Approximation of Fractional Brownian Motion by Martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.     

Prediction of supercritical ethane bulk solvent densities for pyrazine solvation shell average occupancy by 1, 2, 3, and 4 ethanes: combined experimental and ab initio approach

We introduce a method that addresses the elusive local density at the solute in the highly compressible regime of a supercritical fluid. Experimentally, the red shift of the pyrazine n-pi electronic transition was measured at infinite dilution in supercritical ethane as a function of pressure from 0 to about 3000 psia at two temperatures, one close (35.0 degrees C) to the critical temperature and the other remote (55.0 degrees C). Computationally, stationary points were located on the potential surfaces for pyrazine and one, two, three, and four ethanes at the MP2/6-311++G(d,p) level. The vertical n-pi ((1)B(3u)) transition energies were computed for each of these geometries with a TDDFT/B3LYP/6-311++G(d,p) method. The combination of experiment and computation allows prediction of supercritical ethane bulk densities at which the pyrazine primary solvation shell contains an average of one, two, three, and four ethane molecules. These density predictions were achieved by graphical superposition of calculated shifts on the experimental shift versus density curves for 35.0 and 55.0 degrees C. Predicted densities are 0.0635, 0.0875, and 0.0915 g cm(-3) for average pyrazine primary solvation shell occupancy by one, two, and three ethanes at both 35.0 and 55.0 degrees C. Predicted densities are 0.129 and 0.150 g cm(-3) for occupancy by four ethanes at 35.0 and 55.0 degrees C, respectively. An alternative approach, designed to "average out" geometry specific shifts, is based on the relationship Deltanu = -23.9n cm(-1), where n = ethane number. Graphical treatment gives alternative predicted densities of 0.0490, 0.0844, and 0.120 g cm(-3) for average pyrazine primary solvation shell occupancy by one, two, and three ethanes at both 35.0 and 55.0 degrees C, and densities of 0.148 and 0.174 g cm(-3) for occupancy by four ethanes at 35.0 and 55.0 degrees C, respectively.     

Molecular Structure of Neodymium Tribromide from Gas-Phase Electron Diffraction Data

The structural investigation of molecules in the vapor over neodymium tribromide was performed by synchronous gas-phase electron diffraction and mass spectrometric (GED/MS) experiments at 1110(10) K. Besides the monomeric molecules (NdBr₃), a small amount (0.7%) of the dimer (Nd₂Br₆) was detected. For NdBr₃, the thermal-average bond length r _g (Nd–Br) of 2.675(6) Å was determined. The equilibrium structure was estimated to be planar (or nearly planar) with r _e (Nd–Br) of 2.659(7) Å. Three vibrational frequencies were estimated using the GED data: ₁ = 193 cm^–1, ₂ = 35 cm^–1, ₄ = 41 cm^–1. The structural parameters of Nd₂Br₆ could not be refined and were constrained at the estimated values during the analysis.     

Integrability of Solutions to Mixed Stochastic Differential Equations

We prove that the standard conditions for the unique solvability of a mixed stochastic differential equation guarantee that its solution possesses finite moments. We also give conditions supplying the existence of exponential moments. For a special equation whose coefficients do not satisfy the linear growth condition, we prove the integrability of its solution.     

Cage‐like Fe,Na‐Germsesquioxanes: Structure,Magnetism, and Catalytic Activity

A series of four unprecedented heterometallic metallagermsesquioxanes were synthesized. Their cage‐like architectures have a unique type of molecular topology consisting of the hexairon oxo {Fe₆O₁₉} core surrounded in a triangular manner by three cyclic germoxanolates [PhGe(O)O]₅. This structural organization induces antiferromagnetic interactions between the Fe^III ions through the oxygen atoms. Evaluated for this first time in catalysis, these compounds showed a high catalytic activity in the oxidation of alkanes and the oxidative formation of benzamides from alcohols.     

Pressure-induced superconductivity and structural transitions in Ba(Fe<Subscript>0.9</Subscript>Ru<Subscript>0.1</Subscript>)<Subscript>2</Subscript>As<Subscript>2</Subscript>

Electrical transport and structural characterizations of isoelectronically substituted Ba(Fe_0.9Ru_0.1)₂As₂ have been performed as a function of pressure up to ～ 30 GPa and temperature down to ～ 10 K using designer diamond anvil cell. Similar to undoped members of the AFe₂As₂ (A = Ca, Sr, Ba) family, Ba(Fe_0.9Ru_0.1)₂As₂ shows anomalous a-lattice parameter expansion with increasing pressure and a concurrent ThCr₂Si₂ type isostructural (I4/mmm) phase transition from tetragonal (T) phase to a collapsed tetragonal (cT) phase occurring between 12 and 17 GPa where the a is maximum. Above 17 GPa, the material remains in the cT phase up to 30 GPa at 200 K. The resistance measurements show evidence of pressure-induced zero resistance that may be indicative of high-temperature superconductivity for pressures above 3.9 GPa. The onset of the resistive transition temperature decreases gradually with increasing pressure before completely disappearing for pressures above ～ 10.6 GPa near the T-cT transition. We have determined the crystal structure of the high-T _c phase of Ru-doped BaFe₂As₂ to remain as tetragonal (I4/mmm) by analyzing the X-ray diffraction pattern obtained at 10 K and 9.7 ± 0.7 GPa, as opposed to inferring the structural transition from electrical resistance measurement, as in a previous report [S.K. Kim, M.S. Torikachvili, E. Colombier, A. Thaler, S.L. Bud’ko, P.C. Canfield, Phys. Rev. B 84, 134525 (2011)].     

