scholarly journals Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball

2005 ◽  
Vol 2005 (6) ◽  
pp. 563-573
Author(s):  
Tetsutaro Shibata
Keyword(s):  
Population Dynamics ◽  
Eigenvalue Problem ◽  
Asymptotic Formula ◽  
Bifurcation Diagram ◽  
Global Structure ◽  
Spectral Asymptotics ◽  
Point Of View ◽  
Logistic Equations ◽  
Semilinear Elliptic ◽  
Precise Asymptotic

We consider the semilinear elliptic eigenvalue problem−Δu+k(|x|)up=λu,u>0inBR,u=0on∂BR, wherep>1is a constant,BR:={x∈RN:|x|<R}(N≥1), andλ>0is a parameter. We investigate the global structure of the branch of(λ,uλ)of bifurcation diagram from a point of view ofL2-theory. To do this, we establish a precise asymptotic formula forλ=λ(α)asα→∞, whereα:=‖uλ‖2.

SURVEY Towards a global view of dynamical systems, for the C1-topology

2011 ◽  
Vol 31 (4) ◽  
pp. 959-993 ◽  
Author(s):  
C. BONATTI
Keyword(s):  
Dynamical Systems ◽  
Compact Manifold ◽  
Global Structure ◽  
Point Of View ◽  
List Type ◽  
Global View ◽  
Local Phenomenon ◽  
Generic Dynamics

AbstractThis paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) into disjoint C1-open regions whose union is C1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of: •either a robust local phenomenon;•or a global structure forbidding this local phenomenon. Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

scholarly journals Effect of cadmium and zinc contamination on the population dynamics of soil microorgani

2014 ◽  
pp. 73-77
Author(s):  
Zsuzsa Kovács
Keyword(s):  
Population Dynamics ◽  
Hungarian Academy ◽  
Point Of View ◽  
Nitrifying Bacteria ◽  
Microscopic Fungi ◽  
Agricultural Chemistry ◽  
Scientific Results ◽  
Academy Of Sciences ◽  
Zinc Contamination

Changes in the population dynamics of microorganisms in a soil artificially contaminated with various doses of cadmium and zinc was examined from a quantitative point of view, under laboratory circumstances. The research was based on a chernozem soil originating from the area of a long-term microelement contamination model experiment (Nagyhörcsökpuszta, Hungary), which was carried out during 1991 in the Experimental Site of the Institute of Soil Science and Agricultural Chemistry, Centre for Agricultural Researche Hungarian Academy of Sciences, Budapest, Hungary. According to the amount of bacteria, microscopic fungi and nitrifying bacteria, it can be stated that the effect of contamination can be observed even in the perspective of nearly two decades. In more cases significant changes in the number of soil bacteria and microscopic fungi could be observed, and the nitrification activity increased in case of both microelements. Therefore the further research of changes in microbial activity of these soils can provide novel scientific results.

scholarly journals A Renewal Shot Noise Process with Subexponential Shot Marks

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 63
Author(s):  
Yiqing Chen
Keyword(s):  
Asymptotic Formula ◽  
Shot Noise ◽  
Crucial Role ◽  
Random Variables ◽  
Tail Probability ◽  
Noise Process ◽  
Shot Noise Process ◽  
Precise Asymptotic

We investigate a shot noise process with subexponential shot marks occurring at renewal epochs. Our main result is a precise asymptotic formula for its tail probability. In doing so, some recent results regarding sums of randomly weighted subexponential random variables play a crucial role.

scholarly journals An exact bifurcation diagram for a reaction–diffusion equation arising in population dynamics

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jerome Goddard II ◽  
Quinn A. Morris ◽  
Stephen B. Robinson ◽  
Ratnasingham Shivaji
Keyword(s):  
Population Dynamics ◽  
Diffusion Equation ◽  
Bifurcation Diagram ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation

scholarly journals Solution of Eight-vertex Lattice Model Without Elliptic Functions

1974 ◽  
Vol 27 (4) ◽  
pp. 433 ◽  
Author(s):  
Kailash Kumar
Keyword(s):  
Eigenvalue Problem ◽  
Transfer Matrix ◽  
Elliptic Functions ◽  
Point Of View ◽  
Vertex Model ◽  
Type Problem ◽  
Matrix Eigenvalue Problem ◽  
Lattice Statistical Mechanics ◽  
Algebraic Operations ◽  
Functional Matrix

Baxter's method of solving the eight-vertex model in lattice statistical mechanics is examined from an elementary point of view. It is shown that the algebraic operations in the method can be carried out without recourse to elliptic functions. These include: construction of certain subspaces invariant uti.der the action of the transfer matrix; reduction of the transfer matrix eigenvalue problem to an equivalent ice-type problem and construction of certain matrices which commute with the transfer matrix and satisfy a functional matrix equation.

Asymptotics of Permutations with Nearly Periodic Patterns of Rises and Falls

10.37236/1733 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Edward A. Bender ◽  
William J. Helton ◽  
L. Bruce Richmond
Keyword(s):  
Functional Analysis ◽  
Integral Equation ◽  
Eigenvalue Problem ◽  
Asymptotic Formula ◽  
Fredholm Integral Equation ◽  
Random Variables ◽  
Periodic Patterns ◽  
Asymptotic Results ◽  
Alternating Permutations ◽  
Asymptotic Number

Ehrenborg obtained asymptotic results for nearly alternating permutations and conjectured an asymptotic formula for the number of permutations that have a nearly periodic run pattern. We prove a generalization of this conjecture, rederive the fact that the asymptotic number of permutations with a periodic run pattern has the form $Cr^{-n}\,n!$, and show how to compute the various constants. A reformulation in terms of iid random variables leads to an eigenvalue problem for a Fredholm integral equation. Tools from functional analysis establish the necessary properties.

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