We introduce the class of Rγ-convex functions and discuss that it relates to some other classes convexity. study in perspective trapezium-like inequalities, for which we also derive a new integral identity involving k-th order differentiable function. In show significance our results, several special cases offer interesting applications.

reconnaissance drought index (rdi) is based on fitting a log-normal distribution to the ratio of precipitation to evapotranspiration (eto) values in selected periods. in this index value of eto were calculated based on mean temperature by thorenth-waite (th) method. th method, may underestimated eto values comparing to the actual in arid and semi arid regions. the log-normal distribution may no...

N -th order Hankel Transforms are important for the reconstruction in Magnetic Resonance Imaging (MRI), CAT etc. In this contribution we derive new bounds on functions, which have bandlimited their n-th order Hankel Transform.

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite diierence schemes of Liu, Osher and Chan 9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L 1 norm) ENO schemes are (r +1) th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of...

Consider the differential equation $y'=F(x,y)$. We determine weakest possible upper bound on $|F(x,y)-F(x,z)|$ which guarantees that this has for all initial values a unique solution, exists globally.

In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, ...

Abstract. In this paper, we consider the discontinuous Galerkin (DG) methods to solve linear hyperbolic equations with singular initial data. With the help of weight functions, the superconvergence properties outside the pollution region will be investigated. We show that, by using piecewise polynomials of degree k and suitable initial discretizations, the DG solution is (2k+1)-th order accurat...

This work extends to processes with finite moments or order p, 1 < P < 2 and to symmetric a-stable processes, 1 < a < 2, some of the basic linear theory known for processes with finite second moments (p=2) and for Gaussian processes (a=2). Here the IIcovariationll plays a role analogous to the covariance. Specifically, stochastic integrals of two types are introduced and studied for p-th order ...