The National Prize for Applied Sciences and Technologies in Chile, known as "Premio Nacional de Ciencias Aplicadas y Tecnologías," is an award established to recognize and honor significant contributions to the fields of applied sciences and technology in the country. This award underscores the importance of innovation, research, and development in addressing various challenges and advancing knowledge in applied sciences.

The Toshiba-Kongsberg scandal refers to a corruption and bribery investigation involving Toshiba, a Japanese multinational conglomerate, and Kongsberg Gruppen, a Norwegian defense contractor. The scandal emerged in the late 2010s and involved allegations that the companies paid bribes to obtain contracts and influence decisions in international defense and infrastructure projects.

Bar induction is a mathematical technique used to prove statements about all natural numbers, particularly statements concerning well-ordering and induction principles that extend beyond standard mathematical induction. It applies to structures that have the properties of natural numbers (like well-ordering) but may involve more complex or abstract systems, such as ordinals or certain algebraic structures. The concept is particularly important in set theory and is often used in the context of proving results about various classes of sets or functions.

Constructive set theory is an approach to set theory that emphasizes constructions as a way of understanding mathematical objects, rather than relying on classical logic principles such as the law of excluded middle. It is grounded in the principles of constructivism, particularly within the context of logic and mathematics, where the existence of an object is only accepted if it can be explicitly constructed or exhibited.

Optimal control refers to a mathematical and engineering discipline that deals with finding a control policy for a dynamic system to optimize a certain performance criterion. The goal is to determine the control inputs that will minimize (or maximize) a particular objective, which often involves the system's state over time. ### Key Concepts of Optimal Control: 1. **Dynamic Systems**: These are systems that evolve over time according to specific rules, often governed by differential or difference equations.

The Book of Giants is an ancient Jewish apocryphal text that is part of the Enochic literature, traditionally associated with the Book of Enoch. Although it is not included in the canonical Bible, it provides insight into Jewish apocalyptic thought and mythology.

The timeline of electrical and electronic engineering encompasses numerous advancements and milestones that have contributed to the field as we know it today. Here’s a brief overview of key events and developments: ### 19th Century - **1800**: Italian scientist Alessandro Volta invented the voltaic pile, the first chemical battery that could provide a steady source of electricity. - **1820**: Hans Christian Ørsted discovered that electric currents create magnetic fields, forming the basis of electromagnetism.

"Signatures with efficient protocols" generally refers to cryptographic digital signatures that can be generated, verified, and possibly managed using methods that optimize performance and resource consumption. Digital signatures are essential in various applications, such as ensuring data integrity, authentication, and non-repudiation in digital communications. ### Key Concepts: 1. **Digital Signatures**: These are mathematical schemes for verifying the authenticity and integrity of digital messages or documents.

Mathematical terminology refers to the specific language, symbols, and vocabulary used in the field of mathematics. This terminology helps convey concepts, methods, and relationships in a precise and standardized way. Here are some key aspects of mathematical terminology: 1. **Definitions**: Precise descriptions of mathematical concepts, such as "a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Mathematics has evolved through various historical periods, each characterized by different developments, techniques, and areas of focus. Here's a brief overview of key periods in the history of mathematics: ### 1. **Ancient Mathematics (c. 3000 BC - 500 AD)** - **Civilizations:** Early contributions from the Egyptians (geometry and basic arithmetic), Babylonians (base-60 system), and Greeks (geometry and formal proofs).

"Works" about the history of mathematics can refer to a variety of texts, including books, articles, and papers that explore the development of mathematical concepts, theories, and practices over time.

In mathematics, the term **order** can refer to several different concepts depending on the context. Here are a few key interpretations: 1. **Order of an Element**: In group theory, the order of an element \( g \) in a finite group is the smallest positive integer \( n \) such that \( g^n = e \), where \( e \) is the identity element of the group.

Cyclical monotonicity is a concept from mathematics, particularly in the field of optimal transport and convex analysis. It is used to characterize certain types of functions, specifically in the context of measures and distributions over metric spaces.

Uniqueness theorems are a set of principles in mathematical analysis, particularly within the context of differential equations and functional equations. These theorems typically assert conditions under which a particular mathematical object—such as a solution to an equation or a function—can uniquely be determined from given constraints or properties.

Univariate analysis refers to the examination of a single variable in a dataset. The term "univariate" comes from "uni," meaning one, and "variate," which refers to a variable. This type of analysis is fundamental in statistics and is often the first step in exploring data. Key aspects of univariate analysis include: 1. **Descriptive Statistics**: This involves summarizing and describing the main features of a dataset.

In geometry, a "tomahawk" typically refers to a shape or figure resembling the outline or silhouette of a tomahawk, which is a type of axe. However, there isn't a widely recognized geometric term specifically called "tomahawk" in classical geometry.

The term "Index of logarithm articles" isn't a standard phrase or concept in mathematics or academic literature, so it could refer to different things depending on context. Here are a few possibilities: 1. **Logarithm Index**: In mathematics, the index of a logarithm can refer to the exponent of a number in the expression of that logarithm.

Uniform tilings in the hyperbolic plane are arrangements of hyperbolic shapes that cover the entire hyperbolic plane without any gaps or overlaps while exhibiting a regular and repeating pattern. These tilings are characterized by their symmetry and regularity, often defined by their vertex configuration and the types of shapes used in the tiling. In mathematical terms, a uniform tiling can be described as a tessellation of the hyperbolic plane using polygonal shapes that can be generalized by their vertex configurations.