共查询到20条相似文献,搜索用时 32 毫秒
1.
Robert Stephen Cantrell Chris Cosner Yuan Lou 《Journal of Differential Equations》2008,245(12):3687-3703
We consider reaction-diffusion-advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness, where fitness is defined as a logistic local population growth rate. We show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics. The modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution. The analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability. The models are quasilinear parabolic equations with nonlinear boundary conditions. 相似文献
2.
In order to obtain a comprehensive form of mathematical models describing nonlinear phenomena such as HIV infection process and AIDS disease progression, it is efficient to introduce a general class of time-dependent evolution equations in such a way that the associated nonlinear operator is decomposed into the sum of a differential operator and a perturbation which is nonlinear in general and also satisfies no global continuity condition. An attempt is then made to combine the implicit approach (usually adapted for convective diffusion operators) and explicit approach (more suited to treat continuous-type operators representing various physiological interactions), resulting in a semi-implicit product formula. Decomposing the operators in this way and considering their individual properties, it is seen that approximation–solvability of the original model is verified under suitable conditions. Once appropriate terms are formulated to describe treatment by antiretroviral therapy, the time-dependence of the reaction terms appears, and such product formula is useful for generating approximate numerical solutions to the governing equations. With this knowledge, a continuous model for HIV disease progression is formulated and physiological interpretations are provided. The abstract theory is then applied to show existence of unique solutions to the continuous model describing the behavior of the HIV virus in the human body and its reaction to treatment by antiretroviral therapy. The product formula suggests appropriate discrete models describing the dynamics of host pathogen interactions with HIV1 and is applied to perform numerical simulations based on the model of the HIV infection process and disease progression. Finally, the results of our numerical simulations are visualized and it is observed that our results agree with medical and physiological aspects. 相似文献
3.
ChunGilPARK 《数学学报(英文版)》2004,20(6):1047-1056
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen‘s equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen‘s equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra. 相似文献
4.
The spiral is one of nature’s more ubiquitous shapes: It can be seen in various media, from galactic geometry to cardiac tissue.
Mathematically, spiral waves arise as solutions to reaction–diffusion partial differential equations (RDS). In the literature,
various experimentally observed dynamical states and bifurcations of spiral waves have been explained using the underlying
Euclidean symmetry of the RDS—see for example (Barkley in Phys. Rev. Lett. 68:2090–2093, 1992; Phys. Rev. Lett. 76:164–167, 1994; Sandstede et al. in C. R. Acad. Sci. 324:153–158, 1997; J. Differ. Equ. 141:122–149, 1997; J. Nonlinear Sci. 9:439–478, 1999), or additionally using the concept of forced Euclidean symmetry-breaking for situations where an inhomogeneity or anisotropy
is present—see (LeBlanc in Nonlinearity 15:1179–1203, 2002; LeBlanc and Wulff in J. Nonlinear Sci. 10:569–601, 2000).
In this paper, we further investigate the role of medium inhomogeneities on spiral wave dynamics by considering the effects
of several localized sites of inhomogeneity. Using a model-independent approach based on n>1 simultaneous translational symmetry-breaking perturbations of the dynamics near rotating waves, we fully characterize the
local anchoring behavior of the spiral wave in the n-dimensional parameter space of relative “amplitudes” of the individual perturbations. For the case n=2, we supplement the local anchoring results with a classification of the generic one-parameter bifurcation diagrams of anchored
states which can be obtained by circling the origin of the two-dimensional amplitude parameter space. Numerical examples are
given to illustrate our various results. 相似文献
5.
S. V. Sudoplatov 《Algebra and Logic》2007,46(2):134-146
A syntactic approach is described to constructing generic models which generalizes the known semantic one. A sufficient condition
of a generic model being homogeneous is specified. It is shown that, within the syntactic approach, any countable homogeneous
model is generic. Criteria and a sufficient condition are given for the generic models created in syntactic constructions
to be saturated.
Supported by RFBR grant No. 05-01-00411, and by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools via project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 2, pp. 244–268, March–April, 2007. 相似文献
6.
Cody Blaine Hyndman 《Mathematics and Financial Economics》2009,2(2):107-128
We consider factor models for interest rates and asset prices where the risk- neutral dynamics of the factors process is modelled
by an affine diffusion. We characterize the factors process and bond price in terms of forward–backward stochastic differential
equations (FBSDEs), prove an existence and uniqueness theorem which gives the solution explicitly, and characterize the bond
price as an exponential affine function of the factors in a new way. Our approach unifies the results, based on stochastic
flows, of Elliott and van der Hoek (Finance Stoch 5:511–525, 2001) with the approach, based on the Feynman-Kac formula, of
Duffie and Kan (Math Finance 6(4):379–406, 1996), and addresses a mistake in the approach of Elliott and van der Hoek (Finance
Stoch 5:511–525, 2001). We extend our results on the bond price to consider the futures and forward price of a risky asset
or commodity.
