Search results for "Computational Mathematic"
showing 10 items of 987 documents
Varieties of Algebras with Superinvolution of Almost Polynomial Growth
2015
Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let $c_{n}^{\ast }(A)$ be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
Adaptation based on interpolation errors for high order mesh refinement methods applied to conservation laws
2012
Adaptive mesh refinement is nowadays a widely used tool in the numerical solution of hyperbolic partial differential equations. The algorithm is based on the numerical approximation of the solution of the equations on a hierarchical set of meshes with different resolutions. Among the different parts that compose an adaptive mesh refinement algorithm, the decision of which level of resolution is adequate for each part of the domain, i.e., the design of a refinement criterion, is crucial for the performance of the algorithm. In this work we analyze a refinement strategy based on interpolation errors, as a building block of a high order adaptive mesh refinement algorithm. We show that this tec…
A computational study of several heuristics for the DRPP
1995
The problem of designing a route of minimum length for a postman that starts and finishes at his office and has to deliver the mail along a set of streets in a city is known as the Rural Postman Problem. When the postman has to obey the directions of the streets, we have the directed version of this problem. Finding an exact solution, in the general case, is intractably difficult. Hence, we have implemented three heuristic algorithms for approximately solving this problem and a procedure for obtaining a lower bound to the optimal length. Also, we present numerical experimentations based on a collection of random instances with up to 30 connected components, 240 vertices and 801 arcs. A lowe…
Set valued integrability in non separable Fréchet spaces and applications
2016
AbstractWe focus on measurability and integrability for set valued functions in non-necessarily separable Fréchet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.
An order-adaptive compact approximation Taylor method for systems of conservation laws
2021
Abstract We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered ( 2 p + 1 ) -point stencils, where p may take values in { 1 , 2 , … , P } according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p = 1 , 2 , … , P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where ( 2 p + 1 ) is the size of the biggest stencil in which large gradients are n…
Birkhoff's aesthetics, Arnheim's entropy. Some remarks on complexity and fuzzy entropy in arts
2015
A judgement of aesthetic in arts is, by sheer consensus, a daunting task that requires evaluation of a whole host of endogenous and exogenous cultural factors. A few of them can actually provide very useful hints in tackling foundational problems in Information Science in a more natural setting than what is usually provided by a typical engineering stance. This interaction can however work the other way about, as instruments from the Information and Computer Science toolkit may help in focusing the less explored features of art and its evaluation. When all the social, historical, hermeneutical and political considerations are stripped from the living flesh of the piece, we lose most of wha…
Future is where concepts, theories and applications meet (also in fuzzy logic)
2015
No one knows where the future lies, and the idea of serendipity in science is now raised to something of a tropism. This does not impede our will to predict, if not the exact events, at least the short–term trends in the disciplines we live and breathe, and to point at the (subjective) glaring chances for a bright future. This volume is a clear example of the need that any living scientific discipline has for constant regrouping and redirection, in a never–ending process of consolidating results and finding new paths. In this contribution we will try and focus on a number of areas of fuzzy logic and, by extension, in the whole word of uncertainty, where (in our opinion) a number of interest…
Some Numerical Remarks on a Meshless Approximation Method
2016
In this paper we consider sources of enhancement for the Smoothed Particle Hydrodynamics method in approximating a function and its derivatives. It is well known that the standard formulation is usually poor when scattered data distribution is considered or when the approximation near the boundary occurs. In this paper studies on the accuracy are provided and assessed with gridded and scattered data distribution in the problem domain. The improvements of the method are addressed and supporting numerical experiments are included.
A stochastic dynamic model to evaluate the influence of economy and well-being on unemployment control
2018
[EN] This paper presents a stochastic dynamic mathematical model to study the evolution of the unemployment rate and other relevant related variables in a country. This model is composed by three basic interrelated subsystems: demographic, economic and wellbeing ones. A key aspect of this model is that it considers three UN well-being variables simultaneously: Human Development Index, Gender Empowerment Index and Gender Differentiation Index. These variables involve key concepts for human development, as Health, Education, Economy and Female Labor. With this model, the most outstanding variables found in the literature in relation with unemployment control can be used to design strategies a…