Extended Antipodal Theorems

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016).     

Best M-Term Trigonometric Approximations of the Classes B p,θ Ω of Functions of Many Variables

We obtain exact order estimates for the best M-term trigonometric approximations of the classes B _p, of functions of many variables in the space L _q, 1 < p < q < , q > 2.     

A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure

We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals.     

A family of models with blue sky catastrophes of different classes

A generalized model with bifurcations associated with blue sky catastrophes is introduced. Depending on an integer index m, different kinds of attractors arise, including those associated with quasi-periodic oscillations and with hyperbolic chaos. Verification of the hyperbolicity is provided based on statistical analysis of intersection angles of stable and unstable manifolds.     

Dynamic analysis of interacting coplanar cracks in a half space with a clamped boundary condition using boundary integral equations

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 153–159, January–February, 2005     

Solvent mediated reaction of 1-methyl-1<Emphasis Type="Italic">H</Emphasis>-tetrazoline-5-thione with iodine

1-Methyl-1H-tetrazoline-5-thione (1) reacts with iodine in CHCl₃ with formation of 1:1 stable σ-complex (logβ = 3.8 ± 0.1 is found by spectrophotometry). In the ethanol solution irreversible oxidation with formation of disulfide product 5,5′-dithiobis(1-methyl-1H-tetrazole) (2) is observed. The structure of (2) was determined by X-ray diffraction. Strong intermolecular interactions with shortened contacts are observed between sulfur atom of disulfide bridge and heterocyclic nitrogen of the neighboring molecule (S···N 3.0179(15) Å) forming infinite supramolecular chains which are further linked with π–π stacking interaction of tetrazole rings (interplane distance is 3.1685(6) Å).     

Peculiar Photoinduced Electron Transfer in Porphyrin–Fullerene Akamptisomers

Porphyrin–fullerene dyads are promising candidates for organic photovoltaic devices. The electron-transfer (ET) properties of the molecular devices depend significantly on the mutual position of the donor and acceptor. Recently, a new type of molecular isomerism (akamptisomerism) has been discovered. In the present study, we explore how photoinduced ET can be modulated by passing from one akamptisomer to another. To this aim, four akamptisomers of the quinoxalinoporphyrin–[60]fullerene complex are selected for computational study. The most striking finding is that, depending on the isomer, the porphyrin unit in the dyad can act as either electron donor or electron acceptor. Thus, the stereoisomeric diversity allows one to change the direction of ET between the porphyrin and fullerene moieties. To understand the effect of akamptisomerism on the photoinduced ET processes, a detailed analysis of initial and final states involved in the ET is performed. The computed rate for charge separation is estimated to be in the region of 1–10 ns⁻¹. The formation of a long-living quinoxalinoporphyrin anion radical species is predicted.