共查询到20条相似文献,搜索用时 15 毫秒
1.
《Computers & Mathematics with Applications》2002,43(8-9):951-964
We construct an important transform to obtain sufficient conditions for the oscillation of all solutions of delay partial difference equations with positive and negative coefficients of the form Am+1,n + Am,n+1 − Amn + pmnAm−k−1 − qmnAm−k′,n−l′ = 0, where m, n = 0, 1, …, and k, k′, l′, l are nonnegative integers, p, q ϵ (0, ∞), the coefficients {qmn} and {pmn} are sequences of nonnegative real numbers. 相似文献
2.
E. A. Timofeev 《Automatic Control and Computer Sciences》2017,51(7):586-591
Let Ω = AN be a space of right-sided infinite sequences drawn from a finite alphabet A = {0,1}, N = {1,2,…}. Let ρ(x, y)Σk=1∞|x k ? y k |2?k be a metric on Ω = AN, and μ the Bernoulli measure on Ω with probabilities p0, p1 > 0, p0 + p1 = 1. Denote by B(x,ω) an open ball of radius r centered at ω. The main result of this paper \(\mu (B(\omega ,r))r + \sum\nolimits_{n = 0}^\infty {\sum\nolimits_{j = 0}^{{2^n} - 1} {{\mu _{n,j}}} } (\omega )\tau ({2^n}r - j)\), where τ(x) = 2min {x,1 ? x}, 0 ≤ x ≤ 1, (τ(x) = 0, if x < 0 or x > 1 ), \({\mu _{n,j}}(\omega ) = (1 - {p_{{\omega _{n + 1}}}})\prod _{k = 1}^n{p_{{\omega _k}}} \oplus {j_k}\), \(j = {j_1}{2^{n - 1}} + {j_2}{2^{n - 2}} + ... + {j_n}\). The family of functions 1, x, τ(2 n r ? j), j = 0,1,…, 2 n ? 1, n = 0,1,…, is the Faber–Schauder system for the space C([0,1]) of continuous functions on [0, 1]. We also obtain the Faber–Schauder expansion for Lebesgue’s singular function, Cezaro curves, and Koch–Peano curves. Article is published in the author’s wording. 相似文献
3.
Let X and Y be two strings of lengths n and m, respectively, and k and l, respectively, be the numbers of runs in their corresponding run-length encoded forms. We propose a simple algorithm for computing the longest common subsequence of two given strings X and Y in O(kl+min{p1,p2}) time, where p1 and p2 denote the numbers of elements in the bottom and right boundaries of the matched blocks, respectively. It improves the previously known time bound O(min{nl,km}) and outperforms the time bounds O(kllogkl) or O((k+l+q)log(k+l+q)) for some cases, where q denotes the number of matched blocks. 相似文献
4.
《Computers & Mathematics with Applications》2003,45(6-9):1461-1468
The authors consider the mth-order neutral difference equation Dm(y(n) + p(n)y(n − k) + q(n)f(y(σ(n))) = e(n), where m ≥ 1, {p(n)}, {q(n)}, {e(n)}, and {a1(n)}, {a2(n)}, …, {am−1(n)} are real sequences, ai(n) > 0 for i = 1,2,…, m−1, am(n) ≡ 1, D0z(n) = y(n)+p(n)y(n − k), Diz(n) = ai(n)ΔDi−1z(n) for i = 1,2, …, m, k is a positive integer, {σ(n)} → ∞ is a sequence of positive integers, and R → R is continuous with u f(u) > 0 for u ≠ 0. In the case where {q(n)} is allowed to oscillate, they obtain sufficient conditions for all bounded nonoscillatory solutions to converge to zero, and if {q(n)} is a nonnegative sequence, they establish sufficient conditions for all nonoscillatory solutions to converge to zero. Examples illustrating the results are included throughout the paper. 相似文献
5.
《Computers & Mathematics with Applications》2000,39(1-2):1-7
New oscillation and nonoscillation theorems are obtained for the second-order linear difference equation Δ2xn−1 + pnxn = 0, where if pn∞n=1 is a real sequence with pn ≥ 0. 相似文献
6.
7.
