A study of the fractional‐order mathematical model of diabetes and its resulting complications

Diabetes is a worldwide problem that affects one of every 11 persons nowadays. The IDF Diabetes Atlas (Eighth edition, 2017) states that approximately 415 million people in the world are living with the disease and that this number will rise to 629 million by the year 2045. It is a very serious problem of the world. A major part of the world population is affected by this disease and its resulting complications. In this paper, we propose to investigate a fractional‐order model of diabetes and its resulting complications. The mathematical model's parameters define the population of diabetic patients and those who are diabetic with complications at a given time t. We have also discussed the existence, uniqueness, and stability of the fractional‐order model, which we consider here. We make use of the homotopy decomposition method (HDM) in order to solve the problem.     

Diffusion-induced parametric dispersion and amplification in doped semiconductor plasmas

Using the hydrodynamic model of semiconductor plasma, the diffusion-induced nonlinear current density and the consequent second-order effective susceptibility are obtained under off-resonant laser irradiation. The analysis deals with the qualitative behaviour of the anomalous parametric dispersion and the gain profile with respect to the excess doping concentration and pump electric field. The analysis suggests that a proper selection of doping level and pump field may lead to either positive or negative enhanced parametric dispersion, which can be of great use in the generation of sequeezed states. It is found that gain maximizes at moderate doping concentration level, which may drastically reduce the fabrication cost of parametric amplifier based on this interaction.      

Effective refractive index and intermolecular forces associated with a phase of functional groups

Cases in which a functional groups form distinct phases are known in material science in general and specifically in polymer and surfactant sciences. To calculate the van der Waals forces associated with such phases there is a need to evaluate the refractive index of those phases. We expand and generalize a method to estimate the refractive index of such ‘functional group phase’ and discuss how to use the refractive indices to calculate the interaction energies associated with such functional group phases and thereby modify the total theoretically calculated van der Waals forces.     

Semiclassical statistical mechanics ofv-dimensional fluid mixture of hardv-spheres

The problem of calculating the equilibrium properties ofv-dimensional fluid mixture of hardv-spheres is studied. High temperature expansion for the density independent radial distribution function is derived for a hardv-sphere mixture. The ‘excess’ quantum corrections to the second virial coefficient and the excess free energy are also studied. Significant features are the large increase in ‘excess’ quantum correction with increasing dimensionality.     

Equilibria and kinetics for pH-dependent axial ligation of bromomethyl(aquo)cobaloxime by aliphatic amine ligands

Kinetics and equilibria of axial ligation of bromomethyl(aquo) cobaloxime by a series of straight chain primary amines (methylamine, ethylamine, propylamine, butylamine, pentylamine, hexylamine), cycloamines (cyclopentylamine, cyclohexylamine, cycloheptylamine) and secondary amines (N,N-dimethylamine, N,N-diethylamine) have been measured as functions of pH by spectrophotometric technique in aqueous solution, ionic strength 1 M (KCl) at 25°C. The rate of substitution of H₂O varies with the pKa of incoming ligand, thus establishing nucleophilic participation of the ligand in the transition state. Binding and kinetic data are interpreted based on the basicity and steric influence of the entering ligand. To compare the rate constants of the entering ligands, pH independent second-order rate constants (k _on ) are calculated.     

A highly sensitive and selective hydrogen gas sensor from thick oriented films of MoS2

A new process is developed to fabricate a highly sensitive and selective hydrogen sensor by depositing a partially crystalline and highly oriented film of MoS₂ from its single layer suspension on an alumina substrate. When these films are promoted with some catalysts selected from Pt-group metals (Pt, Pd, Ru or any combination of these metals) they exhibit a high sensitivity and selectivity to hydrogen gas. Unlike other metal oxide sensors which are sensitive to many reducing and oxidizing gases and operate at a temperature of 350 °C or higher; this sensor is highly selective to hydrogen gas and its operating temperature is from 25 to 150°C. The lower operating temperature enhances safety when dealing with hydrogen gas. The sensor response to hydrogen at 120 °C is linear in concentration from 30 to 10⁴ ppm with a 10 to 30 second response time and a 45 to 90 second recovery time. Above 10⁴ ppm the sensor is still linear but the slope of conductance versus hydrogen concentration changes.     

A useful elementary correlation inequality

An inequality is given that enables one to estimate the probability of a conjunction by the product of the probabilities when the events have low correlation.