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Satoshi Goto 《Expositiones Mathematicae》2010,28(3):218-253
We give an exposition of Ocneanu's theory of double triangle algebras for subfactors and its application to the classification of irreducible bi-unitary connections on the Dynkin diagrams An, Dn, E6, E7 and E8. More precisely, we give a detailed proof of the complete classification of irreducible K–L bi-unitary connections up to gauge choice, where K and L represent the two horizontal graphs which are among the A–D–E Dynkin diagrams. The result also provides a simple proof of the flatness of D2n, E6 and E8 connections as well as an easy computation of the flat part of E7 as an application. 相似文献
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The connected covering spaces of a connected and locally path-connected topological space X can be classified by the conjugacy classes of those subgroups of π1(X,x) which contain an open normal subgroup of π1(X,x), when endowed with the natural quotient topology of the compact-open topology on based loops. There are known examples of semicoverings (in the sense of Brazas) that correspond to open subgroups which do not contain an open normal subgroup. We present an example of a semicovering of the Hawaiian Earring H with corresponding open subgroup of π1(H) which does not contain any nontrivial normal subgroup of π1(H). 相似文献
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In this article, we construct simply connected symplectic Calabi–Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-Kähler Calabi–Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi–Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p≥1 and q≥2via co-isotropic Luttinger surgery. 相似文献
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It is proved that the cookie-cutter set in R is structurally instable in C1 topology, that means for the invariant set E of the IFS {fi}i, we can always perturb {fi}i arbitrarily small in C1 topology to provide an IFS {gi}i with its invariant set F, such that dimHE=dimHF and E,F are not Lipschitz equivalent. 相似文献
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Given a finite, connected 2-complex X such that b2(X)?1 we establish two existence results for representations of the fundamental group of X into compact connected Lie groups G , with prescribed values on certain loops. If b2(X)=1 we assume G=SO(3) and that the cup product on H1(X;Q) is non-zero. 相似文献
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This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index α is in (0,2), equal to 2, and in (2,∞), respectively. The partial sum weakly converges to a functional of α-stable process when α<2 and converges to a functional of Brownian motion when α≥2. When the process is of short-memory and α<4, the autocovariances converge to functionals of α/2-stable processes; and if α≥4, they converge to functionals of Brownian motions. In contrast, when the process is of long-memory, depending on α and β (the parameter that characterizes the long-memory), the autocovariances converge to either (i) functionals of α/2-stable processes; (ii) Rosenblatt processes (indexed by β, 1/2<β<3/4); or (iii) functionals of Brownian motions. The rates of convergence in these limits depend on both the tail index α and whether or not the linear process is short- or long-memory. Our weak convergence is established on the space of càdlàg functions on [0,1] with either (i) the J1 or the M1 topology (Skorokhod, 1956); or (ii) the weaker form S topology (Jakubowski, 1997). Some statistical applications are also discussed. 相似文献
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We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group G of rank 2 over a field. We exhibit exceptional collections of the expected length for types A2 and B2=C2 and prove that no such collection exists for type G2. This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous G-varieties for split linear algebraic groups G of rank at most 2. 相似文献
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We exhibit an example of a smooth affine threefold A over a field of characteristic 0 for which there exist non-trivial 2-torsion elements in the Euler class group E(A) vanishing in the weak Euler class group E0(A). This gives a positive answer to a question of the first author and Raja Sridharan. 相似文献
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We consider N independent stochastic processes (Xj(t),t∈[0,T]), j=1,…,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ?j and study the nonparametric estimation of the density of the random effect ?j in two kinds of mixed models. A multiplicative random effect and an additive random effect are successively considered. In each case, we build kernel and deconvolution estimators and study their L2-risk. Asymptotic properties are evaluated as N tends to infinity for fixed T or for T=T(N) tending to infinity with N. For T(N)=N2, adaptive estimators are built. Estimators are implemented on simulated data for several examples. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(Xt,α) and diffusion coefficient εa(Xt,β) where α and β are two unknown parameters, while ε is known. For a high frequency sample of observations of the diffusion at the time points k/n, k=1,…,n, we propose a class of contrast functions and thus obtain estimators of (α,β). The estimators are shown to be consistent and asymptotically normal when n→∞ and ε→0 in such a way that ε−1n−ρ remains bounded for some ρ>0. The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function. 相似文献
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In this paper, we investigate the dynamical behavior of a virus infection model with delayed humoral immunity. By using suitable Lyapunov functional and the LaSalle?s invariance principle, we establish the global stabilities of the two boundary equilibria. If R0<1, the uninfected equilibrium E0 is globally asymptotically stable; if R1<1<R0, the infected equilibrium without immunity E1 is globally asymptotically stable. When R1>1, we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity E2. The time delay can change the stability of E2 and lead to the existence of Hopf bifurcations. The stabilities of bifurcating periodic solutions is also studied. We check our theorems with numerical simulations in the end. 相似文献
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Given a bipartite graph G=(V,E), a weight for each node, and a weight for each edge, we consider an extension of the MAX-CUT problem that consists in searching for a partition of V into two subsets V1 and V2 such that the sum of the weights of the edges from E that have one endpoint in each set plus the sum of the weights of the nodes from V that are in V1, is maximal. We prove that this problem can be modeled as a linear program (with real variables) and therefore efficiently solved by standard algorithms. Then, we show how this result can be applied to model a land allocation problem by a 0–1 linear program. This problem consists in determining the cells of a land area, divided into a matrix of identical square cells, which must be harvested and the cells which must be left in old growth so that the weighted sum of the expected populations of some species is maximized. Some computational results are presented to illustrate the efficiency of the method. 相似文献
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In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations with step Δ. The asymptotic framework is: n tends to infinity, Δ=Δn tends to zero while nΔn tends to infinity. First, we use a Fourier approach (“frequency domain”): this allows us to construct an adaptive nonparametric estimator and to provide a bound for the global L2-risk. Second, we use a direct approach (“time domain”) which allows us to construct an estimator on a given compact interval. We provide a bound for L2-risk restricted to the compact interval. We discuss rates of convergence and give examples and simulation results for processes fitting in our framework. 相似文献
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In this paper, the authors propose a numerical method to compute the solution of the Cauchy problem: wt-(wmwx)x=wp, the initial condition is a nonnegative function with compact support, m>0, p?m+1. The problem is split into two parts: a hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a finite element method in space. The convergence of the scheme is obtained. Further, it is proved that if m+1?p<m+3, any numerical solution blows up in a finite time as the exact solution, while for p>m+3, if the initial condition is sufficiently small, a global numerical solution exists, and if p?m+3, for large initial condition, the solution is unbounded. 相似文献