Francisk Skorina Gomel State University

The paper presents the results of research on laser processing of natural and artificial diamond crystals in microelectronics technologies by thermal laser separation. An analysis of physical-chemical phenomena observed as a result of the thermal effect of laser radiation on anisotropic materials in various crystallographic directions is conducted. Based on the Griffiths criterion, the mechanics of brittle fracture as a result of the formation of critical micromechanical stresses caused by the thermal action of laser radiation are analyzed. The non-stationary problem of thermal conductivity was solved, temperature distributions in the volume of the material were calculated, on the basis of which information on the change of elastic properties of crystals leading to its controlled destruction in given directions was obtained. The simulation results were confirmed experimentally in the processes of thermal laser separation of rough diamonds by forming localized areas of critical thermoelastic microstresses at a given depth in the crystal volume, which are the starting point of the line of controlled crystal separation. Optimal modes of controlled separation of crystals of natural and artificial diamonds using a diode-pumped laser with a radiation wavelength of 1064 nm have been identified.

For a formation 𝔉 of finite groups, consider the graph whose vertices are elements of a finite group, with two vertices connected by an edge if and only if they generate a non-𝔉-group as elements of the group. A hereditary formation 𝔉 is said to be regular if the set of all isolated vertices of the described graph coincides with the intersection of all 𝔉-maximal subgroups in every group. In this paper, a constructive description of saturated regular formations of soluble groups is given, which improves the results of Lucchini and Nemmi. In particular, it is shown that saturated regular non-empty formations of soluble groups are just hereditary formations 𝔉 of soluble groups that contain every group whose cyclic primary subgroups are all 𝐾-𝔉-subnormal. Also, we prove that the lattice of saturated regular formations of soluble groups is lattice isomorphic to the Steinitz lattice.

Although conventional chemotherapeutic drugs exhibit broad-spectrum antitumor efficacy, their toxic effects on normal cells cannot be ignored, and there is an urgent need to develop novel drugs to improve therapeutic efficacy and reduce side effects. In this study, we prepared PLGA/TA microspheres with TA as the target drug and PLGA as the carrier, and evaluated their physicochemical properties, including particle size, morphology, and release behavior, with the aim of exploring the potential of PLGA/TA microspheres for tumor therapy. The results of RNA sequencing showed that PLGA/TA microspheres may act on tumor cells mainly through the pathway of PI3K-Akt, and do not interfere with the synthesis of DNA directly. Overall, PLGA/TA microspheres, as a novel drug delivery system, showed good anti-tumor potential and provided new ideas and directions for cancer therapy.

The author has taught programming to schoolchildren of different ages for many years. All this time, the author has been creating literature for independent study by schoolchildren, trying to present the material in the simplest, most visual, and understandable form possible. This article provides an example of such material for teaching problem-solving in computer science on the topic "Working with bits". Such material may be of interest to teachers both as an illustration of the teaching methodology and in terms of content. At the same time, the author believes that this material may be very useful and interesting for schoolchildren engaged in self-study. All interested parties are offered the following work order: put the article aside and try to independently complete the proposed task the first time - after reading the problem statement, the second time - after reading the instructions for the solution.

At the territory of the Lebyazhe City Forest Park (Kazan), 176 species were identified, of which 160 are lichens, nine are lichenicolous fungi, one is a facultatively lichenicolous, and six are saprotrophic non-lichenized fungi. Of these, 46 species are new to the Republic of Tatarstan, including the lichenicolous fungus Epithamnolia xanthoriae is reported for the first time for the Central European Russia. New habitats of protected in Tatarstan lichen Cresponea chloroconia were found. Most of the newly reported species are mainly widespread lichens in European Russia, which indicates that the lichen biota of Tatarstan is poorly investigated.

The article presents the first records: for Russia of one species of chrysophyte algae and one species of agaricoid basidiomycetes, for the Republic of Belarus of three lichenicolous fungi and four species of slime molds, for Uzbekistan and Tajikistan by one species of lichens, and the first records for regions of Russia: one charophyte for the Tambov Region, one diatom species for the Udmurtian Republic, five species of siphonous yellow-green algae for the Republic of Altai, Altai Territory and Nenets Autonomous Okrug, 22 species of basidiomycetes for St. Petersburg, Tyumen Region, and Republic of Altai, including two new species for the Asian part of Russia, two new species for Siberia, and three new species for West Siberia, nine myxomycetes for the Altai Territory, Novosibirsk Region, and Republic of Altai, two species of lichenicolous fungi for the Tver Region, eight species of lichens for the Irkutsk, Omsk, Tver regions, Altai Territory, Republic of Tuva, 19 species of mosses for the Kurgan, Magadan and Ryazan regions, Republic of North Ossetia — Alania, including one new species for the Caucasus. The data on their localities, habitats, distribution are provided. The specimens are kept in the herbaria ALTB, GSU, IBIW, LE, MAG, MSK, NSK, OMSK, PTZ, TOB, YSU, VU, of Institute of Botany, Plant Physiology and Genetics of the National Academy of Sciences of Tajikistan, collection of the Laboratory for Algology in the Papanin Institute for Biology of Inland Waters of the Russian Academy of Sciences, in the private collections of V. S. Vishnyakov, S. M. Goskova, and S. I. Genkal

Let $\sigma = \{ {\sigma }_{i} \mid i \in I \}$ be a partition of the set of all primes. A set $\Sigma = \{H_1, \ldots , H_k\}$ of $\sigma _i$-Hall subgroups of G is said to be a complete Hall set of type $\sigma$ of G if $(|H_i|, |H_j|) = 1$ for all $i \ne j$ and $\pi (G) = \pi (H_1) \cup \cdots \cup \pi (H_k)$. A $\sigma$-subnormality criterion is proved in terms of products of subgroups of a complete Hall set of type $\sigma$.