相似文献
7.
V. I. Dmitriev E. S. Kurkina O. E. Simakova 《Computational Mathematics and Modeling》2011,22(1):54-68
The article models the distribution of cities by population. Two approaches are considered to mathematical modeling of urban
growth: a probability model in which the number of cities depends on the population and the rank model of distribution of
cities by their population. Five population censuses are analyzed for Russia’s cities. The probability density function n(x, α) for the number of cities as a function of their population x is fitted to all the available censuses with a time-dependent coefficient α . The function α(t ) is approximated and a prediction for the nearest future is computed. In particular, it is shown that in 2010 compared with
2002 the number of large cities should increase, while the number of small town should decrease. A model is also proposed
for the interaction of urban areas linked into a single hierarchical system. The model is based on a system of ordinary differential
equations describing the change in urban population. Independently of the initial distribution, all the cities and town line
up by the rank–size law and deviations from this law, as in real life, are observed only for some large and very small cities.
Model parameters are fitted for Russia’s cities. 相似文献
8.
In this paper, we prove that if (U, w) is a finite dimensional Jordan baric algebra such that then, , where R(U) is the nilradical (maximal nil ideal) of U. We also give conditions so that and an example showing that such conditions are necessary.
Received: May 2, 2005. Revised: October 22, 2006. 相似文献
9.
We propose an approach to the analysis of turbulent oscillations described by nonlinear boundary-value problems for partial
differential equations. This approach is based on passing to a dynamical system of shifts along solutions and uses the notion
of ideal turbulence (a mathematical phenomenon in which an attractor of an infinite-dimensional dynamical system is contained
not in the phase space of the system but in a wider functional space and there are fractal or random functions among the attractor
“points”). A scenario for ideal turbulence in systems with regular dynamics on an attractor is described; in this case, the
space-time chaotization of a system (in particular, intermixing, self-stochasticity, and the cascade process of formation
of structures) is due to the very complicated internal organization of attractor “points” (elements of a certain wider functional
space). Such a scenario is realized in some idealized models of distributed systems of electrodynamics, acoustics, and radiophysics.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 217–230, February, 2007. 相似文献
10.
Rui A. C. Ferreira 《Archiv der Mathematik》2009,93(2):153-163
We establish an integral inequality, on a so called time scale, related to those appearing in Constantin (J. Math. Anal. Appl.
197 (1996), 855–863) and Yang and Tan (JIPAM J. Inequal. Pure Appl. Math. 8 (2007), No. 2, Art 57). Our result can be used to obtain estimates for solutions of certain dynamic equations. Moreover,
the bounds obtained in this paper are sharper than those known previously in the literature.
This work was completed with the support of the Portuguese Foundation for Science and Technology (FCT) through the PhD fellowship SFRH/BD/39816/2007. 相似文献
11.
Matrix models of age-and/or stage-structured population dynamics rest upon the Perron-Frobenius theorem for nonnegative matrices,
and the life cycle graph for individuals of a given biological species plays a major role in model construction and analysis.
A summary of classical results in the theory of matrix models for population dynamics is presented, and generalizations are
proposed, which have been motivated by a need to account for an additional structure, i.e., to classify individuals not only
by age, but also by an additional (discrete) characteristic: size, physiological status, stage of development, etc.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 4, pp. 145–164, 2007. 相似文献
12.
Michal Botur 《Mathematica Slovaca》2010,60(2):171-178
Many algebras arising in logic have a lattice structure with intervals being equipped with antitone involutions. It has been
proved in [CHK1] that these lattices are in a one-to-one correspondence with so-called basic algebras. In the recent papers
[BOTUR, M.—HALAŠ, R.: Finite commutative basic algebras are MV-algebras, J. Mult.-Valued Logic Soft Comput. (To appear)]. and [BOTUR, M.—HALAŠ, R.: Complete commutative basic algebras, Order 24 (2007), 89–105] we have proved that every finite commutative basic algebra is an MV-algebra, and that every complete commutative
basic algebra is a subdirect product of chains. The paper solves in negative the open question posed in [BOTUR, M.—HALAŠ,
R.: Complete commutative basic algebras, Order 24 (2007), 89–105] whether every commutative basic algebra on the interval [0, 1] of the reals has to be an MV-algebra. 相似文献
13.
