共查询到20条相似文献,搜索用时 15 毫秒
1.
Carlo Magagna 《Monatshefte für Mathematik》2008,153(1):59-81
For a positive integer N, we define the N-rank of a non singular integer d × d matrix A to be the maximum integer r such that there exists a minor of order r whose determinant is not divisible by N. Given a positive integer r, we study the growth of the minimum integer k, such that A
k
− I has N-rank at most r, as a function of N. We show that this integer k goes to infinity faster than log N if and only if for every eigenvalue λ which is not a root of unity, the sum of the dimensions of the eigenspaces relative
to eigenvalues which are multiplicatively dependent with λ and are not roots of unity, plus the dimensions of the eigenspaces
relative to eigenvalues which are roots of unity, does not exceed d − r − 1. This result will be applied to recover a recent theorem of Luca and Shparlinski [6] which states that the group of rational
points of an ordinary elliptic curve E over a finite field with q
n
elements is almost cyclic, in a sense to be defined, when n goes to infinity. We will also extend this result to the product of two elliptic curves over a finite field and show that
the orders of the groups of
rational points of two non isogenous elliptic curves are almost coprime when n approaches infinity.
Author’s address: Dipartimento di Matematica e Informatica, Via Delle Scienze 206, 33100 Udine, Italy 相似文献
2.
We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent
processor-sharing discipline, where each request receives a service capacity which depends on the actual number of requests
in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which
provides time reversibility including sojourn times for this system, and their minimal non-negative solution gives the LST
of the sojourn time V(τ) of a request with required service time τ. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs,
whose minimal non-negative solution gives the LST of V(τ), and which yields linear systems of ODEs for the moments of V(τ) in the considered neighborhood of zero. Numerical results are presented for the variance of V(τ). In the case of an M/GI/2-PS system, the LST of V(τ) is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For service times bounded
from below, surprisingly simple expressions for the LST and variance of V(τ) in this neighborhood of zero are derived, which yield in particular the LST and variance of V(τ) in M/D/2-PS. 相似文献
3.
Consider the standard non-linear regression model y
i
= g(x
i
, θ
0)+ε
i
, i = 1, ... ,n where g(x, θ) is a continuous function on a bounded closed region X × Θ, θ
0 is the unknown parameter vector in Θ ⊂ R
p
, {x
1, x
2, ... , x
n
} is a deterministic design of experiment and {ε1, ε2, ... , ε
n
} is a
sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result
is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995)
(J. of Multivariate Analysis, vol. 54, pp. 227–238, Corrigenda. vol. 55, p. 350) is not correct.
This research was supported by the Natural Science Foundation of China (Grant No. 19831010 and grant No. 39930160) and the
Doctoral Foundation of China 相似文献
4.
Let R be a ring, n a fixed nonnegative integer and FP
n
(F
n
) the class of all left (right) R-modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module F) is called n-FI-injective (resp., n-FI-flat) if Ext
1(N,M) = 0 (resp., Tor
1(F,N) = 0) for any N ∈ FP
n
. It is shown that a left R-module M over any ring R is n-FI-injective if and only if M is a kernel of an FP
n
-precover f: A → B with A injective. For a left coherent ring R, it is proven that a finitely presented right R-module M is n-FI-flat if and only if M is a cokernel of an F
n
-preenvelope K → F of a right R-module K with F projective if and only if M ∈⊥
F
n
. These classes of modules are used to construct cotorsion theories and to characterize the global dimension of a ring. 相似文献
5.
P. Ferrante 《Lithuanian Mathematical Journal》2009,49(2):162-174
In this paper, we consider lost customers in the M/M/1/1 Erlang loss system. Here we present an explicit form of the probability that the M/M/1/1 system does not lose any customer in the time interval [0, t) and an iterative procedure to determine the distribution of the total number of losses in [0, t). All these probabilities solve the same second-order differential equation which was used to evaluate the corresponding
generating probability function. Finally, the connection between the Erlang’s loss rate and the evaluated probabilities is
showed. 相似文献
6.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献
7.
Dieter Fiems Stijn De Vuyst Sabine Wittevrongel Herwig Bruneel 《Annals of Operations Research》2009,170(1):113-131
In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these
periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals
since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various
moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional
loss probability. Some numerical examples then illustrate our results. 相似文献
8.
A. I. Vagabov 《Differential Equations》2010,46(1):17-23
We consider a system of first-order ordinary linear differential equations with coefficients depending on an arbitrary parameter
λ. For large λ, if the coefficients are smooth with respect to x, then there are known classical exponentially asymptotic (with respect to λ) formulas for the solution of the system. We generalize such formulas to the case in which the coefficients belong to the
class L
q
, q > 1. We use a new method for the reduction of problems to an integral system of special form. 相似文献
9.
Stella Kapodistria 《Queueing Systems》2011,68(1):79-109
In this paper we present a detailed analysis of a single server Markovian queue with impatient customers. Instead of the standard
assumption that customers perform independent abandonments, we consider situations where customers abandon the system simultaneously.
