The “greatest lake period” means that the lakes are in the stage of their maximum areas. As the paleo lake shorelines are widely distributed in the lake basins on the Tibetan Plateau, the lake areas during the “gre...The “greatest lake period” means that the lakes are in the stage of their maximum areas. As the paleo lake shorelines are widely distributed in the lake basins on the Tibetan Plateau, the lake areas during the “greatest lake period” may be inferred by the last highest lake shorelines. They are several, even tens times larger than that at present. According to the analyses of tens of lakes on the Plateau, most dating data fell into the range of 40-25 ka BP, some lasted to 20 ka BP. It was corresponded to the stage 3 of marine isotope and interstitial of last glaciation. The occurrence of maximum areas of lakes marked the very humid period on the Plateau and was also related to the stronger summer monsoon during that period.展开更多
On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and cont...On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].展开更多
For nonlinear feedback shift registers （NFSRs）, their greatest common subfamily may be not unique. Given two NFSRs, the authors only consider the case that their greatest common subfamily exists and is unique. If th...For nonlinear feedback shift registers （NFSRs）, their greatest common subfamily may be not unique. Given two NFSRs, the authors only consider the case that their greatest common subfamily exists and is unique. If the greatest common subfamily is exactly the set of all sequences which can be generated by both of them, the authors can determine it by Grobner basis theory. Otherwise, the authors can determine it under some conditions and partly solve the problem.展开更多
Charles John Huffum Dickens(1812 k1870) was born in a poor petty-bourgeois family. His father was a clerk in the Navy Pay Office. When he was twelve, his father was heavily in debt and was
＂I have worked in ten countries as a reporter and been posted in two, China and Japan,＂ said Jonathan Watts, correspondent of The Guardian in Beijing. ＂I think China is the greatest place for journalists.＂
China has a population that is one-fifth of humanity. Most of its people live in rural areas. This country has been built and developed on the ruins of semi-colonialism and semi-feudalism and on a foundation of ＂pove...China has a population that is one-fifth of humanity. Most of its people live in rural areas. This country has been built and developed on the ruins of semi-colonialism and semi-feudalism and on a foundation of ＂poverty and blankness.＂ The founding of New China created the political condition for the advancement of people＇s democracy. Since the adoption of reform and open policies, or gaige kaifang, China has gradually found an effective way, suited for Chinese conditions,展开更多
In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this ...In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F<sub>0</sub>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1<s , witch is absurd. To reach such a result, we suppose first that (F<sub>0</sub>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F<sub>0</sub>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .展开更多
Let P（x） denote the greatest prime factor of ∏<sub>x【n≤x+x<sup>1/2</sup></sub>n. In this paper, we shall prove that P（x）】x<sup>0.728</sup>holds true for sufficiently large x.
Let P（x, y） denote the greatest prime factor of multiply from x<n≤x+y n. Ramachandra proved that P(x, x1/2)>x15/26 and P(x,x1/2)>x5/8（see J. London Math. Soc., 1（1969）, 303—306 and J. Indian Math. Soc....Let P（x, y） denote the greatest prime factor of multiply from x<n≤x+y n. Ramachandra proved that P(x, x1/2)>x15/26 and P(x,x1/2)>x5/8（see J. London Math. Soc., 1（1969）, 303—306 and J. Indian Math. Soc., 34（1970）, 39—48）. In 1981, Graham improved the exponent to 0.662（J. London Math. Soc., 24（1981）, 427—440）.展开更多
Periodicity is one of the most common phenomena in the physical world. The problem of periodicity analysis （or period detection） is a research topic in several areas, such as signal processing and data mining. Howev...Periodicity is one of the most common phenomena in the physical world. The problem of periodicity analysis （or period detection） is a research topic in several areas, such as signal processing and data mining. However, period detection is a very challenging problem, due to the sparsity and noisiness of observational datasets of periodic events. This paper focuses on the problem of period detection from sparse and noisy observational datasets. To solve the problem, a novel method based on the approximate greatest common divisor （AGCD） is proposed. The proposed method is robust to sparseness and noise, and is efficient. Moreover, unlike most existing methods, it does not need prior knowledge of the rough range of the period. To evaluate the accuracy and efficiency of the proposed method, comprehensive experiments on synthetic data are conducted. Experimental results show that our method can yield highly accurate results with small datasets, is more robust to sparseness and noise, and is less sensitive to the magnitude of period than compared methods.展开更多
In the short period of 70 years between 1949 and 2019, socialist China has lifted itself, through unwavering efforts, from economic and cultural destitution to become the worlds second largest economy, largest manufac...In the short period of 70 years between 1949 and 2019, socialist China has lifted itself, through unwavering efforts, from economic and cultural destitution to become the worlds second largest economy, largest manufacturing nation, largest trader of goods, second largest consumer of commodities, and second largest recipient of foreign investment. It has held the world5s largest foreign exchange reserves and contributed about 30% of global economic growth for many years running, while its GDP accounts for 15.2% of the global total.展开更多
How did you feel about being chosen as football's greatest player?You would never hear me say that,so I feel honored to be selected.I think it had to do with my work ethic and approach to the game.I always wanted ...How did you feel about being chosen as football's greatest player?You would never hear me say that,so I feel honored to be selected.I think it had to do with my work ethic and approach to the game.I always wanted to perform at my best.If I had just 11 catches for more than 100 yards,I wanted to come back next week and have a better game.展开更多
基金National Key Project for Basic Research, G19980408 CAS's Project (KZ951-A1-204, KZ95T-06) for Tibetan Research IGSNRR Project
文摘The “greatest lake period” means that the lakes are in the stage of their maximum areas. As the paleo lake shorelines are widely distributed in the lake basins on the Tibetan Plateau, the lake areas during the “greatest lake period” may be inferred by the last highest lake shorelines. They are several, even tens times larger than that at present. According to the analyses of tens of lakes on the Plateau, most dating data fell into the range of 40-25 ka BP, some lasted to 20 ka BP. It was corresponded to the stage 3 of marine isotope and interstitial of last glaciation. The occurrence of maximum areas of lakes marked the very humid period on the Plateau and was also related to the stronger summer monsoon during that period.
