This study proposes a novel EOQ-based inventory model for deteriorating items under seasonal demand Variation, inflation, and investment in preservation technology Demand is modeled time- dependent Seasonal function while deterioration is treated as controllable through preservation efforts, Creating a cost-benefit trade-off between technology investment and spoilage reduction. The time value of money and inflation are incorporated using a discounted Cash flow approach to reflect realistic economic condition. A Comprehensive total Cost function is formulated including Ordering, holding, deterioration, preservation investment and inflation-adjusted costs. The objective is to determine the optimal replenishment Cycle and preservation inventory cost. Analytical and numerical result indicate that preservation technology significantly under fluctuating demand and rising economic Conditions. The model establishes a bridge between technological intervention and classical inventory theory, enabling adaptive and economically resilient policies for deteriorating items in dynamic market condition
Background: This study focuses on a natural convention flow of Silicon (IV)Oxide-water nanofluid in a magnetically equipped exponentially stretching surface in a three-dimensional frame. The ef ects of buoyancy, nanoparticle volume fractions and magnetism on the flow velocities in all directions, temperature of flow and concentration of the nanoparticles. Material and methods: The study considered a steady boundary layer flow of an electrically conducting nanofluid past a semi-infinite convectively heated flat plate in the presence of a uniform transverse magnetic field. It assumed that the induced magnetic field and the external electric field were negligible. The governing equations were subject to the boundary conditions and were solved numerically by the Runge-Kutta-Fehlberg method with shooting technique. Both velocity and temperature profiles were obtained and utilized to compute the skin-friction coef icient and the local Nusselt number in the equation. Results: The numerical simulations reveal that an increase in Grashof number (𝐺𝑟) lead to an enhancement in both the primary 𝑓 and secondary velocity components. This was due to the buoyancy forces ' ( ) 𝑔 ' ( ) strengthening the convective transport of fluid and nanoparticles so that buoyancy forces became stronger as 𝐺𝑟 increases, and consequently leading to an increase in the fluid velocity. Conclusion: Grashof number and nanoparticle volume fraction enhances primary and secondary velocities, magnetic field reduces both primary and secondary velocities, nanoparticle volume fractions increase temperature profile, and nanoparticle volume fractions concentration of nanoparticles decreases.
This paper introduces a novel Recursive Partitioning Framework that builds upon additive number theory, with specific application to Lemoine's Conjecture, which asserts that every odd integer greater than 5 can be expressed as the sum of a prime and a semiprime. Inspired by recent developments in algorithmic formulations of Goldbachtype conjectures, we adapt the framework proposed by Sankei et al. (2023), originally used to partition even integers via expressions of the form; 𝐸 = (𝑃1 + 𝑃2 )+ (𝑃2 −𝑃1 ) 𝑛 with 𝑃1 , 𝑃2 ∈ ℙ, 𝑃2 > 𝑃1 , and 𝑛 ∈ ℕ, to develop a systematic method for generating and verifying odd number partitions, tested for all odd numbers up to 106 . Our method leverages structured arithmetic sets and recursions over integer pairs (𝑒, 𝑢), where 𝑒 ∈ 2ℤ and 𝑢 ∈ 2ℤ + 1, to explore partitions of an odd integer 𝑂 = 𝑝 + 𝑠, where 𝑝 is an odd prime and 𝑠 is a semiprime. A recursive algorithm is proposed that decomposes residual values resulting from candidate partitions into products of two primes. The method reduces computational complexity compared to brute-force approaches by exploiting arithmetic patterns and interval narrowing based on parity constraints. Empirical validation confirms the algorithm consistently finds valid Lemoine decompositions for all tested odd integers 𝑂 > 5. Furthermore, we define a Lemoine pair function 𝑓(𝑂), which asymptotically satisfies 𝑓(𝑂) ≳ 𝑐 ⋅ 𝑂𝑙𝑜𝑔 𝑙𝑜𝑔 𝑂 𝑙𝑜𝑔2 𝑂 , suggesting the unbounded growth of valid partitions with increasing 𝑂. This offers a probabilistic foundation for the conjecture's global validity. The recursive partitioning framework not only unifies prime-semiprime decompositions with structured partition theory, but also opens new directions in analytic number theory and cryptography by enabling systematic methods for prime generation relevant to cryptographic protocols
In this research work, a five-dimensional LRS Bianchi type-V string cosmological model with the electromagnetic field in the framework of Lyra’s manifold is investigated. A determinate solution of the field equations is obtained with the help of the special law of variation for the Hubble parameter. Some physical and kinematical properties of the model are discussed.
Mathematics is a one major area of science that is of great important that interrelate all other science. One of the important goals of mathematics is to transform a student into an individual with high decision power and creative solving problems and the power of reasoning. Information Communication technology tools and software are of great support for solving mathematical problem. Several application software are available for solving mathematical problem in different academic level. This research work gave a general survey of various mathematical software, ideas of their applications and their effects
Multi-Criteria Decision Making (MCDM) techniques have attracted significant attention from researchers and professionals across diverse industries due to their ability to effectively evaluate, assess, and rank alternatives. However, choosing the most suitable MCDM method for a specific problem can be challenging, especially when several methods appear equally applicable. Among these methods, the Technique for Order of Performance by Similarity to Ideal Solution (TOPSIS) is widely used, leading researchers to propose various improved versions. This research focuses on enhancing the traditional TOPSIS method by integrating criteria weights along with performance ratings and alternative weights using Euclidean distances. This integration enables decision-makers to prioritize criteria based on their relative importance, ensuring that the distance calculation accurately reflects these priorities. Through this enhancement, the proposed approach aims to streamline and strengthen decisionmaking processes, addressing the complexities associated with selecting the optimal MCDM method for a given problem. In this study, both the traditional TOPSIS method and a revised version are applied to car selection using hypothetical data. The study evaluates the best automotive car based on specific criteria.
This study investigates the relationship between Pell numbers and Pell-Lucas numbers, which follow the same recurrence relation but differ in initial conditions. The goal of this study is to establish and prove general identities connecting the two sequences through the Principle of Mathematical Induction. Several key identities involving sums, products, squares, and linear combinations were derived and validated.
This research focuses on an essential aspect of complex analysis, specifically complex integration. The focus is on the Cauchy-Goursat theorem, which states that the line integral of a holomorphic function along a closed contour equals zero when the function is holomorphic within and on that contour, in a domain with a single connection. Various applications derived from this study are analyzed and discussed, aimed at solving integrals of functions that may present singularities. In this regard, more advanced research would enable the contribution of tools in the theory of control and potential flow.
The orthogonal polynomial set’s properties and its use in the least square sense approximation of data or complex functions to a polynomial, are discussed. Performance of Chebyshev, Gram and Alfredo-Giuseppe (A-G) polynomials is examined with a simulated Planck profile with and without noise. For Gram and A-G orthogonal sets with equal spaced grids, the effect of two types of fake data points at the boundaries are examined by computing the root mean square deviation of the data fit. When three or more data points of zero values are added at fake grids, computation orthogonal polynomials of highest allowed degree are possible without divergence (no Runge phenomenon). When fake repeated data points are added, good data fit to polynomials (computed from the orthogonal polynomial for each degree) with highest convergence rate results. Good noise discrimination is seen in the latter case and can be used to identify the best orthogonal polynomial degree to be employed for data fitting applications
This paper investigates sum perfect cube graphs, defined as a graph 𝐺 = (𝑉, 𝐸) with 𝑝 vertices and 𝑞 edges is said to admit sum perfect cube labeling if there exists a bijection 𝑓: 𝑉(𝐺) → {0,1,2,3, … , 𝑝 − 1} such that for each edge 𝑒 = 𝑢𝑣 the induced map 𝑓 ∗ : 𝐸(𝐺) → ℕ is defined by, 𝑓 ∗ (𝑢𝑣) = 𝑓(𝑢) 3 + 3𝑓(𝑢)𝑓(𝑣) 2 + 3𝑓(𝑢) 2𝑓(𝑣)+ 𝑓(𝑣) 3 . All edge labels are distinct. The graph which attains such labeling is termed as a sum perfect cube graph. The study focused on identifying graphs where all edges permit such labeling termed sum perfect cube graphs. This paper explores the study of various sum perfect cube graphs.
In the last two to three decades, significant research has focused on special functions related to statistical distributions. This includes the Generalized Hurwitz-Lerch Zeta Beta type-2 distributions and Gamma distribution, generalized hypergeometric distributions, Parabolic cylinder distribution, generalized Hurwitz Zeta Beta prime distributions, Mathieu distribution, Plank distribution, Mittag-Leffler distribution, Hurwitz Lerch Zeta distribution. Furthermore, the special cases explored include the Zipf-Mandelbrot distribution, Lotka distribution, Good distribution, Logarithmic Series distribution, right truncated form of the HLZ distribution and Estoup distribution. The study explores the properties and statistical measures like moment generating function, distribution function, survivor function, Hazard rate function, mean residue life function, characteristic function, probability generating function, likelihood equations result in method of moments.
In the current competitive and dynamic business world, decision-making at the strategic level is key to deciding the success and survival of companies. Game theory, a mathematical tool for the analysis of strategic interaction between rational decision-makers, provides valuable tools to represent and predict competitive behaviour in markets. This research discusses the use of game theory in the development of competitive business strategies, highlighting its utility in expecting the moves of competitors, minimizing pricing strategies, risk management, and cooperation or competition. Utilizing traditional and recent game-theoretic models—such as Nash equilibrium, mixed strategies, repeated games, and evolutionary games—the research demonstrates how companies can make evidence-based, strategically rational choices in complicated market situations. Examples of case studies from industries like technology, retail, and telecommunications are used to illustrate real-world applications. The work also includes mathematical definitions of prominent game theory concepts and explorations of their implications within areas like market entry, product placement, and competitive bidding. By way of this analytic lens, the research seeks to link theoretical game models with actual business strategy, providing a quantitative method of handling competitive markets.
This paper explores the completion of positive semidefinite (PSD) matrices through graph representation, emphasizing the fundamental properties of PSD matrices and their relevance in various applications, including statistics, machine learning, and optimization. Positive semidefinite matrices, characterized by non-negative eigenvalues, play a critical role in ensuring stability and feasibility in numerous mathematical models. The challenge of matrix completion—filling in missing entries while maintaining the PSD property—is crucial in applied mathematics, particularly in scenarios involving incomplete data. We introduce a novel approach that leverages graph theory to represent PSD matrices, facilitating a more intuitive understanding of the conditions required for matrix completion. Our findings reveal effective algorithms for completing these matrices, demonstrating improved performance over traditional methods. By establishing connections between graph properties and matrix completion criteria, we provide new insights into the structure of PSD matrices. This work not only advances theoretical knowledge but also holds practical implications for fields relying on accurate data representation and analysis, paving the way for future research in matrix completion and its applications.
In this paper, we establish the some common fixed point theorems in rectangular S-metric spaces, an advanced generalization of S-metric spaces. We develop new common fixed point theorems that integrate and extend various well-known results in fixed point theory. Our findings are further supported by illustrative examples.
This study conducts an in-depth analysis and improvement of the asymptotic properties of the prime sequence 𝐶𝑛 = 𝑛𝑝𝑛 − ∑𝑘≤𝑛 𝑝𝑘 (for 𝑛 ≥ 1) and the upper bounds of the prime summation function 𝑆(𝑥), based on the upper and lower bound estimates of the prime counting function 𝜋(𝑥). By developing novel estimation methods, we obtain more precise asymptotic estimates than existing results in the literature. Specifically, this work not only optimizes the upper and lower bound estimates of Cn but also significantly improves the upper bound estimation of 𝑆(𝑥). These refinements deepen our understanding of the structural characteristics of prime sequences and hold potential applications in computational number theory and related fields. Background: The study of prime numbers and their asymptotic behavior has been a central topic in number theory since the pioneering work of Gauss and Legendre on the Prime Number Theorem. The prime counting function 𝜋(𝑥), which enumerates primes not exceeding 𝑥, provides fundamental insights into the distribution of primes. While the Riemann Hypothesis offers the most precise conjectural bounds for 𝜋(𝑥), practical applications often rely on computationally verifiable estimates. The summation of primes 𝑆(𝑥) and related sequences like 𝐶𝑛 = 𝑛𝑝𝑛 − ∑𝑘≤𝑛 𝑝𝑘 naturally arise in various contexts, including prime gap analysis and verification algorithms for prime certificates. Previous work by Rosser and Schoenfeld established rigorous bounds for 𝜋(𝑥), and subsequent refinements by Dusart and others have improved these estimates
The functions of universities and colleges today are no longer limited to the acquisition of professional knowledge and training of skills, but have further become a crucial phase for students to learn occupational safety and health (OSH) education and develop personal safety protection awareness. After entering the workforce, OSH education also becomes essential knowledge for every employee. This study simulates the implementation of OSH training courses at universities and colleges in southern Taiwan under time constraints. In consideration of maximizing school participation, we use scheduling algorithms to achieve optimal allocation
Classic inventory models commonly assume that surplus demand is backordered. However, research analysing customer behaviour in practice demonstrate that in many retail situations, unsatisfied demand is lost or replaced with an alternative item/location. Inventory systems with this lost-sales characteristic appear to be more challenging to analyse and resolve. Furthermore, to save costs, lost-sales inventory systems require different replenishment procedures than backorder systems. In this work, we present a survey on inventory models with lost sales. Furthermore, directions for future investigation are suggested
This research presents an age-structured Susceptible-Vaccinated-Exposed-AsymptomaticSymptomatic-Hospitalized (SVEASH) COVID-19 model that accounts for age-dependent recruitment and transmission rates, contact ratios, and multiple infection forces. It assumes perfect vaccination that guarantees permanent immunity. The study explores the mathematical properties of the model, determining the existence of equilibrium and the local stability of the disease-free equilibrium (𝐸 0 ). The basic reproduction number R0, a key threshold for stability, is calculated as a weighted average from both asymptomatic and symptomatic infection classes. Using the Laplace transform, the model is solved analytically, and simulations show that vaccinating up to 85% of the global population between ages 0-80 significantly reduces the disease's peak and shortens the epidemic's duration. The research also highlights the importance of vaccinating not only susceptible and hospitalized individuals but also those who have recovered, further aiding in controlling the outbreak.
Aim: The overall goal of this thesis work was to examine gender as a factor influencing math achievement, with a focus on secondary schools in the Shai-Osudoku District of the Greater Accra Region. In that the following were the study’s objectives: To 1.Assess the gender-based disparities in mathematics performance of Senior High School students in the ShaiOsudoku district. 2.Ascertain the impact of societal factors on gender-based disparities in the mathematics performance of Senior High School students of Shai-Osudoku district? Method: The study used quantitative research approach which aims to investigate the influence of gender on math performance among secondary school students in the Shai-Osudoku District of the Greater Accra Region with a sample of 347 students randomly selected from the population using systematic random sampling technique. The primary data was collected using questionnaire and a forty-five-minute multiple choice items mathematics achievement test on statistics and probability. The data collected was analyzed using, the regression tool. Results: The t-test value of -1.02 with 82 degrees of freedom and a p-value of 0.312 indicates that the difference between the means of male and female responses is not statistically significant at a conventional significance level (e.g., p < 0.05). This implies that the observed difference between male and female responses in this study could likely have occurred by chance The study therefore found no significant relationship between the independent variable gender and the dependent variable academic performance among senior high school students in Shai-Osudoku district signifying that students’ performance in mathematics do not largely depends on gender. With regards to objective two, the finding aligns with existing research that highlights the disparities in educational resources and opportunities linked to income status. This suggests an acknowledgment of the role that economic background plays in determining the educational opportunities available to students Conclusion: For research question 1, the mean scores for males (Mean = 2.32, SD = 1.17) and females (Mean = 2.58, SD = 1.11) indicate that both genders recognize factors affecting gender-related disparities in mathematics achievement, with females showing a slightly higher mean response. However, the difference between these means was not substantial. Based on the findings that emanated from the data analyzed, the study concluded that gender has no significant relationship with students’ academic performance in mathematics among senior high school students in Shai-Osudoku district of greater Accra region. Recommendation: There should be a development and implementation of a gender-inclusive mathematics curriculum that showcases diverse role models and examples, highlighting the contributions of both male and female mathematicians and scientists. This can help challenge gender stereotypes and create a more inclusive learning environment for all students. Also encourage teachers to use gender equality and social inclusion (GESI) teaching strategies that cater for diverse learning styles and abilities. Employ innovative and interactive teaching methods that engage students and make mathematics more relatable and enjoyable for everyone
