Multi‐input–Multi‐output Molecular Response System Based on Dynamic Redox Behavior of Hexaphenylethane‐type Electron Donors with the Tetrahydrophenanthrazepine Skeleton: Strong Chiroptical Signals through the Transmission of Point Chirality to Helicity

The title heterocyclic donors undergo reversible C? C bond formation/cleavage upon electron transfer (dynamic redox behavior). The helical sense in both neutral and cationic states is interconvertible by facile ring flipping. The π‐type asymmetric center on the azepine nitrogen atom induces a significant degree of diasteromeric preference, thus endowing strong CD activity based on exciton coupling. Chiroptical properties could be modified not only by redox reactions but also by heat and protonation. The present redox pairs can serve as unprecedented three‐way‐input (e, H⁺, Δ) and two‐way‐output (UV/Vis, CD) response systems.     

Kinetic equations for thermal dissociation processes

Relationships between average degree of transformation and time of dissociation were derived for polydisperse granular materials with account to the type of grain size distribution. It has been checked, under what conditions the kinetic curves obtained by numeric solution of those relationships may be described in terms of equations D1 α²=kt , F2 [1/(1 - α) - 1 =kt] and F3 [1/(1 - α)² - 1=kt]. This revised version was published online in August 2006 with corrections to the Cover Date.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

On the stereochemistry of the Horner—Emmons reaction between 3-functionally substituted 2-methyl-2-propenylphosphonates and aliphatic aldehydes

The reaction of diethyl 3-ethoxycarbonyl-2-methyl-2-propenylphosphonate (1a) with 3-methylbutanal (2) in heterogeneous MOH (solid)-benzene systems in the presence of 5–10 mol.% of benzyltriethylammonium chloride (BTEAC) gives the reaction product (3) with a higher, for M=K, or lower, for M=Li, ratio of 2E,4E and 2Z,4E-stereoisomers than that observed in the absence of BTEAC. Tetrabutylammonium bromide (TBAB) as a catalyst of the reaction1a + 2 3 in the system KOH (solid)-wet benzene leads to a higher [2E,4E-3][2Z,4E-3] ratio than BTEAC; this ratio grows from 4456 without TBAB to 8020 at 100 mol.% of TBAB. In the latter case the stereochemical outcome of the reaction is similar to that obtained when tetrabutylammonium hydroxide in dry benzene is used as the deprotonating agent. The corresponding diisopropyl phosphonate (1b) and 3,7-dimethyloctanal (4a) interact in the system KOH (solid)-wet benzene-TBAB to give hydroprene (5) containing 88 % of the 2E,4E-isomer (5a) while in the case of 1 equiv. of [(n-Bu₄)N]OH in dry benzene the content of5a is 92 %. Diisopropyl 3-isopropoxycarbonyl-2-methyl-2-propenylphosphonate (1c) and 7-methoxy-3,7-dimethyloctanal (4b) under either of these conditions afford methoprene (6) containing 93 % of the 2E,4E-isomer.Part 6, see ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1094–1098, June, 1993.