This review synthesizes the state of the art in multiple switching synchronization for chaotic and complex dynamical systems. We formalize the concept, contrast it with single switching and continuous coupling, and survey stability tools including common and multiple Lyapunov functions, average dwell-time, and sliding/adaptive control under switching. Variants such as complete, lag, generalized, projective, intermittent, and fractional-order multiple switching synchronization are compared. We summarize applications in secure communications, power and energy systems, neural dynamics, robotics and multi-agent systems, and outline open problems regarding robustness, implementation, and data-driven switching policies. The article aims to provide a self-contained reference for researchers and practitioners.
Casson hybrid nanofluidover an exponentially accelerated vertical porous surface has been considered. Under the influence of slip velocity in a rotating frame, it takes Hall and ion slip impacts into account. Water and ethylene glycol mixture is considered a base Casson fluid. A steady uniform magnetic field is applied under the postulation of a low magnetic Reynolds number. The ramped temperature and time-altering concentration at the surface are considered. First-order consistent chemical reaction and heat absorption are also regarded. Rotating disks involving chemical reactions find extensive applications in the medical field, particularly in optimizing chemical processes for controlled drug delivery systems, thereby improving precision in therapeutic treatments. In this study, we elucidate the behavior of fluid flow over a rotating disk with Casson ternary hybrid nanofluid with incorporation of chemical reactions. Thus, a similarity transformation approach was employed, converting the boundary layer equations into similarity equations represented as ordinary differential equations. Subsequently, the bvp4c solver in MATLAB is utilized to numerically solve the set of non-linear ordinary differential equations describing the boundary value problem. The graphical representations scrutinize the effects of physical parameters on the significant flow characteristics. The expression for non-dimensional shear stress, heat transfer rate and mass transfer are also evaluated. They are tabulated with different variations in implanted parameters.
We have considered heat and mass transfer on the MHD free convection flow of second grade fluid through porous medium bounded by an infinite vertical porous rotating plate taking hall current into account. The analytical solutions for the governing equations are found by utilization of Laplace transformation methodology. The velocity, temperature and concentration is analysed graphically, and computational results for the skin friction, and Sherwood number are also obtained.
Data security and confidentiality in cryptography depend on mathematical foundations for its implementation. The examination of cryptographic methods throughout this document explains the role of number theory in RSA and elliptic curve algebra in ECC and finite field arithmetic in AES. This research explores two post-quantum cryptographic techniques that employ lattice-based systems and multivariate polynomial systems for their quantum attack defenses. The assessment investigates how statistical and probabilistic techniques operate in cryptanalysis and shows the difficulties of finding an appropriate balance between computational depth and system efficiency. Future studies need to prioritize two aims: establishing quantum-resistant cryptographics along enhancing mathematical security demonstrations while maximizing the efficiency of cryptographic systems.
In the era of rapidly evolving pedagogical methods, gamification and game-based learning have emerged as innovative strategies to enhance student engagement and academic achievement. This study investigates the effectiveness of card games as a pedagogical tool in improving the learning outcomes of secondary-level students in biology, specifically focusing on the topic "The Fundamental Unit of Life – Cell." A quasi-experimental design was adopted, involving 65 Class IX students from a school in Surat, Gujarat. Pre-test and post-test achievement scores were analyzed using t-test, revealing a statistically significant improvement in the experimental group's performance. Additionally, qualitative data from observation schedules and feedback forms underscored the development of key 21st-century skills such as communication, collaboration, critical thinking, and Conceptual correlation. The card game, composed of 52 cards with pairing mechanisms based on biological terminologies and diagrams, not only facilitated conceptual clarity but also fostered student motivation and curiosity towards science learning. The results suggest that integrating card games into the science curriculum is an effective and enjoyable strategy to reinforce complex biological concepts, promote peer learning, and enhance academic performance. This study highlights the potential of gamified instructional strategies to transform science education and recommends broader implementation for improved student engagement and learning outcomes in STEAM disciplines.
