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1.
We study a class of stochastic flows connected to the coalescent processes that have been studied recently by M?hle, Pitman,
Sagitov and Schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size. We
define a bridge to be a right-continuous process (B(r),r[0,1]) with nondecreasing paths and exchangeable increments, such that B(0)=0 and B(1)=1. We show that flows of bridges are in one-to-one correspondence with the so-called exchangeable coalescents. This yields
an infinite-dimensional version of the classical Kingman representation for exchangeable partitions of ℕ. We then propose
a Poissonian construction of a general class of flows of bridges and identify the associated coalescents. We also discuss
an important auxiliary measure-valued process, which is closely related to the genealogical structure coded by the coalescent
and can be viewed as a generalized Fleming-Viot process.
Received: 26 November 2002 / Revised version: 10 February 2003 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60G09, 60J25, 92D30
Key words or phrases: Flow – Coalescence – Exchangeability – Bridge 相似文献
2.
In this paper we consider ordinary differential equations with a known Lyapunov function. We study the use of Runge–Kutta
methods provided with a dense output and a projection technique to preserve any given Lyapunov function. This approach extends
previous work of Grimm and Quispel (BIT 45, 2005), allowing the use of Runge–Kutta methods for which the associated quadrature
formula does not need to have positive or zero coefficients. Some numerical experiments show the good performance of the proposed
technique. 相似文献
3.
Renato. D. C. Monteiro 《Mathematical Programming》2003,97(1-2):209-244
In this paper, we survey the most recent methods that have been developed for the solution of semidefinite programs. We first
concentrate on the methods that have been primarily motivated by the interior point (IP) algorithms for linear programming,
putting special emphasis in the class of primal-dual path-following algorithms. We also survey methods that have been developed
for solving large-scale SDP problems. These include first-order nonlinear programming (NLP) methods and more specialized path-following
IP methods which use the (preconditioned) conjugate gradient or residual scheme to compute the Newton direction and the notion
of matrix completion to exploit data sparsity.
Received: December 16, 2002 / Accepted: May 5, 2003
Published online: May 28, 2003
Key words. semidefinite programming – interior-point methods – polynomial complexity – path-following methods – primal-dual methods
– nonlinear programming – Newton method – first-order methods – bundle method – matrix completion
The author's research presented in this survey article has been supported in part by NSF through grants INT-9600343, INT-9910084,
CCR-9700448, CCR-9902010, CCR-0203113 and ONR through grants N00014-93-1-0234, N00014-94-1-0340 and N00014-03-1-0401.
Mathematics Subject Classification (2000): 65K05, 90C06, 90C22, 90C25, 90C30, 90C51 相似文献
4.
This paper deals with the shear strengthening of Reinforced Concrete (RC) flexural members with externally bonded Fiber-Reinforced
Polymers (FRPs). The interaction between an external FRP and an internal transverse steel reinforcement is not considered
in actual code recommendations, but it strongly influences the efficiency of the shear strengthening rehabilitation technique
and, as a consequence, the computation of interacting contributions to the nominal shear strength of beams. This circumstance
is also discussed on the basis of the results of an experimental investigation of rectangular RC beams strengthened in shear
with “U-jacketed” carbon FRP sheets. Based on experimental results of the present and other investigations, a new analytical
model for describing the shear capacity of RC beams strengthened according to the most common schemes (side-bonded and “U-jacketed”),
taking into account the interaction between steel and FRP shear strength contributions, is proposed.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 339–356, May–June, 2008. 相似文献
5.
