Book of Abstracts: International Workshop on Mathematics and Physical Sciences

This book-proceeding comprises the results of various comprehensive Mathematical and Physical Sciences-based studies accepted for presentation and discussion during the 1st Mathematical and Physical Sciences International Workshop in Évora, in 2023 (Mat- Phys23). The MatPhys23, organized under the auspices of University of Évora throughout the CIMA - Research Center in Mathematics and Applications, the ICT - Institute of Earth Sciences and the NOVA-LINCS - NOVA Laboratory for Informatics and Computer Science (Évora branch). This Workshop brought together many well-known mathematicians, physicists and engineers from University of Beira Interior (UBI, Portugal), University of Cabo Verde (UCV, Cabo Verde), Montclair State University (MSU, NJ, USA) and University of Évora (UÉ, Portugal). This book-proceeding volume involves 24 abstracts on the latest trending and significant challenges in mathematics and physical sciences. The works presented focus on the following areas: statistical and mathematical methods that are relevant to biology, medical and biomedical sciences, computer science, economics, social sciences, music, environmental sciences, climatology, engineering, industry, fluid mechanics and their applications, numerical simulations in various physical, geophysical, chemical, biological and engineering applications. In addition to the usual scientific interaction between participants, this meeting has the presence of PhD students, which we consider relevant. Considering the original contents, aims, and methodologies of all these valuable studies, it is believed that the topical outputs are of interest to all researchers, practitioners, and students and would mainly provide new scientific insights and knowledge for geoscientists and engineers.CIMA-Centro de Investigação em Matemática e Aplicações; ICT-Instituto de Ciências da Terra; NOVALINC

Random Fixed Point Theorems of Random Comparable Operators and an Application

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation

An iterative method for solution of nonlinear operator equation

In the note, for finding a solution of nonlinear operator equation of Hammerstein’s type an iterative process in infinite-dimentional Hilbert space is shown, where a new iteration is constructed basing on two last steps. An example in the theory of nonlinear integral equations is given for illustration

The Hyperdimensional Transform: a Holographic Representation of Functions

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable functions into noise-robust, holographic, high-dimensional representations called hyperdimensional vectors. The central idea is to approximate a function by a linear combination of random functions. We formally introduce a set of stochastic, orthogonal basis functions and define the hyperdimensional transform and its inverse. We discuss general transform-related properties such as its uniqueness, approximation properties of the inverse transform, and the representation of integrals and derivatives. The hyperdimensional transform offers a powerful, flexible framework that connects closely with other integral transforms, such as the Fourier, Laplace, and fuzzy transforms. Moreover, it provides theoretical foundations and new insights for the field of hyperdimensional computing, a computing paradigm that is rapidly gaining attention for efficient and explainable machine learning algorithms, with potential applications in statistical modelling and machine learning. In addition, we provide straightforward and easily understandable code, which can function as a tutorial and allows for the reproduction of the demonstrated examples, from computing the transform to solving differential equations

Existence and Uniqueness Solutions of Fuzzy Fractional Integral Equation of Volterra-Stieltjes Type

In this paper, we establish the existence and uniqueness results to the Cauchy problem posed for a fuzzy fractional Volterra-Stieltjes integrodifferential equation. The method of successive approximations is used to prove the existence, whereas the contraction theory is applied to prove the uniqueness of the solution to the problem

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems