XXI International Scientific and Practical Conference «Modern science: actual problems»

MODERN SCIENCE: ACTUAL PROBLEMS Proceedings of the XXI International Scientific and Practical Conference 30 September – 1 October 2025 MANCHESTER. UK 2025 UDC 001.1 BBC 1 XXI International Scientific and Practical Conference «Modern science: actual problems», September 30 – October 1, 2025, Manchester. UK. 38 p. ISBN 978-91-65424-40-1 DOI https://doi.org/10.5281/zenodo.17287575 Publisher: «SC. Scientific conferences» Main organization: Editor: Hans Muller Layout: Ellen Schwimmer The conference materials are in the public domain under the CC BYNC 4.0 International license. The publisher is not responsible for the materials published in the collection. All materials are provided in the author's edition and express the personal position of the participant of the conference. The sample of the citation for publication is Gugnin Aleksandr, Lisnievska Yuliia ANTI-ADVERTISING IN THE HOTEL BUSINESS // XXI International Scientific and Practical Conference «Modern science: actual problems», September 30 – October 1, Manchester. UK. Pp.9-11, URL: https://sconferences.com Contact information Website: https://sconferences.com E-mail: [email protected] Content Economic sciences Adela Culani, Nora Malaj, Remzi Keco ISSUES OF ETHICS AND CORRUPTION IN EDUCATIONAL SYSTEM 3 Historical sciences Nahid Vəzir THE HASHSHASHINS: A RADICAL SECT IN ISLAM AND THE MIDDLE EAST 10 Mathematical sciences G.T. Körpebay CONTROLLABILITY AND OPTIMAL RAPIDITY OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH PHASE AND INTEGRAL CONSTRAINTS 13 Abbasov Zafar Duman oglu SOLUTION OF A SINGLE BOUNDARY PROBLEM FOR AN N-DIMENSIONAL PARALLELEPIPED USING FOURIER METHODS 15 Pedagogical sciences Medetbekova Aisulu, Almat Tassybekov, Didar Koibagarova ENSURING ACCESS TO EDUCATION FOR ALL: CHALLENGES AND SOLUTIONS OF AN INCLUSIVE APPROACH 19 Koibagarova Didar Kozhageldiyevna, Muratbayev Erlan Otanovich, Kornitskaya Veronika Igorevna INCLUSIVE EDUCATION: CURRENT STATUS, CHALLENGES, AND SOLUTIONS 22 Nuralieva Aknur Orazkhanovna, Kurmambaeva Orynbasar Mekibayevna, Kozhamkulova Ulbossyn Aymakanbetovna INCLUSIVE EDUCATION: ESSENCE, FEATURES, AND APPROACHES TO IMPLEMENTATION 26 Philological sciences Qerenfil Rzayeva JAFAR JABBARLI AS A PROPHET OF WOMEN'S FREEDOM AND DEFENDER OF WOMEN'S RIGHTS 29 Leyla Vezirova RULES AND TECHNIQUES FOR CREATING A GOOD IMPRESSION IN BUSINESS COMMUNICATION 33 Political sciences Kovinskyi Yanislav COMPARISON OF THE FEATURES OF PRESIDENTIAL ELECTION PROMOTION IN THE USA AND EUROPE 36 XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 3 Economic sciences Introduction The global education system, functioning like a self-winding clock yet playing an undeniable role in influencing even the most remote and seemingly insignificant layers of human society, is currently experiencing its most complex period worldwide. The intertwining of knowledge and scientific learning acquired through classical methods with contemporary approaches such as the mass adoption of artificial intelligence (a generator developed in recent years) together with the widespread use of advanced ISSUES OF ETHICS AND CORRUPTION IN EDUCATIONAL SYSTEM Adela Culani Agribusiness Direction, Agricultural University of Tirana, Albania Nora Malaj Department of Psychology and Sociology, Mediterranean University of Albania Remzi Keco Agribusiness Direction, Agricultural University of Tirana, Albania Abstract Education institutions are regarded as the most essential pillars of society due to their generative and formative mission in preparing new generations and fostering human capital development. However, fulfilling this mission faces serious challenges, among which ethical problems in education and the phenomenon of corruption stand out as some of the most pressing. Corruption in education has become a global issue with direct consequences on the quality of knowledge, the credibility of academic institutions and the socio-economic development of nations. This paper seeks to highlight, through a critical review of the literature and practical cases, the most frequent ethical problems and corrupt practices observed in the education system, with a particular focus on both the Albanian experience and the international context. Specifically, it addresses issues related to academic integrity among faculty members, plagiarism and the authenticity of intellectual outputs, external influences on the evaluation of staff and institutions, as well as the abuse of managerial positions and financial resources. The analysis identifies the mechanisms and factors that create fertile ground for corruption in education, including lack of transparency, institutional weaknesses, and failures of accountability and control systems. In this regard, the paper emphasizes the necessity of a combined approach legal, institutional, and cultural to strengthen academic ethics and reduce opportunities for corrupt practices. The implications of such violations are profound: they lower the quality of teaching, undermine meritocratic models of professional development, distort the educational process, and lead to misuse of funds allocated for improving academic infrastructure. Consequently, students are deprived of their right to benefit from facilities and conditions comparable to those in developed countries. Strengthening academic ethics and combating corruption in education require the active engagement of multiple stakeholders, including policymakers, higher education leaders, faculty members, students, and civil society. Building a culture of integrity cannot rely solely on legal frameworks, but must be supported by continuous training, ethical awareness campaigns, transparent recruitment and promotion processes, and the integration of values based education across curricula. Only through a holistic and participatory approach can higher education institutions foster an environment where ethical conduct is not only promoted but also practiced as a fundamental cornerstone of academic and social progress. The study concludes that ethical problems tend to emerge wherever clear rules and procedures are absent, and that only an education system rooted in transparency, accountability, and high integrity can ensure sustainable, fair, and globally competitive development. Keywords: Ethics, Education System, Corruption, Transparency, Digitalization in Education. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 4 technology, the speed and relativity of information, has also brought about several ethical challenges within the education system. At their core, these ethical issues are driven by long-standing objectives, but are now being pursued through new methods of implementation. This makes it more difficult to fully realize the learning process in the education system in accordance with established standards. An important foundation for the development of countries, among other factors, lies in the younger generations in particular and the education system in general. However, an education system that is rooted in ethics is essentially a system of moral principles, norms, and rules of human behavior in society. In recent years, violations of ethics have become a matter of concern not only because of the disruptions they cause, but also due to the spread of such violations as a trend. The dualism of ethics in the education system is evident: on the one hand, the system is affected by unethical practices and corruption; on the other hand, education is regarded as an important sector with a solid foundation for instilling ethics and anticorruption values. [1]. This duality influences the transmission and development of ethics and anticorruption principles among the key groups within the education system, though it creates a fragile transfer. For this transmission to be successful in the fight against unethical practices and corruption, clear norms and rules are needed, along with transparent procedures and a specific policy framework for every step that is taken. Ethical challenges in education In the education system, issues of unethical behavior are seen as significant aspects that negatively affect the entire chain of teaching and learning. This perspective requires enhanced skills in management, monitoring, and auditing, but also awareness and training of administrative staff, teachers’ organizations, parents, trade unions, and civil society. It is also necessary for the public to have full and transparent access to information, which constitutes an irreplaceable measure for building participation and social oversight. All these measures make it possible not only to identify unethical and corrupt practices, but also to pursue and enforce penalties against them. Ethics in the education system is essential to ensure fairness, integrity, and respect for all actors involved students, teachers, parents, and institutions. [2]. However, there are several common ethical issues encountered within this system. Below are some of the most frequent ethical problems in education: Favouritism and discrimination – Teachers or administrators may show preferential treatment toward certain students (e.g., based on family connections, gender, or social status), thereby undermining equality. Corruption and bribery – Practices such as giving grades in exchange for money or gifts, obtaining personal benefits in the name of education, or misusing public funds. Plagiarism and lack of academic integrity – Cheating on exams, purchasing ready-made assignments or copying them from the internet, and disregarding authors’ rights. Lack of professionalism by teachers – Inappropriate behavior, insults, the use of psychological/physical violence, or abuse of authority. Conflict of interest – Cases where a teacher provides paid private lessons to their own students, or when decisions are made to serve personal interests rather than the educational community. Inequality in educational opportunities – Differences between students in urban and rural areas, or between those with disabilities and others. Violation of student privacy – Disclosing personal data or using it without consent, or exposing grades publicly. Manipulation of results – Altering grades or reports to satisfy parents, administrators, or other institutions. Ethics in the use of technology – The use of devices for cheating, lack of control over online content, and the improper use of artificial intelligence in learning. Neglect of the educational role – Focusing only on academic achievements while leaving behind the civic, ethical, and social education of students. Ethics in education is one of the main pillars that determines the quality of a society, since it is through the educational system that the citizens of the future are shaped. Factors affecting ethics in education In the new millennium, ethical challenges in education are no longer limited to the traditional relationship between teacher and student, but have expanded to include technology, globalization, social diversity, and the commercialization of education. These changes make a deeper and more sensitive approach to ethics necessary, in order to preserve the integrity of the educational process and to ensure XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 5 social justice. For this reason, we must take into account and highlight several important factors, such as: The pressure of globalization and academic competition. [3] In the 21st century, pupils and students no longer compete only within the borders of their own country, but in a global knowledge market. This reality has often increased the pressure