International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

The calculus according to S. F. Lacroix (1765-1843)

Silvestre François Lacroix (Paris. 1765 - ibid., 1843) was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous book is a monumental Traité du calcul différentiel et du calcul intégral (three large volumes, 1797-1800; a second edition appeared in 1810-1819) - an encyclopaedic appraisal of 18th-century calculus. He also published many textbooks, one of which is closely associated to this large Traité: the Traité élémentaire du calcul différentiel et du calcul intégral (first edition in 1802; four more editions in Lacroix's lifetime; four posthumous editions). Although most historians acknowledge the great influence of Lacroix's large Traité in early 19th-century mathematics it has not been thoroughly studied. This thesis is a contribution for correcting this omission. The focus is on its first edition, but the second edition and the Traité élémentaire, are also addressed. The thesis starts with a short biography of Lacroix, followed by an overview of the first edition of the large Traité. Next corne five chapters where particular aspects are analyzed in detail: the foundations of the calculus, analytic and differential geometry, approximate integration and conceptions of the integral, types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions), and three aspects related to finite differences and series (the use of subscript indices, types of solutions of finite difference equations, and mixed difference equations); for all these aspects Lacroix's treatment is compared to the 18th-century background, and to his likely sources. Then we examine how the large Traité was adapted to a textbook - the Traité élémentaire, we take a look at the second edition of the large Traité, and conclude the body of the thesis with some final remarks

The calculus according to S. F. Lacroix (1765-1843)

Silvestre François Lacroix (Paris. 1765 - ibid., 1843) was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous book is a monumental Traité du calcul différentiel et du calcul intégral (three large volumes, 1797-1800; a second edition appeared in 1810-1819) - an encyclopaedic appraisal of 18th-century calculus. He also published many textbooks, one of which is closely associated to this large Traité: the Traité élémentaire du calcul différentiel et du calcul intégral (first edition in 1802; four more editions in Lacroix's lifetime; four posthumous editions). Although most historians acknowledge the great influence of Lacroix's large Traité in early 19th-century mathematics it has not been thoroughly studied. This thesis is a contribution for correcting this omission. The focus is on its first edition, but the second edition and the Traité élémentaire, are also addressed. The thesis starts with a short biography of Lacroix, followed by an overview of the first edition of the large Traité. Next corne five chapters where particular aspects are analyzed in detail: the foundations of the calculus, analytic and differential geometry, approximate integration and conceptions of the integral, types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions), and three aspects related to finite differences and series (the use of subscript indices, types of solutions of finite difference equations, and mixed difference equations); for all these aspects Lacroix's treatment is compared to the 18th-century background, and to his likely sources. Then we examine how the large Traité was adapted to a textbook - the Traité élémentaire, we take a look at the second edition of the large Traité, and conclude the body of the thesis with some final remarks.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Inequalities For Zeros Of Jacobi Polynomials Via Sturm’s Theorem: Gautschi’s Conjectures

Let (formula presented) be the zeros of Jacobi polynomials (formula presented) arranged in decreasing order on (formula presented) where (formula presented) and (formula presented) arccos (formula presented) Gautschi, in a series of recent papers, conjectured that the inequalities (formula presented) and (formula presented) hold for all (formula presented) and certain values of the parameters α and β. We establish these conjectures for large domains of the (α, β)-plane by using a Sturmian approach.673549563Ahmed, S., Laforgia, A., Muldoon, M.E., On the spacing of the zeros of some classical orthogonal polynomials (1982) J. London. Math. Soc., 25 (2), pp. 246-252Dimitrov, D.K., Sri Ranga, A., Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle (2013) Math. Nachr., 286, pp. 1778-1791Driver, K., Jordaan, K., Bounds for extreme zeros of some classical orthogonal polynomials (2012) J. Approx. Theory, 164, pp. 1200-1204Gautschi, W., Leopardi, P., Conjectured inequalities for Jacobi polynomials and their largest zeros (2007) Numer. Algoritm., 45, pp. 217-230Gautschi, W., On a conjectured inequality for the largest zero of Jacobi polynomials (2008) Numer. Algoritm., 49, pp. 195-198Gautschi, W., On conjectured inequalities for zeros of Jacobi polynomials (2009) Numer. Algoritm., 50, pp. 93-96Gautschi, W., New conjectured inequalities for zeros of Jacobi polynomials (2009) Numer. Algoritm., 50, pp. 293-296Gautschi, W., Remark on “New conjectured inequalities for zeros of Jacobi polynomials” by Walter Gautschi. Numer. Algorithm. 50, 293–296 (2009), (2011) Numer. Algoritm., 57, p. 511Hesse, K., Sloan, I.H., Worst-case errors in a Sobolev space setting for cubature over the sphere S2 (2005) Bull. Aust. Math. Soc., 71, pp. 81-105Hesse, K., Sloan, I.H., Cubature over the sphere S2 in Sobolev spaces of arbitrary order (2006) J. Approx. Theory, 141, pp. 118-133Koumandos, S., On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials (2007) Numer. Algoritm., 44, pp. 249-253Leopardi, P.C., Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials (2007) Numer. Algoritm., 45, pp. 75-87Szegő, G., (1975) Orthogonal Polynomials, , Amer. Math. Soc. Coll. Publ., Providence