This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived...This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.展开更多
According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed a...According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed as the trace of π（fρ,s） for a function fρ,s with non-compact support whenever Re（s） ≥ 0. Such a function should have useful interpretations in terms of geometry or eombinatories, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jaequet theory for （G, ρ）. In this paper, we derive some basic properties for the basic functions fρ,s and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function.展开更多
This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from m...This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from multivariable joint distribution but only from their dependency matrix. Hence, the scenarios generated by proposed method can contain flail statistical information of multivariate. Here, the details of simu- lating scenarios for multi-wind-farm are explained with four steps： determine margin of one wind farm, fit the copulas, choose optimal copulas and simulate scenarios by Mote Carlo. Moreover, the producing process of scenarios is demonstrated by two adjacent actual wind farms in China. With the scenarios, the STOPF is con- verted into the same amount deterministic sub OPF models which can be solved by available technology per- fectly. Results using copula theory are compared against results from history samples based on two designs： IEEE 30-bus and IEEE 118-bus systems. The comparison results prove the accuracy of the proposed methodology.展开更多
文摘This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.
文摘According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed as the trace of π（fρ,s） for a function fρ,s with non-compact support whenever Re（s） ≥ 0. Such a function should have useful interpretations in terms of geometry or eombinatories, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jaequet theory for （G, ρ）. In this paper, we derive some basic properties for the basic functions fρ,s and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function.
基金supported by National Natural Science Foundation of China(Grant No.51277034,51377027)
文摘This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from multivariable joint distribution but only from their dependency matrix. Hence, the scenarios generated by proposed method can contain flail statistical information of multivariate. Here, the details of simu- lating scenarios for multi-wind-farm are explained with four steps： determine margin of one wind farm, fit the copulas, choose optimal copulas and simulate scenarios by Mote Carlo. Moreover, the producing process of scenarios is demonstrated by two adjacent actual wind farms in China. With the scenarios, the STOPF is con- verted into the same amount deterministic sub OPF models which can be solved by available technology per- fectly. Results using copula theory are compared against results from history samples based on two designs： IEEE 30-bus and IEEE 118-bus systems. The comparison results prove the accuracy of the proposed methodology.
