Band 14, Heft 1

An extremely high-intensity laser interaction with a nucleus that is undergoing spontaneous α -decay is investigated in the framework of the time-dependent one-body Schrödinger equation solved by a Crank-Nicolson scheme associated with transparent boundary conditions. The wave-packet dynamics are determined for various laser intensities and frequencies for continuous waves and for sequences of few-cycle pulses. We show that pulse sequences containing an odd number of half-cycles determine an enhancement of the tunneling probability and therefore a drastic decrease of alpha half-lives compared to the field-free case and the continuous wave case.

The Korteweg-de Vries equation (KdV) and the (2+ 1)-dimensional Nizhnik-Novikov-Veselov system (NNV) are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially) integrable equations. Compared with Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.

In this paper the thin film flow of an Oldroyd 6-constant fluid on a vertically moving belt is investigated. The basic equation of a non-Newtonian fluid in a container with a wide moving belt which passes through the container moving vertically upward with constant velocity, is reduced to an ordinary nonlinear differential equation. This equation is solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM). The solutions take into account the behavior of Newtonian and non-Newtonian fluids. Our procedure intended for solving nonlinear problems does not need small parameters in the equation and provides a convenient way to control the convergence of the approximate solutions.

In this paper, Hirota’s bilinear method is extended to a new modified Kortweg–de Vries (mKdV) hierarchy with time-dependent coefficients. To begin with, we give a bilinear form of the mKdV hierarchy. Based on the bilinear form, we then obtain one-soliton, two-soliton and three-soliton solutions of the mKdV hierarchy. Finally, a uniform formula for the explicit N -soliton solution of the mKdV hierarchy is summarized. It is graphically shown that the obtained soliton solutions with time-dependent functions possess time-varying velocities in the process of propagation.

We obtain the full Hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated Hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated Hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system. We then construct two master lagrangians for the coupled system whose field equations are the ε -parametric Gardner equations obtained from the coupled KdV system through a Gardner transformation. In the weak limit ε → 0 the lagrangians reduce to the ones of the coupled KdV system while, after a suitable redefinition of the fields, in the strong limit ε → ∞ we obtain the lagrangians of the coupled modified KdV system. The Hamiltonian structures of the coupled KdV system follow from the Hamiltonian structures of the master system by taking the two limits ε → 0 and ε → ∞.

A new approach for modeling real world problems called the “Eton Approach” was presented in this paper. The "Eton approach" combines both the concept of the variable order derivative together with Atangana derivative with memory derivative. The Atangana derivative with memory is used to account for the memory and fractional derivative for its filter effect. The approach was used to describe the potential energy field that is caused by a given charge or mass density distribution.We solve the modified model numerically and present supporting numerical simulations.

Global climate change is one of the most important international problems of the 21st century. The overall rapid increase in the dynamics of cataclysms, which have been observed in recent decades, is particularly alarming. Howdo modern scientists predict the occurrence of certain events? In meteorology, unusually powerful cumulonimbus clouds are one of the main conditions for the emergence of a tornado. The former, in their turn, are formed during the invasion of cold air on the overheated land surface. The satellite captures the cloud front, and, based on these pictures, scientists make assumptions about the possibility of occurrence of the respective natural phenomena. In fact, mankind visually observes and draws conclusions about the consequences of the physical phenomena which have already taken place in the invisible world, so the conclusions of scientists are assumptions by their nature, rather than precise knowledge of the causes of theorigin of these phenomena in the physics of microcosm. The latest research in the field of the particle physics and neutrino astrophysics, which was conducted by a working team of scientists of ALLATRA International Public Movement (hereinafter ALLATRA SCIENCE group) allatra-science.org, last accessed 10 April 2016. , offers increased opportunities for advanced fundamental and applied research in climatic engineering.

The aim of thiswork is to study the energy dependence of thermoluminescent dosimeter (TLD-700) for low energy X-ray beams encountered in conventional diagnostic radiology. In the first step, we studied some characteristics (reproducibility and linearity) of TLD-700 chips using a 137 Cs source, and selected TLD chips with reproducibility better than 2.5%. Then we determined TLD-700 energy response for diagnostic radiology X-ray qualities, and investigated its influence on air kerma estimate. A maximum deviation of 60% can be obtained if TLDs are calibrated for 137 Cs radiation source and used in diagnostic radiology fields. However, this deviation became less than 20% if TLDs chips are calibrated for the reference x-ray radiation quality RQR5 (recommended by the IEC 61267 standard). Consequently, we recommend calibrating this kind of TLDdetector with RQR5 diagnostic radiology X-ray quality. This method permits to obtain a good accuracy when assessing the entrance dose in diagnostic radiology procedures.

The following paper presents the possibility of formation of Pt nanowires, achieved by a three-step method consisting of conformal deposition of a carbon nanotube and conformal coverage with platinum by physical vapour deposition, followed by removal of the carbonaceous template. The characterization of this new nanostructure was carried out through scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD).

Imperfections and noise in realistic quantum computers may seriously affect the accuracy of quantum algorithms. In this article we explore the impact of static imperfections on quantum entanglement as well as non-entangled quantum correlations in Grover’s search algorithm. Using the metrics of concurrence and geometric quantum discord, we show that both the evolution of entanglement and quantum discord in Grover algorithm can be restrained with the increasing strength of static imperfections. For very weak imperfections, the quantum entanglement and discord exhibit periodic behavior, while the periodicity will most certainly be destroyed with stronger imperfections. Moreover, entanglement sudden death may occur when the strength of static imperfections is greater than a certain threshold.

