In this paper, we determine a single server retrial queuing system with finite capacity, F-policy, balking, reneging and server maintenance. The arriving customer when notices the server becomes free, then they get service immediately. In case server becomes busy, the customers are move to either orbit or may balk the system. In the orbit, after some random time the customer repeats their attempts for service. The customers are waiting in the orbit for longer time become impatient and leaves the orbit without getting service. Once the number of customers in the orbit reaches its full capacity then the arrival of customer is not allowed to enter into the orbit. The new customer is allowed into the orbit when the F-policy level is reached. If no more customer in the orbit, server will move to the vacation. By using recursive technique, the steady state distributions are obtained and we have developed various performance measures.
本文确定了一个具有有限容量、F 策略、逡巡、背弃和服务器维护的单服务器重试排队系统。当发现服务器空闲时，到达的客户会立即得到服务。如果服务器繁忙，客户会被转移到轨道或逡巡系统。在轨道上，经过一段时间后，客户会重复尝试服务。在轨道上等待时间较长的客户会变得不耐烦，并在没有得到服务的情况下离开轨道。一旦轨道中的客户数量达到饱和，就不允许新客户进入轨道。当达到 F 政策水平时，新客户将被允许进入轨道。如果轨道上不再有客户，服务器将转入休假状态。通过使用递归技术，我们获得了稳态分布，并制定了各种性能指标。
{"title":"Analysis of a Single Server Retrial Queueing System with Finite Capacity, F-Policy, Balking, Reneging and Server Maintenance","authors":"R. Jeyachandhiran, P. Rajendran","doi":"10.37256/cm.5120243745","DOIUrl":"https://doi.org/10.37256/cm.5120243745","url":null,"abstract":"In this paper, we determine a single server retrial queuing system with finite capacity, F-policy, balking, reneging and server maintenance. The arriving customer when notices the server becomes free, then they get service immediately. In case server becomes busy, the customers are move to either orbit or may balk the system. In the orbit, after some random time the customer repeats their attempts for service. The customers are waiting in the orbit for longer time become impatient and leaves the orbit without getting service. Once the number of customers in the orbit reaches its full capacity then the arrival of customer is not allowed to enter into the orbit. The new customer is allowed into the orbit when the F-policy level is reached. If no more customer in the orbit, server will move to the vacation. By using recursive technique, the steady state distributions are obtained and we have developed various performance measures.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139597762","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}
The object of this paper is to bring out the space rqB(g,p) of non-absolute patterns. Also, we will structure its completeness property. Also, the Köthe duals will be determined. Moreover, the Schauder basis for it will be constructed.
{"title":"On Some New Approach of Paranormed Spaces","authors":"Reham A. Alahmadi","doi":"10.37256/cm.5120242398","DOIUrl":"https://doi.org/10.37256/cm.5120242398","url":null,"abstract":"The object of this paper is to bring out the space rqB(g,p) of non-absolute patterns. Also, we will structure its completeness property. Also, the Köthe duals will be determined. Moreover, the Schauder basis for it will be constructed.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139601367","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}
The Kawahara equation is a fifth-order dispersive equation that plays a significant role in explaining the creation of non-linear water waves in the long-wavelength region. In this research, the Kawahara equation is solved numerically using the novel Haar scale-3 wavelet method in conjunction with the collocation method. The quasilinearisation approach and the Caputo derivative are used to characterise the non-linearity and fractional behaviour of the equation, respectively. To verify that the findings obtained are legitimate, residual and error estimates are generated. A thorough comparison is made between the present solutions and the numerical findings that have already been published in the literature, which demonstrates the advantages and effectiveness of the suggested technique. The Haar wavelet method reveals a dynamic system of alternative solutions for a wide variety of physical parameters.
{"title":"Numerical Investigation of Fractional Kawahara Equation via Haar Scale Wavelet Method","authors":"Ratesh Kumar, Jaya Gupta","doi":"10.37256/cm.5120242510","DOIUrl":"https://doi.org/10.37256/cm.5120242510","url":null,"abstract":"The Kawahara equation is a fifth-order dispersive equation that plays a significant role in explaining the creation of non-linear water waves in the long-wavelength region. In this research, the Kawahara equation is solved numerically using the novel Haar scale-3 wavelet method in conjunction with the collocation method. The quasilinearisation approach and the Caputo derivative are used to characterise the non-linearity and fractional behaviour of the equation, respectively. To verify that the findings obtained are legitimate, residual and error estimates are generated. A thorough comparison is made between the present solutions and the numerical findings that have already been published in the literature, which demonstrates the advantages and effectiveness of the suggested technique. The Haar wavelet method reveals a dynamic system of alternative solutions for a wide variety of physical parameters.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139600266","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}
In this article, a new inequality on Jain-Saraswat divergence measure is investigated for s-convex functions, which includes convex functions as a special case. Further, by using this inequality, some special results have also been derived in terms of the different divergences, at distinct values of s. Numerical verification of these results has also been discussed.
