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1.
Winfried K. Grassmann 《Methodology and Computing in Applied Probability》2011,13(4):873-886
In 1953, Smith (Proc Camb Philos Soc 49:449–461, 1953), and, following him, Syski (1960) suggested a method to find the waiting time distribution for one server queues with Erlang-n arrivals and Erlang-m service times by using characteristic roots. Syski shows that these roots can be determined from a very simple equation,
but an equation of degree n + m. Syski also shows that almost all of the characteristic roots are complex. In this paper, we derive a set of equations, one
for each complex root, which can be solved by Newton’s method using real arithmetic. This method simplifies the programming
logic because it avoids deflation and the subsequent polishing of the roots. Using the waiting time distribution, Syski then
derived the distribution of the number in the system after a departure. E
n
/E
m
/1 queues can also formulated as quasi birth-death (QBD) processes, and in this case, the characteristic roots discussed by
Syski are closely related to the eigenvalues of the QBD process. The QBD process provides information about the number in
system at random times, but they are much more difficult to formulate and solve. 相似文献
2.
Qi-Ming He 《European Journal of Operational Research》2000,120(3):641
This paper studies a multi-server queueing system with multiple types of customers and last-come-first-served (LCFS) non-preemptive service discipline. First, a quasi-birth-and-death (QBD) Markov process with a tree structure is defined and some classical results of QBD Markov processes are generalized. Second, the MMAP[K]/PH[K]/N/LCFS non-preemptive queue is introduced. Using results of the QBD Markov process with a tree structure, explicit formulas are derived and an efficient algorithm is developed for computing the stationary distribution of queue strings. Numerical examples are presented to show the impact of the correlation and the pattern of the arrival process on the queueing process of each type of customer. 相似文献
3.
Shin-ichi Kobayashi 《Inventiones Mathematicae》2003,152(1):1-36
We give a new formulation in Iwasawa theory for elliptic curves at good supersingular primes. This formulation is similar
to Mazur’s at good ordinary primes. Namely, we define a new Selmer group, and show that it is of Λ-cotorsion. Then we formulate
the Iwasawa main conjecture as that the characteristic ideal is generated by Pollack’s p-adic L-function. We show that this main conjecture is equivalent to Kato’s and Perrin-Riou’s main conjectures. We also prove an
inequality in the main conjecture by using Kato’s Euler system. In terms of the λ- and the μ-invariants of our Selmer group,
we specify the numbers λ and μ in the asymptotic formula for the order of the Tate-Shafarevich group by Kurihara and Perrin-Riou.
Oblatum 17-VI-2002 & 2-IX-2002?Published online: 18 December 2002 相似文献
4.
Nonholonomic systems are described by the Lagrange-D’Alembert’s principle. The presence of symmetry leads, upon the choice
of an arbitrary principal connection, to a reduced D’Alembert’s principle and to the Lagrange-D’Alembert-Poincaré reduced
equations. The case of rolling constraints has a long history and it has been the purpose of many works in recent times. In
this paper we find reduced equations for the case of a thick disk rolling on a rough surface, sometimes called Euler’s disk, using a 3-dimensional abelian group of symmetry. We also show how the reduced system can be transformed into a single second
order equation, which is an hypergeometric equation. 相似文献
5.
Iddo Eliazar 《Queueing Systems》2007,55(1):71-82
We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated.
We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied
to various examples, including ones with infinite queues and non-summable workloads.
AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10 相似文献
6.
I. S. Lomov 《Differential Equations》2011,47(3):355-362
We study whether V.A. Il’in’s method for proving the uniqueness of the solution of a mixed problem for a hyperbolic equation
applies to a problem with transmission conditions in the interior of the interval. We show that the system of eigenfunctions
corresponding to this problem is complete in the space L
2(0, l) and is a Riesz basis in this space. 相似文献
7.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem 总被引:3,自引:0,他引:3
M. BERKANI 《数学学报(英文版)》2007,23(1):103-110
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators. 相似文献
8.
