The method for calculating any analytic matrix function by means of symmetric polynomials is presented. The method of symmetric polynomials (MSP) is applied to the calculation of the fundamental matrix of a differential equations system. The scaling method is developed for computation of the scattering matrix. An analytical estimate of the scaling parameter, allowing the calculation of the matrix exponential with the required reliability and accuracy is obtained. This parameter depends on the matrix order n, the value of the matrix elements and layer thickness.

This study investigates the influence of nanoparticle concentration on the Marangoni effect in the boundary layer near the free boundary of an incompressible fluid with small kinematic viscosity and thermal conductivity. The study was conducted on the basis of a single-phase model derived from the Navier-Stokes equations by replacing thermal parameters for their effective values. Two cases of stationary axisymmetric fluid flow are considered. In the first case, the fluid is cooled on the free surface near the symmetry axis, and in the second case, the fluid is heated. In the first case, a rotation of the fluid in a thin boundary layer appears near the free boundary, while there is no rotation outside the layer. In both cases, as the concentration of nanoparticles increases, the heat flux and the fluid velocity at the free boundary decrease.

The asymmetric Stokes flow in a circular cylinder due to a rotlet is considered. This is a model for nanotube flow induced by a small rotating particle. The 3D Stokes and continuity equations are reduced to boundary problems for two scalar functions. Analytical solutions in terms of the Fourier transform is obtained.

The absorption of electromagnetic radiation by electrons of the quantum well is investigated. These calculations take into account the spin-orbit interaction (SOI) in the Rashba model. Analytical expression of the absorption coefficient is obtained. Resonant frequencies and positions of the resonance peaks were found.

The propagation of ultra-short optical pulses in a thin film created by graphene grown on a boron nitride base will be considered, taking into account the environment’s dispersion characteristics, electron conduction in such a system described by the framework of an effective long-wave Hamiltonian for low-temperature media. The electromagnetic field is taken as classical Maxwell’s. We reveal the dependence of the electric field on the maximum amplitude of ultra-short optical pulses, as well as on empirical dispersion constants.

The parameters of interatomic potential for 10 fcc metals are presented in this paper. The potential is based on the embedded atom method [6]. Parameters are determined empirically by fitting to the equilibrium lattice constant, cohesion energy, vacancy formation energy, bulk modulus and three elastic constants. The proposed potentials are suitable for atomistic computer simulations of practical applications in areas of material science and engineering.

 The pre-chromatography method of crude separation of light fullerenes (C₆₀ and C₇₀) is based on multistage processes of (re)crystallization — the solution of fullerenes solid solutions in liquid solvent (o-xylene) or in liquid o-xylene solutions at high temperature (85 ˚ C) and crystallization of solid solutions from saturated liquid solutions at low temperature (–20 ˚ C). As a result, for example, the initial standard fullerene extract may be efficiently divided into two different solid solutions — the first, considerably enriched in C₆₀ fullerene and the second, considerably enriched by the C₇₀ fullerene. In this separation process, the concentrate enriched by C₆₀, is also enriched in C₈₄. In that process, 98.6 mass % of C₆₀ was contained in the C₆₀- enriched concentrate (from the sum content of C₆₀ in the initial extract), simultaneously, 65.9 mass % of C₇₀ contained in the C₇₀-enriched concentrate (from the sum content of C₇₀ in the initial extract).

Nanoparticles of solid solutions in GdAlO₃ — GdFeO₃ system have been synthe- sized. Plots of crystalline sizes for GdAl₁−_xFe_xO₃ series versus GdFeO₃ composition have been constructed. The sizes of solid solution nanoparticles were shown to decrease in com- parison to the sizes of nanocrystalline individual compounds. The observed regularities allowed us to assume the formation of nanocrystalline GdAl₁−_xFe_xO₃ series with core-shell morphology.

The dielectric properties of monoclinic manganese tungstate have been studied as a function of frequency and temperature. It was found that the dielectric constant and dielectric loss for all temperatures had high values at low frequencies which decreased rapidly as frequency increased attaining a constant value at higher frequencies. The a.c. conductivity increased as frequency increased, conforming small polaron hopping. As temperature increased, the values of the a.c. conductivity are shifted to higher values. Higher values were also obtained when the particle size decreased. These properties make the nano-sized MnWO₄ as a promising material for fabricating humidity sensors.

