Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications

We obtained new exact inequalities that estimate the L _?? -norm of the Riesz derivative D ^?? f of a function f defined on $ {\mathbb{R}^m} $ in terms of the uniform norm of the function itself and the L _s -norm of the function acted by the Laplace operator. On a class of functions f such that ||??f||s ?? 1, we solved the problem of approximation of an unbounded operator D ^?? by bounded ones and the problem of optimal recovery of the operator D ^?? on elements of this class given with known error.     

Magnetic Field Influence on the Gas Detonation Induced by Spark Discharge

The present paper describes the influence of magnetic field on the spark discharge utilized for initialization of detonation. The method of schlieren time-based scanning shows the increase of shock wave velocity in the case when magnetic field was applied to the area of electrical discharge in the air. The critical energy values are obtained for a direct initialization of detonation in hydrogen–air and hexane–air mixtures. Magnetic field has a significant influence on the deflagration–combustion transition in both mixtures at the critical energy values. Pressure and velocity of the shock front were measured by ICP pressure transducers, flame front was recorded by photo-diodes. Two cases were studied experimentally: external magnetic field is produced by inductance coils connected to capacitor; own magnetic field is induced directly by discharge current in the cables positioned in special way.     

Statistical laws of the pressure fluctuations in a hypersonic turbulent boundary layer

The results of measuring the pressure fluctuations on the wall of the nozzle of a hypersonic wind tunnel beneath a developed turbulent boundary layer are presented for the Mach number M_∞ = 7.5. On the basis of a statistical analysis, it is shown that the action of the turbulent flow is dynamically similar to the propagation of a random sequence of wave packets with continuously distributed temporal and spatial scales. Low-frequency disturbances are associated with large-scale structures of long duration that propagate at a mean-statistical velocity similar in value to the outer flow velocity. The continuous generation of weakly-correlated small-scale disturbances ensuring the maintenance and development of turbulence occurs chiefly in the inner region of the boundary layer. Spectral estimates of the power generated by the turbulent flow in the wall region of the boundary layer are presented.     

Energy transfer (EnT) photocatalysis enabled by gold-N-heterocyclic carbene (NHC) complexes

We present the use of gold sensitizers [Au(SIPr)(Cbz)] (PhotAu 1) and [Au(IPr)(Cbz)] (PhotAu 2) as attractive alternatives to state-of-the-art iridium-based systems. These novel photocatalysts are deployed in [2 + 2] cycloadditions of diallyl ethers and N-tosylamides. The reactions proceed in short reaction times and in environmentally friendly solvents. [Au(SIPr)Cbz] and [Au(IPr)(Cbz)] have higher triplet energy (E_T) values (66.6 and 66.3 kcal mol⁻¹, respectively) compared to commonly used iridium photosensitizers. These E_T values permit the use of these gold complexes as sensitizers enabling energy transfer catalysis involving unprotected indole derivatives, a substrate class previously inaccessible with state-of-the-art Ir photocatalysts. The photosynthesis of unprotected tetracyclic spiroindolines via intramolecular [2 + 2] cycloaddition using our simple mononuclear gold sensitizer is readily achieved. Mechanistic studies support the involvement of triplet–triplet energy transfer (TTEnT) for both [2 + 2] photocycloadditions.

We present the use of gold sensitizers [Au(SIPr)(Cbz)] (PhotAu 1) and [Au(IPr)(Cbz)] (PhotAu 2) as attractive alternatives to state-of-the-art iridium-based systems.     

[3+2] Annulation of 2-substituted 3-nitro-2H-chromenes with mercaptoacetaldehyde: stereoselective synthesis of tetrahydro-4H-thieno[3,2-c]chromen-3-ols

Chemistry of Heterocyclic Compounds - A diastereoselective method was developed for the synthesis of 4-trifluoromethyl- and 4-phenyl-substituted...     

A quasifibration of spaces of positive scalar curvature metrics

In this paper we show that for Riemannian manifolds with boundary the natural restriction map is a quasifibration between spaces of metrics of positive scalar curvature. We apply this result to study homotopy properties of spaces of such metrics on manifolds with boundary.

     

Monitoring enzymic peroxidation of NAD by capillary electrophoresis

NAD⁺ is degraded by horse liver alcohol dehydrogenase in a reaction with p-methylbenzyl hydroperoxide, which acts as a pseudo-substrate. An unstable intermediate product (called compound I) is formed, and this is converted into the final product NADX. The reaction can be monitored by capillary electrophoresis. NADX migrates as two well resolved peaks (NADX₁ and NADX₂), which belong probably to the tautomers of the same substance. The intermediate product, compound I, has the same effective mobility as the conformer NADX₂ and it was impossible to separate compound I from NADX₂. The spectra taken during the separation show clearly that the “9-min” peak contains different compounds during the course of the reaction and the NADX₂ is not identical with compound I.     

The influence of the stretching mode on proton transfer in the H-bonded systems

A comparison between two models of proton transfer in the symmetric H-bond interacting in a thermal reservoir is made. It is shown that in a more general model (including both previous ones as special cases) a new qualitative feature in proton damping appears.