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1.
Gao Ping 《应用数学学报(英文版)》1985,2(4):291-303
LetE=(0, 1,...), Q
b=(qij), i, j=0, 1, ..., whereq
i, i–1=ai, qi, i+1=bi, qii=–(ai+bi), qij=0, when|i–j|>1. a
0=0, b0=b>0, ai, bi>0 (i>0). Lettingb=0 inQ
b, we get the matrixQ
0.The time homogeneous Markov processX
b
={x
b
(t,w), 0t<
b
(w)} (X
0={x0(t,w), 0t<0(w)}), withQ
b (Q
0, respectively) as its density matrix and withE as its state space, is calledQ
b (Q
0, respectively) process in this paper.Q
b andQ
0 processes are all called the birth and death processes, with zero being the reflecting barrier ofQ
b processes, the absorbing barrier ofQ
0 processes.AllQ
b processes have been constructed by both probability and analytical methods (Wang [2], Yang [1]). In this paper, theQ
0 processes are imbedded intoQ
b processes and all theQ
0 processes are directly constructed from theQ
b processes. The main results are:Letb>0 be arbitrarily fixed, then there is a one to one correspondence between theQ
0 processes and theQ
b processes (in the sense of transition probability).TheQ
0 process is unique iffR
*=. SupposingR<, then:IfX
0={x0(t,w), 0t<0(w)} is a non-minimalQ
0 process, then its eigensequence (p, q, r
n, n–1) satisfies § 4(7).Conversely, let a non-negative number sequence (p, q, r
n, n–1) satisfying § 4(7) be arbitrarily given, then there exists a unique non-minimalQ
0 processX
0 with eigensequence (p, q, r
n, n–1). The Laplace transform of the transition probability (p
ij
0
(t)) ofX
0 is determined by § 4(15).
X
0 is honest iffr
–1=0.X
0 satisfies the forward equation iffp=0. 相似文献
2.
Marco Buratti 《Journal of Combinatorial Theory, Series A》2000,90(2):353
A Z-cyclic triplewhist tournament for 4n+1 players, or briefly a TWh(4n+1), is equivalent to a n-set {(ai, bi, ci, di) | i=1, …, n} of quadruples partitioning Z4n+1−{0} with the property that ni=1 {±(ai−ci), ±(bi−di)}=ni=1 {±(ai−bi), ±(ci−di)}=ni=1 {±(ai−di), ±(bi−ci)}=Z4n+1−{0}. The existence problem for Z-cyclic TWh(p)'s with p a prime has been solved for p1 (mod 16). I. Anderson et al. (1995, Discrete Math.138, 31–41) treated the case of p≡5 (mod 8) while Y. S. Liaw (1996, J. Combin. Des.4, 219–233) and G. McNay (1996, Utilitas Math.49, 191–201) treated the case of p≡9 (mod 16). In this paper, besides giving easier proofs of these authors' results, we solve the problem also for primes p≡1 (mod 16). The final result is the existence of a Z-cyclic TWh(v) for any v whose prime factors are all≡1 (mod 4) and distinct from 5, 13, and 17. 相似文献
3.
V. A. Yumaguzhin 《Acta Appl Math》2002,72(1-2):155-181
It is known that a linear ordinary differential equation of order n3 can be transformed to the Laguerre–Forsyth form y
(n)=
i=3
n
a
n–i
(x)y
(n–i) by a point transformation of variables. The classification of equations of this form in a neighborhood of a regular point up to a contact transformation is given. 相似文献
4.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1994,46(3):290-303
For the equationL
0
x(t)+L
1x(t)+...+L
n
x
(n)(t)=O, whereL
k,k=0,1,...,n, are operators acting in a Banach space, we establish criteria for an arbitrary solutionx(t) to be zero provided that the following conditions are satisfied:x
(1–1) (a)=0, 1=1, ..., p, andx
(1–1) (b)=0, 1=1,...,q, for - <a< b< (the case of a finite segment) orx
(1–1) (a)=0, 1=1,...,p, under the assumption that a solutionx(t) is summable on the semiaxista with its firstn derivatives.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 279–292, March, 1994.This research was supported by the Ukrainian State Committee on Science and Technology. 相似文献
5.
