Notes, summaries, assignments, exams, and problems for University

Parametric Representation of Cubic Curves

Curves are widely used in Computer Graphics for designing smooth shapes, objects, fonts, and animations. A curve can be represented in different ways, and one of the most important methods is the Parametric Representation. In this method, the coordinates of points on the curve are expressed as functions of a parameter t. A Cubic Curve is a curve represented by a third-degree polynomial equation. Parametric representation provides greater flexibility and control over the shape of the curve and is widely used in CAD/CAM systems, animation, and graphical modeling.

Parametric Representation Details

In parametric form, both x and y coordinates are represented as functions of a parameter t:

x = x(t)
y = y(t)

For... Continue reading "Advanced Computer Graphics Algorithms and Curve Modeling" »

Evolution and Importance of Behavioural Finance

The Shift from Traditional Finance

Traditional finance assumes investors are rational, wealth-maximizing agents. Theories like the Efficient Market Hypothesis (EMH), CAPM, and Modern Portfolio Theory rely on the assumption that investors process information logically. However, practical observations reveal that investors are frequently influenced by emotions, psychological biases, and social factors. This reality led to the emergence of Behavioural Finance, a field that integrates finance, psychology, and sociology to explain irrational market behaviour.

Meaning of Behavioural Finance

Behavioural Finance studies how psychological, emotional, cognitive, and social factors influence the financial decisions... Continue reading "Understanding Behavioural Finance: Investor Psychology & Markets" »

The Principle of Free Movement of Workers

Article 45 TFEU guarantees the free movement of workers within the European Union. Its purpose is to allow nationals of one Member State to move to another Member State in order to work there, without suffering discrimination or unjustified restrictions.

Defining the Migrant Worker

A migrant worker is, in general, a national of a Member State who performs genuine and effective work in another Member State, under the direction of another person and in return for remuneration.

Non-Discrimination and Equal Treatment

The main right protected by Article 45 is the abolition of discrimination based on nationality. This means that migrant workers must be treated in the same way as national workers as regards access... Continue reading "Free Movement of Workers Under Article 45 TFEU" »

The European Social Charter and Human Rights

The European Social Charter is the main social rights treaty of the Council of Europe and complements the European Convention on Human Rights (ECHR). While the ECHR mainly protects civil and political rights, the Charter focuses on economic and social rights such as labor rights, social security, health protection, and housing. The original Charter was adopted in Turin in 1961 and later revised in 1996 in order to modernize and expand the protection of social rights.

Origins and International Influence

The Charter is strongly influenced by the Universal Declaration of Human Rights, the International Labor Organization standards, and the International Covenant on Economic, Social and Cultural Rights.... Continue reading "European Social Charter: Protecting Economic Rights" »

Respiratory and Cardiovascular Health

• Pneumonia is an infection of the lungs that causes inflammation of the air sacs.
• Bronchioles are small airways in the lungs that carry air to the alveoli.
• An ischaemic stroke is a stroke caused by a blockage of blood flow to the brain.
• A carotid artery is a major artery in the neck that supplies blood to the brain.
• A vein is a blood vessel that carries blood back to the heart.
• Cardiac catheterisation is a medical procedure in which a catheter is inserted into the heart or blood vessels for diagnosis or treatment.

Medical Equipment and Diagnostic Tools

• A stethoscope is a medical instrument used to listen to sounds from the heart, lungs, and other organs.
• A laparoscope is a medical instrument with a camera and light

Capitalist Business Persons and Capitalist Companies

Case 2A focuses on capitalist business persons. A capitalist company is an entity mainly based on capital contribution. In these companies, what matters most is the capital invested, not the personal identity of the partners. Decisions are usually made by a majority of capital, and liability is typically limited.

Types of Capitalist Companies

Capitalist companies are regulated by the Corporate Enterprises Act. The three main types are:

• Joint Stock Company
• Limited Liability Company
• Limited Share Partnership

Joint Stock Company (Sociedad Anónima)

A Joint Stock Company is similar to a Sociedad Anónima. Its key characteristics include:

• Its partners are shareholders.
• The minimum capital required is €60,

Core Principles of Project Communication Management

Project Communication Management is the systematic process that ensures the proper generation, collection, storage, and distribution of project information. Its primary objective is to ensure that the right information reaches the right person at the right time using the appropriate channel.

Key Components

• Stakeholders: People or organizations involved in or affected by the project (e.g., Sponsor, Customer, Project Team).
• Communication Plan: A formal document that defines the 5Ws: What, Who, When, Where, and How information is shared.
• Communication Standards: Rules and procedures, such as templates and protocols, used to ensure consistency and prevent confusion.

Agile Communication

Agile methodologies... Continue reading "Mastering Project Communication Management: Best Practices" »

Fundamental Machining Definitions

• Machine Tool: A power-driven mechanical device used to shape or manufacture metal and other materials by cutting, drilling, grinding, turning, or other machining processes.
• Machining: The process of removing unwanted material from a workpiece in the form of chips.
• Cutting Fluid: A liquid or gas used during machining operations to reduce heat and friction between the cutting tool and the workpiece.
• Tool Signature: The numerical representation of the different angles and dimensions of a single-point cutting tool.
• Lathe: A machine tool in which the workpiece rotates, and the cutting tool removes material.
• Taper Turning: The operation of producing a conical surface on a cylindrical workpiece in a lathe machine.
• Thread

Understanding the Business Person and Personalist Companies

Case 1 examines the concept of the business person and the initial types of companies, specifically personalist companies.

Natural vs. Legal Persons in Business

A business person is the legal subject that carries out a commercial activity. This entity can be a natural person or a legal person:

• Natural Person: The business person is the individual. For example, if Marta opens a clothes shop as a sole trader, Marta herself is the business person; there is no separate company.
• Legal Person: The business person is the company itself. For example, if Marta creates Marta Fashion S.L., the business person is Marta Fashion S.L., not Marta personally. While Marta may be the founder or shareholder,

Newton's Rings are concentric circular bright and dark rings formed due to interference between light waves reflected from the upper and lower surfaces of a thin air film.

Theory of Newton's Rings

When monochromatic light falls on the thin air film formed between the plano-convex lens and a glass plate, two reflected rays are produced:

• One from the upper surface of the air film.
• Another from the lower surface of the air film.

These reflected rays interfere with each other:

• Constructive interference produces bright rings.
• Destructive interference produces dark rings.

Thus, alternate bright and dark concentric circular rings are formed.

Determination of Refractive Index of a Liquid

When a liquid is introduced between the lens and the glass plate, the... Continue reading "Newton's Rings: Theory, Derivation, and Applications" »