It is well known that balancing and Lucas-balancing numbers are expressed as determinants of suitable tridiagonal matrices. The aim of this paper is to express certain subsequences of balancing and Lucas-balancing numbers in terms of determinants of tridiagonal matrices. Using these tridiagonal matrices, a factorization of the balancing numbers is also derived.

The implementation of a load balancing policy on a continuous basis in a delay-limited distributed computing environment may not only drain the computational resources of each computational element (CE), but can also lead to an unnecessary exchange of loads between the CEs. This degrades the system performance, measured by the overall completion time of the total tasks in the system. Thus, for ...

Abstmcl-The implementation of a load balancing policy on a continuous basis in a delay-limited distributed computing environment may not only drain the computational resources of each computational element (CE), hut can also lead to an unnecessary exchange of loads between the CEs. This degrades the system performance, measured by the overall completion time of the total tasks in the system. Th...

As middleware-based distributed applications become more pervasive, the need to improve the scalability of these applications becomes increasingly important. One way to improve scalability is via load balancing. Earlier generations of middleware-based load balancing services were simplistic, however, since they focused on specific use-cases and environments, which made it hard to use these serv...

In dense Wi-Fi networks, achieving load balancing is critical to optimize network utilization and provide equitable consumption among the users. Traditional networks have issues in attaining effective balancing. Software-Defined Networking (SDN) has presented a viable solution by isolating data plane control plane, enabling more agile cost-effective networks. this paper we put forward an Adapti...

Vehicle manufacturers positioned electric vehicles (EVs) and hybrid (HEVs) as reliable, safe environmental friendly alternative to traditional fuel based vehicles. Charging EVs using renewable energy resources reduce greenhouse emissions. The Lithium-ion (Li-ion) batteries used in are susceptible failure due voltage imbalance when connected form a pack. Hence, it requires proper balancing syste...

Due to their simplicity and effectiveness, gossip-based membership protocols have become the method of choice for maintaining partial membership in large P2P systems. A variety of gossip-based membership protocols were proposed. Some were shown to be effective empirically, lacking analytic understanding of their properties. Others were analyzed under simplifying assumptions, such as lossless an...

the main objective of an extrusion die is flow balancing as an unbalanced flow causes a distorted product together with residual stress. in this paper a strategy is presented for flow balancing a u-shaped profile with different wall thicknesses. for this purpose, a choker bar is provided at thicker wall to locally restrict excessive flow passing through the thicker section. for optimal design s...

Balancing numbers n and balancers r are solutions of the Diophantine equation 1 + 2 + . . . + (n 1) = (n + 1) + (n + 2) + . . . + (n + r). It is well-known that if n is a balancing number, then 8n2 + 1 is a perfect square and its positive square root is called a Lucas-balancing number. In this paper, some new identities involving balancing and Lucas-balancing numbers are obtained. Some divisibi...