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.
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
We propose two families of nonconforming elements on cubical meshes:one for the -curlΔcurl problem and the other for the Brinkman problem.The element for the -curlΔcurl problem is the first nonconforming element on ...We propose two families of nonconforming elements on cubical meshes:one for the -curlΔcurl problem and the other for the Brinkman problem.The element for the -curlΔcurl problem is the first nonconforming element on cubical meshes.The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the viscosity coefficient ν.The lowest-order elements for the -curlΔcurl and the Brinkman problems have 48 and 30 DOFs on each cube,respectively.The two families of elements are subspaces of H(curl;Ω)and H(div;Ω),and they,as nonconforming approximation to H(gradcurl;Ω)and[H^(1)(Ω)]^(3),can form a discrete Stokes complex together with the serendipity finite element space and the piecewise polynomial space.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
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, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold （G, H） with H being an almost sub-orbifold of G. Then we use ...In this paper, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold （G, H） with H being an almost sub-orbifold of G. Then we use the Gromov Witten invariants of G, the blow-up of G along H,to give a quantum modification of the relative Chen-Ruan cohomology ring H^R（G, H） when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G.展开更多
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
Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its...Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.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
Classical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div)-norm for general unstructured meshes containing hexahedra and prisms....Classical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div)-norm for general unstructured meshes containing hexahedra and prisms.We propose two new families of high-order elements for hexahedra,triangular prisms and pyramids that recover the optimal convergence.These elements have compatible restrictions with each other,such that they can be used directly on general hybrid meshes.Moreover the H(div)proposed spaces are completing the De Rham diagram with optimal elements previously constructed for H1 and H(curl)approximation.The obtained pyramidal elements are compared theoretically and numerically with other elements of the literature.Eventually,numerical results demonstrate the efficiency of the finite elements constructed.展开更多
In this paper,we consider the equivalent conditions with L^(p)-version(1<p<∞)of the J.L.Lions lemma.As applications,we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then w...In this paper,we consider the equivalent conditions with L^(p)-version(1<p<∞)of the J.L.Lions lemma.As applications,we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality.Furthermore,we consider the relation to other fundamental results.展开更多
We revisit the novel symmetries in N=2 supersymmetric quantum mechanical models by considering specific examples of coupled systems.Further,we extend our analysis to a general case and list out all the novel symmetrie...We revisit the novel symmetries in N=2 supersymmetric quantum mechanical models by considering specific examples of coupled systems.Further,we extend our analysis to a general case and list out all the novel symmetries.In each case,we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry.Thus,we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator.Moreover,we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.展开更多
Integration of large number of electric vehicles(EVs)with distribution networks is devastating for conventional power system devices such as transformers and power lines etc.This paper proposes a methodology for manag...Integration of large number of electric vehicles(EVs)with distribution networks is devastating for conventional power system devices such as transformers and power lines etc.This paper proposes a methodology for management of responsive household appliances management and EVs with water-filling algorithm.With the proposed scheme,the load profile of a transformer is retained below its rated capacity while minimally affecting the associated consumers.When the instantaneous demand at transformer increases beyond its capacity,the proposed methodology dynamically allocates demand curtailment limit(DCL)to each home served by transformer.The DCL allocation takes convenience factors,load profile and information of flexible appliances into account to assure the comfort of all the consumers.The proposed scheme is verified by modeling and simulating five houses and a distribution transformer.The smart appliances such as an HVAC,a water heater,a cloth dryer and an EV are also modeled for the study.Results show that the proposed scheme performs to reduce overloading effects of the transformer efficiently and assures comfort of the consumers at the same time.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 synt... 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
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.
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supported in part by the National Natural Science Foundation of China grants NSFC 12131005 and NSAF U2230402.
文摘We propose two families of nonconforming elements on cubical meshes:one for the -curlΔcurl problem and the other for the Brinkman problem.The element for the -curlΔcurl problem is the first nonconforming element on cubical meshes.The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the viscosity coefficient ν.The lowest-order elements for the -curlΔcurl and the Brinkman problems have 48 and 30 DOFs on each cube,respectively.The two families of elements are subspaces of H(curl;Ω)and H(div;Ω),and they,as nonconforming approximation to H(gradcurl;Ω)and[H^(1)(Ω)]^(3),can form a discrete Stokes complex together with the serendipity finite element space and the piecewise polynomial space.
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.
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.
基金supported by National Natural Science Foundation of China(Grant Nos.11071173 and 11221101)
文摘In this paper, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold （G, H） with H being an almost sub-orbifold of G. Then we use the Gromov Witten invariants of G, the blow-up of G along H,to give a quantum modification of the relative Chen-Ruan cohomology ring H^R（G, H） when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G.
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 the National Natural Science Foundation of China(No.11171161)the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education Ministry(No.2012940)
文摘Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.
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Classical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div)-norm for general unstructured meshes containing hexahedra and prisms.We propose two new families of high-order elements for hexahedra,triangular prisms and pyramids that recover the optimal convergence.These elements have compatible restrictions with each other,such that they can be used directly on general hybrid meshes.Moreover the H(div)proposed spaces are completing the De Rham diagram with optimal elements previously constructed for H1 and H(curl)approximation.The obtained pyramidal elements are compared theoretically and numerically with other elements of the literature.Eventually,numerical results demonstrate the efficiency of the finite elements constructed.
文摘In this paper,we consider the equivalent conditions with L^(p)-version(1<p<∞)of the J.L.Lions lemma.As applications,we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality.Furthermore,we consider the relation to other fundamental results.
基金support from the FRG scheme of National Institute of Technology Calicut。
文摘We revisit the novel symmetries in N=2 supersymmetric quantum mechanical models by considering specific examples of coupled systems.Further,we extend our analysis to a general case and list out all the novel symmetries.In each case,we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry.Thus,we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator.Moreover,we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.
基金supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No.2015R1A2A1A10052459)
文摘Integration of large number of electric vehicles(EVs)with distribution networks is devastating for conventional power system devices such as transformers and power lines etc.This paper proposes a methodology for management of responsive household appliances management and EVs with water-filling algorithm.With the proposed scheme,the load profile of a transformer is retained below its rated capacity while minimally affecting the associated consumers.When the instantaneous demand at transformer increases beyond its capacity,the proposed methodology dynamically allocates demand curtailment limit(DCL)to each home served by transformer.The DCL allocation takes convenience factors,load profile and information of flexible appliances into account to assure the comfort of all the consumers.The proposed scheme is verified by modeling and simulating five houses and a distribution transformer.The smart appliances such as an HVAC,a water heater,a cloth dryer and an EV are also modeled for the study.Results show that the proposed scheme performs to reduce overloading effects of the transformer efficiently and assures comfort of the consumers at the same time.
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.
