Mathematical Principles Research Articles

Exploring the Intersection of Nature and Mathematics: Analysing Mathematical Concepts in Natural Phenomena

Abstract: This research paper investigates the connection between various natural phenomena and their corresponding mathematical concepts. By examining a range of natural phenomena, we explore the mathematical principles and theories that can be applied to understand and describe them. Through this analysis, we aim to deepen our understanding of the intricate relationship between nature and mathematics, uncovering the mathematical concepts that underpin and elucidate natural processes. The findings of this study contribute to the interdisciplinary field of mathematical modeling in relation to natural phenomena, providing valuable insights for future research and applications.

Implementation of Matlab communication and Allen Bradley PLC for control of the AMATROL JUPITER XL Robot

The article introduces a method to enable a robot, the "AMATROL JUPITER XL," without relying on its conventional controllers. Instead, a Human-Machine Interface (HMI) is employed using Allen Bradley's "ControlLogix 5550" software. This setup combines the engineering program MATLAB (via the Simulink extension) to develop control block diagrams containing calculations for robot design and comprehension. A data read-write interface is implemented on an "Allen Bradley 1756-L1" PLC, along with the integration of an Open Platform Communication (OPC) platform using the "RSLinx Classic" software. This configuration empowers the user to manipulate trajectories and objectives using calculations that depict the kinematics and dynamics of the mentioned robot. Consequently, this setup offers a control option that enables direct application of theoretical mathematical principles to the design and control aspects of robotics, leading to enhanced understanding of these principles.

Leveraging product quality and price for attainment of the manufacturer's economic objectives

PurposeThis paper analytically models and numerically investigates two operating levers, namely optimization of product price and optimization of product quality in the context of a manufacturer that sells the products directly in the marketplace. The study attempts to identify how optimizing product quality and product price can fulfill a manufacturer's economic aims such as maximization of the manufacturer's profit and market demand. Anchored to the extant literature, the demand is modeled as a parametric joint multiplicative function of price and quality. Further, price is modeled as a function of product quality.Design/methodology/approachFirst, the authors evolve the analytical expression for the manufacturer's profit. Thereafter, following the mathematical principles of unconstrained optimization, the authors arrive at the conditions for optimal product quality and product price. The authors further perform numerical experiments to understand the behavior of economic dimensions such as profit and demand with respect to sensitivities associated with cost, quality and price.FindingsThe authors find that under product quality optimization, the optimal product quality is a unique solution in that a highest possible theoretical manufacturer's profit is obtained. However, in the case of product price optimization, the optimal product price is non-unique and is a function of product quality. The authors further find that in the context of functional quality-level expectations, product quality optimization as an operating lever gives a better dividend. However, in the case of higher product quality expectations, product price optimization performs better than product quality optimization. Further, several novel findings are also obtained from numerical experimentations.Originality/valueThe findings of the authors' study have implications for types of industries characterized by relatively low as well as relatively high competitive intensity. Further, as opposed to several extant studies that have often carried out joint optimization of quality and price, the authors' study is one of the first to study the impact of product price and product quality on the manufacturer's economic objective in a disparate and focused manner, thus capturing individual effects.

Effect evaluation of ideological and political guidance in university party construction based on hierarchical analysis model

Abstract To further explore the evaluation model of the quality of college students working in vocational colleges, this paper proposes to establish an evaluation index system for the quality of college students working in vocational colleges according to the four main factors of the domestic vocational college, which is based on the analysis of the quality. the work of the party building, the quality and responsibility of the party members, and the mass examination; In the process of evaluating the quality of college students’ dormitory building, various useful and useful information were determined, and the evaluation model was established by using the analytic hierarchy process, and the weight coefficients of various influential factors were determined by the combined method. First of all, according to the characteristics and requirements of the student’s institution, combined with the system of employment management widely used in China, combined with the practice of students’ institution, thoroughly analyzed various factors which affect the quality of the student’s institution building, and establish a more effective and objective evaluation index system. Secondly, using the analytic hierarchy process to scientifically classify the indicators, and determine the evaluation factor set and evaluation criteria, establish a hierarchical structure model. Finally, combined with the hierarchical structure model, the relative weight of each evaluation factor is given using the principle of fuzzy mathematics.

