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
目的探讨成髓细胞瘤转录因子第2亚型(MYB proto-oncogene like 2,MYBL2)基因在子宫内膜癌组织中的表达及拷贝数变异(copy number variation,CNV)情况,评价其与临床特征的关系和对临床预后的影响。方法从癌症基因组图谱(The Cancer Genom...目的探讨成髓细胞瘤转录因子第2亚型(MYB proto-oncogene like 2,MYBL2)基因在子宫内膜癌组织中的表达及拷贝数变异(copy number variation,CNV)情况,评价其与临床特征的关系和对临床预后的影响。方法从癌症基因组图谱(The Cancer Genome Atlas,TCGA)数据库中获取临床病理特征和相应的基因组数据资料完整的子宫内膜癌患者140例,从cBio Cancer Genomics Portal(cBioPortal)数据库下载MYBL2基因CNV和基因组数据资料完整的子宫内膜癌患者137例,以各基因表达水平的中位数作为高低表达的截断值,通过χ2检验和Cox回归分析MYBL2基因高表达及CNV与子宫内膜癌临床特征的关系,Kaplan-Meier曲线分析MYBL2基因表达和CNV与患者预后之间的关系。收集2015年1月至2015年12月南昌大学第二附属医院手术切除经病理组织学确诊的60例子宫内膜癌组织及其癌旁组织。免疫组织化学法检测其MYBL2表达。结果TCGA数据库分析发现,子宫内膜癌MYBL2高表达和低表达患者在病理类型(P=0.034)和组织分级(P<0.01)方面比较,差异均具有统计学意义。cBioPortal数据库分析发现,子宫内膜癌中MYBL2存在CNV(P<0.01),主要变异形式是拷贝数增加,占26.0%。MYBL2 CNV的患者MYBL2 mRNA表达水平上调(P<0.01),MYBL2 CNV患者总生存期与无瘤生存期较短(均P<0.05)。Ⅱ型子宫内膜癌中MYBL2 CNV占比高于Ⅰ型(P<0.01)。结论子宫内膜癌组织中MYBL2呈高表达,且与不良预后相关。MYBL2基因CNV在子宫内膜癌中是一种不良预后因素,其可能成为预测子宫内膜癌临床预后的有效生物标志物。展开更多
An H（2）-move is a local move of a knot which is performed by adding a half-twisted band. It is known an H（2）-move is an unknotting operation. We define the H（2）-unknotting number of a knot K to be the minimum nu...An H（2）-move is a local move of a knot which is performed by adding a half-twisted band. It is known an H（2）-move is an unknotting operation. We define the H（2）-unknotting number of a knot K to be the minimum number of H（2）-moves needed to transform K into a trivial knot. We give several methods to estimate the H（2）-unknotting number of a knot. Then we give tables of H（2）-unknotting numbers of knots with up to 9 crossings.展开更多
AIM To investigate if the down-regulation of N-myc Downstream Regulated Gene 2(NDRG2) expression in colorectal carcinoma(CRC) is due to loss of the NDRG2 allele(s).METHODS The following were investigated in the human ...AIM To investigate if the down-regulation of N-myc Downstream Regulated Gene 2(NDRG2) expression in colorectal carcinoma(CRC) is due to loss of the NDRG2 allele(s).METHODS The following were investigated in the human colorectal cancer cell lines DLD-1, Lo Vo and SW-480: NDRG2 mRNA expression levels using quantitative reverse transcriptionpolymerase chain reaction(qRT-PCR); interaction of the MYC gene-regulatory protein with the NDRG2 promoter using chromatin immunoprecipitation; and NDRG2 promoter methylation using bisulfite sequencing.Furthermore, we performed qPCR to analyse the copy numbers of NDRG2 and MYC genes in the above three cell lines, 8 normal colorectal tissue samples and 40 CRC tissue samples.RESULTS As expected, NDRG2 mRNA levels were low in the three colorectal cancer cell lines, compared to normal colon.Endogenous MYC protein interacted with the NDRG2 core promoter in all three cell lines.In addition, the NDRG2 promoter was heavily methylated in these cell lines, suggesting an epigenetic regulatory mechanism.Unaltered gene copy numbers of NDRG2 were observed in the three cell lines.In the colorectal tissues, one normal and three CRC samples showed partial or complete loss of one NDRG2 allele.In contrast, the MYC gene was amplified in one cell line and in more than 40% of the CRC cases.CONCLUSION Our study suggests that the reduction in NDRG2 expression observed in CRC is due to transcriptional repression by MYC and promoter methylation, and is not due to allelic loss.展开更多
A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set ...A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].展开更多