In this study, pf and df of single order statistic of nonidentical discrete random variables are obtained. These functions are also expressed in integral form. Finally, pf and df of extreme of order statistics of random variables for the nonidentical discrete case are given.

Photoproduction of the charmonium-like state Z c (4200) and the charmed baryon Λc*$\it\Lambda _c^*$(2940) is investigated with an effective Lagrangian approach and the Regge trajectories applying to the COMPASS experiment. Combining the experimental data from COMPASS and our theoretical model we estimate the upper limit of Γ Zc (4200)→ J / ψπ to be of about 37 MeV. Moreover, the possibility to produce Λc*$\it\Lambda _c^*$ (2940) at COMPASS is discussed. It seems one can try to search for this hadron in the missing mass spectrum since the t -channel is dominating for the Λc*$\it\Lambda _c^*$(2940) photoproduction.

We investigate an unsteady incompressible laminar micropolar flow in a semi-infinite porous pipe with large injection or suction through a deforming pipe wall. Using suitable similarity transformations, the governing partial differential are transformed into a coupled nonlinear singular boundary value problem. For large injection, the asymptotic solutions are constructed using the Lighthill method, which eliminates singularity of solution in the high order derivative. For large suction, a series expansion matching method is used. Analytical solutions are validated against the numerical solutions obtained by Bvp4c.

In this paper, a nonlinear flapping equation for large inflow angles and flap angles is established by analyzing the aerodynamics of helicopter blade elements. In order to obtain a generalized flap equation, the Snel stall model was first applied to determine the lift coefficient of the helicopter rotor. A simulation experiment for specific airfoils was then conducted to verify the effectiveness of the Snel stall model as it applies to helicopters. Results show that the model requires no extraneous parameters compared to the traditional stall model and is highly accurate and practically applicable. Based on the model, the relationship between the flapping angle and the angle of attack was analyzed, as well as the advance ratio under the dynamic stall state.

Cracked die is a serious failure mode in the Light Emitting Diode (LED) industry – affecting LED quality and long-term reliability performance. In this paper an investigation has been carried out to find the correlation between severe cracked germanium (Ge) substrate of an aluminum indium gallium phosphate (AlInGaP) LED and its electro-optical performance after the Temperature Cycle (TC) test. The LED dice were indented at several bond forces using a die bonder. The indented dice were analysed using a Scanning Electron Microscope (SEM). The result showed that severe cracks were observed at 180 gF onward. As the force of indentation increases, crack formation also becomes more severe thus resulting in the chipping of the substrate. The cracked dies were packaged and the TC test was performed. The results did not show any electro-optical failure or degradation, even after a 1000 cycle TC test. Several mechanically cross-sectioned cracked die LEDs, were analysed using SEM and found that no crack reached the active layer. This shows that severely cracked Ge substrate are able to withstand a −40°C/+100°C TC test up to 1000 cycles and LED optical performance is not affected. A small leakage current was observed in all of the cracked die LEDs in comparison to the reference unit. However, this value is smaller than the product specification and is of no concern.

The Brusselator with different time scales, which behaves in the classical slow-fast effect, is investigated, and is characterized by the coupling of the quiescent and spiking states. In order to reveal the generation mechanism by using the slow-fast analysis method, the coordinate transformation is introduced into the classical Brusselator, so that the transformed system can be divided into the fast and slow subsystems. Furthermore, the stability condition and bifurcation phenomenon of the fast subsystem are analyzed, and the attraction domains of different equilibria are presented by theoretical analysis and numerical simulation respectively. Based on the transformed system, it could be found that the generation mechanism between the quiescent and spiking states is Fold bifurcation and change of the attraction domain of the fast subsystem. The results may also be helpful to the similar system with multiple time scales.

We introduce a new numerical algorithm for solving one-dimensional time-fractional Tricomi-type equations (T-FTTEs). We used the shifted Jacobi polynomials as basis functions and the derivatives of fractional is evaluated by the Caputo definition. The shifted Jacobi Gauss-Lobatt algorithm is used for the spatial discretization, while the shifted Jacobi Gauss-Radau algorithmis applied for temporal approximation. Substituting these approximations in the problem leads to a system of algebraic equations that greatly simplifies the problem. The proposed algorithm is successfully extended to solve the two-dimensional T-FTTEs. Extensive numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Many difficulties are encountered when attempting to pinpoint a common origin for several observed astrophysical anomalies, and when assessing their tension with existing exclusion limits. These include systematic uncertainties affecting the operation of the detectors, our knowledge of their response, astrophysical uncertainties, and the broad range of particle couplings that can mediate interaction with a detector target. Particularly interesting astrophysical evidence has motivated a search for dark-photon, and focused our attention on a Hidden Valleys model with a GeV-scale dark sector that produces exciting signatures. Results from recent underground experiments are also considered. There is a ‘light’ hidden sector (dark sector), present in many models of new physics beyond the Standard Model, which contains a colorful spectrum of new particles. Recently, it has been shown that this spectrum can give rise to unique signatures at colliders when the mass scale in the hidden sector is well below a TeV; as in Hidden Valleys, Stueckelberg extensions, and Unparticle models. These physics models produce unique signatures of collimated leptons at high energies. By studying these ephemeral particles we hope to trace the history of the Universe. Our present theories lead us to believe that there is something new just around the corner, which should be accessible at the energies made available by modern colliders.

