Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

Kinetics and mechanism of the Pudovik reaction in the azomethine series: III. Acid-catalyzed hydrophosphorylation of imines

A complex spectral (UV, IR, and ³¹P NMR), preparative, and kinetic investigation of the mechanism of the noncatalytic variant of the Pudovik reaction in the series of imines was carried out. The reaction proceeds through a four-center cyclic transition state. The transition state is highly labile, which determines its high sensitivity to the structure of the reagents, the nature of the solvent and catalyst, and some other factors. The necessary condition for the hydrophosphorylation of imines to occur is the participation of proton-donor reagents and acidic admixtures, specifically hydrolysis products of dialkyl hydrogen phosphites, such as monoalkyl dihydrogen phosphates and phosphorous acid, which act as acid catalysts. When the starting reagents are thoroughly purified and no such catalysts are present, the Pudovik reaction fails to occur in the imine series.     

Heptakis(6-deoxy-6-guanidino)-β-cyclodextrin: an artificial model for mitochondrial ADP/ATP carrier

Heptakis(6-deoxy-6-guanidino)-β-cyclodextrin, prepared by one-step reaction of heptakis(6-amino-6-deoxy)-β-cyclodextrin with 1H-pyrozolecarboxamidine, binds ADP/ATP very tightly.     

Solubility and Ionic Processes in the Cu X 2? MX ?H2O ( X ?=Cl?, Br?; M +=Li+, Na+, K+, NH4+, Cs+) Systems

Summary.  Solubility isotherms in the CuBr₂−MBr−H₂O (M ⁺ = Li⁺, Na⁺, Cs⁺) systems at 298.15 K were measured. The results together with other available literature data for copper chloride and bromide systems were treated by hydration analysis, and comparative discussion of ionic processes taking place in the respective saturated solutions was performed. Corresponding author. E-mail: jitka@prfdec.natur.cuni.cz Received August 6, 2002; accepted (revised) November 29, 2002 Published online April 3, 2003     

Synthesis of aza-, oxa-, and thiabicyclo[3.1.0]hexane heterocycles from a common synthetic intermediate

[reaction: see text] An efficient and stereospecific approach to the synthesis of structurally constrained aza-, oxa-, and thiabicyclo[3.1.0]hexane heterocycles has been achieved through application of the intramolecular cyclopropanation reaction of diazoacetates. The various constrained heterocycles (X = N, O, or S) are conveniently prepared from a common diol intermediate accessible from readily available cinnamyl alcohols. Application of the methodology to the synthesis of conformationally constrained oxazolidinone antibacterials is also discussed.     

Synthesis of mesoionic[1,2,3]triazolo[5,1-d][1,2,5]triazepines

Intramolecular cyclization of 1-amino-3-phenacyl-4-carbohydrazido-1,2,3-triazolium-5-olates has been shown to take place via selective interaction of the carbonyl group with the terminal amino function of the hydrazido group to form a 1,2,5-triazepine ring. Minor products, resulting from the interaction of the α-nitrogen atom of the hydrazido group with the carbonyl function, having a N-amino-pyridazine structure were also detected and isolated. A general method for the synthesis of novel mesoionic 2-amino-7-aryl-4-oxo-2,4,5,8-tetrahydro[1,2,3]triazolo[5,1-d][1,2,5]triazepin-9-ium-3-olates was developed.     

Phase-space invariants for aggregates of particles: hyperangular momenta and partitions of the classical kinetic energy

Rigorous definitions are presented for the kinematic angular momentum K of a system of classical particles (a concept dual to the conventional angular momentum J), the angular momentum L(xi) associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described-in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions, isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.     

Bound water measurements for aqueous protein solutions and food gels

The role of aqueous media in the stabilization of globular proteins and formation of gels was studied by absorption millimeter spectroscopy. This method allowed to measure bound water, the fraction of water which had decreased rotational mobility owing to the presence of solute. Hydration data for globular proteins were compared with data obtained previously for low-weight molecules and groups. It was found that rotational mobility of water molecules in the hydration shells of various kinds of solutes (groups) decreased in the following order: water structure breaking compounds>polar groups>unfolded proteins>globular proteins>non-polar groups. Time courses of the storage modulus were determined for the chemical acidification by glucono-δ-lactone (GDL) of milk samples prepared from skimmed milk powder (SMP). Gelation of unheated milk was a monotonous process that started at pH 4.9. Heat-treated milk from SMP (16 and 14 g per 100 ml) acidified by GDL (3 g per 100 ml) at 43 °C gave non-monotonous kinetics of gelation with two phases corresponding to the mechanisms induced by denatured whey proteins at pH>5 and by casein–casein interactions at pH 4.8–4.9. For heat-treated milk, measurement of bound water gave two stages of decrease in water mobility. Additional hydration of SMP during acidification gave 0.15–0.2 g and 0.8 g bound H₂O per gram of SMP for unheated and heat-treated milk, respectively.