Total spikelet number per spike(TSS)is a crucial yield component in wheat.Dissecting and characterizing major stable quantitative trait loci(QTL)associated with TSS can significantly enhance the genetic improvement of...Total spikelet number per spike(TSS)is a crucial yield component in wheat.Dissecting and characterizing major stable quantitative trait loci(QTL)associated with TSS can significantly enhance the genetic improvement of yield potential.In a previous study,we identified a stable major QTL for TSS,named QTss.cas-3D.In the present study,we conducted fine mapping of QTss.cas-3D,interval to approximately 6.35 Mb,ranging from 105.03 to 111.38 Mb,based on the IWGSC RefSeq v2.1.Through genome resequencing and gene function annotation,we identified TraesCS3D03G0308000(TaFT-D2)as the candidate gene.Phenotypic evaluation with paired near-isogenic lines revealed that this locus predominantly increases kernel number per spike by enhancing TSS and fertile spikelet number per spike,without significantly affecting thousand-kernel weight or tiller number.The presence of the TaFT-D2 allele in the parent P3228,which is rare in nature populations,highlights its potential value.This study provides a valuable gene resource and functional marker for wheat molecular breeding aimed at improving TSS and establishes a foundation for gene functional analysis of TaFT-D2.展开更多
Integrating liquid CO_(2)phase transition blasting(LCPTB)technology with hydraulic fracturing(HF)methods can help reduce wellbore damage,create multiple radial fractures,and establish a complex fracture network.This a...Integrating liquid CO_(2)phase transition blasting(LCPTB)technology with hydraulic fracturing(HF)methods can help reduce wellbore damage,create multiple radial fractures,and establish a complex fracture network.This approach significantly increases the recovery efficiency of low-permeability oil and gas fields.Accurately calculating the number of fractures caused by LCPTB is necessary to predict production enhancement effects and optimize subsequent HF designs.However,few studies are reported on large-scale physical model experiments in terms of a method for calculating the fracture number.This study analyzed the initiation and propagation of cracks under LCPTB,derived a calculation formula for crack propagation radius under stress waves,and then proposed a new,fast,and accurate method for calculating the fracture number using the principle of mass conservation.Through ten rock-breaking tests using LCPTB,the study confirmed the effectiveness of the proposed calculation approach and elucidated the variation rule of explosion pressure,rock-breaking scenario,and the impact of varying parameters on fracture number.The results show that the new calculation method is suitable for fracturing technologies with high pressure rates.Recommendations include enlarging the diameter of the fracturing tube and increasing the liquid CO_(2) mass in the tube to enhance fracture effectiveness.Moreover,the method can be applied to other fracturing technologies,such as explosive fracturing(EF)within HF formations,indicating its broader applicability and potential impact on optimizing unconventional resource extraction technologies.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
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
基金supported by the National Natural Science Foundation of China (32101686)the Hebei Province Key Research and Development Program (22326306D).
文摘Total spikelet number per spike(TSS)is a crucial yield component in wheat.Dissecting and characterizing major stable quantitative trait loci(QTL)associated with TSS can significantly enhance the genetic improvement of yield potential.In a previous study,we identified a stable major QTL for TSS,named QTss.cas-3D.In the present study,we conducted fine mapping of QTss.cas-3D,interval to approximately 6.35 Mb,ranging from 105.03 to 111.38 Mb,based on the IWGSC RefSeq v2.1.Through genome resequencing and gene function annotation,we identified TraesCS3D03G0308000(TaFT-D2)as the candidate gene.Phenotypic evaluation with paired near-isogenic lines revealed that this locus predominantly increases kernel number per spike by enhancing TSS and fertile spikelet number per spike,without significantly affecting thousand-kernel weight or tiller number.The presence of the TaFT-D2 allele in the parent P3228,which is rare in nature populations,highlights its potential value.This study provides a valuable gene resource and functional marker for wheat molecular breeding aimed at improving TSS and establishes a foundation for gene functional analysis of TaFT-D2.
基金supported by the National Key R&D Program of China (Grant No.2020YFA0711802).
文摘Integrating liquid CO_(2)phase transition blasting(LCPTB)technology with hydraulic fracturing(HF)methods can help reduce wellbore damage,create multiple radial fractures,and establish a complex fracture network.This approach significantly increases the recovery efficiency of low-permeability oil and gas fields.Accurately calculating the number of fractures caused by LCPTB is necessary to predict production enhancement effects and optimize subsequent HF designs.However,few studies are reported on large-scale physical model experiments in terms of a method for calculating the fracture number.This study analyzed the initiation and propagation of cracks under LCPTB,derived a calculation formula for crack propagation radius under stress waves,and then proposed a new,fast,and accurate method for calculating the fracture number using the principle of mass conservation.Through ten rock-breaking tests using LCPTB,the study confirmed the effectiveness of the proposed calculation approach and elucidated the variation rule of explosion pressure,rock-breaking scenario,and the impact of varying parameters on fracture number.The results show that the new calculation method is suitable for fracturing technologies with high pressure rates.Recommendations include enlarging the diameter of the fracturing tube and increasing the liquid CO_(2) mass in the tube to enhance fracture effectiveness.Moreover,the method can be applied to other fracturing technologies,such as explosive fracturing(EF)within HF formations,indicating its broader applicability and potential impact on optimizing unconventional resource extraction technologies.
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].
