Search results for "divergence"
showing 10 items of 257 documents
Generalized Harnack inequality for semilinear elliptic equations
2015
Abstract This paper is concerned with semilinear equations in divergence form div ( A ( x ) D u ) = f ( u ) , where f : R → [ 0 , ∞ ) is nondecreasing. We introduce a sharp Harnack type inequality for nonnegative solutions which is a quantified version of the condition for strong maximum principle found by Vazquez and Pucci–Serrin in [30] , [24] and is closely related to the classical Keller–Osserman condition [15] , [22] for the existence of entire solutions.
Korn inequality on irregular domains
2013
Abstract In this paper, we study the weighted Korn inequality on some irregular domains, e.g., s-John domains and domains satisfying quasihyperbolic boundary conditions. Examples regarding sharpness of the Korn inequality on these domains are presented. Moreover, we show that Korn inequalities imply certain Poincare inequality.
The General Stokes’s Theorem
2012
Let ω be a differential form of degree k - 1 and class C 1 in a neighborhood of a compact regular k-surface with boundary M of class C 2. The general Stokes’s theorem gives a relationship between the integral of ω over the boundary of M and the integral of the exterior differential dω over M. It can be viewed as a generalization of Green’s theorem to higher dimensions, and it plays a role not unlike that of the fundamental theorem of calculus in an elementary course of analysis. Particular cases of the general Stokes’s theorem that are of great importance are the divergence theorem, which relates a triple integral with a surface integral and what we know as the classical Stokes’s theorem, w…
Instruction-based clinical eye-tracking study on the visual interpretation of divergence : how do students look at vector field plots?
2018
Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N = 41 physics majors. We found that students’ performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88…
Tetrolet-based reduced reference image quality assessment approach
2014
In this paper, we propose a new reduced reference image quality assessment (RRIQA) scheme. For this purpose, we use a statistical-based method in a new adaptive Haar wavelet transform domain, called Tetrolet. Firstly, we decompose the reference and distorted images and we obtain the Tetrolet coefficients for each image. Secondly, we use a marginal Generalized Gaussian Density (GGD) to model each subband coefficients. Finally, the distortion measure is computed using the Kullback Leibler Divergence (KLD) between GGD Probability density function (PDFs). Experimental results show the efficiency of the proposed method when comparing to those reported in the literature.
On the Choice of the Most Suitable Period to Map Hill Lakes via Spectral Separability and Object-Based Image Analyses
2023
Technological advances in Earth observation made images characterized by high spatial and temporal resolutions available, nevertheless bringing with them the radiometric heterogeneity of small geographical entities, often also changing in time. Among small geographical entities, hill lakes exhibit a widespread distribution, and their census is sometimes partial or shows unreliable data. High resolution and heterogeneity have boosted the development of geographic object-based image analysis algorithms. This research analyzes which is the most suitable period for acquiring satellite images to identify and delimitate hill lakes. This is achieved by analyzing the spectral separability of the su…
Multiscale Model Selection for High-Frequency Financial Data of a Large Tick Stock by Means of the Jensen–Shannon Metric
2014
Modeling financial time series at different time scales is still an open challenge. The choice of a suitable indicator quantifying the distance between the model and the data is therefore of fundamental importance for selecting models. In this paper, we propose a multiscale model selection method based on the Jensen–Shannon distance in order to select the model that is able to better reproduce the distribution of price changes at different time scales. Specifically, we consider the problem of modeling the ultra high frequency dynamics of an asset with a large tick-to-price ratio. We study the price process at different time scales and compute the Jensen–Shannon distance between the original…
Future directions in Agile research: Alignment and divergence between research and practice
2017
Editorial article Since the publication of Agile Manifesto in 2001, agile methods have transited from a grass- root initiative among enthusiastic advocates and developers to a mainstream software development approach adopted by both small and large companies worldwide. Meanwhile research on agile methods has grown rapidly and steadily into an established research area, evidenced by dedicated conferences (e.g., XP conference series, research track of previous Agile Conference series), special issues and sections in top Information Systems and Software Engineering journals. However, practitioners and consultants have largely driven the advancement in agile field, and agile research has lagged…
Pleistocene allopatric differentiation followed by recent range expansion explains the distribution and molecular diversity of two congeneric crustac…
2021
AbstractPleistocene glaciations had a tremendous impact on the biota across the Palaearctic, resulting in strong phylogeographic signals of range contraction and rapid postglacial recolonization of the deglaciated areas. Here, we explore the diversity patterns and history of two sibling species of passively dispersing taxa typical of temporary ponds, fairy shrimps (Anostraca). We combine mitochondrial (COI) and nuclear (ITS2 and 18S) markers to conduct a range-wide phylogeographic study including 56 populations of Branchinecta ferox and Branchinecta orientalis in the Palaearctic. Specifically, we investigate whether their largely overlapping ranges in Europe resulted from allopatric differe…
Adaptation to Low Salinity Promotes Genomic Divergence in Atlantic Cod (Gadus morhua L.).
2015
How genomic selection enables species to adapt to divergent environments is a fundamental question in ecology and evolution. We investigated the genomic signatures of local adaptation in Atlantic cod (Gadus morhua L.) along a natural salinity gradient, ranging from 35‰ in the North Sea to 7‰ within the Baltic Sea. By utilizing a 12 K SNPchip, we simultaneously assessed neutral and adaptive genetic divergence across the Atlantic cod genome. Combining outlier analyses with a landscape genomic approach, we identified a set of directionally selected loci that are strongly correlated with habitat differences in salinity, oxygen, and temperature. Our results show that discrete regions within the …