共查询到20条相似文献,搜索用时 31 毫秒
1.
Nadjib Bouzar 《Annals of the Institute of Statistical Mathematics》2008,60(4):901-917
We present a notion of semi-self-decomposability for distributions with support in Z
+. We show that discrete semi-self-decomposable distributions are infinitely divisible and are characterized by the absolute
monotonicity of a specific function. The class of discrete semi-self-decomposable distributions is shown to contain the discrete
semistable distributions and the discrete geometric semistable distributions. We identify a proper subclass of semi-self-decomposable
distributions that arise as weak limits of subsequences of binomially thinned sums of independent Z
+-valued random variables. Multiple semi-self-decomposability on Z
+ is also discussed. 相似文献
2.
Emad-Eldin A. A. Aly Nadjib Bouzar 《Annals of the Institute of Statistical Mathematics》2002,54(1):125-137
The multiplications of van Harn et al. (1982, Z. Wahrsch. Verw. Gebiete, 61, 97–118) are used to generalize the definition of -monotonicity of Olshen and Savage (1970, J. Appl. Probab., 7, 21–34) and Steutel (1988, Statist. Neerlandica, 42, 137–140) for distributions with support in Z
+ and R
+. Several characterizations are offered and a convolution property is established. Some relevant stability equations are solved and a relationship with the important concept of self-decomposability is noted. Poisson mixtures are used to deduce results for the R
+-case from those for the Z
+-case. 相似文献
3.
Letk be a number field,p an odd prime,R
k
the ring ofp-integers ofk. We use Iwasawa theory to study theZ
p
-moduleG(R
k
,Z
p
) (resp.NB (R
k
,Z
p
)) ofclasses ofZ
p
-extensions (resp.Z
p
-extensions having a normal basis overR
k
) ofR
k
. The rank ofG(G
k
,Z
p
) (resp.NB(R
k
,Z
p
)) is related to Leopoldt's conjecture (resp. weak Leopoldt's conjecture) fork andp.
相似文献
4.
Nadjib Bouzar 《Annals of the Institute of Statistical Mathematics》2004,56(3):497-510
The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for
distributions with support inZ
+. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these
distributions posses the property of infinite divisibility and that their probability generating functions admit canonical
representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable
distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and
some examples are constructed. 相似文献
5.
The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give
an algebraic combinatorics formula for the M?bius transform of an abstract simplicial complex K on [m]={1,…,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound on the sum of those Betti numbers using our formula. Next we consider a class of generalized moment-angle
complexes
ZK(\mathbb D, \mathbb S)\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})}, including the moment-angle complex ZK\mathcal{Z}_{K} and the real moment-angle complex
\mathbbRZK\mathbb{R}\mathcal {Z}_{K} as special examples. We show that
H*(ZK(\mathbb D, \mathbb S);k)H^{*}(\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})};\mathbf{k}) has the same graded k-module structure as Tor
k[v](k(K),k). Finally we show that the Halperin–Carlsson conjecture holds for ZK\mathcal{Z}_{K} (resp.
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}) under the restriction of the natural T
m
-action on ZK\mathcal{Z}_{K} (resp. (ℤ2)
m
-action on
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}). 相似文献
6.
Nicolas Chevallier 《Monatshefte für Mathematik》2009,157(2):101-130
Let α be in the two-dimensional torus T
2 = R
2/Z
2. Assume that the translation map T : x → x + α acts ergodically. We present a symbolic coding of the map T which shares several properties with the Sturmian coding of a one-dimensional translation. The symbolic dynamical system
is metrically isomorphic to the geometric dynamical system (T
2, T). The coding is of quadratic growth complexity and 2-balanced. Moreover, there is a geometric underpinning, the coding is
related to a fundamental domain for the action of Z
2 on R
2 and also to bounded remainder sets.
相似文献
7.
Nicolas Chevallier 《Monatshefte für Mathematik》2009,13(1):101-130
Let α be in the two-dimensional torus T
2 = R
2/Z
2. Assume that the translation map T : x → x + α acts ergodically. We present a symbolic coding of the map T which shares several properties with the Sturmian coding of a one-dimensional translation. The symbolic dynamical system
is metrically isomorphic to the geometric dynamical system (T
2, T). The coding is of quadratic growth complexity and 2-balanced. Moreover, there is a geometric underpinning, the coding is
related to a fundamental domain for the action of Z
2 on R
2 and also to bounded remainder sets. 相似文献
8.