In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient condit...In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.展开更多
The conversion of CO_(2)into value-added chemicals coupled with the storage of intermittent renewable electricity is attractive.CuO nanosheets with an average size and thickness of~30 and~20 nm have been developed,whi...The conversion of CO_(2)into value-added chemicals coupled with the storage of intermittent renewable electricity is attractive.CuO nanosheets with an average size and thickness of~30 and~20 nm have been developed,which are in situ reduced into Cu nanosheets during electrochemical CO_(2)reduction reaction(ECO_(2)RR).The derived Cu nanosheets demonstrate much higher selectivity for C2H4production than commercial CuO derived Cu powder,with an optimum Faradaic efficiency of 56.2%and a partial current density of C_(2)H_(4)as large as 171.0 mA cm^(-2)in a gas diffusion flow cell.The operando attenuated total reflectance-Fourier transform infrared spectra measurements and density functional theory simulations illustrate that the high activity and selectivity of Cu nanosheets originate from the edge sites on Cu nanosheets with a coordinate number around 5(4–6),which facilitates the formation of^(*)CHO rather than^(*)COH intermediate,meanwhile boosting the C-C coupling reaction of^(*)CO and^(*)CHO intermediates,which are the critical steps for C_(2)H_(4)formation.展开更多
The 1918 Spanish flu, 2002 severe acute respiratory syndrome (SARS), and 2012 Middle East respiratory syndrome coronavirus (MERS-CoV) were investigated to reveal their causes and routes of transmission. They have the ...The 1918 Spanish flu, 2002 severe acute respiratory syndrome (SARS), and 2012 Middle East respiratory syndrome coronavirus (MERS-CoV) were investigated to reveal their causes and routes of transmission. They have the common features such as 1) the induction by viruses (Spanish flu;avian influenza virus (AIV), SARS and MERS-CoV;coronavirus), 2) the outbreak during the maximal sunspot number, 3) the aeolian desert dust region (Spanish flu;Saharan, SARS;Asian, MERS-CoV;Arabian), and 4) similar incubation period (AIV;5, SARS;2 - 7, MERS-CoV;5 days), 5) different transmission reservoir (Spanish flu;aquatic bird/swine, SARS;bat, MERS-CoV;bat/dromedary camel). When carbon dioxide (CO2) combustion emissions were simultaneously high at the maximal sunspot number, UV radiation in the Poles was so extensive to mutate the aquatic virus through the food web to be the fundamental reason for these pandemic. Guangdong Province and Hong Kong in China are the source of 2002-2003 SARS. The stranded dead whales and dolphins along the coast of the Persian Gulf might be fed on by coastal animals in the Arabian Desert to transmit MERS-CoV. Mutations in the hot temperature in the Arabian Desert and Persian Gulf, and the maximal sunspot numbers were observed in Saudi Arabia. Saudi crude burn in power plants since 2009 with coincidental outbreaks of MERS-CoV in Saudi Arabia since 2012 peaking in 2014. The reduction of CO2 emissions by nuclear power plants is a unique solution to decrease MERS-CoV outbreaks.展开更多
如果 S 是一个统治集合，导致的 subgraph 至多有 k 部件， V 的子集 S 被称为一个连接 k 的统治集合。G 的连接 k 的支配数字 kc (G) 是在 G 的所有最小的连接 k 的统治集合上拿的最小的集的势。在这份报纸，我们与相等的连接支配和 2-...如果 S 是一个统治集合，导致的 subgraph 至多有 k 部件， V 的子集 S 被称为一个连接 k 的统治集合。G 的连接 k 的支配数字 kc (G) 是在 G 的所有最小的连接 k 的统治集合上拿的最小的集的势。在这份报纸，我们与相等的连接支配和 2-connected 支配数字描绘树和 unicyclic 图。展开更多
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 .
