Volume 13, Issue 1

We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222 Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.

The influence of an incoming boundary layer to the standing morphology of an oblique detonation wave (ODW) induced by a compression ramp is numerically studied in this paper. The Spalart-Allmaras (SA) turbulence model is used to perform simulation of detonationboundary- layer interactions. Three different wall conditions are applied to realize control on the boundary-layer separation scales. Accordingly, different standing morphologies of the ODWs are obtained, including smooth ODW (without transverse wave) under no-slip, adiabatic wall condition with large-scale separation, abrupt ODW (with transverse wave) under no-slip, cold wall condition with moderate-scale separation, and bow-shaped detached ODW under slipwall condition without a boundary layer.

Neutrino oscillations present the only robust example of experimentally detected physics beyond the standard model. This review discusses the established and several hypothetical beyond standard models neutrino characteristics and their cosmological effects and constraints. Particularly, the contemporary cosmological constraints on the number of neutrino families, neutrino mass differences and mixing, lepton asymmetry in the neutrino sector, neutrino masses, light sterile neutrino are briefly reviewed.

A systematic experimental Raman spectroscopic study of twisted bilayer graphene (tBLG) domains localized inside wide-area single layer graphene (SLG) produced by low-pressure CVD on Cu foil and transferred onto SiO 2 /Si substrate has been performed. According to the Raman characterization the tBLG domains had a great variety of twisting angles θ between the bottom and top graphene layers (6° < θ < 25°). The twisting angle θ was estimated from the spectral position of the rotating R and R' modes in the Raman spectrum.Under G band resonance conditions the breathing mode ZO' with a frequency of 95- 97 cm −1 was detected, and a breathing mode ZO was found in the spectra between 804 cm −1 and 836 cm −1 , its position depending on the twisting angle θ. An almost linear relationship was found between the frequencies ω ZO and ω R . Also a few other spectral peculiarities were found, e.g. a high-energy excitation of the G band resonance, the 2G overtone appearing at 3170-3180 cm −1 by the G band resonance, revealing a linear dispersion of 80 cm −1 /eV of the 2D band in tBLG

The photon-number distribution between two parts of a given volume is found for an arbitrary photon statistics. This problem is related to the interaction of a light beam with a macroscopic device, for example a diaphragm, that separates the photon flux into two parts with known probabilities. To solve this problem, a Generalized Binomial Distribution (GBD) is derived that is applicable to an arbitrary photon statistics satisfying probability convolution equations. It is shown that if photons obey Poisson statistics then the GBD is reduced to the ordinary binomial distribution, whereas in the case of Bose- Einstein statistics the GBD is reduced to the Polya distribution. In this case, the photon spatial distribution depends on the phase-space volume occupied by the photons. This result involves a photon bunching effect, or collective behavior of photons that sharply differs from the behavior of classical particles. It is shown that the photon bunching effect looks similar to the quantum interference effect.

Realistic network-like systems are usually composed of multiple networks with interacting relations such as school-enterprise research and development (R&D) collaboration networks. Here, we study the percolation properties of a special class of R&D collaboration network, namely institute-enterprise R&D collaboration networks (IERDCNs). We introduce two actual IERDCNs to show their structural properties, and we present a mathematical framework based on generating functions for analyzing an interacting network with any connection probability. Then,we illustrate the percolation threshold and structural parameter arithmetic in the sub-critical and supercritical regimes.We compare the predictions of our mathematical framework and arithmetic to data for two real R&D collaboration networks and a number of simulations. We find that our predictions are in remarkable agreement with the data. We show applications of the framework to electronics R&D collaboration networks

This article makes a brief review of the most important results obtained by the authors and their collaborators during the last four years in the field of the development of metal-insulator-silicon structures with dielectric film containing silicon nanocrystals, which are suitable for applications in radiation dosimetry. The preparation of SiOx films is briefly discussed and the annealing conditions used for the growth of silicon nanocrystals are presented. A two-step annealing process for preparation of metal-oxide-semiconductor structures with three-layer gate dielectrics is described. Electron Microscopy investigations prove the Si nanocrystals growth, reveal the crystal spatial distribution in the gate dielectric and provide evidences for the formation of a top SiO2 layerwhen applying the two-step annealing. Two types of MOS structures with three region gate dielectricswere fabricated and characterized by high frequency capacitance/conductancevoltage (C/G-V) measurements. The effect of gamma and ultraviolet radiation on the flatband voltage of preliminary charged metal-oxide-semiconductor structures is investigated and discussed.