Andrea Vietri 《Graphs and Combinatorics》2007,23(1):111-121
We analyse 3-subset difference families of Z2d+1⊕Z2d+1 arising as reductions (mod 2d+1) of particular families of 3-subsets of Z⊕Z. The latter structures, namely perfect d-families, can be viewed as 2-dimensional analogues of difference triangle sets having the least scope. Indeed, every perfect d-family is a set of base blocks which, under the natural action of the translation group Z⊕Z, cover all edges {(x,y),(x′,y′)} such that |x−x′|, |y−y′|≤d. In particular, such a family realises a translation invariant (G,K3)-design, where V(G)=Z⊕Z and the edges satisfy the above constraint. For that reason, we regard perfect families as part of the hereby defined translation designs, which comprise and slightly generalise many structures already existing in the literature. The geometric context allows
some suggestive additional definitions. The main result of the paper is the construction of two infinite classes of d-families. Furthermore, we provide two sporadic examples and show that a d-family may exist only if d≡0,3,8,11 (mod 12). 相似文献
9.
Smith 《Constructive Approximation》2008,19(3):465-476
Abstract. We consider the problem of approximating vectors from a complemented subspace Z
+
of a Banach space X by the projections onto Z
+
of vectors from a subspace Y
+
with a norm constraint on their projections onto the complementary subspace. Sufficient conditions are found for the existence
of a unique best approximant and a characterization via a critical point equation is provided, thus extending known results
on Hilbert spaces. These results are then applied in the case that X is L
p
(T), where T denotes the unit circle, Z
+
consists of functions supported on a subset of the circle, and Y
+
is the corresponding Hardy space. 相似文献
10.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
11.
《代数通讯》2013,41(12):4821-4833
Abstract In this note, we show that the following are equivalent for a ring R for which the socle or the injective hull of R R is finitely generated: (i) The direct sum of any two CS right R-modules is again CS; (ii) R is right Artinian and every uniform right R-module has composition length at most two. Next we give partial answers to a question of Huynh whether a right countably Σ-CS ring which either is semilocal or has finite Goldie dimension is right Σ-CS. We give characterizations, in terms of radicals, of when such rings are right Σ-CS. In particular, for the semilocal case, Huynh's question is reduced to whether rad(Z 2(R R )) is Σ-CS or Noetherian, where Z 2(R R ) is the second singular right ideal of R. Our results yield new characterizations of QF-rings. 相似文献
12.
Let R be any ring with identity. Let N(R) (resp. J(R)) denote the prime radical (resp. Jacobson radical) of R, and let Spec r (R) (resp. Spec l (R), Max r (R), Prim r (R)) denote the set of all right prime ideals (resp. all left prime ideals, all maximal right ideals, all right primitive ideals) of R. In this article, we study the relationships among various ring-theoretic properties and topological conditions on Spec r (R) (with weak Zariski topology). The following results are obtained: (1) R/N(R) is a Gelfand ring if and only if Spec r (R) is a normal space if and only if Spec l (R) is a normal space; (2) R/J(R) is a Gelfand ring if and only if every right prime ideal containing J(R) is contained in a unique maximal right ideal. 相似文献
13.
David F. Anderson 《代数通讯》2013,41(5):1646-1672
Let R be a commutative ring with 1 ≠ 0 and n a positive integer. In this article, we study two generalizations of a prime ideal. A proper ideal I of R is called an n-absorbing (resp., strongly n-absorbing) ideal if whenever x 1…x n+1 ∈ I for x 1,…, x n+1 ∈ R (resp., I 1…I n+1 ? I for ideals I 1,…, I n+1 of R), then there are n of the x i 's (resp., n of the I i 's) whose product is in I. We investigate n-absorbing and strongly n-absorbing ideals, and we conjecture that these two concepts are equivalent. In particular, we study the stability of n-absorbing ideals with respect to various ring-theoretic constructions and study n-absorbing ideals in several classes of commutative rings. For example, in a Noetherian ring every proper ideal is an n-absorbing ideal for some positive integer n, and in a Prüfer domain, an ideal is an n-absorbing ideal for some positive integer n if and only if it is a product of prime ideals. 相似文献
14.
Yair Caro 《Journal of Combinatorial Theory, Series A》1997,80(2):367-373
A counting argument is developed and divisibility properties of the binomial coefficients are combined to prove, among other results, that[formula]whereKn, resp.Kkn, is the complete, resp. completek-uniform, hypergaph andR(Kn, Zp),R(Kkn, Z2) are the corresponding zero-sum Ramsey numbers. 相似文献
15.
