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 ...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.展开更多
A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H...A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H_(1) and H2.The collection of all least common multiples of H_(1) and H2 is denoted by LCM(H_(1),H_(2))and the size of a least common multiple of H_(1) and H2 is denoted by lcm(H_(1),H_(2)).In this paper lcm(P_(4),□P_(m) P_(n)),lcm(P_(4),C_(m) □C_(n))and lcm(K_(1,3),K_(1,m)□ K_(1,n))aredetermined.展开更多
Let k be an arbitrary positive integer and f(x)a polynomial with integer coefficients.Associated to the least common multiple lcm0≤i≤k{f(n+i)}of any k+1 consecutive terms in the sequence{f(n)}_(n=1)^(∞),we define t...Let k be an arbitrary positive integer and f(x)a polynomial with integer coefficients.Associated to the least common multiple lcm0≤i≤k{f(n+i)}of any k+1 consecutive terms in the sequence{f(n)}_(n=1)^(∞),we define the arithmetic function G_(k,f)(n)to be∏_(i=0)^(k)|f(n+i)|/lcm0≤i≤k{f(n+i)}for all n∈N^(+)\Z_(k,f),where N^(+) is the set of positive integers and Z_(k,f):=∪_(j=0)^(k){n∈N^(+):f(n+j)=0}.When the degree of f(x)is 1 or 2,the periodicity of G_(k,f) were studied well by Hong and Qian.In 2020,Lin and Hong investigated the periodicity of G_(k,f) when f(x)=x^(3)+2.In this paper,we study the periodicity of G_(k,f) with f(x)=x^(3)+4.We show that G_(k,f) is a periodic arithmetic function and then determine the smallest period of G_(k,f).Furthermore,an asymptotic formula for loglcm0≤i≤k{(n+i)^(3)+4}is given as n goes to infinity.The proof of our result uses analytic and p-adic methods.展开更多
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...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.展开更多
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 cons...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.展开更多
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...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.展开更多
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...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.展开更多
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 resol...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.展开更多
文摘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.
文摘A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H_(1) and H2.The collection of all least common multiples of H_(1) and H2 is denoted by LCM(H_(1),H_(2))and the size of a least common multiple of H_(1) and H2 is denoted by lcm(H_(1),H_(2)).In this paper lcm(P_(4),□P_(m) P_(n)),lcm(P_(4),C_(m) □C_(n))and lcm(K_(1,3),K_(1,m)□ K_(1,n))aredetermined.
文摘Let k be an arbitrary positive integer and f(x)a polynomial with integer coefficients.Associated to the least common multiple lcm0≤i≤k{f(n+i)}of any k+1 consecutive terms in the sequence{f(n)}_(n=1)^(∞),we define the arithmetic function G_(k,f)(n)to be∏_(i=0)^(k)|f(n+i)|/lcm0≤i≤k{f(n+i)}for all n∈N^(+)\Z_(k,f),where N^(+) is the set of positive integers and Z_(k,f):=∪_(j=0)^(k){n∈N^(+):f(n+j)=0}.When the degree of f(x)is 1 or 2,the periodicity of G_(k,f) were studied well by Hong and Qian.In 2020,Lin and Hong investigated the periodicity of G_(k,f) when f(x)=x^(3)+2.In this paper,we study the periodicity of G_(k,f) with f(x)=x^(3)+4.We show that G_(k,f) is a periodic arithmetic function and then determine the smallest period of G_(k,f).Furthermore,an asymptotic formula for loglcm0≤i≤k{(n+i)^(3)+4}is given as n goes to infinity.The proof of our result uses analytic and p-adic methods.
基金supported by the National Natural Science Foundation of China(No.10971145)the Ph.D.Programs Foundation of Ministry of Education of China(No.20100181110073)the Science&Technology Program of Sichuan Province(No.2013JY0125)
文摘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.
基金This project was supported by the National Defense I mportant Research Foundation of China(03413070506)
文摘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.
基金Supported partially by the National Natural Science Foundation of China(11501387)Key Program of Universities of Henan Province of China(17A110010)+1 种基金China Postdoctoral Science Foundation Funded Project(2016M602251)the Natural Science Foundation of Henan Province(162300410076)
文摘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.
文摘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.
基金supported by the Joint Fund for Fostering Talents of National Natural Science Foundation of China and Henan Province(Grant No.U1304618)the Open Fund of Key Laboratory of Precision Navigation and Timing Technology of Chinese Academy of Sciences(Grant No.2012PNTT01)+4 种基金the Postdoctoral Grant of China(Grant Nos.2011M501446,2012T50798)the Basic and Advanced Technology Research Foundation of Henan Province(Grant No.122300410169)The Key Science and Technology Foundation of Zhengzhou City(Grant Nos.131PPTGG411-6,131PCXTD594)the Doctor Fund of Zhengzhou University of Light Industry(Grant No.2011BSJJ031)the Fundamental Research Funds for the Central Universities(Grant No.K5051204003)
文摘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.