{"title":"A New Inequality on Jain-Saraswat' s Divergence for S-Convex Functions","authors":"P. Chhabra","doi":"10.37256/cm.5120243095","DOIUrl":"https://doi.org/10.37256/cm.5120243095","url":null,"abstract":"In this article, a new inequality on Jain-Saraswat divergence measure is investigated for s-convex functions, which includes convex functions as a special case. Further, by using this inequality, some special results have also been derived in terms of the different divergences, at distinct values of s. Numerical verification of these results has also been discussed.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139602280","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}
A modified Leslie-Gower plant-herbivore model is studied under the Allee effect. Holling-type II functional response is used to modify the model. Delay differential equations play an essential role in making this model more realistic and complicated. The non-trivial equilibrium E* (P* ≠ 0, H* ≠ 0) of the proposed model is calculated. Moreover, the stability and instability of the state variables, which include plant population P and herbivore population H are described graphically. It is shown that the system represents absolute stability when it has no time parameter (τ). When the time parameter is less than the threshold value, then the system exhibits asymptotic stability. In addition, the system surrenders its stability, and Hopf-bifurcation occurs when the time parameter surpasses the threshold value. The timeseries graphs are also represented. It is demonstrated that the system becomes more stable with the maximum rate of predation. MATLAB software is used to perform the graphs to justify the theoretical results.
在阿利效应下，研究了一个修正的莱斯利-高尔植物-食草动物模型。霍林 II 型功能响应被用来修改该模型。延迟微分方程在使这一模型更加现实和复杂方面发挥了重要作用。计算了所提出模型的非三维平衡 E* （P*≠0，H*≠0）。此外，还用图形描述了包括植物种群 P 和食草动物种群 H 在内的状态变量的稳定性和不稳定性。结果表明，当系统没有时间参数（τ）时，它表示绝对稳定。当时间参数小于临界值时，系统表现出渐近稳定性。此外，当时间参数超过阈值时，系统将失去稳定性，出现霍普夫分岔。同时还表示了时间序列图。结果表明，随着捕食率的最大化，系统变得更加稳定。使用 MATLAB 软件绘制图表，以证明理论结果的正确性。
{"title":"The Study of Stability Analysis of Modified Leslie-Gower Herbivore Model with Allee Effect in Plants","authors":"Pankaj Kumar, Rupali Verma","doi":"10.37256/cm.5120242502","DOIUrl":"https://doi.org/10.37256/cm.5120242502","url":null,"abstract":"A modified Leslie-Gower plant-herbivore model is studied under the Allee effect. Holling-type II functional response is used to modify the model. Delay differential equations play an essential role in making this model more realistic and complicated. The non-trivial equilibrium E* (P* ≠ 0, H* ≠ 0) of the proposed model is calculated. Moreover, the stability and instability of the state variables, which include plant population P and herbivore population H are described graphically. It is shown that the system represents absolute stability when it has no time parameter (τ). When the time parameter is less than the threshold value, then the system exhibits asymptotic stability. In addition, the system surrenders its stability, and Hopf-bifurcation occurs when the time parameter surpasses the threshold value. The timeseries graphs are also represented. It is demonstrated that the system becomes more stable with the maximum rate of predation. MATLAB software is used to perform the graphs to justify the theoretical results.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139604134","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}
Boolean functions play an important role in the design of secure cryptosystems and code division multiple access (CDMA) communication. Several possible generalizations of Boolean functions have been obtained in recent years. In this paper, we analyze the properties of functions from in terms of their Walsh-Hadamard transform (WHT). We provide a relationship between cross-correlation and the WHT of these functions. Also, we present a necessary and sufficient condition for the functions to have complementary autocorrelation. The Parseval’s identity for the current setup of these functions is obtained. Further, we obtained the modulus indicator (MI) and the sum-of-squares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.
