ALBERT

Description: In this paper, we revisit the renowned fixed point theorems belongs to Caristi and Banach. We propose a new fixed point theorem which is inspired from both Caristi and Banach. We also consider an example to illustrate our result.

Description: In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature.

Description: Physics students are rarely exposed to the style of thinking that goes into theoretical developments in physics until late in their education. In this work, we present an alternative to the traditional statement of Newton’s second law that makes theory questions accessible to students early in their undergraduate studies. Rather than a contrived example, the model considered here arises from a popular framework for testing Lorentz symmetry used extensively in contemporary experiments. Hence, this work also provides an accessible introduction to some key ideas in ongoing tests of fundamental symmetries in physics.

Description: A new stringent limit relating to the variation of the fine-structure constant ( α = e 2 4 π ε 0 ℏ c ) has been extracted from Ritz wavelengths of 27 quasi_stellar object (QSO) absorption spectra lines of Fe II. The calculation was combined with laboratory wavelengths and QSO spectra to obtain the result Δ α / α = ( 0.027 ± 0.832 ) × 10 − 6 . This result suggests how dedicated astrophysical estimations can improve these limits in the future and can also constrain space_time variations.

Description: The evolution of multipurpose sensors over the last decades has been investigated with the aim of developing innovative devices with applications in several fields of technology, including in the food industry. The integration of such sensors in food packaging technology has paved the way for intelligent food packaging. These integrated systems are capable of providing reliable information about the quality of the packed products during their storage period. To accomplish this goal, intelligent packs use a variety of sensors suited for monitoring the quality and safety of food products by recording the evolution of parameters like the quantity of pathogen agents, gases, temperature, humidity and storage period. This technology, when combined with IoT, is able to provide a lot more information than conventional food inspection technologies, which are limited to weight, volume, color and aspect inspection. The original system described in this work relies on a simple but effective method of integrated food monitoring, right at the client home, suitable for user prepared vacuum-packed foods. It builds upon the IoT concept and is able to create a network of interconnected devices. By using this approach, we are able to combine actuators and sensing devices also providing a common operating picture (COP) by sharing information over the platforms. More precisely, our system consists of gas, temperature and humidity sensors, which provide the essential information needed for evaluating the quality of the packed product. This information is transmitted wirelessly to a computer system providing an interface where the user can observe the evolution of the product quality over time.

Description: In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers–Ulam stability result via the Gronwall inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo–Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer’s fixed point theorem. Finally, two examples are given to illustrate our main results.

Description: Floral symmetry is widely known as one of the most important structural traits of reproductive organs in angiosperms. It is tightly related to the shape and arrangement of floral parts, and at the same time, it plays a key role in general appearance (visual gestalt) of a flower, which is especially important for the interactions of zoophilous flowers with their pollinators. The traditional classification of floral symmetry divides nearly all the diversity of angiosperm flowers into actinomorphic and zygomorphic ones. Within this system, which is useful for ecological studies, many variations of symmetry appear to be disregarded. At the same time, the diversity of floral symmetry is underpinned not only by ecological factors, but also by morphogenetic mechanisms and constraints. Sometimes it is not an easy task to uncover the adaptive or developmental significance of a change of the floral symmetry in a particular lineage. Using the asterid order Apiales as a model group, we demonstrate that such changes can correlate with the merism of the entire flower or of its particular whorl, with the relative orientation of gynoecium to the rest of the flower, with the presence of sterile floral elements and other morphological characters. Besides, in some taxa, the shape and symmetry of the flower change in the course of its development, which should be taken in consideration in morphological comparisons and evaluations of synapomorphies in a particular clade. Finally, we show that different results can be obtained due to employment of different approaches: for instance, many flowers that are traditionally described as actinomorphic turn out to be disymmetric, monosymmetric, or asymmetric from a more detailed look. The traditional method of division into actinomorphy and zygomorphy deals with the general appearance of a flower, and mainly considers the shape of the corolla, while the geometrical approach handles the entire three-dimensional structure of the flower, and provides an exact number of its symmetry planes.

Description: The paper shows that, in looking for exact solutions to nonlinear PDEs, the direct method of functional separation of variables can, in certain cases, be more effective than the method of differential constraints based on the compatibility analysis of PDEs with a single constraint (or the nonclassical method of symmetry reductions based on an invariant surface condition). This fact is illustrated by examples of nonlinear reaction-diffusion and convection-diffusion equations with variable coefficients, and nonlinear Klein–Gordon-type equations. Hydrodynamic boundary layer equations, nonlinear Schrödinger type equations, and a few third-order PDEs are also investigated. Several new exact functional separable solutions are given. A possibility of increasing the efficiency of the Clarkson–Kruskal direct method is discussed. A generalization of the direct method of the functional separation of variables is also described. Note that all nonlinear PDEs considered in the paper include one or several arbitrary functions.

Description: I fused observed spectra from the white-dwarf star G191-B2B to constrain the spatial and temporal variation of the fine-structure constant, α = e 2 4 π ε 0 ℏ c . The analysis was combined with laboratory-measured and astronomically observed lines in [Ni V] to find Δ α / α = ( − 0.003 ± 0.072 ) × 10 − 6 . The obtained result allows a symmetry of the related comparison with previous studies looking for cosmological variations of α using spectra from Quasi Stellar Objects (QSOs). In this way, we can expect higher sensitivity from white-dwarf spectra than QSO spectra. Therefore, this study should have orders-of-magnitude higher sensitivity per system than previous quasar studies, and we should reduce statistical and systematic errors. The results of this study place a more stringent limit on Δ α / α than previous studies using the same data.

Description: In this work, a Lyapunov-based economic model predictive control (LEMPC) method is developed to address economic optimality and closed-loop stability of nonlinear systems using machine learning-based models to make predictions. Specifically, an ensemble of recurrent neural network (RNN) models via a k-fold cross validation is first developed to capture process dynamics in an operating region. Then, the LEMPC using an RNN ensemble is designed to maintain the closed-loop state in a stability region and optimize process economic benefits simultaneously. Parallel computing is employed to improve computational efficiency of real-time implementation of LEMPC with an RNN ensemble. The proposed machine-learning-based LEMPC method is demonstrated using a nonlinear chemical process example.