Qi-Ming He 《Queueing Systems》2005,49(3-4):363-403
In this paper, we study a discrete time queueing system with multiple types of customers and a first-come-first-served (FCFS) service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual customers have PH-distributions. A GI/M/1 type Markov chain for a generalized age process of batches of customers is introduced. The steady state distribution of the GI/M/1 type Markov chain is found explicitly and, consequently, the steady state distributions of the age of the batch in service, the total workload in the system, waiting times, and sojourn times of different batches and different types of customers are obtained. We show that the generalized age process and a generalized total workload process have the same steady state distribution. We prove that the waiting times and sojourn times have PH-distributions and find matrix representations of those PH-distributions. When the arrival process is a Markov arrival process with marked transitions, we construct a QBD process for the age process and the total workload process. The steady state distributions of the waiting times and the sojourn times, both at the batch level and the customer level, are obtained from the steady state distribution of the QBD process. A number of numerical examples are presented to gain insight into the waiting processes of different types of customers.AMS subject classification: 60K25, 60J10This revised version was published online in June 2005 with corrected coverdate 相似文献
9.
V. A. Gorelov 《Mathematical Notes》2000,67(2):138-151
We prove a generalization of Shidlovskii’s theorem on the algebraic independence of the values ofE-functions satisfying a system of linear differential equations that is well known in the theory of transcendental numbers.
We consider the case in which the values ofE-functions are taken at singular points of these systems. Using the obtained results, we prove Siegel’s conjecture that, for
the case of first-order differential equations, anyE-function satisfying a linear differential equation is representable as a polynomial in hypergeometricE-functions.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 174–190, February, 2000. 相似文献
10.
James Hirschorn 《Israel Journal of Mathematics》2007,157(1):123-153
We extend Jensen’s Theorem that Souslin’s Hypothesis is consistent with CH, by showing that the statement Souslin’s Hypothesis holds in any forcing extension by a measure algebra is consistent with CH. We also formulate a variation of the principle (*) (see [AT97], [Tod00]) for closed sets of ordinals,
and show its consistency relative to the appropriate large cardinal hypothesis. Its consistency with CH would extend Silver’s
Theorem that, assuming the existence of an inaccessible cardinal, the failure of Kurepa’s Hypothesis is consistent with CH,
by its implication that the statement Kurepa’s Hypothesis fails in any forcing extension by a measure algebra is consistent with CH. 相似文献
11.
Michel van Meer 《Selecta Mathematica, New Series》2011,17(1):183-221
The bispectral quantum Knizhnik–Zamolodchikov (BqKZ) equation corresponding to the affine Hecke algebra H of type A
N-1 is a consistent system of q-difference equations which in some sense contains two families of Cherednik’s quantum affine Knizhnik–Zamolodchikov equations
for meromorphic functions with values in principal series representations of H. In this paper, we extend this construction of BqKZ to the case where H is the affine Hecke algebra associated with an arbitrary irreducible reduced root system. We construct explicit solutions
of BqKZ and describe its correspondence to a bispectral problem involving Macdonald’s q-difference operators. 相似文献
12.
Yoshihiro Takeyama 《The Ramanujan Journal》2012,27(1):15-28
We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV’s). In the limit q→1, it turns into Kawashima’s relation for multiple zeta values. As a corollary we find that qMZV’s satisfy the linear relation contained in Kawashima’s relation. In the proof we make use of a q-analogue of Newton series and Bradley’s duality formula for finite multiple harmonic q-series. 相似文献
13.
F. Carbonell K. J. Worsley L. Galan 《Annals of the Institute of Statistical Mathematics》2011,63(1):1-27
The statistical problem addressed in this paper is to approximate the P value of the maximum of a smooth random field of Wilks’s Λ statistics. So far results are only available for the usual univariate
statistics (Z, t, χ2, F) and a few multivariate statistics (Hotelling’s T
2, maximum canonical correlation, Roy’s maximum root). We derive results for any differentiable scalar function of two independent
Wishart random fields, such as Wilks’s Λ random field. We apply our results to a problem in brain shape analysis. 相似文献
14.
We consider the construction of the plateau of the α-function in a hyperbolic and positive definite Lagrangian system, and link the boundries of the α-function’s plateau with the distribution of c-minimal homoclinic orbits to Aubry sets. 相似文献
15.
The equational complexity of Lyndon’s nonfinitely based 7-element algebra lies between n − 4 and 2n + 1. This result is based on a new algebraic proof that Lyndon’s algebra is not finitely based. We prove that Lyndon’s algebra
is inherently nonfinitely based relative to a rather rich class of algebras. We also show that the variety generated by Lyndon’s
algebra contains subdirectly irreducible algebras of all cardinalities except 0, 1, and 4. 相似文献
16.
H. V. Mamonova 《Ukrainian Mathematical Journal》2006,58(5):798-807
We consider an operational queuing system of the type [SM|M|∞]N in the scheme of diffusion approximation. The queueing system is described by a semi-Markov random evolution.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 708–714, May, 2006. 相似文献
17.
We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem
1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li-Yau ’s gradient estimate.
As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also
show that the equality holds in Li-Yau’s gradient estimate, for some positive solution to the heat equation, at some positive
time, implies that the complete Riemannian manifold with nonnegative Ricci curvature is isometric to ℝ
n
.In the second section we derive a dual entropy formula which, to some degree, connects Hamilton’s entropy with Perelman ’s
entropy in the case of Riemann surfaces. 相似文献
18.
The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and of the second author for Euler’s constant γ and its alternating analog ln (4/π), and on the other hand the infinite products of the first author for e, of the second author for π, and of Ser for e
γ
. We obtain new double integral and infinite product representations of many classical constants, as well as a generalization
to Lerch’s transcendent of Hadjicostas’s double integral formula for the Riemann zeta function, and logarithmic series for
the digamma and Euler beta functions. The main tools are analytic continuations of Lerch’s function, including Hasse’s series.
We also use Ramanujan’s polylogarithm formula for the sum of a particular series involving harmonic numbers, and his relations
between certain dilogarithm values.
相似文献
19.
We introduce the class of operators on Banach spaces having property (H) and study Weyl’s theorems, and related results for operators which satisfy this property. We show that a- Weyl’s theorem holds for every decomposable operator having property (H). We also show that a-Weyl’s theorem holds for every multiplier T of a commutative semi-simple regular Tauberian Banach algebra. In particular every convolution operator Tμ of a group algebra L1(G), G a locally compact abelian group, satisfies a-Weyl’s theorem. Similar results are given for multipliers of other important commutative Banach algebras. 相似文献
20.
In this paper, our interest is in the perturbation analysis of level‐dependent quasi‐birth‐and‐death (LD‐QBD) processes, which constitute a wide class of structured Markov chains. An LD‐QBD process has the special feature that its space of states can be structured by levels (groups of states), so that a tridiagonal‐by‐blocks structure is obtained for its infinitesimal generator. For these processes, a number of algorithmic procedures exist in the literature in order to compute several performance measures while exploiting the underlying matrix structure; among others, these measures are related to first‐passage times to a certain level L(0) and hitting probabilities at this level, the maximum level visited by the process before reaching states of level L(0), and the stationary distribution. For the case of a finite number of states, our aim here is to develop analogous algorithms to the ones analyzing these measures, for their perturbation analysis. This approach uses matrix calculus and exploits the specific structure of the infinitesimal generator, which allows us to obtain additional information during the perturbation analysis of the LD‐QBD process by dealing with specific matrices carrying probabilistic insights of the dynamics of the process. We illustrate the approach by means of applying multitype versions of the susceptible‐infective (SI) and susceptible‐infective‐susceptible (SIS) epidemic models to the spread of antibiotic‐sensitive and antibiotic‐resistant bacterial strains in a hospital ward. 相似文献