Mathematical Formula Research Articles

A primer of community ecology using the R language

AbstractCommunity ecology beginners often struggle to understand theories expressed in complex mathematical formulas and to master computer programming. To remedy this situation, this article provides a practical, R‐based introduction to community ecology by illustrating core concepts (vital rates, carrying capacity, density dependence) and models that can be used to explore the patterns of species abundance and diversity. The structure of this article consists of three modeling exercises, each asking a general question that can be answered by a combination of theory and R programming: (1) what determines the abundance of species, and what makes a population persist and go extinct?; (2) what determines the distribution of species and species diversity?; (3) what determines the relative abundance of species and what allows species to coexist? Through the exercises, I discuss the following five concepts and ideas that provide valuable insights into the questions: (i) the tragedy of the commons, (ii) the theory of island biogeography, (iii) competitive exclusion, (iv) the neutral theory of biodiversity, and (v) frequency dependence. These materials are thus designed to guide the reader in developing an intuition for ecological thinking that will help capture the essence of the global environmental and biodiversity crisis. Although this article does not delineate the scope and depth of the vast field of community ecology, I hope that it will motivate the reader to step up to a more formal introduction to community ecology.

Determinación de la densidad vehicular en ciudades intermedias por medio de visión por computador

The objective of this research work is to calculate the vehicle density of cities through the use of computer vision. To carry out the study, we captured videos of vehicular traffic at 8 intersections in the city of Loja using a drone and a high-resolution camera. Subsequently, we used the Python language and the YOLOv8 library to count vehicles of different categories, such as small vehicles, trucks, and motorcycles. Through mathematical formulas used in transportation engineering, the values ​​of vehicle density, vehicle flow rate, and average spacing were obtained. As results, we have that the machine learning model using YOLOv8 has an accuracy of 90% in detecting and classifying vehicles, and thanks to its use, the road with the highest vehicle density was identified. The practical applications of this work could improve vehicle flow and help competent organizations related to traffic management make decisions.

Experimental and numerical study on scroll compressor under different profile correction and discharge ports shapes

The scroll compressor is an essential component in air conditioning and heat pump systems. This study examined an electric scroll compressor using R22 refrigerant, focusing on how modifications in the scroll head profile and discharge structure affect its performance. Initially, a semi-empirical model based on mathematical formulas was developed to predict the performance improvements of the updated scroll compressor. Three-dimensional simulation software was then used to illustrate changes in the internal flow dynamics before and after enhancements. The predictions were validated through experimental testing. Both the semi-empirical model and the three-dimensional unsteady numerical calculation model analyzed the effects of modifications to the tooth head profile and discharge port shape on compressor performance. The adoption of a PMP profile correction delayed the compressor discharge process, shifting the starting discharge angle from 315°to 344°, thereby reducing under-compression occurrences during operation and increasing volumetric efficiency by 1.31%. Additionally, mathematical formulas correlating temperature with compressor performance were developed from fitting data, predicting compressor behavior under various conditions. Moreover, replacing a circular discharge port with a waist-shaped port reduced power consumption by 0.59 kW, resulting in a more uniform temperature distribution and enhanced mass flow rate during compressor operation.

Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories

The research goal is twofold: to articulate neuro-mathematics with the extended theory of mathematical connections that uses onto-semiotic approach tools and to explore the connections established by a teacher and his student when solving a problem about the volume of two boxes, one of toothpaste and the other of tomato. This research was developed in two stages: the theories were articulated assuming concordances and complementarities, highlighting the notion of connection, and a context of reflection was considered carried out in three phases where the participants were selected, participant observation was carried out in the classroom during solving a problem and then analyzing the data with the new tool to explore mathematical and neuro-mathematical connections. The findings present the mathematical connections established by the teacher and the student of meaning, feature, procedural, different representations (alternate, equivalent, and from a horizontal mathematization view), and part-whole, as well as neuro-mathematical connections of: recognition of terms and symbols; visual perception, spatial skills and motor coordination; association of mathematical concepts and formulas; intermediate calculations and unit conversion; solve operations step by step and understand the process; verification and conclusion, activated in the brain areas linked to each mathematical practice sequentially.