Persistence, contractivity and global stability in logistic equations with piecewise constant delays
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2002,270(2):1532-635
We establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium N*=1/(a+∑i=0mbi) of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, ∑i=0mbi>0, bi0, i=0,1,2,…,m, and a+∑i=0mbi>0. These new conditions depend on a,b0 and ∑i=1mbi, and hence these are other type conditions than those given by So and Yu (Hokkaido Math. J. 24 (1995) 269–286) and others. In particular, in the case m=0 and r(t)≡r>0, we offer necessary and sufficient conditions for the persistence and contractivity of solutions. We also investigate the following differential equation with nonlinear delay terms: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, 1−ax−g(x,x,…,x)=0 has a unique solution x*>0 and g(x0,x1,…,xm)C1[(0,+∞)×(0,+∞)××(0,+∞)]. 相似文献
6.
Prof. Dr. Peter Gerl 《Monatshefte für Mathematik》1977,84(1):29-35
LetF
2 be the free group with two generatorsa, b andP be a probability measure onF
2 with support {a, a
–1,b, b
–1}. The asymptotic behavior forn of the convolution powersP
n
(e) at the identitye is found.
Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet 相似文献
Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet 相似文献
7.
The n × n generalized Pascal matrix P(t) whose elements are related to the hypergeometric function 2F1(a, b; c; x) is presented and the Cholesky decomposition of P(t) is obtained. As a result, it is shown that
is the solution of the Gauss's hypergeometric differential equation, . where a and b are any nonnegative integers. Moreover, a recurrence relation for generating the elements of P(t) is given. 相似文献
Full-size image
x(1 − x)y″ + [1 + (a + b − 1)x]y′ − ABY = 0
8.
Let 2
[n] denote the poset of all subsets of [n]={1,2,...,n} ordered by inclusion. Following Gutterman and Shahriari (Order 14, 1998, 321–325) we consider a game G
n
(a,b,c). This is a game for two players. First, Player I constructs a independent maximal chains in 2
[n]. Player II will extend the collection to a+b independent maximal chains by finding another b independent maximal chains in 2
[n]. Finally, Player I will attempt to extend the collection further to a+b+c such chains. The last Player who is able to complete her move wins. In this paper, we complete the analysis of G
n
(a,b,c) by considering its most difficult instance: when c=2 and a+b+2=n. We prove, the rather surprising result, that, for n7, Player I wins G
n
(a,n–a–2,2) if and only if a3. As a consequence we get results about extending collections of independent maximal chains, and about cutsets (collections of subsets that intersect every maximal chain) of minimum possible width (the size of largest anti-chain). 相似文献
9.
An even-order three-point boundary value problem on time scales 总被引:1,自引:0,他引:1
Douglas R Anderson Richard I Avery 《Journal of Mathematical Analysis and Applications》2004,291(2):514-525
We study the even-order dynamic equation (−1)nx(Δ∇)n(t)=λh(t)f(x(t)), t∈[a,c] satisfying the boundary conditions x(Δ∇)i(a)=0 and x(Δ∇)i(c)=βx(Δ∇)i(b) for 0?i?n−1. The three points a,b,c are from a time scale , where 0<β(b−a)<c−a for b∈(a,c), β>0, f is a positive function, and h is a nonnegative function that is allowed to vanish on some subintervals of [a,c] of the time scale. 相似文献
10.
Sanat K. Sarkar 《Annals of the Institute of Statistical Mathematics》1991,43(2):369-375
Based on independent random matices X: p×m and S: p×p distributed, respectively, as N
pm
(, I
m
) and W
p
(n, ) with unknown and np, the problem of obtaining confidence interval for || is considered. Stein's idea of improving the best affine equivariant point estimator of || has been adapted to the interval estimation problem. It is shown that an interval estimator of the form |S|(b
–1, a
–1) can be improved by min{|S|, c|S +XX'|}(b
–1, a
–1) for a certain constant c depending on (a, b). 相似文献
11.
