Search results for "Calculus"
showing 10 items of 617 documents
Some Open Problems
2009
We have extensively considered here the use of Stone's theorem on the paracompactness of metric spaces in order to build up new techniques to construct an equivalent locally uniformly rotund norm on a given normed space X. The discreetness of the basis for the metric topologies gives us the necessary rigidity condition that appears in all the known cases of existence of such a renorming property [Hay99, MOTV06]. Our approximation process is based on co-σ-continuous maps using that they have separable fibers, see Sect. 2.2. We present now some problems that remain open in this area. Some of them are classical and have been asked by different authors in conferences, papers and books. Others h…
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
2007
Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational Formulations for Coupled BE/FE Methods in Elastostatics
1994
Ein gekoppeltes BEM/FEM-Problem aus der Elastostatik, ein typisches Substrukturproblem, wird im Rahmen der symmetrisch-definiten BEM behandelt. Es werden vier verschiedene Variationsformulierungen vorgestellt, in deren jeder die Transmissionsbedingungen gegenuber der Trennflache zwischen FE-Unterregion und BE-Unterregion die Rolle naturlicher Randbedingungen spielen. Zwei der oben erwahnten Formulierungen sind Stationaritatsprinzipien in gemischter Form, die anderen beiden sind Sattelpunkt-Prinzipien, d. h. Kombinationen des Rand-min-max-Prinzips entweder mit dem Prinzip der minimalen Gesamtpotentialenergie oder mit dem Prinzip der minimalen Gesamtkomplementaritatsenergie. Jedes der oben an…
Geometric Calculus Applications to Medical Imaging: Status and Perspectives
2021
Medical imaging data coming from different acquisition modalities requires automatic tools to extract useful information and support clinicians in the formulation of accurate diagnoses. Geometric Calculus (GC) offers a powerful mathematical and computational model for the development of effective medical imaging algorithms. The practical use of GC-based methods in medical imaging requires fast and efficient implementations to meet real-time processing constraints as well as accuracy and robustness requirements. The purpose of this article is to present the state of the art of the GC-based techniques for medical image analysis and processing. The use of GC-based paradigms in Radiomics and De…
Deciding properties of integral relational automata
1994
This paper investigates automated model checking possibilities for CTL* formulae over infinite transition systems represented by relational automata (RA). The general model checking problem for CTL* formulae over RA is shown undecidable, the undecidability being observed already on the class of Restricted CTL formulae. The decidability result, however, is obtained for another substantial subset of the logic, called A-CTL*+, which includes all ”linear time” formulae.
Sialolith and adenoid cystic carcinoma in the submandibular gland: a rare case
2011
Salivary calculi occur most frequently in the submandibular gland of the human beings. It is because of the specific anatomy of both the glands and its duct. Presentation typically consists of a painful swelling of the gland at meal times, when the effect of obstruction is most acute. The clinical signs, in most of times, can lead us to the diagnosis easily. The coexistence of sialolith and malignant tumors are very rare. This case report is about a male patient of 45 year with a swelling in the submandibular region for the last eighteen months with an intermittent episode of moderate to severe pain which increased during a mealtime and diagnosed as sialolith on radiograph, but on biopsy pr…
On the definition of viscosity solutions for parabolic equations
2001
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.
A new algorithm for a robust solution of the fully dynamic Saint-Venant equations
2003
A new procedure for the numerical solution of the fully dynamic shallow water equations is presented. The procedure is a fractional step methodology where the original system is split into two sequential ones. The first system differs from the original one because of the head gradient term, that is treated as constant and equal to the value computed at the end of the previous time step. The solution of this system, called kinematic, is computed in each element using a spatial zero order approximation for both the heads and the flow rates by means of integration of single ODEs. The second system is called diffusive, contains in the momentum equations only the complementary terms and can be e…
Are There Essentially Incomplete Knowledge Representation Systems?
2001
A mathematical model of a knowledge representation system (KR-system) is proposed. Its prototype is the concept of an information system in the sense of Z. Pawlak; however, the model is, in fact, a substantial extension of the latter. In our model, attributes may form an arbitrary category, where morphisms represent built-in functional dependencies, and uncertainty of knowledge is treated in terms of category theory via monads. Several notions of simulation are also considered for such KR-systems. In this general setting, the semiphilosophical problem mentioned in the title, still open, is given a precise meaning.
The Multiscale Stochastic Model of Fractional Hereditary Materials (FHM)
2013
Abstract In a recent paper the authors proposed a mechanical model corresponding, exactly, to fractional hereditary materials (FHM). Fractional derivation index 13 E [0,1/2] corresponds to a mechanical model composed by a column of massless newtonian fluid resting on a bed of independent linear springs. Fractional derivation index 13 E [1/2, 1], corresponds, instead, to a mechanical model constituted by massless, shear-type elastic column resting on a bed of linear independent dashpots. The real-order of derivation is related to the exponent of the power-law decay of mechanical characteristics. In this paper the authors aim to introduce a multiscale fractance description of FHM in presence …