The nonuniform convergence of the Fourier series for discontinuous functions, and in particular the oscillatory behavior of the finite sum, was already analyzed by Wilbraham in 1848. This was later named the Gibbs phenomenon. This article is a review of the Gibbs phenomenon from a different perspective. The Gibbs phenomenon, as we view it, deals with the issue of recovering point values of a fu...

A combined compact difference scheme is proposed for linear second-order partial differential equations with mixed derivative. The scheme is based on a nine-point stencil at interior with sixth-order accurate local truncation error. Fourier analysis is used to analyze the spectral resolution of the proposed scheme. Numerical tests demonstrate at least sixth-order convergence rate with Dirichlet...

MOTIVATION As the invention of DNA sequencing in the 70s, computational biologists have had to deal with the problem of de novo genome assembly with limited (or insufficient) depth of sequencing. In this work, we investigate the opposite problem, that is, the challenge of dealing with excessive depth of sequencing. RESULTS We explore the effect of ultra-deep sequencing data in two domains: (i...

The parametric cubic curve is a well-developed subject in the field of computer-aided design. Yet there are still some aspects of its nature that need to be more fully investigated. In this paper, formulations of composite PC curves are presented in an order of increasing rigorousness and order of accuracy. A unique PC curve formulation is developed for the practical use in circle approximation...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil ...

This paper presents a conservative front-tracking method for shocks and contact discontinuities that is second-order accurate. It is based on a volume-of-fluid method that treats the moving front with concepts similar to those of an embedded-boundary method. Special care is taken in the centering of the data to ensure the right order of accuracy at the front, and a redistribution step guarantee...

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing de...

Difference schemes are treated as operator equations in real linear normed space [l, 23. Twoand three-layer schemes are discussed in real Hilbert space (more precisely, in unitary space, since no use is made of completeness). Stable schemes are classified. Schemes are written in a canonical form that enables stability operators, or what will be termed regularizers, to be introduced. Sufficient ...

Neotropius atherinoides locally known as Batasi fish and considered as freshwater small indigenous species (SIS) in Bangladesh. The present study describes the first complete, inclusive description of length-weight relationships (LWRs), length-length relationships (LLRs), condition factors (Fulton’s, KF; Relative, KR) and the breeding biology in the adjacent river of Chalon beel, Bangladesh. Th...

The current study was an attempt to investigate the impact of grouping type on the grammatical accuracy of Iranian EFL learners in collaborative writing. Through administering the Michigan Test of English Language Proficiency, 64 female university students available participated in this study and were assigned to two groups--heterogeneous and homogeneous. The treatment process lasted 12 weeks o...