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. Part of the book series (LEUS, volume 11) Abstract Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of ‘mathematics as calculation’ had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the ‘equation’ as known in Arabic algebra.
From the point of view of longterm dynamics, we study multivalued and single-valued semigroups of operators acting on complete metric spaces. We provide necessary and sufficient conditions for the existence of the global attractor under minimal requirements in terms of continuity of the semigroup. As an application, we consider the multivalued semigroup generated by the equation ruling the evolution of the specific humidity in a system of moist air, and we prove the existence of a regular global attractor. Euler, we define the elastic energy E(K) of a regular compact set K in the plane as 1/2 times the integral over the boundary of K of the square of the boundary curvature. We will denote by $A(K)$ the area of $K$ and $P(K)$ its perimeter. In this talk, we prove that for any convex set K the quotient A(K)E(K)/P(K) is larger than or equal to pi/2, with equality only for the disk.
We deduce that the disk minimizes the elastic energy with an area constraint. We will also consider analogous tridimensional problems involving the Willmore (or the Helfrich) energy linked to the modelling of vesicles. In this work we introduce a discrete functional space on general polygonal or polyhedral meshes which mimics two important properties of the standard Crouzeix-Raviart space, namely the continuity of mean values at interfaces and the existence of an interpolator which preserves the mean value of the gradient inside each element.
The construction borrows ideas from both Cell Centered Galerkin and Hybrid Finite Volume methods. More specifically, the discrete function space is defined from cell and face unknowns by introducing a suitable piecewise affine reconstruction on a pyramidal subdivision of the original mesh. This subdivision is fictitious in the sense that the original mesh is the only one that needs to be manipulated by the end-user. Two applications are considered in which the discrete space plays an important role, namely (i) the design of a locking-free primal (as opposed to mixed) method for quasi-incompressible linear elasticity on general polygonal meshes; (ii) the design of an inf-sup stable method for the Stokes equations on general polygonal or polyhedral meshes. In both cases, the relation between the proposed method and classical finite volume as well as finite element methods on standard meshes is investigated. Finally, it is shown how similar ideas can be exploited to mimic key properties of the lowest-order Raviart-Thomas space on general polygonal or polyhedral meshes. Contatto: [email protected]; [email protected].
It is well established that ventricular function is of utmost importance in maintaining hemodynamic stability and cardiac performance in its entirety. Oshin theme song free mp3 download. A handful of methods for evaluating flow in the cardiovascular system in vivo have been studied, yet little information has been obtained on the adequate relation of the flow pattern to proper cardiac performance.
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To this end, a novel method that combines both non invasive imaging and computational fluid dynamics has been developed. This integrated approach has been designed and developed with the scope of obtaining more accurate visualization and characterization of the human ventricles than can be obtained from traditional imaging alone.
Imaging-based numerical simulations offer, not only qualitative information, but a quantitative method for characterizing cardiac fluid and tissue mechanics of the ventricles. To name a few, the fluid residence time distribution, pressure gradient and principal strain, can be attained with the hopes of proving their relevance and importance in analyzing the progression of pathologic conditions and cardiac remodeling. An important aspect of this work is the lack of cardiac diagnostic markers obtained in normal subjects and the progression of mechanic adjustments leading to heart failure and remodeling. With this in mind a fundamental factor of the work presented herein is in the evaluation of the mechanical properties in healthy subjects compared with patients that have undergone remodeling as a result of heart failure. Contatto: [email protected].