共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper describes a method for joining two circles with an S-shaped or with a broken back C-shaped transition curve, composed of at most two spiral segments. In highway and railway route design or car-like robot path planning, it is often desirable to have such a transition. It is shown that a single cubic curve can be used for blending or for a transition curve preserving G2 continuity with local shape control parameter and more flexible constraints. Provision of the shape parameter and flexibility provide freedom to modify the shape in a stable manner which is an advantage over previous work by Meek, Walton, Sakai and Habib. 相似文献
2.
Anyue Chen 《Journal of Mathematical Analysis and Applications》2001,260(2):653
A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided. 相似文献
3.
This paper describes a method for joining two circles with a C-shaped and an S-shaped transition curve, composed of a cubic
Bézier segment. As an extension of our previous work; we show that a single cubic curve can be used for blending or for a
transition curve preserving G
2 continuity regardless of the distance of their centers and magnitudes of the radii which is an advantage. Our method with
shape parameter provides freedom to modify the shape in a stable manner. 相似文献
4.
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of the perturbed matrix for additive and multiplicative perturbation models.The limiting non-random value is shown to depend explicitly on the limiting eigenvalue distribution of the unperturbed random matrix and the assumed perturbation model via integral transforms that correspond to very well-known objects in free probability theory that linearize non-commutative free additive and multiplicative convolution. Furthermore, we uncover a phase transition phenomenon whereby the large matrix limit of the extreme eigenvalues of the perturbed matrix differs from that of the original matrix if and only if the eigenvalues of the perturbing matrix are above a certain critical threshold. Square root decay of the eigenvalue density at the edge is sufficient to ensure that this threshold is finite. This critical threshold is intimately related to the same aforementioned integral transforms and our proof techniques bring this connection and the origin of the phase transition into focus. Consequently, our results extend the class of ‘spiked’ random matrix models about which such predictions (called the BBP phase transition) can be made well beyond the Wigner, Wishart and Jacobi random ensembles found in the literature. We examine the impact of this eigenvalue phase transition on the associated eigenvectors and observe an analogous phase transition in the eigenvectors. Various extensions of our results to the problem of non-extreme eigenvalues are discussed. 相似文献
5.
Two decompositions are established for the probability transition function of the queue length process in the M/M/1 queue by a simple probabilistic argument. The transition function is expressed in terms of a zero-avoiding probability and a transition probability to zero in two different ways. As a consequence, the M/M/1 transition function can be represented as a positive linear combination of convolutions of the busy-period density. These relations provide insight into the transient behavior and facilitate establishing related results, such as inequalities and asymptotic behavior. 相似文献
6.
Luigi Manca 《Journal of Evolution Equations》2008,8(2):231-262
We consider a semigroup of operators in the Banach space C
b
(H) of uniformly continuous and bounded functions on a separable Hilbert space H. We prove an existence and uniqueness result for a measure valued equation involving this class of semigroups. Then we apply
the result to the transition semigroup and the Kolmogorov operator corresponding to a stochastic PDE in H. For this purpose, we characterize the generator of the transition semigroup on a core.
相似文献
7.
Heike Siebert 《Mathematics in Computer Science》2009,2(3):421-442
In the well-known discrete modeling framework developed by R. Thomas, the structure of a biological regulatory network is
captured in an interaction graph, which, together with a set of Boolean parameters, gives rise to a state transition graph
describing all possible dynamical behaviors. For complex networks the analysis of the dynamics becomes more and more difficult,
and efficient methods to carry out the analysis are needed. In this paper, we focus on identifying subnetworks of the system
that govern the behavior of the system as a whole. We present methods to derive trajectories and attractors of the network
from the dynamics suitable subnetworks display in isolation. In addition, we use these ideas to link the existence of certain
structural motifs, namely circuits, in the interaction graph to the character and number of attractors in the state transition
graph, generalizing and refining results presented in [10]. Lastly, we show for a specific class of networks that all possible
asymptotic behaviors of networks in that class can be derived from the dynamics of easily identifiable subnetworks.
相似文献
8.
A representation for the moments of the number of customers in a M/M/s queueing system is deduced from the Karlin and McGregor representation for the transition probabilities. This representation allows us to study the limit behavior of the moments as time tends to infinity. We study some consequences of the representation for the mean. 相似文献
9.
In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue. 相似文献
10.
