Stability and regularity results for a size-structured population model

In the present paper a nonlinear size-structured population dynamical model with size and density dependent vital rate functions is considered. The linearization about stationary solutions is analyzed by semigroup and spectral methods. In particular, the spectrally determined growth property of the linearized semigroup is derived from its long-term regularity. These analytical results make it possible to derive linear stability and instability results under biologically meaningful conditions on the vital rates. The principal stability criteria are given in terms of a modified net reproduction rate.     

On the Size of the Exceptional Set in Nevanlinna's Second Fundamental Theorem for Certain Classes of Meromorphic Functions

Some conditions on the size of the exceptional set that arise in Nevanlinna's Second Fundamental Theorem are established, showing that previous sharp results can be improved by restricting the class of functions considered and suggesting a close relationship between the size of the exceptional set and the lower growth of the characteristic function. Examples of functions of rapid growth possessing exceptional sets are built, showing that these conditions are sharp for the class of functions considered.     

Computing high precision Matrix Padé approximants

We describe a new method of computing matrix Padé approximants of series with integer data in an efficient and fraction-free way, by controlling the growth of the size of intermediate coefficients. This algorithm is applied to compute high precision Padé approximants of matrix-valued generating functions of time series. As an illustration we show that we can successfully recover from noisy equidistant sampling data a joint damped signal of four antenna, even in the presence of background signals.     

L -harmonic functions with polynomial growth of a fixed rate

Yau made the following conjecture: For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. we extend the result on the Laplace operator to that on the symmetric diffusion operator, and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finite-dimensional, when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative.     

Measure-valued solutions for a hierarchically size-structured population

We present a hierarchically size-structured population model with growth, mortality and reproduction rates which depend on a function of the population density (environment). We present an example to show that if the growth rate is not always a decreasing function of the environment (e.g., a growth which exhibits the Allee effect) the emergence of a singular solution which contains a Dirac delta mass component is possible, even if the vital rates of the individual and the initial data are smooth functions. Therefore, we study the existence of measure-valued solutions. Our approach is based on the vanishing viscosity method.     

A projection model and a rational policy for the supply and demand of human resources from an educational institution

A projection model based on the concept of fertility and mortality of a closed population was constructed as an analytical tool to investigate the supply of graduates (human resources) in an academic discipline from an educational institution. Student generation, drop-out rate, and transfer rate are defined to construct a projection matrix. This matrix, along with trends of survival and transfer rates, projects the class distribution (first year class size, size of each successive class, and the size of the graduating class) at any future year. With a knowledge of population growth rate and therefore the projected need, this model serves as an aid to the administration to discern the relations among the decision factors and to formulate a rational policy of supplying human resources to meet future need. The model is simple, makes use of available statistical data, and can easily be programmed on a desk computer.     

L-harmonic functions with polynomial growth of a fixed rate

Yau made the following conjecture: For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. we extend the result on the Laplace operator to that on the symmetric diffusion operator, and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finite-dimensional, when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative.     

ESTIMATION OF SALMON ESCAPEMENT: MODELS WITH ENTRY,MORTALITY AND STOCHASTICITY

Understanding the dynamics of Prince William Sound pink salmon requires knowledge of the size of the spawning population in a stream over time. Periodic aerial surveys provide observations on the number of spawners, but the lack of daily observations requires a model to fill in the gaps. We develop a differential equation framework to represent the dynamics of escapement during the season. An exponential population growth model with a time-varying rate of growth is used for the number of spawners. The rate of growth consists of two primary components: the entry of salmon to the stream (escapement) and the mortality of spawners in the stream. The models for entry and mortality are also functions of time. The stochastic element of the model is based on a nonhomogeneous birth-and-death process which leads to a least squares estimation approach with either additive measurement or process errors. We illustrate the approach for a stream in Prince William Sound by fitting various models to observed spawner abundance, mortality counts from ground surveys and weir counts of the entry to the stream. We believe this approach could improve salmon escapement estimation, because the processes governing entry and mortality are explicitly considered.     

On the optimality of the logistic growth

The rate at which a population should grow is determined by finding the best trade-off between the loss due to the deviation from a target population size and the loss associated to the growing effort. It is also shown that, in the case of infinite-time horizon and quadratic loss functions, the optimal growth is logistic. This research was supported by the Centro Teoria dei Sistemi, CNR, and by the Italian Ministry of Public Education.     

