On asymptotic behaviour of the dynamical systems generated by von Foerster-Lasota equations
The two-dimensional linear relation in the errors-in-variables model with replication of one variable
We present a two-dimensional linear regression model where both variables are subject to error. We discuss a model where one variable of each pair of observables is repeated. We suggest two methods to construct consistent estimators: the maximum likelihood method and the method which applies variance components theory. We study asymptotic properties of these estimators. We prove that the asymptotic variances of the estimators of regression slopes for both methods are comparable.
On the positivity of an invariant measure on open non-empty sets
On the generalized Avez method
A generalization of the Avez method of construction of an invariant measure is presented.
A method of construction of an invariant measure
A method of construction of an invariant measure on a function space is presented.
On the random version of Ważewski theorem
On the lifting of invariant measures
On the existence of an invariant measure for the dynamical system generated by partial differential equation
Roman Żuliński and his principles of differential and integral calculus (Devoted memory of Polish mathematicians who gave their lives for the Motherland)
On August 5, 1864 at the Warsaw Citadel gave their lives for their homeland Jan Jeziorański, Rafal Krajewski, Józef Toczyski, Romuald Traugutt and Roman Żuliński. Their blood was not in vain. The next generation of Poles felt obliged to continue their work. Day 11 November 1918 was a natural consequence of the armed Uprising and their traditions.
Monetary systems in the Polish territories in the period 1763--2013.
The present article is based on the talk given by the author at the Conference in History of Mathematics in the year 2013 in Będlewo. The motivation for the creation of this article was the appearance in recent years of works dedicated to textbooks and collections of problems issued in the First Republic and in the period of partitions. The problems occurring in these textbooks concern, as they anyway do nowadays, various financial calculations The knowledge of monetary systems certainly can help...
Over 20 years of competion: student's papers from Mathematics
The article contains no abstract
On the Avez method and its generalizations
In this paper the method of construction of invariant measure are presented. Particularly the method of Avez is presented.This method was used by Professor Lasota.
Existence and uniqueness of solution of some integro-differential equation
A simple proof of a theorem on Markov operators
On random boundary value problems for ordinary differential equations
Some remarks on boundary value problems for linear stochastic differential equations
On an approximation theorem of Wong-Zakai type for the Lasota operator
The authors show that the stochastic evolution equation with Lasota infinitesimal generator satisfies the Wong-Zakai type approximation theorem.
On certain modification of age-dependent predator-prey model
This work proposes a new model of coexistence of a predator population with a population of prey. In works [5] and [7] it is assumed that the number of prey aged x eaten by predators aged y is directly proportional to the number of prey aged x and the number of predators aged y. This paper presents a more general model. First of all, the dependency is functional, i.e. the chances of being eaten are affected by the structure of the whole population. In addition, this dependence is not bilinear because...
Mathematical model of bats' subpopulations development
The paper deals with the description of the mathematical model of bats’ subpopulations and fission-fusion societies development. Model is based on the system of ordinary differential equations. Bats’ behaviour and their searching strategy is presented on the basis of cavity roosting bats living in Białowieża Forest located in Poland. Theoretical results are illustrated by computer simulation and its comparison with biological remarks.
The multiple regression model where independent variables are measured unprecisely.
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