One of the most basic tools in the theory of automorphic forms is the truncation operator, first defined in [Langlands: 1966] but elaborated in later work of Jim Arthur (particularly [Arthur: 1978] and [Arthur: 1980]). In spite of its fundamental nature, there are many mysteries about it. In this article I’ll not dispel many of these, but I’ll at least motivate its definition by relating it to ...

kernel density estimators are the basic tools for density estimation in non-parametric statistics.  the k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in  which  the  bandwidth  is varied depending on the location of the sample points. in this paper‎, we  initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...

To cite: Matsumoto N, Suzuki Y, Yoda S, et al. BMJ Case Rep Published online: [please include Day Month Year] doi:10.1136/bcr-2014205407 DESCRIPTION Recognition of the truncation artefact is important for the control of image quality on myocardial perfusion images in single-photon emission CT (SPECT). Truncation artefact is usually seen in obese patients who may deviate from a γ-ray detector fi...

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

Ideal integrating nephelometers integrate light scattered by particles over all directions. However, real nephelometers truncate light scattered in near-forward and near-backward directions below a certain truncation angle ~typically 7°!. This results in truncation errors, with the forward truncation error becoming important for large particles. Truncation errors are commonly calculated using M...

This comparison paper scrutinizes image compression using Block Truncation Coding. Many algorithms were selected likely the original Block Truncation coding, Absolute Moment Block Truncation Coding, a comparison survey was executed. These above techniques are divided image into non overlapping blocks. They distinguish in the direction of choosing the quantization level in order to remove redund...