共查询到20条相似文献,搜索用时 296 毫秒
1.
H. A. Dzyubenko 《Ukrainian Mathematical Journal》2009,61(4):519-540
In the case where a 2π-periodic function f is twice continuously differentiable on the real axis ℝ and changes its monotonicity at different fixed points y
i
∈ [− π, π), i = 1,…, 2s, s ∈ ℕ (i.e., on ℝ, there exists a set Y := {y
i
}
i∈ℤ of points y
i
= y
i+2s
+ 2π such that the function f does not decrease on [y
i
, y
i−1] if i is odd and does not increase if i is even), for any natural k and n, n ≥ N(Y, k) = const, we construct a trigonometric polynomial T
n
of order ≤n that changes its monotonicity at the same points y
i
∈ Y as f and is such that
*20c || f - Tn || £ \fracc( k,s )n2\upomega k( f",1 \mathord\vphantom 1 n n ) ( || f - Tn || £ \fracc( r + k,s )nr\upomega k( f(r),1 \mathord | / |
\vphantom 1 n n ), f ? C(r), r 3 2 ), \begin{array}{*{20}{c}} {\left\| {f - {T_n}} \right\| \leq \frac{{c\left( {k,s} \right)}}{{{n^2}}}{{{\upomega }}_k}\left( {f',{1 \mathord{\left/{\vphantom {1 n}} \right.} n}} \right)} \\ {\left( {\left\| {f - {T_n}} \right\| \leq \frac{{c\left( {r + k,s} \right)}}{{{n^r}}}{{{\upomega }}_k}\left( {{f^{(r)}},{1 \mathord{\left/{\vphantom {1 n}} \right.} n}} \right),\quad f \in {C^{(r)}},\quad r \geq 2} \right),} \\ \end{array} 相似文献
2.
In this paper, aK classM/G/1 queueing system with feedback is examined. Each arrival requires at least one, and possibly up toK service phases. A customer is said to be in classk if it is waiting for or receiving itskth phase of service. When a customer finishes its phasek ≤K service, it either leaves the system with probabilityp
k, or it instantaneously reenters the system as a classk + 1 customer with probability (1 −p
k). It is assumed thatp
k = 1. Service is non-preemptive and FCFS within a specified priority ordering of the customer classes. Level crossing analysis
of queues and delay cycle results are used to derive the Laplace-Stieltjes Transform (LST) for the PDF of the sojourn time
in classes 1,…,k;k ≤K. 相似文献
3.
For every product preserving bundle functor T μ on fibered manifolds, we describe the underlying functor of any order (r, s, q), s ≥ r ≤ q. We define the bundle Kk,lr,s,q YK_{k,l}^{r,s,q} Y of (k, l)-dimensional contact elements of the order (r, s, q) on a fibered manifold Y and we characterize its elements geometrically. Then we study the bundle of general contact elements of type μ. We also determine all natural transformations of Kk,lr,s,q YK_{k,l}^{r,s,q} Y into itself and of T( Kk,lr,s,q Y )T\left( {K_{k,l}^{r,s,q} Y} \right) into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from Y to Kk,lr,s,q YK_{k,l}^{r,s,q} Y . 相似文献
4.
Vyacheslav M. Abramov 《Acta Appl Math》2008,100(3):201-226
The paper studies closed queueing networks containing a server station and k client stations. The server station is an infinite server queueing system, and client stations are single-server queueing
systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by a
strictly stationary and ergodic sequence of random variables. The total number of units in the network is N. The expected times between departures in client stations are (N
μ
j
)−1. After a service completion in the server station, a unit is transmitted to the jth client station with probability p
j
(j=1,2,…,k), and being processed in the jth client station, the unit returns to the server station. The network is assumed to be in a semi-Markov environment. A semi-Markov
environment is defined by a finite or countable infinite Markov chain and by sequences of independent and identically distributed
random variables. Then the routing probabilities p
j
(j=1,2,…,k) and transmission rates (which are expressed via parameters of the network) depend on a Markov state of the environment.
The paper studies the queue-length processes in client stations of this network and is aimed to the analysis of performance
measures associated with this network. The questions risen in this paper have immediate relation to quality control of complex
telecommunication networks, and the obtained results are expected to lead to the solutions to many practical problems of this
area of research.
相似文献
5.
For x = (x 1, x 2, ..., x n ) ∈ ℝ+ n , the symmetric function ψ n (x, r) is defined by $\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } ,$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } , 相似文献
6.
Noga Alon 《Israel Journal of Mathematics》1986,53(1):97-120
All graphs considered are finite, undirected, with no loops, no multiple edges and no isolated vertices. For two graphsG, H, letN(G, H) denote the number of subgraphs ofG isomorphic toH. Define also, forl≧0,N(l, H)=maxN(G, H), where the maximum is taken over all graphsG withl edges. We determineN(l, H) precisely for alll≧0 whenH is a disjoint union of two stars, and also whenH is a disjoint union ofr≧3 stars, each of sizes ors+1, wheres≧r. We also determineN(l, H) for sufficiently largel whenH is a disjoint union ofr stars, of sizess
1≧s
2≧…≧s
r>r, provided (s
1−s
r)2<s
1+s
r−2r. We further show that ifH is a graph withk edges, then the ratioN(l, H)/l
k tends to a finite limit asl→∞. This limit is non-zero iffH is a disjoint union of stars. 相似文献
7.