In this work, the differences in nanomechanical properties, topography and morphology of carbonpalladium (C-Pd) films were studied. These films were prepared with a Physical Vapour Deposition method on various substrates with different technological parameters. We show that duration of the PVD process is a crucial factor affecting the palladium content in these films. The differences in thickness of films depend on the distance between source boats and substrates. The nanomechanical properties of C-Pd films were studied with nanoindentation. Their topography and morphology was ascertained with Atomic Force Microscopy and Scanning Electron Microscopy. It was found that the mechanical properties of C-Pd films depend on the content of palladium and on the morphology and topography of these films. The various types of carbon-palladium films containing palladium nanograins incorporated in a carbon matrix that were, investigated in this paper, seem to be promising materials for numerous applications.

Iron and nitrogen co-modified titanium dioxide nanocomposites, nFe,N-TiO 2 (where n = 1, 5 and 10 wt% of Fe), were investigated by detailed dc susceptibility and magnetization measurements. Different kinds of magnetic interactions were evidenced depending essentially on iron loading of TiO 2 . The coexistence of superparamagnetic, paramagnetic and ferromagnetic phases was identified at high temperatures. Strong antiferromagnetic interactions were observed below 50 K, where some part of the nanocomposite entered into a long range antiferromagnetic ordering. Antiferromagnetic interactions were attributed to the magnetic agglomerates of iron-based and trivalent iron ions in FeTiO 3 phase,whereas ferromagnetic interactions stemmed from the F-center mediated bound magnetic polarons.

The eigenvalues E d nl (a, c) of the d-dimensional Schrödinger equation with the Cornell potential V(r) = −a/r + c r, a, c > 0 are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is suffcient to know E(1, λ), and the envelope method provides analytic bounds for the equivalent complete set of coupling functions λ(E). Meanwhile the easily-implemented AIM procedure yields highly accurate numerical eigenvalues with little computational effort.

In this paper we have studied the Kantowski- Sachs cosmological model with the quark and strange quark matter in the f (R) theory of gravity. The general solutions of the field equations are obtained by assuming the physical condition shear scalar σ is proportional to scalar expansion θ, which leads to the relation B = An between metric coefficients B and A. The physical and geometrical aspects of the model are also discussed.

We reconsider the idea in spectroscopy of detecting extra dimensions by regarding the nucleus as a homogeneous sphere. In our results, it turns out that the gravitational potential inside the nucleus is much stronger than the potential induced by a particle in the same regime in ref. [16], and thus a more significant correction of the ground state energy of hydrogen-like atoms is obtained, which can be used to determine the existence of ADD’s extra dimensions. In order to get a larger order of magnitude for the correction, it is better to apply our theory to high-Z atoms or muonic atoms, where the volume of the nucleus can’t be ignored and the relativistic effect is important. Our work is based on the Dirac equation in aweak gravity field, and the result is more precise.

The inherent irreversibility in a steady hydromagnetic permeable channel flow of a conducting fluid with variable electrical conductivity and asymmetric Navier slip at the channel walls in the presence of induced electric field is theoretically investigated. The model nonlinear governing equations are obtained and numerically solved using shooting quadrature. Numerical results for velocity and temperature profiles are utilised to compute the entropy generation number and the Bejan number. Pertinent results are displayed graphically and discussed quantitatively.