to achieve rapid and high results, leading to the rise of phenomena such as plagiarism, manipulation of results, and the misuse of scientific work. From this perspective, the ethical challenge lies in creating an academic culture where the learning process is valued more than the final grade or diploma. Technology and new ethical dilemmas. [4]. The growing role of technology, and especially of artificial intelligence, has brought great benefits to the learning process, but at the same time it has opened up new ethical issues. Copying materials from the internet, using artificial intelligence to prepare readymade assignments, and cyberbullying are just some of the challenges that call for an ethical digital education. Teachers of the new millennium must educate not only in academic content, but also in the honest, critical, and responsible use of technology. Diversity, equality, and social inclusion Another ethical issue that is becoming increasingly evident is the equal treatment of pupils and students. Economic inequalities, gender discrimination, the exclusion of people with disabilities, and ethnic differences are often reflected in the school environment. In the new millennium, any form of unequal treatment is ethically unacceptable, since global society regards education as a universal right. Schools and universities must become spaces where the dignity of every individual is respected. Commercialization of education and the loss of values In recent decades, education has increasingly been turned into a commercial service. Private universities often follow a profit-driven logic, placing academic quality and their social mission in the background. In this context, the ethical problem that arises is the risk of transforming knowledge into a market commodity, where diplomas are bought rather than earned. A society that accepts this model loses faith in education as a driver of development and social justice. The role of the teacher as an ethical mentor The teacher of the new millennium is not only a transmitter of information but also a mentor who guides students in building character, integrity, and civic responsibility. The problem arises when teachers themselves commit ethical violations whether through corruption, discrimination, or abuse of authority. This is a double harm, because not only is the educational process damaged, but also the moral model that students should follow is destroyed. Social responsibility and sustainability. The ethics of education in the new millennium do not stop at the individual, but extend to society and the environment. Education must prepare citizens who think not only about their personal careers, but also about the contribution they make to their community and to the protection of the planet. An educational system that does not cultivate this ethical awareness risks producing generations disconnected from social and ecological realities. Taking into account the above factors, we may say that democratic countries, with their priority interest in the qualitative development of education, show great and complex attention on the part of society to achieve education free of ethical probems that would affect not only the economy, but also the individuals of the future, who would no longer be valued for their personal qualities and achievements. The failure to respect and uphold ethical standards is considered highly significant for a democratic society. In education in particular, it is regarded as a threat to the future development of a country. Among other things, Holweger mentions that certain metaethical reflections can foster a much deeper understanding of normative ethics, mitigate what is referred to as “teacher relativism,” and help educators address the related issue of “student relativism” in a more effective and responsible manner. [5]. In addressing issues of unethical behavior and corruption over the past 4–5 years, the World Education Forum has emphasized that these matters are particularly dangerous because: • they cause great harm, as their effects are long-term; • they prevent equal access to both quantitative and qualitative education; • they have severe consequences for poverty, since they either block access to education or impoverish its quality, thereby giving communities fewer opportunities to escape poverty; • they cannot coexist with one of the most important goals of education to educate citizens who respect the law and human rights; XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 6 • the true foundations of society are “undermined” if children come to believe that personal effort and quality are unimportant, and that success is achieved through manipulation, favoritism, and bribery. At the World Education Forum, over the past 4–5 years, important themes have continuously been addressed, such as: • One generation – what is needed to transform education? • Poverty in learning? • How should we maintain vision, respond to changing circumstances, and implement plans while education is being transformed? • How countries have sought to re-establish youth participation in education, including the effective use of distance learning where necessary. • What complementary strategies have been used to address learning loss? • How countries have addressed the needs of the most vulnerable and disadvantaged? • Measures to support the well-being of school communities. According to published statistics and information, there is a clear commitment that varies according to the economic strength and experiences of different countries. In some places more strongly, and in others less, there are positive results of value for education in general and for individual countries in particular. I am referring to the work carried out in Albania in the framework of implementing the abovementioned initiatives. In Albania, we consistently observe year-on-year improvements in curricula, accompanied and supported by the competencies and adaptation of teachers to these changes; the employment of teachers through meritocracy; the reduction of the number of students per class through the restoration and expansion of school facilities; the decrease in the number of combined classes; the annual increase in the number of assistant teachers, thereby attracting more children with special needs into the educational system; the achievement of a very low index of bullying in educational environments; the growing involvement of the private education sector; the expansion of the private education sector in line with educational standards and requirements; the increase in departments according to local needs and resources; the professional orientation of secondary and higher education in accordance with labor market demand in the country; and more. However, despite the entirety of the above commitments and the maximum engagement of institutions and stakeholders, we must acknowledge that issues of unethical conduct and corruption in education can appear in various forms: unethical behavior by teachers or professors; the improper use of funds allocated for improving infrastructure and teaching materials for the benefit of pupils or students; the securing of grades and good exam results without merit; appointments and promotions that are not based on professional standards of meritocracy, but instead on political influence, nepotistic ties, or other corrupt forces. Issues of unethical conduct and corruption in the education sector may also include bypassing the rules and criteria for licensing and accrediting educational institutions, making appointments to leadership positions on the basis of connections and “nepotism,” corruption in procurement and recruitment processes, or even the selling of ready-made exam answers. The implications of such violations are serious, as they can lead to a decline in the quality of teaching, or worse, the “education” of students in a distorted and flawed model that undermines meritocracy. The misuse of funds allocated for the improvement of academic infrastructure reduces the quality of infrastructure and deprives students of the right to benefit from facilities and equipment that are increasingly modern and aligned with the standards of developed countries. Ethical problems can be encountered anywhere there is a lack of clearly defined rules and procedures. Due to insufficient oversight and inadequate punitive measures, the likelihood of unprofessional and unethical behavior is greater, thereby enabling teachers and professors to accept “fees for ordinary services” as well as bribes in exchange for special attention to particular students. [6]. The issues of ethics and corruption within the framework of the Albanian educational system have begun to be discussed and analyzed in a broader context. The Ministry of Education and Sports has acknowledged the existence of problems related to ethics and corruption in the education system. For this reason, they have made ethical and anti-corruption issues a special priority in their program. Measures to prevent unethical and corrupt practices in the educational system can be divided into the following main categories: • Improvements in the evaluation and management of defining and interpreting unethical behavior; • Necessary and direct measures to realistically prevent unethical and corrupt practices; XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 7 • Punitive measures against individuals who do not act in compliance with ethical rules, regulations, and laws. However, ethical and anti-corruption standards are increasingly showing signs of being broken, eroded, and disregarded in their protective role in general, and particularly in the education system, due to new phenomena of social development specifically, informatization and artificial intelligence with all their derivatives. Digitalization and ethics Specifically, informatization and artificial intelligence, along with all their derivatives, have a considerable impact. [7]. The development of the world up to now, in a simple figurative sense, may be said to have progressed mathematically, but the development of the informatized world in recent decades has advanced geometrically, and with the rise of artificial intelligence in recent years, this development has surpassed the capacity of the normal human mind. The results, not infrequently, astonish even the very scientists who have been working on these developments for decades. Yet, beyond the positive aspects, this development closes off certain paths of communication with ethics and anti-corruption in their current form, demanding their transformation, but also their protection during the transitional period from unethical behavior and corruption. There are dozens of questions related to informatization, and hundreds concerning artificial intelligence. But let us remain with the “classical” (so called for what it represents as a relationship). A pupil, a student or a participant in a meeting carries with them a mobile phone and beyond that communicates through it. Is this action unethical? In Albania, in such cases there are two phases. First, the student is publicly warned, even if they have not disturbed anyone. Second, in school settings, the mobile phone is confiscated and placed on display at the teacher’s desk. Is the action of the person leading the process ethical? People under the age of 40 generally do not consider the leader’s behavior ethical. People over the age of 40 (+/–) do consider it ethical. But what if the same groups were using an invisible earpiece something that is already widely possible, at least in Albania? In that case, the leader would not notice it. And what