Future changes of heating degree days （HDD） and cooling degree days （CDD） in the 21st century with and without considering populationfactor are investigated based on four sets of climate change simulations over Ea...Future changes of heating degree days （HDD） and cooling degree days （CDD） in the 21st century with and without considering populationfactor are investigated based on four sets of climate change simulations over East Asia using the regional climate model version 4.4 （RegCM4.4）driven by the global models of CSIRO-Mk3-6-0, EC-EARTH, HadGEM2-ES, and MPI-ESM-MR. Under global warming of 1.5℃, 2℃, 3℃,and 4℃, significant decrease of HDD can be found over China without considering population factor, with greater decrease over high elevationand high latitude regions, including the Tibetan Plateau, the northern part of Northeast China, and Northwest China; while population-weightedHDD increased in areas where population will increase in the future, such as Beijing, Tianjin, parts of southern Hebei, northern Shandong andHenan provinces. Similarly, the CDD projections with and without considering population factor are largely different. Specifically, withoutconsidering population, increase of CDD were observed over most parts of China except the Tibetan Plateau where the CDD remained zerobecause of the cold climate even under global warming; while considering population factor, the future CDD decreases in South China andincreases in North China, the Sichuan Basin, and the southeastern coastal areas, which is directly related to the population changes. The differentfuture changes of HDD and CDD when considering and disregarding the effects of population show that population distribution plays animportant role in energy consumption, which should be considered in future research.展开更多
To determine the risk, malignant degree and clinical progression of prostate cancer （PCa） associated with mouse double-minute 2 protein （MDM2） T309G variants, a meta-analysis was performed on all eligible publishe...To determine the risk, malignant degree and clinical progression of prostate cancer （PCa） associated with mouse double-minute 2 protein （MDM2） T309G variants, a meta-analysis was performed on all eligible published studies. Odds ratios （ORs） with 95% confidence intervals （CIs） were estimated to assess these associations in seven studies that included 5151 cases and 1003 controls. In the overall analysis, the 309G allele was significantly associated with a decreased PCa risk （0R=0.85, 95% CI： 0.74-0.97）; this was also the case for the homozygous comparison （0R--0.72, 95% Ch 0.55-0.95） and the dominant genetic model （0R=0.79, 95% Ch 0.65-0.96）. The 309G allele was also found to be significantly associated with lower degrees of PCa malignancy （0R=0.85, 95% Ch 0.75-0.96） in the overall analysis, as well as in the heterozygous comparison （0R=0.79, 95% Ch 0.65-0.96）, homozygous comparison （0R=0.76, 95% Ch 0.58-0.98） and dominant genetic model （0R=0.81, 95% CI： 0.68-0.96）. Furthermore, grouping analysis showed that the 309G allele in Caucasians was significantly correlated with a decreased PCa risk （0R=0.77, 95% Ch 0.61-0.96）; this was also the case in the homozygous comparison （0R=0.51, 95% Ch 0.31-0.86）. The grouping analysis also showed that the 309G variant in Caucasians was significantly associated with a lower degree of PCa malignancy in all of the genetic models. In addition, we found that the 309G variant in Caucasians was significantly associated with a slower PCa clinical progression in all of the genetic models. In summary, our meta-analysis showed that the MDM2 309G variant was significantly associated with a decreased PCa risk, lower malignant degree and slower clinical progression in Caucasians, but there was no obvious association in the Asian population.展开更多
