Global Aspects of Age-Structured Cigarette Smoking Model

Smoking impacts health and as a result creates several problems related to age which means smoking has a strong correlation with age. Keeping this problem in view, we consider the global asymptotic properties of age-structured smoking model. First, we formulate the model and present the existence and uniqueness of solution. Then we discuss the equilibrium points and construct the Lyapunov function to examine global stability of the free smoking and positive smoking equilibrium points. Finally, we fixed the age factor and use the non-standard finite difference (NSFD) scheme for numerical solutions and compare our results obtained with RK4 and ODE45 graphically with the help of MATLAB.     

The exact Schrieffer–Wolff transformation

The effective s–d spin interaction is derived exactly for the single-impurity Anderson model via a unitary transformation. This unitary transformation was calculated up to infinite order and no restrictions were imposed upon the coefficients of the Hubbard interaction and the hybridization. We also discuss briefly the impact of the obtained result on the magnetic properties of several Kondo compounds. This will shed new light on the understanding of the competition between the Kondo effect and the Ruderman–Kittel–Kasuya–Yosida interaction and reinterpret the Doniach diagram.     

Majorana zero modes in graphene with trigonal warping

We study the low energy properties of warped monolayer graphene, where the symmetry of the original honeycomb lattice reveals itself. The zero energy solutions are Majorana fermions, whose wave function, originating from the corresponding modified Dirac equation is spatially localized. Experimental consequences are discussed. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface

Investigations on thin-film flow play a vital role in the field of optoelectronics and magnetic devices. Thin films are reasonably hard and thermally stable but quite fragile. The thermal stability of a thin film can be further improved by incorporating the effects of nanoparticles. In the current work, a stretchable surface is considered upon which hybrid nanofluid thin-film flow is taken into account. The idea of augmenting heat transmission by making use of a hybrid nanofluid is a focus of the current work. The flow is affected by variations in the viscous forces, along with viscous dissipation effects and Marangoni convection. A time-constrained magnetic field is applied in the normal direction to the flow system. The equations governing the flow system are shifted to a non-dimensional form by applying similarity variables. The homotopy analysis method is employed to find the solution to the resultant equations. It is noticed in this study that the flow characteristics decline with augmentation of magnetic, viscosity and unsteadiness parameters while they increase with enhanced values of thin-film parameters. Thermal characteristics are supported by increasing values of the Eckert number and the unsteadiness parameter and opposed by the viscosity parameter and Prandtl number. The numerical impact of different emerging parameters upon skin friction and the Nusselt number is calculated in tabular form. A comparison of current work with established results is carried out, with good agreement.     

Cross-coupling reactions towards the synthesis of natural products

Molecular Diversity - Cross-coupling reactions are powerful synthetic tools for the formation of remarkable building blocks of many naturally occurring molecules, polymers and biologically active...     

Square-root dynamics of a giving up smoking model

The paper presents a new giving up smoking model for which interaction term is square root of potential and occasional smokers of model presented in Zaman (2011) [15]. First, we will show formulation of the model. Then we will discuss local and global stability of the model and its general solutions. The non-standard finite difference method (NSFD) is used to solve the new giving up smoking model. Both non-negativity and conservative law for differential equations system are discussed. Numerical results are presented graphically and compared well with those obtained by Runge–Kutta fourth-order method (RK4) and ODE45.     

IC-100 accelerator complex for scientific and applied research

Industrial production of nuclear filters has been implemented at the IC-100 cyclotron complex of the Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research. After the complete upgrade, the cyclotron was equipped with the superconducting ECR ion source and the system of external axial beam injection. The implantation complex was equipped with the special transportation channel with the beam scanning system and the setup for irradiation of polymer films. Intense beams of heavy ions Ne, Ar, Fe, Kr, Xe, I, and W with an energy of ～1 MeV/nucleon were obtained. the properties of irradiated crystals were studied, different polymer films were irradiated, and several thousands of square meters of track membranes with pore densities varying in a wide range were produced. Other scientific and applied problems can be solved at the cyclotron complex.     

Analysis of ores by simple grinding and circular thin-layer chromatography and the nichrome wire ring chamber

Summary A method for the preparation of ore solutions by grinding the ore with distilled water is developed for the analysis of minerals and ores in the field by the circular thin-layer Chromatographic technique.

---

Zusammenfassung Die Herstellung von Erzlösungen durch Mahlen des Erzes mit dest. Wasser zur Feldanalyse von Mineralen und Erzen durch Ring-Dünnschichtchromatographie wird empfohlen.

     

Specific laws of polymer fracture

The results of an experimental verification of the activation concept of strength, first proposed by the author in 1952, are described. The theoretical conclusions are confirmed by tests on various vulcanizates, polystyrene, polymethyl methacrylate, cellophane, and polypropylene, New means of improving the strength of polymers are suggested.Mekhanika Polimerov, Vol. 4, No. 3, pp. 474–482, 1968