if, through the earpiece, the individual received information in order to respond to the issues raised in the process in which they were participating? This raises the question: are we prepared to determine what is ethical and non-corruptive, and what we are not prepared for? One fact is clear that the results of developments in the fields of informatics and artificial intelligence are advancing so rapidly that they demand a comprehensive mobilization for the determination of new ethical norms, which must take into consideration these global developments in informatics and artificial intelligence. For this reason, at the World Education Forum, held in London in 2024 at the invitation of the Government of the United Kingdom, the focus was on the use of artificial intelligence in education, on strategies that have proven most successful in advancing education, and on balancing vocational and academic learning in order to better develop the potential of young people challenges that are central to education today across the world. [8]. So far, the process has concentrated on the creation of study groups to achieve a proper understanding and implementation of the innovations brought by informatization and artificial intelligence. This is a major battle. To draw a parallel, military battles remind us that large aircraft could not venture toward new horizons without being accompanied by smaller protective planes that consolidate their journey. [9] Similarly, ethics in general, and the fight against corruption in particular, are the necessary companions of this development in information technology and artificial intelligence. For these to be effective, ethical norms must be established not in a fragmented way, but as a coherent whole. Globalization has minimized borders. Allow me to say that the innovations of the informatization process know no boundaries. I illustrate this idea with the most recent development in Albania, a relatively young democracy that is striving strongly for integration into the European Union. Recently, in the composition of the new government created in 2025, Albania has appointed a virtual minister named Diella (the first case in the world). XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 8 She is part of artificial intelligence and, as such, communicates through the media, government meetings, discussions, and more. Diella, the World’s First Artificial Intelligence Minister Fighting Corruption in Albania, oversees public procurement in order to curb corruption. Albania has taken a bold step by appointing Diella, an artificial intelligence assistant, as a digital cabinet minister responsible for public procurement. The idea is simple: to use technology to fight corruption and to make government contracts more transparent. Since January, Diella whose name means “Sun” in Albanian has been working behind the scenes on the e-Albania platform. She is already helping citizens with almost all government services, using voice commands to guide them through documents, applications, and inquiries, all without the need to visit a government office. The first minister to exist only in digital form will now take responsibility for managing public tenders. Decision making power in awarding government contracts will gradually be transferred from human ministries to artificial intelligence. Diella will review bids and select winners purely on the basis of merit, ensuring that all public spending through tenders is “100 percent transparent.” This approach is not only about modernization; it is an attempt to address the deeply entrenched corruption in Albania’s public procurement system. Historically, public tenders in Albania have been undermined by accusations of bribery and favoritism. The country has also been cited as a hub for money laundering by international criminal networks. This situation naturally raises several questions: Can algorithms truly surpass human oversight in curbing corruption? Will Albania become a model for AI in governance, or might this turn into a cautionary tale? Whether Diella becomes a political success or a controversial experiment remains one of Europe’s governance stories to watch. That is why I mentioned earlier that we live in a Borderless world. I referred to two extreme examples: the student with a mobile phone and the virtual minister. They are extremes to each other, but together they highlight the vast gap that must be filled by ethicists and society as a whole, in order to elevate ethics and the fight against corruption to the level of social development. On our journey together, we work on designing and implementing curricula, on assessment, on publications, on teacher training, and on raising the standards of teaching and learning all within existing ethical norms and in an open fight against corruptive phenomena in education. We create coherent solutions that are scalable, sustainable, and with a record of success working in partnership with local teams to develop knowledge and capacity. However, in my view, ethics in education and the fight against corruption must adapt to the rapid global developments in technology, and should not be reduced to slogans based on outdated frameworks. Unleashing the Democratic Power of Digital Citizenship: The European Year of Digital Citizenship Education 2025 As we move deeper into the digital age, how can we ensure that everyone has the necessary skills to participate responsibly, safely, and effectively in the digital world? An example of this is the European Year of Digital Citizenship Education 2025, which seeks to answer this question by promoting digital citizenship education throughout Europe. This European education initiative, endorsed by 46 countries, aims to equip citizens with the skills needed to thrive in a digitally connected society, while fostering a sense of shared responsibility, democratic participation, and human rights online. [10]. Unleashing the Democratic Power of Digital Citizenship: What is digital citizenship education? Digital citizenship education goes far beyond teaching how to use digital tools. It introduces values, behaviors, skills, and knowledge that enable people to become informed, active, and ethical participants in the digital world. Making digital citizenship an essential element of education systems requires a focus on several areas, such as: • Critical thinking and digital literacy • Respect for digital rights and freedoms • Active participation and civic engagement • Safety and wellbeing in the digital world Initiatives like the European Year of Digital Citizenship Education are vital because, while digital technologies give people unprecedented access to information, education, and communication, they also XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 15 Введение. Метод разделения переменных или метод Фурье, является одним из наиболее распространенных методов решения уравнений с частными производными. Метод Фурье позволяет изучать простейщие процессы к которым сводятся гиперболические, параболические и эллиптические типы уравнений. Как известно, задачу математической физики называют поставленной корректно, если ее решение существует, единственно и непрерывно зависит от данных задачи [1,2,3,7,8]. Для определения собственных значений и собственных функции многомерных эллиптических операторов, допускающих разделение переменных, применяется метод Фурье. Постановка задачи. Пусть независимые переменные разделены на две множества: 𝑥=(𝑥1,𝑥2,...,𝑥𝑘), 𝑦=(𝑦1,𝑦2,...,𝑦𝑙) и 𝛺⊂𝑅𝑘 - область изменения х и 𝐷⊂𝑅𝑙 область S S  D изменения у. Обозначим через и границы областей и соответственно. Тогда (𝑆×𝐷)∪(𝛺×𝑆′) есть граница области 𝛺×𝐷⊂𝑅𝑘+𝑙. Рассмотрим следующую краевую задачу на собственные значения для уравнения эллиптического типа[1-7]. 𝐿𝑢≡σ(𝑎𝑖𝑗(𝑥) 𝑛 𝑖,𝑗=1 𝑢𝑥𝑖)𝑥𝑗 +σ𝑎𝑖 𝑛 𝑖=1 (𝑥)𝑢𝑥𝑖+𝑎(𝑥)𝑢=𝑓(𝑥),𝑥∈𝑄, (1) Lu Mu u  += (𝛼𝑢+𝛽𝜕𝑢 𝜕𝑛)ቚ𝑆×𝐷 =0, (𝛾𝑢+𝛿𝜕𝑢 𝜕𝑛)ቚ𝛺×𝑆′=0 (2) L M ,  где и -эллиптические операторы, не зависящие соответственно от у и х; функции ,    3 не зависят от у , а не зависят от х . SOLUTION OF A SINGLE BOUNDARY PROBLEM FOR AN N-DIMENSIONAL PARALLELEPIPED USING FOURIER METHODS Abbasov Zafar Duman oglu Honorary Professor of the Department of Mathematical Analysis, Ganja State University ORCID: 0009-0005-2769-7922 РЕШЕНИЕ ОДНА КРАЕВОЙ ЗАДАЧИ ДЛЯ N-МЕРНОГО ПАРАЛЕЛЕПИПЕДА МЕТОДАМ ФУРЬЕ Аббасов Зафар Думан оглу почетный профессор кафедры математического анализа Гянджинского государственного университета ORCİD: 0009-0005-2769-7922 Abstract The method of disjoint variables or the Fourier method allures us to study simplest processes to which one leads hyperbolic, parabolic and elliptic types of equations. For defining of Eigen values and Eigen functions of multidimensional elliptic operators alluring disjoining of variables if is applied the Fourier method. Аннотация Для определения собственных значений и собственных функции многомерных эллиптических операторов, допускающих разделение переменных, применяется метод Фурье. Метод разделения переменных или метод Фурье, позволяет изучать простейщие процессы к которым сводятся гиперболические, параболические и эллиптические типы уравнений. Keywords: Furry method, border issue, special function, separation, indecent, the equation, frontier, multidimensional, border, elliptic operator, of the same size, true and s. Ключевые слова: Метод Фурье, граничные задачи, собственные функции, независимые, уравнения, выражение, краевую, многомерных, граница, эллиптические операторы, одномерные, вещественны и др. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 16 Будем искать собственные функции задачи (1) -(2) в виде произведения 𝑢(𝑥,𝑦)=𝑋(𝑥)⋅𝑌(𝑦) (3) Подставляя это выражение в уравнение (1), получаем два уравнения: 𝐿 𝑋=𝜉𝑋 (4) 𝑀 𝑌=𝜂𝑌 (5)   где и неизвестные параметры. Для вывода граничных условий для функций 𝑋(𝑥) и 𝑌(𝑦) подставим выражения (4), (5) в равенство (2), в результате имеем: (𝛼𝑋+𝛽𝜕𝑋 𝜕𝑛)ቚ𝑆=0, 𝑥∈𝑆 (6) 𝛾𝑌+𝛿𝜕𝑌 𝜕𝑛ቚ𝑆′=0, 𝑦∈ 𝑆/ (7) Итак, краевая задача (1)-(2) распалась на две краевые задачи на собственные значения (4)- (6) и (5)-(7) с меньшим числом независимых переменных. Обозначим через 𝜉𝑘, 𝑋𝑘(𝑥),𝑘=1,2,... и 𝜂𝑗, 𝑌𝑗(𝑦), 𝑗=1,2,... все собственные значения и L M собственные функции операторов и соответственно. В силу (3) имеем 𝜆𝑖𝑗 =𝜉𝑖+𝜂𝑗, 𝑢𝑖𝑗 =𝑋𝑖(𝑥)𝑌𝑗(𝑦), 𝑖,𝑗=1,2,... (8) Задача 1. Рассмотрим краевую задачу 𝜕2𝑢 𝜕𝑥2+𝜕2𝑢 𝜕𝑦2+𝜕2𝑢 𝜕𝑧2=−𝜆𝑢, 𝑢|𝜕𝑄 =0 (9) на собственные значения для прямоугольного параллелепипеда 𝐴=(0,𝑎)×(0,𝑏)×(0,𝑐) с границей 𝜕𝑄. В соответствие с общей схемой метода Фурье эта задача распадается на три одномерные краевые задачи: 𝑋″=−𝜉𝑋, 𝑋(0)=𝑋(𝑎)=0 , (10) 𝑌″=−𝜂𝑌, 𝑌(0)=𝑌(𝑏)=0 , (11) 𝑍″=−𝛾𝑍, 𝑍(0)=𝑍(𝑐)=0 , (12) Собственные значения и соответствующие им собственные функции этих краевых задач вычислены (задача Штурма – Лиувилля) 𝜉𝑖=ቀ𝑖𝜋 𝑎ቁ2,𝑋𝑖(𝑥)=ට2 𝑎𝑠𝑖𝑛𝑖𝜋𝑥 𝑎,𝑖=1,2,... (13) 𝜂𝑗=ቀ𝑗𝜋 𝑏ቁ2,𝑌𝑗(𝑦)=ට2 𝑏𝑠𝑖𝑛𝑗𝜋𝑦 𝑏,𝑗=1,2,... (14) 𝛾𝑘=ቀ𝑘𝜋 𝑐ቁ2,𝑍𝑘(𝑧)=ට2 𝑐𝑠𝑖𝑛𝑘𝜋𝑧 𝑐,𝑘=1,2,... (15) Учитывая равенства (13), (14) и (15) в формуле (8) получаем следующие собственные значения и собственные функции краевой задачи (9): 𝜆𝑖𝑗𝑘 =𝜋2ቆ𝑖2 𝑎2+𝑗2 𝑏2+𝑘2 𝑐2ቇ, 𝑢𝑖𝑗𝑘(𝑥,𝑦,𝑧)= 2ξ2 ξ𝑎𝑏𝑐𝑠𝑖𝑛𝑖𝜋𝑥 𝑎𝑠𝑖𝑛𝑗𝜋𝑦 𝑏𝑠𝑖𝑛𝑘𝜋𝑧 𝑐,𝑖,𝑗,𝑘=1,2,... (16)   i jk  В частности, множество собственных значений этой задачи не пусто и не имеет конечных предельных точек; эти собственные значение вещественны и конечной кратности; собственные функции ሼ𝑋𝑖ሽ,൛𝑌𝑗ൟ,ሼ𝑍𝑘ሽ можно выбрать вещественными и ортонормальными: 𝑋𝑖∈𝐶2(ሾ0,𝑎ሿ),𝑌𝑗∈𝐶2(ሾ0,𝑏ሿ),𝑍𝑘∈𝐶2(ሾ0,𝑐ሿ) Обобщенное решение: Теперь перейдем к доказательству существования решений (1), (2) и (9). Для этого воспользуемся методом Фурье, который заключается в следующем: решение смешанной задачи находится в виде ряда по собственным функциям соответствующей эллиптической краевой задачи. ()ux Пусть - обобщенная собственная функция первой краевой задачи 𝑑𝑖𝑣(𝑎𝛻𝑢)−𝑏𝑢=𝜆𝑢, 𝑥∈𝜕𝑄 (17) 𝑢(𝑥)|𝜕𝑄 =0 ( ) 0  = или третьей краевой задачи XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 17 𝑑𝑖𝑣(𝑎𝛻𝑢)−𝑏𝑢=𝜆𝑢, 𝑥∈𝜕𝑄 ቀ𝜕𝑢 𝜕𝑛+𝜎𝑢ቁቚ𝜕𝑄 =0 , 𝑥∈𝜕𝑄 (18) Рассмотрим ортонормированную в 𝐿2(𝑄) систему 𝑢1,𝑢2,...,𝑢𝑘 состоящую из всех 12 , ,..., k    обобщенных собственных функций задачи (17) или соответственно задачи (18): последовательность соответствующих собственных значений. Кроме того рассмотрим краевую задачу на собственные значения 𝜕2𝑈 𝜕𝑥1 2+𝜕2𝑈 𝜕𝑥2 2+...