共查询到20条相似文献,搜索用时 31 毫秒
1.
Noga Alon 《Graphs and Combinatorics》1985,1(1):305-310
LetG=(V,E) be a graph with an initial signs(v)∈{±1} for every vertexv∈V. When a certexv becomesactive, it resets its sign tos′(v) which is the sign of the majority of its neighbors(s′(v)=1 if there is a tie).G is in astable state if,s′(v) for allv∈V. We show that for every graphG=(V,E) and every initial signs, there is a sequencev
1,v
2,...,v
r
of vertices ofG, in which no vertex appears more than once, such that ifv
i
becomes active at timei, (1≤i≤r), then after theser stepsG reaches a stable state. This proves a conjecture of Miller. We also consider some generalizations to directed graphs with
weighted edges. 相似文献
2.
The computation of the Legendre functions Pv(x) for −1 < x ≤ 1, v ∈ ℂ and of the adjoint Legendre functions P
v
−m
(x) for −1 < x ≤ 1, v ∈ ℂ, and m ∈ ℤ+ is the subject of the paper. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 14–30. 相似文献
3.
V. V. Kapustin 《Journal of Mathematical Sciences》2007,141(5):1538-1542
Let θ be an inner function, let K
θ
= H
2 ⊖ θH
2, and let Sθ : Kθ → Sθ be defined by the formula Sθf = Pθzf, where f ∈ Kθ is the orthogonal projection of H2 onto Kθ. Consider the set A of all trace class operators L : Kθ → Kθ, L = ∑(·,un)vn, ∑∥un∥∥vn∥ < ∞ (un, vn ∈ Kθ), such that ∑ūn vn ∈ H
0
1
. It is shown that trace class commutators of the form XSθ − SθX (where X is a bounded linear operator on Kθ) are dense in A in the trace class norm. Bibliography: 2 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 54–61. 相似文献
4.
Günter Heimbeck 《Geometriae Dedicata》1987,22(2):235-245
Let K be any commutative field and V:=K
4. A collection
of ruled quadrics in V is called a flock of ruled quadrics if the following holds true. (1) ⋃ℱ∈
G
ℱ = V; (2) There is a line S⊂V such that ℱ1⋂ℱ2= S for all distinct ℱ1, ℱ2∈
. The group ΓL(V) decomposes the set of all those flocks into equivalence classes. Besides that, we consider any cone R in V, say R:= {x∈V|x
1
x
3 - x
2
2
= 0}. Let R denote the set of all regular points of R. Plane sections of R which do not contain the singular point of ℜ are called regular sections. We consider decompositions of R
* by regular sections and their equivalence classes with respect to the symmetry group ΓL(V)R of the cone ℜ. The main result is as follows. There is a (natural) bijection between the classes of equivalent flocks of
rules quadrics and the classes of equivalent decompositions of R
* by regular sections. A brief discussion of those flocks of ruled quadrics on which the construction of the so-called Betten-Walker
planes is based ends the paper. Provided that char K≠3, these planes exist if and only if x∈K→x
3∈K is bijective.
相似文献
5.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 相似文献
6.
Shi Rong Li 《数学学报(英文版)》2008,24(4):647-654
Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown: (1) G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; (2) G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F(H), the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G. 相似文献
7.
Georg Schneider 《Czechoslovak Mathematical Journal》2005,55(4):947-956
We consider the solution operator S: ℱμ,(p,q) → L
2(μ)(p, q) to the
-operator restricted to forms with coefficients in ℱμ = {f: f is entire and ∫ℂn
|f(z)|2 dμ(z) < ∞}. Here ℱμ,(p,q) denotes (p,q)-forms with coefficients in ℱμ, L
2(μ) is the corresponding L
2-space and μ is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula
S to
. This solution operator will have the property Sv ⊥ ℱ(p,q) ∀v ∈ ℱ(p,q+1). As an application of the solution formula we will be able to characterize compactness of the solution operator in terms
of compactness of commutators of Toeplitz-operators
: ℱμ → L
2(μ). 相似文献
8.