文摘目的探讨成髓细胞瘤转录因子第2亚型(MYB proto-oncogene like 2,MYBL2)基因在子宫内膜癌组织中的表达及拷贝数变异(copy number variation,CNV)情况,评价其与临床特征的关系和对临床预后的影响。方法从癌症基因组图谱(The Cancer Genome Atlas,TCGA)数据库中获取临床病理特征和相应的基因组数据资料完整的子宫内膜癌患者140例,从cBio Cancer Genomics Portal(cBioPortal)数据库下载MYBL2基因CNV和基因组数据资料完整的子宫内膜癌患者137例,以各基因表达水平的中位数作为高低表达的截断值,通过χ2检验和Cox回归分析MYBL2基因高表达及CNV与子宫内膜癌临床特征的关系,Kaplan-Meier曲线分析MYBL2基因表达和CNV与患者预后之间的关系。收集2015年1月至2015年12月南昌大学第二附属医院手术切除经病理组织学确诊的60例子宫内膜癌组织及其癌旁组织。免疫组织化学法检测其MYBL2表达。结果TCGA数据库分析发现,子宫内膜癌MYBL2高表达和低表达患者在病理类型(P=0.034)和组织分级(P<0.01)方面比较,差异均具有统计学意义。cBioPortal数据库分析发现,子宫内膜癌中MYBL2存在CNV(P<0.01),主要变异形式是拷贝数增加,占26.0%。MYBL2 CNV的患者MYBL2 mRNA表达水平上调(P<0.01),MYBL2 CNV患者总生存期与无瘤生存期较短(均P<0.05)。Ⅱ型子宫内膜癌中MYBL2 CNV占比高于Ⅰ型(P<0.01)。结论子宫内膜癌组织中MYBL2呈高表达,且与不良预后相关。MYBL2基因CNV在子宫内膜癌中是一种不良预后因素,其可能成为预测子宫内膜癌临床预后的有效生物标志物。
基金supported by Grant-in-Aid (20540079) for Scientific Research (C),Japan Society for the Promotion of Science
文摘An H（2）-move is a local move of a knot which is performed by adding a half-twisted band. It is known an H（2）-move is an unknotting operation. We define the H（2）-unknotting number of a knot K to be the minimum number of H（2）-moves needed to transform K into a trivial knot. We give several methods to estimate the H（2）-unknotting number of a knot. Then we give tables of H（2）-unknotting numbers of knots with up to 9 crossings.
文摘AIM To investigate if the down-regulation of N-myc Downstream Regulated Gene 2(NDRG2) expression in colorectal carcinoma(CRC) is due to loss of the NDRG2 allele(s).METHODS The following were investigated in the human colorectal cancer cell lines DLD-1, Lo Vo and SW-480: NDRG2 mRNA expression levels using quantitative reverse transcriptionpolymerase chain reaction(qRT-PCR); interaction of the MYC gene-regulatory protein with the NDRG2 promoter using chromatin immunoprecipitation; and NDRG2 promoter methylation using bisulfite sequencing.Furthermore, we performed qPCR to analyse the copy numbers of NDRG2 and MYC genes in the above three cell lines, 8 normal colorectal tissue samples and 40 CRC tissue samples.RESULTS As expected, NDRG2 mRNA levels were low in the three colorectal cancer cell lines, compared to normal colon.Endogenous MYC protein interacted with the NDRG2 core promoter in all three cell lines.In addition, the NDRG2 promoter was heavily methylated in these cell lines, suggesting an epigenetic regulatory mechanism.Unaltered gene copy numbers of NDRG2 were observed in the three cell lines.In the colorectal tissues, one normal and three CRC samples showed partial or complete loss of one NDRG2 allele.In contrast, the MYC gene was amplified in one cell line and in more than 40% of the CRC cases.CONCLUSION Our study suggests that the reduction in NDRG2 expression observed in CRC is due to transcriptional repression by MYC and promoter methylation, and is not due to allelic loss.
