Algebraic Computations with Hausdorff Continuous Functions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Mathematics Subject Classification: 44A05, 46F12, 28A78

Single-function approach to calibrating whatman n.º 42 filter paper based on suction versus water content relationships

Several suction–water-content (s-w) calibrations for the filter paper method (FPM) used for soil-suction measurement have been published. Most of the calibrations involve a bilinear function (i.e., two different equations) with an inflection point occurring at 60 kPa<s<100 kPa (i.e., 40 %<w<50 %). An approach for defining a continuous calibration function with a smooth transition between the high and low suctions based on a regression analysis of various previously published calibrations obtained for filter paper Whatman No. 42 (W42) is presented and discussed. The approach is applied herein to data obtained from three establish bilinear calibrations (six equations) for W42 filter paper to determine the two fitting parameters of the continuous function. An experimental evaluation of the new calibration show that the suctions estimated by the contact FPM test using the proposed function compare well with suctions measured by other laboratory techniques for two different soils for the suction range of 50 kPa<s<400 kPa, which corresponds to a water content range of 30 %<w<55 %.

A discrete forest in a continuous landscape : investigating interactions between natural resource management and sustainable development

Summary Forests are key ecosystems of the earth and associated with a large range of functions. Many of these functions are beneficial to humans and are referred to as ecosystem services. Sustainable development requires that all relevant ecosystem services are quantified, managed and monitored equally. Natural resource management therefore targets the services associated with ecosystems. The main hypothesis of this thesis is that the spatial and temporal domains of relevant services do not correspond to a discrete forest ecosystem. As a consequence, the services are not quantified, managed and monitored in an equal and sustainable manner. The thesis aims were therefore to test this hypothesis, establish an improved conceptual approach and provide spatial applications for the relevant land cover and structure variables. The study was carried out in western Switzerland and based primarily on data from a countrywide landscape inventory. This inventory is part of the third Swiss national forest inventory and assesses continuous landscape variables based on a regular sampling of true colour aerial imagery. In addition, land cover variables were derived from Landsat 5 TM passive sensor data and land structure variables from active sensor data from a small footprint laserscanning system. The results confirmed the main hypothesis, as relevant services did not scale well with the forest ecosystem. Instead, a new conceptual approach for sustainable management of natural resources was described. This concept quantifies the services as a continuous function of the landscape, rather than a discrete function of the forest ecosystem. The explanatory landscape variables are therefore called continuous fields and the forest becomes a dependent and function-driven management unit. Continuous field mapping methods were established for land cover and structure variables. In conclusion, the discrete forest ecosystem is an adequate planning and management unit. However, monitoring the state of and trends in sustainability of services requires them to be quantified as a continuous function of the landscape. Sustainable natural resource management iteratively combines the ecosystem and gradient approaches. Résumé Les forêts sont des écosystèmes-clés de la terre et on leur attribue un grand nombre de fonctions. Beaucoup de ces fonctions sont bénéfiques pour l'homme et sont nommées services écosystémiques. Le développement durable exige que ces services écosystémiques soient tous quantifiés, gérés et surveillés de façon égale. La gestion des ressources naturelles a donc pour cible les services attribués aux écosystèmes. L'hypothèse principale de cette thèse est que les domaines spatiaux et temporels des services attribués à la forêt ne correspondent pas à un écosystème discret. Par conséquent, les services ne sont pas quantifiés, aménagés et surveillés d'une manière équivalente et durable. Les buts de la thèse étaient de tester cette hypothèse, d'établir une nouvelle approche conceptuelle de la gestion des ressources naturelles et de préparer des applications spatiales pour les variables paysagères et structurelles appropriées. L'étude a été menée en Suisse occidentale principalement sur la base d'un inventaire de paysage à l'échelon national. Cet inventaire fait partie du troisième inventaire forestier national suisse et mesure de façon continue des variables paysagères sur la base d'un échantillonnage régulier sur des photos aériennes couleur. En outre, des variables de couverture ? terrestre ont été dérivées des données d'un senseur passif Landsat 5 TM, ainsi que des variables structurelles, dérivées du laserscanning, un senseur actif. Les résultats confirment l'hypothèse principale, car l'échelle des services ne correspond pas à celle de l'écosystème forestier. Au lieu de cela, une nouvelle approche a été élaborée pour la gestion durable des ressources naturelles. Ce concept représente les services comme une fonction continue du paysage, plutôt qu'une fonction discrète de l'écosystème forestier. En conséquence, les variables explicatives de paysage sont dénommées continuous fields et la forêt devient une entité dépendante, définie par la fonction principale du paysage. Des méthodes correspondantes pour la couverture terrestre et la structure ont été élaborées. En conclusion, l'écosystème forestier discret est une unité adéquate pour la planification et la gestion. En revanche, la surveillance de la durabilité de l'état et de son évolution exige que les services soient quantifiés comme fonction continue du paysage. La gestion durable des ressources naturelles joint donc l'approche écosystémique avec celle du gradient de manière itérative.

An indecomposable Banach space of continuous functions which has small density

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight omega(1) < 2(omega) such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

On turbulent, erratic and other dynamical properties of Zadeh's extensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaos induced by turbulent and erratic functions

Let (X, d) be a compact metric space and f: X → X a continuous function and consider the hyperspace (K(X), H) of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d. Let f̄: K(X) → K (X) be defined by f̄(A) = {f(a)/a ∈ A} the natural extension of f to K(X), then the aim of this work is to study the dynamics of f when f is turbulent (erratic, respectively) and its relationships.

Metodologia para analise cinematica da corrida

Universidade Estadual de Campinas. Faculdade de Educação Física

Metodologia para a suavização de dados biomecanicos por função não parametrica ponderada local robusta

Universidade Estadual de Campinas. Faculdade de Educação Física

Pitfalls driven by the sole use of local updates in dynamical

The recent claim that the exit probability (EP) of a slightly modified version of the Sznadj model is a continuous function of the initial magnetization is questioned. This result has been obtained analytically and confirmed by Monte Carlo simulations, simultaneously and independently by two different groups (EPL, 82 (2008) 18006; 18007). It stands at odds with an earlier result which yielded a step function for the EP (Europhys. Lett., 70 (2005) 705). The dispute is investigated by proving that the continuous shape of the EP is a direct outcome of a mean-field treatment for the analytical result. As such, it is most likely to be caused by finite-size effects in the simulations. The improbable alternative would be a signature of the irrelevance of fluctuations in this system. Indeed, evidence is provided in support of the stepwise shape as going beyond the mean-field level. These findings yield new insight in the physics of one-dimensional systems with respect to the validity of a true equilibrium state when using solely local update rules. The suitability and the significance to perform numerical simulations in those cases is discussed. To conclude, a great deal of caution is required when applying updates rules to describe any system especially social systems. Copyright (C) EPLA, 2011

EXISTENCE OF S-ASYMPTOTICALLY omega-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

A bounded continuous function it u : [0, infinity) -> X is said to be S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. This paper is devoted to study the existence and qualitative properties of S-asymptotically omega-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay, Furthermore, applications to partial differential equations are given.

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.