Interdisciplinary Studies in Music Research the Substance of Study and Implications of Fine Arts, Mathematics, and Philosophy

Interdisciplinary studies in music education research can integrate various disciplines that can help enrich the understanding of fine arts, mathematics, and philosophy. In terms of fine arts, this approach can help students understand the relationship between fine arts and music to enrich their experience in understanding and producing works of art. In terms of mathematics, mathematical elements found in music theory can be applied in music education, so that students can understand how mathematical principles can be applied in the arts. In terms of philosophy, an understanding of ontology, epistemology as well as axiology can help students consider the meaning and value of musical artworks. Interdisciplinary study in music research implies that students can gain a richer and more multidimensional learning experience, and develop skills and understanding that are holistic and beneficial to their future lives.

PKM. SDN APUAN BANGLI DALAM PENGEMBANGAN KEMAHIRAN MENGAJAR GURU MATEMATIKA DI SEKOLAH DASAR UNTUK PENINGKATAN PROFESIONAL GURU

Professional teachers are teachers who are able to meet competency standards and are proven by professional certificates. Elementary school teachers are class teachers whose duties are required to master many subjects. Therefore, it is undeniable that the mastery of knowledge (material) in several subjects is not optimal and there is the potential for errors or misconceptions to occur in learning mathematics. There are indications that elementary school teachers lack mastery of the material and are less proficient in learning mathematics. Inadequacy in learning Mathematics is a factor of teacher weakness and hinders the achievement of learning objectives, as well as influencing students' positive disposition towards Mathematics. In order to overcome errors or misconceptions in learning mathematics in elementary schools, each teacher must improve teaching skills by understanding mathematical concepts and principles correctly so that the teacher's knowledge increases and the teacher can change the way he teaches in class. Teacher teaching skills can be improved through workshop activities. Teaching skills development is an effective and structured professional development that results in changes to teachers' knowledge and practice in learning mathematics. Conceptually, teaching proficiency is a product of activities embedded in work. In-learning activities supported by teaching skills enhance teachers' knowledge and help them change the way learning is taught in the classroom. Formally developing teaching skills is part of the range of experiences that can result in professional learning

A versatile volume-based modeling technique of distributed local quadratic convergence for aeroengines

For advanced aero-engine design and research, modeling and simulation in a digital environment is indispensable, especially for engines of complicated configurations, such as variable cycle engines (VCE) and adaptive cycle engines (ACE). Also, in the research of future smart engines, reliable real-time digital twins are paramount. However, the 2 dominant methods that used in solving the simulation models, Newton-Raphson (N-R) method and volume-based method, are not fully qualified for the study requirements, because neither of them reaches the satisfactory balance of convergence rate and calculating efficiency. In this study, by deeply analyzing the mathematical principle of these 2 methods, a novel modeling and solving method for aero-engine simulation, which integrates the advantages of both N-R and volume-based methods, is established. It has distributed architecture and local quadratic convergence rate. And a novel modeling method for variable area bypass injectors (VABI) is put forward. These facilitate simulation of various configurations of aero-engines. The modeling cases, including a high bypass-ratio (BPR) turbofan and an ACE, illustrate that the novel technique decreases the iterations by about two-thirds comparing with volume-based method, while the success rate of convergence remains over 99%. This proves its superiority in both convergence and calculating efficiency over the conventional ones. This technique can be used in advanced gas turbine engine design and control strategy optimization, and study of digital twins.

Discussion on the monotonicity principle of the two-stage problem in joint optimal operation of cascade hydropower stations

The joint optimal dispatching of cascade hydropower stations aims to maximize economic benefits while satisfying various constraints. However, numerous studies have failed to acknowledge the significance of the intrinsic optimization principle and lack discussion on this issue. This study started with a mathematical principle analysis of the optimization problem and studied the optimality principle puzzle of the joint optimal dispatching of cascade hydropower stations. First, a two-stage optimization problem was constructed to describe the relationship between the variation in discharge and the incremental function of the total energy generation of the reservoir. Subsequently, the first and second derivatives of the cascade total generating capacity increment to cascade reservoir discharge variation were derived, and the existence condition of monotonically decreasing the first derivative was proposed. Moreover, the monotonicity principle was proven through numerical simulations by comparing the optimization results of POA and the monotonicity principle coupled IPOA in the cascade hydropower stations operation of the Jinsha River, it was found that in terms of power generation and computational efficiency, IPOA is superior to POA. Finally, using this optimization principle, the optimal operation mode of the two typical cascade reservoirs was analyzed in the case studies. The example results show that the proposed optimal principle can theoretically analyze and clarify the optimal operation mode of cascade reservoirs, and the operation modes of the two typical cascade reservoirs can provide guidance and reference for the operation modes of cascade reservoirs in real life.

Passivity-Based Control of Buck-Boost Converter for Different Loads Research

Normally, the buck-boost converter adopts single or double closed-loop control, and there are differences in control and parameters for different working modes and loads. In this study, a unified control method, the passivity-based control (PBC), is applied to a buck-boost converter for different loads, including constant resistance load (CRL), constant power load (CPL), and battery load. The PBC is a nonlinear control based on energy dissipation principle, and it has strong robustness to parameter interference and external disturbance, and it also has the advantages of simple design and simple implementation. Although many research studies have been conducted before, the voltage and current-related power losses are considered, and different load models are also compared in this research. The detailed mathematical model, control principle, and controller design of the buck-boost converter are thoroughly analysed. In addition, SIMULINK-based simulation results and experimental verification results of different loads are also given in the paper. Also, the PBC has smaller current overshot and smaller current ripples compared with PI control in different loads condition.

Three-Dimensional Inversion of Induced Polarization Effects in Airborne Time Domain Electromagnetic Data Using the GEMTIP Model

This paper discusses the physical and mathematical principles of the airborne induced polarization (IP) method. The possibility of extracting information about the IP properties of rocks from airborne survey data has become a subject of active research recently. We introduce a method for the joint inversion of the airborne EM data into the electrical conductivity and IP parameters based on the generalized effective-medium theory of induced polarization (GEMTIP). We also present the results of the inversion of the airborne EM data collected over the Echum Project Area, in Northwestern Ontario, Canada, into 3D conductivity and chargeability models. Obtaining IP physical property models from an airborne geophysical survey may result in a paradigm change in mineral exploration by pulling more information and value from airborne EM surveys.

Enhanced bare-bones particle swarm optimization based evolving deep neural networks

In this research, we propose a variant of the Bare-Bones Particle Swarm Optimization (BBPSO) algorithm for hyper-parameter selection and deep architecture generation for image, audio and video classification tasks. Since the search process of the original BBPSO model is guided by a single leader and the particles’ personal best experiences, there is a lack of interactions pertaining to the neighbouring elite solutions. To overcome this limitation, we propose a versatile search process for a modified BBPSO model that incorporates a number of effective components and operations. These include the neighbouring and global best signals, search actions with Cauchy/Levy scale factors, sub-dimension operations guided by the local and global elite solutions, and a Levy-driven local search mechanism. Moreover, root-finding algorithms are employed which use informative mathematical principles to estimate new root offspring for leader/particle enhancement. A reinforcement learning algorithm is subsequently used to identify the optimal sequential deployment of these numerical analysis methods to increase robustness. Several medical imaging data sets, i.e., ISIC 2017, PH2 and Dermofit skin lesion databases, the ALL-IDB2 microscopic blood image data set, the MURA musculoskeletal radiographic database, the CK + facial expression data set, as well as the Coswara respiratory audio data set and UCF101 video action data set, are employed for evaluation. The proposed BBPSO-optimized Convolutional Neural Network (CNN), bidirectional Long Short-Term Memory (BiLSTM) with attention mechanism, and CNN-BiLSTM models outperform those devised by other PSO and BBPSO variants, as well as state-of-the-art existing studies, significantly, for image, audio respiratory abnormality and realistic video action recognition.