Moreover, we distinguish two abandonment scenarios; in the first one all present customers become impatient and perform synchronized
abandonments, while in the second scenario we exclude the customer in service from the abandonment procedure. Furthermore,
we extend our analysis to the M/M/c queue under the second abandonment scenario. 相似文献
10.
In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λ
s
(f
2, f
2, …, f
n
) of the Lie group Sp(n), corresponding to the representation with label (f
1, f
2, ..., f
n
), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f
1, f
2, …, f
n
are all even. 相似文献
11.
Kouji Yamamuro 《Queueing Systems》2012,70(2):187-205
An M/G/1 retrial queue with batch arrivals is studied. The queue length K
μ
is decomposed into the sum of two independent random variables. One corresponds to the queue length K
∞ of a standard M/G/1 batch arrival queue, and another is compound-Poisson distributed. In the case of the distribution of the batch size being
light-tailed, the tail asymptotics of K
μ
are investigated through the relation between K
∞ and its service times. 相似文献
12.
Eugenia O’Reilly-Regueiro 《Designs, Codes and Cryptography》2010,56(1):61-63
It has been shown that if a (v, k, λ)-symmetric design with λ ≤ 3 admits a flag-transitive automorphism group G which acts primitively on points, then G must be of affine or almost simple type. Here we extend the result to λ = 4. 相似文献
13.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
14.
We study the R-controllability (the controllability within the attainability set) and the R-observability of time-varying linear differential-algebraic equations (DAE). We analyze DAE under assumptions guaranteeing
the existence of a structural form (which is called “equivalent”) with separated “differential” and “algebraic” subsystems.
We prove that the existence of this form guarantees the solvability of the corresponding conjugate system, and construct the
corresponding “equivalent form” for the conjugate DAE. We obtain conditions for the R-controllability and R-observability, in particular, in terms of controllability and observability matrices. We prove theorems that establish certain
connections between these properties. 相似文献
15.
We give in this paper an algorithm to compute the sojourn time distribution in the processor sharing, single server queue with Poisson arrivals and phase type distributed service times. In a first step, we establish the differential system governing the conditional sojourn times probability distributions in this queue, given the number of customers in the different phases of the PH distribution at the arrival instant of a customer. This differential system is then solved by using a uniformization procedure and an exponential of matrix. The proposed algorithm precisely consists of computing this exponential with a controlled accuracy. This algorithm is then used in practical cases to investigate the impact of the variability of service times on sojourn times and the validity of the so-called reduced service rate (RSR) approximation, when service times in the different phases are highly dissymmetrical. For two-stage PH distributions, we give conjectures on the limiting behavior in terms of an M/M/1 PS queue and provide numerical illustrative examples.This revised version was published online in June 2005 with corrected coverdate 相似文献
16.
G. Falin 《Queueing Systems》2008,58(1):65-76
We consider the M/M/∞ queueing system with arrival and service rate depending on the state of an auxiliary semi-Markov process (which can be
viewed as an external environment) and find the mean number of customers in the system in steady state. In a particular case
when the external environment can be only in two states we find the distribution of the number of customers in the system.
相似文献
17.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
18.
Dan Mangoubi 《Mathematische Annalen》2008,341(1):1-13
We consider Riemannian metrics compatible with the natural symplectic structure on T
2 × M, where T
2 is a symplectic 2-torus and M is a closed symplectic manifold. To each such metric we attach the corresponding Laplacian and consider its first positive
eigenvalue λ1. We show that λ1 can be made arbitrarily large by deforming the metric structure, keeping the symplectic structure fixed. The conjecture is
that the same is true for any symplectic manifold of dimension ≥ 4. We reduce the general conjecture to a purely symplectic
question. 相似文献
19.
Tiziana Calamoneri Emanuele G. Fusco Richard B. Tan Paola Vocca 《Mathematical Methods of Operations Research》2009,69(2):307-321
An L(h, 1, 1)-labeling of a graph is an assignment of labels from the set of integers {0, . . . , λ} to the nodes of the graph such
that adjacent nodes are assigned integers of at least distance h ≥ 1 apart and all nodes of distance three or less must be assigned different labels. The aim of the L(h, 1, 1)-labeling problem is to minimize λ, denoted by λ
h, 1, 1 and called span of the L(h, 1, 1)-labeling. As outerplanar graphs have bounded treewidth, the L(1, 1, 1)-labeling problem on outerplanar graphs can be exactly solved in O(n
3), but the multiplicative factor depends on the maximum degree Δ and is too big to be of practical use. In this paper we give
a linear time approximation algorithm for computing the more general L(h, 1, 1)-labeling for outerplanar graphs that is within additive constants of the optimum values.
This research is partially supported by the European Research Project Algorithmic Principles for Building Efficient Overlay Computers (AEOLUS) and was done during the visit of Richard B. Tan at the Department of Computer Science, University of Rome “Sapienza”, supported
by a visiting fellowship from the University of Rome “Sapienza”. 相似文献