BACKGROUND Type 2 diabetes mellitus(T2DM)has high morbidity and mortality worldwide,therefore there is of paramount importance to identify the risk factors in the populations at risk early in the course of illness.A s...BACKGROUND Type 2 diabetes mellitus(T2DM)has high morbidity and mortality worldwide,therefore there is of paramount importance to identify the risk factors in the populations at risk early in the course of illness.A strong correlation between severity of metabolic syndrome(MetS)and HbA1c,fasting insulin and insulin resistance has been reported.Accordingly,the MetS severity score(or MestS Zscore)can potentially be used to predict the risk of T2DM progression over time.AIM To evaluate the association the of MestS Z-score in first degree relatives(FDRs)of T2DM with the risk of prediabetes and type 2 diabetes in future.METHODS A prospective open cohort study was conducted between 2003-2018.At baseline,the sample comprised of 1766 FDRs of patients with T2DM who had a normal glucose tolerance test.Relative risk(RR)and 95%confidence interval were calculated based on logistic regression.The receiver-operator characteristic analysis and area under the curve based on MetS Z-score were used to evaluate the risk of prediabetes and diabetes among the FDR population.RESULTS Baseline MetS Z-scores were associated with the its latest values(P<0.0001).Compared with individuals who were T2DM free at the end of follow up,those who developed T2DM had higher MetS Z-score at baseline(P<0.001).In multivariable logistic regression analyses for every unit elevation in MetS Z-score at the baseline,the RR for developing future T2DM and prediabetes was(RR=1.94,RR=3.84),(RR=1.5,RR=2.17)in total population and female group,respectively(P<0.05).The associations remained significant after adjusting the potential confounding variables.A cut off value of 0.97 and 0.94 was defined in the receiver-operator characteristic curve based on the MetS Z-score for differentiating female patients with diabetes and prediabetes from the normal population,respectively.CONCLUSION The MetS Z-score was associated with an increased risk of future T2DM.Appropriate interventions at earlier stages for preventing and attenuating MetS effects may be considered as an effective strategy for FDR as at-risk population.展开更多
In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to ...In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect.展开更多
AIM: To study the expression of cyclooxygenase-2 (COX-2)in human gastric cancer tissues and their paired adjacent mucosa, as well as mucosa from gastric antrum and corpus of the first-degree relatives of the recruited...AIM: To study the expression of cyclooxygenase-2 (COX-2)in human gastric cancer tissues and their paired adjacent mucosa, as well as mucosa from gastric antrum and corpus of the first-degree relatives of the recruited cancer patients.METHODS: The expression of COX-2 mRNA in 38 patients with gastric cancer and their 29 first-degree relatives and 18 healthy controls was assessed by the real time RT-PCR.The expression of COX-2 protein was determined by Western blot.RESULTS: A marked increase in COX-2 mRNA expression was found in 20 of 37 (54%) cancerous tissues compared to their respective paired normal mucosa (P＜0.001).Interestingly, increased COX-2 mRNA expression was also found in mucosa of the corpus (6/29) and antrum (13/29)of their first-degree relatives. Increased COX-2 mRNA expression was more frequently observed in the antrum biopsies from cancer patients than in the antrum biopsies from healthy controls (P＜0.05). In addition, 3 of 23 (13%)patients with atrophic mucosa and 6 of 35 (17%) patients with intestinal metaplasia showed increased COX-2 mRNA expression. Furthermore, COX-2 expression increased in H pylori-positive tissues, especially in antrum mucosa.CONCLUSION: Increased COX-2 expression is involved in gastric carcinogenesis, and may be necessary for maintenance of the malignant phenotype and contribute to Helicobacterpylori-associated malignant transformation.展开更多
Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ...Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .展开更多