{"title":"Two Indicators of Cross-Correlation for the Functions from Zqn to Z2q","authors":"Deep Singh, Harsh Mishra, Vitsoto Luho, Amit Paul","doi":"10.37256/cm.5120243489","DOIUrl":"https://doi.org/10.37256/cm.5120243489","url":null,"abstract":"Boolean functions play an important role in the design of secure cryptosystems and code division multiple access (CDMA) communication. Several possible generalizations of Boolean functions have been obtained in recent years. In this paper, we analyze the properties of functions from in terms of their Walsh-Hadamard transform (WHT). We provide a relationship between cross-correlation and the WHT of these functions. Also, we present a necessary and sufficient condition for the functions to have complementary autocorrelation. The Parseval’s identity for the current setup of these functions is obtained. Further, we obtained the modulus indicator (MI) and the sum-of-squares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139602596","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}
In the present study, we provide an efficient numerical approach for solving singularly perturbed nonlinear ordinary differential equations with two integral boundary conditions. We specifically propose a numerical approach for the solution of a nonlinear singular perturbed problem with integral boundary conditions. To solve the nonlinear singularly perturbed issue, we also apply finite difference methods. It explores how a specific derivative and a problemsolving approach behave. Finally, a numerical technique that employs a finite difference scheme is built using a nonuniform mesh.
{"title":"A Robust Numerical Method for a Singularly Perturbed Semilinear Problem with Integral Boundary Conditions","authors":"Zelal Temel, M. Çakir","doi":"10.37256/cm.5120243020","DOIUrl":"https://doi.org/10.37256/cm.5120243020","url":null,"abstract":"In the present study, we provide an efficient numerical approach for solving singularly perturbed nonlinear ordinary differential equations with two integral boundary conditions. We specifically propose a numerical approach for the solution of a nonlinear singular perturbed problem with integral boundary conditions. To solve the nonlinear singularly perturbed issue, we also apply finite difference methods. It explores how a specific derivative and a problemsolving approach behave. Finally, a numerical technique that employs a finite difference scheme is built using a nonuniform mesh.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139604672","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}
The conjugacy class graph of a group G is a graph whose vertices are the non-central conjugacy classes of G and two vertices are adjacent if their cardinalities are not co-prime. In this paper, conjugacy class graphs of Dn, Q4n, Sn are studied. These graphs are found to be either complete graphs or union of complete graphs. Conjugacy classes of Dn × Dm are calculated and the results obtained are used to determine the structure of conjugacy class graphs of Dn × Dm, for odd and even values of m and n. Conjugacy class graphs of Dn are non-planar for n = 8 and n ≥ 11. They are non-hyperenergetic for all n and hypoenergetic only for n = 3, 5. Also, line graphs of these graphs are regular and eulerian for n ≡ 1 (mod 2) and n ≡ 0 (mod 4). The conjugacy class graphs of Q4n are non-planar for n = 4 and n ≥ 6. These graphs are non-hyperenergetic as well as non-hypoenergetic. The line graphs are eulerian for even values of n. It is conjectured that conjugacy class graph of Sn is non-planar for n ≥ 5.
群 G 的共轭类图是一个图，其顶点是 G 的非中心共轭类，如果两个顶点的心数不为同素，则这两个顶点相邻。本文研究了 Dn、Q4n、Sn 的共轭类图。发现这些图要么是完全图，要么是完全图的联合。本文计算了 Dn × Dm 的共轭类图，并根据计算结果确定了 m 和 n 的奇数值和偶数值时 Dn × Dm 的共轭类图的结构。对于所有 n，它们都是非能动的，只有 n = 3、5 时才是低能动的。此外，对于 n ≡ 1（模 2）和 n ≡ 0（模 4），这些图形的线图是规则的、优等的。在 n = 4 和 n ≥ 6 时，Q4n 的共轭类图是非平面图。这些图形既是非超能量图形，也是非低能量图形。猜想 Sn 的共轭类图在 n ≥ 5 时是非平面的。
{"title":"Conjugacy Class Graph of Some Non-Abelian Groups","authors":"Chinmayee Kumar, Kuntala Patra","doi":"10.37256/cm.5120243875","DOIUrl":"https://doi.org/10.37256/cm.5120243875","url":null,"abstract":"The conjugacy class graph of a group G is a graph whose vertices are the non-central conjugacy classes of G and two vertices are adjacent if their cardinalities are not co-prime. In this paper, conjugacy class graphs of Dn, Q4n, Sn are studied. These graphs are found to be either complete graphs or union of complete graphs. Conjugacy classes of Dn × Dm are calculated and the results obtained are used to determine the structure of conjugacy class graphs of Dn × Dm, for odd and even values of m and n. Conjugacy class graphs of Dn are non-planar for n = 8 and n ≥ 11. They are non-hyperenergetic for all n and hypoenergetic only for n = 3, 5. Also, line graphs of these graphs are regular and eulerian for n ≡ 1 (mod 2) and n ≡ 0 (mod 4). The conjugacy class graphs of Q4n are non-planar for n = 4 and n ≥ 6. These graphs are non-hyperenergetic as well as non-hypoenergetic. The line graphs are eulerian for even values of n. It is conjectured that conjugacy class graph of Sn is non-planar for n ≥ 5.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139603381","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}
This study examines the existence, uniqueness, and stability of nonlinear random impulsive integrodifferential equations with time-varying delays under sufficient conditions. Our study is based on the Leray-Schauder alternative fixed point theorem, Pachpatte’s inequality, and the Banach contraction principle. Besides, we generalize, extend, and develop some results for Kasinathan et al.