+𝜕2𝑈 𝜕𝑥𝑘 2=−𝜆𝑈, 𝑈|𝜕𝑄 =0 (19) n для - мерного паралелопипеда 𝐴=(0;𝑎1)×(0;𝑎2)×...×(0;𝑎𝑘)  с границей [6-8]. В соответствие с общей схемой метода Фурье это задача распадается на следующие одномерные краевые задачи: 𝑋1 ″=−𝜉1𝑋1, 𝑋1(0)=𝑋1(𝑎1)=0 (20) 𝑋2 ″=−𝜉2𝑋2, 𝑋2(0)=𝑋2(𝑎2)=0 (201) …………………………….. 𝑋𝑘 ″=−𝜉𝑘𝑋𝑘, 𝑋𝑘(0)=𝑋𝑘(𝑎𝑘)=0 (20к) Собственные значения и собственные функции этих краевых задач вычислены (задача Штурма-Лиувила) 𝜉𝑘1=ቀ𝑘1𝜋 𝑎1ቁ2, 𝑋𝑘1=ට2 𝑎1𝑠𝑖𝑛𝑘1𝜋𝑥 𝑎1,𝑘1=1,2,... (211) 𝜉𝑘2=ቀ𝑘2𝜋 𝑎2ቁ2,𝑋𝑘2=ට2 𝑎2𝑠𝑖𝑛𝑘2𝜋𝑥 𝑎2,𝑘2=1,2,... (212) ……………………………………….. 𝜉𝑘𝑛=ቀ𝑘1𝜋 𝑎1ቁ2,𝑋𝑘𝑛=ට2 𝑎𝑛𝑠𝑖𝑛𝑘𝑛𝜋𝑥 𝑎𝑛,𝑘𝑛=1,2,... (21п) Из (211), (212),…,(21п) в соответствие с формулами (8) имеем: 𝜆𝑘1,𝑘2,...,𝑘𝑛=𝜋2ቀ𝑘1 2 𝑎1 2+𝑘2 2 𝑎2 2+...+𝑘𝑛 2 𝑎𝑛 2ቁ=𝜋2σቀ𝑘𝑖 𝑎𝑖ቁ2 𝑛 𝑖=1 (22) В частности множество собственных значений ൛𝜆𝑘1𝑘2,...,𝑘𝑛ൟ этой задачи не пусто и не имеет конечных предельных точек; собственные значения вещественные и конечной кратности; собственные функции ൛𝑋𝑘1(𝑥)ൟ,൛𝑋𝑘2(𝑥)ൟ,...,൛𝑋𝑘𝑛(𝑥)ൟ можно выбрать, вещественными и ортонормальными: 𝑋1(𝑥)∈𝐶2(ሾ0,𝑎1ሿ),𝑋2(𝑥)∈𝐶2(ሾ0,𝑎2ሿ),...,𝑋𝑛(𝑥)∈𝐶2(ሾ0,𝑎𝑛ሿ) 𝑢𝑘1𝑘2...𝑘𝑛(𝑥1,𝑥2,...,𝑥𝑛)=ඥ2𝑘 ඥ𝑎1𝑎2...𝑎𝑘𝑠𝑖𝑛𝑘1𝜋𝑥1 𝑎1𝑠𝑖𝑛𝑘2𝜋𝑥2 𝑎2...𝑠𝑖𝑛𝑘𝑛𝜋𝑥𝑛 𝑎𝑛= =ቀ 2𝑛 𝑎1𝑎2...𝑎𝑛ቁ1 2ς𝑠𝑖𝑛𝜋 𝑎𝑖 𝑛 𝑖=1 (𝑘𝑥)𝑖 ,( 𝑖=1,2,...,𝑛) (23) В частности, для п -мерного куба 𝐴𝑘=(0;𝑎)×(0;𝑎)×...×(0;𝑎) с границей 𝛺, собственные значения (22) и соответствующее решение принимает следующий вид: 𝜆𝑘1𝑘2...𝑘𝑛=𝜋2ቀ𝑘1 2 𝑎2+𝑘2 2 𝑎2+...+𝑘𝑛 2 𝑎2ቁ=𝜋2 𝑎2σ𝑘𝑖2𝑛 𝑖=1 (221) 𝑢𝑘1𝑘2...𝑘𝑛(𝑥)=ቀ 2𝑛 𝑎1𝑎2...𝑎𝑛ቁ1 2ς𝑠𝑖𝑛𝜋 𝑎𝑖 𝑛 𝑖=1 (𝑘𝑥)𝑖 ,(𝑖=1,2,...,𝑛) , 𝑥=(𝑥1,𝑥2,…,𝑥𝑛) ∈𝑆 (231) Можно доказывают, что для этом задачи существует бесконечное множество вещественных собственных значений: 𝜆1<𝜆2<⋯<𝜆𝑛<⋯ Собственные функции, удовлетворяющие условию (*), будем называют нормированными: ׬𝜌( 1 0𝑥)𝑋𝑘 2(𝑥)𝑑𝑥=1 (*) XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 18 Асимптотическое поведение собственных значений первой краевой задачи для оператора  Лапласа (оператора 𝐿=𝑑𝑖𝑣(𝑎𝛻)−𝑏 при 𝑎≡1,𝑏≡0) в кубе 𝐾𝑖=ሼ0<𝑥𝑖<𝑎,𝑖=1,2,...,𝑛ሽ с ребром 𝑎>0 можно дать аналогичным образом. Обобщенная собственная функция 𝑢(𝑥) первой краевой задачи для оператора 𝛥 в 𝐾𝑖, отвечающая собственному значению 𝜆, определяется как функция из 𝐻1(𝐾𝑖) удовлетворяющая  при всех из 𝐻1(𝐾𝑖) дождесту ׬𝛻𝑢𝛻𝜗𝑑𝑥 𝐾𝑖=−𝜆׬𝑢𝜗𝑑𝑥 𝐾𝑖. Заключение. Таким образом, решения корректно поставленных граничных задач для любого уравнения эллиптического типа всегда оказываются не менее гладкими, чем определяющие их функции. Это свойство решений граничных задач тесно связано с тем, что к граничным задачам приводит изучение установившихся (стационарных) физических процессов равновесий, являющихся конечным результатом предшествующего процесса выравнивания. Список литературы 1. Н.С.Кошляков, Э.Б.Глинер, М.М.Смирнов, Основные дифференциальные уравнение математической физики. Москва 1962, ст.768 2. В.П.Михайлов,Дифференциальные уравнения в частных производных. Москва 1976, ст. 392 3. В.С.Владимиров,Уравнения математической физики., Москва «Наука» 1981, ст.386 4. Тихонов А.Н. и Самарский А.А.,Уравнения математической физики М.,Наука 1977, ст.736 5. Соболев С.Л.,Уравнения математической физики.М., Наука 1966, ст.318 6. Аббасов З.Д, Уравнения математической физики , Баку-2014, ст. 254 7. Аббасов З.Д, Уравнения математической физики , Баку-2018, ст.380 8. Аббасов Зафар Думан., Применение метода Фурье к смешанно граничной задаче., Евразийский Союз Ученых( ЕСУ)#3(60),2019, ст.41-45 XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 19 Pedagogical sciences The modern education system only fully accepts those who meet its specific requirements, children with standard abilities who are able to study according to a common curriculum and achieve results that are normal for everyone. As a result, children with special educational needs often fall out of the general educational process, as the teaching staff of general education institutions do not have the necessary knowledge in the field of corrective and special education to work with them. Inclusive education is designed to solve this and many other problems in modern schools [1]. So what is inclusive education? Inclusive education (french “inclusif” - including, from the Latin word “include” - I include, I include) is a process of developing general education that implies the accessibility of education for all, including children with special needs. Inclusive education is based on an ideology that excludes any discrimination against children and ensures that all people are treated as equals, while also creating the necessary conditions for children with special educational needs. This is precisely the focus of the Republic of Kazakhstan's state policy in the field of education, which provides for the development of inclusive education as one of its priorities. Modern schools in Kazakhstan should become schools for all, where every child, regardless of their physical, intellectual, or social characteristics, is provided with the conditions for full-fledged learning and socialization. This is reflected in the works of domestic specialists, in particular in the textbook “Fundamentals of Inclusive Education” edited by A.T.Iskakova et al., which emphasizes the need to create an educational environment that takes into account the diversity of learners' needs and aims to eliminate all forms of discrimination against children with special educational needs [2]. Inclusive education is a step towards achieving the ultimate goal of creating an inclusive society that allows all children and adults, regardless of gender, age, ethnicity, abilities, presence or absence of developmental disabilities and HIV infection, to participate in and contribute to society. In such a society, differences are respected and valued, and discrimination and prejudice in politics and the daily activities of institutions are actively combated [3]. Today, inclusive education is becoming a reality, steadily “integrating” and “drawing in” all countries of the world. But at the same time, as it's becoming more common, inclusive education is bringing up a bunch of tough questions and new challenges for the education system. Unlike education systems abroad, where inclusion has a lot of experience and is backed by law, our country's inclusion is just starting to take shape and develop. Currently, 4.5% of children living in Kazakhstan are classified as having ENSURING ACCESS TO EDUCATION FOR ALL: CHALLENGES AND SOLUTIONS OF AN INCLUSIVE APPROACH Medetbekova Aisulu1 Candidate of Pedagogical Sciences Almat Tassybekov2 PhD, Director of Educational Programs Didar Koibagarova3 Speech and Language Therapist and Special Education Specialist Abstract The article discusses key issues and solutions related to the implementation of inclusive education in the general education system. Particular attention is paid to barriers that hinder the successful implementation of an inclusive approach: insufficient training of teachers, lack of an adapted educational environment, and weak interaction between participants in the educational process. The need for teachers to be psychologically and professionally prepared to work with children with special educational needs is emphasized. The principles of inclusion are revealed, as well as the role of the teaching staff and society in creating equal conditions for all children to receive education, regardless of their individual characteristics. Keywords: inclusive education, children with disabilities, educational environment, professional readiness of teachers, special educational needs, inclusion, equality in education, corrective pedagogy. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 20 disabilities and require special (remedial) education that meets their specific educational needs [4]. Unfortunately, however, the market for educational services for children with disabilities in our country is currently extremely limited, and in small towns and villages, children with disabilities are often excluded from the education system for purely economic reasons. Special (corrective) educational institutions remain the traditional form of education for children with disabilities. A significant part of the difficulties in teaching and raising children with disabilities is associated with an acute shortage of qualified personnel: speech therapists, psychologists, educators, and social pedagogues, as well as their insufficient level of training. After all, inclusion encompasses profound social aspects of school life: it creates a moral, material, and pedagogical environment adapted to the educational needs of any child, which can only be achieved through close cooperation with parents and the cohesive teamwork of all participants in the educational process. This requires people who are ready to change together with the child and for the sake of the child, not only the “special” child, but also the most ordinary child. For children with disabilities, the principle of inclusive education means that the diversity of the needs of students with disabilities must be matched by an educational environment that is the least restrictive and most inclusive for them. The implementation of this principle means that: ➢ All children should be included in the educational and social life of their local school; ➢ The goal of an inclusive school is to build a system that meets everyone's needs; ➢ In inclusive schools, all children, not just those with disabilities, should be provided with support that allows them to be successful, feel safe, and feel that they belong. Inclusive education cannot be organized on its own, it is linked to changes at the value and moral level. The problems of its organization in modern schools are primarily related to the fact that schools, as social institutions, are geared toward children who are able to keep up with the pace set by the standard curriculum, those for whom typical teaching methods are sufficient. The primary and important step in preparing the education system for the implementation of the inclusion process is the stage of psychological and value changes among its specialists and the level of their professional competencies. Already in the early stages of the development of inclusive education, the problem of the unpreparedness of teachers in mainstream schools (professional, psychological, and methodological) to work with children with special educational needs becomes acute. There is a lack of professional competencies among teachers to work in the inclusive sphere, as well as psychological barriers and professional stereotypes among educators. The main psychological “barrier” is the fear of the unknown, the fear of the harm of inclusion for other participants in the process, negative attitudes and prejudices, professional insecurity of the teacher, unwillingness to change, and psychological unpreparedness to work with “special” children. This poses serious challenges not only for the psychological community in the field of education, but also for methodological services, and most importantly, for the heads of educational institutions implementing inclusive principles. General education teachers need specialized comprehensive assistance from specialists in the field