On exact solutions of a class of interval boundary value problems

summary:In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the proposed approach is that the solution is treated as a set of real functions, not as an interval-valued function, as usual. It is well-known that the existence and uniqueness of the solution is a critical issue, especially in studying BVPs. We provide an existence and uniqueness result for interval BVPs under consideration. We also present a numerical method to compute the lower and upper bounds of the solution bunch. Moreover, we express the solution by an analytical formula under certain conditions. We provide numerical examples to illustrate the effectiveness of the introduced approach and the proposed method. We also demonstrate that the approach is applicable to non-linear interval BVPs

Integral Transformation, Operational Calculus and Their Applications

The importance and usefulness of subjects and topics involving integral transformations and operational calculus are becoming widely recognized, not only in the mathematical sciences but also in the physical, biological, engineering and statistical sciences. This book contains invited reviews and expository and original research articles dealing with and presenting state-of-the-art accounts of the recent advances in these important and potentially useful subjects

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics

New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention

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

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

Z-Numbers-Based Approach to Hotel Service Quality Assessment

In this study, we are analyzing the possibility of using Z-numbers for measuring the service quality and decision-making for quality improvement in the hotel industry. Techniques used for these purposes are based on consumer evalu- ations - expectations and perceptions. As a rule, these evaluations are expressed in crisp numbers (Likert scale) or fuzzy estimates. However, descriptions of the respondent opinions based on crisp or fuzzy numbers formalism not in all cases are relevant. The existing methods do not take into account the degree of con- fidence of respondents in their assessments. A fuzzy approach better describes the uncertainties associated with human perceptions and expectations. Linguis- tic values are more acceptable than crisp numbers. To consider the subjective natures of both service quality estimates and confidence degree in them, the two- component Z-numbers Z = (A, B) were used. Z-numbers express more adequately the opinion of consumers. The proposed and computationally efficient approach (Z-SERVQUAL, Z-IPA) allows to determine the quality of services and iden- tify the factors that required improvement and the areas for further development. The suggested method was applied to evaluate the service quality in small and medium-sized hotels in Turkey and Azerbaijan, illustrated by the example

Advances in Statistical Machine Learning Methods for Neural Data Science

Innovations in neural data recording techniques are revolutionizing neuroscience and presenting both challenges and opportunities for statistical data analysis. This dissertation discusses several recent advances in neural data signal processing, encoding, decoding, and dimension reduction. Chapter 1 introduces challenges in neural data science and common statistical methods used to address them. Chapter 2 develops a new method to detect neurons and extract signals from noisy calcium imaging data with irregular neuron shapes. Chapter 3 introduces a novel probabilistic framework for modeling deconvolved calcium traces. Chapter 4 proposes an improved Bayesian nonparametric extension of the hidden Markov model (HMM) that separates the strength of the self-persistence prior and transition prior. Chapter 5 introduces a more identifiable and interpretable latent variable model for Poisson observations. We develop efficient algorithms to fit each of the aforementioned methods and demonstrate their effectiveness on both simulated and real data