The temperature-dependent Gilbert damping in Co2FeAl thin film grown on a Pb(Mg1/3Nb2/3)O3-30%PbTiO3 substrate is investigated by the systematic measurement of physical property measurement system(PPMS) on a series of...The temperature-dependent Gilbert damping in Co2FeAl thin film grown on a Pb(Mg1/3Nb2/3)O3-30%PbTiO3 substrate is investigated by the systematic measurement of physical property measurement system(PPMS) on a series of samples with different substrate temperatures. Varying the substrate temperatures from 350℃ to 500℃, the B2 ordering degrees of Co2FeAl thin films increase, which can lead the Gilbert damping to decrease, indicated by the field-sweep in-plane PPMS measurements. In addition, the measurement result of PPMS demonstrates that the Gilbert damping decreases first with measurement temperature decreasing down to about 150 K, then increases at a measurement temperature of ~ 50 K, and decreases again with the measurement temperature decreasing. There are two independent damping manners, namely bulk damping and surface damping, which contribute to the Gilbert damping. Moreover, the observed peak of Gilbert damping at ~ 50 K can be attributed to the spin re-orientation transition at the Co2FeAl surface, which is similar to the result of the effective magnetization as a function of measurement temperature. The result presents the evidence for further studying the Gilbert damping in Co2FeAl thin film.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
文摘Future changes of heating degree days （HDD） and cooling degree days （CDD） in the 21st century with and without considering populationfactor are investigated based on four sets of climate change simulations over East Asia using the regional climate model version 4.4 （RegCM4.4）driven by the global models of CSIRO-Mk3-6-0, EC-EARTH, HadGEM2-ES, and MPI-ESM-MR. Under global warming of 1.5℃, 2℃, 3℃,and 4℃, significant decrease of HDD can be found over China without considering population factor, with greater decrease over high elevationand high latitude regions, including the Tibetan Plateau, the northern part of Northeast China, and Northwest China; while population-weightedHDD increased in areas where population will increase in the future, such as Beijing, Tianjin, parts of southern Hebei, northern Shandong andHenan provinces. Similarly, the CDD projections with and without considering population factor are largely different. Specifically, withoutconsidering population, increase of CDD were observed over most parts of China except the Tibetan Plateau where the CDD remained zerobecause of the cold climate even under global warming; while considering population factor, the future CDD decreases in South China andincreases in North China, the Sichuan Basin, and the southeastern coastal areas, which is directly related to the population changes. The differentfuture changes of HDD and CDD when considering and disregarding the effects of population show that population distribution plays animportant role in energy consumption, which should be considered in future research.
文摘To determine the risk, malignant degree and clinical progression of prostate cancer （PCa） associated with mouse double-minute 2 protein （MDM2） T309G variants, a meta-analysis was performed on all eligible published studies. Odds ratios （ORs） with 95% confidence intervals （CIs） were estimated to assess these associations in seven studies that included 5151 cases and 1003 controls. In the overall analysis, the 309G allele was significantly associated with a decreased PCa risk （0R=0.85, 95% CI： 0.74-0.97）; this was also the case for the homozygous comparison （0R--0.72, 95% Ch 0.55-0.95） and the dominant genetic model （0R=0.79, 95% Ch 0.65-0.96）. The 309G allele was also found to be significantly associated with lower degrees of PCa malignancy （0R=0.85, 95% Ch 0.75-0.96） in the overall analysis, as well as in the heterozygous comparison （0R=0.79, 95% Ch 0.65-0.96）, homozygous comparison （0R=0.76, 95% Ch 0.58-0.98） and dominant genetic model （0R=0.81, 95% CI： 0.68-0.96）. Furthermore, grouping analysis showed that the 309G allele in Caucasians was significantly correlated with a decreased PCa risk （0R=0.77, 95% Ch 0.61-0.96）; this was also the case in the homozygous comparison （0R=0.51, 95% Ch 0.31-0.86）. The grouping analysis also showed that the 309G variant in Caucasians was significantly associated with a lower degree of PCa malignancy in all of the genetic models. In addition, we found that the 309G variant in Caucasians was significantly associated with a slower PCa clinical progression in all of the genetic models. In summary, our meta-analysis showed that the MDM2 309G variant was significantly associated with a decreased PCa risk, lower malignant degree and slower clinical progression in Caucasians, but there was no obvious association in the Asian population.
基金Supported by Isfahan Endocrine and Metabolism Research Center,No. 95017.
