The moduli space of flat SU (2) and SO (3) connections over surfaces

All the connected components of the moduli space of flat connections on SU (2) and SO (3) (trivial and non-trivial) bundles over closed oriented surfaces are determined. The symplectic structure and volumes of the non-maximal strata of the moduli space are also determined.     

The Efficiency Distribution Approach in Data Envelopment Analysis: An Application

A method is developed here for characterizing the empirical distribution of the efficient units in data envelopment analysis. Two empirical applications illustrate the various uses of the distribution approach. One involves the cost frontier which exhibits increasing returns to scale and the other involves a dynamic production frontier, where technological change causes a shift of the production frontier over time.     

Monopole charge quantization or why electromagnetism is a U(1)-gauge theory

We obtain Dirac’s classic monopole charge quantization from the point of view of geometric quantization and demonstrate how this leads to the conclusion that the electromagnetic field is a U(1)-gauge field.     

Lanthanum(III) and prasedymium(III) complexes with piperazine dithiosemicarbazones

Lanthanum(III) and praseodymium(III) complexes of the type [Ln(L)Cl(H₂O)]₂ (Ln = La(III) or Pr(III); LH₂ = dithiosemicarbazone ligands derived from piperazine dithiosemicarbazide and benzaldehyde, 4-nitrobenzaldehyde, and 2-methoxybenzaldehyde) have been synthesized in methanol in the presence of sodium hydroxide. The complexes have been characterized by elemental analyses, molecular weight, molar conductance, electronic absorption, IR, and ¹H and ¹³C NMR spectral studies. Nephelauxetic ratio, covalency parameter, and bonding parameter for these complexes have also been calculated. Thermal studies of the complexes have been carried out using TG, DTG, and DSC techniques. Kinetic parameters, such as apparent activation energy and order of reaction, were determined by the Coats-Redfern graphical method. The heats of reaction for different reaction steps were calculated from DSC curves. The article was submitted by the authors in English.     

High energy muon-nucleon inelastic scattering at lowq 2

The inelastic interactions of 150 GeV positive muons produced at Fermi Laboratory have been studied in nuclear emulsion. Secondary particles produced in these interactions have been identified, the energy spectra and angular distributions for pions and protons are given. The inclusive pionproduction reaction is studied and the relative shape ofp _t ² distribution is discussed. The average charged multiplicity relations are determined as a function of different parameters and are compared with the multiplicities produced in pure hadronic interactions. The integral cross sections have been measured and are compared with the first and second powers of 1/(1+q ²/m _p ² ) forσ _exp(q ²,v), the quantity commonly called the “virtualphoton-nucleon total cross section”. The values of the structure function νW ₂ are calculated for 0.02≤q ²≤0.5. The present data are compared with other muon data at the same energy.     

Nomenclature of polymers (based on structure)

In the complete absence of a systematic polymer nomenclature, a scheme of nomenclature based on structure is proposed. The problem of naming a “mer” has been solved for an addition polymer by adding “ne” to the monomer name, the justification being on withdrawal of a π bond a monomer becomes a mer. To furnish completeness to the nomenclature, condensation polymers were included in the system. The present nomenclature system of polymers is very arbitrary. Some polymers are not chemically named, some named incorrectly, and there are some fantastic names. After pointing these out, the possible solutions were shown, encompassing a systematic discussion on nearly every type of polymer–linear, branched, or crosslinked–and copolymer (including block or graft), and plastic, fiber, or rubber, and stereospecific polymer. One or more names were proposed for different cases.     

Synthesis,structural and biochemical aspects of titanocene and zirconocene chelates of acetylferrocenyl thiosemicarbazones

The reactions of bis(cyclopentadienyl)titanium(IV)/zirconium(IV) dichloride with a new class of organometallic thiosemicarbazones (LH), derived by condensing acetylferrocene with substituted thiosemicarbazides, have been studied and two types of bimetallic products, viz. [Cp₂M(L)Cl] (M = Ti or Zr) and [CpZr(L)₃], have been isolated. On the basis of various physicochemical and spectral studies, five- and seven-coordinate structures have been assigned to these derivatives, respectively. Attempts have been made to establish a correlation between biological activity and the structures of the products.     

Oxofluorovanadates(V). IV. Dioxotetrafluorovanadates

Preparation and properties of the salts of the series MVO₂F₄, where M = NH, Na⁺, K⁺, 1/2 Ni²⁺, and 1/3 [Co(NH₃)₆]³⁺ are described. Molecular conductivity of Na₃VO₂F₄ at different dilutions indicates that Na₃VO₂F₄ dissociates into 3 Na⁺ and VOaF ions. Ion exchange study of (NH₄)₃VO₂F₄ solution through cation exchange resin (H⁺ form) suggests that the corresponding acid decomposes partly to vanadium pentoxide. Reaction between (NH₄)₃VO₂F₄ with BaCl₂ and AgNO₃ solutions shows the formation of BaVO₂F₃ and AgVO₃ respectively. Thermogravimetric study of (NH₄)₃VO₂F₄ shows the formation of impure vanadium pentoxide as the ultimate product on heating up to 450°C. X-ray powder diffraction data are given for (NH₄)₃VO₂F₄ and Na₃VO₂F₄.     

Kinetics and mechanism of the interaction of DL-methionine with cis-diaquaethylenediamine platinum(II) perchlorate in aqueous medium

The kinetics of the interaction of DL-methionine with [Pt(en)(H2O)2]2+ have been studied spectrophotometrically as a function of [Pt(en)(H2O)22+], [DL-methionine], PH and temperature. The reaction proceeds via a rapid outer sphere association followed by two slow consecutive steps having first order dependence on the aqua ion and methionine concentrations. Activation parameters have been evaluated using the Eyring equation. The low H1 (15.6 kJ mol–1) and large negative value of S1 (–230 J K–1 mol–1) as well as H2 (19.5 kJ mol–1) and S2 (–226 J K–1 mol–1) indicate an associative mode of activation for both the aqua ligand substitution processes in the two consecutive steps.