This paper examines the process through which students learn to make functional use of computer algebra systems (CAS), and
the interaction between that process and the wider mathematical development of students. The result of ‘instrumentalising‘
a device to become a mathematical tool and correspondingly ‘instrumenting’ mathematical activity through use of that tool
is not only to extend students' mathematical technique but to shape their sense of the mathematical entities involved. These
ideas have been developed within a French programme of research – as reported by Artigue in this issue of the journal – which
has explored the integration of CAS – typically in the form of symbolic calculators – into the everyday practice of mathematics
classrooms. The French research –influenced by socio-psychological theorisation of the development of conceptual systems-
seeks to take account of the cultural and cognitive facets of these issues, noting how mathematical norms – or their absence
– shape the mental schemes which students form as they appropriate CAS as tools. Instrumenting graphic and symbolic reasoning
through using CAS influences the range and form of the tasks and techniques experienced by students, and so the resources
available for more explicit codification and theorisation of such reasoning. This illuminates an influential North American
study– conducted by Heid – which French researchers have seen as taking a contrasting view of the part played by technical
activity in developing conceptual understanding. Reconsidered from this perspective, it appears that while teaching approaches
which ‘resequence skills and concepts’ indeed defer – and diminish –attention to routinised skills, the tasks introduced in
their place depend on another –albeit less strongly codified – system of techniques, supporting more extensive and active
theorisation. The French research high lights important challenges which arise in instrumenting classroom mathematical activity
and correspondingly instrumentalising CAS. In particular, it reveals fundamental constraints on human-machine interaction
which may limit the capacity of the present generation of CAS to scaffold the mathematical thinking and learning of students.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
A. A. Soliman 《Journal of Mathematical Sciences》2009,161(2):308-319
The stability of Lotka–Volterra system has been discussed by many authors for two and three species. In this paper, we will
discussed the notion of stability for a Lotka–Volterra system with four species. Some criteria and results are given. Our
technique depends on the Lyapunov–Razumikhin method.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal
Control, 2008. 相似文献
7.
O. V. Rusakov 《Journal of Mathematical Sciences》2011,176(2):232-238
We apply to a sequence of i.i.d. random variables a time change operator via a Poisson process that is independent of this
sequence. We consider sums of independent copies of processes constructed in this way and having continuous time. Finite limit
distributions of these sums coincide with the finite limit distributions of the Wiener–Ornstein–Uhlenbeck field that is the
tensor product of a Brownian motion and the Ornstein–Uhlenbeck process. The transition characteristics of the limit Ornstein–Uhlenbeck
process are described by Brownian bridges that are builded into the Wiener–Ornstein–Uhlenbeck field. Bibliography: 4 titles. 相似文献
8.
The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within
the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves
in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan
potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations
in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion
curves are analyzed.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008. 相似文献
9.
Valeria D’Amato Steven Haberman Maria Russolillo 《Methodology and Computing in Applied Probability》2012,14(1):135-148
In this paper, we propose a procedure for reducing the uncertainty in mortality projections, on the basis of a log bilinear
Poisson Lee Carter model (Renshaw and Haberman Appl Stat 52:119–137, 2003a). In the literature, because the non-linear nature of the quantities under consideration has prevented analytical solutions,
simulation techniques have been used in order to provide prediction intervals for forecasted quantities (for example, Brouhns
et al. Scand Actuar J 3:212–224, 2005, Renshaw and Haberman Insur Math Econ 42:797–816, 2008). In this respect, we adopt the bootstrap simulation approach in order to measure the uncertainty affecting mortality projections.
In particular, we propose making the bootstrap procedure more efficient by using a specific variance reducing technique, the
so-called Stratified Sampling technique. To this end, we propose a two stage simulation bootstrap procedure where variance
reducing techniques are combined with the simple bootstrap of the Poisson Lee Carter version. Numerical applications are shown
using the results for some datasets. 相似文献
10.
A Simple Proof of the Restricted Isometry Property for Random Matrices 总被引:20,自引:0,他引:20
Richard Baraniuk Mark Davenport Ronald DeVore Michael Wakin 《Constructive Approximation》2008,28(3):253-263
We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices
that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner
products that have recently provided algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers
for finite-dimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and
brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result, we obtain simple and direct
proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs
of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements
have a certain universality with respect to the sparsity-inducing basis.
相似文献
11.
