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- Extension methods for convolution type operatorsPublication . Simões, A. M.The purpose of this work is to present a study of extension methods for convolution type operators. The extension methods presented are useful to construct relations between operators and is well known that the relations between operators presented in this work plays an important role in the study of a large number of mathematical and physical problems in particular in the problems of wave diffraction and receive great importance in many other applications.
- Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equationsPublication . Simões, A. M.; Castro, L. P.The purpose of this paper is to study different kinds of stability for a class of Hammerstein integral equations. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of Hammerstein integral equations. The consequent different cases of a finite interval and an infinite interval are considered, and some concrete examples are included to illustrate the results.
- New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential EquationsPublication . Simões, Alberto M.; Carapau, Fernando; Correia, PauloIn this work, we present suficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the sigma-semi-Hyers-Ulam stability, which is in some sense between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities. These new suficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a speci fic generalization of the Bielecki metric.
- Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of integral equations on finite intervalsPublication . Simões, A. M.; Castro, L. P.The purpose of this work is to study different kinds of stability for a class of integral equations defined on a finite interval. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability by using fixed point techniques and the Bielecki metric.
- Stabilities for a class of higher order integro-differential equationsPublication . Castro, L. P.; Simões, A. M.This work is devoted to analyse different kinds of stabilities for higher order integro-differential equations within appropriate metric spaces. We will consider the σ-semi-Hyers-Ulam stability which is a new kind of stability somehow between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities. Sufficient conditions are obtained in view to guarantee Hyers-Ulam, σ-semiHyers-Ulam and Hyers-Ulam-Rassias stabilities for such a class of integro-differential equations. We will be considering finite and infinite intervals as integration domains. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric.
- Higher education methodologies: from urban planning to mathematical issuesPublication . Virtudes, Ana L.; Rodrigues, Ilda; Simões, A. M.; Serôdio, RogérioThis article will be focused on higher education learning and teaching methodologies, based on the experience of the Master Degree in Civil Engineering at the University of Beira Interior, in Covilhã (Portugal). It aims to present the results of the practises used by scholar of urban planning and mathematical issues, both regarding the civil engineering research field. Actually, there are some similarities in between the research process features of urban planning domain and mathematics field in order to promote the students’ success. In fact, these both scientific subjects follow analogous tasks in their research processes, not only regarding the same starting point which is the definition of the research problem, but also observing the final phase, which is based on the findings of results, or the proposed solution. It joins scholars from the department of civil engineering and architecture, experts in spatial analysis and scholars from the department of mathematics of the University of Beira Interior (UBI). One case study will be presented as an example and pioneer research of the application of these methodological approaches. It will be focused on the urban planning experiences, associated with postgraduate teachings. It is related to a PhD thesis in Civil Engineering focused on urban planning issues.
- Hyers-Ulam stability of a certain Fredholm integral equationPublication . Simões, A. M.; Selvan, PonmanaIn this paper, by using Fixed point Theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind and non-homogeneous equation.
- Convertible Subspaces of Hessenberg-Type MatricesPublication . Cruz, Henrique F. Da; Rodrigues, Ilda Inácio; Serôdio, Rogério; Simões, A. M.; Velhinho, JoseWe describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.
- Research methodologies focused on urban planning and mathematical issuesPublication . Virtudes, Ana L.; Rodrigues, Ilda Inácio; Sá, João Paulo Costa e; Azevedo, Henrique Oliveira de; Simões, Alberto; Serôdio, RogérioThis article aims to present an interdisciplinary approach about the research methodologies used at the civil engineering research field, in the domains of urban planning and mathematics. Actually, there are some similarities in between the research process features of urban planning and mathematics. In fact, these both scientific subjects follow analogous tasks in their research process, which have the same starting point with the definition of the research problem and the final phase, based on the proposed solution. It joins scholars from the department of civil engineering and architecture, experts in spatial analysis and scholars form the department of mathematics of the University of Beira Interior. Two case studies will be presented as examples of the application of these methodological approaches, both of them focused on the urban planning researches, associated with postgraduate teachings, one is related to a PhD thesis and the other one relates to a master degree dissertation.
- A Hyers-Ulam stability analysis for classes of Bessel equationsPublication . Castro, L. P.; Simões, A. M.Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on the consideration of appropriate equations (or systems of equations). Here, differential equations are well-known to be very useful instruments when building mathematical models { specially because that the use of derivatives offers several interpretations associated with real life laws. Differential equations are classi ed based on several characteristics and, in this way, allow different possibilities of building models. In this paper we will be concentrated in analysing certain stability properties of classes of Bessel differential equations. In fact, the main aim of this work is to seek adequate conditions to derive different kinds of stabilities for the Bessel equation and for the modi ed Bessel equation by considering a perturbation of the trivial solution. In this way, suficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, sigma-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations.