Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics

In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

Exact solutions for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit

The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Parameter Self - Learning of Generalized Predictive Control Using BP Neural Network

This paper describes the self—adjustment of some tuning-knobs of the generalized predictive controller(GPC).A three feedforward neural network was utilized to on line learn two key tuning-knobs of GPC,and BP algorithm was used for the training of the linking-weights of the neural network.Hence it gets rid of the difficulty of choosing these tuning-knobs manually and provides easier condition for the wide applications of GPC on industrial plants.Simulation results illustrated the effectiveness of the method.

Nondifferentiable Multiobjective Programming under Generalized d_I-G-Type I Invexity

To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John （G-F-J） and G-Karnsh-Kuhn-Tucker （G-K-K-T） types sufficient optimality conditions were established for a feasible solution to be an efficient solution.Moreover,weak and strict duality results were derived for a G-Mond-Weir type dual under various types of generalized dI-G-type Ⅰ invexity assumptions.

The Commutativity of a *-Ring with Generalized Left *-α-Derivation

In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a homomorphism. The results which proved for generalized left *-derivation of R in [1] are extended by using generalized left *-α-derivation. The commutativity of a *-ring with generalized left *-α-derivation is investigated and some results are given for generalized *-α-derivation.

Hydrocarbon-Generating Model of the Area Covered With Volcanic Rock

The distribution of Oil & gas fields shows their close relationship with the most active tectonic regions. This is not a coincidence but having a scientific reasons. The crustal active regions, refer to the places where the active natural earthquake, volcanic activities, underground water happened, and the areas of the leaking Off of natural gas to the surface of the crust. The magma of volcanic activities brings the organic "kitchen range body" hydrocarbon - generating model and inorganic genetic hydrocarbon to the regions covered by volcanic rock. Underground water brings a catalytic hydrocarbon generating model for organic matter, and the leaking - off of H2 and CO2 contributes a synthetic hydrocarbon - generating model. Volcanic activities bring the assemblage of Source, Reservoir and Seal formed by the sediments and magma the sedimentary basins, and the hydrocarbon - generating system with a "water - volcano" binary structure is formed. All these conditions are favorable and excellent for the formation of oil & gas fields. The distribution of AInerican oil & gas fields have very close relationship with the mines of Fe, Mn, Cr, Mo, W and V, deposits of Zn, Cu, V, Pb, Al and Hg, and the deposits of fluorite, sulfur, potassium salt, phosphate and halite, and the distribution of sulfate - chloride of river water. The reason why few oil & gas fields discovered in the regions covered by volcanic rock in western America maybe because of the view of "inconsistency between petroleum and volcano". Further more, It’s very difficult to carry out a geophysical exploration in such kinds of regions. This paper examined a few hydrocarbon - generating models (systems) mentioned above and came up with some flesh ideas on the exploration in the areas covered with volcanic rocks.

Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method

Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method （GMLSM） and then, discrete equations of motion based on Lagrange＇s equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.

Performance Analysis of Physical Layer Security over α-η-κ-μ Fading Channels

In this paper, we consider the secure data transmission over α-η-κ-μ fading channels, which are recently proposed to encompass nearly all the well-known statistical models adopted in the literature. In particular, we address the secrecy performance in terms of the average secrecy capacity(ASC) and the secrecy outage probability(SOP), for which novel analytical expressions are derived. Simulation results verify the analysis and demonstrate the impact of the physical parameters on the secrecy performance of this new channel fading model.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Analysis of Numerical Results in High Temperature Congealment and Chemistry Non-equilibrium Flow Field

Using the air plasma ignition technique, physicochemical process of burning can be accelerated; concentration limit ofretrofires both can be extended; reliability of retrofires and stability of burning can be improved. In this paper, using internalequivalent heat area in place of electric are that created Ohm heat, the flow fields of thermodynamic equilibrium chemistry con-gealment and chemistry non-equilibrium in the plasma generator were simulated. The influences of the inlet prerotation angleof air, the inlet total pressure of air and the airflow compression angle of spray nozzle on the temperature on the surface of elec-

Attitude control of a rigid spacecraft with one variable-speed control moment gyro

Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro （VSCMG）, which supplies only two internal torques. Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically, when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilib- rium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and deriva- tive controller, using the generalized dynamic inverse （GDI） method. The steady-state instability inherent in the GDI con- troller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude sta- bilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efficacy of the proposed control strategy.

Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems

Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.

Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications

We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),solitary waves,periodic and other wave solutions of the perturbed Kaup-Newell Schrodinger equation in mathematical physics are achieved by utilizing two mathematical techniques,namely,the extended F-expansion technique and the proposed exp(-φ(ξ))-expansion technique.This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger equation.In engineering and applied physics,these wave results have key applications.Graphically,the structures of some solutions are presented by giving specific values to parameters.By using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are exact.These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

Altered relationship between thickness and intrinsic activity amplitude in generalized tonic–clonic seizures

A thinner cortex has higher potential for binding GABA receptor A which is associated with larger amplitudes of intrinsic brain activity(i BA). However, the relationship between cortical thickness and i BA is unknown in intact and epileptic brains. To this end, we investigated the relationship between cortical thickness measured by highresolution MRI and surface-based i BA derived from resting-state functional MRI in normal controls(n = 82) andpatients with generalized tonic–clonic seizures(GTCS)only(n = 82). We demonstrated that the spatial distribution of cortical thickness negatively correlated with surface-based i BA amplitude at both whole-brain and within independent brain functional networks. In GTCS patients,spatial coupling between thickness and i BA amplitude decreased in the default mode, dorsal attention, and somatomotor networks. In addition, the vertex-wise acrosssubject thickness–i BA amplitude correspondence altered in the frontal and temporal lobes as well as in the precuneus in GTCS patients. The relationship between these two modalities can serve as a brain-based marker for detecting epileptogenic changes.

A study on assessment of hydrocarbon potential of the lignite deposits of Saurashtra basin, Gujarat （Western India）

In the present investigation, Bhavnagar lignites of the Saurashtra basin （Gujarat） have been studied to assess their hydrocarbon generating potential. The samples of upper as well as lower lignite seams have been studied through microscopy and subjected to various chemical analyses viz. proximate analysis, ultimate analysis and Rock-Eval Pyrolysis. These lignites have high moisture and low to moderate ash yield but are characterized by high volatile matter. Petro- graphically they comprise predominantly of huminite group maceral while liptinite and inertinite groups occur in sub- ordinated amount. Huminite is chiefly composed of detrohuminite and telohuminite. The Tma~ （av. 416.23 ~C） and huminite reflectivity （0.28%-0.30%） indicate a low degree of maturity for these lignites which is also substantiated by the T,n~~ versus hydrogen index plot. The organic matter is subjugated by kerogen Type-III with a potential to expel hydrocarbon on liquefaction. Study further reveals that the fixed hydrocarbon is several folds higher than the free hydrocarbons. Being high in reactive maceral content, a high ＇conversion＇ and good ＇oil yield＇ values for these lignites were observed. Thus, the empirically derived values match well with those obtained through the experimental values of Rock-Eval Pyrolysis and validate their hydrocarbon generating potential.

Approximate （m, n）-Cauchy-Jensen Additive Mappings in C^＊-algebras

Concerning the stability problem of functional equations, we introduce a general （m, n）- Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general （m, n）-Cauchy Jensen additive mappings in C^＊-algebras, which generalize the result＇s obtained for Cauchy-Jensen type additive mappings.

On π-Regular Rings with Involution

A ring R is π-regular if for every a in R, there is a positive integer n such that a^n R is generated by an idempotent. In this paper, we introduce the notion of π-＊-regular rings, which is the ＊-version of π-regular rings. We prove various properties of π-＊-regular rings, and establish many equivalent characterizations of abelian π-＊-regular rings.

ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX

The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.