Martingale and stationary solutions for stochastic Navier-Stokes equations

Summary We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness.     

Preparation and dielectric properties of the lead-free BaFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> ceramics obtained from mechanically triggered powder

In the paper the influence of mechanical activation of the powder on the final dielectric properties lead-free Ba(Fe_1/2Nb_1/2)O₃ (BFN) ceramic was examined. The BFN ceramics were obtained by 3-steps route. Firstly, the substrates were pre-homogenized in a planetary ball mill. Than, the powder was activated in vibratory mill (the shaker type SPEX 8000 Mixer Mill) for different duration between 25 h and 100 h. The influence of the milling time on the BFN powder was monitored by X-ray diffraction. The diffraction data confirmed that the milling process of the starting components is accompanied by partial synthesis of the BFN materials. The longer of the high-energy milling duration the powders results in increasing the amount of amorphous/nanocrystalline content. The mechanically activated materials were sintered in order to obtain the ceramic samples. During this temperature treatment the final crystallisation of the powder appeared what was confirmed by XRD studies. The performed dielectric measurements have revealed the reduction of the dielectric loss of the BFN ceramics compared to materials obtained by classic methods.     

Regioselective formation of β‐(E)‐ and α‐alkenylsilane moiety attached to silsesquioxane core via Pt‐ and Ru‐based hydrosilylation

The first attempts to use ethynylsiloxysilsesquioxanes as reagents for hydrosilylation in the presence of Pt‐ and Ru‐based catalysts are reported. The results obtained strongly depend on the catalytic system used. The catalysts are proved to promote regioselective introduction of β‐(E)‐ and α‐fragments of the alkenylsilane group to the silsesquioxane core. The favourable features of these catalytic systems are their high selectivity and the requirement for relatively mild conditions. This methodology was also successfully applied to dihydro‐substituted organosilicon compounds to obtain a new class of silsesquioxane‐based compounds.     

Mono-Aryl/Alkylthio-Substituted (Hetero)acenes of Exceptional Thermal and Photochemical Stability by the Thio-Friedel–Crafts/Bradsher Cyclization Reaction

The highly substituted mono-aryl/alkylthio-(hetero)acenes prepared in this study have been found to be thermally more stable (T_decomp.=331–354 °C) than the known di-aryl/alkylthio-substituted acenes by an average of 25 °C. They are also much more photostable at 254 and 365 nm (in both argon and air) than the parent anthracene and other reported anthracenes. The most photostable aryl/alkylthio-anthracenes at 254 nm were found to be 60–70 (in air) and 130 (in argon) times more stable in solution than the unsubstituted anthracene, and much more stable than known EDG/EWG-substituted anthracenes (EDG=electron-donating group, EWG=electron-withdrawing group) with an extended aromatic core. Furthermore, the acenes showed significantly higher photostability at 365 nm in both air and argon. The anthracenes were obtained by the novel thio-Friedel–Crafts/Bradsher cyclization reaction of hitherto unknown [o-(1,3-dithian-2-yl)aryl](aryl)methyl thioethers. The developed approach provides a general access to mono-aryl/alkylthio-substituted (hetero)acene frameworks containing at least three fused (hetero)aromatic rings. The characteristic feature of this approach, which leads to highly substituted acenes, is that the substituents, unlike in other methods, may be introduced at an early stage of the synthesis. DFT and TD-DFT calculations confirmed the stabilizing role of the aryl/alkylthio substituent in the mono-aryl/alkylthio-substituted anthracenes, which are the most stable anthracenes prepared to date. Their high photostability is mainly due to the quenching of singlet oxygen by the acene and the quenching of the acene S₁ state by molecular oxygen.     

The process of front-to-side collision of motor vehicles in terms of energy balance

Nonlinear Dynamics - The reconstruction of a road accident can be treated as the resolution of an “inverse problem” in mechanics using analytical or numerical models. In the road...     

On the symmetry of the seminal Horodecki state

It is shown that the seminal Horodecki 2-qutrit state belongs to the class of states displaying symmetry governed by a commutative subgroup of the unitary group U(3). Taking a conjugate subgroup one obtains another classes of symmetric states and one finds equivalent representations of the Horodecki state. These results are generalized to d⊗d systems.     

A New Route to 3-Phosphonylpyrazoles

The regioselective synthesis of 3-diethoxyphosphonopyrazoles has been accomplished through the addition of aryl or alkyl hydrazines to (3-ethoxyacryloyl)phosphonic acid diethyl ester. An example of hydrolysis of the pyrazolephosphonic ester to the corresponding acid is described.     

Diastereoselective synthesis of tetrahydrofurans via reaction of gamma,delta-epoxycarbanions with aldehydes

[reaction: see text] Hydroxymethyl-substituted tetrahydrofurans were prepared with high diastereoselectivity by reaction of the carbanion derived from 3,4-epoxybutyl phenyl sulfone with aldehydes in the presence of a mixture of lithium and potassium tert-butoxides. Initial formation of aldol-type adducts is a nondiastereoselective but reversible process; thus, subsequent formation of one main diastereoisomer is controlled by the relative rates of cyclization. The configuration of the carbon stereocenter at the oxirane ring is inverted in the course of the S(N)2 process, and two new centers are created diastereoselectively.