OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION:THE METHOD OF A-HARMONIC APPROXIMATION

In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation and directly establish the optimal HSlder exponent for the derivative of a weak solution on its regular set.

Construction of Bode Envelopes Using REP Based Range Finding Algorithms

The frequency domain analysis of systems is an important topic in control theory. Powerful graphical tools exist in classic control, such as the Nyquist plot, Bode plots, and Nichols chart. These methods have been widely used to evaluate the frequency domain behavior of system. A literature survey shows that various approaches are available for the computation of the frequency response of control systems under different types of parametric dependencies, such as affine, multi-linear, polynomial, etc. However, there is a lack of tools in the literature to construct the Bode envelopes for the general nonlinear type of parametric dependencies. In this paper, we address the problem of computation of the envelope of Bode frequency response of a non-rational transfer function with nonlinear parametric uncertainties varying over a box. We propose two techniques to compute the Bode envelopes：first, based on the natural interval extensions （NIE） combined with uniform subdivision and second, based on the existing Taylor model combined with subdivision strategy. We also propose the algorithms to further speed up both methods through extrapolation techniques.

REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE:1

In this article,we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1〈m〈 2.All estimates in the case of m≥2 is no longer suitable,and we can’t obtain the Caccioppoli’s second inequality by using these techniques developed in the case of m≥2.But the Caccioppoli’s second inequality is the key to use A-harmonic approximation method.Thus,we adopt another technique introduced by Acerbi and Fcsco to overcome the difficulty and we also overcome those difficulties due to Dini condition.And then we apply the A-harmonic approximation method to prove partial regularity of weak solutions.

A UTD SOLUTION FOR THE RADIATED FIELD FROM MONOPOLE ON A CONDUCTING CYLINDER SURFACE WITH A DIELECTRIC COATING

A can0nical problem is investigated for high frequency electromagnetic radiation from amonopo1e on a conducting cylinder with c0ating-At first, the exact solution of this problem is given interms of Dyadic Green's function method. Then, using Watson transformation and high frequency asymptotic approximate technique to the exact soluton, a UTD soultion is obtained. The radiation field excitedby a monopole is expressed in terms of the compound Fock' S functions (CFF), which reduce to the geomertrical optics result in the deep lit region and the creeping waves in the shadow region.

The Method of A-Harmonic Approximation and Boundary Regularity for Nonlinear Elliptic Systems under the Natural Growth Condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.

TSKARNA-norm Adaption Based NLMS with Optimized Fractional Order PID Controller Gains for Voltage Power Quality

The operation of a dynamic voltage restorer(DVR)is studied using a three-phase voltage source converter(VSC)-based topology to alleviate voltage anomalies from a polluted supply voltage.The control algorithm used included two components.The first is an adaptive Takagi-Sugeno-Kang(TSK)-based adaptive reweighted L1 norm adaption-based normalized least mean square(TSK-ARNA-NLMS)unit,which is proposed for the extraction of fundamental active and reactive components from the non-ideal supply and is further employed to generate the load reference voltage and switching pulse for the VSC.The step size was evaluated using the proposed TSK-ARNA-NLMS controller,and the TSK unit was optimized by integration with the marine predator algorithm(MPA)for a faster convergence rate.The second,a fractional-order PID controller(FOPID),was employed for AC-and DC-link voltage regulation and was approximated using the Oustaloup technique.The FOPID()PI Dγμprovides more freedom for tuning the settling time,rise time,and overshoot.The FOPID coefficients(Ki,Kd,Kp,γ,andμ)were optimized by employing an advanced ant lion optimization(ALO)meta-heuristics technique to minimize the performance index,namely,the integral time absolute error(ITAE)and assess the accuracy of controllers.The DVR performance was validated under dynamic-and steady-state conditions.

Scattering of water waves by thick rectangular barriers in presence of ice cover

Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate.May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water.The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function.The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function.The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity.These coefficients are depicted graphically against the wave number in a number of figures.Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover,thereby confirming the correctness of the results presented here.It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.

SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS

In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.