We consider the transition to temperature-dependent equations for ultrasecond-quantized problems.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 584–592, March, 2008. 相似文献
11.
We characterize the Besov-Lipschitz spaces with zero boundary conditions on bounded smooth domains. We prove that the appropriate
first and second difference norms are equivalent to the norm given in terms of the transition kernel of the Brownian motion
killed upon exit from the domain. 相似文献
12.
We study a singularly perturbed semi-linear elliptic PDE with a bistable potential on a closed Riemannian surface. We show
that the transition region converges in the sense of varifolds to an embedded (multiple) curve with constant geodesic curvature. 相似文献
13.
Yangrong Li 《Journal of Mathematical Analysis and Applications》2007,328(1):640-654
A column continuous transition function is by definition a standard transition function P(t) whose every column is continuous for t?0 in the norm topology of bounded sequence space l∞. We will prove that it has a stable q-matrix and that there exists a one-to-one relationship between column continuous transition functions and increasing integrated semigroups on l∞. Using the theory of integrated semigroups, we give some necessary and sufficient conditions under which the minimal q-function is column continuous, in terms of its generator (of the Markov semigroup) as well as its q-matrix. Furthermore, we will construct all column continuous Q-functions for a conservative, single-exit and column bounded q-matrix Q. As applications, we find that many interesting continuous-time Markov chains (CTMCs), say Feller-Reuter-Riley processes, monotone processes, birth-death processes and branching processes, etc., have column continuity. 相似文献
14.
D. Bertacchi 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2001,71(1):205-224
We investigate various features of a quite new family of graphs, introduced as a possible example of vertex-transitive graph
not roughly isometric with a Cayley graph of some finitely generated group. We exhibit a natural compactification and study
a large class of random walks, proving theorems concerning almost sure convergence to the boundary, a strong law of large
numbers and a central limit theorem. The asymptotic type of then-step transition probabilities of the simple random walk is determined. 相似文献
15.
Sami Mustapha 《Journal of Theoretical Probability》2006,19(4):773-787
It is shown in this paper that the transition kernels corresponding to simple random walks on certain unimodular solvable
p-adic groups admit upper Gaussian estimates.
相似文献
16.
The p-Laplace equation with random perturbation is studied for the singular case 1<p2 in this paper. Some properties of the invariant measure and transition semigroups are obtained. The main tool is the dimension-free Harnack inequality, which is established by using the coupling argument. As consequences, some ergodicity, compactness and contractive properties are derived for the associated transition semigroups. The main results are applied to stochastic reaction–diffusion equations and the stochastic p-Laplace equation in Hilbert space. 相似文献
17.
This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials.
The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature ϑ, an evolution equation for the phase change parameter χ, including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable u. The main novelty of the model is that the equations for χ and u are coupled in such a way as to take into account the fact that the properties of the viscous and of the elastic parts influence
the phase transition phenomenon in different ways. However, this brings about an elliptic degeneracy in the equation for u which needs to be carefully handled.
First, we prove a global well-posedness result for the related initial-boundary value problem. Secondly, we address the long-time
behavior of the solutions in a simplified situation. We prove that the ω-limit set of the solution trajectories is nonempty, connected and compact in a suitable topology, and that its elements solve
the steady state system associated with the evolution problem.
Dedicated to Jürgen Sprekels on the occasion of his 60th birthday 相似文献
18.
Florent Hivert Jean-Christophe Novelli Lenny Tevlin Jean-Yves Thibon 《Selecta Mathematica, New Series》2009,15(1):105-119
We prove conjectures of the third author [L. Tevlin, Proc. FPSAC’07, Tianjin] on two new bases of noncommutative symmetric
functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by means of
two composition-valued statistics on permutations and packed words, which generalize the combinatorics of Genocchi numbers.
相似文献
19.
We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls. 相似文献
20.
We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov
process such that the level of performance of one component can change only for one level lower than the observed one, and
the failures are independent for different components. We derive the probability distribution of the random vector X, representing the state of the system at the moment of failure and use it for testing the hypothesis of equal transition
intensities. Under the assumption that these intensities are equal, we derive the method of moments estimators for probabilities
of failure in a given state vector and the intensity of failure. At the end we calculate the reliability function for such
systems.
Received: May 18, 2007., Revised: July 8, 2008., Accepted: September 29, 2008. 相似文献