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1.
Let f:X→Yf:XY be a morphism between normal complex varieties, where YY is Kawamata log terminal. Given any differential form σσ, defined on the smooth locus of YY, we construct a “pull-back form” on XX. The pull-back map obtained by this construction is ?Y?Y-linear, uniquely determined by natural universal properties and exists even in cases where the image of ff is entirely contained in the singular locus of YY.  相似文献   

2.
Let MM be a closed subspace of a separable, infinite dimensional Hilbert space HH with dim(H/M)=∞dim(H/M)=. We show that a bounded linear operator A:M→MA:MM has an invertible chaotic extension T:H→HT:HH if and only if AA is bounded below. Motivated by our result, we further show that A:M→MA:MM has a chaotic Fredholm extension T:H→HT:HH if and only if AA is left semi-Fredholm.  相似文献   

3.
We consider a multidimensional diffusion XX with drift coefficient b(α,Xt)b(α,Xt) and diffusion coefficient ?σ(β,Xt)?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔtk=kΔ for k=1…nk=1n on a fixed interval [0,T][0,T]. We study minimum contrast estimators derived from the Gaussian process approximating XX for small ??. We obtain consistent and asymptotically normal estimators of αα for fixed ΔΔ and ?→0?0 and of (α,β)(α,β) for Δ→0Δ0 and ?→0?0 without any condition linking ?? and ΔΔ. We compare the estimators obtained with various methods and for various magnitudes of ΔΔ and ?? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.  相似文献   

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We show that if T:X→XT:XX is a continuous linear operator on an FF-space X≠{0}X{0}, then the set of frequently hypercyclic vectors of TT is of first category in XX, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→XT:XX is a bounded linear operator on a Banach space X≠{0}X{0} and if TT is frequently hypercyclic (or, more generally, syndetically transitive), then the TT-orbit of every non-zero element of XX is bounded away from 0, and in particular TT is not hypercyclic.  相似文献   

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Let kk be a field of characteristic zero and RR a factorial affine kk-domain. Let BB be an affineRR-domain. In terms of locally nilpotent derivations, we give criteria for BB to be RR-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y]R[X1,X2,Y] over RR by the ideal (X1X2−φ(Y))(X1X2φ(Y)) for φ(Y)∈R[Y]?Rφ(Y)R[Y]?R.  相似文献   

9.
We show that for each p∈(0,1]p(0,1] there exists a separable p  -Banach space GpGp of almost universal disposition, that is, having the following extension property: for each ε>0ε>0 and each isometric embedding g:X→Yg:XY, where Y is a finite-dimensional p-Banach space and X   is a subspace of GpGp, there is an ε  -isometry f:Y→Gpf:YGp such that x=f(g(x))x=f(g(x)) for all x∈XxX.  相似文献   

10.
Every submartingale SS of class DD has a unique Doob–Meyer decomposition S=M+AS=M+A, where MM is a martingale and AA is a predictable increasing process starting at 0.  相似文献   

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