Acid-catalyzed dehydration of naphthalene-cis-1,2-dihydrodiols: origin of impaired resonance effect of 3-substituents

Acid-catalyzed dehydrations of substituted naphthalene-cis-1,2-dihydrodiols occur with loss of the 1- or 2-OH group to form 2- and 1-naphthols, respectively. Effects of substituents MeO, Me, H, F, Br, I, and CN at 3-, 6-, and 7-positions of the naphthalene ring are consistent with rate-determining formation of β-hydroxynaphthalenium ion (carbocation) intermediates. For reaction of the 1-hydroxyl group the 3-substituents are correlated by the Yukawa-Tsuno relationship with ρ = -4.7 and r = 0.25 or by σ(p) constants with ρ = -4.25; for reaction of the 2-hydroxyl group the 3-substituents are correlated by σ(m) constants with ρ = -8.1. The correlations for the 1-hydroxyl imply a surprisingly weak resonance interaction of +M substituents (MeO, Me) with a carbocation reaction center but are consistent with the corresponding correlation for acid-catalyzed dehydration of 3-substituted benzene-cis-1,2-dihydrodiols for which ρ = -6.9 and r = 0.43. Substituents at the 6- and 7-positions of the naphthalene rings by contrast are correlated by σ(+) with ρ = -3.2 for reaction of the 1-hydroxyl group and ρ = -2.7 for reaction of the 2-hydroxyl group. The unimpaired resonance implied by these substituent effects appears to be inconsistent with a previous explanation of the weak resonance of the 3-substituents in terms of imbalance of charge development and/or nonplanarity of the benzenium ring in the transition state. An alternative possibility is that the adjacent hydroxyl group interferes sterically with conjugation of +M substituents. "Hyperaromaticity" of the arenium ion intermediates does not appear to be a factor influencing this behavior.     

A tetraalkylated pyrene building block for the synthesis of pyrene-fused azaacenes with enhanced solubility

The synthesis and characterisation of a soluble pyrene-fused tetraazaoctacene derivative has been achieved by developing a key pyrene-based building block with four solubilising groups.     

Rudimentary Languages and Second-Order Logic

The aim of this paper is to point out the equivalence between three notions respectively issued from recursion theory, computational complexity and finite model theory. One the one hand, the rudimentary languages are known to be characterized by the linear hierarchy. On the other hand, this complexity class can be proved to correspond to monadic second-order logic with addition. Our viewpoint sheds some new light on the close connection between these domains: We bring together the two extremal notions by providing a direct logical characterization of rudimentary languages and a representation result of second-order logic into these languages. We use natural arithmetical tools, and our proofs contain no ingredient from computational complexity.     

Principal component analysis combined with truncated-Newton minimization for dimensionality reduction of chemical databases

 The similarity and diversity sampling problems are two challenging optimization tasks that arise in the analysis of chemical databases. As a first step to their solution, we propose an efficient projection/ refinement protocol based on the principal component analysis (PCA) and the truncated-Newton minimization method implemented by our package TNPACK (PCA/TNPACK). We show that PCA can provide the same initial guess as the singular value decomposition (SVD) for the optimization task of solving the distance-geometry optimization problem if each column of a database matrix has a mean of zero. Hence, our PCA/TNPACK approach is analogous to the SVD/TNPACK projection/refinement protocol that we developed recently for visualizing large chemical databases. Using PCA/TNPACK and the Merck MDDR database (MDL Drug Data Report), we further investigate the projection/refinement procedure with regards to the preservation of the original clusters of chemical compounds, the accuracy of similarity and diversity sampling of chemical compounds, and the potential application in the study of structure activity relationships. We also explore by simple experiments accuracy and efficiency aspects of the PCA/TNPACK procedure compared to those of a global optimization algorithm (simulated annealing, as implemented by the program package SIMANN) in terms of producing the projection mapping of a database. Numerical results show that the 2D PCA/TNPACK mapping can preserve the distance relationships of the original database and is thus valuable as a first step in similarity and diversity applications. Of course, the generation of a global rather than local minimizer and its interpretation in terms of pharameceutical applications remains a challenge. Since all numerical tests are performed on the Merck MDDR database, results are representative of realistic cases encountered in the field of drug design, and may help analyze properties of medicinal compounds. Received: December 21, 2000 / Accepted: August 19, 2002 Published online: September 27, 2002 Mathematics Subject Classification (2000): 65K10, 62H25, 92C50     

Molecular dynamics by the Backward-Euler method

This paper introduces a new computational method for molecular dynamics. The method combines the Backward-Euler scheme for the solution of stiff differential equations with a Langevin-equation approach to the establishment of thermal equilibrium. The method allows the user to choose a cutoff frequency ω_c. Vibrational modes with frequencies below ω_c will be fully excited (receive a mean energy of kT per mode), while modes with frequencies greater than ω_c will be effectively frozen by the method. By setting ω_c = kT/h, one can obtain reasonable agreement with the quantum-mechanical energy distribution among the various modes, despite the classical character of the computation.     