文摘On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].
基金supported by the Natural Science Foundation of China under Grant Nos.61272042,61100202and 61170235
文摘For nonlinear feedback shift registers （NFSRs）, their greatest common subfamily may be not unique. Given two NFSRs, the authors only consider the case that their greatest common subfamily exists and is unique. If the greatest common subfamily is exactly the set of all sequences which can be generated by both of them, the authors can determine it by Grobner basis theory. Otherwise, the authors can determine it under some conditions and partly solve the problem.
文摘Charles John Huffum Dickens(1812 k1870) was born in a poor petty-bourgeois family. His father was a clerk in the Navy Pay Office. When he was twelve, his father was heavily in debt and was
文摘＂I have worked in ten countries as a reporter and been posted in two, China and Japan,＂ said Jonathan Watts, correspondent of The Guardian in Beijing. ＂I think China is the greatest place for journalists.＂
文摘China has a population that is one-fifth of humanity. Most of its people live in rural areas. This country has been built and developed on the ruins of semi-colonialism and semi-feudalism and on a foundation of ＂poverty and blankness.＂ The founding of New China created the political condition for the advancement of people＇s democracy. Since the adoption of reform and open policies, or gaige kaifang, China has gradually found an effective way, suited for Chinese conditions,
文摘In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F<sub>0</sub>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1<s , witch is absurd. To reach such a result, we suppose first that (F<sub>0</sub>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F<sub>0</sub>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .
基金Project supported by the Tian Yuan Item in the National Natural Science Foundation of China.
文摘Let P（x） denote the greatest prime factor of ∏<sub>x【n≤x+x<sup>1/2</sup></sub>n. In this paper, we shall prove that P（x）】x<sup>0.728</sup>holds true for sufficiently large x.
文摘Let P（x, y） denote the greatest prime factor of multiply from x<n≤x+y n. Ramachandra proved that P(x, x1/2)>x15/26 and P(x,x1/2)>x5/8（see J. London Math. Soc., 1（1969）, 303—306 and J. Indian Math. Soc., 34（1970）, 39—48）. In 1981, Graham improved the exponent to 0.662（J. London Math. Soc., 24（1981）, 427—440）.
基金Project supported by the National Natural Science Foundation of China （No. 60673082）
文摘Periodicity is one of the most common phenomena in the physical world. The problem of periodicity analysis （or period detection） is a research topic in several areas, such as signal processing and data mining. However, period detection is a very challenging problem, due to the sparsity and noisiness of observational datasets of periodic events. This paper focuses on the problem of period detection from sparse and noisy observational datasets. To solve the problem, a novel method based on the approximate greatest common divisor （AGCD） is proposed. The proposed method is robust to sparseness and noise, and is efficient. Moreover, unlike most existing methods, it does not need prior knowledge of the rough range of the period. To evaluate the accuracy and efficiency of the proposed method, comprehensive experiments on synthetic data are conducted. Experimental results show that our method can yield highly accurate results with small datasets, is more robust to sparseness and noise, and is less sensitive to the magnitude of period than compared methods.
文摘In the short period of 70 years between 1949 and 2019, socialist China has lifted itself, through unwavering efforts, from economic and cultural destitution to become the worlds second largest economy, largest manufacturing nation, largest trader of goods, second largest consumer of commodities, and second largest recipient of foreign investment. It has held the world5s largest foreign exchange reserves and contributed about 30% of global economic growth for many years running, while its GDP accounts for 15.2% of the global total.
文摘How did you feel about being chosen as football's greatest player?You would never hear me say that,so I feel honored to be selected.I think it had to do with my work ethic and approach to the game.I always wanted to perform at my best.If I had just 11 catches for more than 100 yards,I wanted to come back next week and have a better game.
