The Equivalent Effect Function (EEF) is defined as having the identical integral values on the control points of the original time series data; the EEF can be obtained from the derivative of the spline function passing through the integral values on the control points. By choosing control points with different criteria, the EEF can be used to find the intrinsic mode function(IMF, fluctuation) a...

Hawking and the author have proposed a class of singular, finite action instantons for defining the initial conditions for inflation. Vilenkin has argued they are unacceptable. He exhibited an analogous class of asymptotically flat instantons which on the face of it lead to an instability of Minkowski space. However, all these instantons must be defined by introducing a constraint into the path...

In [21] this theorem is used by L. v. Wolfersdorf to consider singular integral equations on the real halfline involving the singular (complex) Hilbert operator. This theory is extended by Askabarov in [1] to the complex case. We want to investigate a special family of singular integral operators in Clifford analysis which has in IR an application to the nonlinear magnetic field equation ([5]) ...

The purpose of this paper is to extend and clarify the methods of the papers [G1] and [G2] by using the methods of [G3], incorporating ideas from Carnot-Caratheodory geometry such as those of the fundamental paper [NSW]. We will thereby prove an analogue for singular Radon transforms to the T (1) theorem of David and Journe [DJ]. As in [G1] and [G2], we will associate a singular integral operat...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...

We prove a local T (b) theorem for singular integral operators in the spirit of the one for perfect dyadic singular integral operators obtained by Hofmann, Muscalu, Thiele, Tao and the first author. The method consists in reducing one situation to the other by representing via the Beylkin-Coifman-Rokhlin algorithm any singular integral operator with truncated kernel as the sum of a bounded oper...

There are several methods for proving the existence of the solution to the elliptic boundary problem Lu = f in D, u|S = 0, (∗). Here L is an elliptic operator of second order, f is a given function, and uniqueness of the solution to problem (*) is assumed. The known methods for proving the existence of the solution to (*) include variational methods, integral equation methods, method of upper a...

This paper is concerned with d = 2 dimensional lattice field models with action V (∇φ(·)), where V : Rd → R is a uniformly convex function. The fluctuations of the variable φ(0) − φ(x) are studied for large |x| via the generating function given by g(x, μ) = ln〈e〉A. In two dimensions g′′(x, μ) = ∂2g(x, μ)/∂μ2 is proportional to ln |x|. The main result of this paper is a bound on g′′′(x, μ) = ∂3g...

Let Ω ∈ L(logL+)2(Sn−1 × Sm−1) (n, m 2) satisfy some cancellation conditions. We prove the Lp boundedness (1 < p < ∞ ) of the singular integral T f (x1,x2) = p. v. ∫ ∫ Rn×Rm Ω(y1,y ′ 2)h(ρ1(y1),ρ2(y2)) ρα 1 (y1)ρ β 2 (y2) f (x1 − y1,x2 − y2)dy1 dy2, where ρ1 , ρ2 are some metrics which are homogeneous with respect to certain non-isotropic dilations. We also study the above singular integral alo...

The goal of this article is to obtain bounds on the coefficients of modular and integral flow and tension polynomials of graphs. To this end we use the fact that these polynomials can be realized as Ehrhart polynomials of inside-out polytopes. Inside-out polytopes come with an associated relative polytopal complex and, for a wide class of inside-out polytopes, we show that this complex has a co...