Analele Universității ”Dunărea de Jos” din Galați. Fascicula II, Matematică, fizică, mecanică teoretică / Annals of the ”Dunarea de Jos” University of Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics

Summary

* * * — 2024-12-13

Volume dedicated to Prof. dr. math. Toader Buhăescu from the Department of Mathematics and Informatics, Faculty of Sciences and Environment, on the occasion of his 90th birthday

Geometric characterization of V-harmonic maps

Aprodu Monica Alice — 2025-02-07

In this paper, we provide a geometric characterization of a V-harmonic map and establish conditions that relate the V-harmonicity of a map to the V-minimality of its fibers.

Delay differential systems. A generalization of the Lotka-Volterra model

Bendrea Constantin — 2024-02-07

The first mathematical laws used in the theory of survival were introduced by Th. Malthus (1798-Principle of population; 1803-The theory of population), B. Gompertz (1860), and W. Makeham (1874). They proposed different exponential laws to describe the intensity of death, which then formed the basis for the biometric functions of survival. In the twentieth century, the development of demographic research, as well as the study of various epidemics affecting populations, led to the emergence and evolution of new methods for solving problems in survival theory. Lotka-Volterra (in their Predator-Prey model) described the differential equations of population growth (in humans, microorganisms, and other species). These models were later improved by E. M. Wright and P. J. Wangersky (1978), who more plausibly assumed that the phenomena of immigration-emigration could represent the biological reaction of self-regulation of a population, and that this factor acts with a certain delay. The use of random processes and, later, stochastic differential equations contributed to the evolution and diversification of mathematical models in biological systems. In this article, we have developed a variational functional framework for the description of problems associated with delayed differential systems. We have thus made a generalization of the Lotka-Volterra model.

Numerical method for approximating a function

Ciochina Stefanut — 2025-02-07

In this paper we present the stages of implementing a numerical method to approximate a function. In order to achieve the objective of this work, we consider a function defined on an interval [a,b] and select three nodes from within the assumed interval. At these three chosen points, we will also know the values of the function at these points and also the values of the first order derivatives at the three points. An interpolation polynomial, of minimum degree, with the assumed nodes will be obtained.

Interactive teaching methods

Gheorghiță Adrian Ștefan — 2024-12-13

In this paper, I aim to present the importance of developing the kinesthetic learning style for understanding the geometric concepts being taught.

The connection between the stochastic series and the time depending phenomena

Cazacu Nina — 2025-02-07

The present paper employs computer-assisted methods in order to solve different type of equations and systems.
The most significant goal is to transform, by modeling, time-depending series, such as stochastic series for
instance, into dynamic systems that can be solved, while also obtaining visual representations of their solutions.
So, we have started with an introduction including different computer-assisted methods for solving differential
equations and systems, followed by a proposed algorithm that leads to both an analytical formula and a graphical
representation of the optimal solution and command for a specific class of dynamical systems.
Through this work, we have shown that stochastic series can be expressed, through mathematical modeling, as a
time-dependent system of equations or even as dynamic system, which we have established an obvious similarity
with the generalised dynamic systems of the age-structured populations, discovered by J.R. Chasnov.
The connection which we have established allows for the application of the classical computer-assisted methods,
as well as particular algorithms, for many other time-dependent series, which can be modeled in the dynamic
system form, particularly when the main term follows a time-recurring formula.

Novel foods - overview, legislation and methods of analysis

Georgescu Ioana Mădălina — 2025-02-07

Novel foods have recently gained increasing popularity. Given their diversity and nutritional values, which are comparable to commonly consumed foods, novel foods had to be regulated both in terms of the procedural stages required for market introduction at the European Union level, implicitly in Romania, and the requirements they must meet for safe consumption. The analysis methods used for their characterization are generally classic, standardized ones or can be developed "in-house", as is the case for methods developed for the determination of mycotoxins. The method of analysis used for the determination of mycotoxins involves high performance liquid chromatography coupled with a mass spectrometer (LCMSMS) after the prior extraction of mycotoxins using QuEChERS extraction. The novelty of recent years is the inclusion on the list of novel foods approved at the European Union level of laboratory-grown meat and insects, such as flour beetle larvae available in frozen, paste, or dried form, and house crickets, available in frozen, powdered or desiccated form.