We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras. 相似文献
A natural exponential family (NEF)F in ?n,n>1, is said to be diagonal if there existn functions,a1,...,an, on some intervals of ?, such that the covariance matrixVF(m) ofF has diagonal (a1(m1),...,an(mn)), for allm=(m1,...,mn) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ?k and ?n-k, for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ?n, that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ?n, under what conditions is its projectionp(F) in ?k, underp(x1,...,xn)∶=(x1,...,xk),k=1,...,n?1, still an NEF in ?k? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofVF(m1,...,mn) does not depend on (mk+1,...,mn). 相似文献
Suppose that { f(n), n N0} is a sequence of positive real numbers and suppose that the sequence { a(n), n N0} is given by a(0) = 0, and, for n 1, by the convolution equation nf(n) = a* f(n). The resulting sequence is denoted by a(n) = f(n) and is called the De Pril transform of { f(n), n N0} . In this paper, we consider first- and second-order asymptotic behavior of { f(n), n N0} for a large class of subexponential sequences { f(n), n N0} . We also discuss some applications. 相似文献
In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost
periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the
notion of pseudo almost periodic vector sequences 相似文献
Suppose that
,
, and
are three discrete probability distributions related by the equation (E):
, where
denotes the k-fold convolution of
In this paper, we investigate the relation between the asymptotic behaviors of
and
. It turns out that, for wide classes of sequences
and
, relation (E) implies that
, where
is the mean of
. The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference
. 相似文献
We study quasi-Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of depends on and the dimension . Strong tractability means that it does not depend on and is bounded by a polynomial in . The least possible value of the power of is called the -exponent of strong tractability. Sloan and Wozniakowski established a necessary and sufficient condition of strong tractability in weighted Sobolev spaces, and showed that the -exponent of strong tractability is between 1 and 2. However, their proof is not constructive.
In this paper we prove in a constructive way that multivariate integration in some weighted Sobolev spaces is strongly tractable with -exponent equal to 1, which is the best possible value under a stronger assumption than Sloan and Wozniakowski's assumption. We show that quasi-Monte Carlo algorithms using Niederreiter's -sequences and Sobol sequences achieve the optimal convergence order for any 0$"> independent of the dimension with a worst case deterministic guarantee (where is the number of function evaluations). This implies that strong tractability with the best -exponent can be achieved in appropriate weighted Sobolev spaces by using Niederreiter's -sequences and Sobol sequences.
Let be Singer's invariant-theoretic model of the dual of the lambda algebra with , where denotes the mod 2 Steenrod algebra. We prove that the inclusion of the Dickson algebra, , into is a chain-level representation of the Lannes-Zarati dual homomorphism
The Lannes-Zarati homomorphisms themselves, , correspond to an associated graded of the Hurewicz map
Based on this result, we discuss some algebraic versions of the classical conjecture on spherical classes, which states that Only Hopf invariant one and Kervaire invariant one classes are detected by the Hurewicz homomorphism. One of these algebraic conjectures predicts that every Dickson element, i.e. element in , of positive degree represents the homology class in for 2$">.
We also show that factors through , where denotes the differential of . Therefore, the problem of determining should be of interest.