Mathematics in Modern Technical University

Maria Gaetana Agnesi – an outstanding woman mathematician

S. R. Moloshna, O. G. Bilyi — Tue, 30 Dec 2025 00:00:00 +0200

The article examines the biography and creative work of an outstanding female mathematician from Italy, one of the first women to hold a professorship in mathematics. It traces her life path from early childhood to her death. Gifted in learning from an early age and supported by wealthy and influential parents, she demonstrated remarkable abilities in language studies, achieved significant success in mathematics and physics, and studied geometry, ballistics, theology, and philosophy. Her subsequent scholarly interests focused primarily on mathematics and mathematics education. Her major work, known worldwide as Foundations of Analysis and exceeding 1,000 pages in length, was published in Italian, quickly gained wide recognition, and was translated into French and English. In this textbook for Italian youth, for the first time, an analytical proof was provided showing that any cubic equation over the complex numbers has exactly three roots. The work also explored a curve that later became known as versiera of Agnesi in recognition of her contributions. A description of this curve is given, its equation is derived, and some of its properties are discussed. The article also presents an analysis of several generalized and related curves connected with the versiera, along with some applications and noteworthy facts. Attention is also paid to Maria’s activities in the field of mathematics education and charity.

Analysis of survey results using the stepwise method in the model of logistic regression on the platform of MS Excel (the survey of Ukrainian students in February 2024)

O. O. Vrublovska, O. V. Mulyk — Tue, 30 Dec 2025 00:00:00 +0200

There are presented base formulas of logistic regression and as exactly they can be realized on the platform of MS Excel (Real Statistics, Logistic of and of Probit Regression). The used statistical measures of the productivity of tests of binary classification are considered widely: Sensitivity, Specificity, Positive Predictive Value (PPV), Negative Predictive Value (NPV), prevalence of case (Prevalence) and other. The content of McFadden's, Cox and Snell's and Nagelkerke's coefficients of determination is considered. Also, we give the detailed analysis of curve of Receiver Operating Characteristic – ROC curve analysis, as well as application of Youden's J statistic.

The model was evaluated using performance indicators such as sensitivity (71.4%), specificity (92%), and the area under the ROC curve (AUC = 0.81), indicating high model accuracy. Additionally, the odds ratio for key factors showed that an increase in the impact of war-related stress by 1 unit decreases the probability of continuing education by 28.57%. The results obtained provide a better understanding of how external factors affect students' psychological state and academic performance, allowing for the development of recommendations to improve student support in crisis conditions.

Generalized linear models and neural networks in insurance

A. A. Novikova, O. I. Vasylyk — Tue, 30 Dec 2025 00:00:00 +0200

Actuarial calculations form the basis for ensuring the solvency of the insurance company. This paper is devoted to the study of recently proposed combined actuarial neural network that combines the traditional generalized linear model used in insurance pricing with a neural network. The main idea behind using a neural network for insurance pricing is to model interactions between functions that are not covered by a generalized linear model.

Vector potential of a solenoidal field

V. O. Bilyi, I. S. Laskin — Tue, 30 Dec 2025 00:00:00 +0200

The article discusses examples of determining the vector potential of a solenoidal field, which is defined by the relation F = ∇ × a, where a is the vector potential and ∇ is the Hamiltonian operator, as well as some of its applications. Unlike the case of a potential field, for which determining the scalar potential u = u(x, y, z) is related to the path-independence of the corresponding line integral — a well-studied issue — the determination of a vector potential is significantly more complex and requires solving an appropriate system of first-order linear partial differential equations. It is noted that such a potential is defined up to the gradient of an arbitrary scalar function. The possibility of decomposing an arbitrary vector field into the sum of its potential and solenoidal components is also demonstrated. Examples of determining the vector potential for solenoidal and harmonic fields are provided. The obtained results can be applied to solving problems in electromagnetic field theory, mathematical physics, and applied mathematics.

Asymptotic ONC distribution of quasi-chirped signal parameters

V. V. Hladun, O. V. Ivanov, A. M. Krugol — Tue, 30 Dec 2025 00:00:00 +0200

The paper considers a continuous-time elementary quasi-chirped signal observed against the background of additive strongly or weakly dependent Gaussian random noise. As an estimate of the unknown parameters of this signal, the least squares estimate (LSE) is considered. The asymptotic properties of the LSE of the studied signal were considered and theorems on the strong consistency and asymptotic normality of the LSE of the unknown parameters of the quasi-chirped signal were obtained.

Asymptotic behavior of thinned multi-level point processes in the generalized birthday problem

V. V. Stamatiieva — Tue, 30 Dec 2025 00:00:00 +0200

The joint asymptotic behavior in the generalized birthday problem is studied using the apparatus of multi-level point processes. The analysis is based on a Poissonized model. We introduce a method that combines a common normalization function with a thinning operation for different completion levels. We prove the vague convergence of the constructed thinned point process to a limiting Poisson process with independent levels. As an application, the joint limiting distribution for the number of classes reaching lower completion levels by a random time is derived.