The COVID-19 pandemic has underscored the critical importance of understanding how social awareness and vaccination influence the spread and control of infectious diseases. This study presents a comprehensive mathematical simulation model that investigates the combined effects of social awareness initiatives and vaccination campaigns on the dynamics of COVID-19 transmission. By integrating epidemiological parameters with behavioral factors, the model captures how increased public awareness—through education, media, and policy measures—affects individuals’ preventive behaviors such as social distancing, mask-wearing, and acceptance of vaccination. The simulation explores various scenarios reflecting different levels of social responsiveness and vaccine coverage, analyzing their impact on key outcomes such as infection rates, hospitalization, and mortality over time. Results demonstrate that higher social awareness significantly amplifies the effectiveness of vaccination programs, reducing disease transmission more rapidly and preventing potential resurgence. Moreover, the model highlights critical thresholds for vaccination rates required to achieve herd immunity, especially when combined with sustained public health messaging and adherence to preventive measures. This integrated approach underscores the need for coordinated strategies that simultaneously promote social awareness and maximize vaccination uptake to effectively mitigate the pandemic. The findings offer valuable insights for policymakers and health authorities to optimize intervention strategies, emphasizing that vaccination alone is insufficient without strong public engagement and awareness to control COVID-19’s spread in the community.
This article explores the mathematical concept of representing positive integers as sums of distinct odd prime numbers. The focus is on understanding the unique combinations and properties that arise when expressing numbers through this framework. Utilizing advanced combinatorial techniques and number theory principles, the study provides a comprehensive analysis of the conditions under which such representations are possible. We delve into the role of prime gaps, the frequency of prime numbers, and their influence on the sum decompositions of integers. Several novel findings are presented, including a set of criteria for determining the representability of specific classes of numbers. The implications of this research extend to cryptographic applications and the optimization of algorithms related to prime number theory. This study not only deepens the theoretical understanding of prime sums but also offers new insights into the structural properties of numbers in the context of discrete mathematics.
This study provides a national profile of major work safety accidents in Malaysia, There have been many major incidents over the years, causing the loss of hundreds of lives. We intended to provide scientific basis for prevention measures and strategies to reduce major work safety accidents and deaths.1, 2 Methods: This is one of the shocking accident in Malaysia beside the “the highland tower collapse”. It remembered us that the project costing millions of dollar does not guarantee safety to the public as long we do not adopt the entire security before starting construction, Data from 2008-2015 Census of major work safety accidents were collected International Business Times. We analyzed the frequency of accidents and deaths, caused by insufficient safety measures. Additionally, we discussed the causes and prevention by types of accidents.2 Results: Throughout this case study the cause of the roof collapse was a failure on all levels of the project from the owner to the designer and to the contractor? The answer to this question lies in the structural design, construction and Safety measures of the building.3 Conclusion: Fifteen years’ major work safety accident data indicate that the frequency of accidents and number of deaths was declined and several safety concerns persist in some segments.3, 4
In this paper we introduced and studies the concepts of independent domination of bipolar fuzzy graph G, (γi(G)). And chromatic number χ (G) of bipolar fuzzy graph .We investigated the relationship of γi and χ with the other known parameters. Finally we give γi for same standard bipolar fuzzy graph
This paper introduces a new distribution named Exponential Modified Weibull logistic distribution. This distribution generalizes the following distributions: (1) Linear Failure Rate Logistic Distribution, (2) Weibull Logistic Distribution, (3) Rayleigh Logistic Distribution, (4) Exponential Logistic Distribution, where the failure rate, Weibull, Rayleigh and exponential distributions are the distributions most used for analyzing lifetime data. The properties of the new distribution are derived that include expressions for the rthmoment, characteristic function and quantile function. The estimation of model parameters are performed by the method of maximum likelihood and hence evaluation of the performance of maximum likelihood estimation using simulation.
The purpose of this research is to develop models for NFL football games which help identify the important factors in determining the outcome of the game. A variety of different methods will be used in developing these models: ordinary least squares regression, logistic regression, and proportional odds. Models will be used to explain an outcome and they will also be used to help predict an outcome based on differences of certain in-game statistics. Values from thirty-five in-game statistics for both teams playing in each game were collected for 752 NFL games over the three seasons between the years 2011 and 2014. Data from the first two seasons in this time period were used to develop the models and data from the last season was used to test the models. Data from these games was found on the websites, NFL Scores and Pro Football [1] and [2].