Improvement of Sound-Absorbing Wool Material by Laminating Permeable Nonwoven Fabric Sheet and Nonpermeable Membrane

Thin sound-absorbing materials are particularly desired in space-constrained applications, such as in the automotive industry. In this study, we theoretically analyzed the structure of relatively thin glass wool or polyester wool laminated with a nonpermeable polyethylene membrane and a permeable nonwoven fabric sheet. We also measured and compared the sound-absorption coefficients of these samples between experimental and theoretical values. The sound-absorption coefficient was derived using the transfer matrix method. The Rayleigh model was applied to describe the acoustic behavior of glass wool and nonwoven sheet, while the Miki model was used for polyester wool. Mathematical formulas were employed to model an air layer without damping and a vibrating membrane. These acoustic components were integrated into a transfer matrix framework to calculate the sound-absorption coefficient. The sound-absorption coefficients of glass wool and polyester wool were progressively enhanced by sequentially adding suitable nonwoven fabric and PE membranes. A sample approximately 10 mm thick, featuring permeable and nonpermeable membranes as outer layers of porous sound-absorbing material, achieved a sound-absorption coefficient equivalent to that of a sample occupying 20 mm thickness (10 mm of porous sound-absorbing material with a 10 mm back air layer).

Theoretical Contributions Regarding the Modelling of the Superfinishing Process

The mathematical modeling applied on the machining process by superfinishing includes the study of the forces that appear during the action of the abrasive body on the surface of the parts subjected to processing, as well as the study of the mathematical equations of the trajectories of the abrasive grains within the various working methods used. This study is necessary to be able to obtain a quality of the processed surfaces in accordance with the technical execution documentation. In this way, various movements of the abrasive tool and the processed part can be combined in order to be sure of obtaining the quality of the part's surface finish in the shortest possible time. The study allows obtaining mathematical formulas that facilitate the use of optimal technological parameters for the processing of different shapes of pieces.

Research on Evaluation Method of Natural Gas Hydrate Resources Based on Probability Distribution Model

Natural gas hydrate, as a highly efficient and clean energy source, has garnered significant attention from both developed and energy-deficient nations. However, to achieve industrial application, several technical challenges must be addressed, including resource exploration, spatial positioning, resource assessment, economic production evaluation, and climate change impact assessment. Currently, our exploration and evaluation system for gas hydrate resources remains immature. This study aims to determine the probability distribution of effective thickness, porosity, and saturation of natural gas hydrate resource parameters in the study area and their variations. Utilizing probability statistics theory, we calculated specific values for all gas hydrate resource parameters from open-source data of 14 exploration well locations, determined their probability distributions, and conducted distribution detection to identify specific distributions. Data analysis was performed using linear graphs and bar charts to summarize patterns. Subsequently, by applying the mathematical formula Q = A×Z×∅×S×E, we categorized natural gas hydrate resource parameters, calculated gas hydrate resources at each effective depth, determined the probability distribution of each obtained data point, and ultimately solved for the total natural gas hydrate resources, yielding a final solution of 31875763695.08.

Mathematical Information Retrieval: A Review

Mathematical formulas are commonly used to demonstrate theories and basic fundamentals in the Science, Technology, Engineering, and Mathematics (STEM) domain. The burgeoning research in the STEM domain results in the mass production of scientific documents that contain both textual and mathematical terms. In scientific information, the definition of mathematical formulas is expressed through context and symbolic structure that adheres to strong domain-specific notions. Whereas the retrieval of textual information is well-researched, and numerous text-based search engines are present. However, textual information retrieval systems are inadequate for searching scientific information containing mathematical formulas, including simple symbols to complicated mathematical structures. The retrieval of mathematical information is infancy, and it requires the inclusion of new technologies and tools to promote the retrieval of scientific information and the management of digital libraries. This paper provides a comprehensive study of mathematical information retrieval, highlights their challenges and future opportunities.

Improved Dissolution Time and Oral Bioavailability of Pioglitazone Using Liquisolid Tablets: Formulation, In Vitro Characterization, and In Vivo Pharmacokinetics in Rabbits.

