共查询到20条相似文献,搜索用时 15 毫秒
1.
In this work we present a numerical approach for finding positive solutions of the type −Δu = λf(u) for x Ω, with Dirichlet boundary condition, where f is a superlinear function of u. We will show in which range of λ, this problem achieves multiple numerical solutions and what is the behavior of the branches of solutions. 相似文献
2.
Two Crank–Nicolson least-squares Galerkin finite element schemes are formulated to solve parabolic integro-differential equations. The advantage of this method is that it is not subject to the LBB condition. The convergence analysis shows that the methods yield the approximate solutions with optimal accuracy in H(div; Ω) × H1(Ω) and (L2(Ω))2 × L2(Ω), respectively. Moreover, the two methods both get the approximate solutions with second-order accuracy in time increment. 相似文献
3.
The scaled factorial moments Fq are studied for 28Si–AgBr collisions at 14.6 AGeV. These moments follow the generalized power law Fq(M)∝[g(M)]q. The values of q/2 obtained from the linear fits of ln Fq versus ln F2 graphs are found to obey the Brax–Peschanski formula with Levy index μ = 1.635 ± 0.012 for η space and μ = 1.801 ± 0.003 for space. These values lie within the Levy stable region 0 μ 2. An analytical continuation of the Brax–Peschanski formula has been used to obtain the multifractal spectra f(q) in negative q region. 相似文献
4.
Tatjana Petek 《Linear algebra and its applications》1999,290(1-3):167-191
The general form of a continuous mapping φ acting on the real vector space of all n × n complex Hermitian or real symmetric matrices, and preserving spectrum and commutativity, is derived. It turns out that φ is either linear or its image forms a commutative set. 相似文献
5.
Stefano Serra 《Linear algebra and its applications》1998,270(1-3):109-129
We are concerned with the behavior of the minimum (maximum) eigenvalue λ0(n) (λn(n)) of an (n + 1) × (n + 1) Hermitian Toeplitz matrix Tn(ƒ) where ƒ is an integrable real-valued function. Kac, Murdoch, and Szegö, Widom, Parter, and R. H. Chan obtained that λ0(n) — min ƒ = O(1/n2k) in the case where ƒ C2k, at least locally, and ƒ — inf ƒ has a zero of order 2k. We obtain the same result under the second hypothesis alone. Moreover we develop a new tool in order to estimate the extreme eigenvalues of the mentioned matrices, proving that the rate of convergence of λ0(n) to inf ƒ depends only on the order ρ (not necessarily even or integer or finite) of the zero of ƒ — inf ƒ. With the help of this tool, we derive an absolute lower bound for the minimal eigenvalues of Toeplitz matrices generated by nonnegative L1 functions and also an upper bound for the associated Euclidean condition numbers. Finally, these results are extended to the case of Hermitian block Toeplitz matrices with Toeplitz blocks generated by a bivariate integrable function ƒ. 相似文献
6.
7.
Guanwei Luo Jianhua Xie Xifeng Zhu Jiangang Zhang 《Chaos, solitons, and fractals》2008,36(5):1340-1347
Based on the analysis of a two-degree-of-freedom plastic impact oscillator, we introduce a three-dimensional map with dynamical variables defined at the impact instants. The non-linear dynamics of the vibro-impact system is analyzed by using the Poincaré map, in which piecewise property and singularity are found to exist. The piecewise property is caused by the transitions of free flight and sticking motions of two masses immediately after the impact, and the singularity of map is generated via the grazing contact of two masses and corresponding instability of periodic motions. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. Simulations of the free flight and sticking solutions are carried out, and regions of existence and stability of different impact motions are therefore presented in (δ, ω) plane of dimensionless clearance δ and frequency ω. The influence of non-standard bifurcations on dynamics of the vibro-impact system is elucidated accordingly. 相似文献
8.
In this paper we study the ergodic properties of non-greedy series expansions to non-integer bases β > 1. It is shown that the so-called ‘lazy’ expansion is isomorphic to the ‘greedy’ expansion. Furthermore, a class of expansions to base β > 1, β , ‘in between’ the lazy and the greedy expansions are introduced and studies. It is shown that these expansions are isomorphic to expansions of the form Tx = βx + (mod 1). 相似文献
9.