of corrective pedagogy, special and educational psychology, which will ensure understanding and implementation of approaches to the individualization of education for children with special educational needs. First and foremost, this means working with children with different learning abilities and taking this diversity into account in their pedagogical approach to each child. Teachers who already have experience working with the principles of inclusive education have developed the following methods of inclusion: ➢ Treat students with disabilities “like any other kids in the class”; ➢ Include them in the same activities, although set different tasks; ➢ Involve students in group work and group problem solving; ➢ Use active forms of learning - manipulation, games, projects, laboratories, field research. An inclusive educational community significantly changes the role of teachers. Teachers play a key role in unlocking the potential of each student, especially in an inclusive education setting. Effective teaching practices involve close collaboration with colleagues in an interdisciplinary environment, without a clear division between specialists in inclusive or general education. By engaging in various forms of communication with students, teachers gain the opportunity to better understand the individual characteristics of each child, build trusting relationships, and adapt the educational process to the needs of all learners. In addition, teachers participate in broad social contacts outside of school, including with social support resources and parents. This professional position allows teachers to overcome their fears and anxieties and reach a whole new level of professional mastery, understanding their students and their calling [4]. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 21 In conclusion, it is necessary to highlight eight principles on which not only inclusive education but also education as a whole is based: ➢ A person's value does not depend on their abilities or achievements; ➢ Every person is capable of feeling and thinking; ➢ Every person has the right to communicate and be heard; ➢ Diversity enriches all aspects of human life; ➢ Genuine education can only take place in the context of real relationships; ➢ All people need the support and friendship of their peers; ➢ For all learners, progress is more likely to be found in what they can do than in what they cannot do; ➢ All people need each other. It should also be noted that all children, regardless of their physical, social, intellectual, and other characteristics, must be included in the education system and raised alongside their peers. However, as experience abroad shows, achieving these goals will take a long time and, most importantly, the participation and interaction of all adults involved in the educational process who work with children with special educational needs. Only under this condition will it be possible to solve the problems of inclusive education. Inclusive education is a progressive method of teaching that has great prospects in modern society, and this gives hope that every child with disabilities will be able to realize their right to a quality education adapted to their abilities and needs, find their place in life, and realize their life chances and potential. Conclusion, inclusive education is not only a pedagogical model, but also an important step towards building a fair and equal society. For the effective implementation of inclusion, systemic changes in educational policy, the improvement of teachers' qualifications, and the elimination of infrastructural and methodological barriers are necessary. The main task of modern schools is to create an educational environment in which every child, regardless of their characteristics, can realize their potential, receive a quality education, and become a full member of society. Inclusive education is the path to a future where individuality, support, and cooperation are valued. References 1. Tassybekov A.E. The role of inclusive education in enhancing society's potential // II International Scientific and Practical Conference “Inclusive Education in Higher Education: Problems and Solutions”. 2025, 9-14 p. 2. Fundamentals of inclusive education: Textbook // A.T.Iskakova [et al.]. - Almaty: Balausa Publishing House, 2016, 320 p. 3. Mitchell D. Effective teaching technologies for special and inclusive education // Using scientifically based teaching strategies in an inclusive educational environment. Chapters from the book // Translated by I.S.Anikeev, N.V. Borisova Moscow, 2009. 4. Oralkanova I.A. Preparing Primary School Teachers for Work in an Inclusive Education Environment: Doctor of Philosophy (PhD) dissertation. Almaty: 2014, 210 p. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 22 According to the Law of the Republic of Kazakhstan “On Education”, education is a unified, purposeful process of upbringing and training that is a socially significant benefit and is carried out in the interests of the individual, family, society, and the state, as well as the acquisition of knowledge, skills, abilities, values, experience, and competencies of a certain scope and complexity for the purposes of intellectual, spiritual, moral, creative, physical, or professional development of the individual and the satisfaction of their educational needs and interests. In this law, the concept of “inclusive education” is defined as ensuring equal access to education for all learners, taking into account the diversity of special educational needs and individual abilities [1]. Inclusion in education is closely linked to processes of inclusion in society. As Z.A.Movkebayeva notes: "The inclusive approach currently represents nothing more than a social demand that has reached a certain level of economic, cultural, legal development of society and the state, where, based on the principles of humanism and tolerance, there is a rethinking of attitudes towards heterogeneous population groups, with recognition not only of their equal rights, but also of the obligation to provide them with opportunities equal to those of all other people, including in terms of access to education" [2]. The belief that education is one of the most important human rights and that it enables the formation of a just society is the basis for the concept of “inclusive education”. Therefore, all children have equal rights to education, and this cannot depend on their problems or personal qualities. Inclusive education (french: inclusif - including, latin: include - to include) is a term that describes the process of educating children with disabilities in general education institutions. Inclusive education is based on an ideology that excludes any discrimination against children, ensures equal treatment of all people, and creates special conditions for children with special educational needs. These are children with developmental differences, disabilities, or impairments [3, 4]. Inclusive learning and education implies support not only for boarding schools and special schools, but also for all other educational institutions. After studying in special institutions, particularly successful children can begin studying in general education schools, which will allow places to be provided for those children who were previously considered difficult and unteachable. INCLUSIVE EDUCATION: CURRENT STATUS, CHALLENGES, AND SOLUTIONS Koibagarova Didar Kozhageldiyevna1 President of the International Academy of Education Muratbayev Erlan Otanovich2 Director of Secondary School No. 184, Almaty Kornitskaya Veronika Igorevna3 English language teacher Abstract The stages of the development of inclusive education in the Republic of Kazakhstan and foreign countries, where conditions are created for all children, including children with disabilities, to receive an education, are considered. The concept of “inclusive education” in the Kazakh context is defined as ensuring equal access to quality education for all students, taking into account their individual characteristics and educational needs. Kazakhstan is actively implementing reforms aimed at developing an inclusive environment in educational institutions. Children with disabilities have the opportunity to study in general education schools on an equal basis with others, which contributes not only to the acquisition of knowledge but also to successful social adaptation. The main principles and factors of inclusive education in the Republic of Kazakhstan are reflected, including accessibility, equality, respect for individual differences, and cooperation among all participants in the educational process. For the successful implementation of the inclusive model, it is necessary to create appropriate conditions, both in society and in educational institutions. An important role is played by the training of teachers who are able to develop and implement effective inclusive practices, taking into account Kazakhstani legislation and international standards. Keywords: children with disabilities, inclusive education, stages, principles, factors. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 23 The modern education system is primarily focused on students who meet certain requirements and are able to study according to a program that is common to all. As a result, children with disabilities do not have the opportunity or conditions to participate in the general educational process. Inclusive education will help solve this problem. After all, the issue of educating children with disabilities is one of the most pressing challenges in modern Kazakhstani society. Inclusive education implies a stage in the development of general education in which the opportunity to acquire knowledge is available to everyone, especially children with disabilities. In other countries, this type of education has been developing for a long time and is enshrined in law. The essence of inclusive education is a system of views that does not allow any discrimination against children and also helps to create the necessary conditions in the educational environment that people need. From 1961 to 1980, Denmark and other Scandinavian countries undertook enormous social and educational work to help teachers understand and implement a multitude of individual initiatives that were not regulated by the authorities. Integration here gradually grew “from below”, initiated and supported by the social democratic movement and the country's positive social and economic development. And only when the country as a whole had practically and morally mastered the phenomenon of integration was it legalized: in January 1980, the Education Reform Act was passed, providing for the introduction of the principle of normalizing relations with persons with disabilities. By the end of the 20th century, in many countries around the world (the US, the UK, Sweden, Germany, Italy, and the Scandinavian countries), sending children to special (correctional) educational institutions was considered a last resort, when all other options had already been exhausted and had not produced the desired result. In the educational practice of these countries, the principle of an integrated approach is implemented - providing children with disabilities with the opportunity to study in a general education school together with ordinary children. At the same time, additional conditions for special support are created to facilitate learning. An important step in the development of inclusive education was the World Conference on Special Needs Education, held in Spain in 1994. At the conference, the Declaration on Principles, Policies, and Practices