In the current study, it was intended to prepare liquisolid tablets of pioglitazone HCl to improve the bioavailability and dissolution time of the drug, as it has low solubility in water. Mathematical formulas were adopted, and the quantities of the carrier (MCC), coating material (colloidal silicon dioxides), and nonvolatile liquid vehicle (Tween 80) were taken. Various ratios of the drug to liquid and carrier to coating had been used in the formulation of liquisolid compacts. The evaluation of the formulated liquisolid compacts was done by performing FTIR, DSC, XRD, and SEM studies. Postcompression parameters, dissolution, stability, and bioavailability were accessed for the optimized formulation. FTIR and DSC studies showed the compatibility of the drugs and excipients. XRD revealed the transition to the amorphous state. It was found that the properties of the newly manufactured liquisolid tablets were within the parameters of what is considered acceptable. The optimized formulation of LST10 showed 99.87 ± 0.19% (p < 0.05) pioglitazone released within 60 min of dissolution. Dissolution data treatments (Q 15, IDR, RDR, %DE, MDT, f 1, and f 2) resulted in better drug release than other drugs studied and marketed tablet formulations. The optimized formulation produced had been proven stable when it was subjected to accelerated stability testing. This suggested that the bioavailability of pioglitazone was enhanced, as indicated by the substantial increase in AUC0-t (3.06-fold) and C max (4.18-fold). According to the findings, the selected combination and method significantly increased the dissolution time and bioavailability of pioglitazone. Moreover, this developed method can be used for other drugs with low water solubility.

Synthesis of magnetic spinal ferrite CrFe2O4 nanoparticles and uses them to remove lead and cadmium ions from aqueous solutions

Abstract This study deals with the preparation of a magnetic ferrite CrFe2O4 by the sol–gel auto-combustion method, using the lemon juice extract as a fuel for the reaction and preventing the precipitation of the components. The prepared nanocomposite was diagnized using various techniques such as FT-IR, XRD, FE-SEM, EDX, Zeta Potential and (BET). X-ray diffraction patterns verified the state of phase purity and the particle size of 33.9 nm. Additionally the study examined the synthesized compound as an adsorbent surface for lead and cadmium ions from their aqueous solutions. The mathematical formulae of the Langmuir and Freundlich isotherms were applied to the actual adsorption data utilising the findings from the temperature effect studies. As a result, the Freundlich equation yielded a more correlated linear link than the Langmuir isotherm. The thermodynamic results showed that the lead and cadmium ions adsorption were endothermic according to the positive (ΔH) values, whereas the lead and cadmium ion adsorption process were spontaneous with negative (ΔG) values. Positive values of (ΔS) indicate an increase in the randomness of the adsorption process. The current study also comprises the practical application of eliminating lead and cadmium ions from marine waters collected from two sites: Al-Faw Al-Kabir Port (Eastern Breaker) and Khor Al-Zubair (berth 13), by means of the prepared surface. The results indicate the removal percentage of the prepared surface for lead was (91.72%) for the first location and (86.00%) for the second location, whereas the removal percentage of cadmium was (85.52%) for the first site and (89.10%) for the second site.

Fuzzy Linear Temporal Logic with Quality Constraints

As an extension of quantitative temporal logic, uncertain temporal logic essentially describes the temporal behavior of uncertain and incomplete systems, thus better solving search and decision-making problems in such systems. Fuzzy linear temporal logic (FLTL) is a focal point in uncertain temporal logic research. However, there are evident shortcomings in the current research outcomes. First, in previous FLTL studies, the practice of obtaining path reachability and formula satisfaction values independently and subsequently selecting the smaller of the two as the satisfaction value metric led to information loss. Furthermore, this simplistic information fusion approach fails to reflect the varying importance of these two types of information to the requirements. Second, computing path reachability and temporal logic formula satisfaction values separately may result in a mismatch between the two pieces of information with respect to the same path segment. Thus, the primary challenge lies in accurately integrating the satisfaction values of temporal logic formulas with the path reachability of the segments that yields these satisfaction values, utilizing various reasonable information synthesis methods, to ensure synchronization between path reachability and formula satisfaction values without incurring information loss. Additionally, it is crucial to reflect the different preference requirements for these two types of information. Moreover, the temporal logic formula characterizes system properties, with its sub-formulas delineating distinct sub-properties. Consequently, considering the varying importance preferences of sub-formulas is also significant. To address these deficiencies, we introduced quality constraint operators into FLTL, resulting in quality-constrained fuzzy linear temporal logic (QFLTL). This incorporation enables the synchronization and comprehensive fusion of path-reachability information and formula satisfaction values within the final semantic metric, thereby resolving the issues related to information synchronization and loss. Furthermore, it can accommodate the differing preference requirements between the two types of information and sub-properties during the information synthesis process. We defined the syntax and semantics of QFLTL and examined its expressive power and properties. Notably, we investigated the decidability of logical decision problems in QFLTL, encompassing validity, satisfiability, and model-checking issues. We proposed corresponding solution algorithms and analyzed their complexities.