A series of M-type hexagonal ferrites with BaCo_xFe_12−xO₁₉ (x = 2.0, 3.0) composition were synthesized using a simple heat treatment method. The aqueous solution, containing metal nitrates and polyvinyle pyrrolidone (PVP) as a capping agent was used to prepare M-type barium hexferrite nanoparticles. The prepared hexaferrite particles were calcined at microwave frequency (2.45 GHz, power 900W, 5 min) as well as at 650 ˚ C temperature. The structural properties of the samples were investigated using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). XRD pattern shows the pure M-phase. The particle size of the powder prepared by this method ranged from 20 nm to 27 nm. The thermal properties of the sample were investigated by thermogravimetric Analysis (TGA), which confirmed the thermal stability of the barium hexaferrite sample prepared by the heat treatment method.

Hydroxyapatite [Ca₁₀(PO₄)₆(OH)₂, HAp] is the major constituents of bones and hard tissues in mammals. In the last few years, HAp nanoparticles have been used as an ideal tool for the transformation of human hard tissues due to their high biocompatibility and easy biodegradability. Currently, metals are widely used in orthopedics to increase the bioactivity of hydroxyapatite. Among these metals, zinc is an essential trace element present in human bones and teeth. It plays important roles in increasing osteoblast adhesion and alkaline phosphatase activity of bone cells. In the present study, different amounts of pure and ZnO (0% – 43%) doped nano Hydroxyapatite powders were synthesized by the sol-gel method. The properties of pure and Zn doped nHAp powders were characterized using X-ray diffraction (XRD), Scanning electron microscopy (SEM), and Energy dispersive X-ray analysis (EDAX). The results of X-ray diffraction studies revealed the progressive increase in the average crystallite size from 49 to 100 nm with increasing ZnO concentration found to be 49–100 nm. The in vitro antimicrobial activities of the synthesized pure and Zn-doped nHAp powders were investigated against gram-negative bacterial strains using the disc diffusion method. The antimicrobial activities of pure and doped nHAp samples were observed irrespective of the ZnO content.

In this paper, we use the finite difference time-domain (FDTD) method to optimize the TE-polarized light transmission of a metal-semiconductor-metal photodetector (MSM-PD) employing a dielectric waveguide on top of metal nano-gratings. Simulation results demonstrate that the funneling transmission of the TE-polarized light through the nanoslit of the MSM-PD structure is highly dependent on the structure geometries, such as the waveguide and nano-grating heights. We also demonstrate that adding a dielectric waveguide layer on top of the nano-metal gratings supports both the TM- and TE polarizations, and enhances the light transmission for TE-polarization around 3-times in comparison with conventional plasmonics MSM- PD structures.

In this paper, we investigate the impact of silver thin film thickness and annealing temperatures for the fabrication of silver nano-particles of controlled size and spacing distributions. We also use these mea- sured distributions to predict the performance of subwavelength grating structures developed using dry and isotropic etching of semiconductor substrates. Silver (Ag) thin films of different thicknesses were deposited on Si and GaAs semiconductor substrates and annealed at different temperatures. Experimental results demonstrate that by annealing the Ag thin films with different temperature profiles it is feasible to develop Ag nanoparticles of an average diameter ranging from 50 nm to 400 nm on silicon substrates and 100 nm to 500 nm on GaAs substrates. In addition, different subwavelength structures developed by etching the Ag nanoparticle deposited Si and GaAs substrates are simulated using a Finite-Difference Time Domain (FDTD) software package. Simulation results show that substantial reduction in light reflection can be achieved by optimizing the heights of the subwavelength structures through the control of the etching process time.

Li+ co-doped ZnO:Tb3+ nanocrystals were synthesized via the chemical co-precipitation method in order to study the effect of Li+ co-doping. The samples were characterized by means of SEM, XRD, FTIR, Reflectance, PL and TL studies. SEM images showed that the samples were composed of nanorods with diameters of 50 to 90 nm and lengths of approximately 600 nm to 1.3 µm. XRD analysis revealed pure phase of ZnO with hexagonal wurtzite structure. XRD study also showed no change in the peak pattern for Li+ co-doping; a slight shift of the (101) peaks towards lower angle can be seen. Sample crystal sizes were found to be in the 10–25 nm range. Photoluminescence intensity was enhanced due to a minute amount of Li+ co-doping in the sample. The X-induced thermoluminescence gave a glow peak at 320 ˚ C for the Li+ co-doped sample, which was shifted to a lower temperature and had twice the intensity of the ZnO:Tb3+ sample.