Elisabetta Monari Martinez 《Annali dell'Universita di Ferrara》1979,25(1):47-61
Riassunto Si definisce una classe diZ
p-moduliQ
β, simili aip-gruppiP
β studiati daE. A. Walker, che danno una caratterizzazione delle sequenze esatte bilanciate diZ
p-moduli e degliZ
p-moduli bilanciati proiettivi. Si definiscono poi dei gruppi misti di rango 1,R
h, che sono un'estensione al caso globale deiQ
β e che generalizzano i gruppi razionali. Per gliR
h vale un teorema analogo a quello di classificazione coi tipi di Baer ed essi danno inoltre una caratterizzazione delle sequenze
esatte bilanciate di gruppi e dei gruppi bilanciati proiettivi.
Summary We define a class ofZ p-modulesQ β, like thep-groupsP β studied byE. A. Walker, that give a characterization of balanced exact sequence ofZ p-modules and balanced projectiveZ p-modules. We introduce also some mixed groups of rank one,R h, which are an extension to the global case ofQ β and which generalize rational groups. Moreover, forR h, there is a theorem, which is analogous to Baer's theorem of classification by types. GroupsR h give too a characterization of balanced exact sequence of groups and of balanced projective groups.相似文献
16.
B. I. Golubov 《Analysis Mathematica》2000,26(4):287-298
Dyadic analogs of the integral Hardy and Hardy-Littlewood operators on R
+ are introduced. It is proved that the first of them is bounded on the dyadic Hardy space H
d
(R
+), while the second one is bounded on the dyadic space BMO
d
(R
+) of functions of bounded mean oscillation on R
+. 相似文献
17.
ABSTRACT A ring R is called an n-clean (resp. Σ-clean) ring if every element in R is n-clean (resp. Σ-clean). Clean rings are 1-clean and hence are Σ-clean. An example shows that there exists a 2-clean ring that is not clean. This shows that Σ-clean rings are a proper generalization of clean rings. The group ring ?(p) G with G a cyclic group of order 3 is proved to be Σ-clean. The m× m matrix ring M m (R) over an n-clean ring is n-clean, and the m×m (m>1) matrix ring M m (R) over any ring is Σ-clean. Additionally, rings satisfying a weakly unit 1-stable range were introduced. Rings satisfying weakly unit 1-stable range are left-right symmetric and are generalizations of abelian π-regular rings, abelian clean rings, and rings satisfying unit 1-stable range. A ring R satisfies a weakly unit 1-stable range if and only if whenever a 1 R + ˙˙˙ a m R = dR, with m ≥ 2, a 1,…, a m, d ∈ R, there exist u 1 ∈ U(R) and u 2,…, u m ∈ W(R) such that a 1 u 1 + ? a m u m = Rd. 相似文献
18.
《代数通讯》2013,41(8):3571-3580
Let R = K[x, y] be a polynomial ring in two disjoint sets of variables x, y over a field K. We study ideals of mixed products L = IkJr + IsJt such that k + r = s + t, where Ik (resp. Jr ) denotes the ideal of R generated by the square-free monomials of degree k (resp. r) in the x (resp. y ) variables. Our main result is a characterization of when a given ideal L of mixed products is normal. 相似文献
19.
Vincent Dumas 《Queueing Systems》1997,25(1-4):1-43
We consider a stochastic queueing network with fixed routes and class priorities. The vector of class sizes forms a homogeneous
Markov process of countable state space Z6
+. The network is said “stable” (resp.“unstable”) if this Markov process is ergodic (resp. transient). The parameters are the
traffic intensities of the different classes. An unusual condition of stability is obtained thanks to a new argument based
on the characterization of the “essential states”. The exact stability conditions are then detected thanks to an associated
fluid network: we identify a zone of the parameter space in which diverging, fluid paths appear. In order to show that this
is a zone of instability (and that the network is stable outside this zone), we resort to the criteria of ergodicity and transience
proved by Malyshev and Menshikov for reflected random walks in Z6
+ (Malyshev and Menshikov, 1981). Their approach allows us to neglect some “pathological” fluid paths that perturb the dynamics
of the fluid model. The stability conditions thus determined have especially unusual characteristics: they have a quadratic
part, the stability domain is not convex, and increasing all the service rates may provoke instability (Theorem 1.1 and section
7).
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
M. Laurent 《Journal of Mathematical Sciences》2012,180(5):592-598
Let Γ = Z
A + Z
n
⊂ R
n
be a dense subgroup of rank n + 1 and let [^(w)] \hat{w} (A) denote the exponent of uniform simultaneous rational approximation to the generating point A. For any real number v ≥
[^(w)] \hat{w} (A), the Hausdorff dimension of the set B
v
of points in R
n
that are v-approximable with respect to Γ is shown to be equal to 1/v. 相似文献