Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result...Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.展开更多
BACKGROUND: There are few data on blood group(BG) types and types of pancreatic cancers. The aims of this study were to study BG types and BG-antigens in pancreatic intraductal papillary mucinous neoplasms(IPMNs). MET...BACKGROUND: There are few data on blood group(BG) types and types of pancreatic cancers. The aims of this study were to study BG types and BG-antigens in pancreatic intraductal papillary mucinous neoplasms(IPMNs). METHODS: BG type and tumor BG-antigen(glycoprotein) expression(studied by immunohistochemistry on tissue microarrays) were analyzed with regard to characteristics of 101 surgically resected pancreatic IPMNs. RESULTS: Non-O BG type predicted invasive carcinoma independently from high serum CA19-9 and male gender. BG type A was observed more frequently in women than in men. Chronic pancreatitis was more frequently seen in patients with BG type B or AB. Aberrant tumor expression(with regard to BG type) of loss of A antigen expression type occurred in 15.0% of IPMNs and of loss of B antigen expression type in 62.5% of IPMNs. Intraneoplasm BG-antigen expression was not related to dysplasia grade or invasion. CONCLUSION: The results of the study suggest that in pancreatic IPMN, non-O BG type predicted invasive carcinoma, whereas for intratumor BG-antigen expression no specific patterns were detected with regard to the progression of glandular epithelial dysplasia or invasion.展开更多
1 Introduction Sareke glutenite-type copper deposit is the large size copper deposit discovered in recent years,and it is located Sarekebayi intracontinental pull-apart basin in the western margin of the Tarim basin.C...1 Introduction Sareke glutenite-type copper deposit is the large size copper deposit discovered in recent years,and it is located Sarekebayi intracontinental pull-apart basin in the western margin of the Tarim basin.Conglomerate of展开更多
We call a group A-simple,if it has no non-trivial normal abelian subgroup.We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are A-simple.
We derive the explicit fundamental solutions for a class of degenerate(or singular)one- parameter subelliptic differential operators on groups of Heisenberg(H)type.This extends the result of Kaplan for the sub-Laplaci...We derive the explicit fundamental solutions for a class of degenerate(or singular)one- parameter subelliptic differential operators on groups of Heisenberg(H)type.This extends the result of Kaplan for the sub-Laplacian on H-type groups,which in turn generalizes Folland's result on the Heisenberg group.As an application,we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups.By choosing the parameter equal to the homogeneous dimension Q and using the Mose-Trudinger inequality for the convolutional type operator on stratified groups obtained in[18].we get the following theorem which gives the best constant for the Moser- Trudiuger inequality for Sobolev functions on H-type groups. Let G be any group of Heisenberg type whose Lie algebra is generated by m left invariant vector fields and with a q-dimensional center.Let Q=m+2q.Q'=Q-1/Q and Then. with A_Q as the sharp constant,where ▽G denotes the subelliptic gradient on G. This continues the research originated in our earlier study of the best constants in Moser-Trudinger inequalities and fundamental solutions for one-parameter subelliptic operators on the Heisenberg group [18].展开更多
Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find...Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).展开更多
A Pohozaev-Rellich type identity for the p-sub-Laplacian on groups of Heisenberg type, G, is given. A Carleman estimate for the sub-Laplacian on G is established and, as a consequence, a unique continuation result is ...A Pohozaev-Rellich type identity for the p-sub-Laplacian on groups of Heisenberg type, G, is given. A Carleman estimate for the sub-Laplacian on G is established and, as a consequence, a unique continuation result is proved.展开更多
We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbit...We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.展开更多
In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.
This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of resear...This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of research.In particular,we only touch the great consequences of the fundamental paper of Liebeck,Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations.In each case the reader can find additional references at the end of Section 1.Some of the methods of investigation can be used to obtain information about finite groups in general,nilpotent algebras and related nearrings.展开更多
Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. Under the assumption of some symmetries, we obtain an existent result for the nonlinear equation △NU + (1 + ∈K(x, z))u2...Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. Under the assumption of some symmetries, we obtain an existent result for the nonlinear equation △NU + (1 + ∈K(x, z))u2*-1 = 0 on N, which generalizes the result of Malchiodi and Uguzzoni to the Kohn's subelliptic context on N in presence of symmetry.展开更多
基金supported by National Science Foundation of China (10771175)
文摘Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.
