Abstract—In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes’ phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are careful...

None of the existing methods for computing the oscillatory integral ∫ b a f(x)e iωg(x) dx achieve all of the following properties: high asymptotic order, stability, avoiding the computation of the path of steepest descent and insensitivity to oscillations in f . We present a new method that satisfies these properties, based on applying the gmres algorithm to a preconditioned differential operator.

We present a new greedy algorithm for minimizing a separable convex function over an integral bisubmodular polyhedron. The algorithm starts with a.n arbitrary feasible solution and a current feasible solution incrementally moves toward an optimal one in a greedy way. \Ve also show that there exists at least one optimal solution in the coordinate-wise steepest descent direction from a feasible s...

Integral representations are derived for the parabolic cylinder functions U(a, x), V (a, x) andW (a, x) and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals in the complex plane, by using methods from asymptotic analysis (saddle point and steepest descent methods), and are stable starting points for evaluating the ...

Integral representations are considered of solutions of the inhomogeneous Airy differential equation w′′ − z w = ±1/π. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standar...

The Holy Quran was descended from Almighty Allah to the Holy Prophet (AS) about the last 14 centuries and there has been a time interval between descent of the Quran and its existing readers and commentators. This Question is posed whether this time interval between descent of the Quran and commentator will effect on verses understanding and their commentary or not? As one of commentary princip...

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.

One of the major problems in commutative algebra is to recover information about a commutative ring A from known properties of the form ring G := GA(q) = ⊕n≥0q /q with respect to some ideal q of A. There are Krull’s classical results saying that A is an integral domain resp. a normal domain if G is an integral domain resp. a normal domain. It follows from the work [1], [2], [8] that several oth...

In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems. Based on the synthetic manipulation of the method of steepest descent path, approximate expressions of the double integrals are derived in terms of the leadin...

Abstract. We are interested in algorithms for constructing surfaces Γ of possibly small measure that separate a given domain Ω into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians, p → 1, under homogeneous Neumann boundary condit...