Show that computing e-th roots modulo n is easier than factoring n with currently known methods, given subexponential access to an oracle outputting the roots of numbers of the form xi + c. The strategy – a general outline. Polynomial construction.

Ideas of vanguard investigators about applying probability models and applications (stochastic processes and inference, distributions and characterizations, Bayesian inference, selection methods, regression methods) in health and economic research.

Importance of correct application of information communication technologies in teaching a foreign language and factors which accompany that process. The concepts of using technologies of the communicative competence of a schoolchild in learning English.

Judicial practice in Ukraine: from judicial generalizations to an open database of judicial decisions. Review of the database of court decisions of the Unified State Register of Court Decisions. Application of artificial intelligence in this area.

The importance of water quality. Applications of machine learning in water quality prediction. Challenges and limitations. Given these multifaceted impacts, the necessity for accurate and timely prediction of water quality cannot be overstated.

Consideration of teaching English in multilevel groups. Outline of the main problems of teaching in multilevel classes. Search / development of graded tasks, educational resources and materials. Ensuring the motivation and interest of all students.

The purpose of the research of article is to highlight the basics of the origin of advertising and advertising activities both in the world and in Ukraine in particular; study of the impact of advertising of various types on consumer demand and choice.

The examination of the phenomenon of trial marriage. Description of advantages and disadvantages of this kind of matrimony, for men and women, for parents of partners of it. Basic approaches to the trial marriage: psychological and socio-demographic.

Analysis of the current state and prospects for the development of distance learning after the end of the Covid-19 pandemic. Characteristics of the main components of online education. The specifics of studying economics in a virtual learning environment.

Identification of the main advantages, disadvantages of using elements of distance learning in the process of mastering economic disciplines in a modern university. Research the process of finding and finding an individual learning style for each student.

A study of the experience of implementing social networks in the process of teaching English by a researcher who worked in this field. The essence of using social networks as a teaching tool in English lessons based on the works of foreign researchers.

Brief introduction to alternative assessment. Features of teaching English. Implementation of the assessment in practice. Problems of language and translation. The strategies, techniques of alternative assessment in teaching English into the classroom.

The role of total quality management (TQM) implementation principles on product quality in the Libyan Metallurgical Company. Peculiarities of the activities of Libyan companies and their difficulties, obstacles in implementing and maintaining modern TQM.

Dynamic model of adverse selection to examine the interactions between new and used goods markets. Predictions of the effects of adverse conditions. Comparison these predictions with this model where brands physically depreciate at different rates.

The Advertising Broker. The New Face of Advertising. The Marketplace and What Happens in it. Trade Marks, Labels, and Logotypes. The Different Kinds of Advertising: corporate, professional, industrial. Marketing Services: copy, art, media, radio-TV.

The relationship between the problem of promotion and the communication strategy of children's publishing. Formation of the reputation and image of children's publishing houses. Advertising and PR methods in the complex of promoting children's books.

The article studies the linguistic means of English Internet news headlines performing advertising function. Viewing headline as a riveting short-cut to the contents of an article, advertising function lies in attracting attention to the full-text.

The concept of studying advertising graphics as a form of sociocultural communications with the analysis of stylistic trends, the problems of visualization of ideas and aesthetics. Analysis of the visual language of advertising of the postmodern period.

Study of the tasks of Advertising Graphics and its relevancy and weighty place in the structure of the integrated art discipline "Design of Advertising" in high school. Stylistics and art-aesthetic problems of modern advertising in communicative sphere.

The role of advertising in the modern life of each person. Purpose and function of advertising, which is part of the communication activities of the company. The results of a poll of city residents relations to advertising, factors of its effectiveness.

Advertising is a tool for experiencing the city as a concern for the urban environment, a tool for forming consumer attitudes of city residents through the formation of a qualitatively new type of social relationships based on the illusion of prosperity.

Description of the current state of the language of advertising in the Ukrainian media space. Typical mistakes in advertising texts, the reasons for their occurrence, violations of literary norms. The samples to improve the language of advertisers.

The role of the Bar in the system of free legal aid provision. The principle of protection and priority of human and civil rights and freedoms. The process of optimising the functioning of the legal aid system in Ukraine and their effectiveness.

The object, nature and artistic forms of Ukrainian avant-gardism of the first third of the twentieth century. Consideration of the connection of energy-information searches for avant-garde aesthetics with the spiritual practices of isychasm in art.

Аналіз стану популяцій рідкісних водоростей української флори, рекомендованих до включення у четверте видання ЧКУ. Їхні описи, номенклатурна історія, екологічні особливості, типологічна приуроченість. огляд інформації про поширення в Україні та світі.

The pagan Greco-Roman past - the main source of inspiration for the late Roman author of Etruscan origin Virgil. The place of the motif of blood and kinship, universal empathy for the fate of humanity in the literary work of Dante and Kotlyarevsky.

Study of the AEO institution’s development in the legislation of the EU and Ukraine. Functions of AEO and related differences in ways and means of introducing this institution. Development of partnerships between customs authorities and businesses.

The development of the AEO Institute in the legislation of the EU and Ukraine. Differences in the perception of the role and functions of AEO. Development of partnerships between customs authorities and business in the concept of a trusted trader.

The relationship between aerobic physical activity in nature as compensation for behavior. Physical activity in nature, also called green exercise, is important in the context of human health research. Aerobic exercise regimen in disease prevention.

The method of aerodynamic condition of the aircraft on the thermal fields was developed. There are identified diagnostics the regularities of formation of temperature gradients in the boundary layer of air that occurs after damage of external contours.