Search results for "Calculus"
showing 10 items of 617 documents
Shock-capturing schemes: high accuracy versus total-variation boundedness
2007
In this reseach work we analyze the total variation growth of some high order accurate reconstruction procedures used for the design of shock capturing schemes. This study allows to measure how oscillatory a high order accurate method is in terms of the basic elementary function chosen to increase the order of accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …
Free energy and states of fractional-order hereditariness
2014
AbstractComplex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.
Theorems of restricted dynamic shakedown
1993
Abstract Dynamic shakedown for a rate-independent material with internal variables is addressed in the hypothesis that the load values are restricted to those of a specified load history of finite or even infinite duration, thus ruling out the possibility—typical of classical shakedown theory—of indefinite load repetitions. Instead of the usual approach to dynamic shakedown, based on the bounded plastic work criterion, another approach is adopted here, based on the adaptation time criterion. Static, kinematic and mixed-form theorems are presented, which characterize the minimum adaptation time (MAT), a feature of the structure-load system, but which are also able to assess whether plastic w…
Characterizations of convex approximate subdifferential calculus in Banach spaces
2016
International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.
A multidisciplinary approach to Neolithic dietary reconstruction: the case of “le Vigneau” site (ca. 4400 BC; Indre-et-Loire, France)
2016
International audience
On students' understanding of Riemann sums of integrals of functions of two variables
2018
International audience; APOS (Action-Process-Object-Schema) Theory is used to pose and test a conjecture of mental constructions that may be used to understand the relation between integrals of two variable functions over rectangles and corresponding Riemann sums. Interviews with ten students who had just finished a multivariable calculus course showed that the conjectured mental constructions are necessary.
The Role of Differential Parameters in Beltrami's Work
1997
Abstract Differential parameters play a relevant role in Beltrami's mathematical work. They are employed in different contexts, in order to express some well-known results in a new way and to extend potential theory and the theory of elasticity to a Riemannian manifold. The author aims to show that differential parameters enabled Beltrami to solve many mathematical questions and that they constitute the first step toward the conception of tensor calculus. Les parametres differentiels jouent un role important dans l'oeuvre mathematique de Beltrami. Ils sont employes en contextes differents, pour exprimer dans une maniere nouvelle quelques resultats bien-connus et pour generaliser la theorie …
On a posteriori error bounds for approximations of the generalized Stokes problem generated by the Uzawa algorithm
2012
In this paper, we derive computable a posteriori error bounds for approximations computed by the Uzawa algorithm for the generalized Stokes problem. We show that for each Uzawa iteration both the velocity error and the pressure error are bounded from above by a constant multiplied by the L2-norm of the divergence of the velocity. The derivation of the estimates essentially uses a posteriori estimates of the functional type for the Stokes problem. peerReviewed
An Archimedean research theme: the calculation of the volume of cylindrical groins
2010
Starting from Archimedes’ method for calculating the volume of cylindrical wedges, I want to get to describe a method of 18th century for cilindrical groins thought by Girolamo Settimo and Nicolo di Martino. Several mathematicians studied the measurement of wedges, by applying notions of infinitesimal and integral calculus; in particular I examinated Settimo’s Treatise on cylindrical groins, where the author solved several problems by means of integrals.