共查询到20条相似文献,搜索用时 31 毫秒
1.
Bodan Arsovski 《Israel Journal of Mathematics》2011,182(1):505-508
We prove Snevily’s conjecture, which states that for any positive integer k and any two k-element subsets {a
1, …, a
k
} and {b
1, …, b
k
} of a finite abelian group of odd order there exists a permutation π ∈ S
k
such that all sums a
i
+ b
π(i) (i ∈ [1, k]) are pairwise distinct. 相似文献
2.
Let G be a finite abelian group with |G| > 1. Let a
1, …, a
k
be k distinct elements of G and let b
1, …, b
k
be (not necessarily distinct) elements of G, where k is a positive integer smaller than the least prime divisor of |G|. We show that there is a permutation π on {1, …,k} such that a
1
b
π(1), …, a
k
b
π(k) are distinct, provided that any other prime divisor of |G| (if there is any) is greater than k!. This in particular confirms the Dasgupta-Károlyi-Serra-Szegedy conjecture for abelian p-groups. We also pose a new conjecture involving determinants and characters, and show that its validity implies Snevily’s
conjecture for abelian groups of odd order. Our methods involve exterior algebras and characters. 相似文献
3.
J. C. Gupta 《Proceedings Mathematical Sciences》2000,110(4):415-430
Let G
n,k
be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencesc
n(β1,β2,…, β
k
), β1,β2,…, βk
= 0,1,2,…, β1+β2 + … +β
k
≤n,c
n(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + β
k
) where Δc
n(β1,β2,…, β
k
) =c
n(β1 + 1, β2,…, β
k
)+c
n(β1,β2+1,…, β
k
)+…+c
n (β1,β2,…, β
k
+1) -c
n(β1,β2,…, β
k
). Further, let Π
n,k
be the set of all symmetric probabilities on {0,1,2,…,k}
n
. We establish a one-to-one correspondence between the sets G
n,k
and Π
n,k
and use it to formulate and answer interesting questions about both. Assigning to G
n,k
the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, β
k
), 1 ≤ Σβ
i
≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σ
m
]; the centering constantsc
0(β1, β2,…, β
k
) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inR
k. 相似文献
4.
5.
Recently, B. Y. Chen introduced a new intrinsic invariant of a manifold, and proved that everyn-dimensional submanifold of real space formsR
m
(ε) of constant sectional curvature ε satisfies a basic inequality δ(n
1,…,n
k
)≤c(n
1,…,n
k
)H
2+b(n
1,…,n
k
)ε, whereH is the mean curvature of the immersion, andc(n
1,…,n
k
) andb(n
1,…,n
k
) are constants depending only onn
1,…,n
k
,n andk. The immersion is calledideal if it satisfies the equality case of the above inequality identically for somek-tuple (n
1,…,n
k
). In this paper, we first prove that every ideal Einstein immersion satisfyingn≥n
1+…+n
k
+1 is totally geodesic, and that every ideal conformally flat immersion satisfyingn≥n
1+…+n
k
+2 andk≥2 is also totally geodesic. Secondly we completely classify all ideal semi-symmetric hypersurfaces in real space forms.
The author was supported by the NSFC and RFDP. 相似文献
6.
Here we prove the following result on Weierstrass multiple points.
Theorem:Fix integers k, g with k≥5 and g>4k. Then there exist a genus g, Riemann surface X and k points P
1, …,P
k
of X such that for all integers b
1≥…≥b
k
≥0we have:
.
By Riemann-Roch the value given is the lowest one compatible withk, g and the inequalityh
0(X,O
X
(P
1+…+P
k
))≥2. Hence this theorem means that (P
1, …,P
k
) is ak-ple Weierstrass set with the lowest weight possible compatible with the integersk andg. Using similar tools we prove a theorem on the non-gap sequence of a Weierstrass point onm-gonal curves and study theg
d
r
’s on a generalk-sheeted covering of an irrational curve. Then we introduce and study a class of vector bundles on coverings of elliptic curves. 相似文献
7.
Noga Alon 《Israel Journal of Mathematics》2000,117(1):125-130
We prove that for every odd primep, everyk≤p
and every two subsets
A={a
1, …,a
k
} andB={b
1, …,b
k
} of cardinalityk each ofZ
p
, there is a permutationπ ∈S
k
such that the sumsa
i
+b
π(i) (inZ
p
) are pairwise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related
results as well.
Research supported in part by a State of New Jersey grant and by the Hermann Minkowski Minerva Center for Geometry at Tel
Aviv University. 相似文献
8.