Given a
-complete (semi)lattice
, we consider
-labeled transition systems as coalgebras of a functor
(−), associating with a set X the set
X of all
-fuzzy subsets. We describe simulations and bisimulations of
-coalgebras to show that L(−) weakly preserves nonempty kernel pairs iff it weakly preserves nonempty pullbacks iff L is join infinitely distributive (JID).Exchanging
for a commutative monoid
, we consider the functor
(−)ω which associates with a set X all finite multisets containing elements of X with multiplicities m M. The corresponding functor weakly preserves nonempty pullbacks along injectives iff 0 is the only invertible element of
, and it preserves nonempty kernel pairs iff
is refinable, in the sense that two sum representations of the same value, r1 + … + rm = c1 + … + cn, have a common refinement matrix (m(i, j)) whose k-th row sums to rk and whose l-th column sums to cl for any 1≤ k ≤ m and 1 ≤ l ≤ n. 相似文献
8.
L. R. Hunt 《Theory of Computing Systems》1978,12(1):361-370
Consider the nonlinear system $$\dot x(t) = f(x(t)) + \sum\limits_{i = 1}^m {u_i (t)g_i (x(t)), x(0) = x_0 \in M}$$ whereM is aC ∞ realn-dimensional manifold,f, g 1,?.,g m areC ∞ vector fields onM, andu 1 ,..,u m are real-valued controls. Ifm=n?1 andf, g 1 ,?,g m are linearly independent, then the system is called a hypersurface system, and necessary and sufficient conditions for controllability are known. For a generalm, 1 ≤m ≤n?1, and arbitraryC ∞ vector fields,f, g 1 ,?,g m , assume that the Lie algebra generated byf, g 1 ,?,g m and by taking successive Lie brackets of these vector fields is a vector bundle with constant fiber (vector space) dimensionp onM. By Chow's Theorem there exists a maximalC ∞ realp-dimensional submanifoldS ofM containingx 0 with the generated bundle as its tangent bundle. It is known that the reachable set fromx 0 must contain an open set inS. The largest open subsetU ofS which is reachable fromx 0 is called the region of reachability fromx 0. IfO is an open subset ofS which is reachable fromx 0,S we find necessary conditions and sufficient conditions on the boundary ofO inS so thatO = U. Best results are obtained when it is assumed that the Lie algebra generated byg 1,?,g m and their Lie brackets is a vector bundle onM. 相似文献
9.
E. A. Timofeev 《Automatic Control and Computer Sciences》2017,51(7):634-638
Recall that Lebesgue’s singular function L(t) is defined as the unique solution to the equation L(t) = qL(2t) + pL(2t ? 1), where p, q > 0, q = 1 ? p, p ≠ q. The variables M n = ∫01t n dL(t), n = 0,1,… are called the moments of the function The principal result of this work is \({M_n} = {n^{{{\log }_2}p}}{e^{ - \tau (n)}}(1 + O({n^{ - 0.99}}))\), where the function τ(x) is periodic in log2x with the period 1 and is given as \(\tau (x) = \frac{1}{2}1np + \Gamma '(1)lo{g_2}p + \frac{1}{{1n2}}\frac{\partial }{{\partial z}}L{i_z}( - \frac{q}{p}){|_{z = 1}} + \frac{1}{{1n2}}\sum\nolimits_{k \ne 0} {\Gamma ({z_k})L{i_{{z_k} + 1}}( - \frac{q}{p})} {x^{ - {z_k}}}\), \({z_k} = \frac{{2\pi ik}}{{1n2}}\), k ≠ 0. The proof is based on poissonization and the Mellin transform. 相似文献
10.
V. R. Fatalov 《Problems of Information Transmission》2010,46(2):160-183
Let {ξ
k
}
k=0∞ be a sequence of i.i.d. real-valued random variables, and let g(x) be a continuous positive function. Under rather general conditions, we prove results on sharp asymptotics of the probabilities
$
P\left\{ {\frac{1}
{n}\sum\limits_{k = 0}^{n - 1} {g\left( {\xi _k } \right) < d} } \right\}
$
P\left\{ {\frac{1}
{n}\sum\limits_{k = 0}^{n - 1} {g\left( {\xi _k } \right) < d} } \right\}
, n → ∞, and also of their conditional versions. The results are obtained using a new method developed in the paper, namely,
the Laplace method for sojourn times of discrete-time Markov chains. We consider two examples: standard Gaussian random variables
with g(x) = |x|
p
, p > 0, and exponential random variables with g(x) = x for x ≥ 0. 相似文献
11.
