevi?ius condition. The results obtained are applicable in derivation of limit theorems in the scheme of series, including the case where the dimension of the considered random vectors is growing indefinitely.