Parametric Integration Techniques

1989 ◽  
Vol 62 (5) ◽  
pp. 318 ◽  
Author(s):  
Aurel J. Zajta ◽  
Sudhir K. Goel
Keyword(s):  
Integration Techniques ◽  
Parametric Integration

Parametric Integration Techniques

1989 ◽  
Vol 62 (5) ◽  
pp. 318-322 ◽  
Author(s):  
Aurel J. Zajta ◽  
Sudhir K. Goel
Keyword(s):  
Integration Techniques ◽  
Parametric Integration

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

Variations on a theme – Euler and the logsine integral

2012 ◽  
Vol 96 (537) ◽  
pp. 451-458 ◽  
Author(s):  
Nick Lord
Keyword(s):  
Numerical Integration ◽  
Integration Techniques ◽  
Image Position ◽  
Variations On A Theme ◽  
Standard Integration

This article concerns the evaluation of the ‘logsine’ integralWe shall encounter it in several guises. Indeed, standard integration techniques used below readily show that (1) has the same value as the following integrals:En passant, it is worth noting that forms (6) and (7) are the best behaved for numerical integration.I first met the logsine integral as a callow youth in that strange hinterland of results that you may not have met at school but were not guaranteed to meet later on either.

Crisp and Fuzzy Optimisation Approaches for Water Network Retrofit

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Seingheng Hul ◽  
Denny K. S. Ng ◽  
Raymond R Tan ◽  
Choon-Lai Chiang ◽  
Dominic C. Y. Foo
Keyword(s):  
Linear Programming ◽  
Water Reuse ◽  
Process Integration ◽  
Paper Mill ◽  
Mixed Integer ◽  
Network Synthesis ◽  
Water Recovery ◽  
Water Network ◽  
Real Process ◽  
Integration Techniques

Material reuse/recycle has gained much attention in recent years for both economic and environmental reasons. Process integration techniques for water network synthesis have evolved rapidly in the past decade. With in-plant water reuse/recycle, fresh water and wastewater flowrates are reduced simultaneously. In this work, linear programming and mixed integer linear programming models that include piping cost and process constraints are developed to retrofit an existing water network in a paper mill that was not originally designed with process integration techniques. Five scenarios are presented, each representing different aspects of decision-making in real process integration projects. The fifth scenario makes use of fuzzy optimisation to achieve a compromise solution that considers the inherent conflict between maximising water recovery and minimising capital cost for retrofit.

scholarly journals PROPER CURVATURE COLLINEATIONS IN NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIMES

2008 ◽  
Vol 23 (05) ◽  
pp. 749-759 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. RAMZAN
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Infinite Dimensional ◽  
Riemann Matrix ◽  
Integration Techniques ◽  
Curvature Collineations ◽  
Proper Curvature

A study of nonstatic spherically symmetric space–times according to their proper curvature collineations is given by using the rank of the 6×6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each case of the above space–times it is shown that when the above space–times admit proper curvature collineations, they turn out to be static spherically symmetric and form an infinite dimensional vector space. In the nonstatic cases curvature collineations are just Killing vector fields.

Stretchable Systems

2021 ◽  
Author(s):  
Yogeenth Kumaresan ◽  
Nivasan Yogeswaran ◽  
Luigi G. Occhipinti ◽  
Ravinder Dahiya
Keyword(s):  
Flexible Electronics ◽  
High Performance ◽  
Electrical Response ◽  
Inorganic Compounds ◽  
Stretchable Electronics ◽  
Material Research ◽  
Active Materials ◽  
Challenges And Opportunities ◽  
Integration Techniques ◽  
Strain Invariant

Stretchable electronics is one of the transformative pillars of future flexible electronics. As a result, the research on new passive and active materials, novel designs, and engineering approaches has attracted significant interest. Recent studies have highlighted the importance of new approaches that enable the integration of high-performance materials, including, organic and inorganic compounds, carbon-based and layered materials, and composites to serve as conductors, semiconductors or insulators, with the ability to accommodate electronics on stretchable substrates. This Element presents a discussion about the strategies that have been developed for obtaining stretchable systems, with a focus on various stretchable geometries to achieve strain invariant electrical response, and summarises the recent advances in terms of material research, various integration techniques of high-performance electronics. In addition, some of the applications, challenges and opportunities associated with the development of stretchable electronics are discussed.

Sign in / Sign up

Export Citation Format

Share Document