Let ¯R_(l,μ) denote the number of overpartitions of an integer n≥0 such that no parts of n is a multiple of l and μ, with l and μ being coprime. In this paper, we have established a number of infinite families of congruences and many Ramanujan-type congruences modulo powers of 2 for ¯R_2,5 (n).
Lucky labeling is a kind of neighborhood summation graph labeling that has been studied for various classes of graphs extensively. However, relatively few efforts have been made to develop algorithms for the systematic verification of lucky and proper lucky labelings. This paper presents an algorithm for verifying lucky and proper lucky labelings of complete multipartite graphs with up to three partitions. The proposed procedure constructs the graph from the given partition sizes, assigns vertex labels according to the prescribed labeling scheme, computes the corresponding neighborhood sums, and verifies the conditions required for both lucky and proper lucky labelings. An illustrative example is provided to demonstrate the correctness of the algorithm.
This study introduces the concept of fuzzy pentapartitioned Neutrosophic soft topological space. We define the interior and closure operators for fuzzy pentapartitioned Neutrosophic soft sets within this topological framework and examine their fundamental properties. Additionally, we introduce the notions of Fuzzy Pentapartitioned Neutrosophic Soft Pre-Open (FPNS-PO), semi-open (FPNS-SO), b-open (FPNS-b-O), and α-open (FPNS-α-O) sets. Suitable numerical examples are provided, and several basic results concerning these generalized open sets are established.
Historical records have examined the origins and significance of zero, yet a fundamental question remains unanswered: What is the value of a/0, where a can be either zero or a non-zero value? Brahmagupta and Bhaskara, two prominent Indian mathematicians, held opposing views on this issue, but neither offered a definitive solution. Various attempts to address this problem—such as introducing new symbols to expand the set of real numbers, applying proposed transreal analysis, utilizing stereographic projection, or employing the sgn function—have proven unsuccessful. The reality is that treating a/0 in isolation does not make sense. A meaningful natural process to elucidate this problem requires the quotients to appear as characteristic numbers. In conformity with the use of applied mathematics and real life, it is necessary to recognize that no natural process involves a zero denominator. This work, illustrated with experimental examples, shows that when the denominator of a quotient approaches zero, using characteristic numbers associated with the limit of that quotient yields finite results, intervening in the definition of infinity. This approach facilitates the management of potential hardware exceptions and helps programmers develop more efficient software to prevent division-by-zero errors.
This study takes a look at the issue of estimating the population means on this particular occasion using samples taken on two separate dates. The characteristics of three possible estimators are presented and examined, all of which rely on the known coefficients of variation, skewness, and kurtosis. We have spoken about the best practices for replacing the estimators. We have compared the suggested estimators to the optimal estimator, which is a linear combination of the means of the matched and unmatched sections of the sample on this occasion, and to the sample mean estimate when no matching is present.
In this paper, we consider a sixth-order variable coefficient singular differential equation with indefinite weights 5 𝑢(6)(𝑡) + ∑ 𝑎𝑖(𝑡)𝑢𝑖(𝑡) = ℎ(𝑡) 𝑖=0 𝑢𝜌 +𝑒(𝑡)， where 𝜔 is a positive constant, ℎ(𝑡),𝑒(𝑡) ∈ 𝐿1(ℝ/𝜔ℤ) and 𝑒(𝑡) > 0 for any 𝑡 ∈ [0,𝜔]. By using the Krasnoselskii-Guo fixed point theorem, we prove the existence of positive periodic solutions to the above equation.
Neutrosophic Semi-Open SuperHyperSoft Sets (NSOSHS) and Neutrosophic Semi-Closed SuperHyperSoft Sets (NSCSHS) are two new concepts in Neutrosophic SuperHyperSoft Topological Spaces that this paper introduces. Both of these concepts extend the classes of classical hypersoft and neutrosophic theories to include multi-parameterized semi-topological environments. The fundamental properties, characterizations, and structural relations of NSOSHS and NSCSHS are established, as well as their interactions under union, intersection, interior, and closure operations. Additionally, the authors define and study new operators (namely, neutrosophic semi-interior and neutrosophic semi-closure) and their algebraic and topological properties. A number of theorems are proven in this paper to illustrate the theoretical consistency and robustness of the proposed framework for decision-making. Finally, the authors demonstrate the practical application of the developed theory in a Multi-Attribute Group Decision Making (MAGDM) scenario for resource allocation in a smart hospital. Therefore, neutrosophic uncertainty combined with hierarchical parameterization creates a powerful and flexible tool for exploring undetermined and/or inconsistent information in complex decision-making systems.