M. Kovalyov 《Journal of Differential Equations》2005,213(1):1-80
Practically every book on the Inverse Scattering Transform method for solving the Cauchy problem for KdV and other integrable systems refers to this method as nonlinear Fourier transform. If this is indeed so, the method should lead to a nonlinear analogue of the Fourier expansion formula . In this paper a special class of solutions of KdV whose role is similar to that of ei(kx-ω(k)t) is discussed. The theory of these solutions, referred to here as harmonic breathers, is developed and it is shown that these solutions may be used to construct more general solutions of KdV similarly to how the functions ei(kx-ω(t)) are used to perform the same task in the theory of Fourier transform. A nonlinear superposition formula for general solutions of KdV similar to the Fourier expansion formula is conjectured. 相似文献
10.
We consider boundary value problemwhere 0, λ > 0 are parameters and f C2[0, ∞) such that f(0) < 0. In this paper we study for the cases p (0, β) and p (β, θ) (p is the value of the solution at x = 0 and β, θ are such that f(β) = 0, , the relation between λ and the number of interior critical points of the positive solutions of the above system. 相似文献
11.
The influence of surface roughness in the prediction of the mean flow and turbulent properties of a high-speed supersonic (M = 2.7, Re/m = 2 × 107) turbulent boundary layer flow over a flat plate is numerically investigated. In particular, the performance of the k–ω and stress–ω turbulence models is evaluated against the available experimental data. Even though the performance of these models have been proven satisfactory in the computation of incompressible boundary layer flow over rough surfaces, their validity for high-speed compressible has not been investigated yet. It is observed from this study that, for smooth surface, both k–ω and stress–ω models perform very well in predicting the mean flow and turbulence quantities in supersonic flow. For rough surfaces, both models matched the experimental data fairly well for lower roughness heights but performed unsatisfactorily for higher roughness conditions. Overall the performance of the k–ω model is better than the stress–ω model. The stress–ω model does not show any strong advantages to make up for the extra computational cost associated with it. The predictions indicate that the ω boundary conditions at the wall in both models, especially the stress–ω model, need to be refined and reconsidered to include the geometric factor for supersonic flow over surfaces with large roughness values. 相似文献
12.
Jaspal Singh Aujla 《Linear algebra and its applications》1999,290(1-3):109-118
There is one to one correspondence between positive operator monotone functions on (0, ∞) and operator connections. For a symmetric connection σ, it is proved that the map X → (AσX)σ(BσX) from positive operators on a Hilbert space to itself, has a unique fixed point. Here σ denotes the dual of σ. It is also proved that |||AσB||| |||A|||σ|||B||| for all unitarily invariant norms ||| · ||| and for all positive operators A,B. 相似文献
13.
Robert Wisbauer 《Journal of Pure and Applied Algebra》1991,70(3):315-320
For an R-module M let σ[M] denote the category of submodules of M-generated modules. M has the Kulikov property if submodules of pure projective modules in σ[M] are pure projective. The following is proved: Assume M is a locally noetherian module with the Kulikov property and there are only finitely many simple modules in σ[M]. Then, for every n ε
, there are only finitely many indecomposable modules of length n in σ[M].
With our techniques we provide simple proofs for some results on left pure semisimple rings obtained by Prest and Zimmermann-Huisgen and Zimmermann with different methods. 相似文献
14.
Gould et al. (Combinatorics, Graph Theory and Algorithms, Vol. 1, 1999, pp. 387–400) considered a variation of the classical Turán-type extremal problems as follows: For a given graph H, determine the smallest even integer σ(H,n) such that every n-term graphic sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2++dnσ(H,n) has a realization G containing H as a subgraph. In this paper, for given integers k and ℓ, ℓ7 and 3kℓ, we completely determine the smallest even integer σ(kCℓ,n) such that each n-term graphic sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2++dnσ(kCℓ,n) has a realization G containing a cycle of length r for each r, krℓ. 相似文献
15.