The field of organic spintronics deals with spin dependent phenomena occurring in organic semiconductors or hybrid inorganic/organic systems that may be exploited for future electronic applications. This includes magnetic field effects on charge transport and luminescence in organic semiconductors, spin valve action in devices comprising organic spacers, and magnetic effects that are unique to hybrid interfaces between (ferromagnetic) metals and organic molecules. A brief overview of the current state of affairs in the field is presented.

In this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G 3 . We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces using Frenet frame in Galilean space. Also, for the sake of visualizing of this study, we plot an example for this surfaces family.

The present study investigates the self healing behavior of both pristine and defected single layer graphene using a molecular dynamic simulation. Single layer graphene containing various defects such as preexisting vacancies and differently oriented pre-existing cracks were subjected to uniaxial tensile loading till fracture occurred. Once the load was relaxed, the graphene was found to undergo self healing. It was observed that this self healing behaviour of cracks holds irrespective of the nature of pre-existing defects in the graphene sheet. Cracks of any length were found to heal provided the critical crack opening distance lies within 0.3-0.5 nm for a pristine sheet and also for a sheet with pre-existing defects. Detailed bond length analysis of the graphene sheet was done to understand the mechanism of self healing of graphene. The paper also discusses the immense potential of the self healing phenomena of graphene in the field of graphene based sub-nano sensors for crack sensing.

In this paper we have studied the flow and heat transfer of a horizontal sheet in a viscous fluid. The stretching rate and temperature of the sheet vary with time. The governing equations for momentum and thermal energy are reduced to ordinary differential equations by means of similarity transformation. These equations are solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM) which provides us with a convenient way to control the convergence of approximation solutions and adjust convergence rigorously when necessary. Some examples are given and the results obtained reveal that the proposed method is effective and easy to use.

In many circumstances the perfect fluid conservation equations can be directly integrated to give a geometric-thermodynamic equation: typically that the lapse N is the reciprocal of the enthalphy h , ( N = 1/ h ). This result is aesthetically appealing as it depends only on the fluid conservation equations and does not depend on specific field equations such as Einstein's. Here the form of the geometric-thermodynamic equation is derived subject to spherical symmetry and also for the shift-free ADM formalism. There at least three applications of the geometric-thermodynamic equation, the most important being to the notion of asymptotic flatness and hence to spacetime exterior to a star. For asymptotic flatness one wants h → 0 and N → 1 simultaneously, but this is incompatible with the geometric-thermodynamic equation. Observational data and asymptotic flatness are discussed. It is argued that a version of Mach's principle does not allow asymptotic flatness.

An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes’ thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton’s second law. This implies Einstein’s geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell’s equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a “free” photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.

To improve the corrosion and mechanical properties of the AM50 magnesium alloy, different amounts of the rare earth element gadolinium were used. The microstructure, corrosion and mechanical properties were evaluated by X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, and electrochemical and mechanical stretch methods. The results indicate that, with Gd addition, the amount of the Al 2 Gd 3 phase increased while the β -Mg 17 Al 12 phase amount decreased. Due to the Gd addition, the grain of the AM50 magnesium alloy was significantly refined, which improved its tensile strength. Further, the decrease in the amount of the β phase improved the corrosion resistance of the alloy. The fracture mechanism of the Gd-modified AM50 magnesium alloy was a quasi-cleavage fracture. Finally, the optimum corrosion residual strength of the AM50 magnesium alloy occurred with 1 wt.%of added Gd.

In this work, we propose a new operational method based on a Genocchi wavelet-like basis to obtain the numerical solutions of non-linear fractional order differential equations (NFDEs). To the best of our knowledge this is the first time a Genocchi wavelet-like basis is presented. The Genocchi wavelet-like operational matrix of a fractional derivative is derived through waveletpolynomial transformation. These operational matrices are used together with the collocation method to turn the NFDEs into a system of non-linear algebraic equations. Error estimates are shown and some illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed technique.

We present a complete energy and wavefunction analysis of a Harmonic oscillator with simultaneous non-hermitian transformations of co-ordinate (x→(x+iλp)(1+βλ))$(x \rightarrow \frac{(x + i\lambda p)}{\sqrt{(1+\beta \lambda)}})$ and momentum (p→(p+iβx)(1+βλ))$(p \rightarrow \frac {(p+i\beta x)}{\sqrt{(1+\beta \lambda)}})$ using perturbation theory under iso-spectral conditions. We observe that two different frequencies of oscillation ( w 1 , w 2 )correspond to the same energy eigenvalue, - which can also be verified using a Lie algebraic approach.

Over the last twenty years, several “different” hyperbolic tangent function methods have been proposed to search solutions for nonlinear partial differential equations (NPDEs). The most common of these methods were the tanh-function method, the extended tanh-function method, the modified extended tanh-function method, and the complex tanh-function method. Besides the excellent sides of these methods, weaknesses and deficiencies of each method were encountered. The authors realized that they did not actually give “very different and comprehensive results”, and some of them are even unnecessary. Therefore, these methods were analysed and significant findings obtained. Firstly, they compared all of these methods with each other and gave the connections between them; and secondly, they proposed a more general method to obtain many more solutions for NPDEs, some of which having never been obtained before, and thus to overcome weaknesses and deficiencies of existing hyperbolic tangent function methods in the literature. This new method, named as the unified method, provides many more solutions in a straightforward, concise and elegant manner without reproducing a lot of different forms of the same solution. Lastly, they demonstrate the effectiveness of the unifed tanh method by seeking more exact solutions of the Rabinovich wave equation which were not obtained before.