Chaohui ZHANG 《数学年刊B辑(英文版)》2011,32(6):885-894
Let S be a Riemann surface that contains one puncture x. Let ℐ be the collection of simple closed geodesics on S, and let ℱ denote the set of mapping classes on S isotopic to the identity on S ∪ {x}. Denote by t
c
the positive Dehn twist about a curve c ∈ ℐ. In this paper, the author studies the products of forms (t
b
−m
∘ t
a
n
) ∘ f
k
, where a, b ∈ ℐ and f ∈ ℱ. It is easy to see that if a = b or a, b are boundary components of an x-punctured cylinder on S, then one may find an element f ∈ ℱ such that the sequence (t
b
−m
∘ t
n
a
) ∘ f
k
contains infinitely many powers of Dehn twists. The author shows that the converse statement remains true, that is, if the
sequence (t
b
−m
∘ t
a
n
) ∘ f
k
contains infinitely many powers of Dehn twists, then a, b must be the boundary components of an x-punctured cylinder on S and f is a power of the spin map t
b
−1 ∘ t
a
. 相似文献
9.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献
10.
H. -D. O. F. Gronau 《Combinatorica》1982,2(1):25-36
LetR be anr-element set and ℱ be a Sperner family of its subsets, that is,X ⊈Y for all differentX, Y ∈ ℱ. The maximum cardinality of ℱ is determined under the conditions 1)c≦|X|≦d for allX ∈ ℱ, (c andd are fixed integers) and 2) nok sets (k≧4, fixed integer) in ℱ have an empty intersection. The result is mainly based on a theorem which is proved by induction,
simultaneously with a theorem of Frankl. 相似文献
11.
For 1/4 < a <√2/4, let S1(x) = ax, S2(x) = 1 - a ax, x ∈ [0,1]. Ca is the attractor of the iterated function system {S1, S2}, then the packing measure of Ca × Ca is Ps(a)(Ca × Ca) = 4.2s(a)(1 - a)s(a),where s(a) = -loga4. 相似文献
12.
Let Λ be a finite-dimensional algebra over an algebraically closed field k. We denote by mod Λ the category of finitely generated left Λ-modules. Consider the family ℱ(u) of the indecomposables M∈mod Λ such that
, where
is the subspace of morphisms which factorize through semisimple modules. If P,Q are projectives in mod Λ, ℱ(u)(P,Q) is the family of those modules M∈ℱ(u) such that a minimal projective presentation is of the formfM: P→Q. We prove that if Λ is of tame representation type then each ℱ(P,Q) has only a finite number of isomorphism classes or is parametrized by μ(u,P,Q) one-parameter families. We give an upper bound for this number in terms of u,P and Q. Then we give some sufficient conditions for tame of polynomial growth type. For the proof we consider similar results for
bocses.
Presented by Y. Drozd
Mathematics Subject Classifications (2000) 16G60, 16G70, 16G20. 相似文献
13.
O. A. Kuryleva 《Algebra and Logic》2008,47(1):42-48
A vector space V over a real field R is a lattice under some partial order, which is referred to as a vector lattice if u + (v ∨ w) = (u + v) ∨ (u + w) and u
+ (v ∧ w) = (u + v) ∧ (u + w) for all u, v, w ∈ V. It is proved that a model N of positive integers with addition and multiplications is relatively elementarily interpreted in the ideal lattice
ℱ
n
of a free vector lattice ℱ
n
on a set of n generators. This, in view of the fact that an elementary theory for N is hereditarily undecidable, implies that an elementary theory for
ℱ
n
is also hereditarily undecidable.
__________
Translated from Algebra i Logika, Vol. 47, No. 1, pp. 71–82, January–February, 2008. 相似文献
14.