{"title":"Existence and Stability Results of Nonlinear Random Impulsive Integro-Differential Evolution Equations with Time-Varying Delays","authors":"Sahar M. A. Maqbol, R. S. Jain, B. S. Reddy","doi":"10.37256/cm.5120242512","DOIUrl":"https://doi.org/10.37256/cm.5120242512","url":null,"abstract":"This study examines the existence, uniqueness, and stability of nonlinear random impulsive integrodifferential equations with time-varying delays under sufficient conditions. Our study is based on the Leray-Schauder alternative fixed point theorem, Pachpatte’s inequality, and the Banach contraction principle. Besides, we generalize, extend, and develop some results for Kasinathan et al.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139607862","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}
Pranati Mishra, R. K. Dash, Deeapak Kumar Panda, Ashish, Bechoo Lal, N. S. Gupta
Reliability is a crucial performance metric for wireless sensor networks (WSNs) because it ensures network functionality even with degraded sensor nodes and wireless connections. Due to the limited availability of power resources associated with the sensor nodes, their efficacy is reduced. In addition, parameters such as the number of neighbours, packet success rate, packet size, and node capacity have a significant impact on how sensor nodes function. Similarly, inter-node distance and signal-to-noise ratio (SNR) have the greatest influence on the functioning of wireless communications in WSNs. Before evaluating the reliability of a WSN, therefore, the node and link reliability must be computed. This paper evaluates the reliability of sensor nodes by taking into account all of the parameters previously mentioned. In addition, the lifetime of each sensor node is estimated in terms of the fractional energy consumed for each wake-up operation and the transmission of packets, respectively. Using the inter-node distance and SNR values, each wireless link’s reliability is determined. Following this, a proposed algorithm evaluates the reliability of WSN by first enumerating all minimal paths between the sensor node and the base station and then converting these minimal paths into their sum-of-disjoint-product terms. Making use of a suitable example network, every step of the proposed method is illustrated. For evaluating the reliability of WSN, the proposed method is simulated in different environments. In addition, the influence of parameters such as inter-node distance, SNR, number of neighbours, packet success ratio, and time on the reliability values of WSN is portrayed and analysed.
{"title":"Reliability Evaluation of a Wireless Sensor Network in Terms of Network Delay and Transmission Probability for IoT Applications","authors":"Pranati Mishra, R. K. Dash, Deeapak Kumar Panda, Ashish, Bechoo Lal, N. S. Gupta","doi":"10.37256/cm.5120242906","DOIUrl":"https://doi.org/10.37256/cm.5120242906","url":null,"abstract":"Reliability is a crucial performance metric for wireless sensor networks (WSNs) because it ensures network functionality even with degraded sensor nodes and wireless connections. Due to the limited availability of power resources associated with the sensor nodes, their efficacy is reduced. In addition, parameters such as the number of neighbours, packet success rate, packet size, and node capacity have a significant impact on how sensor nodes function. Similarly, inter-node distance and signal-to-noise ratio (SNR) have the greatest influence on the functioning of wireless communications in WSNs. Before evaluating the reliability of a WSN, therefore, the node and link reliability must be computed. This paper evaluates the reliability of sensor nodes by taking into account all of the parameters previously mentioned. In addition, the lifetime of each sensor node is estimated in terms of the fractional energy consumed for each wake-up operation and the transmission of packets, respectively. Using the inter-node distance and SNR values, each wireless link’s reliability is determined. Following this, a proposed algorithm evaluates the reliability of WSN by first enumerating all minimal paths between the sensor node and the base station and then converting these minimal paths into their sum-of-disjoint-product terms. Making use of a suitable example network, every step of the proposed method is illustrated. For evaluating the reliability of WSN, the proposed method is simulated in different environments. In addition, the influence of parameters such as inter-node distance, SNR, number of neighbours, packet success ratio, and time on the reliability values of WSN is portrayed and analysed.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139606934","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}
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