We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of ∗-semigroups from the point of view of generation of ∗-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifie...

We study asymptotic behavior of a Markov semigroup on a von-Neumann algebra by exploring a maximal von-Neumann subalgebra where the Markov semigroup is an automorphism. This enables us to prove that strong mixing is equivalent to ergodic property for continuous time Markov semigroup on a type-I von-Neumann algebra with center completely atomic. For discrete time dynamics we prove that an aperio...

We give a general review on the application of Ergodic theory to investigation dynamics Yang-Mills gauge fields and gravitational systems, as well its in Monte Carlo method fluid dynamics. In ergodic maximally chaotic dynamical systems (MCDS) can be defined that have nonzero Kolmogorov entropy. The hyperbolic fulfil Anosov C-condition belong MCDS insofar they exponential instability their phase...

A cohor t is a fixed population. Its membership is permanent (even after death)8, 14). Examples are as follows: people born in Kagoshima, and the alumni of Hirosaki University. A cohort study follows a fixed population. Unfixed populations are called dynamic populations (open populations). The membership of a dynamic cohort is not permanent. Examples are as follows: Hirosaki University students...

The sparsely populated northern Sweden has been the main target area for regional policy efforts since the 1960s. A rich variety of regional policy measures have been launched over the years. However, despite this and a heavy expansion of welfare undertakings a significant depopulation has taken place. Also the first generation of EU Structural Funds show very weak structural impacts on develop...

Concerns about population growth historically revolved around the notion that there may be insufficient arable land, minerals or energy to meet the needs of an exponentially increasing population. Today they are compounded by fears that as wealth increases, so would consumption of natural resources, and that new technologies would enable further exploitation of these resources. Absent empirical...

The study reported here assessed residents' perception of small, fast-growing coastal community on issues of quality of life, conservation, and growth. Data for the study were collected from an on-site survey in Aransas County, Texas from 2006 to 2007. Results show that the residents are concerned about preserving their natural resources, maintaining a small town atmosphere in their community, ...

We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non–cooperative games. The players imitate the most attractive strategies, and the choice is motivated not only by the material payoffs of the strategies, but also by their popularity in the population. The parameter which determines the weights of both ...

This paper builds a small-open-economy, non-scale-growth model with negative population growth and investigates the relationship between trade patterns and per capita consumption growth. Under free trade, if the population growth rate is negative and its absolute value is small, the home country becomes an agricultural country. Then, the long-run growth rate of per capita consumption is positiv...

This paper discusses the disease-free and endemic equilibrium points of a SVEIRS propagation disease model which potentially involves a regular constant vaccination. The positivity of such a model is also discussed as well as the boundedness of the total and partial populations. The model takes also into consideration the natural population growing and the mortality associate to the disease as ...