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991.
The tropical arithmetic operations on R are defined by a⊕b=min{a,b} and a⊗b=a+b. Let A be a tropical matrix and k a positive integer, the problem of Tropical Matrix Factorization (TMF) asks whether there exist tropical matrices B∈Rm×k and C∈Rk×n satisfying B⊗C=A. We show that the TMF problem is NP-hard for every k≥7 fixed in advance, thus resolving a problem proposed by Barvinok in 1993. 相似文献
992.
We consider surjective endomorphisms f of degree >1 on projective manifolds X of Picard number one and their f−1-stable hypersurfaces V, and show that V is rationally chain connected. Also given is an optimal upper bound for the number of f−1-stable prime divisors on (not necessarily smooth) projective varieties. 相似文献
993.
994.
We develop an inductive approach to the representation theory of the Yokonuma–Hecke algebra Yd,n(q), based on the study of the spectrum of its Jucys–Murphy elements which are defined here. We give explicit formulas for the irreducible representations of Yd,n(q) in terms of standard d -tableaux; we then use them to obtain a semisimplicity criterion. Finally, we prove the existence of a canonical symmetrising form on Yd,n(q) and calculate the Schur elements with respect to that form. 相似文献
995.
We study a multi-dimensional nonlocal active scalar equation of the form ut+v⋅∇u=0 in R+×Rd, where v=Λ−2+α∇u with Λ=(−Δ)1/2. We show that when α∈(0,2] certain radial solutions develop gradient blowup in finite time. In the case when α=0, the equations are globally well-posed with arbitrary initial data in suitable Sobolev spaces. 相似文献
996.
997.
A (hidden) multiplication on AZ(n,r), the Z-dual of the integral Schur algebra SZ(n,r) is explicitly constructed, possibly without a unit. The image of the multiplication map is shown to be spanned by bipermanents. Let k be any field of characteristic p>0. The image of the induced multiplication on Ak(n,r)=AZ(n,r)⊗Zk turns out to coincide with the Doty coalgebra Dn,r,p of truncated symmetric powers. Combined with a new straightening formula for bipermanents, it is proved that such a multiplication induces an isomorphism Ak(n,r)⊗Sk(n,r)Ak(n,r)≅Ak(n,r) as Sk(n,r)-bimodules if and only if r≤n(p−1), if and only if Dn,r,p=Ak(n,r). As a result, Sk(n,r) is a gendo-symmetric algebra, and its dominant dimension is at least two and admits a combinatorial characterization as long as r≤n(p−1). 相似文献
998.
We investigate iterations of fixed-point free holomorphic self-maps on a Lie ball of any dimension, where a Lie ball is a bounded symmetric domain and the open unit ball of a spin factor which can be infinite dimensional. We describe the invariant domains of a holomorphic self-map f on a Lie ball D when f is fixed-point free and compact, and show that each limit function of the iterates (fn) has values in a one-dimensional disc on the boundary of D . We show that the Möbius transformation ga induced by a nonzero element a in D may fail the Denjoy–Wolff-type theorem, even in finite dimension. We determine those which satisfy the theorem. 相似文献
999.
Given a non-compact, simply connected homogeneous three-manifold X and a sequence {Ωn}n of isoperimetric domains in X with volumes tending to infinity, we prove that, as n→∞:
- (1)
- The radii of the Ωn tend to infinity. 相似文献
1000.