This chapter examines the legal framework governing mergers, divisions and conversions of companies within the European Union. It analyses the relevant EU directives designed to facilitate corporate restructuring while protecting stakeholders’ rights and ensuring transparency. The chapter explores procedural requirements, cross-border challenges and the impact of these transformations on capital maintenance and creditor protection. By reviewing case law and national implementations, it highlights efforts to harmonize rules and promote business flexibility across Member States. The discussion underscores how these mechanisms support corporate efficiency, market integration and the dynamic nature of the EU’s internal market.

This chapter explores the principles and legal framework of capital maintenance within the European Union’s company law. It examines rules designed to protect creditors and ensure corporate solvency by regulating distributions, reductions and increases of a company’s capital. The chapter analyses key EU directives, national implementations and relevant case law, highlighting the balance between safeguarding financial stability and enabling business flexibility. It also discusses challenges in harmonizing capital maintenance rules across Member States and the impact of recent reforms on corporate governance. The chapter offers insights into how capital maintenance shapes corporate accountability and investor protection in the EU.

This chapter analyses the concept of primary establishment as developed in the case law of the Court of Justice of the European Union (CJEU). It focuses on how the Court has interpreted the freedom of establishment under Articles 49 and 54 TFEU, particularly in relation to the right of companies to incorporate and operate across borders. Key judgments such as Daily Mail and Überseering are examined to illustrate the evolving legal principles governing primary establishment. The chapter also discusses the implications of this jurisprudence for regulatory arbitrage, national company laws and the broader integration of the internal market.

This chapter examines the evolution of cross-border mobility of companies within the EU, tracing its development from foundational CJEU case law to recent statutory reforms. It explores landmark judgments that established principles allowing companies to transfer their registered office or seat across Member States without losing legal personality. The chapter then analyses legislative responses, including the Cross-Border Mergers Directive and Company Mobility Directive, aimed at codifying and clarifying these rights. Challenges related to national sovereignty, regulatory divergence and enforcement are discussed, highlighting ongoing efforts to balance corporate freedom with legal certainty and market integration.

This chapter explores the concept of a lexicon, introduces the notion of the mental lexicon, and raises the question of how we decide what the set of words are that are in a language. It then moves to a focus on borrowing as a lexical source in the history of Chinese, analyzing borrowings in terms of (1) the time period; (2) the contact situation; (3) the mechanism of borrowing; (4) the morphological structure of the borrowed words. Finally, recent changes in the Mandarin lexicon driven by social media and the internet are described and analyzed.

This chapter explores the legal framework governing dissolution and insolvency within the European Union, focusing on harmonization efforts through directives and regulations. It analyses key concepts such as jurisdiction, insolvency definitions and cross-border coordination, highlighting landmark cases like Eurofood IFSC Ltd, which shaped the interpretation of insolvency jurisdiction under EU law. The chapter discusses creditor protection, debtor rights and procedural challenges in insolvency and dissolution processes. By reviewing reforms and national practices, it emphasizes the ongoing development of a coherent EU insolvency regime that balances efficiency, legal certainty and market stability across Member States.

This chapter traces the history of Chinese writing from its creation and early development through to the establishment of the standard traditional script, emphasizing the structural components of the Chinese characters as a reflection of its history. Traditional Chinese classifications of Chinese character structure are introduced through the framework of the Han dynasty dictionary Shuo wen jie zi.

This chapter discusses what it means for a word to have meaning. Starting with the classical traditions in the West and the East about the nature of meaning, the connections between the word and the object it refers to (reference), and a set of inherent and defining properties which determines the referent (sense). It then moves on to the modern analysis of types of meaning, and introduces the way linguists characterize word meanings through semantic analysis. Major lexical relations, including hyponymy/hypernymy, antonymy, synonymy, polysemy, homonymy and homophony, are discussed. This chapter also introduces the notion of collocation.

learning Outcomes

After reading this chapter, the reader will be able to

• Understand the meaning of three processes of heat flow: conduction, convection, and radiation

• Know about thermal conductivity, diffusivity, and steady-state condition of a thermal conductor

• Derive Fourier's one-dimensional heat flow equation and solve it in the steady state

• Derive the mathematical expression for the temperature distribution in a lagged bar

• Derive the amount of heat flow in a cylindrical and a spherical thermal conductor

• Solve numerical problems and multiple choice questions on the process of conduction of heat

6.1 Introduction

Heat is the thermal energy transferred between different substances that are maintained at different temperatures. This energy is always transferred from the hotter object (which is maintained at a higher temperature) to the colder one (which is maintained at a lower temperature). Heat is the energy arising due to the movement of atoms and molecules that are continuously moving around, hitting each other and other objects. This motion is faster for the molecules with a largeramount of energy than the molecules with a smaller amount of energy that causes the former to have more heat. Transfer of heat continues until both objects attain the same temperature or the same speed. This transfer of heat depends upon the nature of the material property determined by a parameter known as thermal conductivity or coefficient of thermal conduction. This parameter helps us to understand the concept of transfer of thermal energy from a hotter to a colder body, to differentiate various objects in terms of the thermal property, and to determine the amount of heat conducted from the hotter to the colder region of an object. The transfer of thermal energy occurs in several situations:

• When there exists a difference in temperature between an object and its surroundings,

• When there exists a difference in temperature between two objects in contact with each other, and

• When there exists a temperature gradient within the same object.