We show that if a closed manifold M admits an ℱ-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular,
this is the case if M admits a non-trivial S
1-action. As a corollary we obtain that the simplicial volume of a manifold admitting an ℱ-structure is zero.?We also show
that if M admits an ℱ-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently, its Yamabe invariant is non-negative.?We show that ℱ-structures
of rank zero appear rather frequently: every compact complex elliptic surface admits one as well as any simply connected closed
5-manifold.?We use these results to study the minimal entropy problem. We show the following two theorems: suppose that M is a closed manifold obtained by taking connected sums of copies of S
4, ℂP
2,
2,S
2×S
2and the K3 surface. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
4,ℂP
2,S
2×S
2,ℂP
2#
2 or ℂP
2# ℂP
2. Finally, suppose that M is a closed simply connected 5-manifold. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
5,S
3×S
2, then on trivial S
3-bundle over S
2 or the Wu-manifold SU(3)/SO(3).
Oblatum 13-III-2002 & 12-VIII-2002?Published online: 8 November 2002
G.P. Paternain was partially supported by CIMAT, Guanajuato, México.?J. Petean is supported by grant 37558-E of CONACYT. 相似文献
15.
Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L
2-norm for any u, v∈L
∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that
is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T
-n
A∩S
-
n
A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L
2(X) for all u, v∈L
∞(X) if and only if T×S is ergodic on X×X and the group generated by T
-1
S, T
-2
S
2,..., T
-c
S
c
acts ergodically on X.
Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
16.
Shinsuke Yorozu 《Israel Journal of Mathematics》1986,56(3):349-354
We give a generalization of the result obtained by C. Currás-Bosch. We consider the Av-operator associated to a transverse Killing fieldν on a complete foliated Riemannian manifold (M, ℱ, g). Under a certain assumption, we prove that, for eachx ∈M, (Av)
x
belongs to the Lie algebra of the linear holonomy group ψv(x). A special case of our result, the version of the foliation by points, implies the results given by B. Kostant (compact
case) and C. Currás-Bosch (non-compact case). 相似文献
17.
Stephen H. Hechler 《Israel Journal of Mathematics》1971,10(4):413-432
A family of infinite subsets of the setN of natural numbers will be called almost disjoint iff any two of its members have finite intersection. We shall define such
a family ℱ to ben-separable iff for every decompositionD = {D
1, …D
n
} ofN inton or fewer disjoint subsets there exist setsF ∈ ℱ andD ∃D such thatF ⊆D, and we shall use this and related notions to classify almost-disjoint families, using, on occasion, special axioms of set
theory. 相似文献
18.
Krzysztof Cieplinski 《Czechoslovak Mathematical Journal》2005,55(4):1079-1088
Let
be a disjoint iteration group on the unit circle
, that is a family of homeomorphisms such that F
v1 ○ F
v2 = F
v1+v2 for v
1, v
2 ∈ V and each F
v
either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial Abelian group). Denote by
the set of all cluster points of {F
v
(z), v ∈ V} for
. In this paper we give a general construction of disjoint iteration groups for which
. 相似文献
19.
Andreas Basse 《Journal of Theoretical Probability》2009,22(4):811-826
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide
necessary and sufficient conditions on the kernel K for X
t
=∫
K
t
(s) dN
s
to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure on a general space S. We study the semimartingale property of X in three different filtrations. First, the ℱ
X
-semimartingale property is considered, and afterwards the ℱ
X,∞-semimartingale property is treated in the case where X is a moving average process and ℱ
t
X,∞=σ(X
s
:s∈(−∞,t]). Finally, we study a generalization of Gaussian Volterra processes. In particular, we provide necessary and sufficient
conditions on K for the Gaussian Volterra process ∫
−∞
t
K
t
(s) dW
s
to be an ℱ
W,∞-semimartingale (W denotes a Wiener process). Hereby we generalize a result of Knight (Foundations of the Prediction Process, 1992) to the nonstationary case. 相似文献
20.
Shirong Li 《中国科学A辑(英文版)》1998,41(11):1121-1127
The class ℱpc of all finite groupsG is defined such thatX≤G implies that there exists an ℱ-subnormal subgroupS ofG containingX such thatX is ℱ-subabnormal inS, where ℱ is a saturated formation, closed under taken subgroups. Groups in ℱpc are characterized by ℱ-projectors and ℱ-covering subgroups.
Project supported by the National Natural Science Foundation of China (Grant No. 19760001) and the Natural Science Foundation
of Guangxi Autonomous Region. 相似文献