The parity of the Maslov index and the even cobordism category

We give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over the real numbers. We define an index two subcategory (the even subcategory) of a 3-dimensional cobordism category. The objects of the category are surfaces are equipped with Lagrangian subspaces of their real first homology. This generalizes a result of the first author where surfaces are equipped with Lagrangian subspaces of their rational first homology.Comment: 7 pages, minor change

Spin Zero Quantum Relativistic Particles in Einstein Universe

In this letter we have considered the eigenvalues and eigenfunctions of relativistic massless scalar particle which conformally coupled to the background of Einstein universe. We found the eigenvalues and eigenfunctions exactly.Comment: 4 pages, no figure, accepted for publication in International Journal of Theoretical Physic

A New Scheme for Minimizing Malicious Behavior of Mobile Nodes in Mobile Ad Hoc Networks

The performance of Mobile Ad hoc networks (MANET) depends on the cooperation of all active nodes. However, supporting a MANET is a cost-intensive activity for a mobile node. From a single mobile node perspective, the detection of routes as well as forwarding packets consume local CPU time, memory, network-bandwidth, and last but not least energy. We believe that this is one of the main factors that strongly motivate a mobile node to deny packet forwarding for others, while at the same time use their services to deliver its own data. This behavior of an independent mobile node is commonly known as misbehaving or selfishness. A vast amount of research has already been done for minimizing malicious behavior of mobile nodes. However, most of them focused on the methods/techniques/algorithms to remove such nodes from the MANET. We believe that the frequent elimination of such miss-behaving nodes never allowed a free and faster growth of MANET. This paper provides a critical analysis of the recent research wok and its impact on the overall performance of a MANET. In this paper, we clarify some of the misconceptions in the understating of selfishness and miss-behavior of nodes. Moreover, we propose a mathematical model that based on the time division technique to minimize the malicious behavior of mobile nodes by avoiding unnecessary elimination of bad nodes. Our proposed approach not only improves the resource sharing but also creates a consistent trust and cooperation (CTC) environment among the mobile nodes. The simulation results demonstrate the success of the proposed approach that significantly minimizes the malicious nodes and consequently maximizes the overall throughput of MANET than other well known schemes.Comment: 10 pages IEEE format, International Journal of Computer Science and Information Security, IJCSIS July 2009, ISSN 1947 5500, Impact Factor 0.42

Offline and online power aware resource allocation algorithms with migration and delay constraints

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In order to handle advanced mobile broadband services and Internet of Things (IoT), future Internet and 5G networks are expected to leverage the use of network virtualization, be much faster, have greater capacities, provide lower latencies, and significantly be power efficient than current mobile technologies. Therefore, this paper proposes three power aware algorithms for offline, online, and migration applications, solving the resource allocation problem within the frameworks of network function virtualization (NFV) environments in fractions of a second. The proposed algorithms target minimizing the total costs and power consumptions in the physical network through sufficiently allocating the least physical resources to host the demands of the virtual network services, and put into saving mode all other not utilized physical components. Simulations and evaluations of the offline algorithm compared to the state-of-art resulted on lower total costs by 32%. In addition to that, the online algorithm was tested through four different experiments, and the results argued that the overall power consumption of the physical network was highly dependent on the demands’ lifetimes, and the strictness of the required end-to-end delay. Regarding migrations during online, the results concluded that the proposed algorithms would be most effective when applied for maintenance and emergency conditions.Peer ReviewedPreprin