A simplified approach for the generation of projection data for cone beam geometry

To test a developed reconstruction algorithm for cone beam geometry, whether it is transmission or emission tomography, one needs projection data. Generally, mathematical phantoms are generated in three dimensions and the projection for all rotation angles is calculated. For non-symmetric objects, the process is cumbersome and computation intensive. This paper describes a simple methodology for the generation of projection data for cone beam geometry for both transmission and emission tomographies by knowing the object’s attenuation and/or source spatial distribution details as input. The object details such as internal geometrical distribution are nowhere involved in the projection data calculation. This simple approach uses the pixilated object matrix values in terms of the matrix indices and spatial geometrical coordinates. The projection data of some typical phantoms (generated using this approach) are reconstructed using standard FDK algorithm and Novikov’s inversion formula. Correlation between the original and reconstructed images has been calculated to compare the image quality.     

An effective Hamiltonian approach to quantum random walk

In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.     

Vibrational Spectroscopy of Stretching and Bending Modes of Nickel Tetraphenyl Porphyrin： an Algebraic Approach

We calculate the vibrational frequencies of nickel tetraphenyl porphyrin for 36 vibrational bands by using the U（2） algebraic approach. The algebraic parameters in the calculations are accurate with the experimental data.     

Energy-dispersive X-ray fluorescence study of elemental uptake in cauliflower

A ¹⁰⁹Cd radioisotope-induced energy-dispersive X-ray fluorescence (EDXRF) study has been performed on samples of cauliflower consisting of the flower, the leaves and the associated root soil. The cauliflowers were collected from farms near the main dumping site of municipal solid waste in the city of Kolkata, India and also from uncontaminated farms about 50 km away from the city. A unified calibration approach was undertaken for the elemental analysis of the samples of widely varying matrices. The present study suggests that the elemental concentrations in the root soils and leaves of the samples vary from farm to farm, whereby the concentrations of Cu, Zn and Pb in root soils of MSW-contaminated farms are higher by almost an order of magnitude compared to uncontaminated farms. But, the most notable feature of this study is the strikingly similar elemental concentrations in the edible flower part of all samples irrespective of the type of soil.     

X-ray fluorescence activities at Saha Institute of Nuclear Physics,India

This paper covers different aspects related to X-ray fluorescence activities at Saha Institute of Nuclear Physics, Kolkata, India. In its first part, experiments on basic physical problems are illustrated and in the second part, some applications related to X-ray fluorescence are discussed.     

Quantifying uncertainties in the high-energy neutrino cross-section

The predictions for high-energy neutrino and antineutrino deep inelastic scattering cross-sections are compared within the conventional DGLAP formalism of next-to-leading order QCD, using the latest parton distribution functions (PDF) such as CT10, HERAPDF1.5 and MSTW08 and taking account of PDF uncertainties. From this, a benchmark cross-section and uncertainty are derived which is consistent with the results obtained earlier using the ZEUS-S PDFs. The use of this is advocated for analysing data from neutrino telescopes, in order to facilitate comparison between their results.     

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero – rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δx) ^α (and (Δt) ^α ) with 0 < α < 1; called as ‘fractional differentials’. For arbitrarily small Δx and Δt (tending towards zero), these ‘fractional’ differentials are greater than Δx (and Δt), i.e. (Δx) ^α > Δx and (Δt) ^α > Δt. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.     

Flowering to bloom of PeV scale supersymmetric left–right symmetric models

Unified models incorporating right-handed neutrino in a symmetric way generically possess parity symmetry. If this is broken spontaneously, it results in the formation of domain walls in the early Universe, whose persistence is unwanted. A generic mechanism for the destabilization of such walls is a small pressure difference signalled by difference in free energy across the walls. It is interesting to explore the possibility of such effects in conjunction with the effects that break supersymmetry in a phenomenologically acceptable way. This possibility when realized in the context of several scenarios of supersymmetry breaking, leads to an upper bound on the scale of spontaneous parity breaking, often much lower than the GUT scale. In the left–right symmetric models studied, the upper bound is no higher than 10¹¹ GeV but a scale as low as 10⁵ GeV is acceptable.     

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

Mechanistic Aspects of Ligand Substitution on the Hydroxopentaaquarhodium(III) Ion in Aqueous Solution by Sulfur‐Containing Bioactive Ligands

The kinetics of the interactions between three sulfur‐containing ligands, thioglycolic acid, 2‐thiouracil, glutathione, and the title complex, have been studied spectrophotometrically in aqueous medium as a function of the concentrations of the ligands, temperature, and pH at constant ionic strength. The reactions follow a two‐step process in which the first step is ligand‐dependent and the second step is ligand‐independent chelation. Rate constants (k₁ ～10^?3 s^?1 and k₂ ～10^?5 s^?1) and activation parameters (for thioglycolic acid: ΔH₁^≠ = 22.4 ± 3.0 kJ mol^?1, ΔS₁^≠ = ?220 ± 11 J K^?1 mol^?1, ΔH₂^≠ = 38.5 ± 1.3 kJ mol^?1, ΔS₂^≠ = ?204 ± 4 J K^?1 mol^?1; for 2‐thiouracil: ΔH₁^≠ = 42.2 ± 2.0 kJ mol^?1, ΔS₁^≠ = ?169 ± 6 J K^?1 mol^?1, ΔH₂^≠ = 66.1 ± 0.5 kJ mol^?1, ΔS₂^≠ = ?124 ± 2 J K^?1 mol^?1; for glutathione: ΔH₁^≠ = 47.2 ± 1.7 kJ mol^?1, ΔS₁^≠ = ?155 ± 5 J K^?1mol^?1, ΔH₂^≠ = 73.5 ± 1.1 kJ mol^?1, ΔS₂^≠ = ?105 ± 3 J K^?1 mol^?1) were calculated. Based on the kinetic and activation parameters, an associative interchange mechanism is proposed for the interaction processes. The products of the reactions have been characterized from IR and ESI mass spectroscopic analysis. A rate law involving the outer sphere association complex formation has been established as