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1.
LetL be the space of rapidly decreasing smooth functions on ? andL * its dual space. Let (L 2)+ and (L 2)? be the spaces of test Brownian functionals and generalized Brownian functionals, respectively, on the white noise spaceL * with standard Gaussian measure. The Donsker delta functionδ(B(t)?x) is in (L 2)? and admits the series representation $$\delta (B(t) - x) = (2\pi t)^{ - 1/2} \exp ( - x^2 /2t)\sum\limits_{n = 0}^\infty {(n!2^n )^{ - 1} H_n (x/\sqrt {2t} )} \times H_n (B(t)/\sqrt {2t} )$$ , whereH n is the Hermite polynomial of degreen. It is shown that forφ in (L 2)+,g t,φ(x)≡〈δ(B(t)?x), φ〉 is inL and the linear map takingφ intog t,φ is continuous from (L 2)+ intoL. This implies that forf inL * is a generalized Brownian functional and admits the series representation $$f(B(t)) = (2\pi t)^{ - 1/2} \sum\limits_{n = 0}^\infty {(n!2^n )^{ - 1} \langle f,\xi _{n, t} \rangle } H_n (B(t)/\sqrt {2t} )$$ , whereξ n,t is the Hermite function of degreen with parametert. This series representation is used to prove the Ito lemma forf inL *, $$f(B(t)) = f(B(u)) + \int_u^t {\partial _s^ * } f'(B(s)) ds + (1/2)\int_u^t {f''} (B(s)) ds$$ , where? s * is the adjoint of \(\dot B(s)\) -differentiation operator? s . 相似文献
2.
Urs Würgler 《manuscripta mathematica》1979,29(1):93-111
Let P(n)*(–) be Brown-Peterson cohomology modulo In and put B(n)*(–)=P(n)*(–)[1/vn]. In this note we construct a canonical multiplicative and idempotent operation n in a suitable completion
(n)*(–) of B(n)*(–) which has the property that its image is canonically isomorphic to the n-th Morava K-theory K(n)*(–). In particular, the ring theory K(n)*(–) is contained as a direct summand in the theory
(n)*(–). A similar result is not true before completing. pleting. Because the completion map B (n)*(–)
(n)*(–) is injective, the above splitting theorem contains also information about B(n)*(–). The proof of the theorem depends on a result about the behaviour of formal groups of finite height over complete graded Fp. 相似文献
3.
P. Sablonniere 《分析论及其应用》1992,8(3):62-76
Suppose that we want to approximate f∈C[0,1] by polynomials inP, using only its values on Xn={i/n, 0≤i≤n}. This can be done by the Lagrange interpolant Ln f or the classical Bernstein polynomial Bn f. But, when n tends to infinity, Ln f does not converge to f in general and the convergence of Bn f to f is very slow. We define a family of operators B
n
(k)
, n≥k, which are intermediate ones between B
n
(0)
=B
n
(1)
=Bn and B
n
(n)
=Ln, and we study some of their properties. In particular, we prove a Voronovskaja-type theorem which asserts that B
n
(k)
f−f=O(n−[(k+2)/2]) for f sufficiently regular.
Moreover, B
n
(k)
f uses only values of Bn f and its derivaties and can be computed by De Casteljau or subdivision algorithms. 相似文献
4.
Raphaële Supper 《Positivity》2005,9(4):645-665
For functions u subharmonic in the unit ball BN of
, this paper compares the growth of the repartition function of their Riesz measure μ with the growth of u near the boundary
of BN. Cases under study are:
and
, with A, B, γ positive constants and
if N=2 or
if N≥ 3. This paper contains several integral results, as for instance: when ∫BN u+(x)[-ω′(|x|2)]dx < +∞ for some positive decreasing C1 function ω, it is proved that
. 相似文献
5.
It is proved that for any unimodular lattice Λ with homogeneous minimum L>0 and any set of real numbers α1, α2,..., αn there exists a point (y1, y2,..., yn) of Λ such that $$\Pi _{1 \leqslant i \leqslant n} |y_i + \alpha _i | \leqslant 2^{ - n/2_\gamma n} (1 + 3L^{8/(3n)/(\gamma ^{2/3} - 2L^{8/(3n)} )} )^{ - n/2} ,$$ where γn= nn/(n?1). 相似文献
6.
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
7.
Consider the classical nonparametric regression problem yi = f(ti) + ii = 1,...,n where ti = i/n, and i are i.i.d. zero mean normal with variance 2. The aim is to estimate the true function f which is assumed to belong to the smoothness class described by the Besov space B
pq
q
. These are functions belonging to Lp with derivatives up to order s, in Lp sense. The parameter q controls a further finer degree of smoothness. In a Bayesian setting, a prior on B
pq
q
is chosen following Abramovich, Sapatinas and Silverman (1998). We show that the optimal Bayesian estimator of f is then also a.s. in B
pq
q
if the loss function is chosen to be the Besov norm of B
pq
q
. Because it is impossible to compute this optimal Bayesian estimator analytically, we propose a stochastic algorithm based on an approximation of the Bayesian risk and simulated annealing. Some simulations are presented to show that the algorithm performs well and that the new estimator is competitive when compared to the more standard posterior mean. 相似文献
8.
V. A. Dem'yanenko 《Journal of Mathematical Sciences》1982,18(6):843-861
Let K be an algebraic number field of degree n; let be the number of divisor classes of the field K; y: v2=u4+au2+B is the Jacobian curve over
where C is an integral divisor, q1, ..., qN are distinct prime divisors. One proves that there exists an effectively computable constant c=c(n, h(K), N), such that the order m of the torsion of any primitive K-point on is bounded by it: mC.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 82, pp. 5–28, 1979. 相似文献
9.
Consider a single server queue with i.i.d. arrival and service processes, $\{ A,A_n ,n \geqslant 0\} $ and $\{ C,\;C_n ,n\;\; \geqslant \;\;0\} $ , respectively, and a finite buffer B. The queue content process $\{ Q_n^B ,n \geqslant 0\} $ is recursively defined as $Q_{n + 1}^B = \min ((Q_n^B + A_{n + 1} - C_{n + 1} )^ + ,B),\;\;q^ + = \max (0,q)$ . When $\mathbb{E}(A - C) < 0$ , and A has a subexponential distribution, we show that the stationary expected loss rate for this queue $E(Q_n^B + A_{n + 1} - C_{n + 1} - B)^ + $ has the following explicit asymptotic characterization: $${\mathbb{E}}\left( {Q_n^B + A_{n + 1} - C_{n + 1} - B} \right)^ + ~{\mathbb{E}}\left( {A - B} \right)^ + {as} B \to \infty ,$$ independently of the server process C n . For a fluid queue with capacity c, M/G/∞ arrival process A t , characterized by intermediately regularly varying on periods σon, which arrive with Poisson rate Λ, the average loss rate $\lambda _{{loss}}^B $ satisfies λ loss B ~ Λ E(τonη — B)+ as B → ∞, where $\eta = r + \rho - c,\;\rho \; = \mathbb{E}A_t < \;\;c;r\;\;(c \leqslant r)$ is the rate at which the fluid is arriving during an on period. Accuracy of the above asymptotic relations is verified with extensive numerical and simulation experiments. These explicit formulas have potential application in designing communication networks that will carry traffic with long-tailed characteristics, e.g., Internet data services. 相似文献
10.
We consider a general linear model
, where the innovations Zt belong to the domain of attraction of an α-stable law for α<2, so that neither Zt nor Xt have a finite variance. We do not assume that (Xt) is a standardARMA process of the form φ(B)Xt=ϕ(B)Zt, but we fit anARMA process of a given order to the data X1,...,Xn by estimating the coefficients of φ and ϕ. Given that (Xt) is anARMA process, it has been proved that the Whittle estimator is a consistent estimator of the true coefficients of ϕ and φ. Moreover,
it then has a heavytailed limit distribution and the rate of convergence is (n/logn)1/α, which compares favorably with the L2 situation with rate
. In this note we study the limit properties of the Whittle estimator when the underlying model is not necessarily anARMA process. Under general conditions we show that the Whittle estimate converges in probability. It converges weakly to a distribution
which does not have a finite moment of order a and the rate of convergence is again (n/logn)1/α. We also give an analytic expression for the limit distribution.
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II, Eger, Hungary, 1994. 相似文献
11.
For 1/p+1/q1, we study the closed ideal
formed by the (c
o
,p,q)-summing operators. It turns out thatT:XY does not belong to
if and only if it factors the mapId:l
p
*l
q
. By localization, we get the ideal
that consists of those operatorsT for which all ultrapowersT
u
are contained in
. Operators in the complement of
are characterized by the property that they factor the mapsId:l
p
*n
l
q
n
uniformly. Our main tools are ideal norms.Supported by DFG grant PI 322/1-2 相似文献
12.
G. Gopalakrishnan Nair 《Journal of Optimization Theory and Applications》1979,28(3):429-434
The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.Notation
E
n
Euclideann-space
- f
Gradient off(x)
- 2
f
Hessian matrix
- (·)
T
Transpose of (·)
-
I
Index set {1, 2, ...,n}
- [x
i1
*(j)
]
Point around which search is made in the (j + 1)th iteration, i.e., [x
1l
*(j)
,x
2l
*(j)
,...,x
n1
*(j)
]
-
r
i
(i)
Range ofx
il
*(i)
in the (j + 1)th iteration
-
l
1
mini {r
i
(0)
}
-
l
2
mini {r
i
(0)
}
-
A
j
Region of search in thejth iteration, i.e., {x E
n:x
il
*(j-1)
–0.5r
i
(j-1)
x
ix
il
*(j-1)
+0.5r
i
(j-1)
,i I}
-
S
j
Closed sphere with center origin and radius
j
-
Reduction factor in each iteration
-
1–
- (·)
Gamma function
Many discussions with Dr. S. N. Iyer, Professor of Electrical Engineering, College of Engineering, Trivandrum, India, are gratefully acknowledged. The author has great pleasure to thank Dr. K. Surendran, Professor, Department of Electrical Engineering, P.S.G. College of Technology, Coimbatore, India, for suggesting this work. 相似文献
13.
J. Hu 《Transformation Groups》2010,15(2):333-370
Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let $ \mathfrak{B}_n^{(f)} Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let
\mathfrakBn(f) \mathfrak{B}_n^{(f)} be the two-sided ideal of the Brauer algebra
\mathfrakBn( - 2m ) {\mathfrak{B}_n}\left( { - 2m} \right) over K generated by e
1
e
3⋯
e
2f-1 where 0 ≤ f ≤ [n/2]. Let HTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} be the subspace of partial-harmonic tensors of valence f in V
⊗n
. In this paper we prove that dimHTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} and dim
\textEn\textdK\textSp(V)( V ?n \mathord