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1.
The class of finitely presented groups
is an extension of the class of triangle groups studied recently. These groups are finite and their orders depend on the Lucas
numbers. In this paper, by considering the three presentations
and
we study Mon(π
i
), i=1,2,3, and Sg(π
i
), i=2,3, for their finiteness. In this investigation, we find their relationship with Gp(π
i
), where Mon(π), Sg(π) and Gp(π) are used for the monoid, the semigroup and the group presented by the presentation π, respectively. 相似文献
2.
V. V. Vysotsky 《Journal of Mathematical Sciences》2007,147(4):6873-6883
Let Si be a random walk with standard exponential increments. The sum ∑
i=1
k
Si is called the k-step area of the walk. The random variable
∑
i=1
k
Si plays an important role in the study of the so-called one-dimensional sticky particles model. We find the distribution of
this variable and prove that
for 0 ≤ t ≤ 1. We also show that
, where the Ui,n are order statistics of n i.i.d. random variables uniformly distributed on [0, 1]. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 48–67. 相似文献
3.
A queueingnetwork that is served by asingle server in a cyclic order is analyzed in this paper. Customers arrive at the queues from outside the network according to independent Poisson processes. Upon completion of his service, a customer mayleave the network, berouted to another queue in the network orrejoin the same queue for another portion of service. The single server moves through the different queues of the network in a cyclic manner. Whenever the server arrives at a queue (polls the queue), he serves the waiting customers in that queue according to some service discipline. Both the gated and the exhaustive disciplines are considered. When moving from one queue to the next queue, the server incurs a switch-over period. This queueing network model has many applications in communication, computer, robotics and manufacturing systems. Examples include token rings, single-processor multi-task systems and others. For this model, we derive the generating function and the expected number of customers present in the network queues at arbitrary epochs, and compute the expected values of the delays observed by the customers. In addition, we derive the expected delay of customers that follow a specific route in the network, and we introduce pseudo-conservation laws for this network of queues.Summary of notation Bi, B
i
*
(s)
service time of a customer at queue i and its LST
- bi, bi
(2)
mean and second moment of Bi
- Ri, R
i
*
(s)
duration of switch-over period from queue i and its LST
- ri, ri
mean and second moment of Ri
- r, r(2)
mean and second moment of
i
N
=1Ri
- i
external arrival rate of type-i customers
- i
total arrival rate into queue i
- i
utilization of queue i; i=i
-
system utilization
i
N
=1i
- c=E[C]
the expected cycle length
- X
i
j
number of customers in queue j when queue i is polled
- Xi=X
i
i
number of customers residing in queue i when it is polled
- fi(j)
- X
i
*
number of customers residing in queue i at an arbitrary moment
- Yi
the duration of a service period of queue i
- Wi,Ti
the waiting time and sojourn time of an arbitary customer at queue i
- F*(z1, z2,..., zN)
GF of number of customers present at the queues at arbitrary moments
- Fi(z1, z2,..., zN)
GF of number of customers present at the queues at polling instants of queue i
- ¯Fi(z1, z2,...,zN)
GF of number of customers present at the queues at switching instants of queue i
- Vi(z1, z2,..., zN)
GF of number of customers present at the queues at service initiation instants at queue i
- ¯Vi(z1,z2,...,zN)
GF of number of customers present at the queues at service completion instants at queue i
The work of this author was supported by the Bernstein Fund for the Promotion of Research and by the Fund for the Promotion of Research at the Technion.Part of this work was done while H. Levy was with AT&T Bell Laboratories. 相似文献
4.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引：7，自引：0，他引：7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
5.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
and
almost surely for any continuity point x of G and for any bounded Lipschitz function f: R → R.
相似文献
6.
Vladislav Kargin 《Probability Theory and Related Fields》2007,139(3-4):397-413
Let X
i
denote free identically-distributed random variables. This paper investigates how the norm of products behaves as n approaches infinity. In addition, for positive X
i
it studies the asymptotic behavior of the norm of where denotes the symmetric product of two positive operators: . It is proved that if EX
i
= 1, then is between and c
2
n for certain constant c
1 and c
2. For it is proved that the limit of exists and equals Finally, if π is a cyclic representation of the algebra generated by X
i
, and if ξ is a cyclic vector, then for all n. These results are significantly different from analogous results for commuting random variables. 相似文献
7.
