In this paper,we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of the development of curves.
We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a correc...We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean’s computations of the zeroth homology group.展开更多
The notion of Higgs-de Rham flows was introduced by Lan et al.(2019),as an analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory.In this paper we investigate a small part of this theory,and study t...The notion of Higgs-de Rham flows was introduced by Lan et al.(2019),as an analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory.In this paper we investigate a small part of this theory,and study those Higgs-de Rham flows which are of level zero.We improve the original definition of level-zero Higgs-de Rham flows(which works for general levels),and establish a Hitchin-Simpson type correspondence between such objects and certain representations of fundamental groups in positive characteristic,which generalizes a classical results of Katz(1973).We compare the deformation theories of two sides in the correspondence,and translate the Galois action on the geometric fundamental groups of algebraic varieties defined over finite fields into the Higgs side.展开更多
Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they...Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they are compatible with Poincaréduality and with the canonical morphisms among such cohomology.We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k.In particular,we prove finiteness ofétale cohomology with partial compact support of any Z_(p)-local systems,and establish the Poincaréduality for such cohomology after inverting p.展开更多
Propyl O-(α-L-rhamncpyranosyl)-(1→3)-[2,4-di-O-(2s-methylbutyryl)-α-L-rham-nopyranosyl]-(1→2)-(3-O-acetyl-β-D-glucopyranosyl)-(1→2)-β-D-fucopyranoside (1), the tetrasac-charide moiety of Tricolorin A, was synth...Propyl O-(α-L-rhamncpyranosyl)-(1→3)-[2,4-di-O-(2s-methylbutyryl)-α-L-rham-nopyranosyl]-(1→2)-(3-O-acetyl-β-D-glucopyranosyl)-(1→2)-β-D-fucopyranoside (1), the tetrasac-charide moiety of Tricolorin A, was synthesized in total 23 steps with a longest linear sequence of 10 steps, and overall yield of 3.7% from D-Glucose. The isomerization of the dioxolane-type berzyli-dene in the presence of NIS/AgOTf was observed. Tetrasaccharide 1 exhibited no activity against the cultured P388 cell as Tricolorin A did.展开更多
In the article, we discuss basic concepts of the residue theory of logarithmic and multi-logarithmic differential forms, and describe some aspects of the theory, de-veloped by the author in the past few years. In part...In the article, we discuss basic concepts of the residue theory of logarithmic and multi-logarithmic differential forms, and describe some aspects of the theory, de-veloped by the author in the past few years. In particular, we introduce the notion of logarithmic differential forms with the use of the classical de Rham lemma and give an explicit description of regular meromorphic differential forms in terms of residues of logarithmic or multi-logarithmic differential forms with respect to hypersurfaces, com-plete intersections or pure-dimensional Cohen-Macaulay spaces. Among other things, several useful applications are considered, which are related with the theory of holo-nomic D-modules, the theory of Hodge structures, the theory of residual currents and others.展开更多
In this paper, as a new contribution to the tensor-centric warfare (TCW) series [1] [2] [3] [4], we extend the kinetic TCW-framework to include non-kinetic effects, by addressing a general systems confrontation [5], w...In this paper, as a new contribution to the tensor-centric warfare (TCW) series [1] [2] [3] [4], we extend the kinetic TCW-framework to include non-kinetic effects, by addressing a general systems confrontation [5], which is waged not only in the traditional physical Air-Land-Sea domains, but also simultaneously across multiple non-physical domains, including cyberspace and social networks. Upon this basis, this paper attempts to address a more general analytical scenario using rigorous topological methods to introduce a two-level topological representation of modern armed conflict;in doing so, it extends from the traditional red-blue model of conflict to a red-blue-green model, where green represents various neutral elements as active factions;indeed, green can effectively decide the outcomes from red-blue conflict. System confrontations at various stages of the scenario will be defined by the non-equilibrium phase transitions which are superficially characterized by sudden entropy growth. These will be shown to have the underlying topology changes of the systems-battlespace. The two-level topological analysis of the systems-battlespace is utilized to address the question of topology changes in the combined battlespace. Once an intuitive analysis of the combined battlespace topology is performed, a rigorous topological analysis follows using (co)homological invariants of the combined systems-battlespace manifold.展开更多
基金partially supported by GDNSF(2021A1515010264)NNSF of China(11571215)。
文摘In this paper,we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of the development of curves.
基金supported by the grant of the Government of the Russian Federation for the state support of scientific research carried out under the supervision of leading scientistsagreement 14.W03.31.0030 dated 15.02.2018.1。
文摘We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean’s computations of the zeroth homology group.
基金supported by National Natural Science Foundation of China(Grant Nos.11622109 and 11721101)Anhui Initiative in Quantum Information Technologies(Grant No.AHY150200)supported by One-Thousand-Talents Program of China。
文摘The notion of Higgs-de Rham flows was introduced by Lan et al.(2019),as an analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory.In this paper we investigate a small part of this theory,and study those Higgs-de Rham flows which are of level zero.We improve the original definition of level-zero Higgs-de Rham flows(which works for general levels),and establish a Hitchin-Simpson type correspondence between such objects and certain representations of fundamental groups in positive characteristic,which generalizes a classical results of Katz(1973).We compare the deformation theories of two sides in the correspondence,and translate the Galois action on the geometric fundamental groups of algebraic varieties defined over finite fields into the Higgs side.
文摘Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they are compatible with Poincaréduality and with the canonical morphisms among such cohomology.We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k.In particular,we prove finiteness ofétale cohomology with partial compact support of any Z_(p)-local systems,and establish the Poincaréduality for such cohomology after inverting p.
基金Project supported by the State Science and Technology Committee of China.
文摘Propyl O-(α-L-rhamncpyranosyl)-(1→3)-[2,4-di-O-(2s-methylbutyryl)-α-L-rham-nopyranosyl]-(1→2)-(3-O-acetyl-β-D-glucopyranosyl)-(1→2)-β-D-fucopyranoside (1), the tetrasac-charide moiety of Tricolorin A, was synthesized in total 23 steps with a longest linear sequence of 10 steps, and overall yield of 3.7% from D-Glucose. The isomerization of the dioxolane-type berzyli-dene in the presence of NIS/AgOTf was observed. Tetrasaccharide 1 exhibited no activity against the cultured P388 cell as Tricolorin A did.
文摘In the article, we discuss basic concepts of the residue theory of logarithmic and multi-logarithmic differential forms, and describe some aspects of the theory, de-veloped by the author in the past few years. In particular, we introduce the notion of logarithmic differential forms with the use of the classical de Rham lemma and give an explicit description of regular meromorphic differential forms in terms of residues of logarithmic or multi-logarithmic differential forms with respect to hypersurfaces, com-plete intersections or pure-dimensional Cohen-Macaulay spaces. Among other things, several useful applications are considered, which are related with the theory of holo-nomic D-modules, the theory of Hodge structures, the theory of residual currents and others.
文摘In this paper, as a new contribution to the tensor-centric warfare (TCW) series [1] [2] [3] [4], we extend the kinetic TCW-framework to include non-kinetic effects, by addressing a general systems confrontation [5], which is waged not only in the traditional physical Air-Land-Sea domains, but also simultaneously across multiple non-physical domains, including cyberspace and social networks. Upon this basis, this paper attempts to address a more general analytical scenario using rigorous topological methods to introduce a two-level topological representation of modern armed conflict;in doing so, it extends from the traditional red-blue model of conflict to a red-blue-green model, where green represents various neutral elements as active factions;indeed, green can effectively decide the outcomes from red-blue conflict. System confrontations at various stages of the scenario will be defined by the non-equilibrium phase transitions which are superficially characterized by sudden entropy growth. These will be shown to have the underlying topology changes of the systems-battlespace. The two-level topological analysis of the systems-battlespace is utilized to address the question of topology changes in the combined battlespace. Once an intuitive analysis of the combined battlespace topology is performed, a rigorous topological analysis follows using (co)homological invariants of the combined systems-battlespace manifold.