This paper focuses on the single state feedback stabilization problem of unified chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled unified chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the unified chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the effectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

The aim of this work is to examine the environmental dependence of stellar velocity dispersion in local galaxies. In studies that likely suffer from the radial selection effect, one has a preference for the use of volumelimited samples. Two volume-limited samples with different redshift and luminosity ranges were constructed from the Main galaxy data of the Sloan Digital Sky Survey Data Release 10 (SDSS DR10). Considering some drawbacks of volume-limited samples, the apparent magnitude-limited Main galaxy sample was also applied. Statistical analyses in these different galaxy samples can reach the same conclusion: galaxies with large stellar velocity dispersions exist preferentially in high density regimes, while galaxies with small stellar velocity dispersions are located preferentially in low density regions, which is inconsistent with that obtained at intermediate redshifts.

In a cosmological perspective, gravitational induction is explored as a source to mechanical inertia in line with Mach’s principle. Within the standard model of cosmos, considering the expansion of the universe and the necessity of retarded interactions, it is found that the assumed dynamics may account for a significant part of an object’s inertia.

In this paper, the magnetohydrodynamic (MHD) Maxwell fluid past a stretching plate with suction/ injection in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations are solved numerically using Bvp4c with MATLAB, which is a collocation method equivalent to the fourth order mono-implicit Runge-Kutta method. The effects of some physical parameters, such as the elastic parameter K, the Hartmann number M, the Prandtl number Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le, on the velocity, temperature and nanoparticle fraction are studied numerically especially when suction and injection at the sheet are considered.

The high temperature and pressure effects on the elastic properties of the AgRE (RE=Sc, Tm, Er, Dy, Tb) intermetallic compounds with B2 structure have been performed from first principle calculations. For the temperature range 0-1000 K, the second order elastic constants for all the AgRE intermetallic compounds follow a normal behavior: they decrease with increasing temperature. The pressure dependence of the second order elastic constants has been investigated on the basis of the third order elastic constants. Temperature and pressure dependent elastic anisotropic parameters A have been calculated based on the temperature and pressure dependent elastic constants.

This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium.

In this paper, we use some well-known techniques of Supersymmetric QuantumMechanics (SUSYQM) namely the factorization method and shape invariance, to generate new analytically solvable potentials from some interacting fermionic models in nonrelativistic limits. These systems are described by the ordinary and the harmonically trapped Schrödinger-Pauli particle models and the Dirac-Coulomb Hamiltonian, this latter being set in its nonrelativistic limits. The spectrum for each of these models is obtained in a simple and transparent way. We then generate new solvable potentials that describe interactions between electromagnetic field and matter, paying due attention to the subtleties inherent in the application of SUSY to higher dimensional problems. SUSY breaking problems related to the partner singularities are dicussed along with the paper.

Fractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier’s lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier’s law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σ x and σ t with dimensions of meters and seconds respectively. The fractional derivative of Caputo type is considered and the analytical solutions are given in terms of the Mittag-Leffler function. The generalization of the equations in spacetime exhibit different cases of anomalous behavior and Non-Fourier heat conduction processes. An illustrative example is presented.

In this work, we consider a fractional nonlinear vibration system of Duffing type with harmonic excitation by using the fractional derivative operator -∞ −1D α t and the averaging method. We derive the steady-state periodic response and the amplitude-frequency and phase-frequency relations. Jumping phenomena caused by the nonlinear term and resonance peaks are displayed, which is similar to the integer-order case. It is possible that a minimum of the amplitude exists before the resonance appears for some values of the modelling parameters, which is a feature for the fractional case. The effects of the parameters in the fractional derivative term on the amplitude-frequency curve are discussed.

Gadolinium neutron capture therapy (GdNCT) is used for treatment of radioresistant malignant tumors. The absorbed dose in GdNCT can be divided into four primary dose components: thermal neutron, fast neutron, photon and natural gadolinium doses. The most significant is the dose created by natural gadolinium. The amount of gadolinium at the irradiated region is changeable and depends on the gadolinium delivery agent and on the structure of the location where the agent is injected. To de- fine the time dependence of the gadolinium concentration ρ(t) in the irradiated region the pharmacokinetics of gadolinium delivery agent (Magnevist) was studied at intratumoral injection in mice and intramuscular injection in rats. A polynomial approximation was applied to the experimental data and the influence of ρ(t) on the relative change of the absorbed dose of gadolinium was studied.