A. I. Aptekarev J. S. Dehesa A. Martínez-Finkelshtein R. Yáñez 《Constructive Approximation》2009,30(1):93-119
Given a nontrivial Borel measure on ℝ, let p
n
be the corresponding orthonormal polynomial of degree n whose zeros are λ
j
(n), j=1,…,n. Then for each j=1,…,n,
with
defines a discrete probability distribution. The Shannon entropy of the sequence {p
n
} is consequently defined as
In the case of Chebyshev polynomials of the first and second kinds, an explicit and closed formula for
is obtained, revealing interesting connections with number theory. In addition, several results of numerical computations
exemplifying the behavior of
for other families are presented.
相似文献
8.
We consider some classes of 2π-periodic functions defined by a class of operators having certain oscillation properties, which include the classical Sobolev class and a class of analytic functions which can not be represented as a convolution class as its special cases. Let be the largest integer not bigger than x. We prove that on these classes of functions the rectangular formula
is optimal among all quadrature formulae of the form
where the nodes 0 ≤ t
1 < ... < t
n
< 2π and the coefficients (weights) are arbitrary, i = 1,...,n, j = 0,1,..., ν
i
− 1, and (ν1,...,ν
n
) is a system of positive integers satisfying the condition . In particular, the rectangular formula is optimal for these classes of functions among all quadrature formulae of the form
with free nodes 0 ≤ t
1 < ... < t
N
< 2π and arbitrary weights . Moreover, we exactly determine the error estimates of the optimal quadrature formulae on these classes of functions.Project supported by the National Natural Science Foundation of China (Grant No. 10671019) and Research Fund for the Doctoral Program Higher Education (Grant No. 20050027007). 相似文献
9.
We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks
with the form of
, where the input-output function is defined as a generalized sigmoid function, such asv
i
=2/π arctan(π/2μiμi),
and
, etc. Numerical simulations are also provided to demonstrate the theoretical results. 相似文献
10.
Let H be an infinite-dimensional real Hilbert space equipped with the scalar product (⋅,⋅)
H
. Let us consider three linear bounded operators,
We define the functions
where a
i
∈H and α
i
∈ℝ. In this paper, we discuss the closure and the convexity of the sets Φ
H
⊂ℝ2 and F
H
⊂ℝ3 defined by
Our work can be considered as an extension of Polyak’s results concerning the finite-dimensional case. 相似文献
11.
Sufficient conditions are established for the oscillation of proper solutions of the system
where f
i
:+ × 2m (i=1,2) satisfy the local Carathéodory conditions and
i
,
i
:+ +(i=1,...,m) are continuous functions such that
i
(t) t for
. 相似文献
12.
M. Guedda 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(5):749-762
This paper is concerned with the ordinary differential equation
on (0, + ∞), subject to the boundary conditions
in which a and b are reals, m > 0 and α < 0. Such problem, with
arises in the study of the free convection, along a vertical flat plate embedded in a porous medium.The analysis deals with existence, non–uniqueness and large–t behaviour of solutions of the above problem under favourable conditions on m, α, a and b.Received: March 20, 2002; revised: January 17 and July 14, 2003 相似文献
13.
We prove several unique prime factorization results for tensor products of type II1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if
is isomorphic to a subfactor in
, for some 2ri,sj, then mn. Mathematics Subject Classification (2000) Primary 46L10; Secondary 20F67 相似文献
14.
