Analysis of Priority Queueing System with Working Breakdown,Vacation and Vacation Interruption under Random Environment

study priority queueing system consisting of working breakdown, repair, single vacation and vacation interruption. At a breakdown instant during the busy period, without stop the servie, the server provides service at slower rate for the current customer. After completion of priority service, depending on the environment, the server can choose type I or type II vacation. Both types of vacation are considered as a single vacation. On completion of type I vacation if the server finds thepriority queue is empty, he has the option to take type II vacation. During the type II vacation, when priority customers arrive the server has the option to interrupt the vacation. We use the established norm which is the corresponding steady state results for time dependent probability generating functions are obtained. Along with that, the expected waiting time for theexpected number of customers for both high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately

In-Dominating Number and Out-Dominating Number of Unidirectional Perfect Binary Trees

A diverging unidirectional perfect binary tree is a unidirectional perfect binary tree in which every internal node has exactly outdegree two and indegree 1 and all the leaf nodes are at the same level. A converging unidirectional perfect binary tree is a unidirectional perfect binary tree in which every internal node has exactly indegree two and outdegree 1 and all the leaf nodes are at the same level. In this paper, we study the out-domination number and in-domination number of the unidirectional perfect binary trees

Bulk queueing system with starting failure and single vacation

To analyze an M^([X])/G(a,b)/1 queue with starting failure, repair and single vacation. This type of queueing model has a wide range of applications in production/manufacturing systems. Important performance measures and stability conditions are obtained. Further, we discuss some particular cases. Finally, numerical results of the proposed model have been derived

A cryptographic technique applying Laplace Transform and Exponetial Function

Secured Information transformation from one person to another is very much essential in this world of internet. In electronic communications such as system security, smart card, mobile communications etc, the data are stored in the various applications used in them. While using all the applications, we give permission to access all the information. Cryptography is based on transformation of multiple rounds of transformation of messages in the form of plain text as input into encrypted text message. Through suitable mathematical technique, secrecy of the information is maintained. This paper proposes a Laplace and its inverse transform technique with a suitable function for encryption and decryption of a message

A Cryptographic Algorithm using Fuzzy Logic and Deck of Cards

Sharing of information in a secured manner is extremely essential in this world of internet technology. In recent times, many people come across situations wherein their personal data are being hacked by trespassers. These stolen data are used for many malpractices including theft of money. Many researchers involve themselves in finding a better path to overcome this difficulty. Cryptography plays a major role in bringing out a solution to rectify this issue. Mathematics provides a helping hand in most of the cryptographic techniques. It helps to secure data from hackers involved in the robbery of data. Fuzzy logic find its application in many field of research. This paper proposes a cryptographic technique which make use of fuzzy logic together with the help of deck of cards and its membership functional value

NOVEL CRYPTOGRAPHIC APPROACH BASED ON PDF AND CDF

Secret Information sharing is all time requirement in this internet world, especially in Electronic communications such as system security, smart card, mobile communications etc. Cryptography is based on transformation of multiple rounds of transformation of messages in the form of plain text as input into encrypted text message. Through suitable mathematical technique, secrecy of the information is maintained. Many researchers have shown their interest in making use of mathematical techniques in Cryptography. This paper proposes a cryptographic technique using PDF and CDF. In this, plain text message is transformed as cipher text using a single key is used for both encryption and decryption. Using this proposed method, the information is also shared in safe manner and an illustration is done

A study on fuzzy connectedness and fuzzy continuity in fuzyy topological spaces

Fuzzy connectedness and fuzzy continuity are important concepts in the field of fuzzy mathematics, and have been studied in various types of fuzzy spaces. In this review paper, we have explored several recent research articles that investigate these concepts in different types of fuzzy spaces, including intuitionistic fuzzy topological spaces, quasi-metric spaces, generalized metric spaces, generalized fuzzy topological spaces, intuitionistic fuzzy soft metric spaces, fuzzy normed linear spaces, fuzzy quasi-metric spaces, fuzzy metric spaces, and b-metric spaces. The methodology and results of each study vary based on the type of fuzzy space under consideration, but all papers aim to provide a better understanding of the properties and behavior of fuzzy connectedness and fuzzy continuity. Common theme across these articles includes the use of various types of fuzzy functions, fuzzy sets, and the extension of classical concepts to fuzzy spaces. This review paper provides a comprehensive overview of the recent advances in the study of fuzzy connectedness and fuzzy continuity, highlighting similarities and differences among the various types of fuzzy spaces and suggesting directions for future research

Chemically radiative dissipative MHD Casson nanofluid flow on a non-linear elongating stretched sheet with numerous slip and convective boundary conditions

The flow of a Casson nanofluid across a nonlinear stretching surface with a velocity slip and a convective boundary condition is investigated in this work in the magnetohydrodynamic (MHD) domain. This technique emphasizes a variety of effects, including chemical reaction, viscosity dissipation, and velocity ratio. In this study, Brownian motion and thermophoresis are also illustrated. It is assumed that suction exists while a magnetic field is uniform. The governing nonlinear partial differential equations are converted into a set of nonlinear ordinary differential equations using the required similarity transformations, and the Runge-Kutta-Fehlberg fourth-fifth method is then used to solve the system. The updated results are fairly similar to the earlier ones. The graphs and tables examine how various variables affect the speeds, temperatures, concentrations of substances, skin friction values, Sherwood numbers and Nusselt numbers

A critical Analysis of ChatGPT's Potential and Pitfallss for Business Use Cases

This literature review explores the impact of ChatGPT on businesses. ChatGPT has been widely adopted in various companies to generate content. This review examines the existing research on the benefits and drawbacks of ChatGPT in business settings, including its effect on business management and operations. Through an analysis of articles and academic literature, we evaluate the impact of ChatGPT on businesses and provide insights into its potential applications. The findings suggest that ChatGPT can significantly improve sales and production processes. Additionally, the review highlights the need for further research to address the limitations and challenges associated with ChatGPT. Overall, this literature review provides a comprehensive analysis of the impact of ChatGPT on businesses and highlights the opportunities and challenges associated with its adoption

Methods and Applications of ChatGPT in Software Development: A Literature Review

This research paper explores the use of language models in software development that has gained significant attention in recent years. One of the most popular models is ChatGPT, a large language model trained by OpenAI. ChatGPT has been applied in some of the software development tasks, like programming Numerical methods, code generation, solving programming bugs, code completion and even in practicing for computer science exam. This paper presents a systematic review of the literature on the application of ChatGPT in software development. The review covers 12 studies that use ChatGPT in some fields of software development. We evaluate their results and the offering for the field. Overall, the findings of this review offer significant contributions to the current understanding and future direction of using ChatGPT in the domain of software development