M.A. Fiol 《Linear algebra and its applications》1999,290(1-3):275-301
Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian) spectrum of a graph and some of its properties. For instance, some characterizations of regular partitions, and bounds for some parameters, such as the independence and chromatic numbers, the diameter, the bandwidth, etc., have been obtained. For each parameter of a graph involving the cardinality of some vertex sets, we can define its corresponding weight parameter by giving some “weights” (that is, the entries of the positive eigenvector) to the vertices and replacing cardinalities by square norms. The key point is that such weights “regularize” the graph, and hence allow us to define a kind of regular partition, called “pseudo-regular,” intended for general graphs. Here we show how to use interlacing for proving results about some weight parameters and pseudo-regular partitions of a graph. For instance, generalizing a well-known result of Lovász, it is shown that the weight Shannon capacity Θ* of a connected graph Γ, with n vertices and (adjacency matrix) eigenvalues λ1 > λ2 … λn, satisfies where Θ is the (standard) Shannon capacity and v is the positive eigenvector normalized to have smallest entry 1. In the special case of regular graphs, the results obtained have some interesting corollaries, such as an upper bound for some of the multiplicities of the eigenvalues of a distance-regular graph. Finally, some results involving the Laplacian spectrum are derived. 相似文献
16.
Ahmed M. Assaf 《Discrete Mathematics》1991,90(3):221-231
Let X be a finite set of size ν, further let λ be a positive integer and let σ(4,λν) denote the maximum number of quadruples such that each pair of elements of X is contained in at most λ of them. The value of σ(4, 1;ν) has been determined by Brouwer (1979) for all v4. The value of σ(4,λν) has been determined by Billington, Stanton and Stinson (1984) for all ν≡0 (mod 3) and λ>1. In this paper we complete the determination of σ(4,λν) for all ν4 and λ>1. 相似文献
17.
Sren Asmussen 《Stochastic Processes and their Applications》1985,20(2):213-229
A general methods is developed for giving simulation estimates of boundary crossing probabilities for processes related to random walks in discreate or continuous time. Particular attention is given to the probability ψ(u, T of ruin before time T in cpumpound Poisson risk processes. When the provbabi;ity law P governing the given process is imbedded in an exponentaial family (Pgq), one can write ψ (u, T) + θRgq for certain random variables Rgq given by Wald's fundamental identity. Using this to simulate from Pgq rather than P, it is possible not only to overcome the difficulties connected with the case T =∞, but also to obtain a considerable variance reduction.It is shown that the solution of the Lundberg equation determines the asymptotically optimal value of θ in heavy traffic when T = ∞, and some results guidelining the choice of θ when T > ∞ are also given. The potential of the method in different is illustrated by two examples. 相似文献
18.
M.W. Smiley 《Journal of Computational and Applied Mathematics》1996,70(2):311-327
The method of alternative problems can be used to show that a semilinear elliptic boundary value problem (Lu + g(x, u) = 0 with gu(x, u) bounded below) is equivalent to a finite-dimensional problem (
,
), in the sense that their solution sets, which are not necessarily singletons, are in a one-to-one correspondence. This correspondence is based on a map σ from low-frequency to high-frequency Fourier components of solutions. A numerical method is presented for approximating σ and hence also solutions of the BVP. The method uses finite element approximations and avoids the use of eigenfunction expansions. Existence, uniqueness, and error estimates for the approximations of σ and solutions u are derived. 相似文献
19.
Let K be a continuum in the plane which does not lie on a line. Then the set of differences, K - K, contains an open set. Let ψ be an automorphism of the field of complex numbers which is bounded on an Fσ set of positive inductive dimension. Then ψ is continuous. 相似文献
20.
John G. Wilson 《Stochastic Processes and their Applications》1985,20(2):315-321
A target, whose initial position is unknown, is performing a random walk on the integers. A searcher, starting at the origin, wants to follow a search plan for which E[τk] is finite, where k ≥ 1 and τ is the time to capture. The searcher, who has a prior distribution over the target's initial position, can move only to adjacent positions, and cannot travel faster than the target. Necessary and sufficient conditions are given for the existence of search plans for which E[τk] is finite and a minimum. 相似文献