Basic Operations Research Articles

Optical hyperdimensional soft sensing: speckle-based touch interface and tactile sensor.

Hyperdimensional computing (HDC) is an emerging computing paradigm that exploits the distributed representation of input data in a hyperdimensional space, the dimensions of which are typically between 1,000-10,000. The hyperdimensional distributed representation enables energy-efficient, low-latency, and noise-robust computations with low-precision and basic arithmetic operations. In this study, we propose optical hyperdimensional distributed representations based on laser speckles for adaptive, efficient, and low-latency optical sensor processing. In the proposed approach, sensory information is optically mapped into a hyperdimensional space with >250,000 dimensions, enabling HDC-based cognitive processing. We use this approach for the processing of a soft-touch interface and a tactile sensor and demonstrate to achieve high accuracy of touch or tactile recognition while significantly reducing training data amount and computational burdens, compared with previous machine-learning-based sensing approaches. Furthermore, we show that this approach enables adaptive recalibration to keep high accuracy even under different conditions.

Microbial Primer: The bacterial flagellum - how bacteria swim.

Bacteria swim using membrane-spanning, electrochemical gradient-powered motors that rotate semi-rigid helical filaments. This primer provides a brief overview of the basic synthesis, structure and operation of these nanomachines. Details and variations on the basic system can be found in suggested further reading.

The Use of Mother Tongue in Communicating Mathematics: Implication for Teaching and Learning of Mathematics

Mathematics as a school subject is designed to solve the everyday problem created by human activities; these problems are domesticated in the different cultures of man all over the world. However, the performance of students keeps dwindling due to the westernize approach of teaching and learning mathematics. In other to solve this precarious situation this paper advocated the use of mother tongue in the teaching of mathematics. Mother tongue approach here refers to first-language education as a medium of instruction. The use of mother tongue in the teaching and learning of mathematics is meant to address the high functional illiteracy of Nigeria where language plays a significant factor. Using mother tongue to teach the basic concepts of numbers, operations and other concepts of mathematics helps build a strong foundation for the understanding and learning of higher mathematics. This approach is effective not only in getting the interest of students in the lesson but as a springboard in teaching new mathematical concepts, principles and in deepening student understanding on how mathematical operations or processes work. The mother tongue concepts of teaching and learning mathematics in this work shall be based on the following sub-topics: Numeration/Counting System, Basic Arithmetic Operations, Rhymes and Geometric Concepts. The paper completely reduced the Eurocentric mathematics beliefs of students and make them discover how best mathematics can be learning from their mother tongue. The paper recommended amongst others that teachers of mathematics should adopt the use of mother tongue in teaching mathematics in order to improve students understanding of the subject.

PERSPECTIVES AND OPPORTUNITIES OF GROATS PRODUCTION IN UKRAINE

Since the beginning of the 21st century, there has been an increase in the share of small enterprises in the grain industry, the number of which is increasing even today. At most of such enterprises, it is impossible to apply the existing longterm full grain processing technologies, there is a reduction in the number of basic technological operations, often not sufficiently substantiated, which affects the quality of the end products, which do not always meet all the basic norms of the regulations applicable to end products. Considering the modern technological solutions offered by leading manufacturers for the production of flaked products and quick-cooking products, it is possible to note the equipment of the Buhler company, which allows to monitor production control and, accordingly, achieve greater production efficiency. To date, the Buhler company offers the batch steamer MBDA for the steaming stage, which is recommended to be combined with the BCFB flaking machine. This technological equipment in combination gives high quality and reliability of the equipment itself, allows to implement energy-saving technologies at enterprises and obtain controlled production of quality products. Today, in addition to traditional grain, such crops as lentils, chickpeas, beans, wheat-spelt, spelt, naked varieties of oats and barley are processed in part or in small batches at the enterprises of the industry. Lentil is a promising leguminous crop for the grain industry. In the world, it is widely grown as a food and fodder crop. Among leguminous crops, lentils occupy an intermediate place in terms of protein content, with a protein content of 25-36%, while the share of carbohydrates is 45-55%, fat - 3-4%. The first variety of «Linza» edible lentils was registered in 2005. After that, the following varieties were registered only in 2017-2018: «Antonina» (2017), «Darinka» (2017), «YeSMaksymum» (2017), «Blondie» (2018), «Harry» (2018), «SNIM 18» (2018), Chrysolite (2018), which indicates an understanding of the potential of this culture both for the domestic market and for increasing the export potential of our country. The last to enter the register were «Serpanok» (2020) and «RED» (2021) varieties, which indicates the continued work of breeders to expand the varietal base of this crop in Ukraine.