Miloslav Feistauer Václav Kučera Karel Najzar Jaroslava Prokopová 《Numerische Mathematik》2011,117(2):251-288
The paper presents the theory of the discontinuous Galerkin finite element method for the space–time discretization of a nonstationary
convection–diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly
perturbed with dominating convection. The discontinuous Galerkin method is applied separately in space and time using, in
general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary
penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used. The paper is concerned with the proof of error estimates
in “L
2(L
2)”- and “DG”-norm formed by the “L
2(H
1)”-seminorm and penalty terms. A special technique based on the use of the Gauss–Radau interpolation and numerical integration
has been used for the derivation of an abstract error estimate. In the “DG”-norm the error estimates are optimal with respect
to the size of the space grid. They are optimal with respect to the time step, if the Dirichlet boundary condition has behaviour
in time as a polynomial of degree ≤ q. 相似文献
12.
Rudolf Winkel 《manuscripta mathematica》1999,100(1):55-79
Schubert polynomials of type B, C, and D have been described first by S. Billey and M. Haiman [BH] using a combinatorial method.
In this paper we give a unified algebraic treatment of Schubert polynomials of types A–D in the style of the Lascoux–Schützenberger
theory in type A, i.e. Schubert polynomials are generated by the application of sequences of divided difference operators
to “top polynomials”. The use of the creation operators for Q-Schur and P-Schur functions allows us to give: (1) simple and
natural forms of the “top polynomials”, (2) formulas for the easy computation with all divided differences, (3) recursive
structures, and (4) simplified derivations of basic properties.
Received: 23 July 1998 相似文献
13.
One of the greatest challenges in structural engineering nowadays is the strengthening, upgrading, and retrofitting of existing
structures. The use of fibre-reinforced polymers (FRPs) bonded to the tension face of a structural member is an attractive
technique in this field of application. The strengthening of reinforced concrete structures by means of an externally bonded
reinforcement (EBR) is achieved by gluing a FRP laminate to the concrete substrate. For an efficient utilization of the FRP
EBR systems, an effective stress transfer is required between the FRP and concrete. The paper discusses the bond behaviour
between a FRP and concrete in the case of flexural strengthening of continuous beams. With respect to this type of beams,
only a few studies have been reported, though continuous members often occur in concrete constructions. The structural behaviour
of statically indeterminate elements is typically characterized by redistributions of the internal forces. These distributions
are related to the nonlinear deformations of the beams and has also a distinct influence on the bond behaviour between the
FRP and concrete.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 389–402, May–June, 2008. 相似文献
14.
Generalized geometric programming (GGP) problems occur frequently in engineering design and management. Recently, some exponential-based
decomposition methods [Maranas and Floudas, 1997,Computers and Chemical Engineering 21(4), 351–370; Floudas et al., 1999 , Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, Boston, pp. 5–105; Floudas, 2000 Deterministic Global Optimizaion: Theory, Methods and Application, Kluwer Academic Publishers, Boston, pp. 257–306] have been developed for GGP problems. These methods can only handle problems
with positive variables, and are incapable of solving more general GGP problems. This study proposes a technique for treating
free (i.e., positive, zero or negative) variables in GGP problems. Computationally effective convexification rules are also
provided for signomial terms with three variables. 相似文献
15.
Dustin Moody 《Designs, Codes and Cryptography》2009,52(3):381-390
Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving
pairings rely on the hardness of the bilinear Diffie–Hellman problem. In contrast to the discrete log (or Diffie–Hellman)
problem in a finite field, the difficulty of this problem has not yet been much studied. In 2001, Verheul (Advances in Cryptology—EUROCRYPT
2001, LNCS 2045, pp. 195–210, 2001) proved that on a certain class of curves, the discrete log and Diffie–Hellman problems
are unlikely to be provably equivalent to the same problems in a corresponding finite field unless both Diffie–Hellman problems
are easy. In this paper we generalize Verheul’s theorem and discuss the implications on the security of pairing based systems.
相似文献
16.
We show that the spectrum of the Dirichlet and Neumann problems for the Laplace operator in the plane perforated by a double–periodic
family of circular holes contains gaps (even any a priori given number of gaps) of certain radii of holes. The result is obtained
by asymptotic analysis of the cell spectral problem, interpreted as a problem in a domain with thin bridges. Some open questions
are stated. 相似文献
17.
