The "parallel parking problem" is a well-known problem in the fields of robotics and computer science, particularly in the area of motion planning and autonomous vehicle navigation. It involves the challenge of maneuvering a vehicle into a parallel parking space, which typically involves reversing into a nook between two parked cars with limited space. ### Key Concepts: 1. **Movement Dynamics**: The vehicle must be able to navigate turnings and adjust its position based on its size and the size of the parking space.
Statistical risk refers to the potential for loss or negative outcomes associated with uncertain events and is often quantified using statistical methods. It is a measure of the likelihood and impact of adverse events occurring within a given context, such as finance, insurance, health, or decision-making processes. In practical terms, statistical risk can be defined in several ways, including: 1. **Probability of Adverse Events**: It often involves calculating the probability of specific negative outcomes.
The **survival function**, often denoted as \( S(t) \), is a fundamental concept in survival analysis and statistics, particularly in the context of time-to-event data. It describes the probability that a subject or an individual survives beyond a certain time \( t \).
Gas discharge lamps are a type of electric light source that produce light by passing an electric current through a gas or a vapor. When the gas is ionized, it emits light as the electrons in the gas atoms transition between energy levels. These lamps are widely used in various applications due to their efficiency and the quality of light they produce.
Richard Canary is a professor in the Department of Mathematical Sciences at the University of Vermont. He is known for his work in mathematical biology, particularly in the areas of population dynamics and ecological modeling. His research often focuses on using mathematical techniques to better understand biological systems and phenomena.
A perfect spline, often referred to in the context of spline interpolation or spline approximation, is a mathematical construct used to create a smooth curve that passes through a given set of points (or control points). In general, "spline" refers to a piecewise polynomial function that is defined on intervals, and a "perfect" spline typically implies that the spline fits the data points exactly without any error.
Philip Rabinowitz was an American mathematician known for his contributions to various areas of mathematics, including functional analysis, numerical analysis, and applied mathematics. He was particularly recognized for his work on approximation theory and rational approximation. Throughout his career, he authored numerous research papers and was involved in academic teaching and mentorship. Rabinowitz’s work has had a lasting influence in his fields of study, and he may be cited in various mathematical literature.
Streamline diffusion is a concept often used in fluid dynamics and related fields to describe the movement of particles or substances within a fluid flow. It refers to the process by which particles or molecules distribute themselves along the streamlines of a flow. In more specific terms, streamline diffusion is typically associated with the way substances diffuse within a moving fluid, influenced by the flow's velocity and direction.
A strictly determined game is a type of two-player zero-sum game in which each player has a clear and linear strategy that leads to a specific outcome based on the strategies chosen by both players. In such games, there is a unique equilibrium strategy for both players, meaning that there is one optimal strategy that each player can follow that guarantees the best possible outcome for themselves, regardless of what the other player does.
Tom Hull is a mathematician known for his work in the field of mathematics and education. He is particularly recognized for his contributions to the study of mathematical patterns, geometry, and recreational mathematics. Hull has also been involved in developing materials for mathematical education and promoting mathematical problem-solving skills. He is perhaps best known in the context of his work with origami and the mathematical principles that govern the art of paper folding.
The **Squeeze operator** is a mathematical concept primarily used in the field of quantum mechanics, quantum optics, and quantum information science. It refers to a specific type of quantum state transformation that reduces the uncertainty (or noise) in one observable while increasing it in another, thereby "squeezing" the quantum state in a particular direction in phase space.
High availability (HA) refers to a system or component that is continuously operational for a long period of time. In the context of IT infrastructure, it is the design and implementation of systems that ensure a high level of operational performance and uptime, minimizing downtime and ensuring continuous access to services and data. Key aspects of high availability include: 1. **Redundancy**: Critical components are duplicated to ensure that if one fails, another can take over without interrupting the service.
A "money pump" is a concept from economics and game theory that describes a situation where an individual can be exploited due to inconsistencies in their preferences or choice-making. The term often applies to situations involving violations of rational choice, particularly in the context of decision-making under uncertainty or with non-standard preferences. In a typical money pump scenario, a person has preferences that are not transitive or consistent.
Yuri Burago is a mathematician known for his contributions to the fields of geometry and topology. He has made significant advancements in the study of metric spaces, as well as in the areas of differential geometry and geodesic flows. In addition to his research, Burago is also known for his role in mathematics education, having authored several textbooks that are used in university-level courses.
The Adams hemisphere-in-a-square projection is a map projection used for representing the spherical surface of the Earth on a flat surface, specifically designed to preserve the relationships and proportions of areas. This projection is characterized by its ability to contain a hemisphere within a square boundary, which makes it useful for visualizations that require compact representation of large areas. In the Adams projection, the hemisphere is represented in such a way that the edges of the square remain straight, while the curvature of the Earth is taken into account.
Transversality conditions are mathematical constraints used primarily in the field of optimal control theory and calculus of variations. They ensure that solutions to optimization problems—particularly those involving differential equations—are well-defined and meet certain criteria at the endpoints of the optimization interval. In a typical setting, when optimizing a functional that involves a continuous state variable over a specified interval, the transversality condition helps to determine the behavior of the control (or path) at the boundary points.
Trend surface analysis is a spatial analysis technique used in geography, geostatistics, and various fields dealing with spatial data. It helps to identify and model the underlying patterns and trends within spatial data sets by fitting a mathematical function to a set of observed data points. The main objective is to create a continuous surface that represents the spatial distribution of a variable of interest.
The W. T. and Idalia Reid Prize is an award given by the American Mathematical Society (AMS) that recognizes outstanding research in the field of mathematics. Established in honor of W. T. Reid, a prominent mathematician, and his wife Idalia Reid, the prize aims to support and encourage mathematical research, particularly for individuals who demonstrate significant achievement in their work. The specific criteria and focus of the prize may vary, but generally, it promotes the importance of innovative contributions to mathematical sciences.