Reflexive Incidence Matrx (RIM) Representation of Petr Nets

Although incidence matrix representation has been used to analyze the Petri net based models of a system, it has the limitation that it does not preserve reflexive properties (i.e., the presence of selfloops) of Petri nets. But in many practical applications self-loops play very important roles. This paper proposes a new representation scheme for general Petri nets. This scheme defines a matrix called "reflexive incidence matrix (RIM) c which is a combination of two matrices, a "base matrix Cb,,, and a "power matrix CP." This scheme preserves the reflexive and other properties of the Petri nets. Through a detailed analysis it is shown that the proposed scheme requires less memory space and less processing time for answering commonly encountered net queries compared to other schemes. Algorithms to generate the RIM from the given net description and to decompose RIM into input and output function matrices are also given. The proposed Petri net representation scheme is very useful to model and analyze the systems having shared resources, chemical processes, network protocols, etc., and to evaluate the performance of asynchronous concurrent systems.

Synthesis and Self-Assembly of Donor-Acceptor-Donor Based Oligothiophenes and Their Optoelectronic Properties

In this work, the synthesis of an oligothiophene having a donor acceptor donor (D-A-D) chromophore with hydrogen bonding groups is described. The D-A-D molecule was demonstrated to self-organize via intermolecular H-bonding between barbituric acid units. Interactions between the oligothiophene subunits were also found to be important, affording nanoribbons that could be observed by atomic force and transmission electron microscopy. The applicability of the oligothiophene for organic electronic applications was investigated by fabricating organic field-effect transistors (OFETs) and organic photovoltaic devices. The OFET measurements yielded p-type mobility of 7 x 10(-7) cm(2)/(Vs), and when blended with C(60)-PCBM, the photovoltaic efficiency was observed to be 0.18%.