The Fine Spectra of the Cesàro Operator C 1 over the Sequence Space bvp, (1 ≤ p ∞)

The sequence space bvp consisting of all sequences (xk) such that (xk - xk-1) in the sequence space lp has recently been introduced by Basar and Altay [Ukrainian Math. J. 55(1)(2003), 136-147]; where 1 &#8804; p &#8804; &#8734;. In the present paper, the norm of the Ces&#224;ro operator C1 acting on the sequence space bvp has been found and the fine spectrum of the Ces&#224;ro operator C1 over the sequence space bvp has been determined, where 1 &#8804; p &#60; &#8734;.</p

Contributions to Mathematics and Statistics : Essays in honor of Seppo Hassi

This Festschrift contains thirteen articles in honor of the sixtieth birthday of Professor Seppo Hassi (University of Vaasa). It centers on three topics: functional analysis and operator theory, boundary value problems, and statistics, stochastics, and the history of mathematics. The collection contains four papers on the topic of functional analysis and operator theory. More precisely, it includes a paper treating the transformation of operator-valued Nevanlinna functions and the congruence of their associated realizing operators, a paper treating Parseval frames in the setting of Krein spaces, a paper treating algebraic inclusions of relations as well as the generalized inverses of relations, and a paper treating Krein-von Neumann and Friedrichs extensions by means of energy spaces. Boundary value problems are considered in six of the contributions. In particular, singular perturbations of the Dirac operator are treated by means of the technique of boundary triplets, the connection between sectorial Schrödinger L-systems and certain classes of Weyl-Titchmarsh functions is considered, PT-symmetric Hamiltonians are treated from the perspective of couplings of dual pairs, the Riesz basis property of indefinite Sturm-Liouville problems is considered, the stability properties of spectral characteristics of boundary value problems are investigated, and the completeness and minimality of systems of eigenfunctions and associated functions of ordinary differential operators are treated. Finally, the collection also contains three contributions connected with the topics of statistics, stochastics, and the history of mathematics. More precisely, a new statistic is introduced for the testing of cumulative abnormal returns in the case of partially overlapping event windows, a new characterization of Brownian motion is established, and, finally, a history of (the department of) mathematics and statistics at the University of Vaasa is presented.fi=vertaisarvioimaton|en=nonPeerReviewed

Applied Mathematics and Fractional Calculus

In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia

Proceedings of the 12th UK Conference on Boundary Integral Methods (UKBIM12)

Boundary integral methods have become established for solving a wide variety of problems in science and engineering. UK based researchers have been active and made substantial contributions in the theory and development of boundary integral formulations, as well as their analysis, discretisation and numerical solution. The UKBIM conference series aims to provide a forum where recent developments in boundary integral methods can be discussed in an informal atmosphere. The first UK conference on boundary integral methods (UKBIM) was held at the University of Leeds in 1997. Subsequent UKBIM conferences have taken place in Brunel (1999), Brighton (2001), Salford (2003), Liverpool (2005), Durham (2007), Nottingham (2009), Leeds (2011), Aberdeen (2013), Brighton (2015) and Nottingham-Trent (2017). The success of these events has made the conference a regular event for researchers based in the UK, and elsewhere, who are working on all aspects of boundary integral methods. This book contains the abstracts and papers presented at the Twelfth UK Conference on Boundary Integral Methods (UKBIM 12), held at Oxford Brookes University in July 2019. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield. I am grateful to the members of the scientific committee for their advice and support during the past year, and to all the authors and reviewers for their hard work in producing the high quality peer-reviewed papers for this book