Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Magnetic field effect on indole exciplexes: an anomalous dielectric dependence

Individual exciplex formation between various aromatic hydrocarbons, anthracene, pyrene, all-s-trans-1,4-diphenylbuta-1,3-diene and a heteroaromatic amine, 1,2-dimethylindole, was investigated by steady-state fluorescence and magnetic field effect (MFE). A comparative study was carried out with two other exciplex systems 9-cyanophenanthrene-1,2-dimethylindole and 9-cyanophenanthrene-N-methylindole. The extent of charge transfer and dielectric dependence of MFE reveals the potential role of specific interactions related to exciplex geometry.     

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.     

Tunable circular patch antennas

A method to control the resonant or operating frequencies of circular patch antennas has been investigated experimentally and theoretically. It consists of the placement of passive metallic or tuning posts at approximate locations within the input region of the antenna. Comparison of measured and analytical results seems to establish the validity of a theoretical model proposed to determine the input performance of such circular patch antennas.     

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.     

Nanoparticles from cationic copolymer and DNA that are soluble and stable in common organic solvents

DNA by virtue of its superlative ability to self-assemble has found use beyond biological research in the design and fabrication of nanomaterials. However, developing novel DNA-based materials for chemical applications might be restricted due to the insoluble nature of DNA in most common organic solvents. In this Communication, we are reporting the first demonstration of making DNA soluble in a variety of nonbiological solvents such as acetonitrile, benzene, dimethyl sulfoxide (DMSO), and tetrahydrofuran with the help of poly(ethylene glycol) (PEG)-based cationic random copolymers. Because of complex formation between cationic copolymer and anionic DNA, nanoparticles are formed. These nanoparticles are expected to exhibit micelle-like structures with a nanometric core of cationic units neutralized by phosphate anions of DNA, surrounded by a shell of PEG segments. As PEG is soluble in the organic solvents used in this study, nanoparticles are stable in these solvents, making entrapped DNA soluble in these organic solvents.