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
＂China Dream＂, not only is the national dream, but also is the dream of all the Chinese people, and highly fits the educational purpose of university education, ＂China Dream＂ leads the university ideal faith educa...＂China Dream＂, not only is the national dream, but also is the dream of all the Chinese people, and highly fits the educational purpose of university education, ＂China Dream＂ leads the university ideal faith education to a higher standard, and embodied in the ＂China Dream＂, and enriched the connotation of the socialist core value system, is the organic unity of national spirit and the spirit of the age; ＂China Dream＂ represents a blue view for the great rejuvenation of the Chinese nation, is the organic unity of ideal and great practice being together; Also, the ideological and political education had also established in the underdevelopment contemporary youth growing up; the value of coordination shaped college student＇s right of personal value and social value. ＂China Dream＂, was the sublimation of university ideological and political education, ever advancing with the time, the ＂China Dream＂ tightly integrated into the university ideological and political education, strives to cultivate the endeavor of having both ability and political integrity, and having the national feelings of dedication. Therefore, college ideological and political education work is to ＂China Dream＂ as the guider, actively promotes the educational model innovation.展开更多
In this paper we give the (L p α, L p ) boundedness of the maximal operator of a class of super singular integrals defined by $$T_{\Omega ,\alpha }^* f(x) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int_{|...In this paper we give the (L p α, L p ) boundedness of the maximal operator of a class of super singular integrals defined by $$T_{\Omega ,\alpha }^* f(x) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int_{|x - y| > \varepsilon } {b(|y|)} \Omega (y)|y|^{ - n - \alpha } f(x - y)dy} \right|,$$ which improves and extends the known result. Moreover, by applying an off-Diagonal T1 Theorem, we also obtain the (L p , L q ) boundedness of the commutator defined by $$C_{\Omega ,\alpha } f(x) = p.v. \int_{\mathbb{R}^n } {(A(x)} - A(y))\Omega (x - y)|x - y|^{ - n - \alpha } f(y)dy.$$展开更多
Connected individuals(ramets)of clonal plants are frequently fragmented due to disturbance,and such clonal fragmentation may influence their growth.However,it is unclear whether different patterns of clonal fragmentat...Connected individuals(ramets)of clonal plants are frequently fragmented due to disturbance,and such clonal fragmentation may influence their growth.However,it is unclear whether different patterns of clonal fragmentation produce differential effects on plant growth and whether such differences vary with genotypes.We collected one group of connected ramets of the stoloniferous floating invasive macrophyte Pistia stratiotes from each of six provinces(Guangdong,Guangxi,Hubei,Jiangsu,Sichuan and Yunnan Provinces)of China,and assumed that these ramets belonged to different genotypes.After several generations of vegetative propagation to remove potential parental effects,new ramets(hereafter referred to as parent ramets)from each of these assumed genotypes were subjected to four patterns of clonal fragmentation,i.e.,all offspring ramets produced during the experiment remained connected to their parent ramet(control),or the primary(1°),secondary(2°)or tertiary(3°)offspring ramets were disconnected from their parent ramet.We found significant growth differences among the assumed genotypes,confirming that the ramets sampled from these six provinces were from different genotypes.Compared with the control,disconnecting the 1°,2°or 3°ramets did not significantly affect biomass of the whole clone(i.e.,the parent ramet plus all offspring ramets)of P.stratiotes.Disconnecting the 1°ramets significantly increased biomass of the parental ramet of all six genotypes compared with the control.However,disconnecting the 2°or 3°ramets had little effect on biomass of the parent ramet for all genotypes except the Guangxi genotype,for which disconnecting the 2°ramets decreased biomass of the parent ramet.Disconnecting the 1°,2°or 3°ramets had no impact on biomass or number of the 1°or the 3°ramets for any of the genotypes.However,disconnecting the 1°ramets decreased biomass of the 2°ramets for the Guangdong and Yunnan genotypes,but had no effect for the other four genotypes.We conclude that different patterns of clonal fragmentation can have different impacts on parent and offspring ramets of P.stratiotes and such an impact may vary with genotypes.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＂China Dream＂, not only is the national dream, but also is the dream of all the Chinese people, and highly fits the educational purpose of university education, ＂China Dream＂ leads the university ideal faith education to a higher standard, and embodied in the ＂China Dream＂, and enriched the connotation of the socialist core value system, is the organic unity of national spirit and the spirit of the age; ＂China Dream＂ represents a blue view for the great rejuvenation of the Chinese nation, is the organic unity of ideal and great practice being together; Also, the ideological and political education had also established in the underdevelopment contemporary youth growing up; the value of coordination shaped college student＇s right of personal value and social value. ＂China Dream＂, was the sublimation of university ideological and political education, ever advancing with the time, the ＂China Dream＂ tightly integrated into the university ideological and political education, strives to cultivate the endeavor of having both ability and political integrity, and having the national feelings of dedication. Therefore, college ideological and political education work is to ＂China Dream＂ as the guider, actively promotes the educational model innovation.
文摘In this paper we give the (L p α, L p ) boundedness of the maximal operator of a class of super singular integrals defined by $$T_{\Omega ,\alpha }^* f(x) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int_{|x - y| > \varepsilon } {b(|y|)} \Omega (y)|y|^{ - n - \alpha } f(x - y)dy} \right|,$$ which improves and extends the known result. Moreover, by applying an off-Diagonal T1 Theorem, we also obtain the (L p , L q ) boundedness of the commutator defined by $$C_{\Omega ,\alpha } f(x) = p.v. \int_{\mathbb{R}^n } {(A(x)} - A(y))\Omega (x - y)|x - y|^{ - n - \alpha } f(y)dy.$$
基金We thank the three anonymous reviewers for their valuable comments and the support from the National Natural Science Foundation of China(grant 31800341).
文摘Connected individuals(ramets)of clonal plants are frequently fragmented due to disturbance,and such clonal fragmentation may influence their growth.However,it is unclear whether different patterns of clonal fragmentation produce differential effects on plant growth and whether such differences vary with genotypes.We collected one group of connected ramets of the stoloniferous floating invasive macrophyte Pistia stratiotes from each of six provinces(Guangdong,Guangxi,Hubei,Jiangsu,Sichuan and Yunnan Provinces)of China,and assumed that these ramets belonged to different genotypes.After several generations of vegetative propagation to remove potential parental effects,new ramets(hereafter referred to as parent ramets)from each of these assumed genotypes were subjected to four patterns of clonal fragmentation,i.e.,all offspring ramets produced during the experiment remained connected to their parent ramet(control),or the primary(1°),secondary(2°)or tertiary(3°)offspring ramets were disconnected from their parent ramet.We found significant growth differences among the assumed genotypes,confirming that the ramets sampled from these six provinces were from different genotypes.Compared with the control,disconnecting the 1°,2°or 3°ramets did not significantly affect biomass of the whole clone(i.e.,the parent ramet plus all offspring ramets)of P.stratiotes.Disconnecting the 1°ramets significantly increased biomass of the parental ramet of all six genotypes compared with the control.However,disconnecting the 2°or 3°ramets had little effect on biomass of the parent ramet for all genotypes except the Guangxi genotype,for which disconnecting the 2°ramets decreased biomass of the parent ramet.Disconnecting the 1°,2°or 3°ramets had no impact on biomass or number of the 1°or the 3°ramets for any of the genotypes.However,disconnecting the 1°ramets decreased biomass of the 2°ramets for the Guangdong and Yunnan genotypes,but had no effect for the other four genotypes.We conclude that different patterns of clonal fragmentation can have different impacts on parent and offspring ramets of P.stratiotes and such an impact may vary with genotypes.
