Recently, amount of work about the A-harmonic equation for the differential forms has been done. In fact, the A-harmonic equation is an important generalization of the p-harmonic equation in R, p > 1, and the p-harmonic equation is a natural extension of the usual Laplace equation see 1 for the details . The reverse Hölder inequalities have been widely studied and frequently used in analysis an...

A class of singular integro-differential equations in Lebesgue spaces are studied. There are many applications of the singular integro-differential equations discussed in this paper. An example in modeling the stress distribution of an elastic medium with holes is discussed in the paper. Direct numerical schemes using a collocation method and a mechanical quadrature rule designed for the singul...

We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal invariant of a oneparameter group is known then a complete set of functionally independent differential invariants can be constructed via one quadrature and differen...

We derive numerical methods for arbitrary small perturbations of exactly solvable differential equations. The methods, based in one instance on Gaussian quadrature, are symplectic if the system is Hamiltonian and are asymptotically more accurate than previously known methods.

This gazette focuses on simulation and experimental studies for all-optical three-input “AND” gate schemes. The proposed exploits the semiconductor optical amplifier Mach-Zehnder Interferometer (SOA-MZI) nonlinearities, particularly cross-phase modulation (XPM) corollary in addition to cross-gain (XGM) corollary, which originates from a SOA-MZI differential concept. Further, system performance ...

The tremendous attention of researchers has been attracted to the unusual properties quasicrystals in coatings. In this paper, exact solutions functionally graded multilayered two-dimensional quasicrystal coating structures a thermal environment are derived for advanced boundary-value problems with mixed boundary conditions. state space method is formulated coupling linear elastic theory that d...

This paper introduces four new resistorless circuits of first-order current-mode all-pass filter (CMAPF) based on dual-X current conveyor transconductance amplifier (DXCCTA). All the four circuits use a single DXCCTA and a capacitor for their realization. The main features of the proposed CMAPFs are: use of minimum active and passive components, resistorless realization, electronically adjustab...

This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations; such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [tn, tn+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical quadrature. The m...

and Applied Analysis 3 The class of Runge-Kutta methods with CQ formula has been applied to delay-integro-differential equations by many authors (c.f. [18, 19]). For the CQ formula (9), we usually adopt the repeated trapezoidal rule, the repeated Simpson’s rule, or the repeated Newton-cotes rule, and so forth, denote η = max{?̃? 0 , ?̃? 1 , . . . , ?̃? m }. It should be pointed out that the adopte...