Pravir Dutt Satyendra Tomar B. V. Rathish Kumar 《Proceedings Mathematical Sciences》2002,112(4):601-639
In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral
methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical
mesh. With this mesh we seek a solution which minimizes a weighted squared norm of the residuals in the partial differential
equation and a fractional Sobolev norm of the residuals in the boundary conditions and enforce continuity by adding a term
which measures the jump in the function and its derivatives at inter-element boundaries, in an appropriate fractional Sobolev
norm, to the functional being minimized. Since the second derivatives of the actual solution are not square integrable in
a neighborhood of the corners we have to multiply the residuals in the partial differential equation by an appropriate power
of rk, where rk measures the distance between the pointP and the vertexA
k
in a sectoral neighborhood of each of these vertices. In each of these sectoral neighborhoods we use a local coordinate system
(τk, θk) where τk
= lnrk and (rk, θk) are polar coordinates with origin at Ak, as first proposed by Kondratiev. We then derive differentiability estimates with respect to these new variables and a stability
estimate for the functional we minimize.
In [6] we will show that we can use the stability estimate to obtain parallel preconditioners and error estimates for the
solution of the minimization problem which are nearly optimal as the condition number of the preconditioned system is polylogarithmic
inN, the number of processors and the number of degrees of freedom in each variable on each element. Moreover if the data is
analytic then the error is exponentially small inN. 相似文献
8.
We obtain new sharp Kolmogorov-type inequalities, in particular the following sharp inequality for 2π-periodic functions x ∈ L
∞
r
(T):
9.
Let r
1, …, r
s
be non-zero integers satisfying r
1 + ⋯ + r
s
= 0. Let G be a finite abelian group with k
i
|k
i-1(2 ≤ i ≤ n), and suppose that (r
i
, k
1) = 1(1 ≤ i ≤ s). Let denote the maximal cardinality of a set which contains no non-trivial solution of r
1
x
1 + ⋯ + r
s
x
s
= 0 with . We prove that . We also apply this result to study problems in finite projective spaces.
相似文献
10.
The signed distance-k-domination number of a graph is a certain variant of the signed domination number. If v is a vertex of a graph G, the open k-neighborhood of v, denoted by N
k
(v), is the set N
k
(v) = {u: u ≠ v and d(u, v) ⩽ k}. N
k
[v] = N
k
(v) ⋃ {v} is the closed k-neighborhood of v. A function f: V → {−1, 1} is a signed distance-k-dominating function of G, if for every vertex
. The signed distance-k-domination number, denoted by γ
k,s
(G), is the minimum weight of a signed distance-k-dominating function on G. The values of γ
2,s
(G) are found for graphs with small diameter, paths, circuits. At the end it is proved that γ
2,s
(T) is not bounded from below in general for any tree T. 相似文献
11.
V. A. Kofanov 《Ukrainian Mathematical Journal》2006,58(10):1538-1551
We establish new exact Bernstein-type and Kolmogorov-type inequalities. The main result of this work is the following exact
inequality for periodic splines s of order r and defect 1 with nodes at the points iπ/n, i ∈ Z, n ∈ N:
12.
For κ ⩾ 0 and r0 > 0 let ℳ(n, κ, r0) be the set of all connected, compact n-dimensional Riemannian manifolds (Mn, g) with Ricci (M, g) ⩾ −(n−1) κ g and Inj (M) ⩾ r0. We study the relation between the kth eigenvalue λk(M) of the Laplacian associated to (Mn,g), Δ = −div(grad), and the kth eigenvalue λk(X) of a combinatorial Laplacian associated to a discretization X of M. We show that there exist constants c, C > 0 (depending only on n, κ and r0) such that for all M ∈ ℳ(n, κ, r0) and X a discretization of
for all k < |X|. Then, we obtain the same kind of result for two compact manifolds M and N ∈ ℳ(n, κ, r0) such that the Gromov–Hausdorff distance between M and N is smaller than some η > 0. We show that there exist constants c, C > 0 depending on η, n, κ and r0 such that
for all
.
Mathematics Subject Classification (2000): 58J50, 53C20
Supported by Swiss National Science Foundation, grant No. 20-101 469 相似文献
13.
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L
2(ℝ
s
). Suppose ψ = (ψ1,..., ψ
r
)
T
and are two compactly supported vectors of functions in the Sobolev space (H
μ(ℝ
s
))
r
for some μ > 0. We provide a characterization for the sequences {ψ
jk
l
: l = 1,...,r, j ε ℤ, k ε ℤ
s
} and to form two Riesz sequences for L
2(ℝ
s
), where ψ
jk
l
= m
j/2ψ
l
(M
j
·−k) and , M is an s × s integer matrix such that lim
n→∞
M
−n
= 0 and m = |detM|. Furthermore, let ϕ = (ϕ1,...,ϕ
r
)
T
and be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, and M, where a and are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr
)
T
and , ν = 1,..., m − 1 such that two sequences {ψ
jk
νl
: ν = 1,..., m − 1, l = 1,...,r, j ε ℤ, k ε ℤ
s
} and { : ν=1,...,m−1,ℓ=1,...,r, j ∈ ℤ, k ∈ ℤ
s
} form two Riesz multiwavelet bases for L
2(ℝ
s
). The bracket product [f, g] of two vectors of functions f, g in (L
2(ℝ
s
))
r
is an indispensable tool for our characterization.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123) 相似文献
14.
15.
V. A. Kofanov 《Ukrainian Mathematical Journal》2009,61(6):908-922
For an arbitrary fixed segment [α, β] ⊂ R and given r ∈ N, A
r
, A
0, and p > 0, we solve the extremal problem
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