Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor

In this paper, we present a general mathematical framework for integrating smooth vector fields in the vicinity of a fixed point with a spiral saddle. We restrict our study to the three-dimensional setting, where the stable manifold is of spiral type (and thus two-dimensional), and the unstable manifold is one-dimensional. The aim is to produce a general purpose set of bounds that can be applied to any system of this type. The existence (and explicit computation) of such bounds is important when integrating along the flow near the spiral saddle fixed point. As an application, we apply our work to a concrete situation: the cubic Chua's equations. Here, we present a computer assisted proof of the existence of a trapping region for the flow.     

Synthesis of Some Novel N-Substituted Phthalazinone and Pyridopyridazinone Derivatives

Phthalazinone and pyridopyridazinone derivatives 3, 5, and 9 were prepared via reaction ofappropriate lactams 2 and 8 with 2-bromoethylphthalimide, N-tosylaziridine, and N,O-ditosyl derivatives of N-methylethanolamine in a two-step process in the presence of MeONa/MeOH or NaH/dimethylformamide (DMF). Starting compounds 2 and 8 were obtained by reaction of hydrazine hydrate with isoindolinones 1 or azaisoindolinones 6. Selected N-(2-phthalimidoethyl)-phthalazinones were converted into corresponding 2-[2-(methylamino) ethyl]- derivatives in satisfactory yields by treatment with hydrazine.     

Water Triggers Hydrogen-Bond-Network Reshaping in the Glycoaldehyde Dimer

Carbohydrates are ubiquitous biomolecules in nature. The vast majority of their biomolecular activity takes place in aqueous environments. Molecular reactivity and functionality are, therefore, often strongly influenced by not only interactions with equivalent counterparts, but also with the surrounding water molecules. Glycoaldehyde (Gly) represents a prototypical system to identify the relevant interactions and the balance that governs them. Here we present a broadband rotational-spectroscopy study on the stepwise hydration of the Gly dimer with up to three water molecules. We reveal the preferred hydrogen-bond networks formed when water molecules sequentially bond to the sugar dimer. We observe that the dimer structure and the hydrogen-bond networks at play remarkably change upon the addition of just a single water molecule to the dimer. Further addition of water molecules does not significantly alter the observed hydrogen-bond topologies.     

(-)-Menthol as a source of new N,N-diamine ligands for asymmetric transfer hydrogenation

The synthesis of new chiral N-monotosylated-1,2-diamines based on the (-)-menthol skeleton is presented. The elimination of HCl from neomenthyl chloride obtained from an Appel reaction led to p-menth-3-ene in excellent yield. Further functionalization of the double bond in p-menth-3-ene with chloramine-T gave the corresponding N-tosylaziridines, which upon reaction with sodium azide and subsequent reduction of the azide functional group, formed the 1,2-diamine system. The synthesized chiral ligands proved effective in the asymmetric transfer hydrogenation of aromatic ketones and an endocyclic imine.     

Recombination processes related to Eu2+ energy level position in ionic CaxCd1-xF2 crystals

Abstract

We study efficiency of autoionization and recombination transitions for europium in Ca_xCd_1-xF₂ host lattice depending on the energy level position of Eu²⁺ 4f⁶5d¹(e) excited states in respect to the conduction band (CB) states. From photoluminescence (PL) and absorption measurements we conclude that for x in the range of 1 - 0.65 thermalization within the 4f⁶5d¹(e) multiplet is faster than the appropriate autoionization transition. For x > 0.65, when all the excited 4f⁶5d¹ states are degenerate with the CB autoionization is immediate, Eu²⁺ intra-ion emission is quenched and a new Eu-related emission appears, which we tentatively assign to a radiative capture emission of hot nonequilibrium electrons.     