De-xiang Ma Wei-gao Ge Xue-gang Chen 《应用数学学报(英文版)》2005,21(4):661-670
In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{（ φp（u＇））＇＋q（t）f（t,u,u＇）=0,0〈t〈1,u（0）=∑i=1^nαiu（ξi）,u＇（1）=∑i=1^nβiu＇（ξi）,whereφp（s）=｜s｜^p-2s,p≥2;ξi∈（0,1）（i=1,2,…,n）,0≤αi,βi〈1（i=1,2,…n）,0≤∑i=1^nαi,∑i=1^nβi〈1,and q（t） may be singular at t=0,1,f（t,u,u＇）may be singular at u＇=0 相似文献
15.
Let β
0=0.308443… denote the Littlewood-Salem-Izumi number, i.e., the unique solution of the equation
In this paper it is proved that if a
0≥a
1≥⋅⋅⋅≥a
n
>0 and
, k≥1 then for all θ∈(0,π)
and furthermore, the number β
0 is best possible in the sense that for any β∈(0,β
0)
where the coefficients c
k
(β) are defined as
Results for the sine sums are obtained as well.
These results generalize and sharpen the well known trigonometric inequalities of Vietoris.
This research was supported by a grant from the Australian Research Council. The second author was also supported in part
by the NSERC Canada under grant G121211001. The third author was also supported in part by the NSFC of China under grant 10471010. 相似文献
16.
Cristinel Mortici 《Archiv der Mathematik》2009,93(1):37-45
We prove in this paper that for every x ≥ 0,
where and α = 1.072042464..., then
where and β = 0.988503589... Besides the simplicity, our new formulas are very accurate, if we take into account that they are much stronger
than Burnside’s formula, which is considered one of the best approximation formulas ever known having a simple form.
相似文献
17.
M. I. Gil’ 《Acta Appl Math》2007,99(2):117-159
Let f be an entire function. Denote by z
1(f),z
2(f),… the zeros of f with their multiplicities. In the paper, estimates for the sums
and for the counting function of the zeros of f are established. If f is of finite order ρ(f), we derive bounds for the series
as well as relations between the series
and the traces of certain matrices. The contents of the paper is closely connected with the following well-known results:
the Hadamard theorem on the convergence exponent of the zeros of an entire function, the Jensen inequality for the counting
function, the Cauchy theorem on the comparison of the zeros of polynomials, Ostrowski’s inequalities for the real and imaginary
parts of the zeros of polynomials and the Cartwright–Levinson theorem. The suggested approach is based on the recent development
of the spectral theory of linear operators.
This research was supported by the Kamea fund of the Israel. 相似文献
18.
Witold Bednorz 《Journal of Theoretical Probability》2007,20(4):917-934
For a Young function φ and a Borel probability measure m on a compact metric space (T,d) the minorizing metric is defined by
In the paper we extend the result of Kwapien and Rosinski (Progr. Probab. 58, 155–163, 2004) relaxing the conditions on φ under which there exists a constant K such that
for each separable process X(t), t∈T which satisfies
. In the case of φ
p
(x)≡x
p
, p≥1 we obtain the somewhat weaker results.
Partially supported by the Funds of Grant MENiN 1 P03A 01229. 相似文献
19.
Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition
where
are the order statistics of a random sample {X
i, i n}, X
0, n
–, X
n+1, n
+ and F(x) is a continuous distribution function. A characterization of continuous distributions based on
is obtained. Namely, a sequence of random observations {X
i, i1} comes from a continuous cumulative distribution function (cdf) F(x) if and only if
where = 0.577 is Euler's constant. If {X
i, i1} come from a density g(x) and F is a cdf with density f(x), some limit theorems for
are established, e.g.,
Statistical estimation as well as a goodness-of-fit test based on
are also discussed. 相似文献
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20.
Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case 总被引：1，自引：0，他引：1
We consider the system of Fredholm integral equations
and also the system of Volterra integral equations
where T>0 is fixed and the nonlinearities h
i
(t,u
1,u
2,…,u
n
) can be singular at t=0 and u
j
=0 where j∈{1,2,…,n}. Criteria are offered for the existence of constant-sign solutions, i.e., θ
i
u
i
(t)≥0 for t∈[0,1] and 1≤i≤n, where θ
i
∈{1,−1} is fixed. We also include examples to illustrate the usefulness of the results obtained.
相似文献