in Special Needs Education was adopted. The main goal of this document is to call on countries to establish educational institutions such as “schools for all”. Teachers in such educational institutions are guided by their personal conviction that differences between people are natural and that the process of acquiring knowledge should be adapted to the characteristics of the child, rather than the child having to adapt to a predefined definition of the pace and nature of learning. In special education, inclusion is understood as the process of increasing the participation of all citizens in society, especially those with physical disabilities. It involves the development and implementation of specific solutions that will enable every person to participate equally in academic and social life. The transformation of the special education system in a global context and the development of inclusive approaches in education are based, first and foremost, on key international legal acts - declarations and conventions concluded under the auspices of the United Nations (UN) and the United Nations Educational, Scientific and Cultural Organization (UNESCO) concerning human rights and the inadmissibility of discrimination on any grounds. Today, the main documents regulating inclusive education in the Republic of Kazakhstan are the Constitution of the Republic of Kazakhstan, the Code “On Public Health and the Health Care System”, the Law of the Republic of Kazakhstan “On Education”, and the Law “On the Rights of the Child in the Republic of Kazakhstan”. In addition, Kazakhstan is a party to international agreements such as the UN Convention on the Rights of Persons with Disabilities and the UN Convention on the Rights of the Child, which also serve as a legal basis for the implementation of inclusive education. The history of educating children with special needs in schools can be divided into the following stages: ➢ Mid-1960s - the “medical model”, which led to the isolation of people with disabilities; ➢ Mid-1960s to mid-1980s - the “normalization model”, which focused on integrating people with disabilities into public life; ➢ Mid-1980s to present - the “inclusion model”, i.e., inclusion. After analyzing the state of legislation in the Republic of Kazakhstan in the field of education, it can be concluded that creating conditions for inclusive education in modern Kazakhstan is possible and is gradually being implemented in practice. The state is taking measures to ensure equal access to quality education for all categories of students, including children with special educational needs. However, from the point of view of introducing inclusion into the educational process, the following difficulties may be encountered: the lack of the necessary regulatory framework and sufficient XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 24 funding, as well as the inertia of teachers and parents, who are burdened by stereotypes. Inclusion in education is reflected in the principles of making school education accessible to all children: ensuring physical access to schools for students with disabilities (transport, ramps, lifts), developing a flexible curriculum structure and a variety of educational methods to meet the needs of all students, including: ➢ the need for full and diverse personal growth and development, taking into account individual inclinations, interests, motivations, and abilities (personal success); ➢ the need for the individual to integrate organically into their social environment and participate fruitfully in the life of society (social success); ➢ the need for the individual to develop universal work and practical skills and be ready to choose a profession (professional success) [5]. A number of factors contributed to the emergence of an inclusive educational environment: ➢ Social issues: More and more children are being born with emotional and intellectual disorders, as well as autism and other disorders, yet they also need to receive an education, society is placing ever new demands on the accessibility and quality of education, there is a need to implement ideas for the humanization and democratization of society and to develop a “family policy” that involves parents in the educational process as subjects of learning, which manifests itself in responsibility for the education, upbringing, and development of children; ➢ Legislative and regulatory - ratification of legislative acts such as the UN Convention on the Rights of the Child of November 20, 1989, the UN Convention on the Rights of Persons with Disabilities of December 13, 2006, the Law of the Republic of Kazakhstan “On Education” of July 27, 2007, No. 319III, and other regulatory and legal acts serve as the legal basis for the implementation of inclusive education in the country; ➢ Theoretical - contemporary trends in science aimed at achieving the goal of developing a person's ability to live independently, forming motivation to achieve, actualizing the need for self-development, the concept of continuous education, the transition from a “medical” model of understanding disability to a “social” one. ➢ Practical trends: the active involvement of parents of “special” children in the educational process as educators, the emergence of the position of “inclusion coordinator-methodologist”, the creation of professional communities, the organization of round tables, scientific and practical conferences, and retraining courses for specialists in the field of supporting the inclusive educational process. ➢ Economic - the new educational system allows for the formation and increase of “human resources” thanks to the fact that people actively realize their potential, and individual developmental characteristics cannot prevent them from doing so. The education of students with disabilities can be organized either jointly with other students or in separate classes, groups, or organizations engaged in educational activities. It is assumed that children with developmental disabilities today do not necessarily need to be educated in special institutions: in a regular general education school, they can not only receive a better quality education, but also successfully adapt to life and fulfill their need for emotional and physical development. To implement inclusive education, attention must be paid to curricula, staff support and cooperation, measurement and evaluation, facilities and equipment, and ultimately, the creation of appropriate conditions in society. As a result, there is a growing need for teachers who are able to create and implement an inclusive educational environment in educational institutions, as well as work skillfully and productively in this environment with different groups of students. It is also important to develop the competencies of educational institution leaders to enable them to create and develop a corporate culture of a heterogeneous organization that ensures the inclusion of different social groups into a single community. Working with different groups of students undoubtedly requires the creation of specific conditions and the use of scientifically based methods, tools, and techniques of inclusive education. References 1. Law of the Republic of Kazakhstan “On Education” No. 319-III of July 27, 2007 (as amended as of April 2025). [Electronic resource]. URL: https://adilet.zan.kz/rus/docs/Z070000319_ (accessed on 16.09.2025). 2. Movkebayeva Z.A., Oralkanova I.A. Inclusion of children with disabilities in the general education process: a teaching aid. Almaty, 2014. - 241 p. 3. Movkebayeva Z.A., Denisova I.A., Orankova I.A., Zhakupova D.S. Methodological recommendations for training teachers to implement inclusive education. Almaty, 2013. - 165 p. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 31 Jafar Jabbarli's play "Sevil" is one of the strongest expressions of the idea of women's liberation in Azerbaijani literature. The theme of the work - the development of women from lawlessness to freedom - has become one of the most important problems of national literature. The idea of the work is connected with the enlightenment of women, the affirmation of their equal position in public life. The image of Sevil is not only a fictional heroine, but also a symbol of Azerbaijani women, an artistic expression of the path to freedom and progress. Therefore, "Sevil" can be assessed not only as a dramatic work, but also as a socio-political manifesto. Let us pay attention to the writer's next work "Almaz", which deals with the issue of the role and rights of women in society. The play "Almaz", written by the writer in 1931, is one of the important works reflecting the formation of Azerbaijani women in the new social environment with the ideas of enlightenment. In this play, women are presented not only within the family, but also as educators, intellectuals and public figures. The theme of the play “Almaz” is the struggle against ignorance and superstition in the Azerbaijani rural environment, the active position of women in the new social conditions, and their educational activities. The main character of the play, Almaz, focuses on the role of literacy, science, and education in society through the image of the teacher Almaz. The events take place in the village, and an environment dominated by old customs, superstitions, and ignorance is depicted here. Almaz brings a new breath to this environment. As a teacher, she tries to spread educational work in the village, educate women and children, and free the rural population from ignorance. Thus, the theme of the play is related to both the mission of women’s education and the struggle for the renewal of society. The main idea of the play “Almaz” is that the progress of society is connected with education, women’s education, and their active participation in public life. Jabbarli shows that: ✓ Education is the main path to progress – through the image of Almaz, the author emphasizes that literacy and education play a decisive role in the development of society. ✓ The place of women in public life – In the work, women are presented not as passive beings, but as active intellectuals and public figures. Teacher Almaz fights against ignorance in the village and influences the formation of the future generation. ✓ The struggle between the old and the new – The idea of the work is also based on the confrontation between ignorance and enlightenment, backwardness and progress. Almaz represents innovation, science and enlightenment, and her opponents represent backwardness and superstition. (5, p.113) The image of Almaz is a new face of a woman in national dramaturgy - she is not only a woman in the family, but also an educator of future generations, a guide to the path of progress. Jafar Jabbarli's play "Almaz" reflects a new stage of the image of a woman in Azerbaijani dramaturgy. The theme of the work - the activity of a woman in a rural environment as an educator and intellectual - artistically expresses the increase in the role of a woman in public life. The idea of the work is related to enlightenment, literacy and women's freedom. The image of Almaz is presented as a symbol of a modern Azerbaijani woman, a symbol of progress. From this point of view, "Almaz" is not only a drama, but also an artistic manifesto of a woman's new position in society. There is no work by Jafar Jabbarli that does not contain a female image. "The Bride of Fire" (1922) - The image of Shavkat is the embodiment of love, selflessness and loyalty. “Aydın” (1919) – female images are presented as carriers of innovative, progressive ideas. “In 1905” (1921) – female heroes are depicted together with the people in the struggle for national liberation. In these works, women are not depicted as passive beings, but sometimes as forces that change the course of events. As for the artistic and aesthetic merits of Jafar Jabbarli’s female images, it can be said that the main feature of these women is their internal change and psychological development. Sevil’s development from ignorance to enlightenment, Almaz’s fighting and strong-willed character are developed with psychological depth. Jabbarli’s women are both connected to national roots and carriers of universal humanist ideas. Their struggle for freedom and equality has a universal character. The above-mentioned images of Sevil and Almaz are not only artistic images, but also ideological symbols. They embody the historical development path of Azerbaijani women, their transition from illiteracy to enlightenment, from slavery to freedom. (6, p.47) XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 32 In conclusion, we can say that Jafar Jabbarli's female images are the strongest exponents of the idea of women's freedom in Azerbaijani literature. His heroes are the bearers of the ideas of enlightenment, progress, and equality. Jabbarli's female images opened a new stage in national dramaturgy and had a great impact on the rise of the social status of Azerbaijani women. The images of "Sevil" and "Almaz" have become artistic symbols of women's freedom in national literature. These images are still relevant today and are valuable in terms of illuminating the path of development of modern Azerbaijani women. Literature 1. Huseynzade A. Jafar Jabbarli and our national dramaturgy. Baku: Sharq-Qarb, 2004. 