Unsolvability of binary forms

A property of a binary unit is obtained which is invariant in all number fields of fixed degree n, n ≥ 3. This property is then used to formulate a necessary condition for the solvability of a binary form.     

Random sequential adsorption of line segments with a finite jamming limit

The traditional formulation for random sequential adsorption (RSA) of line segments onto a plane does not possess a jamming limit; there is always space for a 1D object on a 2D plane. We propose a qualitatively different RSA formulation for line segments which does lead to a finite jamming limit, 1.5707+/-0.0001 segments per square one segment on the side. To our knowledge, this is the first appearance of the number pi in the jamming limit of an RSA problem. This RSA formulation can be applied to adsorption of rigid, very high aspect ratio rods on a flat surface. These rods are not well modeled by the traditional RSA formulation. As an example of such a problem we describe the deposition of carbon nanotube-DNA hybrids on a surface and show that our theoretical formulation is consistent with experimental results.     

Resonant generation of surface acoustic waves between moving and stationary piezoelectric crystals

The propagation of surface acoustic waves in a system composed of two piezoelectric crystals moving with respect to each other and separated by a vacuum gap is considered. The waves are localized on different sides of the gap and coupled only through the electrostatic interaction. It is shown that when the velocity of the relative motion of crystals is close to some value, there occurs a wave instability resulting in a resonant generation of these surface waves. The rate of growth of Bleustein-Gulyaev waves in piezoelectric crystals of 6mm symmetry class is determined analytically.     

Phosphorus heterocycle synthesis using phosphenium ions and 1,4-dienes

The stabilized phosphenium ion, [Prⁱ₂NPCl]⁺, reacts readily with 1,4-dienes to afford high yields of bicyclic phosphonium salts, the structure of one of which has been determined by X-ray crystallography.     

Simple and Selective Spectrophotometric Method for the Determination of Iron (III) and Total Iron Content, Based on the Reaction of Fe(III) with 1,2-Dihydroxy-3,4-Diketocyclo-Butene (Squaric Acid)

 Squaric acid (1,2-dihydroxy-3,4-diketo-cyclobutene) is used in a specific reaction with Fe(III) for the spectrophotometric determination of Fe(III) and total iron content. The optimization of the experimental parameters leads to the establishment of a simple, fast and accurate analytical method. The analytical procedure includes mixing ammonium squarate (40 mM), prepared in a phthalate buffer solution of pH 2.7, with the sample and measuring the absorbance at 515 nm. The molar absorptivity of the colored product is 3.95×10³ L·mol⁻¹·cm⁻¹, at 515 nm. Calibration graphs for Fe(III) are rectilinear for 0.5–20 mgL⁻¹, with a detection limit of 0.3 mgL⁻¹ and r.s.d. not exceeding 2.5%, for five replicates of a 3.0 mgL⁻¹ standard solution. The method has been successfully applied to the determination of iron (III) and the total iron content after quantitative oxidation of iron (II). The results for several analyzed samples when compared with those acquired by using the FAAS technique, were found to be in satisfactory agreement. Author for correspondence: University of Ioannina, Department of Chemistry, Laboratory of Analytical Chemistry, Ioannina 451 10, Greece. E-mail: panavelt@cc.uoi.gr Received July 27, 2002; accepted December 20, 2002 Published online April 11, 2003     

Alkyl Ether Analogs of Chlorophyll-a Derivatives: Part 1. Synthesis, Photophysical Properties and Photodynamic Efficacy

The synthesis, preliminary in vivo biological activity, singlet oxygen and fluorescence yields of a series of alkyl ether derivatives of chlorophyll-a analogs are described. For short-chain carbon ethers (1–7carbon units), it was observed that the biological activity increased by increasing the length of the carbon chain, being maximum in compounds with n-hexyl and n-heptyl chains. Related sensitizers prepared by reacting 2-(1-bromoethyl)-2-devinylpyropheophorbide-a with (sec)alcohols were found to be less effective. Under similar treatment conditions, photosensitizers containing cis- and trans- 3-hexenyl side chains were ineffective. Thus, both stereochemical and steric factors caused differences in sensitizing activity. In general, pyropheophorbide-a analogs were found to be more active than related chlorin e₆ derivatives, in which the isocyclic ring (ring “E”) was cleaved. Related photosensitizers in the 9-deoxy- series were found to be as effective as the corresponding pyropheophorbide-a analogs. The photosensitizers prepared from pyropheophorbide-a methyl ester and chlorin e₆ trimethyl ester have long wavelength absorption at 660 nm (ε 45000 to 50000). Reduction of the carbonyl group in the pyropheophorbide-a to methylene (ring E) resulted in a blue shift to 648 nm (ε 38000).     

Graph complexity and the laplacian matrix in blocked experiments

connections between the efficiency of statistical designs, the Laplacian matrix studied in algebra, and graphs of maximal complexity are being described. Up to a positive scalar multiple the Laplacian (or Kirchhoff) matrix concides with the information matrix that arises out of a statistical additive model with treatment and block effects. By way of the matrix-tree theorem design efficiency is shown to be closely related to graph complexity. Several open questions regarding graphs of maximal complexity are being brought to attention.     

Acylaminoacetyl derivatives of active methylene compounds. 4

Meldrum's acid has been found to be effectively acylated using the imidazolides of N-protected glycines, X-NHCH₂COOH (X = -COPh, -COMe, -Z, -Boc, -COOMe and -COOEt). The corresponding C-acylation compounds were isolated in high yields and were readily converted to the N-protected tetramic acids. It was shown by pmr spectroscopy that these acids exist as the enol tautomers in DMSO-d₆ solution, whereas in deuteriochloroform solution both the enol and keto tautomers can be observed.     

Assignment of stereochemistry to cyclohexenylidenecyanoacetates by 1H NMR spectroscopy

The stereochemistry of various pairs of isomeric 2-cyclohexen-1-ylidenecyanoacetates was assigned using ¹H NMR spectroscopy. The isomers with the γ-methylene or the γ-vinyl protons cis to the carbalkoxy group were found to have the signals of these protons at approximately 0.3 ppm and 1 ppm, respectively, downfield relative to their geometrical isomers or the corresponding 2-cyclohexen-1-ylidenemalononitriles. The observation regarding the γ-vinyl proton proved useful for the assignment of configuration to cyclohex-enylidenecyanoacetates derived form cholest-4-en-3-one. The large and constant downfield shift (c. 1 ppm) of the γ-vinyl proton when cis to the ester group results from the rigid cyclohexenylidenecyanoacetate system, in which the vinylic proton can approach more closely to the magnetically anisotropic ester carbonyl group.