共查询到20条相似文献,搜索用时 15 毫秒
1.
Rafał Filipów Nikodem Mrożek Ireneusz Recław Piotr Szuca 《Czechoslovak Mathematical Journal》2011,61(2):289-308
We consider various forms of Ramsey’s theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey’s theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey’s theorem (these are similar to generalizations shown in [P. Frankl, R. L. Graham, and V. Rödl: Iterated combinatorial density theorems. 相似文献
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Hans G. Kellerer 《Archiv der Mathematik》1999,72(3):206-213
Given a nonatomic finite-dimensional vector measure on a topological space, a criterion is established for obtaining its full range by considering open (or closed) sets only. 相似文献
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Sen-Zhong Huang 《Semigroup Forum》1999,58(3):323-335
Let {e tA: t ≥ 0} be a C0—semigroup on the Hilbert space ?. If x 0 ∈ ? is such that the local resolvent R(λ,A) x 0 admits a bounded holomorphic extension to the open half plane {Reλ > 0}, then lim t→∞‖e tA R(λ0, A) x 0‖ = 0 for each λ0 ∈ ρ(A). This resuit is used to find mild spectral conditions which ensure the decay at infmity to zero of solutions of higher order abstract Cauchy problems. 相似文献
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Let $X$ be a manifold. The classification of all equivariant bilinear maps between tensor density modules over $X$ has been investigated by Grozman (Funct Anal Appl 14(2):58–59, 1980), who has provided a full classification for those which are differential operators. Here we investigate the same question without the hypothesis that the maps are differential operators. In our paper, the geometric context is algebraic geometry and the manifold $X$ is the circle $\text{ Spec}\, \mathbb{C }[z,z^{-1}]$ . Our main motivation comes from the fact that such a classification is required to complete the proof of the main result of Iohara and Mathieu (Proc Lond Math Soc, 2012, in press). Indeed it requires to also include the case of deformations of tensor density modules. 相似文献
5.
Annette Maier 《Mathematische Annalen》2014,359(3-4):759-784
We consider (Frobenius) difference equations over \((\mathbb {F}\!_q(s,t), \phi _q)\) where \(\phi _q\) fixes \(t\) and acts on \(\mathbb {F}\!_q(s)\) as the Frobenius endomorphism. We prove that every semisimple, simply-connected linear algebraic group \(\mathcal {G}\) defined over \(\mathbb {F}\!_q\) can be realized as a difference Galois group over \((\mathbb {F} \! _{q^i} (s,t),\phi _{q^i})\) for some \(i \in \mathbb {N}\) . The proof uses upper and lower bounds on the Galois group scheme of a Frobenius difference equation that are developed in this paper. The result can be seen as a difference analogue of Nori’s theorem which states that \(\mathcal {G}(\mathbb {F}\!_q)\) occurs as a (finite) Galois group over \(\mathbb {F}\!_q(s)\) . 相似文献
6.
A recent result, conjectured by Arnold and proved by Zarelua, states that for a prime number p, a positive integer k, and a square matrix A with integral entries one has ${\textrm tr}(A^{p^k})
\equiv {\textrm tr}(A^{p^{k-1}}) ({\textrm mod}{p^k})${\textrm tr}(A^{p^k})
\equiv {\textrm tr}(A^{p^{k-1}}) ({\textrm mod}{p^k}). We give a short proof of a more general result, which states that if the characteristic polynomials of two integral matrices
A, B are congruent modulo p
k
then the characteristic polynomials of A
p
and B
p
are congruent modulo p
k+1, and then we show that Arnold’s conjecture follows from it easily. Using this result, we prove the following generalization
of Euler’s theorem for any 2 × 2 integral matrix A: the characteristic polynomials of A
Φ(n) and A
Φ(n)-ϕ(n) are congruent modulo n. Here ϕ is the Euler function, ?i=1l piai\prod_{i=1}^{l} p_i^{\alpha_i} is a prime factorization of n and $\Phi(n)=(\phi(n)+\prod_{i=1}^{l}
p_i^{\alpha_i-1}(p_i+1))/2$\Phi(n)=(\phi(n)+\prod_{i=1}^{l}
p_i^{\alpha_i-1}(p_i+1))/2. 相似文献
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8.
Panyue Zhou 《代数通讯》2018,46(1):82-89
Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. We prove a right triangulated version of Gentle-Todorov’s theorem by introducing the notion of right homotopy cartesian square. 相似文献
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Huan Xiong 《数学学报(英文版)》2013,29(8):1597-1606
In this paper, we consider a discrete version of Aleksandrov's projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice's y-coordinates' absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov's projection theorem which was proposed by Gardner, Gronchi and Zong in 2005. 相似文献
12.
Grigoris Paouris Petros Valettas Joel Zinn 《Stochastic Processes and their Applications》2017,127(10):3187-3227
We study the dependence on in the critical dimension for which one can find random sections of the -ball which are -spherical. We give lower (and upper) estimates for for all eligible values and as , which agree with the sharp estimates for the extreme values and . Toward this end, we provide tight bounds for the Gaussian concentration of the -norm. 相似文献
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In this paper, we present a sharp version of Bauer–Fike’s theorem. We replace the matrix norm with its spectral radius or sign-complex spectral radius for diagonalizable matrices; 1-norm and ∞-norm for non-diagonalizable matrices. We also give the applications to the pole placement problem and the singular system. 相似文献
15.
E. A. Lebedeva 《Mathematical Notes》2010,88(5-6):717-722
We study the asymptotic behavior of the roots of polynomials given by a linear summation method for partial sums of the Fourier series. 相似文献
16.
John R. Reay 《Israel Journal of Mathematics》1979,34(3):238-244
In a generalization of Radon’s theorem, Tverberg showed that each setS of at least (d+1) (r ? 1)+1 points inR d has anr-partition into (pair wise disjoint) subsetsS =S 1 ∪ … ∪S r so that \(\bigcap\nolimits_i^r {\underline{\underline {}} } _1 \) convS i # Ø. This note considers the following more general problems: (1) How large mustS σR d be to assure thatS has anr-partitionS=S 1∪ … ∪S r so that eachn members of the family {convS i ~ i-1 r have non-empty intersection, where 1<=n<=r. (2) How large mustS ∪R d be to assure thatS has anr-partition for which \(\bigcap\nolimits_i^r {\underline{\underline {}} } _1 \) convS r is at least 1-dimensional. 相似文献
17.
Nekhoroshev discovered a beautiful theorem in Hamiltonian systems that includes as special cases not only the Poincaré theorem on periodic orbits but also the theorem of Liouville–Arnol’d on completely integrable systems [7]. Sadly, his early death precluded him publishing a full account of his proof. The aim of this paper is twofold: first, to provide a complete proof of his original theorem and second a generalization to the noncommuting case. Our generalization of Nekhoroshev’s theorem to the nonabelian case subsumes aspects of the theory of noncommutative complete integrability as found in Mishchenko and Fomenko [5] and is similar to what Nekhoroshev’s theorem does in the abelian case. 相似文献
18.
A. L. Kanunnikov 《Moscow University Mathematics Bulletin》2011,66(3):119-122
We prove graded variants of Goldie’s theorem of existence, structure, and coincidence of right classical quotient ring and
right maximal quotient ring of a semiprime (prime) right Goldie’s ring (Theorems 10, 11, and 13). The main difficulty consisting
in the problem of existence of a homogeneous regular element in each gr-essential right ideal is solved by posing some additional
requirements onto the group grading the ring or onto the homogeneous components of the ring. 相似文献
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