J. Korevaar 《Indagationes Mathematicae》1999,10(4):539
The convolution a * b of the sequences a = a0, a1, a2, and b is the sequence with elements ∑0n akbn − k. One sets 1, 1, 1, equal to σ. Given that a * a with a ≥ 0 is close to σ * σ, how close is a to σ? More generally, one asks how close a is to σ if the p-th convolution power, a*P with a ≥ 0, is close to σ*P. Power series and complex analysis form a natural tool to estimate the ‘summed deviation’ ρ = σ * (a — σ) in terms of b = a * a — σ * σ or b = a*P − σ*P. Optimal estimates are found under the condition ∑k=0n bk2 = %plane1D;512;(n2β + 1) whenever −½ < β < p − 1. It is not known what the optimal estimates are for the special case bn = %plane1D;512;(nβ). 相似文献
12.
Let A={a1,a2,…}(a1<a2<) be an infinite sequence of nonnegative integers, let k≥2 be a fixed integer and denote by rk(A,n) the number of solutions of ai1+ai2++aik≤n. Montgomery and Vaughan proved that r2(A,n)=cn+o(n1/4) cannot hold for any constant c>0. In this paper, we extend this result to k>2. 相似文献
13.
Let F(s, t) = P(X > s, Y > t) be the bivariate survival function which is subject to random censoring. Let
be the bivariate product limit estimator (PL-estimator) by Campbell and Földes (1982, Proceedings International Colloquium on Non-parametric Statistical Inference, Budapest 1980, North-Holland, Amsterdam). In this paper, it was shown that
, where {ζi(s, t)} is i.i.d. mean zero process and Rn(s, t) is of the order O((n−1log n)3/4) a.s. uniformly on compact sets. Weak convergence of the process {n−1 Σi = 1n ζi(s, t)} to a two-dimensional-time Gaussian process is shown. The covariance structure of the limiting Gaussian process is also given. Corresponding results are also derived for the bootstrap estimators. The result can be extended to the multivariate cases and are extensions of the univariate case of Lo and Singh (1986, Probab. Theory Relat. Fields, 71, 455–465). The estimator
is also modified so that the modified estimator is closer to the true survival function than
in supnorm. 相似文献
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14.
E. W. Lambeck 《Designs, Codes and Cryptography》1991,1(3):261-266
Let be a distance regular graph with intersection array b
0, b
1,..., b
d–1; c
1,..., c
d. It is shown that in some cases (c
i–1, a
i–1, b
i–1) = (c
1, a
1, b
1)and (c
2i–1, a
2i–1, b
2i–1) imply k 2b
i + 1. As a corollary all distance regular graphs of diameter d = 3i – 1 with b
i = 1 and k > 2 are determined. 相似文献
15.
K. W. Gruenberg 《Algebras and Representation Theory》2001,4(1):105-108
Given a finite group G and a G-free resolution F
* of Z, then d
G
(Im(F
m+1F
m
))–(–1)
m–i
d
G
(F
i
) is almost always an invariant of G. 相似文献
16.
A scheme is proposed for the feedback control of distributed-parameter systems with unknown boundary and volume disturbances and observation errors. The scheme consists of employing a nonlinear filter in the control loop such that the controller uses the optimal estimates of the state of the system. A theoretical comparison of feedback proportional control of a styrene polymerization reactor with and without filtering is presented. It is indicated how an approximate filter can be constructed, greatly reducing the amount of computing required.Notation
a(t)
l-vector noisy dynamic input to system
-
A(t, a)
l-vector function
-
A
frequency factor for first-order rate law (5.68×106 sec–1)
-
b
distance to the centerline between two coil banks in the reactor (4.7 cm)
-
B
k-vector function defining the control action
-
c(, )
concentration of styrene monomer, molel
–1
-
C
p
heat capacity (0.43 cal · g–1 · K–1)
-
C
ij
constants in approximate filter, Eqs. (49)–(52)
-
E
activation energy (20330 cal · mole–1)
-
expectation operator
-
f(t,...)
n-vector function
-
g
0,g
1(t,...)
