Search results for "Mathematica"

The stability problem and noisy projections in discrete tomography

2004

Abstract The new field of research of discrete tomography will be described in this paper. It differs from standard computerized tomography in the reduced number of projections. It needs ad hoc algorithms which usually are based on the definition of the model of the object to reconstruct. The main problems will be introduced and an experimental simulation will prove the robustness of a slightly modified version of a well known method for the reconstruction of binary planar convex sets, even in case of projections affected by error. To the best of our knowledge this is one of the first experimental study of the stability problem with a statistical approach. Prospective applications include c…

Riccati equation-based generalization of Dawson's integral function

2007

A new generalization of Dawson's integral function based on the link between a Riccati nonlinear differential equation and a second-order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is built up and to this end an explicit formula for a generic cofactor of a triangular matrix is deduced.

Personal Reflections on Dirk Jan Struik By Joseph W. Dauben

2018

Dirk Jan Struik, who taught for many years at the Massachusetts Institute of Technology and died on 21 October 2000 at the age of 106, was a distinguished mathematician and influential teacher. He was also widely known as a leading Marxist scholar and social activist. His early work on vector and tensor analysis, undertaken together with Jan Arnoldus Schouten, helped impart new mathematical techniques needed to master Einstein’s general theory of relativity. This collaboration lasted for over 20 years, but by the end of the 1930s, Struik came to realize that the heyday of the Ricci calculus had passed. After the Second World War, having now entered his 50s, he gave up mathematical research …

Markovian Connection, Curvature and Weitzenböck Formula on Riemannian Path Spaces

2001

Abstract We shall consider on a Riemannian path space P m o ( M ) the Cruzeiro–Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbock formula will be established. To this end, we shall introduce an “inner product” between the tangent processes and simple vector fields.

Graded metrics adapted to splittings

1997

Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul, are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry: It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion an…

The Bochner and Riesz integral representations for the Radon transform

1984

A non-stationary one-ring scattering model

2013

This paper introduces a non-stationary one-ring scattering model in which the mobile station (MS) can move along a straight line from the ring's center to the border of the ring. This movement results in a time-variant angle-of-arrival (AOA), which is modeled by a stochastic process. We derive the first-order density of the AOA process in closed form. Subsequently, a closed-form expression is provided for the local power spectral density (PSD) of the channel. We also formulate the local autocorrelation function (ACF) of the complex channel gain in integral form, from which a highly accurate closed-form approximation is derived. Furthermore, the average Doppler shift and the Doppler spread o…

Application of Graded Fuzzy Preconcept Lattices in Risk Analysis

2021

A Generalization of the Mean-Variance Analysis

2008

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This "mean-partial moments" utility generalizes not only the mean-variance utility of Tobin and Markowitz, but also the mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision…

On Aggregation of Risk Levels Using T-Conorms

2019

This paper deals with solutions for numeric evaluation of risks containing several different risk factors assessed by experts. The proposed methods can be used to assess the risks and obtain the risk scores in different industries, including financial industry, but they are also suitable for assessing risks in other areas, e.g. project management. While risk is usually considered as a function of probability and impact with strong quantitative background, there are many practical cases when only qualitative risk assessment based on expert opinions can be used. At the same time there are still requirements and needs for applying numerical values and mathematical models to such qualitative as…