‘Problems’ at School: Mathematical Testimonies from the Fayum in the Roman Period

Abstract The common association between the teaching of numbers and basic arithmetical operations, on the one hand, and the earliest levels of linguistic-literary education, on the other, is a datum on which interpreters of Greek papyrological sources are now essentially agreed. A more controversial and less often considered question is whether, in these same ‘scholastic courses’, this basic knowledge also encompassed geometrical and metrological calculations in the form of ‘problems’ (which are typical of the papyrological mathematical tradition). Only a few witnesses to the latter type of texts in Greek have characteristics that would most likely associate them with instructional contexts. The four oldest of these date between the 1st and 3rd centuries AD and are of proven or hypothetical Fayumic provenance. Although they are few in number, these witnesses attest to certain practices in the teaching of mathematics, at least in this historical-geographical context, which are worthy of note.

P, q-Spherical fuzzy sets and their aggregation operators with application to third-party logistic provider selection

The selection of an appropriate third-party logistics (3PL) provider has become an inescapable option for shippers in today’s business landscape, as the outsourcing of logistics activities continues to increase. Choosing the 3PL supplier that best meets their requirements is one of the most difficult difficulties that logistics consumers face. Effective decision-making (DM) is critical in dealing with such scenarios, allowing shippers to make well-informed decisions within a restricted timeframe. The importance of DM arises from the possible financial repercussions of poor decisions, which can result in significant financial losses. In this regard, we introduce p, q-spherical fuzzy set (p, q-SFS), a novel concept that extends the concept of T-spherical fuzzy sets (T-SFSs). p, q-SFS is a comprehensive representation tool for capturing imprecise information. The main contribution of this article is to define the basic operations and a series of averaging and geometric AOs under p, q-spherical fuzzy (p, q-SF) environment. In addition, we establish several fundamental properties of the proposed aggregation operators (AOs). Based on these AOs, we propose a stepwise algorithm for multi-criteria DM (MCDM) problems. Finally, a real-life case study involving the selection of a 3PL provider is shown to validate the applicability of the proposed approach.

Fault Diagnosis for Road Heading Bearings Based On a Multiscale Enhanced Cascaded Difference Filter

Abstract In this paper, a novel multiscale morphological filter, called multiscale enhanced cascaded difference filter (MECDF), is proposed for the fault detection of road heading bearings. Firstly, the cascaded morphological operators are established based on the cascade of the basic morphological operators with similar properties, and then the morphological difference operation is introduced to propose the cascaded difference operators. Subsequently, the enhanced cascaded difference operator (ECDO) is constructed through the convolution of cascaded difference operators. Moreover, since the scale range of structure element (SE) also determines the filtering performance of multiscale morphological filter, an improved multiscale analysis method is presented to select the optimal scale range. Finally, the bearing experimental signals are implemented to validate the effectiveness of MECDF. Experimental results testify that the scale range determined by the MECDF is better than other multiscale morphological filters. Meanwhile, the feature extraction capability of ECDO is also better than other existing morphological difference operators.

