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

Evaluation of Growth Yield of Spirulina maxima in Photobioreactors

The paper deals with the evaluation of the parameters for the cultivation of Spirulina maxima in two reactors (large-laboratory scale (LL) and semi-technical scale (ST)), whose illuminated areas in respect of the illuminated volume are different, and with the operating costs. We evaluated the growth yield coefficients for Spirulina maxima cultures. In the LL, the following factors were identified: YO2/X – 65.5; YX/CO2 – 0.0806; YX/P2O5 – 0.0082, while in the ST: YO2/X – 583; YX/CO2 – 0.017; YX/P2O5 – 0.0023. Although the reactor in the ST was equipped with many devices that should have improved the efficiency of cultivation, the obtained result was lower compared to the culture conducted in the LL. It was proved that it was possible to perform the cultivation of Spirulina maxima under temperate climate conditions in simply constructed, low cost reactors

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 /