QED bremsstrahlung in decays of electroweak bosons

Isolated lepton momenta, in particular their directions are the most precisely measured quantities in pp collisions at LHC. This offers opportunities for multitude of precision measurements. It is of practical importance to verify if precision measurements with leptons in the final state require all theoretical effects evaluated simultaneously or if QED bremsstrahlung in the final state can be separated without unwanted precision loss. Results for final-state bremsstrahlung in the decays of narrow resonances are obtained from the Feynman rules of QED in an unambiguous way and can be controlled with a very high precision. Also for resonances of non-negligible width, if calculations are appropriately performed, such separation from the remaining electroweak effects can be expected. Our paper is devoted to validation that final-state QED bremsstrahlung can indeed be separated from the rest of QCD and electroweak effects, in the production and decay of Z and W bosons, and to estimation of the resulting systematic error. The quantitative discussion is based on Monte Carlo programs PHOTOS and SANC, as well as on KKMC which is used for benchmark results. We show that for a large class of W and Z boson observables as used at LHC, the theoretical error on photonic bremsstrahlung is 0.1 or 0.2 %, depending on the program options used. An overall theoretical error on the QED final-state radiation, i.e. taking into account missing corrections due to pair emission and interference with initial state radiation is estimated respectively at 0.2 % or 0.3 % again depending on the program option used.     

B-spline solver for one-electron Schrödinger equation

A numerical algorithm for solving the one-electron Schrödinger equation is presented. The algorithm is based on the Finite Element method, and the basis functions are tensor products of univariate B-splines. The application of cubic or higher order B-splines guarantees that the searched solution belongs to a continuous and one time differentiable function space, which is a desirable property in the Kohn–Sham equation context from the Density Functional Theory with pseudopotential approximation. The theoretical background of the numerical algorithm is presented, and additionally, the implementation on parallel computers with distributed memory is described. The current implementation of the algorithm uses the MPI, HYPRE and ParMETIS libraries to distribute matrices on processing units. Additionally, the LOBPCG algorithm from HYPRE library is used to solve the algebraic generalized eigenvalue problem. The proposed algorithm works for any smooth interaction potential, where the domain of the problem is a finite subspace of the ?³ space. The accuracy of the algorithm is demonstrated for a selected interaction potential. In the current stage, the algorithm can be applied to solve the linearized Kohn–Sham equation for molecular systems.     

Double thioalkylation/arylation of nitroarenes with the reduction of nitro- to amino group

Some active bicyclic nitroarenes readily react with an excess of alkyl/arylthiols in the presence of DBU and bis-trimethylsilylacetamide (BSA) in DMF solution, to give dithioalkyl/aryl substituted anilines in moderate to good yields via displacement of ortho- and para-hydrogen atoms with simultaneous reduction of the nitro- to amino-group.     

Complexity principle of extremality in evolution of living organisms by information-theoretic entropy

We consider evolution from a multiorgan (multistage) organism, which has a number of identical organs (e.g. a trilobite with many pairs of legs), to another organism, which has one organ modified (specialized) into a different part of the body (e.g. claws of a crab) at the expense of reduction in the number of non-modified organs. We observe that in early stages of evolution multiple organs (pairs of legs) may be created, and that extra organs may rapidly be reduced during later stages. We ask: Why do extra organs evolve during early stages of evolution? To answer the question we construct and then analyze a simple although basic model of evolution based on information-theoretic entropy. We show that an extremality principle is valid in which the increase in number of identical organs is led by the gradient of information entropy increasing with the number of these organs. On the other hand, the reduction in number of these organs, observed for later stages of evolution, results from catastrophes between submanifolds of evolution, the surfaces on which modifications (specializations) of organs may occur. Our conclusion is that modification (specialization) of organs, while in principle consistent with the entropy principle of extremality, may lead evolution to a region of catastrophes, and that these catastrophes may explain extinction of some species. The same mathematical model is applied for explanation of parallel evolution of animals and for some evolution problems of flowers.     

Novel class of saccharide-based organogelators: glucofuranose derivatives as one of the smallest and highly efficient gelators

Gluco- and allofuranose derivatives, having unprotected three OH groups, were investigated as potential gelators, showing high gelating ability for a variety of organic solvents and result in new consistent class of organogelators. The minimum gelator concentration reaches 0.03%, which is one of the lowest concentrations achieved so far. The correlation between the saccharide crystal structure and its gelating ability was also examined. The SEM pictures of xerogeles obtained from concentrated and diluted gels (1.0-0.03%) show significant differences in μm-scale structure.