Efficient Load Balancing with MANET Propagation of Least Common Multiple Routing and Fuzzy Logic

Mobile Ad Hoc Network(MANET)is a group of node that would interrelate among each other through onemulti-hop wireless link,wherein the nodes were able to move in response to sudden modifications.The objective of MANET routing protocol is to quantify the route and compute the best path,but there exists a major decrease in energy efficiency,difficulty in hop selection,cost estimation,and efficient load-balancing.In this paper,a novel least common multipath-based routing has been proposed.Multipath routing is used to find a multipath route from source and destination.Load balancing is of primary importance in the mobile ad-hoc networks,due to limited bandwidth among the nodes and the initiator of the load routing discovery phase in the multipath routing protocol.Fuzzy logic for load balancing multipath routing in MANETs is proposed,which ensures the data packets are sent through a path with the variance of binary sets to predict the original transformation of the data to be received in the system.The main objective of the proposed system is to reduce the routing time of data packets and avoid the traffic based on multipath source and destination.The experimental results have to verify 96.7%efficiency in balancing the load.

New Lower Bounds for the Least Common Multiples of Arithmetic Progressions

Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk ：= u0 ＋ kr. Let Ln ：= 1cm（u0,u1,... ,un） and let a,l≥2 be any integers. In this paper, the authors show that, for integers α≥ a, r ≥max（a,l - 1） and n ≥lατ, the following inequality holds Ln≥u0r^（l-1）α＋a-l（r＋1）^n.Particularly, letting l = 3 yields an improvement on the best previous lower bound on Ln obtained by Hong and Kominers in 2010.

Efficient structures for wideband digital receiver

Digital receivers have become more and more popular in radar, communication, and electric warfare for the advantages compared with their analog counterparts. But conventional digital receivers have been generally considered impractical for bandwidth greater than several hundreds MHz. To extend receiver bandwidth, decrease data rate and save hardware resources, three novel structures are proposed. They decimate the data stream prior to mixing and filtering, then process the multiple decimated streams in parallel at a lower rate. Consequently it is feasible to realize wideband receivers on the current ASIC devices. A design example and corresponding simulation results are demonstrated to evaluate the proposed structures.

On the Smarandache LCM Sequence

For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n^k),and give some interesting relevant results.

Phase group synchronization between any signals and its physical characteristics

The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the time&frequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.

Further Results on Generalized LCM Matrices

Let S={x_1,x_2,...,x_n } be a set of n distinct positive integers and f be an arithmetic function.By（f[S]）（resp.（ f[S]））,we denote the n＊n matrix whose i,j entry is Σ[x_i,x_j]｜l l∈S f（l） （resp.Σx∈Sf（x）-Σ x_i,｜l l∈S f（l）-Σ x_j,｜l l∈S f（l）＋Σ[x_i,x_j]｜l l∈S f（l））.In this paper,we first investigate the structures of the matrices （ f[S]） and（ f[S]）,then we give the formulae for the determinants of these matrices.These extend the results obtained by Bege in 2011.Finally,we give two examples to demonstrate the validity of our main results.