This work concentrates on stagnation point flow of a nanofluid over an impermeable stretching cylinder with mass transfer and slip effects. Carbon nanotubes (CNTs) and water are used as a nanofluid in the present investigation. Two types of CNTs are used as nanoparticles (i) Single-wall carbon nanotubes (SWCNTs) and (ii) multiwall carbon nanotubes (MWCNTs). Appropriate transformations are used to achieve a system of ordinary differential equations. Convergent series solutions are obtained. Behavior of various parameters on the velocity, temperature and concentration profiles are discussed graphically. Numerical values of skin friction coefficient, Nusselt number and Sherwood number are computed and analyzed.

We investigate the effects of phase shift on entanglement, quantum discord, geometric discord, and spinsqueezing of a Heisenberg chain under dephasing. An analytical solution of the present model is obtained. Our results show that the initial correlations of the spin chain could be partially stored for a long time in the presence of dephasing and the amount of steady state correlations can be adjusted via phase shift. Particularly, we find the effects of phase shift on quantum discord and geometric discord are not always the same, i.e., the increase of geometric discord does not always imply the increase of quantum discord. Then, we calculate the spin-squeezing of the spin chain and find that spin-squeezing first increases with time and then reaches a plateau. The amount of spin-squeezing can be controlled via phase shift.

Based on the bosonization approach, the N = 1 supersymmetric Burgers (SB) system is transformed to a coupled pure bosonic system. The Painlevé property and the Bäcklund transformations (BT) of the bosonized SB (BSB) system are obtained through standard singularity analysis. Explicit solutions such as the muti-solitarywaves and error functionwaves are provided for the BT. The exact solutions of the BSB system are obtained from the generalized tanh expansion method.

This paper is devoted to the analysis of the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer on a permeable stretching sheet embedded in a moving incompressible viscous fluid. The combined effects of Ohmic heating, thermal radiation, frictional heating and internal heat absorption/generation are taken into account. The governing time dependent nonlinear boundary layer equations are converted into a systemof nonlinear ordinary differential equations by similarity transformations. Some analytical results that give the characteristics of the velocity field in the boundary layer are presented and proved. The governing equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The analytical properties proved in this paper are consistent with those obtained by the numerical method. Furthermore, the effects of the various parameters on the velocity and temperature fields are presented graphically and discussed in detail.

The concept of "primacy" as introduced by Jefferson in 1939 in urban geography leads to the notion of "dominant city" also known as the primate city. Practically, the notion was extended by Sheppard in view of discussing some "hierarchy". The type of dominance is not universal nor any hierarchy reversal. Both can be time and sample dependent. Thus, as an example taking into consideration the existence of both pieces of the puzzle, we consider and discuss the Bulgarian urban system. It is also interesting to compare data on two groups of cities in different time intervals: (i) the whole Bulgaria city system which contains about 250 cities, - studied in the time interval between 2004 and 2011, and (ii) a system of 33 cities, - studied over the time interval 1887 till 2010. These latter cities are selected because the population was already over 10 000 inhabitants in 1946. It is shown that new additional indices are interestingly introduced in order to compensate defects in the Sheppard index. Numerical illustrations are illuminated through a "length ratio" measure, which allows to distinguish the (often) observed departures from the hyperbolic ranking seen by Jefferson.

