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1.
Global stability of a rational difference equation   总被引:1,自引:0,他引:1  
In this paper, we study the global stability of the difference equation , where the parameters a,ai(0,) for i=0,…,k, x-k,…, x-1[0,) and x0(0,). We prove that the unique positive equilibrium is globally asymptotically stable if and only if it is locally asymptotically. Also we provide sufficient condition for it to be globally asymptotically stable and our results solve the open problem proposed by Kulenović and Ladas (Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002).  相似文献   

2.
By constructing a class of solutions to the integral inequality for t  t0 large enough, where 0<A1a(τ)A2<+ and λ>1, that tend to zero as t→+ we address an open problem in the theory of nonlinear oscillations.  相似文献   

3.
We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time , and the randomized algorithm runs in expected time O(kout+kinlogn+n(logn)1+ε). Here kin is the number of edges in all the paths of Π, and kout is the number of edges in the output paths.  相似文献   

4.
Using a numerical methods based on sub–super solution, we will find positive solution for the diffusive logistic equation Δu+au-bu2=0 for xΩ, with Dirichlet boundary condition.  相似文献   

5.
Let M1 and M2 be two matroids on the same ground set S. We conjecture that if there do not exist disjoint subsets A1,A2,…,Ak+1 of S, such that ispM1(Ai)≠Ø, and similarly for M2, then S is partitioned into k sets, each independent in both M1 and M2. This is a possible generalization of König's edge-coloring theorem. We prove the conjecture for the case k=2 and for a regular case, in which both matroids have the same rank d, and S consists of k·d elements. Finally, we prove another special case related to a conjecture of Rota.  相似文献   

6.
Let m and r be positive integers. Define f(m,r) to be the least positive integer N such that for every coloring of the integers 1,…,N with r colors there exist monochromatic subsets B1 and B2 (not necessarily of the same color), each having m elements, such that (a) max(B1)-min(B1)max(B2)-min(B2), and (b) max(B1)B2). We improve previous upper bounds to determine that f(m,4)=12m-9.  相似文献   

7.
The independence polynomial, ω(G,x)=∑wkxk, of a graph, G, has coefficients, wk, that enumerate the ways of selecting k vertices from G so that no two selected vertices share an edge. The independence number of G is the largest value of k for which wk≠0. Little is known of less straightforward relationships between graph structure and the properties of ω(G,x), in part because of the difficulty of calculating values of wk for specific graphs. This study presents a new algorithm for these calculations which is both faster than existing ones and easily adaptable to high-level computer languages.  相似文献   

8.
A discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi-discrete and a family of Fully-discrete time approximate scheme are formulated. These schemes can be symmetric or nonsymmetric. Hp-version error estimates are analyzed for these schemes. Just because of a damping term ·(b(u)ut) included in Sobolev equation, which is the distinct character different from parabolic equation, special test functions are chosen to deal with this term. Finally, a priori L(H1) error estimate is derived for the semi-discrete time scheme and similarly, l(H1) and l2(H1) for the Fully-discrete time schemes. These results also indicate that spatial rates in H1 and time truncation errors in L2 are optimal.  相似文献   

9.
P. Chase and F. Ruskey each published a Gray code for length n binary strings with m occurrences of 1, coding m-combinations of n objects, which is two-close—that is, in passing from one binary string to its successor a single 1 exchanges positions with a 0 which is either adjacent to the 1 or separated from it by a single 0. If we impose the restriction that any suffix of a string contains at least k−1 times as many 0's as 1's, we obtain k-suffixes: suffixes of k-ary Dyck words. Combinations are retrieved as special case by setting k=1 and k-ary Dyck words are retrieved as a special case by imposing the additional condition that the entire string has exactly k−1 times as many 0's as 1's. We generalize Ruskey's Gray code to the first two-close Gray code for k-suffixes and we provide a loop-free implementation for k2. For k=1 we use a simplified version of Chase's loop-free algorithm for generating his two-close Gray code for combinations. These results are optimal in the sense that there does not always exist a Gray code, either for combinations or Dyck words, in which the 1 and the 0 that exchange positions are adjacent.  相似文献   

