The tangent half-angle formulas relate the tangent of half of an angle to the sine and cosine of the angle itself. The tangent half-angle formulas are given by: 1. In terms of sine and cosine: \[ \tan\left(\frac{\theta}{2}\right) = \frac{\sin(\theta)}{1 + \cos(\theta)} \] 2.

Vector algebra, also known as vector analysis or vector mathematics, comprises the mathematical rules and operations used to manipulate and combine vectors in both two-dimensional and three-dimensional space. Vectors are quantities that possess both magnitude and direction, and they are often represented graphically as arrows or numerically as ordered pairs or triples. Here are some fundamental relations and operations in vector algebra: ### 1.

The Center of Mathematical Sciences at Zhejiang University is a research institution that focuses on various fields of mathematics and its applications. This center typically aims to promote mathematical research, foster academic collaboration, and support education in mathematics at both the undergraduate and graduate levels. Zhejiang University, located in Hangzhou, China, is one of the country's leading universities and has a strong emphasis on research and innovation.

The Centro de Investigación en Matemáticas (CIMAT) is a prominent research center in Mexico focused on mathematics, statistics, and computer science. Founded in 1980 and located in Guanajuato, CIMAT engages in a wide range of research activities and offers educational programs at both the undergraduate and graduate levels. The center aims to advance mathematical research and its applications while fostering collaboration among scientists and industries.

The Institut de Mathématiques de Toulouse (IMT) is a mathematics research institute located in Toulouse, France. It is affiliated with the University of Toulouse and is part of the larger educational and research consortium in the region. IMT focuses on a wide range of mathematical fields, including pure and applied mathematics. It serves as a hub for research, collaboration, and education in mathematics, hosting seminars, workshops, and conferences to promote mathematical research and community engagement.

The Institute of Statistical Mathematics (ISM) is a research institution located in Tokyo, Japan, dedicated to the field of statistical mathematics. It was established with the aim of promoting research in statistics and its applications, as well as advancing education and training in this area. The ISM conducts both theoretical and applied research in various domains of statistics, including but not limited to statistical theory, methodology, computational statistics, and statistical applications in fields such as social science, medicine, and environmental science.

The Institute of Applied Physics and Computational Mathematics (IAPCM) is an academic institution often associated with research and education in applied physics and computational mathematics. While specific details may vary by country or region, institutions with similar names generally focus on: 1. **Research**: Conducting advanced research in areas such as applied physics, computational methods, numerical analysis, and related fields. This includes both theoretical studies and practical applications.

The Istituto Nazionale di Alta Matematica Francesco Severi, commonly known as INdAM, is an Italian research institute dedicated to advanced studies in mathematics. Established in 1939, it was named after the Italian mathematician Francesco Severi. The institute aims to promote research and education in various fields of mathematics, supporting both theoretical and applied mathematics. INdAM organizes conferences, workshops, and lecture series, providing a platform for mathematicians and researchers to collaborate and share their findings.

The Low Basis Theorem is a concept from algebraic geometry and commutative algebra, particularly within the context of syzygies, which are relations among generators of a module. The theorem deals with certain properties of a graded free resolution of a module over a polynomial ring.

Jacek Malinowski could refer to multiple individuals, as it is a relatively common name in Poland. One notable mention is Jacek Malinowski, an academic known for his contributions to fields such as computer science or linguistics. However, without more context, it's difficult to identify a specific person or topic related to that name.

The European Summer School in Logic, Language, and Information (ESSLLI) is an academic event that typically takes place annually, focusing on the intersection of logic, language, and information across various disciplines. This summer school brings together researchers, students, and practitioners interested in these fields to share knowledge, present research findings, and engage in collaborative discussions.

Gabbay's separation theorem is a result in the field of logic, specifically in the study of modal logic and the interplay between different kinds of logical systems. While the exact details can vary depending on the context in which it's presented, a common interpretation relates to the separation of various logical operations, particularly in relation to the modal operators of necessity and possibility.

The projective hierarchy is a classification of certain sets of real numbers (or more generally, sets in Polish spaces) based on their definability in terms of certain operations involving quantifiers and projections. It is particularly relevant in descriptive set theory, a branch of mathematical logic and set theory that studies different types of sets and their properties.

The Bernays–Schönfinkel class (often denoted as \( \text{BSec} \)) is a class of logical formulas in the context of first-order logic (FOL) that are particularly notable in model theory and computational logic. The class is named after the logicians Paul Bernays and Hugo Schönfinkel.

In mathematics, particularly in the field of topology, a **separating set** refers to a set of points that can distinguish or separate certain subsets of a topological space. However, the term is often used in various contexts, so its precise meaning can vary depending on the field of study.

The Kleene–Rosser paradox is a result in the field of mathematical logic, particularly in the area of recursion theory and the foundations of mathematics. It highlights an issue related to self-reference in formal systems, specifically in the context of lambda calculus and computable functions. The paradox arises when considering certain systems that attempt to define or represent computable functions.

Sonja Smets is a prominent figure in the field of artificial intelligence and quantum information, known for her contributions to quantum logic, quantum computation, and the philosophy of quantum mechanics. She has worked on connecting various disciplines, including computer science, physics, and philosophy, particularly in understanding the implications of quantum theory for information processing. In addition to her research, Smets has been involved in academia, holding positions at institutions where she teaches and mentors students in these fields.

Ticio Escobar is a Paraguayan art critic, curator, and cultural advocate known for his contributions to contemporary art in Paraguay and Latin America. He has been influential in promoting Paraguayan artists and fostering the development of cultural initiatives within the region. Escobar has served in various roles within art institutions and has been involved in organizing exhibitions, conferences, and projects that highlight the significance of art and culture in addressing social issues.

A soft set is a mathematical concept introduced by D. Molodtsov in 1999, which is used to model uncertainty and vagueness in various fields, including decision-making, artificial intelligence, and information science. It generalizes the traditional set theory by incorporating a parameterized framework for representing uncertain data.

The term "theory of pure equality" is not widely recognized in academic discourse, and its meaning can vary depending on context. However, it generally pertains to philosophical, political, or economic discussions about the concept of equality among individuals or groups. Here are a few interpretations of what a "theory of pure equality" might refer to: 1. **Philosophical Equality**: This could relate to the philosophical notion that all individuals have the same inherent value and rights.