Fractional integrals and weakly singular integral equations of the first kind in then-dimensional ball

The purpose of the paper is to introduce and to investigate a new class of fractional integrals connected with balls in ?ⁿ. A Riesz potentialI _Ω ^α ρ over a ball Ω is represented by a composition of such integrals. Using this representation we obtain necessary and sufficient solvability conditions for the equationI _Ω ^α ρ =f in the space L_p(Ωw) with a power weight w(x) and solve the equation in a closed form. The investigation is based on a special Fourier analysis adopted for operators commuting with rotations and dilations in ?ⁿ.     

Quantum-algebras and elliptic algebras

We define a quantum-algebra associated to as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of , or theq-deformed classical-algebra algebra of . We construct free field realizations of the quantum-algebra and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in.The research of the second author was partially supported by NSF grant DMS-9501414.     

Oxidative coupling of malononitrile with formation of 1,1,2,3,3-pentacyanopropene salts

A simple and convenient route for the synthesis of 1,1,2,3,3-pentacyanopropene salts is reported. These salts are formed by interaction of malononitrile with SeO₂ in presence of organic N-containing bases or pyridinium salts.     

Extraction of environmental information from large aerosol data sets through combined application of cluster and factor analyses

To reveal useful environmental information which is contained in large analytical data sets, an approach, based on the successive application of hierarchical cluster analysis and factor analysis, is proposed. Estimation criteria to determine the most suitable number of clusters and/or factors, are discussed and the interpretation of the cluster and factor analyses results is performed using visual techniques. The data sets were obtained by scanning electron microscope-energy-dispersive X-ray analysis of individual North Sea aerosol particles.     

Effect of Photosensitizer Delivery System and Irradiation Parameters on the Efficiency of Photodynamic Therapy of B16 Pigmented Melanoma in Mice

Abstract— Previous studies (Biolo et al., Photochem. Photobiol. 59, 362-365, 1994) showed that liposome-delivered Si(IV)-na-phthalocyanine (SiNc) photosensitizes B16 pigmented melanoma subcutaneously transplanted in C57 mice to the action of 776 nm light. However, the efficacy of the phototreatment was limited by a lack of selectivity of tumor targeting by SiNc as well as by incomplete necrosis of the neoplastic mass. The present investigations show that the use of a different delivery system (Cremophor emulsion vs liposomes of dipalmitoylphosphatidylcholine) causes no significant increase in the selectivity of tumor targeting for three injected doses of SiNc (0.5, 1, 2 mg/kg). However, upon 776 nm light irradiation (300 mW/cm²; 520 J/cm²), the delay in the rate of tumor growth was maximal (7-8 days) for the highest naphthalocyanine dose. On the other hand, a remarkable improvement in the tumor response was obtained by inducing an intratumoral temperature increase to 44°C immediately after PDT. The thermal effect appeared to be due to photoexcitation of melanin by 776 nm light (550 mW/cm²; 520 J/cm²) and subsequent partial conversion of absorbed energy into heat.     

Ion interaction approach to calculations of volumetric properties of aqueous multiple-solute electrolyte solutions

The ion interaction approach developed by Pitzer was used for the prediction of volumetric properties of mixed electrolyte solutions at 25°C based on parameters calculated from experimental data for single-solute electrolyte solutions. Such an approach was shown to be especially effective for application to the calculation of volumetric properties of natural hypersaline brines and of industrial electrolyte solutions of large complexity. The use of the latest recommended sets of volumetric ion interaction parameters for single electrolyte solutions and symmetrical mixing parameters for Na–K–Cl ion combinations considerably improved the precision of the density calculations of highly concentrated mixed electrolyte solutions and of various natural waters.     

Molecular structure of the boron(III) oxide molecule in the SCF approximation

The potential surface for the boron(III) oxide (B₂O₃) ground state has been calculated in restricted HF approximation with a minimal STO—3G basis set. The equilibrium geometry has C_2v symmetry; the corresponding structural parameters are as follows: r(O_i—B₁)= 1.241 Å; r(B_i—O)= 1.341 Å ; ∠B₁QB₂ = 142° and ǒO₁B₁O = 177°. Calculations were also carried out using the SCF-Xα approach for two configurations of B₂O₃ with C_2v and D_∞h symmetry.     

Ab initio study of the electronic and structural properties of the crystalline polyethyleneimine polymer

Polyethyleneimine is a very interesting polymer, not only for its extensive use in biological applications, but also for its crystal structure as a double-stranded helix in the anhydrous state. In order to elucidate the electronic bulk properties of the crystalline (or linear) polyethyleneimine built from ethylenediamine molecules in anhydrous conditions, we performed ab initio density functional theory calculations on water-free molecular crystal structures. The resulting polymer is a semiconductor with a small band gap: Eg = 0.40 eV.     

Easy α- to β-migration of an enol moiety on a pyrrole ring

Functionalized pyrrolic enols, 2-(2,2-dicyano-1-hydroxyethenyl)-1-methylpyrroles, synthesized from 2-ethenylpyrroles by a nucleophilic SEt-OH exchange, upon heating (75-142 °C) are readily rearranged to their 3-isomers in near to quantitative yield. The inter or intramolecular auto-protonation of a pyrrole ring by the acidic enol hydroxyl to form a mesomeric pyrrolium cation or zwitterion is suggested to be a key step in the rearrangement.