Learning Outcomes

After reading this chapter, the reader will be able to

• Express the meaning of sphere of influence and collision frequency

• Derive the distribution function for the free paths among the molecules and demonstrate the concept of mean free path

• Calculate the expression for mean free path following Clausius and Maxwell

• Derive the expression for pressure exerted by a gas using the survival equation

• Calculate the expressions for viscosity, thermal conductivity, and diffusion coefficient of a gaseous system

• Demonstrate Brownian motion with its characteristics and calculate the mean square displacement of a particle executing Brownian motion

• State the idea of a random walk problem

• Solve numerical problems and multiple choice questions on the mean free path, viscosity, thermal conduction, diffusion, Brownian motion, and random walk

4.1 Introduction

The molecules of an ideal gas are considered as randomly moving point particles. From the concept of kinetic theory of gases (KTG), it is well established that even at room temperature, such point molecules of the ideal gas move at very large speeds. The average value of this speed can be determined assuming that the molecules obey Maxwell's speed distribution law and is given by the following expression

Learning Outcomes

After reading this chapter, the reader will be able to

• State the assumptions of kinetic theory of gases (KTG)

• Explain the concept of pressure and calculate the expression for it

• Demonstrate mathematically the gas laws using the expression for pressure derived from KTG

• Present the kinetic interpretation of temperature

• Derive the expression for specific heat at constant volume 𝐶𝑉 and constant pressure 𝐶𝑃

• Explain the concept of degree of freedom

• Solve numerical problems and multiple choice questions on KTG

2.1 Introduction

The kinetic theory of gases (KTG) is a theoretical model that describes the physical properties of a gaseous system in terms of a large number of submicroscopic particles, such as atoms, molecules, and small particles. These constituent elements are in random motion and collide constantly with each other and also with the walls of the container. Considering the molecular composition and characteristic features of such random motion of the molecules, various macroscopic properties of the gaseous system, such as pressure, temperature, viscosity, thermal conductivity, and mass diffusivity can be explained with the help of KTG. In this theory, it is postulated that the pressure exerted by a gas is due to the collision of atoms or molecules moving at different velocities on the walls of a container. It basically attempts to explain the macroscopic properties that are related to the microscopic phenomenon. The physical properties of solids and liquids, in general, are described by their shape, size, mass, volume, etc. Gases, however, have no definite shape, and size. Furthermore, their mass and volume are not directly measurable. In such cases, the KTG can be successfully applied to extract the physical properties of the gaseous system.

Learning Outcomes After reading this chapter, the reader will be able to

• Know various types of thermodynamic systems such as open, closed, and isolated, and the surroundings

• Classify between intensive and extensive thermodynamic variables

• Understand various types of equilibrium conditions satisfied by a thermodynamic system

• State the zeroth law of thermodynamics and highlight its physical significance

• Comprehend the idea of temperature from the zeroth law of thermodynamics

• Solve numerical problems and multiple choice questions on thermodynamic equilibrium and the zeroth law of thermodynamics

7.1 Introduction

Heat is a form of energy. It can be transformed from one form to another as well as can be transferred between various objects maintained at suitable temperatures. For example, in an electric motor, heat is transformed into mechanical energy by the turbine to power the motor. This mechanical energy is then transformed into electrical energy by the engine to illuminate light bulbs. “Thermodynamics” is a branch of physics that deals with heat and the transformation of heat from one form to another, work, temperature, and their relation to energy, entropy, and other physical properties of matter and radiation. It establishes the relation between heat and various forms of energy and describes the transformations that occur in thermal energy from one energy state to another and how this transformation affects matter. A thermodynamic system is described within a framework based on the four laws of thermodynamics that facilitate a quantitative description of the average macroscopic properties of the system in equilibrium. Macroscopic matter refers to large objects that consist of many atoms and molecules. The average properties of such macroscopic systems are determined by the physical quantities such as volume, pressure, and temperature that do not depend upon the detailed microscopic positions and velocities of the atoms and the molecules comprising the macroscopic system. In the equilibrium state of a thermodynamic system, these average properties also do not change with time. These physical quantities are called thermodynamic coordinates, variables, or parameters. If a subset of these properties are experimentally measured, the rest of them can be calculated using thermodynamic relations. Thermodynamics not only gives the exact description of the state of equilibrium but also provides an approximate description (to a very high degree of precision!) of relatively slow processes. This branch of physics can be successfully applied to a wide variety of topics in science, such as physics, physical chemistry, biochemistry, chemical engineering, and mechanical engineering, but also in other complex fields, such as meteorology.