Zonation of Lithuanian Silurian graptolites and other faunal groups

The Baltic Silurian Basin, Lithuanian Depression and other structures are shown in the map, with marked by isopachs (contour lines of equal thickness) of the Silurian beds with graptolites and fauna of other groups. The Silurian facies vary greatly in the Depression – from clayey open-sea deep shelf to carbonaceous ones of shallow shelf, and low-energy lagoon facies. The history of investigations on East Baltic area graptolites begins from 1953–1958, when 15 graptolite zones were singled out, and proceeds to 35 zones defined now. Peculiarities in the graptolite scale from C. cyphus to N. lochkovensis inclusive are discussed. Transgressions and regressions of the Silurian marine basin, as well as shorter transgressions with wedges and graptolites of clayey facies shifted towards basin shores and regressions with partial extinction of graptolites are elucidated. During these investigations the graptolite scale has been detailed and added with new zones. Graptolite evolution in the zones has been analysed. Stages of graptolite evolution are analysed in relation to the following bioevents: Stačiūnai, Likėnai, Valgu, Ireviken, Mulde, Linde, Lau, Klev and Šilalė. Finally, two tables present graptolite zone correlation with conodont, vertebrate and ostracod zones revealing a highly detailed stratigraphy of the Lithuanian Silurian.

Dynamic Behaviors of a Competitive System with Beddington-DeAngelis Functional Response

This article studies a competitive system with Beddington-DeAngelis functional response and establishes sufficient conditions on permanence, partial extinction, and the existence of a unique almost periodic solution for the system. The results supplement and generalize the main conclusions in recent literature. Numerical simulations have been presented to validate the analytical results.

THE IMPACT OF ARCHITECTURAL AND HISTORICAL ENVIRONMENT ON RELIGIOUS OBJECTS OF SAMARA

The purpose of the article is to identify the impact of the system of identifi ers of the architectural and historical environment on the religious architecture of Samara on the considered and identifi ed historical stages of the development of the city. It is shown that due to the particularly rapidly developing cities of our time, including historical ones, the historical heritage is the fi rst to be in danger of complete or partial extinction. From here it becomes apparent the preservation of the heritage of cities and the preservation of the identity of the historical city. As a result, a typical image of the Samara religious architecture was determined throughout its development, characteristic types, styles, infl uences of external and internal ethnos were established, and productive forces were identifi ed, which are the basis for the development of the city of Samara at each historical period.

Extinction Probabilities of Branching Processes with Countably Infinitely Many Types

We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated Galton-Watson processes with finite sets of types and modified progeny generating functions. In addition, we discuss the connection of the convergence norm of the mean progeny matrix with extinction criteria. Finally, we give a sufficient condition for a population to become extinct almost surely even though its population size explodes on the average, which is impossible in a branching process with finitely many types. We conclude with some numerical illustrations for our algorithmic methods.

Extinction Probabilities of Branching Processes with Countably Infinitely Many Types

We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated Galton-Watson processes with finite sets of types and modified progeny generating functions. In addition, we discuss the connection of the convergence norm of the mean progeny matrix with extinction criteria. Finally, we give a sufficient condition for a population to become extinct almost surely even though its population size explodes on the average, which is impossible in a branching process with finitely many types. We conclude with some numerical illustrations for our algorithmic methods.

Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey

We investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.