Asian Journal of Mathematical Sciences(AJMS)
Mathematics in the Asian region has grown tremendously in recent years. There is a need to have a journal to unite such a development. The Asian Journal of Mathematical Sciences (AJMS) is a new journal that aims to stimulate mathematical research in the Asian region. It publishes original research papers and survey articles on all areas of pure mathematics and theoretical applied mathematics. High standards will be applied in evaluating submitted manuscripts, and the entire editorial board must approve the acceptance of any paper. Asian Journal of Mathematical Sciences (AJMS) is an international Referred and Peer Reviewed Online Journal with E-ISSN: 2581-3463 published by B.R. Nahata Smriti Sansthan for the enhancement of Pure and Applied Mathematics, Mathematical Physics, Theoretical Mechanics, Probability and Mathematical Statistics, and Theoretical Biology. AJMS is an Open Access Online Journal that publishes full-length papers, reviews and short communications exploring and to promote diverse and integrated areas as Applied Mathematics and Modeling, Analysis and Its Applications, Applied Algebra and Its Applications, Geometry and Its Applications, Algebraic Statistics and Its Applications, Algebraic Topology and Its Applications. SUBJECT CATEGORY Papers reporting original research and innovative applications from all parts of the world are welcome. Subject areas suitable for publication include, but are not limited to the following fields: Applied Mathematics and Modeling: Computational Methods, Ordinary and partial Differential Equations, Mathematical Modeling and Optimization, Probability and Statistics Applications, Operations research, Model selection, Bio Mathematics, Data Analysis and related topics. Mathematical Finance, Numerical Solution of Stochastic Differential Equations, Stochastic Analysis and Modeling. Analysis and Its Applications: Approximation Theory and Its Applications, Ergodic Theory, Sequence Spaces and Summability, Fixed Point Theory, Functional Analysis and Its Applications and related topics. Applied Algebra and Its Applications: Information Theory and Error Correcting Codes, Cryptography, Combinatorics and Its Applications, Cellular Automata, Fuzzy and Its Applications, Computational Algebra, Computational Group Theory and related topics Geometry and Its Applications: Algebraic Geometry and Its Applications, Differential Geometry, Kinematics and related topics Algebraic Statistics and Its Applications: Algebraic statistics and its applications Algebraic Topology and Its Applications: Algebraic Topology and Its Applications, Knot Theory and related topics Pure and Applied Mathematics and its Applications: Biology, Chemistry, Physics, Zoology, Health Science, Earth Science, Geology, Social Sciences, Industrial research, Computer Science, Agriculture and Forestry, Environmental Sciences, Statistics, Engineering, Natural Sciences, Political Sciences. JOURNAL PARTICULARS Title Asian Journal of Mathematical Sciences Frequency Quarterly E- ISSN 2581-3463 P-ISSN - DOI https://doi.org/10.22377/ajms.v1i1 Publisher Mr. Rahul Nahata, B.R. Nahata College of Pharmacy, Mhow-Neemuch Road, Mandsaur-458001, Madhya Pradesh Chief Editor Dr. M.A. Naidu Starting Year 2017 Subject Mathematics subjects Language English Language Publication Format Online Email Id editorajms@brnsspublicationhub.org,editor@brnsspublicationhub.org Mobile No. +91-7049737901 Website www.ajms.in Address B.R. Nahata Smriti Sansthan, BRNSS PUBLICATION HUB, B.R. Nahata College of Pharmacy, Mhow-Neemuch Road, Mandsaur-458001, Madhya Pradesh
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A Finite-Element Analogy For Distributed Computing Resilience: Predictive, Non-Invasive Resiliency Engineering Beyond Chaos Testing
Distributed computing resilience is often evaluated by reactive, empirical approaches such as chaos engineering, which—while valuable—require injecting failures and cannot fully anticipate emergent fragility. This paper develops a predictive, non-invasive framework by adapting finite-element analysis (FEA) principles to distributed systems. We model nodes as elements with capacities, communication as stiffness couplings, workloads as load vectors, and performance degradation as displacements. Fragility is measured using a von-Mises style stress formulation. This revised manuscript incorporates reviewer feedback by: adding a clear problem statement, introducing a concise state-of-the-art section, providing narrative bridges be- fore equations, presenting telemetry- based parameter estimation, expanding proofs into for- mal theorems, and including a fully worked 4-node toy example with numerical results and TikZ/PGFPlots figures. The approach yields resilience scores, fragility indicators, and closed-form critical-load thresholds, validated with illustrative calculations
Copyright (c) 2026 ANAND SUNDER https://creativecommons.org/licenses/by-nc/4.0
Resource-Constrained Multi-objective Optimization Model for Global Warming Resilient Emergency Response and Welfare Networks
This study introduces an uncertain multi-objective, multi-commodity, multi-period, and multi-vehicle mixed-integer programming model with social equity designed for the critical response phase of humanitarian operations. The framework strategically addresses the complexities of disaster relief by integrating five key echelons: affected regions, distribution centers, hospitals, temporary accommodation facilities, and temporary care centers. The model is driven by four primary objectives: the minimization of overall costs associated with facility location, resource allocation, social equity and crucially, the reduction of relief supply shortages. Uncertainty inherent in disaster scenarios is robustly managed through a probabilistic scenario-based approach. Significant strategic decisions facilitated by the model encompass the optimal siting of temporary care and accommodation centers, the efficient allocation of affected populations to designated centers and hospitals, and the effective distribution of supplies from major hubs to temporary shelters. Furthermore, the model determines optimal flows for injured individuals and commodities between facilities, specifies the required number of vehicles for inter-facility transport, and manages both shortage and inventory levels at all centers. A comprehensive set of constraints ensures practical applicability, covering aspects such as demand fulfillment, relief commodity flow, facility capacities, transportation logistics for both people and goods, and the utilization of backup centers across multiple planning periods. The developed model’s efficacy was demonstrated through its application to a real-world case study: the city of Warri and its environs in Nigeria, a region significantly impacted by floods exacerbated by global warming. To solve this complex problem, three distinct methods were employed: the epsilon- constraint method, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), and a modified multi- objective particle swarm optimization (MMOPSO). Perfor- mance analysis, utilizing various multi- objective evaluation metrics, confirmed the superior performance of MMOPSO. A significant innovation of this model is its inherent integration of social equity principles, ensuring that the allocation of resources and services prioritizes the most vulnerable populations within the affected area. A preferred solution, selected from the MMOPSO-generated non-dominated set based on these equity considerations and expert judgment, was thoroughly analyzed to exemplify the model’s practical implications for resilient and equitable disaster response.
Copyright (c) 2025 OMINIGBO O. J https://creativecommons.org/licenses/by-nc/4.0
Spectral Signatures of Distributed Software Systems: Eigenvalue Profiling for Enterprise-Scale Proactive Resilience Engineering
This paper develops a rigorous spectral framework for profiling distributed software systems at enterprise scale. We represent a distributed system as a discretized assemblage of computational elements and construct complexity- aware stiffness and mass matrices. By performing spectral decomposition of the resulting generalized eigenproblem, we extract spectral signatures — normalized sets of eigenvalues and derived statistics — which uniquely characterize system resilience, bottlenecks, and failure propagation dynamics. We define a Spectral Resilience Index (SRI) and vertical-grade functions for different enterprise domains (finance, healthcare, retail, telco). To improve robustness and adaptivity, we overlay a Hidden Markov Model (HMM) that maps observed telemetry to latent resilience states and refines deterministic spectral predictions. We validate the methodology using public datasets (DORA metrics, Death Star Bench traces, and Google SRE reports), present synthetic and trace-driven examples, and show how spectral fingerprints can be used for early-warning, prediction, and proactive resilience engineering — reducing the need for ad-hoc chaos engineering
Copyright (c) 2025 Anand Sunder https://creativecommons.org/licenses/by-nc/4.0
Detecting Fraud Transactions in Financial Institutions
Detecting fraud and anomalies in financial transactions is crucial in safeguarding institutional assets, maintaining regulatory compliance and ensuring customers trust in financial system. This study investigated methods of detecting frauds or anomalies in transactions within financial institutions, a vital task to prevent financial losses, reduce investigative costs, and comply with regulatory standards. We compared the efficiency of three statistical models: Logistic Regression, Linear Discriminant analysis (LDA).and Quadratic Discriminant (QDA), in identifying fraudulent activity. Secondary data of over 280,000 financial transactions from an online website (Kaggle) was used to evaluate each model based on accuracy, precision, and error rates, for both fraudulent and non-fraudulent classifications. The results indicated that Logistic Regression outperformed LDA, and QDA, achieving the highest accuracy and lowest error rate, making it the most effective model among the models considered in the study for fraud detection in this context.
Copyright (c) 2025 Awogbemi Clement Adeyeye https://creativecommons.org/licenses/by-nc/4.0
Fermat's Last Theorem (or Fermat's last theorem) is one of the most popular theorems in mathematics. Formulated in French mathematician Pierre Fermat in 1637. Despite the simplicity of the formulation, literally, at the “school” arithmetic level, proof of the theorem sought by many mathematicians for more than three hundred years. And only in 1994 year the theorem was proven by the English mathematician Andrew Wilson with colleagues; The proof was published in 1995. [1]-[5] With this article, the author completes his research on the given topic, makes corrections and eliminates the errors of the previous ones.
Copyright (c) 2025 Khusid Mykhaylo https://creativecommons.org/licenses/by-nc/4.0
In the article, the author shows the transition from the ternary Goldbach problem to the binary and then to the solution of the problem of the infinity of twins. This article is the final one, in which the errors and shortcomings of his previous articles on this topic are corrected.
Copyright (c) 2025 Mykhaylo Khusid https://creativecommons.org/licenses/by-nc/4.0
On Computational Review of the Block Schaeffer’s Iteration Formula for Strongly Pseudocontractive Maps of the System of Linear Equations
This work reviews the background concepts of the Block Schaeffer’s fixed point iteration for- mula, states and proves its associated theorems before applying the method in the solution of a given system of linear equation, the aim of which is to computationally confirm that the traditional Block Schaeffer’s iteration formula is strongly Pseudo-contractive on convergence. Again this research seeks to computationally reaffirm that the choice of any initial guess closer to the solution for an iteration formula converges faster to the solution. The obviousness of this is reflected in the main result highlighted in our computation which showed that a slight ad- justment in the initial guess becoming x¯∗ = x¯0 ± x¯0 10−1 ; x¯0 ̸ = ¯0 produces faster convergence automatically, no matter how close x¯0 is to the solution, x∗.
Copyright (c) 2025 Eziokwu https://creativecommons.org/licenses/by-nc/4.0
A New Proof of the Pythagorean Theorem Using a Rhombus
This short note presents a new proof of the Pythagorean Theorem using the concept of a rhombus. MSC Code: 97-01, 97G10 , 97G40.
Copyright (c) 2025 Firdous Ahmad Khan https://creativecommons.org/licenses/by-nc/4.0
Numerical Range Distortion Under Unitary Equivalence
This paper investigates the preservation properties of numerical ranges under unitary equivalencen transformations in operator theory. We establish that if operators T and S are unitarily equivalent via S = U ∗ TU , then their numerical ranges are identical: W (S) = W (T ). Beyond this fundamental equality, we prove that unitary equivalence preserves critical geometric properties of numerical ranges, including extreme points, exposed points, supporting lines, contact points, and the geometric multiplicity of boundary points. For normal operators, we demonstrate that numerical range equality characterizes unitary equivalence, providing a geometric criterion for this algebraic relation. Additionally, we show that the curvature of the boundary of numerical ranges remains invariant under unitary transformations. These results highlight the deep connection between the algebraic structure of operators and the geometric properties of their numerical ranges, contributing to our understanding of operator behavior under unitary equivalence.
Copyright (c) 2025 Faith Mwangi Muthoni https://creativecommons.org/licenses/by-nc/4.0
COMPARATIVE STUDY OF TUMOR STAGE PREDICTION IN BREAST CANCER THROUGH FACTOR ANALYSIS AND MULTINOMIAL LOGISTIC REGRESSION
Breast cancer remains one of the leading causes of cancer-related morbidity and mortality among women globally. Early-stage detection of tumor of breast cancer assists in providing preventive measures against its spread to other parts of the body. In this study, factor analysis was employed in reducing the number of genes to fewer principal components. The Scree and Eigenvalue methods of selecting the number of principal components were employed for comparison purpose. Multinomial logistic regression model was employed to fit the stage of tumor of the breast cancer on the scores of the principal component variables along with the patient’s age and tumor size. The findings of the study showed that the eigenvalue approach outperformed the Scree approach ranging from the percentage of variance explained to the accuracy level. Hence, the eigenvalue method of selecting number of components to include in factor analysis is recommended.
Copyright (c) 2025 AWOGBEMI CLEMENT ADEYEYE1 https://creativecommons.org/licenses/by-nc/4.0
ON THE USE OF BAYESIAN PROBABILITY NETWORKS WITH A REVIEW OF MALARIA CASE
In spite of the versatile and general acceptability of estimation of disease cases from the various available methods in literature, incorporating model uncertainty remains an open issue. In this article, we derived a probability based graphical model using expert opinions in related studies on malaria and its hypothesized predictors with a Bayesian belief network (BBN). This approach is well applied in ecological studies and other environmental sciences in recent times for various estimations and predictions based on Bayesian reasoning. We gave a brief description of a BBN framework, its pros and cons, examine the principle of conditional independence. Also, we explore Markov Chain principles as it relates to a BBN formulation and useful guidelines for developing the preliminary structure of the network. We finally derived the topology of a BBN as a directed acyclic graph with malaria predictors as network nodes. We also illustrated the use of the network with an illustrative example.
Copyright (c) 2025 Emmanuel Segun Oguntade https://creativecommons.org/licenses/by-nc/4.0
BANACH'S FIXED POINT THEOREM ON THE EXISTENCE AND UNIQUENESS OF VOLTERRA INTEGRAL EQUATION SOLUTION
An integral equation is an inversion of a differential equation. Therefore, an integral equation can be seen as the solution of a differential equation with a given condition at an interval. So that through this integral equation, it can be ensured that the existence of a solution to the differential equation can be ascertained. In this article, it is shown in a functional analysis how Banach's fixed-point theorem can show the existence and uniqueness of the solution of integral equations, so that it can guarantee the existence of the solution of a differential equation.
Copyright (c) 2025 GANI GUNAWAN https://creativecommons.org/licenses/by-nc/4.0
BRAND IMAGE ANALYSIS OF ANDROID SMARTPHONES IN NIGERIA USING FACTOR ANALYSIS AND MULTINOMIAL REGRESSION TECHNIQUES
Brand image encompasses consumers’ perceptions and associations with a brand that is pivotal in shaping how individuals recognize and connect with products or services. This study explored the brand image of Android Smartphones in Nigeria, emphasizing the role of brand perception in shaping customer loyalty and purchasing decisions within a competitive market. A quantitative method is employed through online data collection from a sample of 100 users of Android Smartphones in Nigeria by considering a series of questions related to brand attributes. By analyzing user responses using factor analysis technique, the attributes such as product quality, competitiveness, loyalty, innovation, design and customer service support were identified as key dimensions of brand image. Multinomial regression further revealed that brand perception demographic variables significantly influences consumer choices, with Samsung being viewed as highly competitive and preferred by older age groups, while Infinix showed varied loyalty among younger users. Techno, a leading brand, generally had a neutral perception across demographic groups. These findings provide insights for Android brands to tailor their strategies, foster positive customer perceptions, and strengthen market positioning in emerging economies.
Copyright (c) 2025 C.A. Awogbemi https://creativecommons.org/licenses/by-nc/4.0
ON THE ANALYSIS OF SOME THEORETIC GRAPH PROPERTIES OF THE INTERSECTION GRAPH OF Zn
Abstract. This study investigates the structural properties of the Intersection Graph Γint(Zn) of the subgroups of Zn, focusing on cases where n = p, n = pq, n = p2 (p, q primes), and n = 2k (k a natural number). The research examines the connectedness of the graph. The results reveal unique properties of Γint(Zn) for each case of connectedness. Notably, for n = 2k, the graph is regular, complete, and exhibits rapid growth in size as k increases. This study provides a comprehensive understanding of the structural properties of Γint(Zn) and contributes to the existing body of knowledge on graph theory and group theory.
Copyright (c) 2025 A.M. Dogondaji https://creativecommons.org/licenses/by-nc/4.0
EXACT SOLUTION FOR TWO-DIMENSIONAL FLOW THROUGH CHANNELS WITH A PLANE PERMEABLE BOUNDARY BETWEEN TWO CHAMBERS WITH UNIFORM SUCTION/INJECTION
A one-dimensional model to determine the laminar ow of a fluid in a porous channel with wall suction or injection is proposed. The approach is based on the integration of the Navier–Stokes equations using the analytical solutions for the two-dimensional local velocity and pressure fields obtained from the asymptotic developments at low filtration Reynolds number proposed by Berman [1] and Yuan and Finkelstein [2]. It is noticeable that the resulting one-dimensional model preserves the whole ow properties, in particular the inertial terms which can affect the wall suction conditions. The model is validated in the case of a single porous channel of rectangular or circular cross-section with uniform or variable wall suction. Then the model is applied to a two-dimensional multi-channel system which consists of a great number of adjacent entrance and exit channels connected by a filter porous medium. All existing models aren’t analytical, and need to use complex numerous calculations. The present model is a first an attempt to reduce the problem to a simple analytical scheme based on Berman Similarity and perturbation series solution method that allows it to be used by general engineers not using complex mathematical methods.
Copyright (c) 2025 Igor Gaissinski https://creativecommons.org/licenses/by-nc/4.0
ALGEBRAIC SOLUTION OF FERMAT'S THEOREM (MATHEMATICS, NUMBER THEORY)
Fermat's Last Theorem (or Fermat's last theorem) is one of the most popular theorems in mathematics. Formulated in French mathematician Pierre Fermat in 1637. Despite the simplicity of the formulation, literally, at the “school” arithmetic level, proof of the theorem sought by many mathematicians for more than three hundred years. And only in 1994 year the theorem was proven by the English mathematician Andrew Wilson with colleagues; the proof was published in 1995. With this article, the author completes his research on the given topic, makes corrections and eliminates the errors of the previous ones.
A CROSS SECTIONAL ANALYSIS OF MALARIA TRASMISSION AND HEALTH SERVICE NEEDS AMONG NOMADIC POPULATION IN TARABA STATE OF NIGERIA
Malaria is endemic and a major cause of morbidity and death among nomads. Nomadic populations in Nigeria are more susceptible to malaria due to their way of living. They are often excluded from disease control programs because of their high degree of mobility, which makes it more difficult for them to get treatment and preventive measures. Care-seeking behavior patterns, local methods of transmission, and community perceptions of the disease are all taken into account by effective malaria control efforts. To effectively lower the disease burden among the nation's nomads, attention must be paid to the groups most at risk of contracting malaria and the ones least provided with access to basic medical care. The objective of this baseline study is to evaluate the prevalence of malaria and healthcare service needs among the nomadic people in Taraba State. Focus groups, key informant interviews, and household surveys are some of the techniques employed in this study. Incidence, prevalence, and distributions of LGAs with nomad settlements were noted. The acquired data were examined descriptively using percentages, tables, and charts. The findings demonstrate that malaria is a serious public health issue in nomadic groups due to high rates of transmission through environmental exposure, inadequate vector control methods, and restricted access to medical care. The primary risk factors that have been identified include limited access to healthcare and a lack of knowledge and preventive actions, such as bed net use and comprehension of malaria prevention. Improving healthcare services for these vulnerable groups was crucial to reducing the prevalence of malaria and improving overall health outcomes in Taraba State.
Copyright (c) 2025 Mohammed Usman https://creativecommons.org/licenses/by-nc/4.0
6TH-ORDER RUNGE-KUTTA FORWARD-BACKWARD SWEEP ALGORITHM FOR SOLVING OPTIMAL CONTROL MODELS OF EPIDEMIOLOGICAL TYPE
This paper seeks to formulate a more accurate forward-backward algorithm for solving optimal control problems using the 7-stage Runge-Kutta of order 6 (RK6) numerical scheme. The control variable were approximated using the interpolating polynomial or spine while the RK6 forward and backward sweeps were used in approximating the state and adjoint variables respectively because its A-stability, accuracy and higher rate of convergence. Three numerical examples were simulated to ascertain the accuracy and convergence of the 6th order Runge-Kutta forward-backward sweep method (K6FBSM). It was discovered that the RK6FBSM performs better when compared with the Euler and the 4th order Runge- Kutta Forward-Backward Sweep method RK4FBSM.
Copyright (c) 2025 AJE TEMITOPE https://creativecommons.org/licenses/by-nc/4.0
THE CIA AND U.S. FOREIGN POLICY: A SYMBIOTIC RELATIONSHIP AND MATHEMATICAL EXPLORATION
The Central Intelligence Agency (CIA) plays a pivotal role in shaping and executing U.S. foreign policy through intelligence gathering, covert operations, and strategic interventions. This paper explores the intricate relationship between the CIA and U.S. foreign policy, framing it as a dynamic, symbiotic interaction. U.S. foreign policy objectives influence CIA activities, while the outcomes of CIA operations, in turn, shape future policy decisions. A mathematical model is proposed to quantify this relationship, incorporating key factors such as geopolitical context, public perception, operational constraints, and historical outcomes. By assigning weighting coefficients to these variables, the model aims to illustrate how shifts in policy directives, global power structures, and public sentiment impact CIA operations. The analysis highlights the agency’s adaptability in responding to changing international landscapes while operating within legal, ethical, and diplomatic constraints. Understanding this interplay provides valuable insights into the mechanisms driving intelligence-based foreign policy decisions and the implications of covert operations on global stability. This study underscores the necessity of a balanced approach to intelligence activities, ensuring alignment with democratic principles while effectively advancing national security interests.
AN IMPROVED MULTI-DERIVATIVE HYBRID LINEAR MULTISTEP METHODS FOR DIRECT SOLUTION OF THIRDORDER ORDINARY DIFFERENTIAL EQUATIONS
This article considered an improved multi-derivative Hybrid linear multistep methods (IMDHLMM) for direct solution of third-order ordinary differential equations. Power series was used as the basis function in the derivation of the method. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The basic properties of the method such as order, consistency, zero stability, region of absolute stability and convergence was tested. The method was implemented in block mode to solve third order ordinary differential equations inlcuding Genesio equation to demonstrate the usability and efficiency of the methods. The absolute error obtained in the numerical experiments showed a better performance of the present method over some of the existing methods in the literature.
Copyright (c) 2024 T.V. Abejide https://creativecommons.org/licenses/by-nc/4.0
PAGERANK-INSPIRED APPROACH FOR MODELING LONG-TERM BEHAVIOR IN STOCHASTIC GENE REGULATORY NETWORKS
Gene regulatory network (GRN) play a crucial role in understanding the complex interac-tions between genes and their regulatory elements. However, accurately modeling the long-term behavior of GRNs under stochasticity remains a challenging task. In this study, we propose a methodology that leverages the concept of PageRank, originally developed for ranking web pages, to analyze the long-term behavior of GRNs. This approach involves constructing a directed graph representation of the GRN, where genes are represented as nodes and regulatory interactions as directed edges. We then adapt the PageRank algorithm to the GRN context, considering the stochastic nature of gene expression and incorporating the inherent randomness in regulatory interactions. By iteratively computing the PageRank scores, we obtain a ranking of the transition states based on their long-term influence within the network. To evaluate the effectiveness of our approach, we apply it to synthetic GRN models. Our findings cap-tured essential aspects of the long-term behavior in stochastic GRNs. We observe that genes with higher PageRank scores tend to have a greater influence on the overall network dynamics and exhibit more stable and persistent expression patterns
Copyright (c) 2024 Ebaifiyegha Ebimapogba Anthony https://creativecommons.org/licenses/by-nc/4.0
COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC AND BI-UNIVALENT FUNCTION ASSOCIA
Characterizing and estimating coefficients for subclasses of analytic and bi-univalent functions using fractional derivative operators. In this paper, we propose two novel subclasses within the realm of analytic and bi-univalent functions defined in the open unit disk U. By introducing these subclasses, we derive estimates for the initial two Taylor-Maclaurin coefficients, specifically | | 2 a and | | 3 a , pertaining to functions falling within these newly defined categories. This research paper sheds light on the behavior of functions in these subclasses and contributes to the broader understanding of their analytic and geometric properties.
Copyright (c) 2024 Krisn Pratap Meena https://creativecommons.org/licenses/by-nc/4.0
SPECTRAL THEORY AND FUNCTIONAL CALCULI IN THE REFLEXIVE BANACH SPACES
This article establishes the correspondence between the functional calculi for the operator defined on the Banach spaces and the spectral decomposition. We show that there is a functional calculus on Borel algebra for each well-bounded operator ABLX  , which uniquely corresponds with a multiplication operator on some  , ,  p L    .
Copyright (c) 2024 Mykola Ivanovich Yaremenko https://creativecommons.org/licenses/by-nc/4.0
SUM OF PRIME NUMBERS (SUGGESTED SOLUTIONS)
The author has improved the published articles. about this theme. In turn, the author strives to convey to reader important conclusions in his opinion, which in this article, namely that a transition from the ternary problem is possible to binary and further to solving the problem of infinity of numbers of twins.
Copyright (c) 2024 Khusid Mykhaylo https://creativecommons.org/licenses/by-nc/4.0
PREDICTING DIABETES USING DEEP LEARNING TECHNIQUES: A STUDY ON THE PIMA DATASET
Diabetes is one of the key reasons of growing death rates around the world. Diabetes is a medical condition that arises from chronic issues that influence carbohydrate metabolism and raise blood glucose levels. Scientific research is needed to diagnose diabetes early for prevention and treatment due to the growing rates of the disease. Researchers have recognized the value of classification models for disease prediction developed using machine learning and deep learning techniques. This study explores the efficacy of deep learning techniques Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Multi-Layer Perceptron (MLP)—in forecasting diabetes using the Pima dataset. Preprocessing steps encompassed normalization, handling missing values, and outlier removal. The models were trained and evaluated, yielding noteworthy performance metrics. The CNN exhibited the highest accuracy of 0.77, while achieving precision, recall, and ROC-AUC scores of 0.69, 0.67, and 0.83, respectively. The LSTM and MLP models also demonstrated competitive results, achieving accuracies of 0.75 with similar precision, recall, and ROC-AUC values around 0.64-0.67 and 0.80-0.82, respectively. These findings highlight the potential of deep learning methodologies for predictive diabetes analysis and emphasize the significance of proper preprocessing techniques in enhancing model performance.
Copyright (c) 2024 Emad Majeed Hameed https://creativecommons.org/licenses/by-nc/4.0
BRIDGING THE KNOWLEDGE GAP: ENHANCING TRACHEOSTOMY CARE SKILLS THROUGH STRUCTURED LEARNING
Background-Tracheostomy care is essential for patients with severe respiratory issues, yet traditional nursing education often inadequately prepares students for this complex procedure. This study explores the impact of a structured educational program on improving the knowledge and skills of nursing students in tracheostomy care.Aim-The primary objective of this study is to evaluate the effectiveness of a structured educational program in enhancing the knowledge, skills, and confidence of nursing students regarding tracheostomy care.Methods-An evaluative approach with a pre-experimental one-group pretest-post-test design was employed. The study was conducted at SCPM College of Nursing and Paramedical Sciences, Gonda, UP, involving 40 second-year GNM students. A structured questionnaire assessed knowledge levels before and after the intervention and study samples were recruited with the help of purposive sampling technique. Data collection was performed by six trained BSc nursing tutors and analysed using SPSS, with a significance level of <0.05 and a 95% confidence interval.Results-The pretest mean score was 11.42 (SD = 1.9596), while the post-test mean score increased to 17.50 (SD = 2.2870), with a mean difference of 6.08. The standard error was 0.47, and the calculated t-value was 12.76, compared to the tabulated value of 1.685, indicating a significant improvement in knowledge levels.Conclusion-The structured educational program significantly enhanced the knowledge and practical skills of nursing students regarding tracheostomy care, demonstrating its effectiveness as a teaching method.
Copyright (c) 2024 Jeya Beulah D, https://creativecommons.org/licenses/by-nc/4.0
Fermat's Last Theorem (or Fermat's last theorem) is one of the most popular theorems in mathematics. Formulated in French mathematician Pierre Fermat in 1637. Despite the simplicity of the formulation, literally, at the “school” arithmetic level, proof of the theorem sought by many mathematicians for more than three hundred years. And only in 1994 year the theorem was proven by the English mathematician Andrew Wilson with colleagues; The proof was published in 1995. [1]-[5] The author of this article has been searching for his own for a long time. accessible algebraic solution to this problem and believes that he succeeded,which he presents in this article.
The author has been researching on the topic for many years, indicated in the title. He published the results of his research that shown at the end of the review under the "Resources" heading. Primary goal, which is a proof of the binary or strong Goldbach problem. From[1-10] in the resources the ternary Goldbach problem is taken as a basis, which was reportedly finally resolved in 2013, which is not is currently confirmed. At the same time, the author admits his incorrect solution to the proof of a binary problem in a number of publications[5],[6] and others, which are detailed in section 2.1.Recent publications [11, 12] in the opinion of the author are universal and not are not tied to Goldbach's ternary problem, but vice versa proves it. In section 2.3 the author will show two possible proofs. And in conclusion, a new formulation regarding the sum of n prime numbers.
MAGNETOHYDRODYNAMIC BIOCONVECTION FLOW OF WALTER’S – B NANOFLUID OVER AN EXPONENTIALLY STRETCHING SURFACE
The combination of nanofluids and bioconvection has a wide range of applications in biological systems, agriculture, pharmaceuticals, biotechnology and industrial applications. This paper presents a numerical analysis of the Magnetohydrodynamic bioconvection flow of a two-dimensional, steady, incompressible Walter’s – B nanofluid flow in the presence of gyrotactic microorganisms over an exponentially stretching surface. The Buongiorno model together with the Boussinesq approximation is adopted and takes into account the effects of Brownian motion and thermophoresis in formulating the fluid flow governing equations. The governing equations are non-dimensionalised using appropriate similarity transformations. The resulting first-order ordinary differential equations are numerically solved using the Shooting Technique together with the fourth-order Runge-Kutta method. Simulation of the model and investigation of the effects of pertinent parameters on the fluids’ temperature, velocity, nanomaterial concentration and dimensionless motile microorganism density is carried out using MATLAB bvp4c. It is observed that the velocity field is enhanced with the Weissenberg number, Brownian motion parameter and Grashof number but reduced with the Buoyancy ratio parameter and Thermophoretic parameter. The temperature profiles increased with Brinkman number and Hartmann number nevertheless, the Prandtl number has the opposite effect. The nanomaterial concentration and motile microorganisms’ density profiles enhanced subject to Buoyancy ratio parameter, however, the Bioconvection Peclet number and Bioconvection Lewis parameter have bi-influence toward motile microorganisms’ density profile.
Copyright (c) 2024 Aziz Mohamed Kipolelo https://creativecommons.org/licenses/by-nc/4.0
APPLICATION OF NON-LINEAR EVOLUTION STOCHASTIC EQUATIONS WITH ASYMPTOTIC NULL CONTROLLABILITY ANALYSIS
This paper investigated system of stochastic differential equations with prominence on disparities of drift parameters. These problems were solved analytical by adopting the Ito’s method of solution and three different investment solutions were obtained consequently. The necessary conditions were achieved which govern various drift parameters in assessing financial markets. Therefore, the impressions on each solution of investors in financial markets were analyzed graphically. Secondly, stock price data of Transco, LTD were analyzed which covariance matrix were considered and analysis were logically extended to stochastic vector differential equation where control measures were incorporated that would help in predicting different stock price processes, and the result obtained by exploring the properties of the fundamental matrix solution where asymptotic null controllability results were obtained by the singularity of the controllability matrix a function of the drift. Finally, the effects of the significant parameters of stochastic variables were successfully discussed.
Copyright (c) 2024 Amadi I.U https://creativecommons.org/licenses/by-nc/4.0