The effect of turbulence on propagating laser beams has been a subject of interest since the evolution of lasers back in 1959. In this work, an inexpensive and reliable technique for producing interferograms using a point diffraction interferometer (PDI) was considered to experimentally study the turbulence effects on a laser beam propagating through air. The formed interferograms from a propagating beamwere observed and digitally processed to study the strength of atmospheric turbulence. This technique was found to be sensitive enough to detect changes in applied temperature with distance between the simulated turbulence and laser path. These preliminary findings indicated that we can use a PDI method to detect and localise atmospheric turbulence parameters. Such parameters are very important for use in the military (defence laser weapons) and this is vital for South Africa (SA) since it has natural resources, is involved in peace keeping and mediation for other countries, and hence must have a strong defence system that will be able to locate, detect and destroy incoming missiles and other threatening atmospheric systems in order to protect its environment and avoid the initiation of countermeasures on its land.

Development of resistance limits efficiency of present anticancer therapies and preventing it remains a big challenge in cancer research. It is accepted, at the intuitive level, that resistance emerges as a consequence of the heterogeneity of cancer cells at the molecular, genetic and cellular levels. Produced by many sources, tumor heterogeneity is extremely complex time dependent statistical characteristics which may be quantified by measures defined in many different ways, most of them coming from statistical mechanics. In this paper, we apply the Markovian framework to relate population heterogeneity to the statistics of the environment. As, from an evolutionary viewpoint, therapy corresponds to a purposeful modi- fication of the cells’ fitness landscape, we assume that understanding general relationship between the spatiotemporal statistics of a tumor microenvironment and intratumor heterogeneity will allow to conceive the therapy as an inverse problem and to solve it by optimization techniques. To account for the inherent stochasticity of biological processes at cellular scale, the generalized distancebased concept was applied to express distances between probabilistically described cell states and environmental conditions, respectively.

Thermodynamic properties of semiconductor compounds have been studied based on Debye-Waller factors (DWFs) described by the mean square displacement (MSD) which has close relation with the mean square relative displacement (MSRD). Their analytical expressions have been derived based on the statistical moment method (SMM) and the empirical many-body Stillinger-Weber potentials. Numerical results for the MSDs of GaAs, GaP, InP, InSb, which have zinc-blende structure, are found to be in reasonable agreement with experiment and other theories. This paper shows that an elements value for MSD is dependent on the binary semiconductor compound within which it resides.

In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

In the paper, spin waves in a ferromagnetic nanotube of an elliptic cross-section in the presence of a spinpolarized electric current are investigated. The linearized Landau-Lifshitz equation in themagnetostatic approximation is used, with the exchange interaction, the dipoledipolemagnetic interaction, the anisotropy effects and the dissipation effects taken into account; the influence of the spin-polarized current is considered by the Slonczewski- Berger term. After elimination of the magnetization density perturbation, an equation for the magnetic potential for the above-described spin excitations is obtained. From this equation, a dispersion relation for spin waves in the nanosystem described previously is obtained. Analysis of the dispersion relation shows that the presence of the spinpolarized current can strengthen or weaken the dissipation, creating an “effective dissipation”; the effect is analogous to the “effective dissipation” in a two-layer ferromagnetic film in the presence of a spin-polarized current. Depending on the direction and the density of the current the spinwave can decay faster or slower than in the absence of the current, transform into a self-sustained wave or grow in amplitude, thus leading to a spin wave generation.

Using two volume-limited Main galaxy samples of the Sloan Digital Sky Survey Data Release 10 (SDSS DR10), we examine the environmental dependence of galaxy age at fixed parameters or for different galaxy families. Statistical results show that the environmental dependence of galaxy age is stronger for late type galaxies, but can be still observed for the early types: the age of galaxies in the densest regime is preferentially older than that in the lowest density regime with the same morphological type. We also find that the environmental dependence of galaxy age for red galaxies and Low Stellar Mass (LSM) galaxies is stronger, while the one for blue galaxies and High Stellar Mass ( HSM ) galaxies is very weak.