J. T. Marti 《Computing》1989,42(2-3):239-243
We derive new inequalities for the eigenvaluesλ k of the Sturm-Liouville problem?u″+qu=λu, u(0)=u(π)=0 under the usual hypothesis thatq has mean value zero. The estimates give upper and lower bounds of the form |λ k ?k 2|≤p 1,m k ?m +P 2,m k 2m ,k 2≥3‖q‖ m ,m=1, 2 where ‖q‖ m is the norm ofq in a Sobolev spaceH m (0, π) and theP's are homogeneous polynomials of degree at most 3 in ‖q‖ m . Such bounds are used in the analysis of the inverse Sturm-Liouville problem. 相似文献
12.
Giuliano G. La Guardia 《Quantum Information Processing》2012,11(2):591-604
Two new families of asymmetric quantum codes are constructed in this paper. The first one is derived from the Calderbank-Shor-Steane
(CSS) construction applied to classical Reed-Solomon (RS) codes, providing quantum codes with parameters [[N = l(q
l
−1), K = l(q
l
−2d + c + 1), d
z
≥ d/d
x
≥ (d−c)]]
q
, where q is a prime power and d > c + 1, c ≥ 1, l ≥ 1 are integers. The second family is derived from the CSS construction applied to classical generalized RS codes, generating
quantum codes with parameters [[N = mn, K = m(2k−n + c), d
z
≥ d/d
x
≥ (d−c)]]
q
, where q is a prime power, 1 < k < n < 2k + c ≤ q
m
, k = n − d + 1, and n, d > c + 1, c ≥ 1, m ≥ 1 are integers. Although the second proposed construction generalizes the first one, the techniques developed in both constructions
are slightly different. These new codes have parameters better than or comparable to the ones available in the literature.
Additionally, the proposed codes can be utilized in quantum channels having great asymmetry, that is, quantum channels in
which the probability of occurrence of phase-shift errors is large when compared to the probability of occurrence of qudit-flip
errors. 相似文献
13.
Mingyu Xiao 《Theory of Computing Systems》2010,46(4):723-736
Given a graph G=(V,E) with n vertices and m edges, and a subset T of k vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most l edges (non-terminal vertices), whose removal from G separates each terminal from all the others. These two problems are NP-hard for k≥3 but well-known to be polynomial-time solvable for k=2 by the flow technique. In this paper, based on a notion farthest minimum isolating cut, we design several simple and improved algorithms for Multiterminal Cut. We show that Edge Multiterminal Cut can be solved in O(2 l kT(n,m)) time and Vertex Multiterminal Cut can be solved in O(k l T(n,m)) time, where T(n,m)=O(min?(n 2/3,m 1/2)m) is the running time of finding a minimum (s,t) cut in an unweighted graph. Furthermore, the running time bounds of our algorithms can be further reduced for small values of k: Edge 3-Terminal Cut can be solved in O(1.415 l T(n,m)) time, and Vertex {3,4,5,6}-Terminal Cuts can be solved in O(2.059 l T(n,m)), O(2.772 l T(n,m)), O(3.349 l T(n,m)) and O(3.857 l T(n,m)) time respectively. Our results on Multiterminal Cut can also be used to obtain faster algorithms for Multicut: $O((\min(\sqrt{2k},l)+1)^{2k}2^{l}T(n,m))Given a graph G=(V,E) with n vertices and m edges, and a subset T of k vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most l edges (non-terminal vertices), whose removal from G separates each terminal from all the others. These two problems are NP-hard for k≥3 but well-known to be polynomial-time solvable for k=2 by the flow technique. In this paper, based on a notion farthest minimum isolating cut, we design several simple and improved algorithms for Multiterminal Cut. We show that Edge Multiterminal Cut can be solved
in O(2
l
kT(n,m)) time and Vertex Multiterminal Cut can be solved in O(k
l
T(n,m)) time, where T(n,m)=O(min (n
2/3,m
1/2)m) is the running time of finding a minimum (s,t) cut in an unweighted graph. Furthermore, the running time bounds of our algorithms can be further reduced for small values
of k: Edge 3-Terminal Cut can be solved in O(1.415
l
T(n,m)) time, and Vertex {3,4,5,6}-Terminal Cuts can be solved in O(2.059
l
T(n,m)), O(2.772
l
T(n,m)), O(3.349
l
T(n,m)) and O(3.857
l
T(n,m)) time respectively. Our results on Multiterminal Cut can also be used to obtain faster algorithms for Multicut:
O((min(?{2k},l)+1)2k2lT(n,m))O((\min(\sqrt{2k},l)+1)^{2k}2^{l}T(n,m))
-time algorithm for Edge Multicut and O((2k)
k+l/2
T(n,m))-time algorithm for Vertex Multicut. 相似文献
14.
Given q+1 strings (a text t of length n and q patterns m1,…,mq) and a natural number w, the multiple serial episode matching problem consists in finding the number of size w windows of text t which contain patterns m1,…,mq as subsequences, i.e., for each mi, if mi=p1,…,pk, the letters p1,…,pk occur in the window, in the same order as in mi, but not necessarily consecutively (they may be interleaved with other letters). Our main contribution here is an algorithm solving this problem on-line in time O(nq) with an MP-RAM model (which is a RAM model equipped with extra operations). 相似文献
15.
《Computers & Mathematics with Applications》2003,45(6-9):1181-1194
Consider a three-point difference scheme −h−2Δ(2)yn + qn(h)yn = fn(h), n ϵ Z = {0, ±1, ±2, …}, where h ϵ (0, h0], h0 is a given positive number, Δ(2)yn = yn+1 + yn−1, f(h) = {fn(h)}n ϵ Z ϵ L∞(h), L∞(h) = {f(h) : ∥f(h)∥L∞(h) < ∞}, ∥f(h)∥L∞(h) = supnϵZ ∥fn(h)∥.We assume a unique a priori requirement 0 <- qn(h) < ∞ for any n ϵ Z and h ϵ (0, h0]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L∞(h). 相似文献
16.
《Computers & Mathematics with Applications》2003,45(6-9):1235-1243
In this paper, we consider the difference equation on an arbitrary Banach space (X, ∥·∥x), Δ(qnΔxn + fn(xn) = 0, where {qn} is a positive sequence and fn is X-valued. We shall give conditions so that for a given x ϵ X, there exists a solution of this equation asymptotically equal to x. 相似文献
17.
Maximum number of edges joining vertices on a cube 总被引:1,自引:0,他引:1
Khaled A.S. Abdel-Ghaffar 《Information Processing Letters》2003,87(2):95-99
Let Ed(n) be the number of edges joining vertices from a set of n vertices on a d-dimensional cube, maximized over all such sets. We show that Ed(n)=∑i=0r−1(li/2+i)2li, where r and l0>l1>?>lr−1 are nonnegative integers defined by n=∑i=0r−12li. 相似文献
18.
《Computers & Mathematics with Applications》2001,41(5-6):553-561
In this paper, we consider the delay difference equation xn+1 − xn + pnxn−k = 0, n = 0, 1, 2, …, where pn is a sequence of nonnegative real numbers and k is a positive integer. Some new results for the oscillation of this equation are obtained. Our theorems improve all known results in the literature. 相似文献
19.
Pravin M. Vaidya 《Algorithmica》1989,4(1-4):569-583
We study the problem of finding a minimum weight complete matching in the complete graph on a set V ofn points ink-dimensional space. The points are the vertices of the graph and the weight of an edge between any two points is the distance between the points under someL q,-metric. We give anO((2c q )1.5k ??1.5k (α(n, n))0.5 n 1.5(logn)2.5) algorithm for finding an almost minimum weight complete matching in such a graph, wherec q =6k 1/q for theL q -metric, α is the inverse Ackermann function, and ? ≤ 1. The weight of the complete matching obtained by our algorithm is guaranteed to be at most (1 + ?) times the weight of a minimum weight complete matching. 相似文献
20.
《Mathematics and computers in simulation》1996,42(1):35-45
Some results related to the problem of interpolation of n vertical segments (xk, Yk), k = 1,…,n, in the plane with generalized polynomial functions that are linear combinations of m basic functions are presented. It is proved that the set of interpolating functions (if not empty) is bounded in every subinterval (xk, xk+1) by two unique such functions ηk− and ηk+. An algorithm with result verification for the determination of the boundary functions ηk−, ηk+ and for their effective tabulation is reported and some examples are discussed. 相似文献