2. Aliyev A. Azerbaijani woman in literature and life. Baku: Science, 1998. 3. Mammadli N. Enlightenment ideas in the work of Jafar Jabbarli. – Baku, 2010. 4. Mammadova T. Female images in Azerbaijani dramaturgy. Baku: Science and Education, 2018. 5. Mammadova T. Female images in Azerbaijani dramaturgy. Baku: Science and Education, 2018. 6. Mammadli N. Enlightenment ideas in the dramaturgy of Jafar Jabbarli. Baku, 2010 XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 33 Для создания хорошего впечатления и формирования положительного имиджа в устном общении используются различные правила и приёмы: 1. То, как человек использует некоторые вводные слова, часто встречающиеся в повседневной речи, имеет большое значение для формирования его имиджа. Так, порой мы не замечаем, как часто используем те или иные слова. Например, бесконтрольное использование таких слов, как «вероятно», «безусловно», «конечно», «но», «так», «так» и т. д. в деловом общении может негативно сказаться на имидже человека. 2. Манера речи не менее важна для вербального имиджа. Например, некоторые люди представляются, «сцепив руки», что создаёт у собеседника впечатление, что представляющийся ненадёжен. Невнятная речь, незнание сути сказанного, отсутствие чёткого плана действий и чёткого плана действий создают у собеседника плохое впечатление. Правильные паузы и интонация позитивной устной речи создают у собеседника впечатление уверенного в себе человека. Если собеседник говорит слишком тихо и разговор не слышен с расстояния нескольких метров, часть информации будет потеряна. Если собеседник не очень заинтересован в информации, он просто не будет слушать. Слышать не значит слушать. Возможно, собеседник слышит, но не слушает, не воспринимает информацию. Если речь характеризуется слишком быстрым, а иногда и медленным произношением, это может вызывать раздражение со стороны собеседника. Поэтому темп речи следует менять в зависимости от ситуации общения. Кроме того, необходимо быть внимательным в процессе получения информации. Иногда монотонная речь снижает внимание, отвлекает получателя от темы разговора. 3. Положительный образ формируется и манерой приветствия. Кстати, произношение подходящего имени — хороший сигнал для человека, соответствующего требованиям формирования привлекательности: называя человека по имени, вы создаете у него приятное чувство. Называть человека по имени — значит проявлять интерес к его личности, а не к его социальным или иным функциям. Произносить имя собеседника громким голосом означает, что RULES AND TECHNIQUES FOR CREATING A GOOD IMPRESSION IN BUSINESS COMMUNICATION Leyla Vezirova Doctor of Philology, Professor. Azerbaijan, Baku. Azerbaijan State Pedagogical University ПРАВИЛА И ПРИЁМЫ СОЗДАНИЯ ХОРОШЕГО ВПЕЧАТЛЕНИЯ В ДЕЛОВОМ ОБЩЕНИИ Везирова Лейла доктор филологических наук, профессор. Азербайджан, гор. Баку. Азербайджанский Государственный Педагогический Университет Abstract The article discusses the rules and techniques for creating a good impression in business communication. Specific techniques are indicated and explanations are given as to why these techniques and rules are good. The article examines these techniques, starting with speech and ending with clothing. Аннотация В статье говориться о правилах и приемах создания хорошего впечатления при деловом общении. Здесь указываются конкретные приемы и даются пояснения, почему именно эти приемы и правила хороши. В статье рассматриваются данные приемы, начиная с речи, заканчивая одеждой. Keywords: good impression, image, pause, intonation, interlocutor, speech, voice, emotions, conversation, personality. Ключевые слова: хорошее впечатление, имидж, пауза, интонация, собеседник, речь, голос, эмоции, разговор, личность. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 34 вы уделяете внимание его личности. Одновременно вы вызываете в его сердце положительные эмоции, притягивая его к себе. Кроме того, методика «правильного имени» — отличный инструмент для диагностики межличностных отношений: подумайте, почему вы не упоминаете имя своего коллеги (или однокурсника). Психологи считают, что если у человека в целом плохая память на имена, то дело не в рассеянном склерозе, а в том, что этот человек психологически дистанцирован от людей по принципу. 4. Способы общения: Каждое приветствие, включая улыбку, дружеский взгляд, рукопожатие и вежливые слова, играет важную роль. При этом большое значение имеют знакомство, обмен визитными карточками, проявления дружелюбного поведения, шутки, юмор, комплименты, выражение уважения к партнеру, выраженное словами, мимикой, жестами, позой, организацией пространственной среды и т. д. 5. Формирование позитивного образа требует постоянной работы над собой. Положительное впечатление, позитивный образ создает уверенный в себе человек. Человек вызывает положительные эмоции, когда он «открыт» другим. «Открытость» человека проявляется, когда он уверен в себе, знает свои цели и чего хочет. Он ищет и находит в других, прежде всего, хорошее. Он жизнерадостен, позитивен, относится к окружающим с пониманием, часто умеет говорить «да» или «нет». Он уделяет достаточно времени всем своим проектам и планам. Он внимательно слушает собеседника, старается как можно больше узнать о других. Это проистекает из доброты и внутреннего спокойствия. Неуверенный в себе человек все подвергает сомнению, долго размышляет. Ему присущи типичные черты «закрытого» человека. Неуверенный в себе человек испытывает страх, нерешительность, не верит в свои силы, пессимистичен, недоверчив, ожидает от другой стороны только плохое, редко смеётся и не радуется. Он часто отказывается, чаще говорит «нет», чем «да», постоянно говорит, что работа создаёт для него стрессовые ситуации, что у него практически нет свободного времени. Он много говорит о себе и мало слушает, часто нервничает, действует с нервной раздражительностью и излучает по отношению к себе угнетённую, недоброжелательную атмосферу. Таким образом, только уверенный в себе человек может производить хорошее впечатление на окружающих и, как следствие, формировать позитивный образ себя. Для развития уверенности в себе следует придерживаться следующих рекомендаций: • не критиковать себя; • не жаловаться; • вести активный образ жизни; • обретать независимость; • смотреть на мир позитивно. 6. Внешний вид также играет важную роль в деловом общении. Визуальный контакт, в принципе, формирует первоначальную оценку собеседника. Конечно, одежда может дать информацию о социальном статусе человека, его личностных качествах и самооценке. Для большинства людей одежда является признаком определенного образа жизни и мировоззрения. Одежда, рубашки, обувь, которые носит человек, могут многое сказать. Цвета одежды говорят сами за себя и характеризуют человека. Украшения, очки, шарфы и т. д. — все это способствует формированию образа, свидетельствующего о вкусе и личных качествах. Важное правило — одеваться соответствующе. Людям нравятся люди, похожие на них, поэтому важно соответствовать общему стилю вашей будущей аудитории. Соответствовать чужому стилю не означает жертвовать собой. Вы можете мотивировать других, хорошо выглядя. Всё это показывает, что вы способны преодолевать трудности и проблемы и добиваться своего. Никогда не позволяйте внешности брать верх над вашими профессиональными навыками. Ваша команда должна ценить вас прежде всего как эксперта в своей области. То есть, они должны принимать ваш профессионализм, а не ваш пол. Это относится как к мужчинам, так и к женщинам. Если вы хотите представить себя знатоком, вам больше поможет сдержанная и строгая одежда. Никогда не решайте заранее, что надеть в последний вечер (особенно перед важной встречей). Решите это немного раньше, чтобы всё было подготовлено, выглажено и проверено заранее. В традиционных жанрах делового общения (публичные выступления, доклады, комментарии, консультации) реализуются коммуникативные стратегии деловых партнёров, XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 35 которые требуют не только умения преподнести себя, но и способности представить философию, организационные ценности и корпоративный имидж сторон. В деловом общении речевая или коммуникативная стратегия определяется особенностями речевой ситуации, индивидуальными особенностями говорящих, особенностями речевых традиций социальной группы, страны. Избирательность стратегии связана, главным образом, с целевыми параметрами участников диалога: заключение взаимовыгодной сделки, разрешение конфликтной ситуации, обсуждение деталей или хода реализации соглашения, контракта, важной организационной дискуссии и т. д. В деловых переговорах стороны представляют экономические интересы юридических лиц, их безопасность, интересы превосходства и престижа. В современных условиях компании часто несут расходы, чтобы сохранить лидирующие позиции на рынке и не быть стеснёнными конкурентами. Переговоры с точки зрения защиты своих интересов полезны даже тогда, когда другая сторона упорствует в своей позиции. Существуют фразы, которые делают любые переговоры более успешными: • Это в ваших и наших интересах... • Это одинаково важно и для вас, и для нас. • Наши интересы в решении этой проблемы совпадают. • Надеюсь, что вместе с вами мы заинтересованы в поиске выхода из этой конфликтной ситуации. Понятия и словарный запас принимающего и передающего информацию различаются. В этом случае между сторонами может возникнуть семантическое недопонимание. Для устранения этого семантического недопонимания крайне важно, чтобы партнёры говорили на одном «языке» при обмене информацией. Иногда на передаваемую партнёрам информацию влияют возрастные, социальные, культурные и другие различия. Одно и то же слово может иметь несколько значений, и, используя одно и то же слово, партнёры по общению могут выражать разные смыслы. Поэтому в процессе делового общения передающий информацию должен стараться выражать свои мысли максимально просто и ясно. Использованная литература 1. Ботавина Р.Н. Этика деловых отношений: учебное пособие. – М.: Финансы и статистика, 2001. – 208 с. 2. Клюев Е.