Enhancing Math education for visually impaired students: alternative text implementation in LATEX, MathJax, MathML and LAMBDA

Abstract This article outlines an innovative procedure to improve the accessibility of Mathematics for secondary school students with visual impairments. Using LATEX, a widely used typesetting system, a transformative approach is developed that converts traditional mathematical content into three accessible formats: PDF, MathJax and LAMBDA. Central to this system is the integration of alternative text, which offers full descriptions of images and mathematical formulae and promotes a richer understanding of its content. The broader implications of this project include the introduction of novel teaching models for educators, enhanced accessibility of Mathematics programmes, and the potential to encourage the enrolment of visually impaired students in science degree courses. Ultimately, this work contributes to the creation of the conditions for the development of an inclusive and barrier-free learning environment in Mathematics education.

Toward self-regulated learning: effects of different types of data-driven feedback on pupils' mathematics word problem-solving performance.

Mathematical word problems refer to word problems where the information that is presented needs to be integrated, typically into a mathematical formula, to arrive at a solution to the problem. When solving mathematics word problems, elementary school students often have difficulties improving their performance due to a lack of self-regulated learning (SRL). However, SRL can be developed by adopting an appropriate teaching approach which offers quantitative feedback or learning prompts. With the sophistication of interactive and data-driven feedback technology, it is possible to provide timely and personalized strategies for promoting students' SRL. In this study, an interactive e-book editing platform was used to design self-regulation-level-based feedback(SRLF) and task-level-based feedback(TLF) teaching models, which were respectively conducted in two similar fifth-grade classes for the mathematics word problem solving lessons. Using ANCOVA and repeated ANOVA, this study found that (1) the SRLF had a remarkably greater impact on elementary school students' mathematics word problem-solving performance than the TLF, with a partial η 2-value of .107; (2) In the short period of time, there was no significant difference between the two kinds of feedback on the learners' SRL. The TLF was slightly superior to the SRLF, especially in terms of total self-regulated learning scores and cognitive strategies; (3) The TLF had a significant interaction effect on self-regulated learning and cognitive strategies, respectively with a partial η 2-value of .059 and .056.

A semi-analytical prediction model for fluid elastic instability in the streamwise direction of a normal triangular tube array

Fluid elastic instability (FEI) is widely regarded as the most destructive mechanism of flow-induced vibration. Numerous failures of heat exchanger tubes have been attributed to this phenomenon. This paper focuses on a normal triangular tube array and develops a semi-analytical time-domain solving model to address FEI in the streamwise direction. Utilizing computational fluid dynamics simulations and image processing techniques, a comprehensive set of tube-in-channel model parameters is derived, including the area perturbation amplitude, phase difference, mean area along the flow channel, and steady-state term of flow velocity. Tube motion in the streamwise direction generates a disturbance distinct from that caused by transverse flow, leading to revisions in the expressions of relevant model parameters. Furthermore, variations in these parameters across different positions and velocities are quantitatively analyzed through function fitting, yielding specific mathematical formulas. Ultimately, the derived tube-in-channel model parameters applicable to streamwise FEI are validated against experimental data, affirming the model's accuracy.

On the use of kolmogorov–arnold networks for adapting wind numerical weather forecasts with explainability and interpretability: application to madeira international airport

Abstract This study examines the application of machine learning to enhance wind nowcasting by using a Kolmogorov-Arnold Network model to improve predictions from the Global Forecast System at Madeira International Airport, a site affected by complex terrain. The research addresses the limitations of traditional numerical weather prediction models, which often fail to accurately forecast localized wind patterns. Using the Kolmogorov-Arnold Network model led to a substantial reduction in wind speed and direction forecast errors, with a performance that reached a 48.5% improvement to the Global Forecast System 3 h nowcast, considering the mean squared error. A key outcome of this study comes from the model’s ability to generate mathematical formulas that provide insights into the physical and mathematical dynamics influencing local wind patterns and improve the transparency, explainability, and interpretability of the employed machine learning models for atmosphere modeling.

Epicyclic oscillations and particle collision with trajectories around quantum corrected black holes

The present study deals with the orbital, oscillatory motion, and trajectories of test particles around quantum-corrected black holes. The angular momentum within specific energy is calculated to discuss stable circular orbits. The effective potential through Hamiltonian is calculated around quantum-corrected black holes. The trajectories scenario around particles of considered black hole solutions are discussed. Further, we provide the mathematical formulas for both latitudinal and radial frequencies. The primary properties of test particle quasi-periodic oscillations in stable circular orbits in the black hole’s equatorial plane are investigated. We provide a Markov Chain Monte Carlo analysis of the restrictions on quantum-corrected black hole attributes. We analyze QPOs detected in X-ray binaries, namely the cores of the galaxies Sgr A∗, M82 X-1, microquasars XTE J1550-564, GRS 1915+105 and GRO J1655-40. Additionally, the process of Periastron precession is examined. We show that the velocity of particles around black holes is strongly dependent on the parameters of the model. Notably, the pictorial behavior that describes our results feasibility.

Investigation of the TaOx unipolar switching memory on high efficiency computing

Memristor has shown great potential application for data storage, neuromorphic computing chip, and memory logic, but its bi-directional operation from setting in positive bias voltage region to resetting in a negative bias voltage region would introduce a complex control circuit. Herein, a memristor with the structure of Au/TaOx/F-doped SnO2 presents unipolar switching behavior, enabling the memristor to operate the set and reset processing in a single voltage direction. By comparison with bipolar switching memristor, using this unipolar switching memristor to operate the logic expression of the letter “D” based on American standard code for information interchange (ASCII) can reduce power consumption by 55.56% while switching the logic state from “0” to “1” and then back to “0” can save up to 48% of power consumption. This work provides a feasible method for the low power consumption computing as well as a road to simplify circuit design.

Mathematical Model of FWE Branching Type with Effect on Energy

: Mathematical modeling is one of the most important topics in teaching mathematics and converting real world problems into mathematical formulas in order to solve them. In this research we will take the behavior of lateral branching, tib-tib anostomosis with its effect on the energy of the growth of fungi. We will use the system of equations (PDEs) to solve a mathematical model and we will use mathematical techniques in order to reach the solution using non-dimensionality, stability, traveling wave, and numerical solution and use computer programs to facilitate the solution, including the Maple program, the MATLAB program, use Pdep code and the pplane7 code.

DETERMINING THE OPTIMAL NUMBER OF STRETCH FILM LAYERS FOR ENSURING PALLETIZED CARGO STABILITY: A SIMULATION STUDY

Numerical simulation tests were carried out to determine the influence of the characteristic features of a load unit (such as: weight, height, number of load layers, coefficient of friction between the layers) per number of wraps with stretch film necessary to ensure unit stability. Manufacturers of stretch film sometimes provide guidelines on how many layers of film should be used depending on the weight and height of the load. But they do not explain on the basis of which studies these values were determined. Performing simulations similar to those made in this work in laboratory conditions would be very expensive. The work attempts to determine such relationships by simulation methods. A developed by the author in his earlier works dynamic model of a layered cargo unit wrapped with stretch film was used. The study plan was to check 108 cases. On the basis of the collected data, an attempt was made to develop a mathematical formula that would allow to estimate the optimal number of foil wraps when certain parameters of the load unit are known. In the author's opinion such an estimate could reduce film consumption, which would have a positive impact on the environment.

Mathematical Model of Fungal Growth with Hyphae Death and Substrate

One of the most crucial subjects in mathematics education is mathematical modeling, which involves connecting situations from the real world to mathematical formulas and vice versa. Our study will focus on how substrate affects fungal growth and lateral branching behaviors, hyphal death, and tip death due to overcrowding. In order to solve a mathematical model, we will employ the system's three-dimensional of equations (PDEs). using numerical solutions, traveling wave theory, stability, and non-dimensionality in our mathematical approach as well as we use trace and determine to find stable states.Computer programs, such as the Maple program and Pdep code in MATLAB, will also be used to aid in the solution process.