Propagators approximated by meromorphic functions with complex conjugated poles are widely used to model the infrared behavior of QCD Green’s functions. In this paper, analytical solutions for two point correlators made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences and instead of Lehmann it rather satisfies Gribov integral representation.

In this paper a four stages twelfth algebraic order symmetric two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives is developed for the first time in the literature. For the new proposed method: (1) we will study the phase-lag analysis, (2) we will present the development of the new method, (3) the local truncation error (LTE) analysis will be studied. The analysis is based on a test problem which is the radial time independent Schrödinger equation, (4) the stability and the interval of periodicity analysis will be presented, (5) stepsize control technique will also be presented, (6) the examination of the accuracy and computational cost of the proposed algorithm which is based on the approximation of the Schrödinger equation.

This paper presents the alternative construction of the diffusion-advection equation in the range (1; 2). The fractional derivative of the Liouville-Caputo type is applied. Analytical solutions are obtained in terms of Mittag-Leffler functions. In the range (1; 2) the concentration exhibits the superdiffusion phenomena and when the order of the derivative is equal to 2 ballistic diffusion can be observed, these behaviors occur in many physical systems such as semiconductors, quantum optics, or turbulent diffusion. This mathematical representation can be applied in the description of anomalous complex processes.

Based on some previous works, an equivalent equations is obtained for the differential equations of fractional-order q ∈(1, 2) with non-instantaneous impulses, which shows that there exists the general solution for this impulsive fractional-order systems. Next, an example is used to illustrate the conclusion.

In this article, we apply the generalized Kudryashov method for finding exact solutions of three nonlinear partial differential equations (PDEs), namely: the Biswas-Milovic equation with dual-power law nonlinearity; the Zakharov--Kuznetsov equation (ZK(m,n,k)); and the K(m,n) equation with the generalized evolution term. As a result, many analytical exact solutions are obtained including symmetrical Fibonacci function solutions, and hyperbolic function solutions. Physical explanations for certain solutions of the three nonlinear PDEs are obtained.

In this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional order α .

In this paper, we study the rotational surfaces in the isotropic 3-space 𝕀 3 satisfying Weingarten conditions in terms of the relative curvature K (analogue of the Gaussian curvature) and the isotropic mean curvature H . In particular, we classify such surfaces of linear Weingarten type in 𝕀 3 .

The objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.

We consider initial value problems for the nonlinear Klein-Gordon equation in de Sitter spacetime. We use the differential transform method for the solution of the initial value problem. In order to show the accuracy of results for the solutions, we use the variational iteration method with Adomian’s polynomials for the nonlinearity. We show that the methods are effective and useful.

The nonlinear stability and the existence of the periodic solutions for an optimal control problem on the Schrödinger Lie group are discussed. The analytic solutions via optimal homotopy asymptotic method of the dynamics and numerical simulations are presented, too.

This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

In this paper, a sinc-collocation method is described to determine the approximate solution of fractional order boundary value problem (FBVP). The results obtained are presented as two new theorems. The fractional derivatives are defined in the Caputo sense, which is often used in fractional calculus. In order to demonstrate the efficiency and capacity of the present method, it is applied to some FBVP with variable coefficients. Obtained results are compared to exact solutions as well as Cubic Spline solutions. The comparisons can be used to conclude that sinc-collocation method is powerful and promising method for determining the approximate solutions of FBVPs in different types of scenarios.

Functional differential equations have importance in many areas of science such as mathematical physics. These systems are difficult to solve analytically.In this paper we consider the systems of linear functional differential equations [1-9] including the term y(αx + β) and advance-delay in derivatives of y .To obtain the approximate solutions of those systems, we present a matrix-collocation method by using Müntz-Legendre polynomials and the collocation points. For this purpose, to obtain the approximate solutions of those systems, we present a matrix-collocation method by using Müntz-Legendre polynomials and the collocation points. This method transform the problem into a system of linear algebraic equations. The solutions of last system determine unknown co-efficients of original problem. Also, an error estimation technique is presented and the approximate solutions are improved by using it. The program of method is written in Matlab and the approximate solutions can be obtained easily. Also some examples are given to illustrate the validity of the method.

In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM) and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE) with time dependent coefficients.

In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ) system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.

In this paper, firstly, we give a connection between well known and commonly used methods called the (G'G)$\left( {{{G'} \over G}} \right)$ -expansion method and the modified extended tanh method which are often used for finding exact solutions of nonlinear partial differential equations (NPDEs). We demonstrate that giving a convenient transformation and formula, all of the solutions obtained by using the (G'G)$\left( {{{G'} \over G}} \right)$ - expansion method can be converted the solutions obtained by using the modified extended tanh method. Secondly, contrary to the assertion in some papers, the (G'G)$\left( {{{G'} \over G}} \right)$-expansion method gives neither all of the solutions obtained by using the other method nor new solutions for NPDEs. Namely, while the modified extended tanh method gives more solutions in a straightforward, concise and elegant manner without reproducing a lot of different forms of the same solution. On the other hand, the (G'G)$\left( {{{G'} \over G}} \right)$-expansion method provides less solutions in a rather cumbersome form. Lastly, we obtain new exact solutions for the Lonngren wave equation as an illustrative example by using these methods.

