Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, usi...Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, using a new result of Bilu, Hanrot and Voutier on primitive divisors, we proved that N 1(A,B,k)≤1 except N 1(1,-2,1)=5[n=1,2,3,5,13], N 1(1,-3,1)=3, N 1(1,-5,1)=3,N 1(1,B,1)=2(B{-2,-3,-5}), N 1(12,-55,1)=2, N 1(12,-377,1)=2, N 1(A,B,1)=2(A 2+B=±1, A>1), N 1(1,-2,3)=2, N 1(A,B,A)=2(A 2+2B=±1,A>1. For Lehmer sequence, we got a similar result. In addition, we also obtained some applications of the above results to some Diophantime equations.展开更多
Based on the degradation characteristics of municipal solid waste(MSW)in China,the traditional anaerobic sequencing batch bioreactor landfill(ASBRL)was optimized,and an improved anaerobic sequencing batch bioreactor l...Based on the degradation characteristics of municipal solid waste(MSW)in China,the traditional anaerobic sequencing batch bioreactor landfill(ASBRL)was optimized,and an improved anaerobic sequencing batch bioreactor landfill(IASBRL)was put forward on the basis of leachate self-recirculation.By monitoring MSW composition,leachate characteristics variation and landfill gas(LFG)generation,the effect of IASBRL was comparatively studied by simulation landfill.Based on the adjusting,scouring and carrying effects of leachate self-recirculation,IASBRL can rapidly decrease Eh value to about-500mV and form a suitable biochemical environment for methanogens,which provides a precondition for stable cooperation between non-methanogens and methanogens.IASBRL can avoid the accumulation of organic acids,make VFA(volatile fatty acid)concentration and CODCr decrease along with the small range fluctuations,and form a stable decomposition-consumption synergy during MSW degradation,therefore,the hydrolysis rate of easy hydrolyze material reaches 71.2% in IASBRL.From the viewpoint of LFG resources in IASBRL,the cumulative LFG production increases to 2327.0L,CH4 mass fraction stabilizes at about 50%,and these provide a favorable precondition for LFG development.展开更多
Since the high-voltage spinel LiNi0.5Mn1504 （LNMO） is one of the most attractive cathode materials for lithium-ion batteries, how to improve the cycling and rate performance simultaneously has become a critical ques...Since the high-voltage spinel LiNi0.5Mn1504 （LNMO） is one of the most attractive cathode materials for lithium-ion batteries, how to improve the cycling and rate performance simultaneously has become a critical question. Nanosizing is a typical strategy to achieve high rate capability due to drastically shortened Li- ion diffusion distances. However, the high surface area of nanosized particles increases the side reaction with the electrolyte, which leads to poor cycling performance. Spinels with disordered structures could also lead to improved rate capability, but the cyclability is low due to the presence of Mn3＋ ions. Herein, we systematically investigated the synergic interaction between particle size and cation ordering. Our results indicated that a microsized disordered phase and a nanosized ordered phase of LNMO materials exhibited the best combination of high rate capability and cycling performance.展开更多
This Paper gives a Fan’s type minimax theorem, a nearest point theorem and two existence theorems of solutions for a kind of generalized quasi-variational inequalities in H-spaces without any linear structure.
Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurrin...Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .展开更多
文摘Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, using a new result of Bilu, Hanrot and Voutier on primitive divisors, we proved that N 1(A,B,k)≤1 except N 1(1,-2,1)=5[n=1,2,3,5,13], N 1(1,-3,1)=3, N 1(1,-5,1)=3,N 1(1,B,1)=2(B{-2,-3,-5}), N 1(12,-55,1)=2, N 1(12,-377,1)=2, N 1(A,B,1)=2(A 2+B=±1, A>1), N 1(1,-2,3)=2, N 1(A,B,A)=2(A 2+2B=±1,A>1. For Lehmer sequence, we got a similar result. In addition, we also obtained some applications of the above results to some Diophantime equations.
基金Project(41072236)supported by the National Natural Science Foundation of ChinaProject supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,ChinaProject(2009A027)supported by Youth Research Foundation of China University of Mining and Technology
文摘Based on the degradation characteristics of municipal solid waste(MSW)in China,the traditional anaerobic sequencing batch bioreactor landfill(ASBRL)was optimized,and an improved anaerobic sequencing batch bioreactor landfill(IASBRL)was put forward on the basis of leachate self-recirculation.By monitoring MSW composition,leachate characteristics variation and landfill gas(LFG)generation,the effect of IASBRL was comparatively studied by simulation landfill.Based on the adjusting,scouring and carrying effects of leachate self-recirculation,IASBRL can rapidly decrease Eh value to about-500mV and form a suitable biochemical environment for methanogens,which provides a precondition for stable cooperation between non-methanogens and methanogens.IASBRL can avoid the accumulation of organic acids,make VFA(volatile fatty acid)concentration and CODCr decrease along with the small range fluctuations,and form a stable decomposition-consumption synergy during MSW degradation,therefore,the hydrolysis rate of easy hydrolyze material reaches 71.2% in IASBRL.From the viewpoint of LFG resources in IASBRL,the cumulative LFG production increases to 2327.0L,CH4 mass fraction stabilizes at about 50%,and these provide a favorable precondition for LFG development.
基金Acknowledgements This work was supported by programs of the National Basic Research Program （973 Program） of China （No. 2011CB935900）, the National Natural Science Foundation of China （Nos. 21231005 and 21076108）, and the Discipline Innovative Intelligence Plan （111 Project, No. B12015）.
文摘Since the high-voltage spinel LiNi0.5Mn1504 （LNMO） is one of the most attractive cathode materials for lithium-ion batteries, how to improve the cycling and rate performance simultaneously has become a critical question. Nanosizing is a typical strategy to achieve high rate capability due to drastically shortened Li- ion diffusion distances. However, the high surface area of nanosized particles increases the side reaction with the electrolyte, which leads to poor cycling performance. Spinels with disordered structures could also lead to improved rate capability, but the cyclability is low due to the presence of Mn3＋ ions. Herein, we systematically investigated the synergic interaction between particle size and cation ordering. Our results indicated that a microsized disordered phase and a nanosized ordered phase of LNMO materials exhibited the best combination of high rate capability and cycling performance.
基金the Foundation of the Technology Commission of Zhejiang Province, China.(No.19990500), the National Natural Science Foundation
文摘This Paper gives a Fan’s type minimax theorem, a nearest point theorem and two existence theorems of solutions for a kind of generalized quasi-variational inequalities in H-spaces without any linear structure.
基金supported by National Key Basic Research Program of China(973 Program)(Grant No.2013CB834204)National Natural Science Foundation of China(Grant Nos.61171082 and 10990011)
文摘Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .
