Search results for "Partial derivative"
showing 10 items of 22 documents
Macroscopic expressions of molecular adiabatic compressibility of methyl and ethyl caprate under high pressure and high temperature
2014
The molecular compressibility, which is a macroscopic quantity to reveal the microcompressibility by additivity of molecular constitutions, is considered as a fixed value for specific organic liquids. In this study, we introduced two calculated expressions of molecular adiabatic compressibility to demonstrate its pressure and temperature dependency. The first one was developed from Wada’s constant expression based on experimental data of density and sound velocity. Secondly, by introducing the 2D fitting expressions and their partial derivative of pressure and temperature, molecular compressibility dependency was analyzed further, and a 3D fitting expression was obtained from the calculated…
Tabu and Scatter Search for Artificial Neural Networks
2003
In this paper we address the problem of training multilayer feed-forward neural networks. These networks have been widely used for both prediction and classification in many different areas. Although the most popular method for training these networks is back propagation, other optimization methods such as tabu search or scatter search have been applied to solve this problem. This paper presents a new training algorithm based on the tabu search methodology that incorporates elements for search intensification and diversification by utilizing strategic designs where other previous approaches resort to randomization. Our method considers context and search information, as it is provided by th…
Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumpi…
2019
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $\delta$ functions) discontinuities, the Dirac $\delta$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the …
A remark on differentiable functions with partial derivatives in Lp
2004
AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.
Image Inpainting Methods Evaluation and Improvement
2014
With the upgrowing of digital processing of images and film archiving, the need for assisted or unsupervised restoration required the development of a series of methods and techniques. Among them, image inpainting is maybe the most impressive and useful. Based on partial derivative equations or texture synthesis, many other hybrid techniques have been proposed recently. The need for an analytical comparison, beside the visual one, urged us to perform the studies shown in the present paper. Starting with an overview of the domain, an evaluation of the five methods was performed using a common benchmark and measuring the PSNR. Conclusions regarding the performance of the investigated algorith…
The edge-of-the-wedge theorem for systems of constant coefficient partial differential operators. I
1988
On demontre des resultats sur l'extendabilite holomorphe des fonctions holomorphes definies sur deux coins ou plus et pour lesquelles la somme des valeurs limites s'annulent
A Robustness Approach to Reliability
2012
Reliability of products is here regarded with respect to failure avoidance rather than probability of failure. To avoid failures, we emphasize variation and suggest some powerful tools for handling failures due to variation. Thus, instead of technical calculation of probabilities from data that usually are too weak for correct results, we emphasize the statistical thinking that puts the designers focus on the critical product functions. Making the design insensitive to unavoidable variation is called robust design and is handled by (i) identification and classification of variation, (ii) design of experiments to find robust solutions, and (iii) statistically based estimations of proper safe…
A nonlinear algorithm for monotone piecewise bicubic interpolation
2016
We present an algorithm for monotone interpolation on a rectangular mesh.We use the sufficient conditions for monotonicity of Carlton and Fritsch.We use nonlinear techniques to approximate the partial derivatives at the grid points.We develop piecewise bicubic Hermite interpolants with these approximations.We present some numerical examples where we compare different results. In this paper we present an algorithm for monotone interpolation of monotone data on a rectangular mesh by piecewise bicubic functions. Carlton and Fritsch (1985) develop conditions on the Hermite derivatives that are sufficient for such a function to be monotone. Here we extend our results of Arandiga (2013) to obtain…
Mappings of Finite Distortion:¶Discreteness and Openness
2001
We establish a sharp integrability condition on the partial derivatives of a mapping with L p -integrable distortion for some p>n− 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.
On functions with derivatives in a Lorentz space
1999
We establish a sharp integrability condition on the partial derivatives of a Sobolev mapping to guarantee that sets of measure zero get mapped to sets of measure zero. This condition is sharp also for continuity and differentiability almost everywhere.