In this paper we investigate graded compactly packed rings, which is defined as; if any graded ideal I of R is contained in the union of a family of graded prime ideals of R , then I is actually contained in one of the graded prime ideals of the family. We give some characterizations of graded compactly packed rings. Further, we examine this property on h – Spec ( R ). We also define a generalization of graded compactly packed rings, the graded coprimely packed rings. We show that R is a graded compactly packed ring if and only if R is a graded coprimely packed ring whenever R be a graded integral domain and h – dim R = 1.

In this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.

In many physical systems, reliability evaluation, such as ones encountered in telecommunications, the design of integrated circuits, microwave relay stations, oil pipeline systems, vacuum systems in accelerators, computer ring networks, and spacecraft relay stations, have had applied consecutive k -out-of- n system models. These systems are characterized as logical connections among the components of the systems placed in lines or circles. In literature, a great deal of attention has been paid to the study of the reliability evaluation of consecutive k -out-of- n systems. In this paper, we propose a new method to compute the reliability of consecutive k -out-of- n :F systems, with n linearly and circularly arranged components. The proposed method provides a simple way for determining the system failure probability. Also, we write R-Project codes based on our proposed method to compute the reliability of the linear and circular systems which have a great number of components.

In this paper, well-posedness, controllability and optimal control for a time-delay beam equation are studied. The equation of motion is modeled as a time-delayed distributed parameter system(DPS) and includes Heaviside functions and their spatial derivatives due to the finite size of piezoelectric patch actuators used to suppress the excessive vibrations based on displacement and moment conditions. The optimal control problem is defined with the performance index including a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time and a penalty term defined as the control voltage used in the control duration. Optimal control law is obtained by using Maximum principle and hence, the optimal control problem is transformed the into a boundary-, initial and terminal value problem.The explicit solution of the control problem is obtained by eigenfunction expansions of the state and adjoint variables. Numerical results are presented to show the effectiveness and applicability of the piezoelectric control.

In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.

In this paper, a new mathematical model has been developed to calculate the optical properties of nano materials a function of their size and structure. ZnO has good characterizatics in optical, electrical, and structural crystallisation; We will demonstrate that the direct optical gap energy of ZnO films grown by US and SP spray deposition can be calculated by investigating the correlation between solution molarity, doping levels of doped films and their Urbache energy. A simulation model has been developed to calculate the optical band gap energy of undoped and Bi, Sn and Fe doped ZnO thin films. The measurements by thus proposed models are in agreement with experimental data, with high correlation coefficients in the range 0.94-0.99. The maximum calculated enhancement of the optical gap energy of Sn doped ZnO thin films is always higher than the enhancement attainable with an Fe doped film, where the minimum error was found for Bi and Sn doped ZnO thin films to be 2,345 and 3,072%, respectively. The decrease in the relative errors from undoped to doped films can be explained by the good optical properties which can be observed in the fewer number of defects as well as less disorder.

In this work, a theoretical study of diffusion of neumatic liquid crystals was done using the concept of fractional order derivative. This version of fractional derivative is very easy to handle and obey to almost all the properties satisfied by the conventional Newtonian concept of derivative. The mathematical equation underpinning this physical phenomenon was solved analytically via the so-called homotopy decomposition method. In order to show the accuracy of this iteration method, we constructed a Hilbert space in which we proved its stability for the time-fractional Hunder-Saxton equation.

Sequences of functions play an important role in approximation theory. In this paper, we aim to establish a (presumably new) sequence of functions involving the Aleph function by using operational techniques. Some generating relations and finite summation formulas of the sequence presented here are also considered.

We investigate the structure of negacyclic codes over the chain ring ℤ p [ u ]/〈 u k 〉, which plays an important role in data transmission technologies. We study the set of generators for these codes. We also discuss the rank and hamming distance for these codes. We give some examples of negacyclic codes which are near to optimal.

In this paper, based on Jumarie’s modified Riemann-Liouville derivative, we apply the fractional variational iteration method using He’s polynomials to obtain solitary and compacton solutions of fractional KdV-like equations. The results show that the proposed method provides a very effective and reliable tool for solving fractional KdV-like equations, and the method can also be extended to many other fractional partial differential equations.

In this work, we have considered the modified simple equation (MSE) method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW) and the modified equal width (mEW) equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

In this paper, we discuss non-local derivatives on fractal Cantor sets. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared. Related physical models are also suggested.

In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.

We will study uninorms on the unit square endowed with the natural partial order defined coordinate-wise. We will show that we can choose arbitrary pairs of incomparable elements, ( a , e ) and construct a uninorm whose neutral element is e and annihilator is a . As a special case we construct uninorms which are at the same time also nullnorms (or, expressed another way, we construct proper nullnorms with neutral element). We will also generalize this result to the direct product of two bounded lattices. I.e., we will show that it is possible to construct nullnorms with a neutral element on the direct product of two bounded lattices.

The Wigner-Moyal approach is applied to investigate the dynamics of the Gaussian wave packet moving in a double-well potential in the ‘Mexican hat’ form. Quantum trajectories in the phase space are computed for different kinetic energies of the initial wave packet in the Wigner form. The results are compared with the classical trajectories. Some additional information on the dynamics of the wave packet in the phase space is extracted from the analysis of the cross-correlation of the Wigner distribution function with itself at different points in time.

