Contemporary Mathematics

Peirce Decomposition of Quasi Jordan Algebras

Reem K. Alhefthi, Akhlaq A. Siddiqui, Haifa M. Tahlawi — Fri, 10 Jan 2025 00:00:00 +0800

Idempotents play a basic role in the study of algebras. Peirce decomposition induced by an idempotent is an important tool in the structure theory of non-associative algebras. In this note, we investigate the Peirce decomposition of a unital quasi Jordan algebra.

An Analytical and Numerical Approach to Solve the Tsunami Wave Propagation Equation

Juhi Kesarwani, Abhijit Majumder, Ishita Sharma, Ashish Kumar Kesarwany — Thu, 09 Jan 2025 00:00:00 +0800

We study the mathematical model of tsunami wave propagation (TWP) along the coastline of an ocean. The described model is represented by a system of non-linear partial differential equations. In this study, we employ two different techniques: one is the Adomian decomposition method (ADM, which is an analytical approach), and another is the finite difference method (FDM, which is a numerical approach) to obtain the solution for the proposed TWP model successfully. The solutions gained are numerically represented in graphs and tables. The validity of the solutions is investigated by comparing this proposed method with the fractional reduced differential transform method (FRDTM). The novelty of this paper is that we have demonstrated that the numerical method (FDM) better approximates the solution of our partial differential equation than the analytical method (ADM), and this has not been explored before in any other works. We examine the velocity and height of the coastline of an ocean from the tsunami wave equation using numerical and analytical techniques. MATLAB and MAPLE are used to obtain numerical and graphical representations.

Integration of Theoretical Foundations and Practical Implications for Neutrosophic Set Theory in Real-Time Maintenance Decision Systems

Settu K, Jayalakshmi M — Wed, 08 Jan 2025 00:00:00 +0800

In the present era, the concepts of neutrosophic set theory are essential for handling uncertain data with three distinct components. Researchers across various fields widely use these concepts due to their significant applications. Our world is filled with unpredictability, ambiguity, and vagueness, making it crucial to replace items at the appropriate time. This research paper focuses on the importance of addressing the replacement issue to improve reliability in maintenance scheduling. Ambiguity and uncertainty were present challenges in resolving maintenance issues. For example, the group replacement model has been solved using single-valued unique hexagonal neutrosophic numbers and the enhanced score function for hexagonal neutrosophic numbers (HNN) discussed in this paper. Additionally, the removal area method is used to determine the de-eutrophication of the linear neutrosophic hexagonal number, showing significant improvement in the clarification of HNN. MATLAB code is employed for de-eutrophication and to assess the effectiveness of this method. Numerical examples are provided to validate the proposed method. Using this enhanced score function, the replacement problem has been solved in a hexagonal neutrosophic environment. A comparative study was conducted between the established and proposed methods, which will benefit researchers in the field of neutrosophic domain in the future.

Assessing the Efffects of Vaccination on Tuberculosis and COVID-19 Co-Infection Modelling

Harshita Kaushik, V. S. Verma, Ram Singh, A. Manickam — Wed, 03 Jan 2024 00:00:00 +0800

In this paper, an epidemiological model is proposed to study the dynamics of coinfection diseases (TB) and COVID-19 with the effect of vaccination. Tuberculosis (TB) and COVID-19 both are infectious diseases that pose significant global health challenges. Evidence suggests that individuals with TB have a higher risk of acquiring the COVID-19 infection. With the emergence of the COVID-19 pandemic, concerns have arisen regarding the potential impact of the concomitant presence of TB and COVID-19. The epidemiological model is qualitatively analysed using stability analysis theory. The dynamic system exhibits a stable endemic equilibrium point while R₀ < 1 and unstable when R₀ > 1. The Lyapunov function is used to investigate the global stability of an endemic equilibrium point. The sensitivity analysis is carried out to identify the effective parameters that have the greatest influence on the reproduction number. Numerical results are carried out to assess the effect of various biological parameters in the dyanamic of both coinfection classes of TB & COVID-19. This study aims to analyze the implications of these concurrent diseases and predict the effect of vaccination in managing their coexistence. Our simulation results show that both the coinfection disease TB and COVID-19 can be reduced by increasing rate of vaccination.

Topological Analysis of Fractal Binary and Ternary Trees

Thanga Rajeswari K, Manimaran A — Thu, 16 Jan 2025 00:00:00 +0800

Fractals are complex geometric objects that seem the same at different scales and have self-similarity. Because of this special characteristic, fractals can be used to simulate intricate biological processes. Fractal binary and ternary trees are novel data types that combine the productiveness of tree architectures with the ideas of fractal geometry. In addition to self-similarity and scalability, these trees have potential across a range of computer science and medical applications. The main goal of the study is to identify and analyze topological indices and graph entropy for fractal binary and fractal ternary trees. By examining indices such as the Randić index, Zagreb indices, and entropy measurements, the study aims to obtain a comprehensive knowledge of the structural complexity and information-theoretic properties of these fractal graphs. The study starts with the vertex and edge partitioning of fractal binary and ternary trees in order to distinguish different structural classes. Using these partitions, we obtained topological indices and graph entropy values for the fractal trees. Also, this study compares the topological indices for each fractal tree with the number of copies in the fractal dimension for a succession of graphs.

Trend Analysis of BSE Stock Prices Using Hidden Markov Models and Viterbi Algorithm

S. Aarthi, S. Indrakala — Mon, 30 Dec 2024 00:00:00 +0800

Many forecasting techniques have been put forth and used in recent years to predict stock market trends. Recently, many researchers developed models based on Artificial Neural Network (ANN), Support Vector Machine (SVM), Fuzzy Logic (FL) and Moving Average (MA). This paper presents the trend analysis of the stock market prediction using the Hidden Markov Model and Viterbi algorithm with a 1-day, 2-day, 3-day, 4-day and 5-day variation in the close value for the specified time frame. In this work, we developed a BSE price forecasting model based on Hidden Markov Model due to its proven fittingness for modeling vigorous systems and pattern classification. We apply the HMM methodology to forecast the BSE closing price from Jan 2021 to Dec 2021 using available past datasets from Investopedia. The trend percentage of stock prices, which is computed for every observed sequence and hidden sequence, is provided by the probability values π. In situations of uncertainty, decision makers can use the proportion of probability values derived from the steady state probability distribution as a guide when making judgments.

Robust Dimensionality Reduction: A Bootstrap-Based Evaluation of PCA with Applications in Nutritional and Environmental Sciences

Sat, 25 Jan 2025 00:00:00 +0800

The complex structures of vast amounts of data provide a considerable challenge to researchers. Dimensional reduction methods are reliable and transform high-dimensional data into lower-dimensional representations while preserving most original information. Principal Component Analysis (PCA) is a commonly used approach for dimensionality reduction that transforms data into a lower-dimensional space while preserving important information. The variability within the sample may affect the stability and reliability of PCA results. The constraint of existing approaches compromises the accuracy of PCA stability assessments in practical data scenarios. These methodologies frequently depend on linear assumptions and encounter difficulties when addressing high-dimensional data. This study used the bootstrap method to assess the stability of PCA by assessing the variability of eigenvalues and principal components over several bootstrap iterations. We evaluate how stability metrics, particularly confidence intervals for eigenvalues and the proportion of variance clarified, can assist in determining the optimal number of principal components. The results indicate that the bootstrap provides a helpful framework for evaluating the robustness of PCA and guiding informed decisions on dimensionality reduction in many applications, including data compression, visualization, and classification. Moreover, the results illustrate the efficacy of this method in enhancing the reliability and interpretability of PCA findings among distinct data-driven research endeavors. This study enhances understanding of how principal component analysis (PCA) tackles data unpredictability while delivering valuable insights for professionals in several disciplines.

On Soft Submaximal and Soft Door Spaces

Ohud F. Alghamdi, Mesfer H. Alqahtani, Zanyar A. Ameen — Wed, 15 Jan 2025 00:00:00 +0800

This paper is divided into two parts. The first part deals with soft submaximal spaces, where we present new theorems and some basic facts. Further, we successfully find a requirement that indicates the soft one-point compactification of a soft topological space is soft submaximal. In the second part, we study soft door spaces. We notice that every soft door space is a soft submaximal space, but a soft submaximal space need not be soft door. The class of soft door spaces is hereditary. We give couterexamples showing that this class is neither additive nor productive. We further show that images of soft door spaces under certain soft functions are also soft door spaces. After that, we characterize certain soft topological spaces in terms of soft limit points and the Krull dimension. At last, we discuss when the soft one-point compactification of a soft topological space is soft door.

Supplier Selection Utilizing AHP and TOPSIS in a Fuzzy Environment Based on KPIs

Asal Safavi, Bahram Sadeghi Bigham, Mazyar Zahedi-Seresht — Mon, 13 Jan 2025 00:00:00 +0800

In today’s competitive and rapidly changing business landscape, organizations face significant challenges such as resource limitations, fluctuating demand, and evolving customer needs. Addressing these challenges requires effective strategies, with supplier selection playing a vital role in building resilient and efficient supply chains. This study introduces an innovative framework for supplier evaluation and selection, integrating the analytic hierarchy process (AHP) and the technique for order preference by similarity to the ideal solution (TOPSIS) within a fuzzy environment. The AHP method was employed to systematically identify and prioritize key performance indicators (KPIs) critical for evaluating suppliers. Criteria such as transportation cost, flexibility in meeting product requirements, defect reduction, and effective communication and responsiveness were identified as the most significant factors. These priorities formed the foundation for applying the fuzzy TOPSIS method, which facilitated the ranking of suppliers under conditions of uncertainty. The analysis revealed Sepidar Darb, Aram Plastic Sabalan, Sanaye Plastic Markaz, and Amin Avar Plastic as the top-performing suppliers, followed by Pegah Zanjan Company. The relevance of this research is heightened by the impact of the COVID-19 pandemic, which has disrupted global supply chains and fundamentally altered supplier selection criteria. While pre-pandemic evaluations predominantly focused on cost efficiency and product quality, the pandemic has underscored the importance of additional criteria such as supplier agility, risk management capabilities, geographical proximity, and digital integration. These emerging priorities highlight the necessity of rethinking traditional approaches to supplier selection and adapting to the evolving demands of global supply chains. By incorporating these updated criteria into the AHP-TOPSIS framework, this study offers a robust and practical tool for supplier evaluation in uncertain and dynamic environments. The proposed framework not only improves upon traditional methods but also provides valuable insights for organizations striving to create resilient and adaptable supply chains capable of withstanding future disruptions.

Discussions on the Vertex Euclidean Properties of Graphs

Zhen-Bin Gao, Sin—Min Lee, Yun-Fei Zhang — Sun, 07 Jan 2024 00:00:00 +0800

In 2022, the result that the sum of the lengths of any two edges of a triangle is greater than the length of the third edge in Euclidean geometry, is applied to labeling graph theory, a new concept-the vertex Euclidean graph is introduced. A simple graph G = (V, E) is said to be vertex Euclidean if there exists a bijection f from V to {1, 2, ..., |V|} such that f(u) + f(v) > f(w) for each C3 subgraph with vertex set {u, v, w}, where f(u) < f(v) < f(w). The vertex Euclidean deficiency of a graph G, denoted µvEuclid(G), is the smallest positive integer m such that G ∪Nm is vertex Euclidean. In this paper, the sufficient condition that the disjoint union of G and H is vertex Euclidean is given, meanwhile, the vertex Euclidean properties of four classes graphs are discussed, the vertex Euclidean deficiency of these graphs are obtained.

F-Hardy Rogers Type Contractions Endowed with Mann's Iterative Scheme in Convex Generalized b-Metric Spaces

Amna Naz, Samina Batul, Dur-e-Shehwar Sagheer — Sat, 06 Jan 2024 00:00:00 +0800

This article presents novel fixed point results using Mann’s iterative process in complete convex b-metric spaces, building upon Isa Yildirim’s recent work. The author established the definition of the -Hardy-Rogers contraction of the Nadler type by relaxing two conditions of Wardowski’s -mapping. Our approach employs Mann’s iterative scheme in -metric spaces under convex conditions. A supporting example with detailed calculations validates our result. Furthermore, we demonstrate the applicability of our findings by solving an integral equation through fixed point equation along with the axioms of the provided result. The obtained results are generalizations of several existing results in the literature.

Analysis of Radial Distribution Systems Using Particle Swarm Optimization under Uncertain Conditionsditions

M. Naveen Babu, P. K. Dhal — Thu, 09 Jan 2025 00:00:00 +0800

Efficiently mitigating losses in power distribution networks is imperative for their optimal operation. This research employs the particle swarm optimization (PSO) algorithm to investigate the joint optimization of phase balance and conductor sizing in imbalanced distribution systems. Objective functions encompass power loss, voltage unbalance, total neutral current, and complex power unbalance. Each objective is individually optimized before being integrated with weights to address multi-objective optimization. The study aims to minimize losses in inherently unequal electrical distribution networks. PSO techniques, namely power flow and optimal distributed generation (DG) placement, effectively curtail losses. These techniques are seamlessly integrated into existing systems using a tailored load-flow method for three-phase imbalanced radial distribution networks. Precise evaluation of network conditions relies on key metrics, including node voltage, angle, branch current, active and reactive power losses, and branch losses. A systematic approach identifies relevant variables, calculating target voltage angle and magnitude. Despite the time and effort required, this process yields accurate outcomes. A uniform voltage of 1 p.u. is maintained from substation to terminal node, with variable magnitude and phase angle adjustments yielding voltage drop computations. The proposed study is demonstrated on 19- and 25-node networks with unbalanced distribution. The results of the study underscore DG's potential for cost reduction and performance enhancement.

New Modified Gamma and Beta Functions with an Application

S. Mubeen, I. Aslam, Ghazi S. Khammash, Saralees Nadarajah, Ayman Shehata — Thu, 23 Jan 2025 00:00:00 +0800

This note presents a novel set of modified Gamma and Beta k functions. The authors introduce these new functions along with their first and second summation relations, functional relations, symmetry relations, Mellin transforms, and integral representations that incorporate algebraic powers and Mittag-Leffler functions, as well as those involving trigonometric terms, powers, and Mittag-Leffler functions. In contrast to other studies that generalize Gamma and Beta functions, this note highlights a statistical application, demonstrating the practical utility of the proposed functions across various fields.

An Optimized Beluga Whale Approach for Migration to Reduce Power and Service Level Agreement in Real-Time System

Rukmini S, Shridevi Soma — Mon, 30 Dec 2024 00:00:00 +0800

Managing power consumption in cloud data centers has become a critical challenge. Live container migration is a technology supporting energy efficiency in this context. To address the hurdles of power consumption management, thereby mitigating carbon emissions and minimizing service level agreement (SLA) violations, we propose an approach utilizing a real-time server with the Beluga Whale Optimization Algorithm (BWOA) for container migration. The proposed approach aims to optimize energy consumption while ensuring SLA compliance. The BWOA, a machine learning-based method, is employed to predict the resource requirements of containers and migrate them to hosts with sufficient resources. We implemented the proposed approach in a real-time cloud server and compared its performance with other algorithms in terms of response time. The results demonstrate a remarkable 30% improvement in response time, leading to reduced SLA violations and optimized power consumption in containerized data centers.

Particle Swarm Optimization of a Single Server Retrial Queue with Delayed Repair Under Working Vacation From Optional Service to ReService

Kalaiselvi J, Saravanarajan MC — Mon, 20 Jan 2025 00:00:00 +0800

Queueing systems (QS) play a critical role in modeling and optimizing various real-world processes by managing the flow of entities within systems involving queues. To address this, the proposed QS integrates features such as single arrivals, a retrial mechanism, optional re-service, working vacations, and delay repair scenarios. The system’s dynamics are comprehensively analyzed using the supplementary variable technique, which provides deeper insights into its behavior and performance metrics. Furthermore, to enhance operational efficiency, an advanced cost optimization technique is employed to identify the optimal cost structure for the system. This holistic approach not only sheds light on the operational intricacies of the QS but also offers practical strategies for cost reduction and validation of analytical findings, thereby advancing queueing theory and broadening its practical applications across multiple domains.

Computational Behavior of Trihybrid Casson Nanofluid Blood Flow Occurring Inside the Conical Gap Between the Rotating Disk and the Cone

Thu, 26 Dec 2024 00:00:00 +0800

The investigation of the flow patterns of a trihybrid nanofluid flow situated in the conical gap that is created among a revolving disc and a stationary cone computationally examined in this study. Three different types of nanoparticles, Al2O₃, TiO₂ and Ag are examined with blood as the base fluid according to flow properties and energy phenomenon. While discussing the heat transfer mechanism in trihybrid nanofluid flow crossing through the disc and cone, four different types of cases are explored likewise the disc and cone may be rotating at the same rate or at different rates, or one may be stationary about the other. The numerical scheme is planted to observe the fluid flow and heat transfer patterns. In the current article, we investigated rheological parameters, including rotating speed, cone angle, and concentration of nanoparticles, and the effect of heat transfer performance over velocity and temperature patterns. The results shed light on the complex interactions between the geometric and nanofluid characteristics, providing useful information for fluid dynamics and thermal management applications. This fluid model is also useful for the study of blood pressure, arthritis, brain therapy, and malignant tumors. The graphs are plotted using the MATLAB program BVP4C to ensure convergence. Several variables, such as a magnetic parameter, Prandtl's number, and Reynold's number, have an impact on temperature and velocity profiles. It is evident that the amalgamation of the fraction of three nanoparticles reduces the velocity and enhances the temperature of the nanofluid. The momentum boundary layer expands when the cone and disc rotate in the same direction.

Neutrosophic Lindley Distribution: Simulation, Application, and Comparative Study

Fri, 10 Jan 2025 00:00:00 +0800

Classical statistical methods are commonly applied in distribution theory across various disciplines; however, they often fall short in addressing uncertainty, imprecision, and indeterminacy. In situations when classical distributions fail, such as when there is uncertainty, ambiguity, or missing information, the neutrosophic lindley distribution (NLiD) is important because it models indeterminate data. The classical Lindley distribution is extended by incorporating neutrosophic notions, providing flexibility for methods of ambiguous inference. Applications involving reliability analysis, risk management, and other domains with internal data uncertainties are especially well-suited for NLiD. This paper introduces the neutrosophic Lindley distribution (NLiD) to incorporate imprecision into the statistical framework. We derive key properties of the NLiD, including survival, hazard, and reverse hazard functions, as well as the odds ratio, Mills ratio, mean, and variance. Additionally, we explore entropy measures such as Neutrosophic Renyi, Neutrosophic Tsallis, and Neutrosophic Arimoto entropies, complemented by a simulation study and graphical analysis. Maximum likelihood estimation is employed to estimate the distribution parameters, with simulation validating the accuracy of these estimates. Our findings reveal that the proposed distribution can exhibit symmetric, left-skewed, and right-skewed characteristics. An empirical evaluation using a on dioxin consumption in food demonstrates that the proposed model is effective and practical for real-world application.

Stored Energy in the Exterior Schwarzschild Space-Time

M. Abdelgaber, M. F. Mourad, H. M. Fathy — Thu, 16 Jan 2025 00:00:00 +0800

In the present study, we develop a well-behaved null tetrad for the exterior Schwarzschild metric. Additionally, under certain conditions, we were able to extract the tetrad components of the Maxwell field tensors for exterior Schwarzschild. In addition, in the presence of the geometry of the Schwarzschild solution, we found a real behaved energy density stored in electromagnetic.

The Modified Log-Logistic Distribution: Properties and Inference with Real-Life Data Applications

Ahmed Z. Afify, Yassmen Y. Abdelall, Hadeel AlQadi, Hisham A. Mahran — Thu, 23 Jan 2025 00:00:00 +0800

This paper introduces a new three-parameter extension of the log-logistic distribution called the generalized Kavya-Manoharan log-logistic distribution. The proposed distribution extends the Kavya-Manoharan log-logistic model, and its density exhibits symmetric, right-skewed, reversed-J, and left-skewed shapes. Its hazard function can provide non-monotonic and monotonic shapes, which makes it particularly valuable for accurately modeling complex time-to-event data. Several distributional properties are addressed. The introduced model parameters are estimated via eight frequentist estimation approaches. Moreover, extensive simulations are obtained to explore the performance of the proposed methods of estimations. Finally, the performance of the proposed distribution is investigated using three real-lifetime datasets from medicine and reliability engineering. The analyzed data illustrated that the proposed distribution provided an adequate fit as compared to other competing log-logistic distributions.

Results on Enhanced Continuous Random Variable’s Probability Distribution Using a Different Exponential Function for the Normal Probability Distribution

C V Rao — Thu, 16 Jan 2025 00:00:00 +0800

In the history of probability and statistics, general normal probability has played an important role. I utilize a different exponential function to create a new continuous probability density function akin to the Laplace Gauss distribution function. Finding an alternate probability distribution is required so that the probability can be determined without referring to the table data. I noticed that the findings are pretty comparable to the normal probability distribution values. I checked the new results against a few standard cases. The advantage of this exponential function is that we can calculate the probability of a z value with more than two decimals, whereas with a normal distribution, we can only use z values with two decimals.

Comparative Analysis of Factorial Analysis-Multiple Regression and Random Forest for the Prediction of the Stabilization Time in Furnaces in the Heat Treatment Area in a Metalworking Company

Sun, 07 Jan 2024 00:00:00 +0800

The purpose of this study is to determine the relationship between the values and attributes of the loads in forged rings made of materials such as nickel, titanium and waspaloy in furnaces for their heat treatment and a prediction model on the preparation and temperature stabilization time of the furnaces, and to be able to carry out the loads and start their holding time according to the recipe assigned for their heat treatment. Applying the Factorial Analysis method, it is possible to identify a reduced number of significant factors that can represent the relationship of the independent variables set, as well as a Multiple Regression Analysis and Random Forest that allows establishing an estimation or prediction system for the time it takes for the furnace to operate the preheating and receive the scheduled load. 6,135 data were collected from full loads in 2020 and six months of 2021, the results had a total variance of 64.61%, a Kaiser-Meyer-Olkin index of 0.620 and a Bartlett sphericity test with a significance of 0.00. The study significantly identifies three important factors on the preparation time of furnaces obtained from the factor analysis, which are: the conditions between loads that represent 33.203% of the total variance, the temperature accuracy for the load 18.149% and the exposure of material in furnaces 13.263%. From the factors identified in the Multiple Regression and Random Forest analysis, it was obtained that the relevant variables are: the temperature difference with respect to the previous load, the weight of the load, the time of holding the load and the treatment temperature for its maintenance have a significant impact on the preparation time. The best prediction method is through the Random Forest algorithm, explaining 95.11% of the variability, its accuracy with respect to the mean square error (MSE) is 6.94 minutes, a mean absolute percentage error (MAPE) of 3.1%, while Multiple Regression manages to explain 77.5% of the variability, a MSE of 69.25 minutes and a MAPE of 9.4%. The result of this research benefits programmers to formulate load sequencing more efficiently in the heat treatment area using the Random Forest algorithm, allowing to increase the productivity and utilization of the furnaces.

Modelling and Simulation of the Effect of Irradiance Related Temperature on Microalgae Cell Growth in an Outdoor Culture for a Horizontal Loop Tubular Photobioreactor

Thu, 09 Jan 2025 00:00:00 +0800

Microalgae growth is influenced by numerous culture parameters, and temperature is considered one of the vital growth factors among them. In this study, a computational growth model related for a microalgae cell growth to irradiance related temperature for an outdoor operated Horizontal Loop Tubular Photobioreactor (HLTP) is developed. The effects of direct and diffuse solar radiation on the Photobioreactor (PBR) temperature are considered in this model. An HLTP measuring length 20.5 m and radius 0.025 m has been assumed for the simulation model. The simulation is carried out on a specific date where the sunlight is considered available. Thus, the meteorological data associated with a geographic location has been collected for the simulation while the species of microalgae is Chlorella vulgaris. The present model is simulated by COMSOL Multiphysics version 4.2 and a temperature fluctuation between 24.85 °C and 38.45 °C is observed throughout the PBR domain. The velocity profile of the suspension flow is also analysed in this study. The present study suggests that necessary measures are needed to control the temperature to reduce cell damage.

Study of Burger Equation Using q-HAM with Yang-Abdel-Cattani Derivative

Faten Aldosari, Manvendra Narayan Mishra — Thu, 16 Jan 2025 00:00:00 +0800

In order to solve the generalized Burgers equation, this research work introduces one of the most recent operators in fractional calculus. An easier-to-understand version of the problem can be obtained by using the Yang-Abdel-Cattani fractional operator. The generalized Burgers equation's result is obtained analytically effectively using the q-homotopy analysis method (q-HAM). A visual study is also acquired to demonstrate the operation of the technique. By employing this approach to solve the generalized Burgers problem, this study advances the field of nonlinear differential equations.

Ensemble Technique for Diabetic Precision Medicine Classification

Badugu Sobhanbabu, K. F. Bharati — Tue, 14 Jan 2025 00:00:00 +0800

It is precisely 100 years after giving an insulin shot to a human, which created a revolution in diabetes treatment. Since the fate of diabetes patients has changed in humankind. In this regard, the exact dosage and same set of medicine for diabetes patients may not fit. Thus, there is a requirement for Precision medicine which can change the treatment of diabetes. There is a requirement for building automated intelligent systems to recommend precision medicine that can help practitioners. This paper discusses precision medicine, which has a complete schema for deriving Precision medicine from Big data. In our proposed schema, the component Intelligent Precision Medicine Engine, a new phase is added to filter the non-diabetic patient records to be processed by the Recommender engine, which would reduce the computational energies. With this object, a multi-layered bagging technique is used to classify with the best result nearing 96% with the UCI machine learning dataset for diabetes. Three layers of classification multi-models with majority voting are designed, and results are discussed.

On the Edge Irregularity Strength of Finite Graphs

Asma Almazaydeh, Bilal N. Al-Hasanat, Remal S. Al-Gounmeein — Fri, 03 Jan 2025 00:00:00 +0800

In this paper, we state the value of edge irregularity strength for the complete graphs K_nof order n ≥ 3, wheel graphs W_nwhere n ≥ 3 and the union of disjoint graphs. Also we state a lower bound for edge irregularity strength for the complete sun graph of order 2n and size .

Mathematical Modeling of Velocity Field Induced by the Vortex

I. Kangro, H. Kalis, A. Aboltins — Mon, 30 Dec 2024 00:00:00 +0800

In new technological applications, it is important to use vortex distributions in the area for obtaining large velocity fields. Analogous to electromagnetic and fluid mechanics inductions, vortices are described by the same relationship: the Biot-Savart law. When vortex threads form a vortex track due to fluid mechanics, they induce, analogous to electrical coils on an iron core, a core flow that can be faster than the wind that generates it. In this publication, the velocity field induced in a cylinder using the axially symmetric system of vortex rings and screw vortices and the hydrodynamic flow function in the ideal incompressible fluid are calculated. Also similar problem for mathematical modelling of the heat generation in fluids with alternating current using vortexes is considered. In this paper, it was calculated the distribution of the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of finite number of vortex threads: (1) circular vortex lines in a finite cylinder, positioned on its inner, (2) spiral vortex threads, positioned on the inner surface of the finite cylinder or cone, (3) linear vortex lines in the plane channel, positioned on its boundary. An original method was used to calculate the components of the velocity vectors. Such kind of procedure allows calculating the velocity fields inside the domain depending on the arrangement, the intensity, and the radii of vortex lines. In this paper, we have developed a mathematical model for the process in the element of Hurricane Energy Transformer. This element is a central figure in the so-called RKA (ReaktionsKraftAnlage) used on the cars' roofs.

Studying the Hidden Relationships in Mixed Data Via Principal Component Analysis with Application in Traumatic Brain Injury Data

Zakiah I. Kalantan, Rafal Z. Alqarni, Hanan Baaqeel — Mon, 20 Jan 2025 00:00:00 +0800

The analysis of complex biomedical datasets often involves a mix of numerical and categorical variables, posing challenges for traditional statistical techniques. To address this limitation, this study proposes the using of Principal Component Analysis for Mixed Data (PCAmix). PCAmix is a powerful technique that can effectively reduce the dimensionality of complex datasets while preserving the most important information. By combining the strengths of Principal Component Analysis (PCA) and Multiple Correspondence Analysis (MCA), PCAmix can handle both numerical and categorical variables simultaneously. This flexibility allows for a more comprehensive analysis of complex datasets, particularly in biomedical research. In this study, we applied PCAmix to a real-world biomedical dataset to investigate the intricate relationship between brain injury, functional outcomes, and genetic factors. The results we obtained illustrate not only the efficacy of PCAmix but also its practical uses in recognizing underlying frameworks, streamlining analysis by minimizing the number of variables while retaining essential information, creating predictive models to anticipate patient results, including functional recovery and cognitive deficits, and categorizing patients according to shared traits to facilitate tailored treatment approaches. Through the applying PCAmix, we gained a deeper understanding of the complex interplay between these factors and identified potential biomarkers for predicting patient outcomes. These findings have significant implications for the development of more effective diagnostic tools, prognostic models, and therapeutic interventions for traumatic brain injury. Ultimately, researchers can contribute to advancements in healthcare and medicine by unlocking valuable insights from complex biomedical data via leveraging the potential of PCAmix.

Evaluating Stress-Strength Reliability Estimation Technique: A Study on Ranked Set Sampling for the Beta-Lomax Distribution

Mujtaba Zuhair Ali Abuhedary, Hossein Jabbari Khamnei, Ali Akbar Heydari — Thu, 09 Jan 2025 00:00:00 +0800

Reliability, a crucial aspect in engineering and project management, signifies the likelihood of a system or project enduring without malfunction over a specified duration. Typically, the random variable X embodies the lifespan of the system or project. Stress-strength reliability, on the other hand, gauges the assurance that a product or process remains unaffected by stress Y. Extensive literature explores the point estimation and testing of R(t) = P(X > t) (the survival function of the random variable), and P = P(Y < X), delving into methods to enhance reliability assessment. This paper delves into the estimation of R(t) and stress-strength reliability P through ranked set sampling (RSS), assuming independence between stress Y and strength X, both following the Beta-Lomax (BL) distribution. Through rigorous analysis, the maximum likelihood (ML) estimator for R(t) and P is derived, subsequently juxtaposed with its simple random sampling (SRS) equivalent to gauge performance. By applying this methodology to real data from Wheaton River, the study underscores the practicality and efficacy of the proposed approach. By offering a comprehensive analysis of reliability and stress-strength reliability estimation utilizing RSS and the BL distribution, this research furnishes valuable insights for practitioners and researchers in the field. The integration of innovative sampling techniques and statistical methodologies not only enhances the precision of estimations but also underscores the importance of robust reliability assessments in ensuring the longevity and efficiency of systems and projects.

Multiple Timewise Coefficient Determination Problem From Heat Moment Observations

M. J. Huntul — Tue, 21 Jan 2025 00:00:00 +0800

Consider the inverse problem of determining multiple timewise coeffcient and the solution function satisfying the parabolic equation with the direct initial and Dirichlet boundary conditions from the heat moment observations. This formulation ensures the unique solvability of the inverse problem. However, the problem still suffers from ill-posedness. Since small errors in the input data cause large errors in the output solution. The finite difference method is developed as a direct solver, whilst the inverse problem solver is reformulated as nonlinear least-squares minimization. The optimization problem was solved numerically using the lsqnonlin routine from the MATLAB toolbox. The exact and noisy input data are inverted numerically. Numerical results are presented and discussed to illustrate the performance of the inversion for timewise coefficients.

Commutative Rings and Corresponding V-Graphs

Nasr Zeyada, S. A. Bashamakh, Ohoud Almalawi — Fri, 10 Jan 2025 00:00:00 +0800

Algebraic graph theory, which applies algebraic techniques to graph problems, is a pivotal area of study. Many ring algebraic properties have representations in graph theory. In this paper, we introduce an innovative type of graph related to rings that we call the V-graph. Let T be a ring with identity. The V-graph of T, denoted by V(T), consists of a set of vertices equal to all non-zero elements of T. Two different vertices u and v are adjacent if and only if uv is a regular element in T. We present several examples to demonstrate how this form of graph differs from the known ring-based graphs, such as zero-divisor graphs, unit graphs, and quasi-regular graphs. We calculate the diameter and independent number, as well as the domination number for the V-graph of the ring of integers Zn.

Structural Stability of the Stokes Fluid System in a Channel

Yanping Wang, Yuanfei Li — Thu, 09 Jan 2025 00:00:00 +0800

This paper considers the two-dimensional Stokes system in a semi-infinite channel and is committed to deriving the structural stability of the model. Using the differential inequality technique, we obtain the expression of energy function. By making use of the earlier work, a second order differential inequality for energy function is obtained. By solving this second-order differential inequality, the continuous dependence on the coefficient of the system is established. This paper shows how to derive a priori estimates of nonlinear terms.

Thermo-Diffusion Effects on Fractional Ordered Model of Unsteady Casson Blood Flow with Magnetic Field Effect

Nilesh Patel, Harshad Patel — Sat, 06 Jan 2024 00:00:00 +0800

This paper deals with the effects of magnetic fields on unsteady Casson blood fluid flow in a stenosis artery. The effects of thermo-diffusion, thermal radiation, metabolic heat sources, and heat absorption are also considered. The flow is confined by the oscillating pressure gradient. The governing equations are remodeled into a system of PDEs in cylindrical form, which is then converted to dimensionless form using the similarity transformation. A definition of the Caputo-Fabrizio fractional order derivative is applied to the governing dimensionless form. The Laplace transform and the finite Hankel transform are used to obtain the analytic results. From the graphical results, it is illustrated that the external magnet reduced the rate of blood flow. It is also deduced that radiation tends to improve the rate of heat transfer, whereas the thermo-diffusion parameter tends to reduce the mass transfer process.

Entrepreneurial Strategies in Livestock Inventory Management with Trade Credit

Jayashri P, Umamaheswari S — Thu, 09 Jan 2025 00:00:00 +0800

Amelioration and deterioration rates play a vital role in inventory management. Some animals lose value due to illness, death, or other incidents as they gain weight when kept on farms in good health. Organizations and entrepreneurs can maximize the operational efficiency and health of their animals through a well-organized and efficient inventory system. The proposed inventory model provides a more realistic assumption of livestock with a Weibull amelioration rate and constant deterioration rate. In the inventory domain, trade credit plays a vital role in minimizing costs, in maintaining an adequate livestock supply, and in maximizing the credit period. The main objective of this article is not only to improve financial performance but also to enable livestock operations to satisfy market demands, to manage resources, and to successfully navigate the complex world of credit-based transactions. This inventory system is mathematically modelled by differential equations, and the total cost is determined. The optimality of the solved nonlinear minimization problem is verified by using pseudo concavity. Partial Swam Optimization (PSO) and Genetic Algorithm (GA) are designed to determine the optimal cycle length, the optimal credit period and the order quantity. Numerical examples are presented to illustrate the solution procedure for various cases of the proposed inventory model. Sensitivity analysis serves as a validation tool, providing a discerning assessment of the strength and flexibility of the model in response to variations in key parameters.

Exploring the Hidden Symmetry of Quaternions: Dual Balancing and Cobalancing Numbers and Their Corresponding Quaternions

Süleyman Aydınyüz — Wed, 03 Jan 2024 00:00:00 +0800

This paper unveils the hidden symmetry of quaternions through the introduction of Dual Balancing and Dual Cobalancing numbers, along with their corresponding quaternions. We provide Binet's formulas, generating functions, and a multitude of intriguing properties to foster a comprehensive understanding of these concepts. Furthermore, we present matrix representations to offer a fresh perspective on the Dual Balancing and Dual Cobalancing quaternions. The implications of this study go beyond theoretical applications and may have practical implications in diverse fields.

Spatio-Temporal Analysis and Prediction by Logistic Regression of Respiratory Diseases in India

Priyanka Subramani, Kalpanapriya Dhakshnamoorthy — Thu, 09 Jan 2025 00:00:00 +0800

Respiratory illnesses rank among the top causes of death and disability in India, influenced by factors such as limited healthcare access, air pollution, smoking, allergens, and a lack of awareness. Despite government efforts to improve respiratory health policies, increase awareness, enhance healthcare facilities, and promote preventive measures, the incidence of respiratory diseases has been on the rise in recent years. This study uses Geographic Information System (GIS) technology to analyze the spatial and temporal distribution patterns of respiratory diseases, aiming to improve our understanding of the contributing factors. Principal component extraction and spatial statistical analyses were utilized to identify the main respiratory illnesses and their geographical distribution. The study concentrated on three major respiratory diseases Tuberculosis, Pneumonia, and Acute Respiratory Distress Syndrome (ARDS) which are related to each other diseases. The findings shows significant variations in the geographical distribution of these diseases across the time period 2019-2021. This spatio-temporal data is essential for enhancing current prevention, control, and treatment strategies for respiratory illnesses in the study area. The methodology applied in this study can be adapted to other regions with similar geographical characteristics and patient data. The study investigated the association of 14 variables with respiratory illnesses. The results indicate that certain variables are associated with an increased risk of frequent flare-ups and hospital admissions due to respiratory diseases. Furthermore, the severity of flare-ups leading to hospital admissions is significantly linked to the presence of comorbidities. These critical and easily measurable variables provide valuable insights for the optimal management of ambulatory patients with respiratory diseases.

Application of Laplace Transform Method to Solve Neutral-Type Delay Differential Equation

Tue, 31 Dec 2024 00:00:00 +0800

This study investigates the use of the Laplace transform method to resolve a particular class of second-order linear initial-value neutral delay differential equations, which are prevalent in fields such as physics and engineering. By employing this analytical approach, we derive exact solutions that facilitate a deeper awareness of the dynamics of the system and its stability characteristics. A thorough illustrative example is provided to illustrate the Laplace transform method's efficacy, showcasing its practical utility in addressing real-world problems. This study not only highlights the advantages of the Laplace transform in providing clear insights into complex delay systems but also emphasizes its relevance in both theoretical and applied contexts.

Generalization and Properties of κ-Intuitionistic Fuzzy Metric Spaces with Applications to Fixed-Point Theorems

Vinoth R, Jayalakshmi M — Thu, 23 Jan 2025 00:00:00 +0800

This study introduces κ-intuitionistic fuzzy metric spaces, significantly broadening the scope of intuitionistic fuzzy metric spaces. This framework offers greater flexibility and applicability by incorporating multiple parameters (κ) into an intuitionistic fuzzy set. The study explores the properties of κ-intuitionistic fuzzy metric spaces, demonstrating that their topology is first-countable and that the corresponding metric space is Hausdorff. We establish a fixed-point theorem that generalizes and extends existing results for intuitionistic fuzzy metric spaces.

Strong Sandwich Results Involving the Riemann-Liouville Fractional Integral of an Extended q-Hypergeometric Function

Alina Alb Lupaş — Tue, 31 Dec 2024 00:00:00 +0800

The classical theories of differential superordination and subordination have been extended to strong differential superordination and respectively, strong differential subordination. The two new theories have progressed well, revealing significant findings when various operators and specific hypergeometric functions have been included in the studies. The research revealed by this work expands the topic of the investigation by incorporating aspects of fractional calculus and quantum calculus. An extended version of q-hypergeometric function is introduced to correspond to the study of functions from the classes that were previously described and that are particularly defined for strong differential superordination and subordination theories. This work defines the Riemann-Liouville fractional integral applied to the extended q-hypergeometric function, used to get strong differential subordinations and superordination results. The theorems established for the strong differential superordination and subordination, establish the best subordinants and respectively the best dominants. Interesting corollaries are exposed for certain functions regarded as best subordinant or best dominant due to their particular geometric characteristics. Sandwich-type theorems and consequences conclude the study, stated to connect the outcomes obtained by applying the dual theories.

Multifractal Analysis on Ozone Depletion and Climate Change: The Time Series Approaches

M. Meenakshi, A. Gowrisankar — Mon, 13 Jan 2025 00:00:00 +0800

The ozone layer has acted as the planet’s natural sunscreen, protecting people, plants, and animals from harmful ultraviolet rays. The Antarctic ozone hole was first announced in a paper by the British Antarctic Survey’s Joe Farman, Brian Gardiner, and Jonathan Shanklin in 1985. Many investigations are still conducting to determine the connection between ozone depletion and climate change. This research study investigates the impact of the ozone layer’s depletion at the Antarctic pole on global climate change data such as temperature and precipitation, after the year 1985 through a fractal dimension, Multifractal Detrended Fluctuation Analysis (MFDFA), and standard correlation coefficient. For this, the research work has analyzed 45 years of climate change variables such as global monthly temperature anomaly, global monthly precipitation anomaly, and Southern Hemisphere minimum ozone time series data from 1979 to 2023. The fractal dimension of the time series is obtained by rescaled range analysis, which is used to identify the fractality of the time series and long-range correlations and persistence. To study the multifractality of these fractal time series, MFDFA procedure has been applied. By applying MFDFA to these time series data, this research has identified significant multifractal characteristics, indicating complex dynamics and long-range correlations, and identified potential nonlinear patterns. This research provides valuable insights into the complex dynamics of time series data, as revealed by the calculated exponent values and MFDFA spectrum. The strong correlation observed between the exponent values of temperature anomalies, and precipitation anomalies, with ozone depletion time series provides compelling evidence for the significant impact of ozone depletion on climate change. These results highlight the potential of multifractality for understanding the intricate mechanisms underlying climate change.

Information Geometry for Decoding

A. Addadi, K. Abdelmoumen, H. Ben-Azza, I. Chana — Wed, 15 Jan 2025 00:00:00 +0800

We revisit the idea of using elements of information geometry for decoding low-density parity-check (LDPC) codes, as introduced by Ikeda et al. In this work, we explicitly compute the m-projection to an e-flat submanifold, in the case of a binary symmetric channel and the Gaussian channel. We exemplify the algorithm by testing moderate size Gallager codes. To approach decoding problems, we show general theorems based on alternating projections in the framework of information geometry, inspired by von Neumann’s theorem for the convergence of alternating projections in Hilbert spaces. More precisely, consider the manifold S of the probability distributions on the n-dimensional hypercube (i.e., the set of binary sequences of length n). Let p be in S. In the case of two intersecting m-flat or e-flat submanifolds, the method of alternating projections on the two submanifolds converges to the projection of p on their intersection. This result is also generalized to a finite family of submanifolds of S.

Ovals of Constant Width in Polar Coordinates

Adel Al-rabtah — Thu, 09 Jan 2025 00:00:00 +0800

We explore ovals of constant width in polar coordinates in this paper. Conversion of a parametric function defined on a rectangular domain of angles, to a polar representation defined on a domain of polar angles is introduced, and the relationship between the rectangular angles and the polar angles is discussed. The length of the parametric curve in polar coordinates between opposite points and from one vertex point to the next can be determined using the oval’s vertices. A new verification of Barbier's theorem in polar coordinates is presented. We show that the extreme values of the radial coordinate of the discussed polar oval are obtained at both its vertices and opposite points. Ovals and specific circles with the origin at the center are compared, and we demonstrate that every given oval is analytically and geometrically enclosed between those two specific circles. Intersection points between a polar oval and any circle related to it, centered at the origin, are formulated. Simulation and numerical examples are presented to support the analytical and theoretical results.

Interconnection Between Schur Stability and Structured Singular Values

M. Rehman, J. Alzabut, M. Tayyab, F. Amir — Mon, 30 Dec 2024 00:00:00 +0800

In this paper, we present new results on the interconnections between Schur stability and structured singular values of real-valued matrices, denoted as R^n×n. Most new findings are obtained for n = 2 and n = 3. These novel insights into the relationship between Schur stability and structured singular values are developed by applying various tools from linear algebra, system theory, and matrix analysis. Schur stability ensures that all eigenvalues lie within the unit circle in the complex plane, which is fundamental for the boundedness and stability of system responses. Structured singular values, on the other hand, provide a measure of robustness, stability, and performance against structured perturbations in system parameters, offering valuable insights into the stability margins and performance limits under such uncertainties.

Risk Assessment for Start-Up Business in SMEs: Qualitative and Mathematical Approach

Wed, 03 Jan 2024 00:00:00 +0800

Due to its crucial role in economic growth and job creation, there has been a notable increase in start-up businesses, particularly small and medium enterprises (SMEs). Many start-up entrepreneurs, however, struggle to sustain their businesses beyond the first five years, and some ultimately fail. This can be attributed to their various risks and challenges during their entrepreneurial journey. Consequently, risk management emerges as a valuable tool for entrepreneurs to identify and effectively address these risks. Hence, this research paper aims to devise a new mathematical formulation for the risk management index of start-up businesses in SMEs, employing qualitative and quantitative approaches. Interviews were conducted with experts to identify the risk factors specific to start-up businesses, and the data collected was subsequently analyzed using the Atlas ti software. Furthermore, a mathematical formulation for the risk management index was developed using a fundamental composite index formulation. The findings reveal the presence of five distinct risk factors in start-up businesses within SMEs. A mathematical formulation and a key indicator index were also established for assessing start-up business readiness in SMEs. These formulations and key indicator indexes are pivotal in enabling entrepreneurs to gauge their readiness for a new business venture. The findings contribute to alternative risk management tools for SMEs, especially for small businesses that are just getting started.

On Qualitative Behaviour of Solutions of Third Order Matrix Delay Differential Equations

Adetunji. A. Adeyanju, Cemil Tunç, Babatunde. S. Ogundare — Tue, 31 Dec 2024 00:00:00 +0800

We analyze, using the Lyapunov-Krasovskii method, the conditions for the stability, boundedness and periodicity of solutions to a class of nonlinear matrix differential equation of third order with variable delay. Criteria under which the solutions to the equation considered possess solutions that are stable and bounded on the real line as well as existence of at least one periodic solution are given. Our results generalize and extend many existing results in the literature on scalar, vector and matrix differential equations with or without delay. The integrity of our results is demonstrated by two numerical examples included.

Collocation Technique Based on Chebyshev Polynomial to Solve Lane-Emden-Fowler Boundary Value Problem

Shabanam Kumari, Arvind Kumar Singh, Utsav Gupta — Wed, 03 Jan 2024 00:00:00 +0800

We present an innovative technique to find numerical solutions of the Lane-Emden-Fowler singular-type BVPs which plays a crucial role in comprehending a wide range of physical phenomena. The core concept of this technique is based on transforming the differential equation into the Fredholm integral equation, then it is converted into system of linear or nonlinear algebraic equations by utilizing the collocation technique based on Chebyshev polynomials. Subsequently, we employ an iterative numerical method, such as the Newton’s method, for solving the system to get the approximate solution. Error analysis is included which helps to assess the accuracy of the obtained solutions and provides insights into the reliability of the numerical results. Furthermore, we have also considered various examples to demonstrate the applicability of the collocation technique based on Chebyshev polynomials and compared with the existing results.

Some Common Fixed-Point Theorem on Complex-Valued Metric Spaces and Its Application to Solve Urysohn Integral Equations

P. Vishnukumar, A. Anbarasan, T. Sathiyaraj, Mohammad Sajid — Wed, 22 Jan 2025 00:00:00 +0800

In this paper, a new and generalized contraction principles are proved on complex-valued metric space. By adopting a suitable hypothesis on sequence converging in complex-valued metric space new contractions are established for proving the common fixed-point theorem. Moreover, a rational contractive condition is improved in the complex-valued metric spaces. The obtained results through theoretical study are verified by solving the solution of the nonlinear system of Urysohn integral equations.

Solvability of a Doubly Singular Boundary Value Problem Arising in Front Propagation for Reaction-Diffusion Equations

Cristina Marcelli — Tue, 31 Dec 2024 00:00:00 +0800

The paper deals with the solvability of the following doubly singular boundary value problem

naturally arising in the study of the existence and properties of travelling waves for reaction-diffusion-convection equations

governed by the p-Laplacian operator. Here c, α are real parameters, with α > 0, and f, g, h are continuous functions in [0, 1], with

h(0) = h(1), h(u) > 0 in (0, 1).

On PGK₂-algebras and Perfect Extensions

Mohiedeen Ahmed, Abd El-Mohsen Badawy, Essam El-Seidy, Ahmed Gaber — Mon, 13 Jan 2025 00:00:00 +0800

Exploring the New Exponentiated Inverse Weibull Distribution: Properties, Estimation, and Analysis via Classical and Bayesian Approaches

Pankaj Kumar, Laxmi Prasad Sapkota, Vijay Kimar, Nirajan Bam — Wed, 22 Jan 2025 00:00:00 +0800

The “New Exponentiated Inverse Weibull” (NEIW) distribution is a novel probability distribution with versatile applications in reliability engineering, survival analysis, and related fields. This study explores the properties of the NEIW distribution, including moments, hazard function behavior, and reliability measures, through rigorous theoretical analysis and simulation studies. Additionally, maximum likelihood estimators (MLEs) for NEIW parameters are investigated via simulation studies to evaluate their performance under various scenarios. Empirical analysis using real-world data sets demonstrates the applicability of the NEIW model in capturing the underlying data structure and extracting meaningful insights. Parameter estimation and analysis are conducted using classical and Bayesian approaches, showcasing the robustness and flexibility of the NEIW distribution. The latest Bayesian analysis software STAN is used to perform the Bayesian analysis using Hamiltonian Monte Carlo (HMC) under No-U-Turn Sampler (NUTS). Overall, this research contributes to the advancement of statistical modeling and analysis by providing a comprehensive framework for utilizing the NEIW distribution in practice, with implications for diverse fields and potential for further exploration and innovation.

Families of Gracefuls Spiders with ℓ(2k + 1) − k, ℓ(2k + 1) − k + 1 and ℓ(2k + 1) + k + 1 Legs

N. B. Huamaní, M. Atoche Bravo, F. Poma — Tue, 21 Jan 2025 00:00:00 +0800

We say that a tree is a spider if has at most one vertex of degree greater than two. We obtain existence of families of gracefuls spiders with ℓ(2k +1)−k, ℓ(2k +1)−k +1 and ℓ(2k +1)+k +1 legs. We provide specific labels for each spider graph, these labels are constructed from graceful path graphs that have a particular label, so there is acorrespondence between some paths and graceful spiders that we are studying, this correspondence is described in an algorithm outlined in the preliminaries.

Optimum Flows in Directed Planar Dynamic Networks. The Dynamic Approch

Camelia Schiopu, Eleonor Ciurea — Wed, 03 Jan 2024 00:00:00 +0800

Optimum flows in directed planar dynamic networks are essential for several reasons, impacting a variety of fields. These networks present unique challenges that require advanced optimization techniques to ensure efficient and reliable performance. In this paper we consider a time-varying directed planar network without parallel arcs and loops, where a flow must take a certain time to traverse an arc. The problem is to find an optimal (minimal or maximal) solution to send the optimum (minimum or maximum) flow from the source node to the sink node, within a given time T.

Indecomposable Modules, Relative Projectivity and Radical Subgroups in Finite Groups

Zwelethemba Mpono — Thu, 09 Jan 2025 00:00:00 +0800

In the various blocks of a finite group G, irreducible characters sit with the indecomposable modules which afford them and such indecomposable modules in those blocks have got vertices and sources and in fact, every p-subgroup of G is a vertex of some indecomposable FG-module. For any finite group G and a field F of characteristic p, where p is a prime that divides the order |G| of G, every indecomposable FG-module possesses a vertex and a source. Furthermore for a finite group G, kernels of the irreducible FG-modules, vertices of the irreducible FG-modules and defect groups of blocks of G all contain Op(G). Furthermore, the kernels of blocks of G are normal p′-subgroups of G which are contained in Op′(G), where Op′(G) is the kernel of the principal block of G. The kernels of blocks of G are related to the kernels of the indecomposable FG-modules in those blocks. The object in this paper is to study characteristics and/or properties of vertices of indecomposable FG-modules in relation to irreducible ordinary characters that they afford and sit with in blocks of G and furthermore study characteristics and/or properties that exist between kernels of irreducible FG-modules, vertices of irreducible FG-modules and defect groups of blocks of G and even establish as to when and how any and/or all of these would (if at all possible) coincide.