Two point problems and analyticity of solutions of abstract parabolic equations

Fort ∈ [a, b], letA(t) be the unbounded operator inH ^0,p (G) associated with an elliptic-boundary value problem that satisfies Agmon’s conditions on the rays λ=±iτ, τ ≥0. Existence and uniqueness results are obtained for weak and strict solutions of two-point problems of the type (du/dt)−A(t) u(t) =f(t),E ₁(α)u (α)=u _α,E ₂ (β)u (β)=u _β. Here [α, β) χ- [a, b],E ₁ (α) andE ₂ (β) are spectral projections associated withA(α) andA(β) respectively, andA(α)E ₁ (α) and =A (β)E ₂ (β) are infinitesimal generators of analytic semigroups. WhenA(t) andf(t) are analytic in a convex, complex neighborhoodO of [a, b] we show that for someθ _i ,i=1,2, any solution ofdu/dt =A(t)u (t)=f(t) in [a, b] is analytic and satisfies the above equation in the setO∩{t; t ≠ a, t ≠ b, | arg (t −a) | <θ ₁, | arg (b −t) |θ ₂}. Research partially supported by N. N. F. grant at Brandeis University.     

Arc plasma synthesized LaB<Subscript>6</Subscript> nanocrystallite film on various substrates as a field emitter

Lanthanum hexaboride (LaB₆) nanocrystallites/nanowires have been successfully synthesized using gas phase condensation in arc plasma. Our results show that the LaB₆ nanowires have ~20 nm diameter and length of several micrometers. The as-synthesized LaB₆ nanocrystallites and nanowires are crystalline in nature. Field emission studies were carried out on as synthesized LaB₆ nano-powder deposited on W and Re tips and foils, and also on Si foil substrates under ultra high vacuum. The Fowler–Nordheim plots obtained from the current–voltage characteristics are found to be linear in accordance with the quantum mechanical tunneling phenomenon. High value of field enhancement factor (8177) is observed for LaB₆ on Re substrate, indicating that the electron emission is from the nanometric features of the LaB₆. Our results show that the arc plasma synthesized LaB₆ nanocrystalline film exhibits good emission stability as emitter without severe deviations from the initial set value and also a strong ability to withstand the ion bombardment, which is useful for low operation voltage vacuum micro/nano electronic devices.     

Low threshold field electron emission from solvothermally synthesized WO2.72 nanowires

Field emission studies of WO_2.72 nanowires synthesized by a solvothermal method have been performed in the planar diode configuration under ultra high vacuum conditions. Fowler–Nordheim plots obtained from the current-voltage characteristics follow the quantum mechanical tunneling process and a current density of ∼8.3×10⁶ μA/cm² can be drawn at an applied electric field of 2 V/μm. The field enhancement factor is 33025, while the turn-on field is only 1.4 V/μm. The emission current-time plot recorded at the pre-set value of emission current of 1 μA over a period of more than 3 h exhibits an initial increase and a subsequent stabilization of the emission current. The results reveal that the WO_2.72 nanowire emitters synthesized by the solvothermal method are promising cathode materials for practical applications.     

Formation of aligned ZnO nanorods on self-grown ZnO template and its enhanced field emission characteristics

We report a novel method for producing aligned ZnO nanorods (ANR) on self-grown ZnO template in a single step process involving growth of ZnO by vapor transport, followed by quenching of growing ZnO flux in liquid nitrogen. In the present study Zn powder turns into ZnO sheet under oxygen flow at ∼900 °C and bottom surface of the sheet acts as template for the growth of ANR. It is revealed from XRD and EDAX analysis that the bottom of the sheet is Zn rich region and acts as self catalyst for the growth of ANR. The grown nanorods have length up to several tens of micrometers with diameters ranging from ∼100 to 150 nm. Microstructural analysis of ANR indicates the fractal like configuration. The field emission properties have been investigated for ANR with fractal geometry using the ANR on self-grown ZnO template as a cathode directly. The turn-on electric field required to draw current density of ∼1.0 μA/cm² has been found to be ∼0.98 V/μm. The field enhancement factor based on Fowler-Nordheim (F-N) plot was found to be ∼7815 for ANR. The fractal geometry of ANR has been shown to be advantageous for achieving improved field emission features. The present investigations of synthesis involving formation of ANR over self-grown ZnO template, together with fractal configuration of the as-synthesized ANR, are first of their type.     

Topology and measure in logics for region-based theories of space

Space, as we typically represent it in mathematics and physics, is composed of dimensionless, indivisible points. On an alternative, region-based approach to space, extended regions together with the relations of ‘parthood’ and ‘contact’ are taken as primitive; points are represented as mathematical abstractions from regions.Region-based theories of space have been traditionally modeled in regular closed (or regular open) algebras, in work that goes back to [5] and [21]. Recently, logics for region-based theories of space were developed in [3] and [19]. It was shown that these logics have both a nice topological and relational semantics, and that the minimal logic for contact algebras, ${\mathbb{L}}_{min}^{cont}$ (defined below), is complete for both.The present paper explores the question of completeness of ${\mathbb{L}}_{min}^{cont}$ and its extensions for individual topological spaces of interest: the real line, Cantor space, the rationals, and the infinite binary tree. A second aim is to study a different, algebraic model of logics for region-based theories of space, based on the Lebesgue measure algebra (or algebra of Borel subsets of the real line modulo sets of Lebesgue measure zero). As a model for point-free space, the algebra was first discussed in [2]. The main results of the paper are that ${\mathbb{L}}_{min}^{cont}$ is weakly complete for any zero-dimensional, dense-in-itself metric space (including, e.g., Cantor space and the rationals); the extension ${\mathbb{L}}_{min}^{cont}+(Con)$ is weakly complete for the real line and the Lebesgue measure contact algebra. We also prove that the logic ${\mathbb{L}}_{min}^{cont}+(Univ)$ is weakly complete for the infinite binary tree.