Version [1.1]- [Handling decision-making in intuitionistic fuzzy environment: PyIFDM package

The paper introduces the update of the Python Intuitionistic Fuzzy Decision Making (PyIFDM) package, emphasizing its focus on Multi-Criteria Decision Analysis (MCDA) with uncertain data modeled as Intuitionistic Fuzzy Sets (IFS). The update enhances PyIFDM’s capabilities, introducing five new IF-MCDA methods and basic mathematical operations on IFS. The update includes the implementation of Max normalization, a Hausdorff measure-based Euclidean distance, and a module for IFS-similarity measures. The release contributes to a significant library upgrade, providing advanced tools for modeling fuzzy data in and outside the MCDA space. PyIFDM now supports a greater variety of popular IF-MCDA methods, offering flexibility and applicability in decision-making scenarios. The added visualization module facilitates the graphical representation of IFS, aiding the interpretation of complex decision models involving intuitionistic fuzzy data. The enhanced version of the PyIFDM library expands its applicability in research methodologies, making it a more efficient tool for conducting multi-criteria decision analysis in an intuitionistic fuzzy environment.

More Generalization of Union Soft Hyperideals of Ordered Semihypergroups

In this paper, we introduce the notions of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals of ordered semihypergroups. Some basic operations are investigated and some related properties are also studied. We present characterizations of ordered semihypergroups in terms of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals. We prove that every (M,N)union soft hyperideal is an (M,N)-union soft interior hyperideal but the converse is not true which is shown with help of an example. However we show that the notions of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals coincide in a regular as well as in intra-regular ordered semihypergroups. Moreover we introduce the notion of (M,N)-union soft simple ordered semihypergroups. Finally, we characterize (M,N)-union soft simple ordered semihypergroups by means of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals.

Стандартизація еліптичних кривих: аналіз та впровадження в криптографічні протоколи

The purpose of the article is to consider the current state of elliptic cryptography, the prerequisites for its use, as well as the requirements of modern standards related to the use of elliptic cryptography The use of elliptic curves in cryptography is considered one of the most promising areas of development of modern security algorithms. This mathematical approach is based on the complexity of solving the discrete logarithm problem in a group of points of an elliptic curve over a finite field. The use of cryptography on elliptic curves allows you to ensure the security of data exchange using effective encryption algorithms and the creation of digital signatures (DI). This study examines elliptic curves for cryptographic purposes, and provides basic operations on the point group of elliptic curves. Special attention is paid to Elliptic curve Diffie-Hellman (ECDH) and Elliptic Curve Digital Signature Algorithm (ECDSA) key exchange algorithms. The standards regulating the use of elliptic curves in cryptographic systems are also analyzed, and the advantages of this cryptographic paradigm compared to the main asymmetric algorithms are considered. Potential threats and vulnerabilities of cryptographic algorithms based on elliptic curves are investigated. Examples of popular standardized curves recommended by relevant organizations, such as NIST, used in real-world cryptographic applications are also provided. Elliptic curve cryptography (ECC) is currently one of the foundations for the development of modern public-key cryptographic algorithms. ECC has gained recognition in cryptography for providing a high level of security with shorter key lengths (compared to other cryptographic approaches), high speed, resource savings, and versatility, giving it an advantage over other methods such as RSA and others. It provides a secure network connection, generates secret keys for TLS servers and their clients, and is also used to create digital signatures that guarantee the authenticity of transactions in cryptocurrency systems.

Innovative Theoretical Approach: Bipolar Pythagorean Neutrosophic Sets (BPNSs) in Decision-Making

In this paper, the concept of bipolar Pythagorean fuzzy neutrosophic sets (BPNSs) will be introduced which represents an innovative synthesis, incorporating bipolarity, Pythagorean fuzzy sets, and neutrosophic sets to provide a comprehensive solution to the multifaceted issues encountered in decision-making challenges. BPNS is proposed to enhance the expressiveness and flexibility of the model by incorporating both positive and negative preferences that can lead to more accurate and realistic modeling of complex decision scenarios. The essential idea of BPNSs is defined and some definitions for instance complement, intersection, and union are described. The basic operation, the derivation of its properties, and the numerical example of the method are integrated to execute the proposed model.

Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius

<abstract><p>The circular intuitionistic fuzzy set (<italic>CIFS</italic>) extends the concept of <italic>IFS</italic>, representing each set element with a circular area on the <italic>IFS</italic> interpretation triangle (<italic>IFIT</italic>). Each element in <italic>CIFS</italic> is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for <italic>CIFS</italic>, not all have been thoroughly explored and generalized. The radius domain has been extended from $ [0, 1] $ to $ [0, \sqrt{2}] $. However, the operations on the radius domain are limited to $ min $ and $ max $. We aimed to address these limitations and further explore the theory of <italic>CIFS</italic>, focusing on operations for membership and non-membership degrees as well as radius domains. First, we proposed new radius operations on <italic>CIFS</italic> with a domain $ [0, \psi] $, where $ \psi \in [1, \sqrt{2}] $, called a radius algebraic product (<italic>RAP</italic>) and radius algebraic sum (<italic>RAS</italic>). Second, we developed basic operators for generalized union and intersection operations on <italic>CIFS</italic> based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of <italic>CIFS</italic>, providing valuable insights into its potential applications, particularly in decision-making theory.</p></abstract>

Does the use of the calculator reduce anxiety in the study of differential and integral calculus?

The objective of this research is to study if the use of the calculator decreases students’ anxiety in the subject of differential and integral calculus. Specifically, the research is carried out with 30 engineering students. Auzmendi anxiety factor questions are used to measure anxiety. The study is carried out in two moments; in the first the calculator is not used and in the second if they use it. In the second case, the calculator is used in problems involving the application of derivatives and integrals. The results indicate that the students reduce their anxiety when they use the calculator. Thus, in seven of the nine questions, students who use the calculator obtain a higher mean, it helps to reduce anxiety. In general, t-student test indicates that the moment students use the calculator they have less anxiety, and it helps to reduce errors in the mathematical process. Teachers should consider the calculator as a resource that motivates the student and helps reduce anxiety. In addition, the use of the calculator helps to reduce mathematical errors in basic operations and in the application of derivatives and integrals.

Credal Valuation Networks for Machine Reasoning Under Uncertainty

Contemporary undertakings provide limitless opportunities for widespread application of machine reasoning and artificial intelligence in situations characterised by uncertainty, hostility and sheer volume of data. The paper develops a valuation network as a graphical system for higher-level fusion and reasoning under uncertainty in support of the human operators. Valuations, which are mathematical representation of (uncertain) knowledge and collected data, are expressed as credal sets, defined as coherent interval probabilities in the framework of imprecise probability theory. The basic operations with such credal sets, combination and marginalisation, are defined to satisfy the axioms of a valuation algebra. A practical implementation of the credal valuation network is discussed and its utility demonstrated on a small scale example.

A Study on Interval Valued Temporal Neutrosophic Fuzzy Sets

In this research, we introduce the Interval Valued Temporal Neutrosophic Fuzzy Sets (IVTNFS) and some of its basic operations. Also, examine some of their properties. The Neutrosophic Fuzzy Sets of membership and non-membership values are not always possible up to our satisfaction, but the IVTNFS part has a more important role here, because the time movement with an interval in NFS gave the best solution to making a decision, deciding their careers in our real-life situation.

Algebraic Solution of the Quantum Harmonic Oscillator

The Wave-particle duality and the Schrodinger cat paradox pose important notions on quantum mechanical systems, in which a quantum system can exist in two physically opposite or distinct states. This motivates scientists from the days of Louis de Broglie to confidently look at matter as having a dual nature, which is a physical particle that can also be visualized as a wave entity. This paper seeks to provide an elegant method of solving the time-independent Schrodinger Equation (TISE) for a quantum simple harmonic oscillator (QSHO). A fully algebraic method is presented, the paper explains in detail how simple algebra, coupled with basic quantum mechanical operator commutation algebra can be employed to solve the TISE without resorting to complicated mathematical methods of solving second-order differential equations. The construction of the Hamiltonian is explained and an analogy between the classical simple harmonic oscillator (CSHO) and the QSHO is drawn to develop the solution method. The action of creation and annihilation operators on wave functions is exploited to generate states with higher and lower energies respectively and to generate a Hamiltonian that can act on a system and generate required quantum states. The aim is to generate the ground state of the QSHO and its associated energy value. From this state, other higher energy states can be generated by the action of the creation operator. The use of algebraic methods has been seen to be versatile as it does not explicitly rely on any particular basis or coordinate system. The method allows operators to be manipulated in different bases for example the momentum operator can be given as P ̂ x=-iℏ (∂/∂x) in a spatial coordinate basis or as a pure number p ̂ =p in the momentum basis.

