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...
Existence and uniqueness of solution of some integro-differential equation
A simple proof of a theorem on Markov operators
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.
On the age-dependent predator-prey model
The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.
The speech - a specific feature of the evolution of the modern human (Homo sapiens)
The specific feature of humans, that distinguishes them from the animal world, is the speech. The speech is a form of communication in which we use comprehensive signs to express verbally ourselves and the surrounding reality. This definition imposes the opinion that the origin of the speech can be considered from the appropriately high level of the brain development. In order to trace the evolution of the ability to speak among the Primates, the measurements of the superofacial triangle of the...
Hominization tendencies in the evolution of primates in multidimensional modeling
Evolutionary radiation of primates determined many developmental paths among which there is a hominization tendency that leads to the emergence of modern human. This evolution was studied on the basis of measurements constituting Morant and Sergi’s index (Sergi(1940)), which were taken on 68 skulls of chosen adult monkeys, apes and fossil hominids. They were classified into 10 separate taxons. The skull measurements were worked out with the help of the following methods: descriptive statistics and...
Evolution stages of some monkey and ape taxons.
The aim of this work is to present taxons which link various species and genera as morphological stages in the evolution of primates. The research material consists of 115 skulls of monkeys and apes. Their variability in neurocranium and splanchnocranium ratios can be characterized by Morant and Sergi’s index and by direct measurements that is formed of. The analysis of results allows the following conclusions. Determining taxon concerning PAPIO (baboons) shows that sex dimorphism exceeds differences...
On the dense trajectory of Lasota equation.
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