n-vector functions
-
h(t, u)
m-vector function relating observations to states
-
H(t)
function defined in Eq. (36)
-
k
dimensionality of control vectorv(x, t)
-
k
i
constants in approximate filter, Eqs. (49)–(52)
-
K
dimensionless proportional gain
-
l
dimensionality of dynamic inputa(t)
-
m
dimensionality of observation vectory(t)
-
n
dimensionality of state vectoru(x, t)
-
P
(vv)(x, s, t)
n×n matrix governed by Eq. (9)
-
P
(va)(x, t)
n×l matrix governed by Eq. (10)
-
P
(aa)(t)
l×l matrix governed by Eq. (11)
-
q
i
(t)
diagonal elements ofm×m matrixQ(x, s, t)
-
Q(x, s, t)
m×m weighting matrix
-
R
universal gas constant (1.987 cal · mole–1 · K–1)
-
R(x, s, t)
n×n weighting matrix
-
R
i
(t)
n×n weighting matrix
-
s
dimensionless spatial variable
-
S(x, s, t)
matrix defined in Eq. (11)
-
t
dimensionless time variable
-
T(, )
temperature, K
-
u(x, t)
n-dimensional state vector
-
u
c
(t)
wall temperature
-
u
d
desired value ofu
1(1,t)
-
u
c
*
reference control value ofu
c
-
u
c
max
maximum value ofu
c
-
u
c
min
minimum value of
c
-
v(x, t)
k-dimensional control vector
-
W(t)
l×l weighting matrix
-
x
dimensionless spatial variable
-
y(t)
m-dimensional observation vector
-
i
constants in approximate filter, Eqs. (49)–(52)
-
dimensionless parameter defined in Eq. (29)
-
H
heat of reaction (17500 cal · mole–1)
-
dimensionless activation energy, defined in Eq. (29)
-
(x)
Dirac delta function
-
(x, t)
m-dimensional observation noise
-
thermal conductivity (0.43×10–3 cal · cm–1 · sec–1 · K–1)
-
density (1 g · cm–3)
-
time, sec
-
dimensionless parameter defined in Eq. (29)
-
spatial variable, cm
- *
reference value
- ^
estimated value 相似文献
17.
In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson
process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure qθ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe
n + 1 data at tin = ihn,
. We suppose hn → 0, nhn → ∞, nhn2 → 0.
Final version 20 December 2004 相似文献
18.
J. Lang 《Journal of Approximation Theory》2006,140(2):141-146
Consider the Hardy-type operator T : Lp(a,b)→Lp(a,b),-∞a<b∞, which is defined byIt is shown thatwhere ρn(T) stands for any of the following: the Kolmogorov n-width, the Gel’fand n-width, the Bernstein n-width or the nth approximation number of T. 相似文献
19.
Sheila Sundaram 《Journal of Algebraic Combinatorics》1995,4(1):69-92
Let
denote the subposet obtained by selecting even ranks in the partition lattice
. We show that the homology of
has dimension
, where
is the tangent number. It is thus an integral multiple of both the Genocchi number and an André or simsun number. Using the general theory of rank-selected homology representations developed in [22], we show that, for the special case of
, the character of the symmetric group S
2n
on the homology is supported on the set of involutions. Our proof techniques lead to the discovery of a family of integers b
i(n), 2 i n, defined recursively. We conjecture that, for the full automorphism group S
2n, the homology is a sum of permutation modules induced from Young subgroups of the form
, with nonnegative integer multiplicity b
i(n). The nonnegativity of the integers b
i(n) would imply the existence of new refinements, into sums of powers of 2, of the tangent number and the André or simsun number a
n(2n).Similarly, the restriction of this homology module to S
2n–1 yields a family of integers d
i(n), 1 i n – 1, such that the numbers 2–i
d
i(n) refine the Genocchi number G
2n
. We conjecture that 2–i
d
i(n) is a positive integer for all i.Finally, we present a recursive algorithm to generate a family of polynomials which encode the homology representations of the subposets obtained by selecting the top k ranks of
, 1 k n – 1. We conjecture that these are all permutation modules for S
2n
. 相似文献
20.
Assume that (X
n) are independent random variables in a Banach space, (b
n) is a sequence of real numbers, Sn=
1
n
biXi, and Bn=
1
n
b
i
2
. Under certain moment restrictions imposed on the variablesX
n, the conditions for the growth of the sequence (bn) are established, which are sufficient for the almost sure boundedness and precompactness of the sequence (Sn/B
n ln ln Bn)1/2).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1225–1231, September, 1993. 相似文献