Structural analysis and probing the conformational space of dansylamide by means of gas-phase electron diffraction and quantum chemistry

Dansylamide is perhaps the most ubiquitous fluorophore due to its donor-acceptor bifunctionality and its ability to form intra- and intermolecular hydrogen bonding. Among the diversity of its applications is the development of new generation of biosensors for the in vivo monitoring of traces of metals. The structure and conformational stability of dansylamide in the gas phase were investigated for the first time by a combined gas-phase electron diffraction-mass spectrometry (GED/MS), complemented by quantum chemical calculations. GED data indicate that different skewed conformers exist at T?=?464 K, which are characterized by the deviation of two S–N bonds from the perpendicular orientation relative to the naphthalene plane. Maybe the most indicative structural parameters for electronic interactions between the donor-acceptor substituents and the aromatic naphthalene and the subsequent stabilization of the favorable skewed eclipsed-syn conformer are the dihedral angles C₉–C₁–S–N and C₁₀–C₅–N–C with the experimentally determined values of 66.8° (32) and 68.1° (72), respectively. The role of –SO₂NH₂ by forming intramolecular hydrogen bonds was scrutinized by employing the natural bond orbital approach (NBO), quantum theory atoms in molecules (QTAIM), and molecular electrostatic potential (MESP). The non-planarity of the naphthalene skeleton due to the electronic interactions with the substituents and its consequence for the fluorescence activity of dansylamide have been discussed.     

Azolo[1,5-a]pyrimidines and Their Condensed Analogs with Anticoagulant Activity

Hypercytokinemia, or cytokine storm, is one of the severe complications of viral and bacterial infections, involving the release of abnormal amounts of cytokines, resulting in a massive inflammatory response. Cytokine storm is associated with COVID-19 and sepsis high mortality rate by developing epithelial dysfunction and coagulopathy, leading to thromboembolism and multiple organ dysfunction syndrome. Anticoagulant therapy is an important tactic to prevent thrombosis in sepsis and COVID-19, but recent data show the incompatibility of modern direct oral anticoagulants and antiviral agents. It seems relevant to develop dual-action drugs with antiviral and anticoagulant properties. At the same time, it was shown that azolo[1,5-a]pyrimidines are heterocycles with a broad spectrum of antiviral activity. We have synthesized a new family of azolo[1,5-a]pyrimidines and their condensed polycyclic analogs by cyclocondensation reactions and direct CH-functionalization and studied their anticoagulant properties. Five compounds among 1,2,4-triazolo[1,5-a]pyrimidin-7-ones and 5-alkyl-1,3,4-thiadiazolo[3,2-a]purin-8-ones demonstrated higher anticoagulant activity than the reference drug, dabigatran etexilate. Antithrombin activity of most active compounds was confirmed using lipopolysaccharide (LPS)-treated blood to mimic the conditions of cytokine release syndrome. The studied compounds affected only the thrombin time value, reliably increasing it 6.5–15.2 times as compared to LPS-treated blood.     

Cage‐like Copper(II) Silsesquioxanes: Transmetalation Reactions and Structural,Quantum Chemical,and Catalytic Studies

The transmetalation of bimetallic copper–sodium silsesquioxane cages, namely, [(PhSiO_1.5)₁₀(CuO)₂(NaO_0.5)₂] (“Cooling Tower”; 1 ), [(PhSiO_1.5)₁₂(CuO)₄(NaO_0.5)₄] (“Globule”; 2 ), and [(PhSiO_1.5)₆(CuO)₄(NaO_0.5)₄(PhSiO_1.5)₆] (“Sandwich”; 3 ), resulted in the generation of three types of hexanuclear cylinder‐like copper silsesqui‐ oxanes, [(PhSiO_1.5)₁₂(CuO)₆(C₄H₉OH)₂(C₂H₅OH)₆] ( 4 ), [(PhSiO_1.5)₁₂(CuO)₆(C₄H₈O₂)₄(PhCN)₂(MeOH)₄] ( 5 ), and [(PhSiO_1.5)₁₂(CuO)₆(NaCl)(C₄H₈O₂)₁₂(H₂O)₂] ( 6 ). The products show a prominent “solvating system–structure” dependency, as determined by X‐ray diffraction. Topological analysis of cages 1 – 6 was also performed. In addition, DFT theory was used to examine the structures of the Cooling Tower and Cylinder compounds, as well as the spin density distributions. Compounds 1 , 2 , and 5 were applied as catalysts for the direct oxidation of alcohols and amines into the corresponding amides. Compound 6 is an excellent catalyst in the oxidation reactions of benzene and alcohols.