New indoline spiropyrans with highly stable merocyanine forms

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Boolean delay equations: A simple way of looking at complex systems

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time; such BDEs can be seen therefore as metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil’s staircases and “fractal sunbursts.” All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades of loading and failure in earthquake modeling and prediction, as well as in genetics. In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid-earth problems. The former have used small systems of BDEs, while the latter have used large hierarchical networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space (“partial BDEs”) and discuss connections with other types of discrete dynamical systems, including cellular automata and Boolean networks. This research-and-review paper concludes with a set of open questions.     

An unusual reaction of cyclopropenylphosphonium bromide with sodium polyphosphides – A novel approach to sodium 3,4,5-triphenyl-1,2-diphosphacyclopentadienide

1,2,3-Triphenylcyclopropenylphosphonium bromide reacts with sodium polyphosphides to give sodium 3,4,5-triphenyl-1,2-diphosphacyclopentadienide in high yield.     

Noise in a Small Genetic Circuit that Undergoes Bifurcation

Based on the consideration of Boolean dynamics, it has been hypothesized that cell types may correspond to alternative attractors of a gene regulatory network. Recent stochastic Boolean network analysis, however, raised the important question concerning the stability of such attractors. In this paper a detailed numerical analysis is performed within the framework of Langevin dynamics. While the present results confirm that the noise is indeed an important dynamical element, the cell type as represented by attractors can still be a viable hypothesis. It is found that the stability of an attractor depends on the strength of noise related to the distance of the system to the bifurcation point and it can be exponentially stable depending on biological parameters.     

Stress Distribution in a Periodontal Shell with Varying Thickness

A stress analysis of the teeth periodontium is carried out. The periodontium has the form of a thin-walled elastic shell whose thickness varies along the generatrix. The problem is solved by invoking the theory of elasticity, theoretical mechanics, and spline functions that describe the lateral surfaces of the periodontium. Plots show how the change in the periodontium thickness affects the stress distribution     

New 1,3,5-triphenyl-2-pyrazoline-containing 3-hydroxychromones as highly solvatofluorochromic ratiometric polarity probes

Two novel 1,3,5-triphenyl-2-pyrazoline moiety containing derivatives of 3-hydroxychromone were synthesized and studied by ¹H NMR, absorption and fluorescence spectroscopy. The prospects of practical application of these compounds exhibiting high solvatofluorochromism into analytical chemistry and biophysics as effective ratiometric polarity probes were discussed proceeding from the data on their fluorescent properties.     

Application of Discrete Fourier Series in the Stress Analysis of Cylindrical Shells of Variable Thickness with Arbitrary End Conditions

An approach is proposed to solve boundary-value stress—strain problems for cylindrical shells with thickness varying in two coordinate directions. The approach employs discrete Fourier series to separate circumferential variables. This makes it possible to reduce the problem to a one-dimensional one, which can be solved by the stable discrete-orthogonalization method. Examples are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 85–94, June 2005.