Hyperbolic Chaos in Systems Based on FitzHugh – Nagumo Model Neurons

In the present paper we consider and study numerically two systems based on model FitzHugh–Nagumo neurons, where in the presence of periodic modulation of parameters it is possible to implement chaotic dynamics on the attractor in the form of a Smale–Williams solenoid in the stroboscopic Poincaré map. In particular, hyperbolic chaos characterized by structural stability occurs in a single neuron supplemented by a time-delay feedback loop with a quadratic nonlinear element.     

Asymptotic growth of trajectories of multifractional Brownian motion,with statistical applications to drift parameter estimation

We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein–Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with probability 1 for the rate of the growth of the trajectories of multifractional Brownian motion (mBm) and of some other functionals of mBm, including increments and fractional derivatives. As the auxiliary results having independent interest, we produce the asymptotic bounds with probability 1 for the rate of the growth of the trajectories of the general Gaussian process and some functionals of it, in terms of the covariance function of its increments.     

Asymptotic multiphase Σ-solutions to the singularly perturbed Korteweg–de Vries equation with variable coefficients

The paper deals with constructing the asymptotic solution to the singularly perturbed Korteweg–de Vries equation with variable coefficients. The notion of an asymptotic multiphase Σ-solution is proposed, and an algorithm of its construction in a neighborhood of the point t = 0 is given. Some theorems concerning the exactness, with which such local asymptotic solution satisfies the equation under study are proved.     

Effects of Spiro-Cyclohexane Substitution of Nitroxyl Biradicals on Dynamic Nuclear Polarization

Spiro-substituted nitroxyl biradicals are widely used as reagents for dynamic nuclear polarization (DNP), which is especially important for biopolymer research. The main criterion for their applicability as polarizing agents is the value of the spin–spin exchange interaction parameter (J), which can vary considerably when different couplers are employed that link the radical moieties. This paper describes a study on biradicals, with a ferrocene-1,1′-diyl-substituted 1,3-diazetidine-2,4-diimine coupler, that have never been used before as DNP agents. We observed a substantial difference in the temperature dependence between Electron Paramagnetic Resonance (EPR) spectra of biradicals carrying either methyl or spirocyclohexane substituents and explain the difference using Density Functional Theory (DFT) calculation results. It was shown that the replacement of methyl groups by spirocycles near the N-O group leads to an increase in the contribution of conformers having J ≈ 0. The DNP gain observed for the biradicals with methyl substituents is three times higher than that for the spiro-substituted nitroxyl biradicals and is inversely proportional to the contribution of biradicals manifesting the negligible exchange interaction. The effects of nucleophiles and substituents in the nitroxide biradicals on the ring-opening reaction of 1,3-diazetidine and the influence of the ring opening on the exchange interaction were also investigated. It was found that in contrast to the methyl-substituted nitroxide biradical (where we observed the ring-opening reaction upon the addition of amines), the ring opening does not occur in the spiro-substituted biradical owing to a steric barrier created by the bulky cyclohexyl substituents.     

One-step synthesis of substituted 6-amino-5-cyanospiro-4-(piperidine-4')- 2H,4H-dihydropyrazolo[3,4-b]pyrans

Three-component condensation of 4-piperidinones (7), 5-pyrazolones (8), and malononitrile (4) proceeds chemically and electrochemically and is a convenient one-step means of synthesis of substituted 6-amino-5-cyanospiro-4-(piperidine-4')-2H,4H-dihydropyrazolo[3,4-b]pyrans (12). The electrochemical reactions proceed under milder conditions and with yields 12-15% greater than those of the reactions catalyzed by chemical bases.     

A new reaction of phosphorylated N-sulfonylimines with hydrophosphoryl agents involving C → N transfer of phosphoryl groups

Hydrophosphoryl nucleophilic agents add to the CN bond of N-sulfonyltrichloroacetimidoylphosphonates to give unstable C,C-diphosphorylated adducts, which undergo competitive 1,2-C → N phosphorotropic rearrangement and dehydrochlorination with the formation of aza-Perkow reaction products, C,N-diphosphorylated dichlorovinylsulfonamides. This is the first reliably identified case of an aza-Perkow transformation for acid phosphites and their initial nucleophilic attack at the C atom of the azomethine bond in the aza-substrates.     