В. Речевая коммуникация; Успешность речевого взаимодействия: учебное пособие. –М. РИПОЛ классик, 2002– 320 с. 3.Колтунова М.В. Деловое обшение: нормы, риторика, этикет: учебное пособие для вузов. – М. Логос, 2005. – 308 с. 4.Мокшанцев Р.И.Психология коммуникаций на переговорах: учебное пособие для вузов. – М.: Новосибирск: Инфра-М: Сибирское соглашение, 2004. – 367 с. XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 36 Political sciences Президентські вибори є центральним елементом демократичного політичного процесу, який визначає легітимність влади, встановлює пріоритети державної політики та формує стратегічний напрям розвитку країни на наступні роки. В умовах глобалізації, поширення цифрових технологій та активного використання соціальних мереж виборчі кампанії перестають бути суто національними подіями, стаючи значущими чинниками міжнародного політичного впливу [1]. Порівняння американських та європейських президентських виборів дозволяє виявити як спільні тенденції — цифровізація, персоналізація кандидатів, таргетинг виборців, — так і суттєві відмінності, зумовлені історичними традиціями, політичною культурою, структурою виборчих систем і регуляторними нормами [2]. Американські кампанії вирізняються високим рівнем персоналізації, тривалістю внутрішньопартійних перегонів і значним фінансовим навантаженням, тоді як у Європі більшість країн застосовує суворі правила фінансування, державну підтримку кандидатів та більше уваги приділяє ідеологічній та коаліційній складовим кампаній [7][8]. Американська модель президентських виборів США мають унікальну систему праймеріз і кокусів, яка визначає кандидатів від партій ще до загального голосування [3]. Праймеріз проводяться у всіх штатах, протягом яких кандидати активно взаємодіють з локальними виборцями, формують власний імідж та залучають підтримку ключових партійних груп. Наприклад, вибори 2000 року між Джорджем Бушем та Аль Гором демонструють, що перемога на праймеріз стає важливою базою для побудови загальнонаціональної кампанії та впливає на комунікаційні стратегії кандидата [4]. Американські праймеріз стимулюють тривалі внутрішньопартійні змагання. Кандидати змушені вести активну агітацію протягом кількох місяців, балансуючи між ідеологічною чіткістю та прагматичними політичними компромісами. Цей етап виборів також дозволяє оцінити популярність кандидата серед різних соціальних груп та скоригувати стратегію перед національним голосуванням [3]. Фінансування кампаній у США Фінансування виборчих кампаній є критично важливим для просування кандидата. Кампанії витрачають мільярди доларів, і вплив приватних донорів, політичних комітетів (PAC і Super PAC) та лобістських організацій визначає можливості кандидата щодо рекламних кампаній і медійної присутності [5]. Вибори 2016 року показали, що Дональд Трамп активно використовував власні фінансові ресурси та соціальні мережі для прямого контакту з виборцями, обходячи традиційні медіа [6]. Кампанія Барака Обами 2008 року символізувала еру цифрового політичного маркетингу, де через онлайн-платформи мобілізувалося молоде покоління, формувалася активістська мережа, і реагування на політичні події стало максимально оперативним [3]. Кампанія Джо Байдена 2020 року поєднувала класичні та цифрові канали, демонструючи інтегровану стратегію просування кандидата та мобілізації електорату [6]. Роль медіа та персоналізація кандидатів Американські вибори характеризуються високим рівнем персоналізації політики. Виборці оцінюють не лише програму кандидата, а й його особисті якості, харизму, здатність реагувати на кризові ситуації, формування довіри та симпатії [2]. Теледебати, рекламні ролики, COMPARISON OF THE FEATURES OF PRESIDENTIAL ELECTION PROMOTION IN THE USA AND EUROPE Kovinskyi Yanislav Ukraine ПОРІВНЯННЯ ОСОБЛИВОСТЕЙ ПРОСУВАННЯ ПРЕЗИДЕНТСЬКИХ ВИБОРІВ У США ТА ЄВРОПІ Ковінській Яніслав Адрійович Україна XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 37 інтерактивні платформи та активність у соціальних мережах формують уявлення про кандидата й відіграють вирішальну роль у мобілізації електорату [1]. Історичні приклади підтверджують цю тенденцію. У 2008 році Обама активно використовував YouTube та Facebook для персоналізації своєї кампанії. У 2012 році кампанія Ромні, хоча й мала великі фінансові ресурси, не змогла ефективно інтегрувати цифрові платформи, що знизило її ефективність серед молодих виборців. У 2016 році Трамп домігся значного медійного ефекту завдяки прямому контакту з аудиторією через Twitter, обминаючи традиційні канали. Вибори 2020 року показали, що інтегровані цифрові й традиційні стратегії можуть підвищити ефективність кампанії та мобілізацію різних груп виборців [6]. Європейські президентські вибори: структура та особливості Європейські президентські вибори демонструють значну варіативність моделей, що зумовлена багатопартійністю, історичними традиціями та політичною культурою кожної країни [7]. У більшості європейських держав встановлено суворе регулювання фінансування кампаній, що забезпечує рівні умови для кандидатів і знижує ризик комерційного впливу. Державне фінансування, обмеження на приватні внески та максимальні витрати є типовими для Франції, Німеччини, Польщі та Австрії [8]. Французька двотурова система президентських виборів передбачає, що якщо жоден кандидат не отримує більшості у першому турі, відбувається другий тур між двома лідерами [8]. Це стимулює кандидата формувати коаліції, шукати підтримку менших партій і адаптувати повідомлення під різні соціальні групи. Наприклад, вибори 2017 року, в яких переміг Еммануель Макрон, демонструють ефективність комбінованої стратегії: перший тур передбачав широке залучення виборців через медіа та цифрові платформи, другий тур вимагав акценту на коаліційній підтримці та мобілізації поміркованого електорату [8]. У Польщі та Австрії застосовується подібна двотурова система. Вибори 2020 року в Польщі показали, що кандидати активно використовують соціальні мережі та мобільні платформи для прямої комунікації з виборцями, поєднуючи їх із традиційними медіа. У Австрії 2016 року кампанії поєднували класичні теледебати та пресу з активним онлайн-маркетингом, що дозволило залучити молодіжний електорат [7]. Німеччина відрізняється тим, що президент обирається Федеральними зборами, які складаються з членів Бундестагу та представників земельних парламентів. Така система робить кампанію менш масовою, зосереджуючи увагу на експертному середовищі та партійних структурах, а не на безпосередній взаємодії з широким електоратом [7]. Італія також має непряму модель, де президент обирається парламентом і делегатами регіонів, що робить медіастратегії більш аналітичними та орієнтованими на політичну еліту. Медіастратегії та цифрові технології Медіа у європейських кампаніях відіграють важливу роль, однак традиційні канали, такі як телебачення, радіо та преса, залишаються основними. Законодавство забезпечує рівний доступ кандидатів до ефіру та обмежує рекламні витрати, що запобігає домінуванню коштовних кампаній [8]. Соціальні мережі поступово набувають значущості, проте їхній вплив ще не досягає рівня США [1]. Європейські кандидати активно інтегрують цифрові платформи, соціальні мережі та мобільні додатки, щоб охопити молодіжну аудиторію та залучити волонтерів до кампанії. Використання Big Data дозволяє формувати персоналізовані повідомлення для окремих груп виборців, аналізувати ефективність кампаній і реагувати на кризові ситуації в режимі реального часу [3][6]. Вибори 2017 року у Франції показали ефективність комплексного використання медіа та цифрових технологій: кампанія Макрона активно інтегрувала теледебати, PR-ролики та соціальні мережі для залучення різних верств населення. В Австрії 2016 року кандидат Александр ван дер Беллен поєднував класичні медіа із соціальними платформами, що дозволило підвищити ефективність мобілізації молоді [7]. Польща 2020 року продемонструвала аналогічну тенденцію: кандидати поєднували традиційні телереклами із таргетованою рекламою у Facebook і Instagram, використовуючи алгоритми для визначення найбільш активних аудиторій [7]. Фінансування кампаній у Європі Фінансування європейських кампаній суворо регламентоване. У Франції встановлено максимальні витрати та обмеження на приватні внески, при цьому частково покривається державою [8]. У Польщі та Австрії існують подібні обмеження: контролюються джерела XXI INTERNATIONAL SCIENTIFIC CONFERENCE. MANCHESTER. UNITED KINGDOM. 30.09-01.10.2025 38 фінансування, максимальні витрати та порядок звітності. Це забезпечує більш рівні умови для кандидатів і знижує ризик надмірного впливу бізнес-структур на вибори [7]. У США фінансування значно більш відкрито і включає приватних донорів, PAC і Super PAC, що дозволяє витрачати мільярди доларів на кампанії [5]. Це створює сильну конкуренцію за ресурси і впливає на медіастратегії кандидатів. В Європі обмеження на фінансування стимулюють кандидатів ефективно використовувати державні ресурси та цифрові інструменти для максимального охоплення аудиторії [8]. Сучасні виклики та ризики Сучасні виборчі кампанії стикаються з подібними викликами у США та Європі: дезінформація, фейкові новини, зовнішнє втручання, вплив спонсорів та лобістів [6]. Використання Big Data, алгоритмічного таргетингу та штучного інтелекту стає нормою, але водночас породжує етичні та правові питання щодо прозорості кампаній, конфіденційності персональних даних і маніпуляцій свідомістю виборців [3][6]. Наприклад, під час виборів 2016 року у США активно використовувалися таргетовані рекламні кампанії у соціальних мережах, що впливали на сприйняття політичних повідомлень різними групами виборців. В Європі аналіз виборчих кампаній Франції та Польщі показав аналогічні тенденції: використання цифрових платформ для залучення молодіжного електорату та прямої комунікації з виборцями [7][8]. Політична культура та глобалізація практик Політична культура визначає характер виборчих кампаній. Американська політика тяжіє до медійності та шоу, де харизма кандидата і вміння взаємодіяти з медіа вирішальні. Європейські кампанії більше акцентують ідеологічність, коаліційність та змістовність програм [7][8]. Глобалізація політичних практик сприяє взаємозапозиченню методів: цифрові стратегії США використовуються у Європі, а принципи прозорості і фінансового контролю європейських країн впливають на американські вибори [1][7]. Прогноз розвитку виборчих кампаній Прогноз розвитку передбачає подальше поєднання цифрових технологій з традиційними медіа, персоналізацію з ідеологічною чіткістю, технологічність із прозорістю й легітимністю процесу [1][2][3]. Активно використовуватиметься аналітика даних, автоматизований таргетинг, інтерактивні цифрові платформи, мобільні додатки, що підвищить ефективність мобілізації виборців і дозволить прогнозувати результати кампаній із високою точністю. Використані джерела/ List of references 1. Norris, P. (2020). Political Communications in the Digital Age: Social Media and Elections in the United States and Europe. Cambridge University Press. 2. Herrnson, P. S. (2016). Congressional Elections: Campaigning at Home and in Washington. CQ Press. 3. Kreiss, D. (2016). Prototype Politics: Technology-Intensive Campaigning and the Data of Democracy. Oxford University Press. 4. Federal Election Commission (FEC). (2020). Campaign Finance Data and Reports. 5. National Conference of State Legislatures (NCSL). (2020). State Campaign Finance Laws. 6. Stromer-Galley, J. (2014). Presidential Campaigning in the Internet Age. Oxford University Press. 7. European Parliament Research Service. (2019). Political Advertising and Election Campaigns in Europe. 8. France’s Commission nationale de contrôle de la campagne électorale (CNCCEP). (2017). Rapport sur l’élection présidentielle.