The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed in Schichl and Neumaier (J. Global
Optim. 33, 541–562, 2005). For representing numerical problems, the authors use DAGs whose nodes are subexpressions and whose
directed edges are computational flows. Compared to tree-based representations [Benhamou et al. Proceedings of the International
Conference on Logic Programming (ICLP’99), pp. 230–244. Las Cruces, USA (1999)], DAGs offer the essential advantage of more
accurately handling the influence of subexpressions shared by several constraints on the overall system during propagation.
In this paper we show how interval constraint propagation and search on DAGs can be made practical and efficient by: (1) flexibly
choosing the nodes on which propagations must be performed, and (2) working with partial subgraphs of the initial DAG rather than with the entire graph. We propose a new interval constraint propagation technique which exploits the influence of subexpressions on all the constraints together rather than on individual constraints. We then show how the new propagation technique can be integrated into branch-and-prune search to solve numerical constraint satisfaction problems. This algorithm is able to outperform its obvious contenders,
as shown by the experiments. 相似文献
18.
Cognitive and self-selective routing for sensor networks 总被引:1,自引:0,他引:1
Erol Gelenbe Peixiang Liu Boleslaw K. Szymanski Christopher Morrell 《Computational Management Science》2011,8(3):237-258
New approaches to Quality-of-Service (QoS) routing in wireless sensor networks which use different forms of learning are the
subject of this paper. The Cognitive Packet Network (CPN) algorithm uses smart packets for path discovery, together with reinforcement
learning and neural networks, while Self-Selective Routing (SSR) is based on the “Ant Colony” paradigm which emulates the
pheromone-based technique which ants use to mark paths and communicate information about paths between different insects of
the same colony (Koenig et al. in Ann Math Artif Intell 31(1–4): 41–76, 2001). In this paper, we present first experimental
results on a network test-bed to evaluate CPN’s ability to discover paths having the shortest delay, or shortest length. Then,
we present small test-bed experiments and large-scale network simulations to evaluate the effectiveness of the SSR algorithm.
Finally, the two approaches are compared with respect to their ability to adapt as network conditions change over time. 相似文献
19.
J Ansell T Archibald J Dagpunar L Thomas P Abell D Duncalf 《The Journal of the Operational Research Society》2003,54(4):343-349
The high cost of maintenance in the processing industry implies the need for optimal planning of maintenance strategy. In order to achieve this there is a need to understand the underlying failure processes, which are often very complex. In this paper, a new semi-parametric approach, combining Cox regression with density kernal smoothing, is introduced to estimate the underlying performance. The approach has been applied to several processes and it allowed insight into each process, which would not have been achieved if traditional approaches had been used. Particularly, the refurbishment of processes had a significant impact on the rate failure. This paper concludes by assessing this impact of refurbishment on the maintenance programme. 相似文献
20.
S. Ramachandran 《Discrete Mathematics》1979,25(2):165-173
Bondy and Hemminger (Graph reconstruction—a survey, J. Graph Theory 1 (1977) 227–268) give three necessary conditions namely subgraph condition, degree sequence condition and symmetric array condition (of Randic) for Legitimate decks. We have strengthened the degree sequence condition (SDSC) and extended the symmetric array condition (ESAC). We prove that both these are necessary conditions for legitimate decks and ESAC implies SDSC and symmetric array condition. ESAC gives a graph G1 which has the same degree sequence as the prospective graph determined by the deck and the point deletions of G1 have the same degree sequence as the given cards. Examples of illegitimate decks satisfying ESAC, legitimate decks giving G1 with point deletions different from the given deck, deck giving more than one (non isomorphic) G1 etc. are given. We develop this ESAC to a test to determine whether a deck is legitimate or not. Also we point out how the failure of reconstruction conjecture (if it is so) for (p?1)-point graphs can hamper the characterization of legitimate decks of p-point graphs. We extend these results to colored graphs and digraphs also. 相似文献