High-level algebra-algorithmic software tools for automated design of parallel code in the OpenMP environment are developed for the purpose of both producing efficient parallel code and increasing the performance of program developers. Application of the tools is illustrated with an example of a problem in atmosphere circulation modeling, represented as a service belonging to an Internet portal providing meteorological forecasting services. Results of execution of the parallel weather forecasting program on multiprocessor platforms are given.

The paper deals with the biomechanical investigation on the human lumbar intervertebral disc under the static load. The disc is regarded as a two - phased ambient consisting of a fibrous outer part called annulus fibrosis and a liquid inner part nucleus pulposus. Due to the fibrous structure, the annulus fibrosis can be treated by using a special case of anisotropy - transversal isotropy. In the paper the corresponding tensor of material constants is derived. The tensor consequently incomes to the constitutive equations determining the stress - strain relation in the material. In order to study the mechanical behaviour the disc is observed within the motion segment, the basic unit for motion tracing. The motion segment involves two neighbouring vertebrae and the intervertebral disc between them that connect them both. When constitutive equations are accomplished, they can be incorporated in the finite element analysis. The illustrative example of the intervertebral disc L2/L3, the disc between the second and the third lumbar vertebrae the lumbar part of spine, with its computer implementation is performed. Finally the comparison of the results of using anisotropic and homogenized approach is provided. The comparison illustrates the eligibility of such a kind of approach.

In this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.

Image steganography is one of the ever growing computational approaches which has found its application in many fields. The frequency domain techniques are highly preferred for image steganography applications. However, there are significant drawbacks associated with these techniques. In transform based approaches, the secret data is embedded in random manner in the transform coefficients of the cover image. These transform coefficients may not be optimal in terms of the stego image quality and embedding capacity. In this work, the application of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) have been explored in the context of determining the optimal coefficients in these transforms. Frequency domain transforms such as Bandelet Transform (BT) and Finite Ridgelet Transform (FRIT) are used in combination with GA and PSO to improve the efficiency of the image steganography system.

This communication presents a functional prototype, named PTAH, implementing a linguistic model focused on regulations in Spanish. Its global architecture, the reasoning model and short statistics are provided for the prototype. It is mainly a conversational robot linked to an Expert System by a module with many intelligent linguistic filters, implementing the reasoning model of an expert. It is focused on bylaws, regulations, jurisprudence and customized background representing entity mission, vision and profile. This Structure and model are generic enough to self-adapt to any regulatory environment, but as a first step, it was limited to an academic field. This way it is possible to limit the slang and data numbers. The foundations of the linguistic model are also outlined and the way the architecture implements the key features of the behavior.

Mobile ad hoc networks (MANETs) are a group of mobile nodes that are connected without using a fixed infrastructure. In these networks, nodes communicate with each other by forming a single-hop or multi-hop network. To design effective mobile ad hoc networks, it is important to evaluate the performance of multi-hop paths. In this paper, we present a mathematical model for a routing protocol under energy consumption and packet delivery ratio of multi-hop paths. In this model, we use geometric random graphs rather than random graphs. Our proposed model finds effective paths that minimize the energy consumption and maximizes the packet delivery ratio of the network. Validation of the mathematical model is performed through simulation.

The problem of resource management for server virtualization under the limitation of recovery time objective was considered in this paper. Models and methods of workload and resource management of IT infrastructure with server virtualization in terms of time limit for services recovery in case of provision of services by virtual private servers were proposed. Mathematical models for excess and lack of resources was formulated as linear and nonlinear 0-1 programming problems. To solve these problems branch and bound, heuristic and modified genetic algorithms were proposed.

In this paper we focus on the new version of computer program MODY for calculations of symmetryadapted functions based on the theory of groups and representations. The choice of such a functional frame of coordinates for description of ordered structures leads to a minimal number of parameters which must be used for presentation of such structures and investigations of their properties. The aim of this work is to find those parameters, which are coefficients of a linear combination of calculated functions, leading to construction of different types of structure ordering with a given symmetry. A spreadsheet script for simplification of this work has been created and attached to the program.

Dealing with astronomical observations represents one of the most challenging areas of big data analytics. Besides huge variety of data types, dynamics related to continuous data flow from multiple sources, handling enormous volumes of data is essential. This paper provides an overview of methods aimed at reducing both the number of features/attributes as well as data instances. It concentrates on data mining approaches not related to instruments and observation tools instead working on processed object-based data. The main goal of this article is to describe existing datasets on which algorithms are frequently tested, to characterize and classify available data reduction algorithms and identify promising solutions capable of addressing present and future challenges in astronomy.

In wavelet-based solution of eigenvalue-type differential equations, like the Schrödinger equation, refinement in the resolution of the solution is a costly task, as the number of the potential coefficients in the wavelet expansion of the solution increases exponentially with the resolution. Predicting the magnitude of the next resolution level coefficients from an already existing solution in an economic way helps to either refine the solution,or to select the coefficients, which are to be included into the next resolution level calculations, or to estimate the magnitude of the error of the solution. However, after accepting a solution with a predicted refinement as a basis, the error can still be estimated by a second prediction, i.e., from a prediction to the second finer resolution level coefficients. These secondary predicted coefficients are proven to be oscillating around the values of the wavelet expansion coefficients of the exact solution. The optimal averaging of these coefficients is presented in the following paper using a sliding average with three optimized coefficients for simple, one-dimensional electron structures.

