Contemporary Mathematics最新文献

{"title":"Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type","authors":"Ahmed Salem, Rawia Babusail, Moustafa El-Shahed, M. Eloasli","doi":"10.37256/cm.4420232546","DOIUrl":"https://doi.org/10.37256/cm.4420232546","url":null,"abstract":"The purpose of this work is to look at the solution’s representation for the non-homogeneous fractional timedelay Cauchy problem of Hilfer type in terms of the cosine and sine fractional delayed matrices of two parameters. The solutions are determined using the constant variation approach. Following that, finite-time stability under moderate circumstances is examined. At last, an example is offered to show how the theoretical results may be used.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"4 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135273111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semi-analytical Approach to Nonlinear Partial Differential Equations Using Homotopy Analysis Technique (HAM)","authors":"Kiran Dhirawat, Ramakanta Meher","doi":"10.37256/cm.4420232467","DOIUrl":"https://doi.org/10.37256/cm.4420232467","url":null,"abstract":"This work considers a novel semi-analytical method named the homotopy analysis method (HAM) to study the nonlinear gas dynamic equation. The obtained HAM solution is validated by comparing it with the exact available solution and compared with the (Adomian decomposition method) ADM solution and numerical solution to test the efficiency of the proposed method. The efficiency of the proposed approach can be demonstrated numerically and graphically, and it is found to be in excellent agreement with the current approach.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"5 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135273934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Synergistic Optimization of Unit Commitment Using PSO and Random Search","authors":"Rajasekhar Vatambeti, P. K. Dhal","doi":"10.37256/cm.5120243638","DOIUrl":"https://doi.org/10.37256/cm.5120243638","url":null,"abstract":"Optimizing the order of thermal units for power generation plays a pivotal role in meeting load demand while minimizing fuel consumption. This paper introduces an enhanced hybrid method designed to schedule generating units with the simultaneous objectives of cost and emission reduction, which often pose a trade-off challenge. The hybrid approach integrates the parametric adaptation of particle swarm optimization (PSO) with the randomness of a random search algorithm. The introduction of intermediate variables enhances the performance of particles in the PSO framework, contributing to more effective optimization. To update the individual population's locations within the particle swarm optimization process, randomness is judiciously introduced using a random search method. To assess the potential of the proposed method, it is applied to the IEEE-39 bus system and a four-unit thermal system. The results obtained through the proposed approach are compared with those achieved by existing methods, demonstrating its effectiveness in achieving optimal solutions for the unit commitment problem.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135367017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Integration of the Higher Order Toda Lattice with a Self-Consistent Integral Type Source","authors":"Bazar Babajanov, Murod Ruzmetov","doi":"10.37256/cm.4420232391","DOIUrl":"https://doi.org/10.37256/cm.4420232391","url":null,"abstract":"This work presents an algorithm that uses the inverse scattering method to find a solution for the higher-order Toda lattice with a self-consistent source. The higher-order Toda lattice with an integral-type source is also a significant theoretical model belonging to very integrable systems. The problem is solved by applying the direct and inverse scattering methods to the discrete Sturm-Liouville operator, and the time dependence of the scattering data for this operator is attained. The solution to the problem is set up using the inverse scattering transform (IST) approach.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hilbert Space Decomposition Properties of Complex Functions and Their Applications","authors":"Myroslava I. Vovk, Petro Ya. Pukach, Volodymyr M. Dilnyi, Anatolij K. Prykarpatski","doi":"10.37256/cm.4420232386","DOIUrl":"https://doi.org/10.37256/cm.4420232386","url":null,"abstract":"We analyzed the classical problem of decomposing the Hilbert space of holomorphic functions, especially their splitting into the product or sum of domain-separated components. For the Bergman space of analytical functions, we obtained a special decomposition satisfying the assigned growth degree properties. Concerning a general Hilbert space of analytical functions on a connected domain, we studied its α-invariant decomposition and related ergodic consequences. As an interesting consequence, we obtained the decomposition theorem for an ergodic α-mapping on the Bergman space of holomorphic functions.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Approach for Energy-Efficient Container Migration by Using Gradient Descent Namib Beetle Optimization","authors":"Rukmini Satyanarayan","doi":"10.37256/cm.5120243085","DOIUrl":"https://doi.org/10.37256/cm.5120243085","url":null,"abstract":"Cloud services are increasingly available through containers due to their scalability, portability, and reliable deployment, particularly in microservices and smart vehicles. The scheduler component of cloud containers plays a crucial role in optimizing energy efficiency and minimizing costs due to the diversity of workloads and cloud resources. The growing demand for cloud services poses a challenge in terms of energy consumption. Optimizing energy consumption in servers is possible by utilizing live migration technology. This study aims to propose a hybrid model that facilitates the migration of containers from one server to another using Gradient Descent Namib Beetle Optimization (GNBO) algorithms, thereby reducing the energy consumption of cloud servers. The work is carried out through cloud simulation using Physical Machines (PM), Virtual Machines (VM), and Containers. Tasks are allocated to VMs in a round-robin manner. The Actor-Critic Neural Network (ACNN) is employed to predict the load of PMs, and overloading and underloading conditions are determined based on the load. The proposed GNBO hybrid optimization calculates the optimal solution considering predicted load, migration costs, resource utilization, energy consumption, and network bandwidth. This approach achieves a load of 0.177 MIPS, migration costs of 10.146 J, and optimizes energy consumption to 0.068 W.