Thin-Layer Chromatography of Metal Cations Modified with Amines and Surfactants and the Sorption-Catalytic Detection of Cobalt(II) and Copper(II)

JPC – Journal of Planar Chromatography – Modern TLC - The thin-layer chromatography (TLC) procedures of metal cations, modified with amines and cationic surfactant micelles, followed by...     

Self-sorting dimerization of tetraurea calix[4]arenes

Calix[4]arenes substituted by four urea functions are self-complementary molecules that spontaneously combine in apolar solvents in the presence of an ammonium salt to form dimeric capsules held together by a belt of hydrogen bonds. In the presence of tetraethylammonium salts, the Et4N+ cation is included as a guest. The sorting between dimeric capsules formed in a mixture of calix[4]arenes directly depends on the steric crowding of the substituents grafted on the urea groups whether aromatic derivatives or aliphatic chains linking urea functions in mono-, di-, or tetraloop structures. Simple rules allow one to anticipate which capsules will be exclusively formed when calix[4]arenes are mixed in different proportions. The stabilization of the dimeric structures by hydrogen bonds is thwarted by the overlaps of aliphatic loops and/or by bulky groups that cannot pass through these loops. Despite the structural similarity of the calixarenes, the exclusive formation of dimers of well-defined compositions and clear titration breaks are observed by electrospray mass spectrometry. This technique yields reliable information on stoichiometries and composition despite measurements in the gas phase rather than in solution and it does not suffer from excessive peak overlaps in contrast with NMR.     

Synthesis of (1′S*,2R*,3R*)- and (1′S*,2R*,3S*)-N-arylsulfonyl-2-(1′-halogenethyl)-3-methylindolines and their selective toxicity against SH-SY5Y cell line

N-tosyl-2- and N-tosyl-4-halogen-substituted derivatives of 2-(1-methylbut-2-en-1-yl)aniline were synthesized and their molecular iodine-mediated cyclization was investigated. The cyclization upon interaction of N-tosyl-6-methyl-2-(1-methylbut-2-en-1-yl)aniline with molecular iodine in methyl tert-butyl ether or acetonitrile was studied, as well as the interaction of this sulfonamide with N-bromosucinimide in dichloromethane. Synthesized (2R*,3R*)- and (2R*,3S*)-N-arylsulfonyl-2-(1-halogenoethyl)-3-methylindoline derivatives showed cytotoxic activity against HEK293 cells, SH-SY5Y, Jurkat, and HepG2 cell lines. The compounds (2R*,3S*)-N-arylsulfonyl-7-bromo-2-(1-halogenoethyl)-3-methylindoline cis- 4a , stereoisomeric (2R*,3R*)-trans- 4h and (2R*,3S*)-N-tosyl-7-chloro-2-(1-halogenoethyl)-3-methylindoline cis- 4h demonstrated selective toxicity against SH-SY5Y cell line (IC₅₀ ≈ 3 ÷ 5 μM), and did not affect HEK293, Jurkat, and HepG2 cells.     

Microphase separation in multiblock copolymer melts: Nonconventional morphologies and two-length-scale switching

The phase behavior of AfmN(BN2AN2)B(1-fmN) multiblock copolymer melts is studied within the weak segregation theory. The interplay between ordering on different length scales is shown to cause dramatic changes both in the ordered phase symmetry and periodicity upon small variation of the architectural parameters of the macromolecules. Phase diagrams are presented in the (f,chiN) plane (chi is the Flory-Huggins parameter) for various values of the architecture parameters n and m. Near the critical surface, i.e., for (f-0.5)2<1, such nonconventional cubic phases as the face-centered cubic (FCC), simple cubic (SC), (double) gyroid, and the so-called BCC(2) (single gyroid) are found to be stable. The lamellar morphology is shown to be replaced by BCC2, FCC, or SC (depending on the structural parameters) as the most stable low-temperature phase.