Current Applied Sciences

Abstract Let G be a finite group. The power graph of the group G, with notation P (G) is a graph such that it’s vertex set is the group G and two distinct elements x, y are adjacent if and only if x = yⁿ or y = xⁿ for some positive integer . In this note, we compute bounds of independence number of power graph of a cyclic group.

Abstract The inverted pendulum problem is an interesting equilibrium problem because the uncontrolled system is unstable and if the base does not move to maintain the vertical position, the pendulum will simply fall and its dynamics are also nonlinear. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) solution of the least squares' method. The Kalman filter supports the estimation of past, present, and even future states, and can perform the estimation well even when the exact nature of the modeled system is unknown. This paper aims to estimate the state of the system to optimize the state created by the base in the inverted pendulum problem model so that the pendulum remains in the upright state. The generated random noise signals are added to the real measurement data generated using the system dynamics and these data are used to estimate the system states using the Kalman filter and the extended Kalman filter. The results of these estimates are analyzed and compared.

Abstract Over recent decades, numerous methodologies have been developed to address the heterogeneity within populations. These methodologies vary in their application to both parametric and semi-parametric models, which are crucial for a broad spectrum of uses in reliability and survival analysis. Research indicates that mixture distributions serve as an effective approach to representing population heterogeneity. This study delves into geometric mixture models for survival functions (or distribution functions), exploring their inherent properties and features. We discuss various stochastic and distributional aspects of these mixtures. Additionally, we establish some conditions for stochastic comparisons based on the usual stochastic order, hazard rate order, and reversed hazard rate order. Furthermore, we integrate our findings with prominent semi-parametric models in reliability theory, including the additive hazard rate model, the proportional hazard rate model, the accelerated lifetime model, and the proportional reversed hazard rate model, which serve as foundational models in our geometric mixtures. To corroborate our findings, we will demonstrate numerical examples.

Abstract Fuzzy optimization techniques have proven to be highly effective in the field of optimization, particularly in scenarios where decision-making processes are complex and influenced by uncertainty. These methods address vagueness and ambiguity by leveraging the principles of fuzzy logic, making them applicable across various domains such as economics, engineering, healthcare, and environmental management. Optimization techniques are essential for enhancing performance and efficiency in numerous industries. Among these, fuzzy logic provides a robust framework for handling uncertainties and imprecision commonly encountered in real-world problems. In this paper, we explore fuzzy genetic algorithms as a solution to certain fuzzy optimization problems. We demonstrate that this approach yields a reliable approximation of solutions for such problems. Additionally, we illustrate the application of this algorithm in three key areas: maximum fuzzy flow, fuzzy regression, and fuzzy controller design. The foundation of fuzzy genetic algorithms lies in the discretization of interval-based fuzzy subsets. These algorithms offer an innovative way to generate approximate solutions for fuzzy optimization problems where variables are arbitrary fuzzy subsets of specific intervals. This makes them versatile and applicable to a wide range of challenges.

Abstract In IEEE 802.16 wireless metropolitan area networks, users can take their broadband connections with them as they move from one location to another with different speeds. Thus, providing seamless handovers and QoS (Quality-of-Service) is challenging, especially for mobile subscribers at vehicular speeds. On the other hand, time variability and unpredictability of the wireless channel may cause QoS degradation and handover losses for these users. This paper proposes a new downlink handover-based priority scheduling scheme for different scheduling services which is providing lossless handovers and QoS. Taking the power degradation rates into consideration that enables monitoring users' locations, speeds and accelerations, this scheme assigns higher priority to the users having higher probability performing handover in the near future. An AMC (Adaptive Modulation and Coding) scheme and a pre-selection method are also proposed for providing high system performance, i.e., higher system throughput and lower packet dropping rate. The analytical results show the efficiency of proposed scheme.

Abstract Cancer, as one of the leading causes of global mortality, requires novel therapeutic approaches with high efficiency and low side effects. In this regard, combining artificial intelligence (AI), particularly machine learning (ML), with nanocarbon materials such as carbon nanotubes and graphene has brought new hope. Hence, this review aims to investigate the role of ML in optimizing diagnosis, predicting treatment response, and designing smart nanocarriers based on nanocarbon. Nanotechnology and AI enable targeted drug delivery, photothermal therapy, and more accurate imaging. For example, carbon nanoparticles can deliver chemotherapy drugs directly to tumors, while ML predictive models analyze medical images to accurately assess a patient’s response to treatment and recommend the best course of action. This convergence of technologies has opened up new hopes for the fight against cancer. However, there are challenges, such as the potential toxicity of nanocarbons, the need for extensive clinical data to train ML models, and integrating these technologies into therapeutic systems. In the future, the development of smarter nanocarriers, aided by machine learning and further studies on the biocompatibility of nanocarbons, could lead to more personalized and effective therapies. In conclusion, the integration of ML and nanocarbons has the potential to revolutionize oncology, but interdisciplinary research and large-scale clinical trials are necessary to achieve practical application.