文摘BACKGROUND: There are few data on blood group(BG) types and types of pancreatic cancers. The aims of this study were to study BG types and BG-antigens in pancreatic intraductal papillary mucinous neoplasms(IPMNs). METHODS: BG type and tumor BG-antigen(glycoprotein) expression(studied by immunohistochemistry on tissue microarrays) were analyzed with regard to characteristics of 101 surgically resected pancreatic IPMNs. RESULTS: Non-O BG type predicted invasive carcinoma independently from high serum CA19-9 and male gender. BG type A was observed more frequently in women than in men. Chronic pancreatitis was more frequently seen in patients with BG type B or AB. Aberrant tumor expression(with regard to BG type) of loss of A antigen expression type occurred in 15.0% of IPMNs and of loss of B antigen expression type in 62.5% of IPMNs. Intraneoplasm BG-antigen expression was not related to dysplasia grade or invasion. CONCLUSION: The results of the study suggest that in pancreatic IPMN, non-O BG type predicted invasive carcinoma, whereas for intratumor BG-antigen expression no specific patterns were detected with regard to the progression of glandular epithelial dysplasia or invasion.
基金supported by the metallogenic regularities and prediction of glutenite type Cu-Pb-Zn deposit in Tarim west margin(201511016-1)the special mapping techniques and its application demonstration in Sareke overall-exploration area in Xinjiang(12120114081501)
文摘1 Introduction Sareke glutenite-type copper deposit is the large size copper deposit discovered in recent years,and it is located Sarekebayi intracontinental pull-apart basin in the western margin of the Tarim basin.Conglomerate of
基金the author Rong at Capital Normal University,which was partially supported by NSFC Grant 11821101,Beijing Natural Science Foundation Z19003,and a research fund from Capital Normal University.
文摘We call a group A-simple,if it has no non-trivial normal abelian subgroup.We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are A-simple.
文摘We derive the explicit fundamental solutions for a class of degenerate(or singular)one- parameter subelliptic differential operators on groups of Heisenberg(H)type.This extends the result of Kaplan for the sub-Laplacian on H-type groups,which in turn generalizes Folland's result on the Heisenberg group.As an application,we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups.By choosing the parameter equal to the homogeneous dimension Q and using the Mose-Trudinger inequality for the convolutional type operator on stratified groups obtained in[18].we get the following theorem which gives the best constant for the Moser- Trudiuger inequality for Sobolev functions on H-type groups. Let G be any group of Heisenberg type whose Lie algebra is generated by m left invariant vector fields and with a q-dimensional center.Let Q=m+2q.Q'=Q-1/Q and Then. with A_Q as the sharp constant,where ▽G denotes the subelliptic gradient on G. This continues the research originated in our earlier study of the best constants in Moser-Trudinger inequalities and fundamental solutions for one-parameter subelliptic operators on the Heisenberg group [18].
基金supported by National Natural Science Foundation of China(Grant No.11471282)
文摘Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).
基金The project supported by National Natural Science Foundation of China, Grant No. 10371099.
文摘A Pohozaev-Rellich type identity for the p-sub-Laplacian on groups of Heisenberg type, G, is given. A Carleman estimate for the sub-Laplacian on G is established and, as a consequence, a unique continuation result is proved.
基金the Japan Society for Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C)15K04776, 2015-2018, and by the CIB in EPFL. The second author was supported by the German Science Foundation (DFG) Scientific Priority Programme SPP-1489 "Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory".
文摘We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.
文摘In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.
文摘This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of research.In particular,we only touch the great consequences of the fundamental paper of Liebeck,Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations.In each case the reader can find additional references at the end of Section 1.Some of the methods of investigation can be used to obtain information about finite groups in general,nilpotent algebras and related nearrings.
基金Supported by the Fundamental Research Funds for the Central Universities (Grant No. 1082001)National Natural Science Foundation of China (Grant No. 10571044)
文摘Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. Under the assumption of some symmetries, we obtain an existent result for the nonlinear equation △NU + (1 + ∈K(x, z))u2*-1 = 0 on N, which generalizes the result of Malchiodi and Uguzzoni to the Kohn's subelliptic context on N in presence of symmetry.