In contrast to one-component Bose-Einstein condensate case, the vortices in two-component condensate can have various complicated structures. The vortices in a space-homogeneous Bose-Einstein condensate have been studied in this paper. It is shown that the vortex structure is described by three dimensionless parameters. This is totally different from the usual one-component condensate case,where an isolated vortex is described by a parameterless dimensionless equation. The two-component vortex structure strongly depends on the sign of “interaction” constant of the components. A few types of vortices with different qualitative structure are explored. We show that the “super-density vortices” can exist, when the “interaction” constant is positive. The “super-density vortices” have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We also show that the vortices with opposite direction of the condensate component rotation near the axis and far off the axis can exist.

A systematic dependence of Grodzins product (E(2 + 1 ) * B(E2)↑) on the asymmetry parameter Υ 0 is studied in the Z = 50 − 82, N = 82 − 126 major shell space. The Grodzins product provides contributions of E(2 + 1 ) and B(E2) " simultaneously, which further reflects the shape phase transitions with asymmetry parameter 0. In the region of deformed nuclei, Grodzins product (E(2 + 1 )*B(E2)↑) shows direct dependence on the asymmetry parameter 0. We discuss here for the first time the correlation between Grodzins product (E(2 + 1 ) * B(E2)↑) and the asymmetry parameter Υ 0 .

In this paper, the AKNS isospectral problem and its corresponding time evolution are generalized by embedding three coefficient functions. Starting from the generalizedAKNS isospectral problem, a mixed spectralAKNS hierarchy with variable coefficients is derived. Thanks to the selectivity of these coefficient functions, the mixed spectral AKNS hierarchy contains not only isospectral equations but also nonisospectral equations. Based on a systematic analysis of the related direct and inverse scattering problems, exact solutions of the mixed spectral AKNS hierarchy are obtained through the inverse scattering transformation. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. This paper shows that the AKNS spectral problem being nonisospectral is not a necessary condition to construct a nonisospectral AKNS hierarchy and that the inverse scattering transformation can be used for solving some other variable-coefficient mixed hierarchies of isospectral equations and nonisospectral equations.

We investigate the dynamical properties of the two-boson quantum walk in systems with different degrees of coherence, and where the effect of the coherence on the two-boson quantum walk can be naturally introduced. A general analytical expression for the two-boson correlation function, for both pure states and mixed states, is given.We propose a possible two-photon quantum-walk scheme with a mixed initial state, and find that the twophoton correlation function and the average distance between two photons can be influenced by the initial photon distribution, the relative phase, or the degree of coherence. The propagation features of our numerical results can be explained by our analytical two-photon correlation function.

Direct analytical calculations of the static dielectric permittivity-dependent electron mobility due to different elastic scattering mechanisms for n-type InSb were carried out. The calculated static dielectric permittivity increases by increasing of donor concentration. The temperature dependence of the electron mobility from 10 K up to 300 K has been demonstrated. Generally, the electron mobility shows peak behavior in this range of temperatures. The direct correlation between the electron mobility and the static dielectric permittivity at 300 K was investigated. The dependence of the electron mobility on donor concentration was discussed both when the static dielectric permittivity is assumed to be varying and when it is assumed to be a constant. The difference in behavior was noticed particularly at high donor concentrations.

It is assumed that the two-component spinor formalisms for curved spacetimes that are endowed with torsionful affine connexions can supply a local description of dark energy in terms of classical massive spin-one uncharged fields. The relevant wave functions are related to torsional affine potentials which bear invariance under the action of the generalized Weyl gauge group. Such potentials are thus taken to carry an observable character and emerge from contracted spin affinities whose patterns are chosen in a suitable way. New covariant calculational techniques are then developed towards deriving explicitly the wave equations that supposedly control the propagation in spacetime of the dark energy background. What immediately comes out of this derivation is a presumably natural display of interactions between the fields and both spin torsion and curvatures. The physical properties that may arise directly fromthe solutions to thewave equations are not brought out.

2-D(Two-dimensional) isotropic negative refractive index (NRI) is explicitly realized via the orthogonal signal and coupling standing-wave fields coupling the Ntype four-level atomic system. Under some key parameters of the dense vapour media, the atomic system exhibits isotropic NRI with simultaneous negative permittivity and permeability (i.e. left-handedness) in the 2-D x-y plane. Compared with other 2-D NRI schemes, the coherent atomic vapour media in our scheme may be an ideal 2-D isotropic NRI candidate and has some potential advantages, significance or applications in the further investigation.

In the present study,we investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Burgers’ model in an inclined tube. We suppose that the viscosity is variable in the radial direction. This analysis has been carried out under low Reynolds number and long-wavelength approximations. An analytical solution to the problem is obtained using a fractional calculus approach. Figures are plotted to show the effects of angle of inclination, Reynolds number, Froude number, material constants, fractional parameters, parameter of viscosity and amplitude ratio on the pressure gradient, pressure rise, friction force, axial velocity and on the mechanical efficiency.

In this paper, a new computational algorithm called the "Improved Bernoulli sub-equation function method" has been proposed. This algorithm is based on the Bernoulli Sub-ODE method. Firstly, the nonlinear evaluation equations used for representing various physical phenomena are converted into ordinary differential equations by using various wave transformations. In this way, nonlinearity is preserved and represent nonlinear physical problems. The nonlinearity of physical problems together with the derivations is seen as the secret key to solve the general structure of problems. The proposed analytical schema, which is newly submitted to the literature, has been expressed comprehensively in this paper. The analytical solutions, application results, and comparisons are presented by plotting the two and three dimensional surfaces of analytical solutions obtained by using the methods proposed for some important nonlinear physical problems. Finally, a conclusion has been presented by mentioning the important discoveries in this study.

This paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x 0 , y 0 ) is used. The integrals that appear in this method are computed exactly and some of these integrals are computed with the Cauchy principal value without using numerical quadratures. The solution in the Legendre polynomial form generates a system of linear algebraic equations, this system is solved numerically. Through numerical examples, performance of the present method is discussed concerning the accuracy of the method.

In this paper, multivariate Padé approximation is applied to power series solutions of nonlinear diffusion equations. As it is seen from tables, multivariate Padé approximation (MPA) gives reliable solutions and numerical results.

Firstly in this article, the exact solution of a time fractional Burgers’ equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger’s equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter ~ which we also determine. The numerical solution of Burgers’ equation with the analytical solution obtained by using the Hopf-Cole transform is compared.

In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.

In this paper, we are concerned with the oscillatory behavior of a class of fractional differential equations with functional terms. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a certain variable transformation, by using a generalized Riccati transformation, generalized Philos type kernels, and averaging techniques we establish new interval oscillation criteria. Illustrative examples are also given.

All technical systems have been designed to perform their intended tasks in a specific ambient. Some systems can perform their tasks in a variety of distinctive levels. A system that can have a finite number of performance rates is called a multi-state system. Generally multi-state system is consisted of components that they also can be multi-state. The performance rates of components constituting a system can also vary as a result of their deterioration or in consequence of variable environmental conditions. Components failures can lead to the degradation of the entire multi-state system performance. The performance rates of the components can range from perfect functioning up to complete failure. The quality of the system is completely determined by components. In this article, a possible state for the single component system, where component is subject to two stresses, is considered under stress-strength model which makes the component multi-state. The probabilities of component are studied when strength of the component is Erlang random variables and the stresses are independent exponential random variables. Also, the probabilities of component are considered when the stresses are dependent exponential random variables.

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

In this paper, the sinc-Galerkin method is used for numerically solving a class of nonlinear differential equations with boundary conditions. The importance of this study is that sinc approximation of the nonlinear term is stated as a new theorem. The method introduced here is tested on some nonlinear problems and is shown to be a very efficient and powerful tool for obtaining approximate solutions of nonlinear ordinary differential equations.

A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers’ equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers’ equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on somewell-known problems for the Burgers’ equation.

In this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.

We investigate the stability and invariant manifolds of generalized Beddington model with the host population subject to the Allee effect.We obtain the condition for the existence of the fixed points and investigate the stability of the system.

The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L ∞ and relative error norm for problems respectively.