Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fer...We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat＇s method in classical computing. All these algorithms may be polynomial in the input size.展开更多
Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)...Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).展开更多
Emodin is a kind of anthraquiones with pharmaceutical activities.The solubilities of emodin in ethanol,1-octanol,and ethanol+1-octanol at different temperatures were measured using an analytical method.The solubility ...Emodin is a kind of anthraquiones with pharmaceutical activities.The solubilities of emodin in ethanol,1-octanol,and ethanol+1-octanol at different temperatures were measured using an analytical method.The solubility of emodin in these solvents increased with an increase in temperature.With the temperature deviating from room temperature,the dependence of the solubility of emodin on temperature became a lot more remarkable.The solubility of emodin in ethanol was more sensitive to temperature than that in 1-octanol.The solubility data of emodin in the same species of solvent at different temperatures was correlated with an empirical equation.The calculated results agreed with the experimental data well.展开更多
In this paper, we study the binary Goldbach problem in the set of the Piatetski-Shapiro primes. We obtain that for all most all large even integer n, the equationn = p1+p2, pi∈Pγi, i = 1, 2has solutions, where 0 &l...In this paper, we study the binary Goldbach problem in the set of the Piatetski-Shapiro primes. We obtain that for all most all large even integer n, the equationn = p1+p2, pi∈Pγi, i = 1, 2has solutions, where 0 < γ1,γ2 ≤ 1 are fixed real numbers, such that 73(1 - γ2) < 9, 73(1 - γ1) + 43(1 - γ2) < 9.展开更多
It is exciting that the gravitational wave has been confirmed, according to the announcement of LIGO. Perhaps, this is the time for physicists to fix the Einstein equation for the gravitational wave and the nonexisten...It is exciting that the gravitational wave has been confirmed, according to the announcement of LIGO. Perhaps, this is the time for physicists to fix the Einstein equation for the gravitational wave and the nonexistence of the dynamic solution. These two problems are inextricably related. As a first step, theorists should improve their pure mathematics beyond Einstein on non-linear mathematics and related physical considerations. Then, theoretically we must first show that the gravitational waves necessarily exist that Einstein was not certain. We find that the existence of gravitational waves is due to that the photons must have a gravitational wave component. Next, we must rectify the Einstein equation that has no gravitational wave solution which Einstein has recognized, and no dynamic solution that Einstein failed to see. However, it is very questionable that the measured gravitational waves are due to the black holes that can be definitely valid due to the long distance of the sources. Moreover, since the repulsive gravitation can also generate a gravitational wave, the problem of gravitational wave is actually far more complicated than we have known. A useful feature of the gravitational wave based on repulsive gravitation is that it can be easily generated on earth. Thus this can be a useful tool for communication because it can penetrate any medium.展开更多
For any fixed odd prime p, let N（p） denote the number of positive integer solutions （x, y） of the equation y^2 = px（x^2 ＋ 2）. In this paper, using some properties of binary quartic Diophantine equations, we pro...For any fixed odd prime p, let N（p） denote the number of positive integer solutions （x, y） of the equation y^2 = px（x^2 ＋ 2）. In this paper, using some properties of binary quartic Diophantine equations, we prove that ifp ≡ 5 or 7（mod 8）, then N（p） = 0; ifp ≡ 1（mod 8）, then N（p） 〈 1; if p〉 3 andp ≡ 3（rood 8）, then N（p） ≤ 2.展开更多
The origin and quality of groundwater in the Southeastern region （belongs to Southern Plain） were identified by using isotopic techniques and geochemical analysis. Groundwater samples were collected from 7 aquifers...The origin and quality of groundwater in the Southeastern region （belongs to Southern Plain） were identified by using isotopic techniques and geochemical analysis. Groundwater samples were collected from 7 aquifers： the Holocene, upper Pleistocene, middle Pleistocene, lower Pleistocene, upper Pliocene, middle Pliocene and Miocene aquifers. The water isotopic compositions （82H and 8180） were determined to elucidate the origin and the interaction between surface water and groundwater studies. Transit time （age） of the groundwater samples was determined to explain the direction of groundwater flow. The dating techniques included 3H and ^14C isotopes measurement, followed by a correction for the initial ^14C-activity by the ^13C-composition （^13C） in TDIC （Total Dissolved Inorganic Carbon）. Geochemical parameters of the groundwater samples were measured either directly in the field or in the laboratory. The results showed that the groundwater from the Holocene and upper Pleistocene aquifers was most recharged from the local meteorological and hydrological systems, including local precipitation, fiver and reservoirs. Thus, it has short transit time and its stable isotopic composition is spread around the local meteoric waterline and lines for rivers or reservoirs water. The groundwater in the deeper aquifers： middle and lower Pleistocene, and Neogene aquifers has old age up to 22.5 ka BP. Its water seems to be recharged from the areas with an altitude from 600 to 700 m higher to the Neogene deposit layer altitude. The groundwater in the SE SP （South-Eastern Southern Plain） region has a high quality. The water type is Na-Ca-Mg-HCO3 with low content of chloride and TDS （Total Dissolved Solids）. Calcite/dolomite and gypsum dissolution, organic matter decomposition and sequence of red-ox reactions proceeding through different electron acceptors sediment were controlled the chemistry of the groundwater in the study region.展开更多
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
文摘In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
基金The project supported by the 973 Program under Grant No. 2006CB921106, National Natural Science Foundation of China under Grant Nos. 10325521 and 60433050, and the Key Project 306020 and Science Research Fund of Doctoval Program of the Ministry of Education of China
文摘We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat＇s method in classical computing. All these algorithms may be polynomial in the input size.
