In this article, we will explore the basic concepts of the Markov chain, its relation to the Bernoulli scheme, and the transition matrix. We will also consider the importance of this theory in social life.

In an era marked by globalization, proficiency in foreign languages has become increasingly vital for success in various fields. Higher education institutions play a crucial role in equipping students with these skills. However, teaching foreign languages involves more than merely imparting vocabulary and grammar; it requires fostering cognitive engagement to facilitate deeper understanding and retention.

This article is dedicated to investigating innovative approaches to managing working capital in small business entities under modern economic conditions. The article analyzes the essential methods for effectively managing working capital, the significance of technological and financial innovations, as well as the role of social media and digital marketing, and the challenges associated with their implementation. Additionally, the article aims to clarify the role of each innovative approach in maintaining the financial stability and competitiveness of businesses. It provides strategic recommendations for small businesses to operate effectively in contemporary conditions.

Mazkur maqolada O‘zbekiston Respublikasi Tiklanish va taraqqiyot jamg‘armasi faoliyatining tashkil etilish zarurligi tahlil qilinadi. Jamg‘armaning iqtisodiy rivojlanish jarayonida tutgan o‘rni, uning mamlakatning ijtimoiy va iqtisodiy taraqqiyotiga qo‘shgan hissasi, shuningdek, innovatsiyalarni joriy etish va yangi investitsiyalarni jalb qilishdagi roli haqida fikrlar bildiriladi. Maqola O‘zbekiston iqtisodiyotining barqaror rivojlanishini ta’minlash va raqobatbardoshligini oshirish maqsadida jamg‘armaning asosiy vazifalarini ochib beradi.

The history of the science of psychology, based on the combination of philosophy and medicine, goes back to ancient times. In the classical period, thinkers such as Hippocrates and Democritus introduced the first concepts that linked consciousness to the activity of the brain. In the Middle Ages, psychological progress slowed due to supernatural beliefs, but scholars such as Ibn Sina continued to develop the field. The Renaissance saw figures such as Leonardo da Vinci contribute to the understanding of human knowledge. By the XIX th century, psychology became an independent experimental science, using systematic study methods. Today, psychology has become a multidisciplinary field that studies different aspects of human behavior and mental processes in different contexts.