In geometry, a lens is a shape formed by the intersection of two circular arcs. Specifically, it is the region bounded by two circles that overlap. The area enclosed by these arcs resembles the shape of a lens, which is the reason for its name. There are two main types of lenses: 1. **Convex Lens**: This occurs when both arcs are part of circles that are convex towards each other. The resulting lens shape bulges outward.

John von Neumann was a pioneering mathematician, physicist, computer scientist, and polymath whose contributions have inspired numerous concepts, theories, and entities. Here’s a list of notable things named after him: 1. **Von Neumann Architecture**: A computer architecture design model that outlines a system where a single memory space stores both data and instructions.

Von Neumann is a large lunar impact crater located on the Moon's surface, named after the famous mathematician and physicist John von Neumann. It is situated in the eastern part of the Moon's near side, near the edge of the Oceanus Procellarum (Ocean of Storms).

Projections onto convex sets is a mathematical concept often used in optimization, functional analysis, and convex geometry. The idea centers around finding a point in a convex set that is closest to a given point outside that set.

The Hilbert–Schmidt integral operator is a specific type of integral operator that arises in functional analysis and is connected to the theory of compact operators on Hilbert spaces. It is particularly important in the context of integral equations and various applications in mathematical physics and engineering. ### Definition Let \( K(x, y) \) be a measurable function defined on a product space \( [a, b] \times [a, b] \).

Shape Modeling International (SMI) is an annual academic conference focused on research in the field of shape modeling and related areas. It aims to bring together researchers, practitioners, and industry professionals to discuss advancements in the understanding, representation, and manipulation of shapes in various contexts, including computer graphics, computer-aided design (CAD), and geometric modeling.

WolframAlpha is a computational knowledge engine developed by Wolfram Research. Unlike traditional search engines that provide links to web pages, WolframAlpha is designed to generate specific answers and insights from a vast store of curated data, algorithms, and computational capabilities. It can answer factual queries by performing calculations, generating graphs, and providing detailed information across various domains, including mathematics, science, engineering, history, geography, and more.

MuMATH, which stands for "Multiple Use Mathematics," is a software tool designed for teaching and learning mathematics through interactive visualizations and simulations. It allows users, especially students, to explore mathematical concepts in a hands-on manner, facilitating a deeper understanding of complex topics. MuMATH is often utilized in educational settings to demonstrate various mathematical principles, including algebra, geometry, and calculus.

Mxparser is a lightweight and highly configurable mathematical expression parser and evaluator designed for Java and other programming languages. It allows users to parse, evaluate, and manipulate mathematical expressions represented as strings. Mxparser supports a wide range of mathematical functions, operators, and features, making it suitable for applications that require mathematical calculations, such as scientific computing, educational tools, and financial applications.

In the context of mathematics, particularly linear algebra and numerical analysis, a **convergent matrix** often refers to matrices that exhibit certain convergence properties under iterative processes. However, the term "convergent matrix" isn't a standard term broadly recognized like "convergent series" or "convergent sequence.

A **copositive matrix** is a special type of matrix that arises in the context of optimization and mathematical programming, particularly in the study of quadratic forms and convexity. A symmetric matrix \( A \) is said to be copositive if for any vector \( x \) in the non-negative orthant \( \mathbb{R}^n_+ \) (i.e.

The One-Child Policy was a population control policy instituted by the Chinese government in 1979 to curb the rapid population growth in the country. The policy restricted urban couples to having only one child, although there were some exceptions based on ethnicity, parental status, and other factors. In rural areas, families were often allowed to have a second child if the first was a girl, as a way to address cultural preferences for male heirs.

Reindeer, also known as caribou in North America, have a distribution that primarily spans the Arctic and Subarctic regions. Their populations are found across the northern parts of Europe, Asia, and North America. Here are some key points on their distribution: 1. **Habitat**: Reindeer are adapted to cold environments and are typically found in tundra, boreal forests, and alpine regions.

Reproductive rights refer to the legal rights and freedoms related to reproduction and reproductive health. These rights encompass a range of issues that affect individuals' ability to make informed choices about their reproductive lives. Key components of reproductive rights include: 1. **Access to Contraception**: The right to obtain and use contraceptives to prevent unwanted pregnancies. 2. **Abortion Rights**: The right to access safe and legal abortion services without facing discrimination, stigma, or undue restrictions.

Zero Population Growth (ZPG) refers to a statistical condition in which a population's size remains constant over time, meaning that the number of births is equal to the number of deaths, leading to no net growth. This concept is often used in discussions about sustainable development and environmental impact.

Optimized Consumer Intensity Analysis (OCIA) is a method used primarily in the context of market research, consumer behavior analysis, and business strategy. While the term may not be widely standardized across all industries, it generally relates to analyzing how intensely consumers engage with a product or brand, and it aims to optimize this engagement for better business outcomes.

The "Homicidal Chauffeur Problem" is a well-known concept in the field of motion planning and robotics, specifically within the area of control theory and game theory. It addresses a scenario where a "chauffeur" (or driver) is trying to evade a pursuer while navigating through a defined environment. The pursuer typically seeks to capture or reach the chauffeur, who is attempting to avoid being caught.

A pursuit curve is a type of mathematical curve that describes the path taken by a pursuer attempting to catch a moving target. In the context of pursuit curves, the pursuer moves in a way that continually adjusts its direction toward the target, which may also be moving. The classic example involves two entities: a pursuer and a target.

Trajectory optimization is a mathematical and computational approach used to determine the most efficient path or sequence of states (trajectories) that a system should follow over time to achieve specific goals while satisfying certain constraints. This concept is commonly applied in various fields, including robotics, aerospace, control systems, and biomechanics. ### Key Aspects of Trajectory Optimization: 1. **Objective Function**: The optimization process typically involves minimizing or maximizing an objective function, which quantifies the performance of the trajectory.

Pseudospectral optimal control is a mathematical and computational approach used to solve optimal control problems. It combines the principles of pseudospectral methods with optimal control theory to find control inputs that minimize or maximize a given cost function while satisfying dynamic constraints defined by differential equations.