It is proved in this paper that (1) Fermat’s Last Theorem: If π is an odd prime, there are no relatively prime positive integers x,y,z satisfying the equation zπ = xπ+yπ, and (2) Beal’s Conjecture :The equation zξ = xµ +yν has no solution in relatively prime positive integers x,y,z with µ,ξ and ν odd primes at least 3. It is also proved that these two statements, (1) and (2), are equivalent.
This paper provides a new lifetime distribution model named as Compound Rayleigh Lifetime Distribution -I which is derived from Rayleigh distribution by imposing the restriction on the distribution of its parameter towards obtaining the properties of fine tuning manoeuvres and shift process in mean which is useful in reliability and statistical quality control analysis. The theoretical results obtained are illustrated with appropriate practical example.
Modified Adomian Decomposition Method (MADM) was used in this research to solve singular initial value problems in the second-order ordinary differential equation. In the beginning, we studied the genral equation, and we gave several illustrations for this equation. In addition, we studied some different cases of second order ordinary differential equations which we got from genral equation. From these cases, we got different types of equations such as multi singular initial value problems, like Bessel’s equation from half order and other equations as well. Using the examples under investigation, we conclude that the solution is converging towards the exact solution.
Incomplete Block Designs were introduced by Yates (1936) with a restriction on the block size that all treatments are not present in the blocks k < v, which are eliminating heterogeneity to a greater extent when the number of treatments is large. Several researchers made attempts on the existence and constructions of Incomplete Block Designs This paper presents a new series of construction of Balanced Incomplete Block Design using Partially Balanced incomplete Block Designs.
Mathematicians have been fascinated for centuries by the properties and patterns of numbers. They have noticed that some numbers are equal to the sum of all of their factors (not including the number itself). Such numbers are called perfect numbers. Thus a positive integer is called a perfect number if it is equal to the sum of its proper positive divisors. The search for perfect numbers began in ancient times. The four perfect numbers 6, 28, 496, and 8128 seem to have been known from ancient times. In this paper, we will investigate some important properties of perfect numbers. We give easy and simple proofs of theorems using finite series. We give our own alternative proof of the well-known Euclid’s Theorem (Theorem I). We will also prove some important theorems which play key roles in the mathematical theory of perfect numbers.
The methodological approach to solving the problems of optimal sharing of transboundary groundwater is determined as a result of mathematical modelling. Differential equation reproduces the confined-unconfined filtration of groundwater in the multi-stratified system as the basic approximation. Must be considered a single flow of underground waters, whose existence and properties depend on the areas of supply and discharge, which may be located in the territories of different countries. For regulation of transboundary water use the following criteria are suggested: quantitative estimation of ground and surface water depletion due to long time water discharge, calculation of extending time from contamination sources, identification of unknown location a possible source of contamination by groundwater flow velocity inversion. As an example, the results of modelling of cross-border flows underground in the territories Russia-Ukraine and Russia-Kazakhstan are given. The hydrodynamic math models have to be a subsystem of the total monitoring. Using such approach, both geological service and government authorities meet the real instrument for assessing and forecasting conditions of underground hydrosphere and efficient regulating of the anthropogenic load.
In this paper, we investigate the l-l Tranlativity Extended Abel Matrix. 2010 Mathematical Subject Classification: Primary 40A05, 40D99; Secondary 40C05
Because of their flexibility, recently, much attention has been given to the study of generalized distributions. A complete study of the transmuted Kumaraswamy Logistic distribution is proposed, introducing some basic properties of this distribution, such as quantile function, characteristic function and entropy are derived, as well as the derivation of maximum likelihood estimates of the parameters and the information matrix, Real life data is used as an application to this distribution with a comparison with other distributions to illustrate the flexibility and ability to model lifetime data. Also, a simulation study is conducted to demonstrate the effect of the sample on the estimates of the parameters.
The Mulatu numbers were studied [1] and [2]. The numbers are sequences of numbers of the form: 4,1, 5,6,11,17,28,45... The numbers have wonderful and amazing properties and patterns. In mathematical terms, the sequence of the Mulatu numbers is defined by the following recurrence relation: In [1] and [2] some properties and patterns of the numbers were considered. In this paper, we investigate additional properties and patterns of these fascinating numbers. Many beautiful mathematical identities involving the Mulatu numbers in relation with the two celebrity numbers of Fibonacci numbers and the Lucas numbers will be more explored. 2000 Mathematical Subject Classification: 11