文摘BACKGROUND Type 2 diabetes mellitus(T2DM)has high morbidity and mortality worldwide,therefore there is of paramount importance to identify the risk factors in the populations at risk early in the course of illness.A strong correlation between severity of metabolic syndrome(MetS)and HbA1c,fasting insulin and insulin resistance has been reported.Accordingly,the MetS severity score(or MestS Zscore)can potentially be used to predict the risk of T2DM progression over time.AIM To evaluate the association the of MestS Z-score in first degree relatives(FDRs)of T2DM with the risk of prediabetes and type 2 diabetes in future.METHODS A prospective open cohort study was conducted between 2003-2018.At baseline,the sample comprised of 1766 FDRs of patients with T2DM who had a normal glucose tolerance test.Relative risk(RR)and 95%confidence interval were calculated based on logistic regression.The receiver-operator characteristic analysis and area under the curve based on MetS Z-score were used to evaluate the risk of prediabetes and diabetes among the FDR population.RESULTS Baseline MetS Z-scores were associated with the its latest values(P<0.0001).Compared with individuals who were T2DM free at the end of follow up,those who developed T2DM had higher MetS Z-score at baseline(P<0.001).In multivariable logistic regression analyses for every unit elevation in MetS Z-score at the baseline,the RR for developing future T2DM and prediabetes was(RR=1.94,RR=3.84),(RR=1.5,RR=2.17)in total population and female group,respectively(P<0.05).The associations remained significant after adjusting the potential confounding variables.A cut off value of 0.97 and 0.94 was defined in the receiver-operator characteristic curve based on the MetS Z-score for differentiating female patients with diabetes and prediabetes from the normal population,respectively.CONCLUSION The MetS Z-score was associated with an increased risk of future T2DM.Appropriate interventions at earlier stages for preventing and attenuating MetS effects may be considered as an effective strategy for FDR as at-risk population.
文摘In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect.
基金Supported by the National Natural Science Foundation of China,No. 30370637
文摘AIM: To study the expression of cyclooxygenase-2 (COX-2)in human gastric cancer tissues and their paired adjacent mucosa, as well as mucosa from gastric antrum and corpus of the first-degree relatives of the recruited cancer patients.METHODS: The expression of COX-2 mRNA in 38 patients with gastric cancer and their 29 first-degree relatives and 18 healthy controls was assessed by the real time RT-PCR.The expression of COX-2 protein was determined by Western blot.RESULTS: A marked increase in COX-2 mRNA expression was found in 20 of 37 (54%) cancerous tissues compared to their respective paired normal mucosa (P＜0.001).Interestingly, increased COX-2 mRNA expression was also found in mucosa of the corpus (6/29) and antrum (13/29)of their first-degree relatives. Increased COX-2 mRNA expression was more frequently observed in the antrum biopsies from cancer patients than in the antrum biopsies from healthy controls (P＜0.05). In addition, 3 of 23 (13%)patients with atrophic mucosa and 6 of 35 (17%) patients with intestinal metaplasia showed increased COX-2 mRNA expression. Furthermore, COX-2 expression increased in H pylori-positive tissues, especially in antrum mucosa.CONCLUSION: Increased COX-2 expression is involved in gastric carcinogenesis, and may be necessary for maintenance of the malignant phenotype and contribute to Helicobacterpylori-associated malignant transformation.
文摘Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51671099,11974149,and 51901163)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35).
文摘The temperature-dependent Gilbert damping in Co2FeAl thin film grown on a Pb(Mg1/3Nb2/3)O3-30%PbTiO3 substrate is investigated by the systematic measurement of physical property measurement system(PPMS) on a series of samples with different substrate temperatures. Varying the substrate temperatures from 350℃ to 500℃, the B2 ordering degrees of Co2FeAl thin films increase, which can lead the Gilbert damping to decrease, indicated by the field-sweep in-plane PPMS measurements. In addition, the measurement result of PPMS demonstrates that the Gilbert damping decreases first with measurement temperature decreasing down to about 150 K, then increases at a measurement temperature of ~ 50 K, and decreases again with the measurement temperature decreasing. There are two independent damping manners, namely bulk damping and surface damping, which contribute to the Gilbert damping. Moreover, the observed peak of Gilbert damping at ~ 50 K can be attributed to the spin re-orientation transition at the Co2FeAl surface, which is similar to the result of the effective magnetization as a function of measurement temperature. The result presents the evidence for further studying the Gilbert damping in Co2FeAl thin film.
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. .