10.
This paper deals with p-Laplacian systems
with null Dirichlet boundary conditions in a smooth bounded domain ΩRN, where p,q>1, , and a,b>0 are positive constants. We first get the non-existence result for a related elliptic systems of non-increasing positive solutions. Secondly by using this non-existence result, blow-up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=BR={xRN:|x|<R}(R>0). Then under appropriate hypotheses, we establish local theory of the solutions and obtain that the solutions either exists globally or blow-up in finite time.  相似文献   

11.
Given a graph G, a proper labeling f of G is a one-to-one function . The bandwidth sum of a graph G, denoted by Bs(G), is defined by Bs(G)=min∑uvE(G)|f(u)-f(v)|, where the minimum is taken for all proper labelings f of G. In this paper, we give some results for the bandwidth sum problem for the join of k graphs G1,G2,…,Gk, where each Gi is a path, cycle, complete graph, or union of isolated vertices. We also discuss the bandwidth sum for the composition of two graphs G and H, where G and H are path, cycle, or union of isolated vertices.  相似文献   

12.
We consider L1-isotonic regression and L isotonic and unimodal regression. For L1-isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for L isotonic and unimodal regression.  相似文献   

13.
We have a ring homomorphism Θ from the cohomology of the extended Morava stabilizer group Gn with coefficients in F[w±1] to the cohomology of Gn+1 with coefficients in the graded field F((un))[u±1]. In this note we study the behavior of Θ on H1. Then it is shown that Θ is injective on H1 for n1 and for all primes p.  相似文献   

14.
Area-preserving approximations of polygonal paths   总被引:1,自引:0,他引:1  
Let P be an x-monotone polygonal path in the plane. For a path Q that approximates P let WA(Q) be the area above P and below Q, and let WB(Q) be the area above Q and below P. Given P and an integer k, we show how to compute a path Q with at most k edges that minimizes WA(Q)+WB(Q). Given P and a cost C, we show how to find a path Q with the smallest possible number of edges such that WA(Q)+WB(Q)C. However, given P, an integer k, and a cost C, it is NP-hard to determine if a path Q with at most k edges exists such that max{WA(Q),WB(Q)}C. We describe an approximation algorithm for this setting. Finally, it is also NP-hard to decide whether a path Q exists such that |WA(Q)−WB(Q)|=0. Nevertheless, in this error measure we provide an algorithm for computing an optimal approximation up to an additive error.  相似文献   

15.
We study the unitarizability of premodular categories constructed from representations of quantum group at roots of unity. We introduce Grothendieck unitarizability as a natural generalization of unitarizability to classes of premodular categories with a common Grothendieck semiring. We obtain new results for quantum groups of Lie types F4 and G2, and improve the previously obtained results for Lie types B and C.  相似文献   

16.
Two uniform asymptotic expansions are obtained for the Pollaczek polynomials Pn(cosθ;a,b). One is for , , in terms of elementary functions and in descending powers of . The other is for , in terms of a special function closely related to the modified parabolic cylinder functions, in descending powers of n. This interval contains a turning point and all possible zeros of Pn(cosθ) in θ(0,π/2].  相似文献   

17.
In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that:
where μ is the Lebesgue measure on and f,g:[0,1]→[0,) are two continuous and strictly monotone functions, both increasing or both decreasing. Also, some examples and applications are presented.  相似文献   

18.
Let T be a partial latin square and L be a latin square with TL. We say that T is a latin trade if there exists a partial latin square T with TT= such that (LT)T is a latin square. A k-homogeneous latin trade is one which intersects each row, each column and each entry either 0 or k times. In this paper, we construct 3-homogeneous latin trades from hexagonal packings of the plane with circles. We show that 3-homogeneous latin trades of size 3 m exist for each m3. This paper discusses existence results for latin trades and provides a glueing construction which is subsequently used to construct all latin trades of finite order greater than three.  相似文献   

19.
The combinatorial tool of generating functions for restricted partitions is used to generalize a quantum physics theorem relating distinct multiplets of different angular momenta in the composite Fermion model of the fractional quantum Hall effect. Specifically, if g(N,M) denotes the number of distinct multiplets of angular momentum and total angular momentum M, we prove that
where the sum is taken over all positive divisors of N and L(k)=kℓ-kN/2+3k/2-N+N/(2k)-1/2. The original Quinn–Wójs theorem results when k=1 and it appears that this generalization will be useful in further investigations of nuclear shells modeling elementary particle interactions when the particles are clustered together.  相似文献   

20.
The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C4 nanotubes and nanotori are computed.  相似文献   

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