文摘A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].
文摘In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.
基金funded by the National Key Research and Development Program of China(2017YFA0700103,2018YFA0704502)the National Natural Science Foundation of China(21703248)staffs in BL11B beamline in Shanghai Synchrotron Radiation Facility(SSRF)for their technical assistance(2020-SSRF-PT-012223 and 2021-SSRF-PT-015319)。
文摘The conversion of CO_(2)into value-added chemicals coupled with the storage of intermittent renewable electricity is attractive.CuO nanosheets with an average size and thickness of~30 and~20 nm have been developed,which are in situ reduced into Cu nanosheets during electrochemical CO_(2)reduction reaction(ECO_(2)RR).The derived Cu nanosheets demonstrate much higher selectivity for C2H4production than commercial CuO derived Cu powder,with an optimum Faradaic efficiency of 56.2%and a partial current density of C_(2)H_(4)as large as 171.0 mA cm^(-2)in a gas diffusion flow cell.The operando attenuated total reflectance-Fourier transform infrared spectra measurements and density functional theory simulations illustrate that the high activity and selectivity of Cu nanosheets originate from the edge sites on Cu nanosheets with a coordinate number around 5(4–6),which facilitates the formation of^(*)CHO rather than^(*)COH intermediate,meanwhile boosting the C-C coupling reaction of^(*)CO and^(*)CHO intermediates,which are the critical steps for C_(2)H_(4)formation.
文摘The 1918 Spanish flu, 2002 severe acute respiratory syndrome (SARS), and 2012 Middle East respiratory syndrome coronavirus (MERS-CoV) were investigated to reveal their causes and routes of transmission. They have the common features such as 1) the induction by viruses (Spanish flu;avian influenza virus (AIV), SARS and MERS-CoV;coronavirus), 2) the outbreak during the maximal sunspot number, 3) the aeolian desert dust region (Spanish flu;Saharan, SARS;Asian, MERS-CoV;Arabian), and 4) similar incubation period (AIV;5, SARS;2 - 7, MERS-CoV;5 days), 5) different transmission reservoir (Spanish flu;aquatic bird/swine, SARS;bat, MERS-CoV;bat/dromedary camel). When carbon dioxide (CO2) combustion emissions were simultaneously high at the maximal sunspot number, UV radiation in the Poles was so extensive to mutate the aquatic virus through the food web to be the fundamental reason for these pandemic. Guangdong Province and Hong Kong in China are the source of 2002-2003 SARS. The stranded dead whales and dolphins along the coast of the Persian Gulf might be fed on by coastal animals in the Arabian Desert to transmit MERS-CoV. Mutations in the hot temperature in the Arabian Desert and Persian Gulf, and the maximal sunspot numbers were observed in Saudi Arabia. Saudi crude burn in power plants since 2009 with coincidental outbreaks of MERS-CoV in Saudi Arabia since 2012 peaking in 2014. The reduction of CO2 emissions by nuclear power plants is a unique solution to decrease MERS-CoV outbreaks.
文摘如果 S 是一个统治集合，导致的 subgraph 至多有 k 部件， V 的子集 S 被称为一个连接 k 的统治集合。G 的连接 k 的支配数字 kc (G) 是在 G 的所有最小的连接 k 的统治集合上拿的最小的集的势。在这份报纸，我们与相等的连接支配和 2-connected 支配数字描绘树和 unicyclic 图。