We derive a numerical scheme to compute invariant manifolds for time-variant discrete dynamical systems, i.e., nonautonomous
difference equations. Our universally applicable method is based on a truncated Lyapunov–Perron operator and computes invariant
manifolds using a system of nonlinear algebraic equations which can be solved both locally using (nonsmooth) inexact Newton,
and globally using continuation algorithms. Compared to other algorithms, our approach is quite flexible, since it captures
time-dependent, nonsmooth, noninvertible or implicit equations and enables us to tackle the full hierarchy of strongly stable,
stable and center-stable manifolds, as well as their unstable counterparts. Our results are illustrated using a test example
and are applied to a population dynamical model and the Hénon map. Finally, we discuss a linearly implicit Euler–Bubnov–Galerkin
discretization of a reaction diffusion equation in order to approximate its inertial manifold. 相似文献
14.
Iterative Approximation of Statistical Distributions and Relation to Information Geometry 总被引:1,自引:0,他引:1
The optimal control of stochastic processes through sensor estimation of probability density functions is given a geometric
setting via information theory and the information metric. Information theory identifies the exponential distribution as the
maximum entropy distribution if only the mean is known and the Γ distribution if also the mean logarithm is known. The surface
representing Γ models has a natural Riemannian information metric. The exponential distributions form a one-dimensional subspace
of the two-dimensional space of all Γ distributions, so we have an isometric embedding of the random model as a subspace of
the Γ models. This geometry provides an appropriate structure on which to represent the dynamics of a process and algorithms
to control it. This short paper presents a comparative study on the parameter estimation performance between the geodesic
equation and the B-spline function approximations when they are used to optimize the parameters of the Γ family distributions. In this case,
the B-spline functions are first used to approximate the Γ probability density function on a fixed length interval; then the coefficients
of the approximation are related, through mean and variance calculations, to the two parameters (i.e. μ and β) in Γ distributions.
A gradient based parameter tuning method has been used to produce the trajectories for (μ, β) when B-spline functions are used, and desired results have been obtained which are comparable to the trajectories obtained from
the geodesic equation.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
15.
Robert M. Yamaleev 《Advances in Applied Clifford Algebras》2000,10(1):15-38
We consider a commutative part of the Generalized Clifford Algebras, denominated asalgebra of multicomplex numbers. By using the multicomplex algebra as underlying algebraic structure we construct oscillator model for the Nambu’s formulation
of dynamics. We propose a new dynamicals principle which gives rise to two kinds of Hamilton-Nambu equations inD≥2-dimensional phase space. The first one is formulated with (D−1)-evolution parameter and a single Hamiltonian. The Haniltonian of the oscillator model in such dynamics is given byD-degree homogeneous form. In the second formulation, vice versa, the evolution of the system along a single evolution parameter
is generated by (D−1) Hamiltonian. 相似文献
16.
17.
Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrices 总被引:1,自引:0,他引:1
Li Xia YE Zhi Xiang WU Xue Feng MEI 《数学学报(英文版)》2007,23(10):1729-1744
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d(y), which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d(y) and weak A-forms of wUq^d(y). 相似文献
18.
V. L. Selivanov 《Algebra and Logic》2007,46(2):120-133
We introduce and study some natural operations on a structure of finite labeled forests, which is crucial in extending the
difference hierarchy to the case of partitions. It is shown that the corresponding quotient algebra modulo the so-called h-equivalence
is the simplest non-trivial semilattice with discrete closures. The algebra is also characterized as a free algebra in some
quasivariety. Part of the results is generalized to countable labeled forests with finite chains.
Supported by a DAAD project within the program “Ostpartnerschaften.”
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Translated from Algebra I Logika, Vol. 46, No. 2, pp. 217–243, March–April, 2007. 相似文献
19.
The paper investigates model reduction techniques that are based on a nonlocal quasi-continuum-like approach. These techniques
reduce a large optimization problem to either a system of nonlinear equations or another optimization problem that are expressed
in a smaller number of degrees of freedom. The reduction is based on the observation that many of the components of the solution
of the original optimization problem are well approximated by certain interpolation operators with respect to a restricted
set of representative components. Under certain assumptions, the “optimize and interpolate” and the “interpolate and optimize”
approaches result in a regular nonlinear equation and an optimization problem whose solutions are close to the solution of
the original problem, respectively. The validity of these assumptions is investigated by using examples from potential-based
and electronic structure-based calculations in Materials Science models. A methodology is presented for using quasi-continuum-like
model reduction for real-space DFT computations in the absence of periodic boundary conditions. The methodology is illustrated
using a basic Thomas–Fermi–Dirac case study. 相似文献
20.
James P. Kelliher 《Mathematische Annalen》2009,343(3):701-726
We say that a solution of the Navier–Stokes equations converges in the vanishing viscosity limit to a solution of the Euler
equations if their velocities converge in the energy (L
2) norm uniformly in time as the viscosity ν vanishes. We show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the
space–time energy density of the solution to the Navier–Stokes equations in a boundary layer of width proportional to ν vanish with ν, and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band
centered around 1/ν.
The author was supported in part by NSF grant DMS-0705586 during the period of this work. 相似文献