Let ?(n;3,5,…,2k+1) denote the class of non-bipartite graphs on n vertices having no odd cycle of length ≤2k+1. We prove that for every G∈?(n;3,5,…,2k+1) and characterize the extremal graphs. We also study the subclass ℋ(n;3,5,…,2k+1) consisting of the hamiltonian members of ?(n;3,5,…, 2k+1). For this subclass the above upper bound holds for odd n. For even n we establish the following sharp upper bound:
and characterize the extremal graphs.
Received: February 28, 1997 Final version received: August 31, 2000 相似文献
9.
W. G. Bridges 《Israel Journal of Mathematics》1972,12(4):369-372
Bounds on the number of row sums in ann×n, non-singular (0,1)-matrixA sarisfyingA
tA=diag (k
1-λ1,…,k
n-λn),k
j>λj>0,λ1=…=λe,λe+1=…=λn are obtained which extend previous results for such matrices. 相似文献
10.
K. A. Kopotun 《Constructive Approximation》2001,17(2):307-317
One of the main results of this paper is the following Whitney theorem of interpolatory type for k-monotone functions (i.e., functions f such that divided differences f[x
0,…, x
k
] are nonnegative for all choices of (k + 1) distinct points x
0,…, x
k
. 相似文献
11.
Ignacy Kotlarski 《Annali di Matematica Pura ed Applicata》1966,74(1):129-134
Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x1, x2, …, xn be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals fk(t) = E[ei(t,x
k)], (k=1, 2, …, n): let y1=x1 + xn, y2=x2 + xn, …, yn−1=xn−1 + xn.
If the characteristic functional f(t1, t2, …, tn−1) of the random variables (y1, y2, …, yn−1) does not vanish, then the joint distribution of (y1, y2, …, yn−1) determines all the distributions of x1, x2, …, xn up to change of location. 相似文献
12.
Let H be an atomic monoid. For
k ? \Bbb Nk \in {\Bbb N} let Vk (H){\cal V}_k (H) denote the set of all
m ? \Bbb Nm \in {\Bbb N} with the following property: There exist atoms (irreducible elements) u
1, …, u
k
, v
1, …, v
m
∈ H with u
1· … · u
k
= v
1 · … · v
m
. We show that for a large class of noetherian domains satisfying some natural finiteness conditions, the sets Vk (H){\cal V}_k (H) are almost arithmetical progressions. Suppose that H is a Krull monoid with finite cyclic class group G such that every class contains a prime (this includes the multiplicative monoids of rings of integers of algebraic number
fields). We show that, for every
k ? \Bbb Nk \in {\Bbb N}, max V2k+1 (H) = k |G|+ 1{\cal V}_{2k+1} (H) = k \vert G\vert + 1 which settles Problem 38 in [4]. 相似文献
13.
K. N. Venkataraman K. Suresh Chandra 《Annals of the Institute of Statistical Mathematics》1984,36(1):101-118
Summary LetX(t) be a linear autoregressively generated explosive time series, with autoregressive coefficientsb
1,…,bq, and a constant termb
0, and an error term
; a0=1. Where ε(t),t≧1 are independent, Eε(t)=0, and Eε
2(t)=σ2 is positive and finite. In this paper two categories of
-consisent and asymptotically singularly normal estimators are proposed for (b
1,…,bq, b0) thus settling an open problem since the publication of the paper (Venkataraman [5]). Based on these estimators several additional
limit theorems based on estimated error residuals are proved. The parameter-free limit theorems of Spectral and Quenouille
types of this paper serve as asymptotic goodness of fit tests for the model generatingX(t). 相似文献
14.
Samit Dasgupta Gyula Károlyi Oriol Serra Balázs Szegedy 《Israel Journal of Mathematics》2001,126(1):17-28
LetA={a
1, …,a
k} andB={b
1, …,b
k} be two subsets of an Abelian groupG, k≤|G|. Snevily conjectured that, whenG is of odd order, there is a permutationπ ∈S
ksuch that the sums α
i
+b
i
, 1≤i≤k, are pairwise different. Alon showed that the conjecture is true for groups of prime order, even whenA is a sequence ofk<|G| elements, i.e., by allowing repeated elements inA. In this last sense the result does not hold for other Abelian groups. With a new kind of application of the polynomial method
in various finite and infinite fields we extend Alon’s result to the groups (ℤ
p
)
a
and
in the casek<p, and verify Snevily’s conjecture for every cyclic group of odd order.
Supported by Hungarian research grants OTKA F030822 and T029759.
Supported by the Catalan Research Council under grant 1998SGR00119.
Partially supported by the Hungarian Research Foundation (OTKA), grant no. T029132. 相似文献
15.
Saugata Basu 《Foundations of Computational Mathematics》2008,8(1):45-80
For any ℓ>0, we present an algorithm which takes as input a semi-algebraic set, S, defined by P
1≤0,…,P
s
≤0, where each P
i
∈R[X
1,…,X
k
] has degree≤2, and computes the top ℓ Betti numbers of S, b
k−1(S),…,b
k−ℓ
(S), in polynomial time. The complexity of the algorithm, stated more precisely, is
. For fixed ℓ, the complexity of the algorithm can be expressed as
, which is polynomial in the input parameters s and k. To our knowledge this is the first polynomial time algorithm for computing nontrivial topological invariants of semialgebraic
sets in R
k
defined by polynomial inequalities, where the number of inequalities is not fixed and the polynomials are allowed to have
degree greater than one. For fixed s, we obtain, by letting ℓ=k, an algorithm for computing all the Betti numbers of S whose complexity is
.
An erratum to this article can be found at 相似文献
16.
The concept of absolutely monotone functions is generalized by replacing the conditionsφ
(k)(t)≧0,k=0, 1, … by an infinite sequence of differential inequalitiesφ(t)≧0,L
kφ(t)≧0,k=1, 2, …, where theL
k are differential operators of a special type. It is shown that these functions have a valid series expansion in terms of
basic functions associated with the operatorsL
k. 相似文献
17.
LetA={a
1, …,a
k} and {b
1, …,b
k} be two subsets of an abelian groupG, k≤|G|. Snevily conjectured that, when |G| is odd, there is a numbering of the elements ofB such thata
i+b
i,1≤i≤k are pairwise distinct. By using a polynomial method, Alon affirmed this conjecture for |G| prime, even whenA is a sequence ofk<|G| elements. With a new application of the polynomial method, Dasgupta, Károlyi, Serra and Szegedy extended Alon’s result to
the groupsZ
p
r
andZ
p
rin the casek<p and verified Snevily’s conjecture for every cyclic group. In this paper, by employing group rings as a tool, we prove that
Alon’s result is true for any finite abelianp-group withk<√2p, and verify Snevily’s conjecture for every abelian group of odd order in the casek<√p, wherep is the smallest prime divisor of |G|.
This work has been supported partly by NSFC grant number 19971058 and 10271080. 相似文献
18.
Ferenc Móricz 《Periodica Mathematica Hungarica》2011,62(1):61-73
The well-known characterization indicated in the title involves the moving maximal dyadic averages of the sequence (X
k
: k = 1, 2, …) of random variables in Probability Theory. In the present paper, we offer another characterization of the SLLN
which does not require to form any maximum. Instead, it involves only a specially selected sequence of moving averages. The
results are also extended for random fields (X
kℓ: k, ℓ = 1, 2, …). 相似文献
19.
A. V. Zheleznyak 《Vestnik St. Petersburg University: Mathematics》2009,42(4):269-274
In the middle of the 20th century Hardy obtained a condition which must be imposed on a formal power series f(x) with positive coefficients in order that the series f
−1(x) = $
\sum\limits_{n = 0}^\infty {b_n x^n }
$
\sum\limits_{n = 0}^\infty {b_n x^n }
b
n
x
n
be such that b
0 > 0 and b
n
≤ 0, n ≥ 1. In this paper we find conditions which must be imposed on a multidimensional series f(x
1, x
2, …, x
m
) with positive coefficients in order that the series f
−1(x
1, x
2, …, x
m
) = $
\sum i_1 ,i_2 , \ldots ,i_m \geqslant 0^b i_1 ,i_2 , \ldots ,i_m ^{x_1^{i_1 } x_2^{i_2 } \ldots x_m^{i_m } }
$
\sum i_1 ,i_2 , \ldots ,i_m \geqslant 0^b i_1 ,i_2 , \ldots ,i_m ^{x_1^{i_1 } x_2^{i_2 } \ldots x_m^{i_m } }
satisfies the property b
0, …, 0 > 0, $
bi_1 ,i_2 , \ldots ,i_m
$
bi_1 ,i_2 , \ldots ,i_m
≤ 0, i
12 + i
22 + … + i
m
2 > 0, which is similar to the one-dimensional case. 相似文献
20.
On sharp conditions for the global stability of a difference equation satisfying the Yorke condition
Continuing our previous investigations, we give simple sufficient conditions for the global stability of the zero solution
of the difference equation x
n+1 = qx
n + ƒn(x
n, …, x
n−k), n ∈ ℤ, where the nonlinear functions ƒn satisfy the Yorke condition. For every positive integer k, we represent the interval (0, 1] as the union of [(2k + 2)/3] disjoint subintervals, and, for q from each subinterval, we present a global-stability condition in explicit form. The conditions obtained are sharp for the
class of equations satisfying the Yorke condition.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 73–80, January, 2008. 相似文献