The algebraic classification of nilpotent Tortkara algebras

Abstract

We classify all complex 6-dimensional nilpotent Tortkara algebras.

Communicated by Alberto Facchini     

Triangulenes: From Precursor Design to On-Surface Synthesis and Characterization

Triangulene and its higher homologues are a class of zigzag-edged triangular graphene molecules (ZTGMs) with high-spin ground states. These open-shell molecules are predicted to host ferromagnetically coupled edge states with net spin values scaling with molecular size and are therefore considered promising candidates for future molecular spintronics applications. Unfortunately, the synthesis of unsubstituted [n]triangulenes and the direct observation of their edge states have been a long-standing challenge due to a high reactivity towards oxygen. However, recent advances in precursor design enabled the on-surface synthesis and characterization of unsubstituted [3]-, [4]-, and [5]triangulene. In this Minireview, we will highlight key aspects of this rapidly developing field, ranging from the principles of precursor design to synthetic strategies and characterization of a homologous series of triangulene molecules synthesized on-surface. We will also discuss challenges and future directions.     

An approach to optimize the design of microfluidic chips for electrophoretic separations

The precise design and operational control of the separation process of liquid matrices is key to the performance of on-chip liquid analysis. Present research attempts from the engineering point of view to investigate of the process occurring in the microfluidic channels for chip design with the best separation efficiency. An one-dimensional model of electrokinetic sample motion was developed to simulate the separation process of sample containing amino acids (tryptophan, tyrosine, proline, methionine) that migrate in a buffer solution through a straight separation channel made of poly(methyl methacrylate) within a microfluidic chip under different conditions. On the basis of the simulations by the finite-difference method the effects of the channel size, the chip material, the applied voltage difference and the test solution pH on separation rate are discussed. It was found that for the channel length of 2 cm the resolution of peaks is optimal and the fastest time of amino acids separation is 4 s.     

Partial cohomology of groups and extensions of semilattices of abelian groups

We extend the notion of a partial cohomology group $H^n(G,A)$ to the case of non-unital A and find interpretations of $H^1(G,A)$ and $H^2(G,A)$ in the theory of extensions of semilattices of abelian groups by groups.     

Synthesis of oligosiloxane methacrylates and their application to anaerobic sealants

The synthesis of oligosiloxane methacrylates via the transesterification of oligomethoxyphenylmethylsiloxanes by 1,2-hydroxyethyl methacrylate is described. The dependences of the properties of synthesized oligomers on the content of methacrylate fragments are studied. The possibility of creating thermally stable anaerobic sealants with the required properties is shown on their basis.     

On scatteredly continuous maps between topological spaces

A map f:X→Y between topological spaces is defined to be scatteredly continuous if for each subspace AX the restriction f|A has a point of continuity. We show that for a function f:X→Y from a perfectly paracompact hereditarily Baire Preiss–Simon space X into a regular space Y the scattered continuity of f is equivalent to (i) the weak discontinuity (for each subset AX the set D(f|A) of discontinuity points of f|A is nowhere dense in A), (ii) the piecewise continuity (X can be written as a countable union of closed subsets on which f is continuous), (iii) the G_δ-measurability (the preimage of each open set is of type G_δ). Also under Martin Axiom, we construct a G_δ-measurable map f:X→Y between metrizable separable spaces, which is not piecewise continuous. This answers an old question of V. Vinokurov.     

New methods for the synthesis of substituted 4,5,6,7-tetrahydro[1,2,3]triazolo[1,5-a]pyrazines (microreview)

Chemistry of Heterocyclic Compounds - The microreview summarizes the data on the methods of heterocyclization leading to the formation of the 4,5,6,7-tetrahydro[1,2,3]triazolo[1,5-a]pyrazine system...     

The intramolecular Diels-Alder vinylthiophen (IMDAV) reaction: An easy approach to thieno[2,3-f]isoindole-4-carboxylic acids

The reaction of readily accessible 3-(thien-2-yl)allylamines with maleic anhydride, followed by a domino sequence involving successive acylation/[4+2] cycloaddition steps, leads to the formation of the thieno[2,3-f]isoindole core. The key step, the intramolecular Diels-Alder vinylaren (IMDAV) reaction, proceeds with high level of diastereoselectivity and with formation of a single diastereoisomer of the target product 4,4a,5,6,7,7a-hexahydro-3aH-thieno[2,3-f]isoindole-4-carboxylic acids in excellent yields. If the reaction is carried out at room temperature, it occurs in 2–3 days and the proton migration (H-shift) does not take place at the last stage. In boiling benzene, the reaction is complete after three hours, but in this case a slight impurity of byproducts bearing aromatic thiophene ring – 4a,5,6,7,7a,8-hexahydro-4H-thieno[2,3-f]isoindole-4-carboxylic acids is formed.     

Long-period fiber gratings as ultrafast optical differentiators

It is demonstrated that a single, uniform long-period fiber grating (LPFG) working in the linear regime inherently behaves as an ultrafast optical temporal differentiator. Specifically, we show that the output temporal waveform in the core mode of a LPFG providing full energy coupling into the cladding mode is proportional to the first derivative of the optical temporal signal (e.g., optical pulse) launched at the input of the LPFG. Moreover, a LPFG providing full energy recoupling back from the cladding mode into the core mode inherently implements second-order temporal differentiation. Our numerical results have confirmed the feasibility of this simple, all-fiber approach to processing optical signals with temporal features in the picosecond and subpicosecond ranges.