The purpose of this paper is to investigate the theoretical foundations of Markov chains and to develop a model for forecasting stock price volatility based on return series. Building on this framework, the study constructs an optimal investment portfolio composed of securities with superior expected performance. The proposed model is then applied to real-world data from stocks listed on the Ho Chi Minh City Stock Exchange (HOSE). The findings of this research provide a quantitative basis for supporting investors in making more informed and effective capital allocation decisions.
In this paper, the notion of generalized reverse derivations on Krasner hyperrings is introduced, and investigated the commutativity of prime hyperrings. In particular, it establishes several results showing that under suitable conditions on generalized reverse derivations and their associated reverse derivations, a prime hyperring becomes commutative in some cases, reverse derivation 𝛿=0. The obtained results contribute to the development of derivation theory in algebraic hyperstructures and provide new insights into the structural properties of hyperrings.
In this paper, we analyze annual precipitation records from Daytona Beach, Florida, by utilizing interpolation and extrapolation, focusing on years where the data are missing or unevenly spaced. We apply several interpolation methods to fill the gaps and extrapolation techniques to predict the future precipitation. We use polynomial interpolation based on a Vandermonde matrix and compare it with MATLAB’s built-in interpolation functions. Specifically, we test linear interpolation, piecewise cubic interpolation, and higher-degree polynomial models to see how each method behaves when the data contains large gaps. We also use a least-squares approach to extrapolate short-term trends in annual precipitation. In our observation, we found that piecewise interpolation provides the most stable estimates for the missing values. Although extrapolation is less reliable, it suggests a slight upward trend in precipitation over the selected period. These results show that interpolation methods can be practically useful, but they also remind us of the uncertainty that comes with making long-term climate predictions.
Fuzzy numbers figuring indispensable roles in problems in decision making, analysis of data, and socioeconomics arrangement. Finding the ranking of any fuzzy numbers is an inevitable step in many mathematical models. Many of the methods proposed produced the best solution to the transportation problems. This paper introduces a Proposed Ranking method that applies the same approach we used to transform the fuzzy transportation problem to an exquisite valued one, subsequently into a new proposed process to uncover the fuzzy realistic solution. The numerical illustration demonstrates that the new projected method offers an awesome means for managing the transportation problems using fuzzy algorithms.
In this paper, the Norm of the Sum of two basic elementary operators is determined in the tensor product of a C*algebra. Using the Cauchy-Schwarz inequality and finite rank operators, the Norm of the Sum of two basic elementary operators is ‖𝑀A⊗B,C⊗D +𝑀E⊗F,G⊗H|𝐵(𝐻 ⊗K)‖ = ‖𝐴‖‖𝐵‖‖𝐶‖‖𝐷‖+‖𝐸‖‖𝐹‖‖𝐺‖‖𝐻‖ in the tensor product of C*algebras.
The goal of this research is to promote sustainable development by presenting an integrated approach to addressing the Transportation Problem (TP) with a focus on minimizing fuel consumption and reducing carbon dioxide emissions. Mathematical modeling techniques and Transportation algorithms are combined in the proposed solution, which is tailored to the specific context of the Indian Transport Authority transportation network. This approach’s effectiveness in achieving a balance between reducing fuel consumption and transportation costs while maintaining service quality and customer satisfaction is demonstrated in the study. The optimization of the allocation of different routes can greatly reduce carbon dioxide emissions and Fuel consumption in different transportation methods like NWC, LCM, and VAM methods. The findings have significant implications for transportation planning and management, with an emphasis on the benefits of adopting sustainable transportation solutions to mitigate the adverse environmental impacts of transportation.
In the present paper, we study N(k)-contact metric manifolds with respect to semi-symmetric non-metric connection in which concircular curvature tensor is 𝜉−concircularly flat; also 𝜑−concircularly semisymmetric and concircularly pseudo symmetric.
This paper investigates several graphs that are absolute mean graceful graphs. We establish new results concerning absolute mean graceful graphs. The main objective of this work is to study the absolute mean graceful nature of various graph structure families. We present explicit labeling constructions to show that the eight-sprocket graph 𝑆𝐶𝑛, octopus graph 𝑂𝑛, flower pot graph 𝐹𝑃𝑛, triangular book graph 𝐵(3,𝑛), Kayak paddle graphs 𝐾𝑃(3,4,𝑛), armed crown graph 𝐴𝐶𝑛 and the corona product of the path graph 𝑃𝑛 and a complement of a complete graph 𝐾𝑚̅̅̅̅ (i.e.,𝑃𝑛⊙𝐾𝑚̅̅̅̅) admits an absolute mean graceful labeling.
The objective of this study is to develop a mathematical model to understand cancer progression driven by chronic inflammation. The model is formulated using a system of nonlinear ordinary differential equations incorporating tumor growth, inflammation, immune suppression, and vascular support. Analytical techniques, including equilibrium analysis and Jacobian- based stability analysis, are used to examine system behavior. The results indicate that chronic inflammation increases tumor growth by enhancing the effective growth rate and promoting immune suppression, which reduces immune response effectiveness. Stability analysis shows that the system attains a locally asymptotically stable equilibrium, indicating persistent cancer progression. The study concludes that cancer progression is sustained by feedback interactions between tumor growth, inflammation, and immune suppression. These findings highlight the importance of targeting both inflammation and immune mechanisms in cancer treatment strategies.
Domination is an important theoretical concept in graph theory. The fastest-growing area in graph theory is the study of domination and related problems. By [J, K] set domination, a subset D ⊆ V in a graph G = (V, E) is a [J, K] set if every vertex v ∈ V – D, J ≤ | N (v) ∩D | ≤ K, for non-negative integer J and K, that is every vertex v ∈ V – D is adjacent to at least J but not more than K vertices in D. The domination number of G is denoted by Ɣ[𝐽,𝐾] (G), which is the minimum cardinality of a dominating set G. In this paper, the [J, K]-domination number of Sunlet graphs, Helm graphs, and their applications has been studied.
Considering the breakthrough that happened recently in math, which established the condition for primality versus composite numbers, the decomposition of large numbers has been put to rest. To fully comprehend factorization of integers, this paper presents this issue with regard to the area of cryptography. A cryptosystem has two primary functions: to encipher, which means to prepare the message in a coding scheme, and to decipher the information, which means to decode the message. This decryption cannot be accomplished without knowledge of the secret deciphering key. For this reason, it is natural to look at an ancient problem of number theory, the problem of finding the complete factorization of a large composite integer whose prime factors are not known in advance. To reach this goal, an algebraic system is presented herein that is robust enough to handle large numbers. This system will encompass all that we know about algebraic properties, including the integration of some known theories of integers (e.g., lattice points representation). Parametric representation of curves as single points is necessary because these curves, after analysis, will be a piece of information toward the limit of the function f. A pattern will be established using the gap between a point on the rational plane and a point on the irrational plane. In doing so, it will be proven that the curves under study converge to the curve that holds the key to factorization. A demo is available that will perform the principle of factorization in nlogn complexity (i.e., the length of the input of integers versus the running time of the output of the function). This is called the time complexity of the algorithm, and it will be shown, herein, that indeed it is nlogn complexity. This work is designed to answer related problems in the field of mathematics, such as trisecting angles in geometric figures, banking issues such as transfer of funds, and communication integrity. However, the strongest modern algorithms (quadratic sieve, elliptic-curve method, and number field sieve) have been unable to resolve any of these ten numbers. It can be stated that the current effective limit of systematic factoring is ~100 digits, but it is still instructive and rewarding to find factors of much larger numbers. This is where a sandwich could make a difference; where a triangulation can take place to control false readings in conjunction with backtracking, leveraging new computers and graphic abilities. This new math breakthrough that has occurred enables the capability of distinguishing prime numbers from composite numbers. Resolving the latter into its prime factors is the last hurdle that needs to be crossed.
This research paper examines how a change in temperature and variability in precipitation affects the seasonal water runoff of the Subarnarekha River in the Ranchi area. There was an analysis of hydro-meteorological data such as rainfall, temperature, and streamflow during a specific time period. Statistical techniques like the Mann-Kendall test and slope estimator of Sen were used to identify trends and the magnitude of change of climatic variables and river discharge in a nonparametric manner. Findings reveal that there is a strong upward trend in the temperature and variability in the pattern of precipitation, which directly affects seasonal river flow. The analysis indicates that the flow of the monsoon is still predominant, with dry season discharge exhibiting a decreasing trend. The research indicates that the variability of precipitation is a significant variable in regulating streamflow, but an increase in temperature leads to less water supply in increased evapotranspiration. The results highlight the vulnerability of the Subarnarekha River to climate change and stress the sustainability of water resources management in the area.
In this research article, we introduce and define a new specific instance of a trapezium, called Kashif’s Trapezium. The paper details the derivation of its slant height and the determination of two distinct values for its altitude (height). Also, present a new theorem proving that Kashif’s Trapezium is a cyclic quadrilateral. Moreover, the semi-perimeter of the trapezium is examined, where a novel characteristic is found.