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak Contractions via λ-sequences","authors":"Collins Amburo Agyingi, Yaé Ulrich Gaba","doi":"10.37256/cm.4420232877","DOIUrl":"https://doi.org/10.37256/cm.4420232877","url":null,"abstract":"In this note, we discuss a common fixed point for a family of self-mapping defined on a metric-type space and satisfying a weakly contractive condition. In our development, we make use of the λ-sequence approach and of a certain class of real-valued maps. We derive some implications for self-mappings on quasi-pseudometric type spaces.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Radial Distribution Systems by using Particle Swarm Optimization under Uncertain Conditions","authors":"M. Naveen Babu","doi":"10.37256/cm.5120243478","DOIUrl":"https://doi.org/10.37256/cm.5120243478","url":null,"abstract":"Abstract: Losses in the network are one of the most important parts of a power distribution network, and work should be done to lower their value. The research used the Particle Swarm Optimisation (PSO) metaheuristic algorithm to investigate the impact of concurrently optimising phase balance and conductor size on the planning issues and objective functions of an imbalanced distribution system. These objective functions include power loss, voltage unbalance, total neutral current, and complicated power unbalance. Firstly, the optimisation process is applied to each goal function. Then, they are put together with weights to form a multi-objective optimisation problem. In this study, it was tried to find out how to minimise losses in electrical power distribution networks that aren't fair. Power flow and optimal DG placement are two PSO techniques that may be used to reduce losses. These changes may be applied to existing distribution systems using an effective load-flow method for a three-phase imbalanced radial distribution network. Knowing the node voltage, angle, branch current, actual power loss, wattles power loss, branch losses, etc. helps determine the network's true state. Simple formulae may be used to describe the relationship between the voltage at one end of the distribution system, the voltage at the other end, and the voltage drops throughout the whole system. An approach is developed to identify the relevant variables. The voltage's angle at the target is calculated with its magnitude. It's a process that requires time and effort. From the substation to each terminal node, the constant voltage of 1p.u. is considered. Voltage magnitude and phase angle are varied between repetitions, and voltage reductions are computed using the new parameters. The suggested approach has been applied to 19- and 25-node networks with unequal distribution. To demonstrate its efficacy, the recommended approach's speed requirements were compared to those of another recently developed technology. Good outcomes are achieved, and DG proves to be a viable option for reducing costs and improving performance.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135667479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ML-Based Approach to Predict Carotid Arterial Blood Flow Dynamics","authors":"T Raja Rani, Abdullah Al Shibli, Mohamed Siraj, Woshan Srimal, Nooh Zayid Suwaid Al Bakri, T S L Radhika","doi":"10.37256/cm.5120243224","DOIUrl":"https://doi.org/10.37256/cm.5120243224","url":null,"abstract":"In the current study, a numerical model has been developed to simulate the blood flow characteristics in the human carotid artery. The data thus generated is analyzed to understand the blood flow variations and predict the flow characteristics using Machine Learning techniques. In developing the numerical model, the key features of the system, namely, the blood, is modeled as an incompressible Newtonian fluid, and the artery is an elastic pipe. This model is simulated using COMSOL software by varying the material properties of the artery. Univariate analysis was performed to gain insight into the features' behaviour and target variables. Subsequently, machine-learning regression models were trained using the data generated from the idealized human carotid artery. Furthermore, the validity of the data was ensured by comparing it with flow division ratios available in the literature. The evaluation of these models was conducted by calculating the Mean Absolute Error values for the test dataset, resulting in the following values: polynomial regressor (0.0106), hyper-tuned support vector regressor (0.0487), decision tree regressor (0.000), random forest regressor (0.0156), Adaboost (0.0508), gradient-boosting (0.0044), and XGboost (0.0043). A quantile loss function was employed to assess the prediction uncertainty. According to the theory of loss function, models with low loss values are considered good predictors. The prediction uncertainty was measured by applying quantile loss function, and it identified that the random forest regressor as the best predictor model for the data, followed by the polynomial regression of degree 3. Prediction intervals for the target variable were computed by leveraging the random forest quantile regressor model. Moreover, the developed polynomial model was utilized to investigate the presence of stenosis in the artery.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135995307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of Blood Viscosity Variation on the Flow of Blood in an Artery Having Time Dependent Stenosis","authors":"Lovely Jain, Mansi Kushwaha","doi":"10.37256/cm.4420232585","DOIUrl":"https://doi.org/10.37256/cm.4420232585","url":null,"abstract":"The aim of this paper is to examine the impact of blood viscosity variation on the flow of blood in a diseased artery having time-dependent stenosis. The viscosity of blood is axial co-ordinate dependent so that the viscosity of the blood increases up to the highest point of stenosis in the whole artery after which it decreases. Analytical methods have been used to explore the problem. The equations of volumetric rate of flow, resistance to flow, wall shear stress, and axial velocity have been obtained. It is noticed that as stenosis height increases, the resistance to flow and the wall shear stress increases. Also, investigation has been done to investigate how the wall sheer stress and flow resistance vary with different time-related parameters and varying viscosity index values.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}