In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold ...In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.展开更多
We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce ...We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.展开更多
This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generaliz...This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li＇s results in [2] and [3].展开更多
Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this shor...Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.展开更多
A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view...A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.展开更多
This paper aims to determine the possible role of estrogen receptor-β （ERβ） gene Rsal polymorphism on sperm fertility and early embryonic development in humans. Three groups of Chinese men were recruited： in vitr...This paper aims to determine the possible role of estrogen receptor-β （ERβ） gene Rsal polymorphism on sperm fertility and early embryonic development in humans. Three groups of Chinese men were recruited： in vitro fertilization （IVF） group, including 374 couples who underwent conventional IVF; intracytoplasmic sperm injection （ICSI） group, including 294 couples who underwent an ICSI procedure using ejaculated sperm; and azoospermic group, consisting of 197 couples who underwent ICSI using either testis or epididymis sperm. Rsal polymorphism in the ERβ gene was detected by polymerase chain reaction （PCR）-restriction fragment length polymorphism technique; fertilization and high-quality embryo rates were evaluated for each group. In each group, no significant differences were found in the overall rates of fertilization and high-quality embryos among GG, AG and AA genotypes. However, the proportion of cycles possessing a satisfactory high-quality embryo rate with the AA genotype was significantly lower than that in the wild-type GG genotype from each group. These results demonstrated that sperm possessing the ERβ RsalA genotype may have reduced fertilization ability and decreased early embryonic developmental potential, which could directly or indirectly contribute to the low fertilization rate and early embryonic developmental arrest in some cases.展开更多
Objectives Peroxisome proliferator-activated receptor-γ2（PPARγ2） variant Pro12Ala was demonstrated with risk of coronary heart disease （CHD） and type 2 diabetes mellitus （T2DM）. Another variant C-689T in the p...Objectives Peroxisome proliferator-activated receptor-γ2（PPARγ2） variant Pro12Ala was demonstrated with risk of coronary heart disease （CHD） and type 2 diabetes mellitus （T2DM）. Another variant C-689T in the promoter was reported with lower receptor activity but lack of reports on association between C-689T and CHD or T2DM. Methods A total of 351 subjects without CHD and T2DM （controls） and 125 patients with CHD and T2DM （cases） were enrolled in our case-control study. Polymerase chain reaction-restricted fragments length polymorphism （PCR-RFLP） was used to detect Pro12Ala and C-689T polymorphisms. And effects on CHD merged with T2DM of the two polymorphisms were analyzed in individual and haplotype analyses. Results In the study, Pro12Pro, Pro12Ala and Ala12Ala genotype frequencies were 92.9%, 6.8% and 0.3% in controls; 92.8%, 7.2% and 0.0% in cases respectively whilst CC, CT and TT genotype frequencies were 93.4%, 6.3% and 0.3% in controls; 92.8%, 7.2% and 0.0% in cases respectively. Pro12Ala and C-689T polymorphisms were in strong linkage disequilibrium （D＇=0.81, P=0.000） and the observed haplotype frequency of Pro-C, Pro-T, Ala-C and Ala-T was 0.957, 0.006, 0.008 and 0.028 respectively. No significant associations were detected between the two polymorphisms and CHD merged with T2DM in either individual or haplotype analyses. In subjects with obesity [body mass index （BMI）≥25 kg/m^2], we found that both Pro12Ala and C-689T polymorphisms were associated with BMI. In haplotype analyses, we found that Pro12Ala and C-689T haplotypes had associations with systolic blood pressure in total population, with BMI, waist circle and total cholesterol（TC） in obesity subgroup and with fasting blood glucose and TC in males. Conclusions PPARγ2 Pro12Ala and C-689T polymorphisms and haplotypes affect the profiles of CHD merged with T2DM in Chinese Han people.展开更多
In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to...In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.展开更多
文摘In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.
基金This work is supported by the National Natural Science Foundation of China(10471001)
文摘We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.
基金Supported partially by the NNSF of China(10871171)
文摘This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li＇s results in [2] and [3].
基金supported by the Qilu funding of Shandong University (62550089963197)financially supported by the National Natural Science Foundation of China (11701045)the Yangtze Youth Fund (2016cqn56)
文摘Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.
文摘A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.
文摘This paper aims to determine the possible role of estrogen receptor-β （ERβ） gene Rsal polymorphism on sperm fertility and early embryonic development in humans. Three groups of Chinese men were recruited： in vitro fertilization （IVF） group, including 374 couples who underwent conventional IVF; intracytoplasmic sperm injection （ICSI） group, including 294 couples who underwent an ICSI procedure using ejaculated sperm; and azoospermic group, consisting of 197 couples who underwent ICSI using either testis or epididymis sperm. Rsal polymorphism in the ERβ gene was detected by polymerase chain reaction （PCR）-restriction fragment length polymorphism technique; fertilization and high-quality embryo rates were evaluated for each group. In each group, no significant differences were found in the overall rates of fertilization and high-quality embryos among GG, AG and AA genotypes. However, the proportion of cycles possessing a satisfactory high-quality embryo rate with the AA genotype was significantly lower than that in the wild-type GG genotype from each group. These results demonstrated that sperm possessing the ERβ RsalA genotype may have reduced fertilization ability and decreased early embryonic developmental potential, which could directly or indirectly contribute to the low fertilization rate and early embryonic developmental arrest in some cases.
文摘Objectives Peroxisome proliferator-activated receptor-γ2（PPARγ2） variant Pro12Ala was demonstrated with risk of coronary heart disease （CHD） and type 2 diabetes mellitus （T2DM）. Another variant C-689T in the promoter was reported with lower receptor activity but lack of reports on association between C-689T and CHD or T2DM. Methods A total of 351 subjects without CHD and T2DM （controls） and 125 patients with CHD and T2DM （cases） were enrolled in our case-control study. Polymerase chain reaction-restricted fragments length polymorphism （PCR-RFLP） was used to detect Pro12Ala and C-689T polymorphisms. And effects on CHD merged with T2DM of the two polymorphisms were analyzed in individual and haplotype analyses. Results In the study, Pro12Pro, Pro12Ala and Ala12Ala genotype frequencies were 92.9%, 6.8% and 0.3% in controls; 92.8%, 7.2% and 0.0% in cases respectively whilst CC, CT and TT genotype frequencies were 93.4%, 6.3% and 0.3% in controls; 92.8%, 7.2% and 0.0% in cases respectively. Pro12Ala and C-689T polymorphisms were in strong linkage disequilibrium （D＇=0.81, P=0.000） and the observed haplotype frequency of Pro-C, Pro-T, Ala-C and Ala-T was 0.957, 0.006, 0.008 and 0.028 respectively. No significant associations were detected between the two polymorphisms and CHD merged with T2DM in either individual or haplotype analyses. In subjects with obesity [body mass index （BMI）≥25 kg/m^2], we found that both Pro12Ala and C-689T polymorphisms were associated with BMI. In haplotype analyses, we found that Pro12Ala and C-689T haplotypes had associations with systolic blood pressure in total population, with BMI, waist circle and total cholesterol（TC） in obesity subgroup and with fasting blood glucose and TC in males. Conclusions PPARγ2 Pro12Ala and C-689T polymorphisms and haplotypes affect the profiles of CHD merged with T2DM in Chinese Han people.
文摘In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.
