Independent sets of some graphs associated to commutative rings

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph. %An independent set with cardinality Let $R$ be a commutative ring with nonzero identity and $I$ an ideal of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is an undirected graph whose vertices are the nonzero zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. Also the ideal-based zero-divisor graph of $R$, denoted by $\Gamma_I(R)$, is the graph which vertices are the set {x\in R\backslash I | xy\in I \quad for some \quad y\in R\backslash I\} and two distinct vertices $x$ and $y$ are adjacent if and only if $xy \in I$. In this paper we study the independent sets and the independence number of $\Gamma(R)$ and $\Gamma_I(R)$.Comment: 27 pages. 22 figure

Improving Makespan in Dynamic Task Scheculing for Cloud Robotic Systems with Time Window Constraints

A scheduling method in a robotic network cloud system with minimal makespan is beneficial as the system can complete all the tasks assigned to it in the fastest way. Robotic network cloud systems can be translated into graphs where nodes represent hardware with independent computing power and edges represent data transmissions between nodes. Time-window constraints on tasks are a natural way to order tasks. The makespan is the maximum amount of time between when a node starts executing its first scheduled task and when all nodes have completed their last scheduled task. Load balancing allocation and scheduling ensures that the time between when the first node completes its scheduled tasks and when all other nodes complete their scheduled tasks is as short as possible. We propose a new load balancing algorithm for task allocation and scheduling with minimal makespan. We theoretically prove the correctness of the proposed algorithm and present simulations illustrating the obtained results.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Automotive can network response time analysis with variable jitter

Many methods to calculate message latencies for Controller Area Network (CAN) have previously been presented based upon the static worst-case behaviour of the system. With the use of modern simulation tools however, the behaviour of CAN networks can be simulated dynamically in order to find the likely worst-case response times for CAN messages. This paper shows the development of an automotive body control network model to be used as the basis for further simulations. A method to simulate the Worst-Case Response Time of this model is then presented, taking into account random queuing jitter.<br /

Study of Pseudo BL–Algebras in View of Left Boolean Lifting Property

In this paper, we define left Boolean lifting property (right Boolean lifting property) LBLP (RBLP) for pseudo BL–algebra which is the property that all Boolean elements can be lifted modulo every left filter (right filter) and next, we study pseudo BL-algebra with LBLP (RBLP). We show that Quasi local, local and hyper Archimedean pseudo BL–algebra that have LBLP (RBLP) has an interesting behavior in direct products. LBLP (RBLP) provides an important representation theorem for semi local and maximal pseudo BL–algebra

Optimal mapping of joint faults into healthy joint velocity space for fault-tolerant redundant manipulators

redundant manipulator

Evaluating the impact of VAT-free promotion:the role of loyalty program membership and category characteristics

This study examines the impact of value-added tax (VAT)-free promotions on sales performance. VAT-free promotions are a recently adopted form of price promotions where consumers are exempted from paying the VAT amount across almost all products in the assortment during a limited number of days. They are typically organized once per year and surrounded by a large amount of media attention from the involved retailer. To test the effects of this promotion on store and category sales, and investigate the differences between loyalty program (LP) members and non-LP members, the authors use scanner data from a Dutch durable goods retailer across a range of categories. The results show that VAT-free promotions positively impact store performance. Moreover, the findings indicate that more non-LP members are attracted to the store and that they increase the amount they spend in the store. While LP members also spend more in the store, this increase in shopping basket size does not compensate for the significant drop in the number of LP members that visit the store, leading to an overall decrease in sales coming from LP members during VAT-free days. We furthermore find that the positive effect of VAT-free promotions for non-LP members (rather than LP members) generalizes across all investigated categories. Our results provide key insights for retailers and direct marketers with regard to the effectiveness of VAT-free promotions in order to strategically segment the customer base