We construct infinite series of subgroup m -functors and regular subgroup m -functors $\theta$ such that the Frattini $\theta$-subgroup of every normal Hall subgroup H in any finite group G is equal to the intersection of H with the Frattini $\theta$-subgroup of G .

Form-factor analysis of pseudoscalar π±- and vector ρ±- mesons with zero transmitted momentum has been carried out in the model based on the point form of Poincaré-invariant quantum mechanics. The original method of model parameters’ calculations from leptonic decays π±→ℓ±νℓ± , τ±→ρ±ντ± using pseudoscalar density gπ± constant is proposed. The method is generalized in radiative decays ρ0→ℓ+ℓ- and ρ±→π±γ with the following anomalous magnetic moments calculation of constituent u- and d- quarks. It has been shown that the obtained parameters lead to the values of magnetic and quadrupole moment of ρ±- meson which are comparable with other models as well as hadronic transition ρ±→π±π0 observables. A comparative analysis of the obtained values of μu and μd quark magnetic moments has been carried out. It has been found that the proposed model gives numerical evaluations which are comparable to other approaches and models.

The present study examines the synthesis, properties, and applications of nanostructured materials based on titanium dioxides (TiO2) via the sol–gel method. The sol–gel method makes it possible to vary the physicochemical properties of nanostructured materials over a wide range and achieve significant interaction be-tween components at the stage of the initial sol. Simultaneously, sol–gel synthesis of nanostructured materials is more energy efficient compared to vacuum and plasma methods. The main physical and chemical processes that occur throughout the preparation and maturation stages of sol are determined. The influence of synthesis conditions on the dispersion, phase composition, and properties of nanostructured materials based on titanium dioxide is established. A description of the sol–gel method for producing bulk nanostructured materials is provided. Extensive studies have been conducted to examine the optical and structural properties of nanostructured materials based on TiO2. Numerous investigations have been carried out on the photocatalytic activity of nanostructured films and xerogels obtained through the sol–gel method. The study findings indicate that nanostructured films and xerogels derived from TiO2 possess photocatalytic properties, making them suitable for application in water purification systems.

The article is about describing peculiarities of the realization of the category of emotiveness in scientific dialogue the latter being interpreted as a type of public speech combining characteristics of both scientific and everyday discourse. It is the ability to possess traits of everyday discourse that predetermines a highly emotive character of scientific dialogue revealed through a regular explication / nomination of different emotions. Thus, the paper focuses on identifying varieties of emotions explicated in scientific dialogue (cognitive and affective emotions), specificity of their realization (which is intensified) as well as semantic, pragmatic and structural properties of speech acts where they are verbally manifested. The research is done on the basis of Russian and English, which helps determine a universal character of functioning emotive speech acts in scientific dialogue.

The article aims at examination of illocutionary, compositional and linguistic properties of the English-speaking (American) judicial discourse based on one of its speech genres, such as preliminary instructions given by the presiding judge to the jury members. Structural and functional blocks of the genre (requirements for jurors, logic of the trial, semantization of concepts), their speech acts varieties (orders, prohibitions, permissions, clarifications, explanations) and the lin-guistic markers representing such speech actions are defined. The results obtained allow us to make a conclusion that pre-liminary instructions, as a part of the English-speaking judicial discourse, are predominantly directive by nature.

Let G be a finite group, and let ${\mathcal{L}}(G)$ be the lattice of all subgroups of G. A subgroup M of G is called modular in G if M is a modular element (in the Kurosh sense) of the lattice ${\mathcal{L}}(G)$, i.e., if (1) $\langle X,M\cap Z\rangle=\langle X,M\rangle\cap Z$ for all $X\leq G,Z\leq G$ such that $X\leq Z$, and (2) $\langle M,Y\cap Z\rangle=\langle M,Y\rangle\cap Z$ for all $Y\leq G,Z\leq G$ such that $M\leq Z$. If A is a subgroup of G, then $A_{mG}$ is the subgroup of A generated by all its subgroups that are modular in G. We say that a subgroup A is N-modular in G ($N\leq G$) if, for some modular subgroup T of G containing A, N avoids the pair $(T,A_{mG})$, i.e., $N\cap T=N\cap A_{mG}$. Using these notions, we give new characterizations of p-soluble and p-supersoluble finite groups.

We reduce the solution of the Kegel–Wielandt $\sigma$-problem for an arbitrary partition $\sigma$ of the set of all primes to its solution in the class of all $\sigma$-complete simple nonabelian groups. We also give a sufficient criterion for the $\sigma$-subnormality of a subgroup in a finite group for a partition $\sigma$ in which 2 and 3 belong to the same component.

A formation F is called a Baer – Shemetkov formation in a class X of groups if in any finite X -group the intersection of all F -maximal subgroups coincides with the F -hypercenter. It is proved that for a non-empty hereditary saturated formation F there exists the greatest by inclusion hereditary saturated formation BS F such that F is a Baer – Shemetkov formation in BS F. The connection of this result with the solution of Agrawal’s (1976) and Shemetkov’s (1995) questions is discussed. For the class U of all supersolvable groups the class BS U is described and the algorithm for its recognition is presented.