文摘Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).
基金Supported by the National Natural Science Foundation of China （20406008）.
文摘Emodin is a kind of anthraquiones with pharmaceutical activities.The solubilities of emodin in ethanol,1-octanol,and ethanol+1-octanol at different temperatures were measured using an analytical method.The solubility of emodin in these solvents increased with an increase in temperature.With the temperature deviating from room temperature,the dependence of the solubility of emodin on temperature became a lot more remarkable.The solubility of emodin in ethanol was more sensitive to temperature than that in 1-octanol.The solubility data of emodin in the same species of solvent at different temperatures was correlated with an empirical equation.The calculated results agreed with the experimental data well.
基金Supported by the Foundation of Shandong Provincial Education Department(03F06)
文摘In this paper, we study the binary Goldbach problem in the set of the Piatetski-Shapiro primes. We obtain that for all most all large even integer n, the equationn = p1+p2, pi∈Pγi, i = 1, 2has solutions, where 0 < γ1,γ2 ≤ 1 are fixed real numbers, such that 73(1 - γ2) < 9, 73(1 - γ1) + 43(1 - γ2) < 9.
文摘It is exciting that the gravitational wave has been confirmed, according to the announcement of LIGO. Perhaps, this is the time for physicists to fix the Einstein equation for the gravitational wave and the nonexistence of the dynamic solution. These two problems are inextricably related. As a first step, theorists should improve their pure mathematics beyond Einstein on non-linear mathematics and related physical considerations. Then, theoretically we must first show that the gravitational waves necessarily exist that Einstein was not certain. We find that the existence of gravitational waves is due to that the photons must have a gravitational wave component. Next, we must rectify the Einstein equation that has no gravitational wave solution which Einstein has recognized, and no dynamic solution that Einstein failed to see. However, it is very questionable that the measured gravitational waves are due to the black holes that can be definitely valid due to the long distance of the sources. Moreover, since the repulsive gravitation can also generate a gravitational wave, the problem of gravitational wave is actually far more complicated than we have known. A useful feature of the gravitational wave based on repulsive gravitation is that it can be easily generated on earth. Thus this can be a useful tool for communication because it can penetrate any medium.
基金Foundation item： Supported by the Natural Science Foundation of Shaanxi Province（2009JM1006）
文摘For any fixed odd prime p, let N（p） denote the number of positive integer solutions （x, y） of the equation y^2 = px（x^2 ＋ 2）. In this paper, using some properties of binary quartic Diophantine equations, we prove that ifp ≡ 5 or 7（mod 8）, then N（p） = 0; ifp ≡ 1（mod 8）, then N（p） 〈 1; if p〉 3 andp ≡ 3（rood 8）, then N（p） ≤ 2.
文摘The origin and quality of groundwater in the Southeastern region （belongs to Southern Plain） were identified by using isotopic techniques and geochemical analysis. Groundwater samples were collected from 7 aquifers： the Holocene, upper Pleistocene, middle Pleistocene, lower Pleistocene, upper Pliocene, middle Pliocene and Miocene aquifers. The water isotopic compositions （82H and 8180） were determined to elucidate the origin and the interaction between surface water and groundwater studies. Transit time （age） of the groundwater samples was determined to explain the direction of groundwater flow. The dating techniques included 3H and ^14C isotopes measurement, followed by a correction for the initial ^14C-activity by the ^13C-composition （^13C） in TDIC （Total Dissolved Inorganic Carbon）. Geochemical parameters of the groundwater samples were measured either directly in the field or in the laboratory. The results showed that the groundwater from the Holocene and upper Pleistocene aquifers was most recharged from the local meteorological and hydrological systems, including local precipitation, fiver and reservoirs. Thus, it has short transit time and its stable isotopic composition is spread around the local meteoric waterline and lines for rivers or reservoirs water. The groundwater in the deeper aquifers： middle and lower Pleistocene, and Neogene aquifers has old age up to 22.5 ka BP. Its water seems to be recharged from the areas with an altitude from 600 to 700 m higher to the Neogene deposit layer altitude. The groundwater in the SE SP （South-Eastern Southern Plain） region has a high quality. The water type is Na-Ca-Mg-HCO3 with low content of chloride and TDS （Total Dissolved Solids）. Calcite/dolomite and gypsum dissolution, organic matter decomposition and sequence of red-ox reactions proceeding through different electron acceptors sediment were controlled the chemistry of the groundwater in the study region.