Self-Made Business Proposal Presentation: Authentic Learning in General Mathematics

Authentic learning is a style of learning that encourages the students to produce an outcome that might be a big help in a real-world situation. And this was used in one of the subjects of senior high school, General Mathematics. A study was conducted to determine how authentic learning could aid teachers in discussing General Mathematics. The method of research used was focused action research to the senior high school students of one of the private schools in Marikina City. Learners were requested to have a reflection on their presentation of the self-made business proposals and be compared to their performances and outputs. Analyzing the data lead to three main themes, namely, focused Mathematical concepts, personal development, and principles of learning. Doing this kind of authentic learning shows ownership of the students on their output, which provided different areas of enhancements and learnings, not only in mathematical skills but also improvements for themselves as a person. Thus, Self-made Business Proposal Presentation shows real-world problems engagements, the used of flexible inquiry, intellectual skills and metacognition, students involve in social learning in a community of learners, and ownership of learning. Likewise, doing authentic learning could provide an opportunity for students to solve and explain problems mentally and promotes students’ sensemaking, creativity, personal development, and sense of being a mathematician. Keywords: Authentic Learning, General Mathematics, Self-Made Business Proposal Presentation, Focus Action Research, Philippines

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Its Applications in QSPR Studies of Octane and Its Isomers

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure–property relationships (QSPRs), and topological indices are a valuable source of information about molecular properties, such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. A molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs and windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results show that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

ПРИМЕНЕНИЕ ПРАВИЛА ЗОЛОТОГО СЕЧЕНИЯ В ЮРИСПРУДЕНЦИИ: АНАЛИЗ И ПЕРСПЕКТИВЫ

This article examines the application of the golden ratio, also known as the golden proportion, in jurisprudence. The golden ratio is a mathematical and aesthetic principle that has been known since ancient times, and its application in various fields of knowledge has attracted the interest of researchers. The article explores examples of the use of the golden ratio in legal practice, including the analysis of legal texts, argumentation, and the making of judicial decisions. Drawing on existing research and theoretical concepts, the article also discusses the prospects of applying the golden ratio rule to enhance effectiveness and fairness in jurisprudence. The author was inspired by the monograph "The Golden Ratio and Evolution: An Introduction to the General Theory of Non-local Evolution" by Kokin A. V. and Kokin A. A., published in 2022, where the authors examined the theory of the golden ratio through the lens of the synergistic paradigm.

Synchronization of Frequency-Modulated Multiagent Systems

Oscillation synchronization phenomenon is widely observed in natural systems through frequency modulated signals, especially in biological neural networks. Frequency modulation is also one of most widely used technologies in engineering. However, due to the technical difficulty, oscillations are always simplified as unmodulated sinusoidal-like waves in studying the synchronization mechanism in the bulky literature over the decades. It lacks mathematical principles, especially systems and control theories, for frequency modulated multi-agent systems. This paper aims to bring a new formulation of synchronization of frequency modulated multi-agent systems. It develops new tools to solve the synchronization problem by addressing three issues including frequency observation in nonlinear frequency modulated oscillators subject to network influence, frequency consensus via network interaction subject to observation error, and a well placed small gain condition among them. The architecture of the paper consists of a novel problem formulation, rigorous theoretical development, and numerical verification.

Applications of deep neural networks on music emotion recognition

Music Emotion Recognition (MER) is a subfield of Music Information Retrieval (MIR) that focuses on finding a relationship between music and human emotions by applying machine learning and signal processing techniques. In recent years, neural networks have achieved great success in a large number of areas, such as speech recognition and image processing, sparking many attempts to utilize neural networks in the MER task. Although new models for MER are constantly emerging, there are few systematic reviews in this field that involves the latest models and datasets. Therefore, in this paper, we provide a detailed review of this task. Our work first expounds on the practical significance and research status of the MER problem. Then, we encapsulate the background research and contributions of predecessors in both machine learning and psychology fields. Our work also includes a thorough analysis of several important datasets and their mathematical principles. Finally, we summarize four novel models from an application perspective and conclude a few potential challenges for the task.

A Critique of Yablo’s If-thenism

Abstract Using ideas proposed in Aboutness and developed in ‘If-thenism’, Stephen Yablo has tried to improve on classical if-thenism in mathematics, a view initially put forward by Bertrand Russell in his Principles of Mathematics. Yablo’s stated goal is to provide a reading of a sentence like ‘The number of planets is eight’ with a sort of content on which it fails to imply ‘Numbers exist’. After presenting Yablo’s framework, our paper raises a problem with his view that has gone virtually unnoticed in the literature. If we are right, then Yablo’s version of if-thenism cannot succeed.

Analysis of mathematical methods and principles of molecular dynamics and monte carlo method

In this era, molecular dynamics and Monte Carlo methods have become the primary simulation methods. With the emergence of computer simulation research methods, it has been possible to solve the sizeable computational volume and some other problems in the simulation process. At present, molecular dynamics simulations have taken an essential place in the substantial computational system and have a remarkable ability to solve multi-body problems. Therefore, researchers widely use it in many fields such as physics, chemistry, and materials science. Meanwhile, the Monte Carlo method is also a very effective statistical simulation method. This method can far surpass ordinary integration in efficiency with guaranteed computational accuracy. Furthermore, the derived kinetic Monte Carlo method can simulate and study dynamics problems. It can be seen that both simulation methods play an vital role in various disciplines. Therefore, it is very significant to understand the mathematical principles behind them and to know their advantages and disadvantages.

Some properties of generalized greyness of interval grey number

PurposeIn order to make full use of the generalized greyness of interval grey number, this paper analyzes the properties and its applications of generalized greyness.Design/methodology/approachFirstly, the static properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain are analyzed. Then, this paper gives the dynamic properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain and explains the dialectical principle contained in it. Finally, the generalized greyness is used to judge the effectiveness of interval grey number transformation.FindingsThe results show that the generalized greyness of interval grey number has relativity, normativity, unity, eternity and conservation. The static and dynamic properties of generalized greyness are the same in the infinite and infinitesimal background domain, while they are different in the bounded background domain. The generalized greyness can be used as an index to judge whether the grey number transformation is greyness or information preservation.Practical implicationsThe research shows that the generalized greyness can be used as an index to judge the validity of the grey number transformation and also can be applied in grey evaluation, grey decision-making and grey prediction and so on.Originality/valueThe paper succeeds in realizing the mathematical principle of “white is black”, the “greyness clock-slow effect” of the value domain of interval grey number and the generalized greyness conservation principle, which provides a theoretical basis for the rational use of generalized greyness of interval grey number.

A unified method for assessing the observability of dynamic complex systems

ProblemSystems theory applied to biology and medicine assumes that the complexity of a system can be described by quasi-generic models to predict the behavior of many other similar systems. To this end, the aim of various research works in systems theory is to develop inductive modeling (based on data-intensive analysis) or deductive modeling (based on the deduction of mechanistic principles) to discover patterns and identify plausible correlations between past and present events, or to connect different causal relationships of interacting elements at different scales and compute mathematical predictions. Mathematical principles assume that there are constant and observable universal causal principles that apply to all biological systems. Nowadays, there are no suitable tools to assess the soundness of these universal causal principles, especially considering that organisms not only respond to environmental stimuli (and inherent processes) across multiple scales but also integrate information about and within these scales. This implies an uncontrollable degree of uncertainty. MethodologyA method has been developed to detect the stability of causal processes by evaluating the information contained in the trajectories identified in a phase space. Time series patterns are analyzed using concepts from geometric information theory and persistent homology. In essence, recognizing these patterns in different time periods and evaluating their geometrically integrated information leads to the assessment of causal relationships. With this method, and together with the evaluation of persistent entropy in trajectories in relation to different individual systems, we have developed a method called Φ-S diagram as a complexity measure to recognize when organisms follow causal pathways leading to mechanistic responses. ResultsWe calculated the Φ-S diagram of a deterministic dataset available in the ICU repository to test the method's interpretability. We also calculated the Φ-S diagram of time series from health data available in the same repository. This includes patients' physiological response to sport measured with wearables outside laboratory conditions. We confirmed the mechanistic nature of both datasets in both calculations. In addition, there is evidence that some individuals show a high degree of autonomous response and variability. Therefore, persistent individual variability may limit the ability to observe the cardiac response. In this study, we present the first demonstration of the concept of developing a more robust framework for representing complex biological systems.