The spreading and permeation of droplets on porous substrates is a fundamental process in a variety of applications, such as coating, dyeing, and printing. The spreading and permeating usually occur synchronously but play different roles in the practical applications. The mechanisms of the competition between spreading and permeation is significant but still unclear. A lattice Boltzmann method is used to study the spreading and permeation of droplets on hybrid-wettability porous substrates, with different wettability on the surface and the inside pores. The competition between the spreading and the permeation processes is studied in this work from the effects of the substrate and the fluid properties, including the substrate wettability, the porous parameters, as well as the fluid surface tension and viscosity. The results show that increasing the surfacewettability and the porosity contact angle both inhibit the spreading and the permeation processes. When the inside porosity contact angle is larger than 90° (hydrophobic), the permeation process does not occur. The droplets suspend on substrates with Cassie state. The droplets are more easily to permeate into substrates with a small inside porosity contact angle (hydrophilic), as well as large pore sizes. Otherwise, the droplets are more easily to spread on substrate surfaces with small surface contact angle (hydrophilic) and smaller pore sizes. The competition between droplet spreading and permeation is also related to the fluid properties. The permeation process is enhanced by increasing of surface tension, leading to a smaller droplet lifetime. The goals of this study are to provide methods to manipulate the spreading and permeation separately, which are of practical interest in many industrial applications.

Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions and problem scales are designed to examine the fidelity and robustness of the model. High precision (relative deviation 1.0 × 10 −4 % ~ 2.3 × 10 −1 %) and large acceleration (speed-up 880 ~ 98454 times) of POD model are found in these cases. Moreover, the computational time of POD model is quite insensitive to the complexity of problems. These results indicate POD model is especially suitable for large-scale complex problems in engineering.

Due to the complexity of porous media, it is difficult to use traditional experimental methods to study the quantitative impact of the pore size distribution on multiphase flow. In this paper, the impact of two pore distribution function types for three-phase flow was quantitatively investigated based on a three-dimensional pore-scale network model. The results show that in the process of wetting phase displacing the non-wetting phase without wetting films or spreading layers, the displacement efficiency was enhanced with the increase of the two function distribution’s parameters, which are the power law exponent in the power law distribution and the average pore radius or standard deviation in the truncated normal distribution, and vice versa. Additionally, the formation of wetting film is better for the process of displacement.

Hydrocarbon fuel has been widely used in air-breathing scramjets and liquid rocket engines as coolant and propellant. However, possible heat transfer deterioration and threats from local high heat flux area in scramjet make heat transfer enhancement essential. In this work, 2-D steady numerical simulation was carried out to study different schemes of heat transfer enhancement based on a partially filled porous media in a tube. Both boundary and central layouts were analyzed and effects of gradient porous media were also compared. The results show that heat transfer in the transcritical area is enhanced at least 3 times with the current configuration compared to the clear tube. Besides, the proper use of gradient porous media also enhances the heat transfer compared to homogenous porous media, which could help to avoid possible over-temperature in the thermal protection.

Aimed at enhancing the oil recovery of tight reservoirs, the mechanism of hot water flooding was studied in this paper. Experiments were conducted to investigate the influence of hot water injection on oil properties, and the interaction between rock and fluid, petrophysical property of the reservoirs. Results show that with the injected water temperature increasing, the oil/water viscosity ratio falls slightly in a tight reservoir which has little effect on oil recovery. Further it shows that the volume factor of oil increases significantly which can increase the formation energy and thus raise the formation pressure. At the same time, oil/water interfacial tension decreases slightly which has a positive effect on production though the reduction is not obvious. Meanwhile, the irreducible water saturation and the residual oil saturation are both reduced, the common percolation area of two phases is widened and the general shape of the curve improves. The threshold pressure gradient that crude oil starts to flow also decreases. It relates the power function to the temperature, which means it will be easier for oil production and water injection. Further the pore characteristics of reservoir rocks improves which leads to better water displacement. Based on the experimental results and influence of temperature on different aspects of hot water injection, the flow velocity expression of two-phase of oil and water after hot water injection in tight reservoirs is obtained.

The time-dependent density functional theory (TDDFT) method was performed to investigate the excited-state intramolecular double proton transfer (ESIDPT) reaction of calix[4]arene (C4A) and the role of the intramolecular hydrogen bonds in the ESIDPT process. The geometries of C4A in the ground state and excited states (S 1 , S 2 and T 1 ) were optimized. Four intramolecular hydrogen bonds formed in the C4A are strengthened or weakened in the S 2 and T 1 states compared to those in the ground state. Interestingly, upon excitation to the S 1 state of C4A, two protons H1 and H2 transfer along the two intramolecular hydrogen bonds O1-H1···O2 and O2-H2···O3, while the other two protons do not transfer. The ESIDPT reaction breaks the primary symmetry of C4A in the ground state. The potential energy curves of proton transfer demonstrate that the ESIDPT process follows the stepwise mechanism but not the concerted mechanism. Findings indicate that intramolecular hydrogen bonding is critical to the ESIDPT reactions in intramolecular hydrogen-bonded systems.

