Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Bishadowing and hyperbolicity

Shadowing of a dynamical system is often used to justify the validity of computer simulations of the system, and in numerical calculations an inverse form of the shadowing concept is also of some interest. In this paper we characterize the notion of shadowing in terms of stability, and express the notion of hyperbolicity using the concept of inverse shadowing.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Guidelines for the treatment of postmenopausal osteoporosis for general practitioners

BACKGROUND: Osteoporosis Australia has been committed to the education of general practitioners and the community with a series of updated guidelines on the management of osteoporosis. Since the last series was published in Australian Family Physician (August 2000), there have been further advances in our understanding of the treatments involved in both prevention of bone loss and the management of established osteoporosis. OBJECTIVE: This article represents updated guidelines for the treatment of postmenopausal osteoporosis to assist GPs identify those women at risk and to review current treatment strategies. DISCUSSION: Osteoporosis and its associated problems are major health concerns in Australia, especially with an aging population. While important principles of management are still considered to be maximising peak bone mass and preventing postmenopausal bone loss, new clinical trial data about drugs such as the bisphosphonates, raloxifene and oestrogen have recently become available and the relative role of various agents is gradually becoming clearer. The use of long term hormone replacement therapy has mixed risks and benefits that requires individual patient counselling.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Colet??nea planejamento e or??amento governamental: volume 2: pref??cio

Estabelece o objetivo da publica????o de se tornar material did??tico para a forma????o de servidores da Administra????o P??blica brasileira

Colet??nea planejamento e or??amento governamental: volume 2: a aus??ncia de uma teoria or??ament??ria

A respeito do aspecto mais significativo da or??amenta????o p??blica, ou seja, a aloca????o de gastos para diferentes prop??sitos de forma a se atingir o melhor retorno, a literatura or??ament??ria norte-americana ?? bastante ??rida. Esfor??ados estudiosos do campo or??ament??rio t??m-se ocupado principalmente com a organiza????o e o procedimento para a prepara????o do or??amento, as formas como as solicita????es de fundos s??osubmetidas, o formato da pe??a or??ament??ria em si e quest??es similares1.N??o se pode negar que esses aspectos merecem a considera????o a eles dispensada, quando se lembra da inacredit??vel resist??ncia ?? ado????o dos mais rudimentares quesitos b??sicos do or??amento e se observa sua condi????o insatisfat??ria ainda hoje em algumas jurisdi????es. No entanto, a dedica????o de energia para o estabelecimento da mec??nica do or??amento desviou a aten????o do problema essencial do or??amento (no lado do gasto), a saber: em que se deve basear a decis??o de se alocar x d??lares para a atividade a em vez de ser para a atividade b

Colet??nea planejamento e or??amento governamental: volume 2: conflitos e solu????es no or??amento federal

Esta obra trata da pol??tica e dos processos de elabora????o do or??amento federal e das pol??ticas que surgem da??. N??o h?? discuss??o completa sobre or??amento sem levar em considera????o esses tr??s aspectos. Muitas atividades governamentais combinam processo e pol??tica, por??m o or??amento ?? diferente, porque determinadas tarefas b??sicas precisam ser conclu??das a cada ano. Independentemente de qu??o dif??ceis sejam as escolhas e qu??o incerto seja o cen??rio futuro, o presidente precisa apresentar uma proposta e o Congresso precisa autorizar as dota????es. Se o presidente ou o Congresso decidirem que n??o ?? o momento de fazer mudan??as na pol??tica tribut??ria ou de abordar determinada proposta legislativa, qualquer um dos dois pode postergar as a????es at?? que se chegue a um acordo. Por??m, n??o podem esquivar-se da sua responsabilidade de decidir sobre o or??amento. Caso contr??rio, programas federais e organismos param, por aus??ncia de financiamento, e assim, tamb??m, o trabalho do governo. Ainda assim, mesmo quando ocorrem paralisa????es ??? mais recentemente em 1995-1996 ???, no final das contas, chega-se a um acordo entre o presidente e o Congresso

Colet??nea planejamento e or??amento governamental: volume 2: do or??amento por programas para o or??amento de desempenho: o desafio para economias de mercado emergentes

Primeiramente, este documento revisa a evolu????o do antigo modelo de or??amento de desempenho, introduzido nos Estados Unidos h?? mais de meio s??culo, para o novo modelo de or??amento de desempenho. Este, que cont??m muitos dos elementos do antigo modelo, est?? sendo cada vez mais aplicado em economias avan??adas, incluindo a dos Estados Unidos. Usando a classifica????o de modelos de or??amento derivada deste estudo, pode-se considerar que muitas das economias de mercado emergentes introduziram algum tipo de or??amento por programas, embora se saiba que o termo ?? utilizado de v??rias maneiras. Contudo, essas economias ainda precisam avan??ar para o or??amento por produtos e, subseq??entemente, incorporar as reformas necess??rias para o novo or??amento de desempenho. Neste documento, ser?? discutido que, pelo fato de n??o realizarem esse avan??o, as economias de mercado emergentes n??o conseguiram utilizar plenamente seus or??amentos por programas para melhorar a gest??o de seus or??amentos. Reconhece-se que dar esse passo n??o ?? f??cil e exige que quatro principais elementos sejam introduzidos e/ou fortalecidos para assegurar o sucesso de tal investida. Esses elementos devem ser considerados como a base da estrat??gia para a introdu????o do novo modelo de or??amento de desempenho.