Cam Profile Design of Low-Speed Marine Diesel Engine Based on the Grey Theory

The camshaft profile is one of the important parameters of the engine, the reasonableness or otherwise of its design directly influences the engine’s power output, fuel consumption, emissions, noise and reliability. However, most existing cam profile optimization designs are based on the basic software operation, profile parameter selection and tuning lack a scientific theoretical basis. In order to address this issue, this study establishes a single valve kinematic model of the gas delivery mechanism of diesel engines by using the AVL-EXCITE Timing Drive, and performs a model-based multinomial kinematic acceleration cam profile design. Subsequently, an orthogonal design method is employed to obtain the parameter combinations that can satisfy the dynamic requirements. The research investigates the influence of cam profile design parameters (C 4, p, q, r, and s) on valve fullness, maximum jerk, cam contact stress, and valve seating force through a systematic study. Lastly, based on the grey correlation theory, a thorough analysis of the performance indices of cams with different profile parameter combinations is conducted. The optimization problem of the profile parameters with multiple performance indicators is transformed into a single-objective grey relational optimization problem, resulting in the optimal cam profile parameter combination of C4 =0.1, p=14, q=20, r=28 and s=36. The optimal method proposed in the paper is straightforward to implement and is applicable to the optimum design of cam profiles of the engine, which is of great importance for the optimal design of cam fabrication processes.

Evaluation of the efficiency of parallel algorithms using intel parallel studio

The paper analyzes the means of evaluating the effectiveness of parallel programs. The research focuses on im- proving the performance of basic linear algebra operations performed on parallel computing systems with shared memory. The Intel Parallel Studio environment is used, which provides a powerful set of tools and resources for analyzing and optimizing parallel programs. The results of the study make it possible to solve performance-related problems and improve the operation of parallel programs.

Symbolic model checking quantum circuits in Maude.

This article presents a symbolic approach to model checking quantum circuits using a set of laws from quantum mechanics and basic matrix operations with Dirac notation. We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach. As case studies, we use the approach to formally specify several quantum communication protocols in the early work of quantum communication and formally verify their correctness: Superdense Coding, Quantum Teleportation, Quantum Secret Sharing, Entanglement Swapping, Quantum Gate Teleportation, Two Mirror-image Teleportation, and Quantum Network Coding. We demonstrate that our approach/implementation can be a first step toward a general framework to formally specify and verify quantum circuits in Maude. The proposed way to formally specify a quantum circuit makes it possible to describe the quantum circuit in Maude such that the formal specification can be regarded as a series of quantum gate/measurement applications. Once a quantum circuit has been formally specified in the proposed way together with an initial state and a desired property expressed in linear temporal logic (LTL), the proposed model checking technique utilizes a built-in Maude LTL model checker to automatically conduct formal verification that the quantum circuit enjoys the property starting from the initial state.

ON THE NORM OF FINITE LENGTH ELEMENTARY OPERATOR IN TENSOR PRODUCT OF C*-ALGEBRAS

Many properties of Elementary operators, including spectrum, numerical ranges, compactness, rank, and norm have been studied in depth and some results have been obtained. However, little has been done in determining the norm of finite length elementary operator in tensor product of C*-algebras. The norm of basic elementary operator in tensor product of C*-algebras have been determined and results obtained. This paper determines the norm of finite length elementary operator in a tensor product of C*-algebras. More precisely, the bounds of the norm of finite length elementary operator in a tensor product of C*-algebras are investigated. The paper employs the techniques of tensor products and finite rank operators to express the norm of an elementary operator in terms of its coefficient operators.