A STRUCTURALLY BASED ANALYTIC MODEL OF GROWTH AND BIOMASS DYNAMICS IN SINGLE SPECIES STANDS OF CONIFERS

A theoretically based analytic model of plant growth in single species conifer communities based on the species fully occupying a site and fully using the site resources is introduced. Model derivations result in a single equation simultaneously describes changes over both, different site conditions (or resources available), and over time for each variable for each species. Leaf area or biomass, or a related plant community measurement, such as site class, can be used as an indicator of available site resources. Relationships over time (years) are determined by the interaction between a stable foliage biomass in balance with site resources, and by the increase in the total heterotrophic biomass of the stand with increasing tree size. This structurally based, analytic model describes the relationships between plant growth and each species’ functional depth for foliage, its mature crown size, and stand dynamics, including the self‐thinning. Stand table data for seven conifer species are used for verification of the model. Results closely duplicate those data for each variable and species. Assumptions used provide a basis for interpreting variations within and between the species. Better understanding of the relationships between the MacArthur consumer resource model, the Chapman–Richards growth functions, the metabolic theory of ecology, and stand development resulted.     

Generalized Liouville Theorem in Nonnegatively Curved Alexandrov Spaces

In this paper, Yau＇s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.     

Convex dominates concave: An exclusion principle in discrete-time Kolmogorov systems

We establish an exclusion principle in discrete-time Kolmogorov systems by using average Liapunov functions. The exclusion principle shows that a weakly dominant species with a convex logarithmic growth rate function eliminates species with concave logarithmic growth rate functions. A general result is applied to specific population models. This application gives an improved exclusion principle for the specific population models.

     

Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions

Motivated by recent work on the rate of growth of frequently hypercyclic entire functions due to Blasco, Grosse-Erdmann and Bonilla, we investigate conditions to ensure that the differentiation operator is chaotic or frequently hypercyclic on generalized weighted Bergman spaces of entire functions studied by Lusky, whenever the differentiation operator is continuous. As a consequence we partially complete the knowledge of possible rates of growth of frequently hypercyclic entire functions for the differentiation operator.     

Escape Rate of Markov Chains on Infinite Graphs

We study the escape rate of continuous time symmetric Markov chains associated with weighted graphs. The upper rate functions are given in terms of volume growth of the weighted graphs. For a class of symmetric birth and death processes, we obtain sharp upper rate functions.     

Sampling Theorem for Entire Functions of Exponential Growth

Applying the theory of generalized functions we obtain the Shannon sampling theorem for entire functions F(z) of exponential growth and give its error estimate which shows how much the error depends on the sampling size and bandwidth for given domain of the signal F(z). As an application we obtain a uniqueness theorem for entire functions and temperature functions.     

基于改进加权Poisson CUSUM控制图的发病率监控研究

现代社会医疗质量管理的重要性不言而喻,如何科学有效地开展发病率监控,具有重要的研究意义和实用价值。本文主要研究加权Poisson CUSUM控制图的改进及其在发病率监控上的应用。通过引入"标准化"处理思想,即将对数似然比统计量除以对应样本容量,本文提出"标准化"对数似然比加权Poisson CUSUM控制图,用以提高对发病率的监控水平。通过设定合适的人口模型,模拟计算验证了本文设计的模型能够有效提高监控效果,且对于不同人口模型和不同加权函数均有显著优势。最后,基于美国新墨西哥州男性甲状腺癌患病数据开展的实证检验也印证了以上结论。     

HARMONIC FUNCTIONS ON A COMPLETE NONCOMPACT MANIFOLD WITH ASYMPTOTICALLY NONNEGATIVE CURVATURE

The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.     

Polyharmonic splines: An approximation method for noisy scattered data of extra-large size

The aim of this paper is to provide a fast method, with a good quality of reproduction, to recover functions from very large and irregularly scattered samples of noisy data, which may present outliers. To the given sample of size N, we associate a uniform grid and, around each grid point, we condense the local information given by the noisy data by a suitable estimator. The recovering is then performed by a stable interpolation based on isotropic polyharmonic B-splines. Due to the good approximation rate, we need only M?N degrees of freedom to recover the phenomenon faithfully.     

Calculus on the Sierpinski gasket I: polynomials, exponentials and power series

We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which have previously been studied in connection with Taylor approximations and splines. Here the main technical result is an estimate of the size of the monomials analogous to xⁿ/n!. We propose a definition of entire analytic functions as functions represented by power series whose coefficients satisfy exponential growth conditions that are stronger than what is required to guarantee uniform convergence. We present a characterization of these functions in terms of exponential growth conditions on powers of the Laplacian of the function. These entire analytic functions enjoy properties, such as rearrangement and unique determination by infinite jets, that one would expect. However, not all exponential functions (eigenfunctions of the Laplacian) are entire analytic, and also many other natural candidates, such as the heat kernel, do not belong to this class. Nevertheless, we are able to use spectral decimation to study exponentials, and in particular to create exponentially decaying functions for negative eigenvalues.     

An allometric scaling relation based on logistic growth of cities

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed “exponential allometry”, which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the above mentioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed “logistic allometry”. The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.