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In this paper, we propose a new class of micro-electromechanical oscillators. Some investigations based on Melnikov's approach are applied for identifying some chaotic possibilities. We demonstrate also some specialized modules for investigating the dynamics of these oscillators. This will be included as an integral part of a planned much more general Web-based application for scientific computing. It turns out that the theoretical apparatus for studying the circuit implementation (design, fabricating, etc.) of the considered differential model for large parameter values is extremely complex and requires a serious investigation. This is the reason to offer this model to the attention of specialists working in this scientific direction. Some open problems related to the use of existing computer algebraic systems for the study of this class of oscillators for large values of n , m and N are also posed. In general, the entire article is subordinated to this frank conversation with the readers with the sole purpose being the professional upgrading of the specialized modules provided for this purpose in subsequent licensed versions of CAS. [ABSTRACT FROM AUTHOR]

The Fourier transform occupies a central place in applied mathematics, statistics, computer sciences, and engineering. In this work, we introduce the one-dimensional quaternion Fourier transform, which is a generalization of the Fourier transform. We derive the conjugate symmetry of the one-dimensional quaternion Fourier transform for a real signal. We also collect other properties, such as the derivative and Parseval's formula. We finally study the application of this transformation in probability theory. [ABSTRACT FROM AUTHOR]

Symmetries play a vital role in the study of physical phenomena in diverse areas such as dynamic systems, optimization, physics, scientific computing, engineering, mathematical biology, chemistry, and medicine, to mention a few. These phenomena specialize mostly in solving equilibria-like problems in abstract spaces. Motivated by these facts, this research provides two innovative modifying extragradient strategies for solving pseudomonotone equilibria problems in real Hilbert space with the Lipschitz-like bifunction constraint. Such strategies make use of multiple step-size concepts that are modified after each iteration and are reliant on prior iterations. The excellence of these strategies comes from the fact that they were developed with no prior knowledge of Lipschitz-type parameters or any line search strategy. Mild assumptions are required to prove strong convergence theorems for proposed strategies. Various numerical tests have been reported to demonstrate the numerical behavior of the techniques and then contrast them with others. [ABSTRACT FROM AUTHOR]

Clustering is a mathematical approach that allows one to find a group of data with similar attributes. This approach is also often used in the field of computer science to group a large amounts of data. Triclustering analysis is an analysis technique on 3D data (observation—attribute—context). Triclustering analysis can group observations on several attributes and contexts simultaneously. Triclustering analysis has been frequently applied to analyze microarray gene expression data. We proposed the δ -Trimax method to perform triclustering analysis on microarray gene expression data. The δ -Trimax method aims to find a tricluster that has a mean square residual smaller than δ and a maximum volume. Tricluster is obtained by deleting nodes from 3D data using multiple node deletion and single node deletion algorithms. The tricluster candidates that have been obtained are checked again by adding some previously deleted nodes using the node addition algorithm. In this research, the program improvement of the δ -Trimax method was carried out and also the calculation of the resulting tricluster evaluation result. The δ -Trimax method is implemented in two microarray gene expression data. The first implementation was carried out on gene expression data from the differentiation process of human-induced pluripotent stem cells (HiPSCs) from patients with heart disease, resulting in the best simulation when δ = 0.0068 , λ = 1.2 , and obtained five tricluster, which are considered as characteristics of heart disease. The second implementation was implemented on HIV-1 data, best simulation when δ = 0.0046 , λ = 1.25 and produced three genes as biomarkers, with the gene names AGFG1, EGR1 and HLA-C. This gene group can be used by medical experts in providing further treatment. [ABSTRACT FROM AUTHOR]

During the last two centuries, after the question asked by Euler concerning mutually orthogonal Latin squares (MOLS), essential advances have been made. MOLS are considered as a construction tool for orthogonal arrays. Although Latin squares have numerous helpful properties, for some factual applications these structures are excessively prohibitive. The more general concepts of graph squares and mutually orthogonal graph squares (MOGS) offer more flexibility. MOGS generalize MOLS in an interesting way. As such, the topic is attractive. Orthogonal arrays are essential in statistics and are related to finite fields, geometry, combinatorics and error-correcting codes. Furthermore, they are used in cryptography and computer science. In this paper, our current efforts have concentrated on the definition of the graph-orthogonal arrays and on proving that if there are k MOGS of order n , then there is a graph-orthogonal array, and we denote this array by G - O A (n 2 , k , n , 2).   In addition, several new results for the orthogonal arrays obtained from the MOGS are given. Furthermore, we introduce a recursive construction method for constructing the graph-orthogonal arrays. [ABSTRACT FROM AUTHOR]

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been acknowledged as being an applicable and well-organized tool to epitomize and solve many multifarious real-world problems in which vague data and information are essential. Owing to unpredictable and unspecified information being an integral component in real-life problems that are often uncertain, it is highly challenging for an expert to illustrate those problems through a fuzzy graph. Therefore, resolving the uncertainty accompanying the unpredictable and unspecified information of any real-world problem can be done by applying a vague incidence graph (VIG), based on which the FGs may not engender satisfactory results. Similarly, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, and also other issues such as medical sciences, and traffic planning. Dominating sets (DSs) enjoy practical interest in several areas. In wireless networking, DSs are being used to find efficient routes with ad-hoc mobile networks. They have also been employed in document summarization, and in secure systems designs for electrical grids; consequently, in this paper, we extend the concept of the FIG to the VIG, and show some of its important properties. In particular, we discuss the well-known problems of vague incidence dominating set, valid degree, isolated vertex, vague incidence irredundant set and their cardinalities related to the dominating, etc. Finally, a DS application for VIG to properly manage the COVID-19 testing facility is introduced. [ABSTRACT FROM AUTHOR]

Symmetry is an international journal in the research fields of physics, chemistry, biology, mathematics, computer science, theory and methods, and other scientific disciplines and engineering. The first paper was published in 2009. Here, we make a bibliometric analysis of publications in Symmetry from 2009 to 2019. According to Web of Science (WoS), we obtained 3215 publications in this journal. First, we explore the publications, citation number, and citation structure based on bibliometric indicators. Second, we analyze the most influential objects, including countries/regions, institutions, authors, and papers. Cooperation networks are also presented. Next, the co-citation and burst detection analyses are conducted according to the techniques of visualization tools, i.e., VOSviewer and CiteSpace. Furthermore, the co-occurrence analyses and timeline view analyses of keywords are investigated, aiming to explore the research hotspots. Finally, this paper provides relatively thorough perspectives and reviews and discloses the future development trend of this journal and challenges for scholars, which will promote the development of the journal and in-depth research of scholars. [ABSTRACT FROM AUTHOR]

This article researched the security and application of smart locks in Internet of Things environments in the domain of computer and engineer science and symmetry. Smart locks bring much convenience for users. However, most smart lock systems are cloud-based and it is problematic managing and enforcing the permissions of an authorized device if the device is offline. Moreover, most smart lock systems lack fine-grained access control and cascading removal of permissions. In this paper, we leverage attribute-based access control mechanisms to manage the access of visitors with different identities. We use identity-based encryption to verify the identity of the visitor. In our proposed system, the administrator uses the policy set in the smart lock to implement access control on the device side, which reduces the dependence of access control on the server. We set attributes such as role, time, date, and location to have fine-grained control over access to different permissions and roles that might appear in the house. And the scheme provides the cascading delete function while providing the group access function. Our solution considers multiple roles in the home as well as hierarchical management issues, and improves the applicability of the smart lock system in complex residential and commercial situations. In the experimental section, we show that our system can be applied to premises with many different inhabitant identities. [ABSTRACT FROM AUTHOR]