The solute–solvent interactions of 4-nitro-1,8-naphthalimide (4NNI) as a hydrogen bond acceptor in hydrogen donating methanol (MeOH) solvent in electronic excited states were investigated by means of the time-dependent density functional theory(TDDFT). We calculated the S 0 state geometry optimizations, electronic transition energies and corresponding oscillation strengths of the low-lying electronically excited states for the isolated 4NNi and hydrogen-bonded 4NNi-(MeOH) 1,4 complexes using the density functional theory (DFT) and TDDFT methods. The electronic excitation energies of the hydrogen-bonded complexes are correspondingly decreased compared to that of the isolated 4NNi, which revealed that the intermolecular hydrogen bond C=O···H–O and N=O···H–O in the hydrogen-bonded 4NNi-(MeOH) 1,4 are strengthened in the electronically excited state. The calculated results are consistent with the mechanism that hydrogen bond strengthening will induce a redshift of the corresponding electronic spectra, while hydrogen bond weakening will cause a blueshift. Furthermore, we believe that the deduction we used to depict the trend of the hydrogen bond changes in excited states exists in many other fuorescent dyes in solution.

Based on the density function theory (DFT) method, the interaction between the graphene and oxygen atom is simulated by the B3LYP functional with the 6-31G basis set. Due to the symmetry of graphene (C 54 H 18 , D 6 h ), a representative patch is put forward to represent the whole graphene to simplify the description. The representative patch on the surface is considered to gain the potential energy surface (PES). By the calculation of the PES, four possible stable isomers of the C 54 H 18 -O radical can be obtained. Meanwhile, the structures and energies of the four possible stable isomers, are further investigated thermodynamically, kinetically, and chemically. According to the transition states, the possible reaction mechanism between the graphene and oxygen atom is given.

The influence of molybdenum on the microstructure and kinetics of the austenization of the Fe-Mo-C ternary alloys is analyzed using differential scanning calorimetry (DSC) and the Johnson-Mehl-Avrami-Kolmogorov model (JMAK) in the temperature range from 293 K to 1373 K. The as-cast microstructure and microstructure after DSC test are obtained using optical microscopy (OM) and scanning electron microscopy (SEM). It was seen that with an increasing Mo concentration, the lamellar pearlite is spherized and the austenite grain size decreases. In addition, both DSC curves and the JMAK model show that the initial (Ac1) and the final (Ac3) temperature of the phase transition increases with an increasing Mo concentration. It was also seen that increasing the Mo concentration, the diffusion activation energy (DAE) increases and the pre-exponential factor of diffusion (DPEF) decreases due to a change in both the austenitic nucleation rate and the diffusion of the elements caused by the introduction of Mo.

This paper addresses the possibilities of synthesizing copper indium gallium selenide nanoparticles with properties that are desired in photovoltaics. The use of oleylamine as solvent and capping agent improved the growth and dispersivity of stoichiometric CuIn 0.75 Ga 0.25 Se 2 nanoparticles through conventional colloidal synthesis. Relatively small sized CuIn 0.75 Ga 0.25 Se 2 nanocrystals were assembled in devices as quantum dot sensitized solar cells and exhibited electrical properties with a fill factor of 33% which may be improved for any photovoltaic application.

This work focuses on the generation of conductive networks through the localised alignment of nano fillers, such as multi-walled carbon nanotubes (MWCNTs). The feasibility of alignment and positioning of functionalised MWCNTs by external DC magnetic fields was investigated. The aim of this manipulation is to enhance resin curing through AC induction heating due to hysteresis losses from the nanotubes. Experimental analyses focused on in-depth assessment of the nanotube functionalisation, processing and characterisation of magnetic, rheological and cure kinetics properties of the MWCNT solution. The study has shown that an external magnetic field has great potential for positioning and alignment of CNTs. The study demonstrated potential for creating well-ordered architectures with an unprecedented level of control of network geometry. Magnetic characterisation indicated cobalt-plated nanotubes to be the most suitable candidate for magnetic alignment due to their high magnetic sensitivity. Epoxy/metal-plated CNT nanocomposite systems were validated by thermal analysis as induction heating mediums. The curing process could therefore be optimised by the use of dielectric resins. This study offers a first step towards the proof of concept of this technique as a novel repair technology.

The pair-interactions approximation, when applied to describe elemental clusters, only takes into account bonding between neighboring atoms. According to this approach, isomers of wrapped forms of 2D clusters – nanotubular and fullerene-like structures – and truly 3D clusters, are generally expected to be more stable than their quasi-planar counterparts. This is because quasi-planar clusters contain more peripheral atoms with dangling bonds and, correspondingly, fewer atoms with saturated bonds. However, the differences in coordination numbers between central and peripheral atoms lead to the polarization of bonds. The related corrections to the molar binding energy can make small, quasi-planar clusters more stable than their 2D wrapped allotropes and 3D isomers. The present work provides a general theoretical frame for studying the relative stability of small elemental clusters within the pair interactions approximation.

An attempt has been made to describe the effects of geothermal viscosity with viscous dissipation on the three dimensional time dependent boundary layer flow of magnetic nanofluids due to a stretchable rotating plate in the presence of a porous medium. The modelled governing time dependent equations are transformed a from boundary value problem to an initial value problem, and thereafter solved by a fourth order Runge-Kutta method in MATLAB with a shooting technique for the initial guess. The influences of mixed temperature, depth dependent viscosity, and the rotation strength parameter on the flow field and temperature field generated on the plate surface are investigated. The derived results show direct impact in the problems of heat transfer in high speed computer disks (Herrero et al . [1]) and turbine rotor systems (Owen and Rogers [2]).