We report the transport behavior of an open-end metallic single wall carbon nanotube (SWCNT) with and without local structural defects using the non-equilibrium Green’s functions approach together with the density functional theory (DFT). The transmission spectra and the projected density of states for the devices such as SWCNT (3, 3), (4, 4), (5, 5) and (6, 6) with and without defects were compared. In all cases, we found that the Stone-Wales defect had an almost negligible impact on the electrical performance compared to the monovacancy defect of the single wall carbon nanotubes at the Fermilevel. The Current-Voltage (I-V) characteristics of the devices were studied using the generalized Landauer - Buttiker formalism under low bias conditions. From our results, we concluded that our systems were suitable for use in various CNT based nano-electronic devices.

In an effort to improve the corrosion resistance of monolayer Zn-Ni alloy coatings, nanostructure multilayer coating (NMC) has been developed using a pulsed current. Successive layers of alloys with alternately changing compositions were deposited on mild steel (MS) by making the cathode current cycle between two values during deposition. Multilayer coatings with different configurations in terms of composition and number of layers were developed and their corrosion behaviors were studied by electrochemical methods. The effect of cyclic cathode current densities (CCCD’s), and the number of layers have been studied, and coating configurations have been optimized for highest corrosion resistances. Multilayer coatings and their degradation during corrosion were confirmed by Scanning Electron Microscopy (SEM) analysis. The improved corrosion resistance of NMC in relation to monolayer alloy coatings, deposited from same bath has been analyzed and results were discussed in terms of increased number of interfaces due to layering.

This paper discusses adaptive noise cancellation in magnetocardiographic systems within unshielded environment using two algorithms, namely, the Least-Mean-Squared (LMS) algorithm and the Genetic Algorithm (GA). Simu- lation results show that the GA algorithm outperforms the LMS algorithm in extracting a weak heart signal from a much-stronger magnetic noise, with a signal-to-noise ratio (SNR) of -35.8 dB. The GA algorithm displays an improvement in SNR of 37.4 dB and completely suppresses the noise sources at 60Hz and at low frequencies; while the LMS algorithm exhibits an improvement in SNR of 33 dB and noisier spectrum at low frequencies. The GA algorithm is shown to be able to recover a heart signal with the QRS and T features being easily extracted. On the other hand, the LMS algorithm can also recover the input signal, however, with a lower SNR improvement and noisy QRS complex and T wave.

Realizing large anisotropic electrical conductivity in systems wherein the magnitude of the anisotropy can be switched and controlled by employing an external field such as magnetic, electrical or optical fields is of significant interest. The large electrical conductivities possible with carbon nanotubes (CNT) have been combined with the field-switchable orientation of liquid crystals (LC), although the stabilization of such composites is a difficult proposition. Recently we have performed measurements over reasonable lengths of time where the LC-CNT composites are stable without any serious segregation. Here, we describe the results of electrical conductivity, which establish that the LC-CNT composites have a bright future in applications using switchable electrical insulator-conductor devices, for example Mott insulator-conductor systems. The added advantage, as a result of LC use, is the phenomenal ease with which large scale devices can be fabricated. The present work also discusses possible methods for increasing the loading factor, which currently is quite low.

Cobalt ferrite nanoparticles have been synthesized by the sol-gel method. The prepared sample was sintered at four different temperatures (300 ˚ C, 400 ˚ C, 500 ˚ C and 700 ˚ C) for four hours. The structural charac- terizations of all the prepared samples were done using XRD, TEM and FTIR. Crystallite size was found to increase with sintering temperature and this can be attributed to the grain growth of the particles. The par- ticle size of each sample was determined using TEM. The FTIR spectra show two strong absorption bands in the range of 1000–400 cm−1, characteristic of spinel ferrites. The room temperature magnetic measurements showed a strong influence of sintering temperature on saturation magnetization and coercivity