A Self-Consistent Model for Positronium Formation from Helium Atoms

The differential and total cross sections for electron capture by positrons from helium atoms are calculated using a first-order distorted wave theory satisfying the Coulomb boundary conditions. In this formalism, a parametric potential is used to describe the electron screening in a consistent and realistic manner. The present procedure is self-consistent because (a) it satisfies the correct boundary conditions and post–prior symmetry, and (b) the potential and the electron binding energies appearing in the transition amplitude are consistent with the wave functions describing the collision system. The results are compared with the other theories and with the available experimental measurements. At the considered range of collision energies, the results agree reasonably well with recent experiments and theories.     

Time-division multiplexing of the orbital angular momentum of light

We present an optical setup for generating a sequence of light pulses in which the orbital angular momentum (OAM) degree of freedom is correlated with the temporal one. The setup is based on a single q plate within a ring optical resonator. By this approach, we demonstrate the generation of a train of pulses carrying increasing values of OAM, or, alternatively, of a controlled temporal sequence of pulses having prescribed OAM superposition states. Finally, we exhibit an "OAM-to-time conversion" apparatus that divides different input OAM states into different time bins. The latter application provides a simple approach to digital spiral spectroscopy of pulsed light.     

Lithium-7 NMR Study of Several Li+-Crown Ether Complexes in Binary Acetone-Nitrobenzene Mixtures

⁷Li NMR measurements were employed to monitor the stoichiometry andstability of Li⁺ ion complexes with 12-crown-4 (12C4), 15-crown-5 (15C5), benzo-15-crown-5 (B15C5) l8-crown-6 (18C6), dicyclohexano-18-crown-6 (DC18C6) and dibenzo-18-crown-6 (DB18C6) in binary acetone-nitrobenzene mixtures of varying composition. In all cases studied, the variation of ⁷Li chemical shift with the crown/Li⁺ mole ratio indicated the formation of 1:1 complexes. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. In all solvent mixtures used, the stabilities of the resulting 1:1 complexes varied in the order15C5 > B15C5 > DC18C6 > 18C6 > 12C4 >DB18C6. It was found that,in the case of all complexes, an increase in the percentage of acetone in thesolvent mixtures significantly decreased the stability of the complexes.     

Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.     

Heat-resistant and soluble fluorinated poly(amide imide)s based on non-coplanar ortho-linked diimide-dicarboxylic acid

A series of novel fluorinated heat-resistant poly(amide imide)s (PAIS) based on non-coplanar diimide-diacid monomer (DIDA) were synthesized and characterized. The poly(amide imide)s were obtained in high yields and possessed inherent viscosities in the range of 0.47-0.91 dL g⁻¹. All of the polymers were amorphous in nature, showed outstanding solubility and could be readily soluble in common organic solvents such as N,N-dimethylacetamide, N-methyl-2-pyrrolidinoned, dimethyl sulfoxide, N,N-dimethylformamide, pyridine and tetrahydrofuran. Glass transition temperatures were in the range of 221-263 °C, as determined by differential scanning calorimetry. Degradation temperatures for 10% weight loss occurred all above 520 °C and char yields was more than 50% at 700 °C in nitrogen atmosphere. Moreover, these PAIs possessed low refractive indexes (n = 1.58-1.59), birefringence (Δn = 0.008-0.013), and dielectric constants (? ≈ 2.5) due to the trifluoromethyl pendent groups and ortho-catenated aromatic rings that interrupt chain packing and increase free volume.     

On the Schröder–Bernstein property for modules

The well known Schröder–Bernstein Theorem states that any two sets with one to one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic? The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. We extend the study of this question for modules in this paper. We say that a module Msatisfies the Schröder–Bernstein property (S-B property) if any two direct summands of M which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete and modules with ACC on direct summands. It is also shown that over a Noetherian ring R, every extending module satisfies the S-B property. Among applications, it is proved that the class of rings R for which every R-module satisfies the S-B property is precisely that of pure-semisimple rings. We show that over a commutative domain R, any two quasi-continuous subisomorphic R-modules are isomorphic if and only if R is a PID. We study other conditions related to the S-B property and obtain characterizations of certain classes of rings via those conditions. Examples which delimit and illustrate our results are provided.     

Comparative electrochemical study of new self-assembled monolayers of 2-{[(Z)-1-(3-furyl)methylidene]amino}-1-benzenethiol and 2-{[(2-sulfanylphenyl)imino]methyl}phenol for determination of dopamine in the presence of high concentration of ascorbic acid and uric acid

The comparative electrochemical behavior of self-assembled monolayers of two Schiff's bases, 2-{[(Z)-1-(3-furyl)methylidene]amino}-1-benzenethiol (FMAB) and 2-{[(2-sulfanylphenyl)imino]methyl}phenol (SIMP) on a bare gold electrode (Au FMAB SAM-modified electrode and Au SIMP SAM-modified electrode, respectively), was investigated by means of cyclic voltammetry and electrochemical impedance spectroscopy in a 0.1 mol L(-1) KCl solution that contains 5.0 × 10(-3) mol L(-1) [Fe(CN)(6)](3-/4-). The results revealed that the modified electrodes showed an electrocatalytic activity toward the anodic oxidation of dopamine by a marked enhancement in the current response and lower overpotential (60 and 90 mV for the Au FMAB and Au SIMP SAM-modified electrodes, respectively) in phosphate buffer solution at pH 6.0. The Au SIMP SAM-modified electrode was applied successfully to the determination of dopamine in the presence of a high concentration of ascorbic acid. Selective detection was realized in total elimination of ascorbic acid response-a method different from the ones based on the potential separations. The detection limit of dopamine was 5.0 × 10(-8) mol L(-1) in a linear range from 1.0 × 10(-6) to 1.2 × 10(-4) mol L(-1) in the presence of 1.0 × 10(-3) mol L(-1) ascorbic acid. The interference studies also showed that the Au SIMP SAM-modified electrode exhibited good selectivity in the presence of a large excess of uric acid and could be employed for the determination of dopamine in pharmaceutical formulations, plasma samples and human urine with adequate selectivity and precision.     

Silica-bonded N-propylsulfamic acid as a recyclable catalyst for the synthesis of 2,3-dihydroquinazolin-4(1H)-ones

2,3-Dihydroquinazolin-4(1H)-one derivatives are synthesized via a one-pot,three component reaction of isatoic anhydride and an aromatic aldehyde with ammonium acetate or primary amine catalyzed by silica-bonded N-propylsulfamic acid(SBNPSA) in refluxing ethanol.     

Existence of solutions in variational relation problems without convexity

Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts.     

Graphs With Few Matching Roots

We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomials.