In this article, an EOQ inventory model of ameliorating items is considered, and the system total cost is optimised in a supply chain framework. The system facilitates growing the live purchased young items up to the targeted maturity stage for customers' consumption. This study is suitable for poultry and fisheries management and marketing, with a focus on revenue generation. We assume that the items are newborn poultry or fish that can grow rapidly after intensive feeding. An inventory cycle is as follows: Purchase of new-born items, screening to sort out weaker items (defective items), feeding period in which it is implemented intensive technological growth process with proper medication and observation, sorting out unsuitable items that do not reach the desired weight, serving the customers until the items are empty, and allowing the shortages that are completely backlogged which are satisfied in next cycle. The novelty of the model is ensured by incorporating screening before amelioration, eliminating deadly stocks after amelioration, and satisfying backlogs immediately after amelioration altogether. Essential cost functions are derived to minimise system cost by an analytical approach. It is recommended by numerical illustration, which gives more light to the investors who are involved in the sale of poultry and fisheries items in optimising total cost.
This study investigates the dispersion of a solute in Casson fluid, representing blood flow, under the influence of an external transverse magnetic field1. The Casson model is utilized to capture the nonNewtonian yield stress and shear-thinning behavior characteristic of blood in micro circulation. By extending the classical theory of Gill and Sankarasubramanian, the mathematical framework accounts for magnetohydro dynamic (MHD) effects, porous boundaries, and chemical reactions. Analytical and numerical results show that increasing the Hartmann number and the Casson parameter significantly reduces the effective dispersion coefficient while increasing mean solute concentration. Furthermore, wall slip is shown to enhance solute transport, providing an additional mechanism for flow control. These findings provide theoretical insights for optimizing targeted drug delivery, contrast agent transport, and tracer movement in cardiovascular systems.
The power graph of a finite group G is a special type of undirected simple graph whose vertex set is a set of elements of G, in which two distinct vertices x and y are adjacent if either x is an element of (y) or y is an element of (x). In this article, we establish a new class of vertex odd as well as even mean graphs through the power graphs of 2-abelian groups Z(2)(k - 1), Z(2)(k - 1) x Z(4) and Z(2)(k - 1) x Z(4) x Z(4).
This article discusses the problem of practical h-stability for certain classes of dynamic equations in Banach spaces. The main objective is to give sufficient conditions on the linear and perturbed term for practical h-stability based on certain nonlinear Gronwall-type integral inequalities over time. ladder. Two examples are given to illustrate the effectiveness and advantages of the results obtained.
. India is the world's third-largest electricity producer. There were 1,378 TWh produced by utilities in the nation in the 2018-19 fiscal year (FY). Globally, there is an increasing need for electrical power because of the growth of industrial activities and the size of the population. A reliable projection of future output is vital for the effective planning and development of policies pertaining to electrical power. In the present study, ARIMA, Support Vector Regression optimized by LSTM, and Modulated Support Vector Regression using python were employed to analyse the electricity generation from coal, gas, hydro, solar, oil, wind, and renewable energy sources in India. The MSE, MAPE, R-2, and RMSE criteria were used to evaluate the models created using those techniques. Among these three models, by the least error metrics of MSVR, RMSE is 0.00726227, R2 is 0.989280593, MSE is 5.27E-05 and MAPE is 1.24E-03%, by DM statistical test and by the graphical representation, MSVR is the best model to fit the electrical generation of India. So the future generations will benefit from early forecasts of India's electricity production by MSVR.
Graph theory has been an essential branch of mathematics with applications in various scientific disciplines and engineering fields. The classical mean property on graphs is a well-known mathematical concept involving the relationship between mean values and graph structures. Consider the graph G with q edges and the injection ohm from the vertex set to {1, 2, 3, ... , q + 1} and the promoted edge labeling ohm(& lowast;) is {1, 2, 3,. .., q} such that ohm(& lowast;) is defined by flooring function of the average of root square, harmonic, geometric and arithmetic means of the vertex labels of the end vertices of each edge, is bijective. A graph is described as a classical mean graph if it allows a classical mean labeling. The present study investigates the fascinating relationship between snake graphs and the classical mean property.
In this paper, we present a novel three-step root-finding algorithm designed to solve non-linear equations. The proposed method integrates the Newton-Raphson method, the exponential method, and an optimal fourth-order convergence technique, achieving a convergence order of four. Our results demonstrate the algorithm's effectiveness and highlight its potential applications in engineering and other areas of mathematical analysis. Several numerical examples are provided to illustrate and validate the method. Additionally, implementations in Maple and Python are presented, along with sample computations.
. The aim of this manuscript is to demonstrate the existence of an entire complex function of order one that interpolates the tau-Li coefficients associated with a function F in the class S-& sharp;b. This class includes both the Selb erg class of function and the class of all automorphic L functions. Additionally, we derive entire functions of order one and finite exponential type that interpolate both the archimedean and non-archimedean contributions to lambda(n, tau). We show that these functions can be interpreted as zeta functions, constructed over the trivial zeros and all zeros of a function F is an element of S-& sharp;b, respectively. Finally, we present some numerical investigations of the tau-Li coefficients for 1 <= tau < 2 and for tau values close to 1 and 2.
The paper is concerned with the approximate controllability of semilinear fractional Sobolev-type differential system with retarded memory in Banach spaces. To study the approximate controllability of our control system, we construct the fundamental solution operator and establish a variation of constant formula of mild solutions. Thanks to the properties of the fundamental solution operators, we obtain the approximate controllability results under the assumption that the linear system is approximate controllable. Finally, we present some examples to illustrate the results obtained.
In this study, the task of grading of raw flax fibers has been undertaken using an intuitionistic fuzzy multi-criteria decision-making (FMCDM) framework. Three technical professionals were engaged to mitigate the inherent uncertainty associated with the properties of raw flax fibers. In this paper, five distinct criteria such as strength, fineness, length, color, and color homogeneity are considered for the evaluation of flax fibre quality. Ten batches of flax fibers have been assessed using a hybrid Fuzzy-TOPSIS method. The rankings determined by the experts are very close to the result obtained by the proposed method. This strong agreement underscores the effectiveness of the proposed hybrid MCDM approach in achieving accurate and consistent flax fiber grading.
In this paper, we investigate the properties of the Fibonacci-Euler polynomials by deriving their associated difference equations. Beginning with the fundamental difference equation, we further establish higher-order relations through the application of the Golden Heat equation. Moreover, we explore the symmetric properties of the corresponding differential equations, revealing elegant structural identities inherent in the Fibonacci-Euler framework. These results not only extend the theory of Fibonacci-Euler polynomials but also highlight their rich interplay between difference equations, differential equations, and symmetry.
Let (N-n)(n >= 0) be the Narayana's cows sequence and (P-n)(n >= 0) the Padovan sequence. The aims in this paper is to find all Narayana numbers which are products of two Padovan numbers and all Padovan numbers which are products of two Narayana numbers.
. This paper introduces a novel family of number sequences, termed the Leonardo-Narayana sequence, which combines the properties of the well-known Leonardo and Narayana sequences. The LeonardoNarayana sequence is defined recursively by the relation LNn = LNn-1 + LNn-3 + 1 with initial conditions LN0 = LN1 = LN2 = 1. We explore various algebraic properties of this sequence, including its recurrence relations, characteristic equation, and generating function. Additionally, we derive Binet's formula for the Leonardo-Narayana numbers and present their matrix representation. The paper also investigates sums of terms in the sequence and establishes connections to the Narayana numbers. The results highlight the potential applications of the Leonardo-Narayana sequence in diverse fields such as mathematics, physics, and engineering.
This paper emphasises the study of Eccentric Connectivity Polynomial of Cartesian product of Unitary Cayley graphs and major standard graphs which explains the easy derivation of Eccentric Connectivity Polynomial and opening the path to further research and applications in Eccentric Connectivity Polynomial of Cartesian product graphs.
Suppose that {U-n} and {V-n} are Lucas sequences of the first and second kind. This research aims to study the appearance of Fermat prime numbers of the form fn = 2(2n) + 1, where n is a non-negative integer, within the first and second Lucas sequences after transforming this form into an elliptic curve that can be solved using the Magma software. The appearance shows that the Fermat primes appear only in limited cases and are associated with structural constraints on the curve. The limitation of these numbers indicates the weak reliability of using these numbers in cryptographic applications, which confirms their unsuitability for generating secure keys.
. In this paper, we introduce and study )-deformed bivariate Hermite polynomials, which naturally arise as )-analogues of falling factorial sequences. By analyzing their generating function, we derive associated differential equations and obtain explicit symmetric identities through the coefficient structures. Furthermore, we investigate the distribution and symmetry of the zeros of these polynomials, revealing regular reflection and stacking patterns in both the real and complex domains. These results enrich the theory of deformed special functions and suggest new directions for analytic and computational approaches to zero distributions.
. Next-basket recommendation is a critical problem in sequential behavioural modelling, requiring the integration of temporal dynamics, item co-occurrence, and user-specific preferences. This study proposes a two-stage framework that combines Item2Vec-based item embeddings with classical learning-to-rank (LTR) models to predict future basket interactions. The architecture encodes multi-scale temporal features, hierarchical item relationships, and co-interaction affinities into structured hybrid feature vectors, which are subsequently optimized using gradient-boosted rankers. Experimental evaluations demonstrate that the proposed method achieves Precision@5 = 0.468, Recall@5 = 0.311, NDCG@5 = 0.479, and MRR@5 = 0.356, outperforming embedding-only and ranker-only baselines by 15-40% across key ranking metrics. Robustness analyses indicate stable performance under temporal drift and user sparsity conditions, with coverage exceeding 90% and silhouette indices of approximately and recency-based indicators contribute over 60% of the overall predictive gain. Comparative evaluation against four literature baselines confirms a relative improvement of 6-12% in NDCG@10, underscoring the effectiveness of sequence-of-sets representations combined with scalable non-neural rankers. Overall, the proposed framework delivers an interpretable, computationally efficient, and reproducible solution for next-basket recommendation, advancing temporal behaviour modelling and ranking optimization.
A relatively new method called the conformable homotopy perturbation Elzaki transform method (CHPETM) is applied to solve conformable time fractional Burgers equation. The method proved to be valid and effective as evidenced by the close correspondence between its results and the exact solutions. As illustration examples provide additional evidence of the method's reliability. Furthermore, the numerical solutions graphically helps in assessing the efficiency of the method.
In this article, we present the inequalities between vertex and edge version of the inverse sum indeg Szeged indices of trees in terms of main parameters determining their relations are number of vertices and number of product vertices.
This study investigates a retrial queueing system with collision, server deterioration, and recovery under vacation. Two parallel servers handle incoming customers; if both are busy, arrivals join an orbit and retry later. During a retry, if the server is occupied, a collision occurs, sending both the retrying and being served customer back to the orbit. The first server works normally, while the second server deteriorates-its service rate decreases over time due to fatigue or wear. After serving nth customers, it takes a short recovery break before resuming work. Using the matrix analytic method, steady-state probabilities and key performance metrics are derived. Numerical experiments show how system parameters affect performance. Results are further compared with ANFIS predictions. Finally, Biogeography-Based Optimization (BBO), Cuckoo Search Algorithm (CSA), and Bat Algorithm (BA) are applied to identify the most cost-effective solution and analyze the convergence behavior of these optimization techniques.
