Pulay stress is a phenomenon that arises in electronic structure calculations, particularly in the context of density functional theory (DFT) and other wavefunction-based methods. It occurs due to the finite basis set used to represent the electronic wavefunctions in these calculations. When performing electronic structure calculations, especially for periodic systems (such as crystals), one typically uses a finite basis set (like plane waves or localized atomic orbitals) to approximate the electronic wavefunctions.

A differential ideal is a concept from the field of differential algebra, which studies algebraic structures that are equipped with a derivation (a generalization of the idea of differentiation). In this context, a derivation is a unary operation that satisfies the properties of linearity and the Leibniz rule (product rule). ### Definition: A differential ideal is a special type of ideal in a differential ring (a ring equipped with a derivation) that is closed under the action of the derivation.

The Rössler attractor is a chaotic attractor named after the German physicist Otto Rössler, who introduced it in 1976. It is a system of three non-linear ordinary differential equations that model certain dynamical systems, and it is notable for its relatively simple structure compared to other chaotic systems like the Lorenz attractor. The equations that define the Rössler attractor are: 1. \(\frac{dx}{dt} = -y - z\) 2.

Pollsters are individuals or organizations that conduct surveys and polls to gather information about public opinion on various issues, candidates, or events. They often use statistical methods to design their surveys, select representative samples of the population, and analyze the results to provide insights into how people think and feel about certain topics. Pollsters play a significant role in political campaigns, market research, and social science research by helping to gauge voter preferences, identify trends, and inform decision-making processes.

"Lion Attacking a Dromedary" refers to a famous painting by the French artist Antoine-Louis Barye, created in the 19th century. Barye was known for his animal sculptures and paintings, and this particular work depicts the dramatic moment of a lion attacking a dromedary (a one-humped camel). The painting is noted for its dynamic composition and the vivid depiction of the struggle between the powerful predator and its prey.

In graph theory, **multiple edges** refer to a situation in a graph where two vertices are connected by more than one edge. This is common in **multigraphs**, which are a type of graph that allows for multiple edges between the same pair of vertices as well as loops (edges that connect a vertex to itself).

"Chicken" is a concept that appears in various contexts, including games, social psychology, and decision theory. In the most common usage, Chicken refers to a type of game in game theory that involves two players driving towards each other on a collision course. The objective is to see who will swerve or back down first. The player who swerves is deemed the 'chicken', while the player who stays the course, risking a collision, is considered braver.

"Squaring the square" refers to a mathematical problem in tiling, specifically involving the arrangement of squares within a square. The challenge is to subdivide a larger square into smaller squares, all of different sizes, such that there are no gaps or overlaps. The most famous solution to this problem was found by the mathematician Henry Dudeney in 1907. He created a square that was subdivided into 36 smaller squares, all of which were of distinct sizes.

A voodoo doll is a pop culture representation often associated with the religious practice of Voodoo, which originates from West African spiritual traditions and is particularly associated with Haiti and Louisiana. In popular belief, a voodoo doll is a figure that represents a person, and practitioners use it to influence or affect that person in some way—typically to cause harm, though it can also be used for healing or protection.

Doppler tracking refers to a technique used in various fields, including astronomy, telecommunications, and navigation, to determine the speed and position of an object by analyzing the changes in frequency or wavelength of signals received from that object. The method is based on the Doppler effect, which describes how the frequency of a wave changes for an observer moving relative to the source of the wave.

Paul Ruffin could refer to multiple individuals, but without more context, it's challenging to provide a specific answer. However, one known figure is Paul Ruffin, a prominent legal scholar and professor associated with the field of law.

Anatole Katok (1928-2020) was a prominent Russian-American mathematician known for his significant contributions to the fields of dynamical systems, ergodic theory, and topology. He played a key role in the development of the theory of dynamical systems and was particularly known for his work on Hamiltonian systems, toral automorphisms, and the geometric theory of dynamical systems.

Marcelo Viana is a Brazilian mathematician known for his work in various fields, including dynamical systems, geometric topology, and mathematical physics. He has made significant contributions to the understanding of dynamical systems, particularly in areas related to attractors, bifurcations, and the mathematical foundations of chaos theory. Viana also has an interest in intersections of mathematics with other disciplines, such as biology and economics.

Maryam Mirzakhani was an Iranian mathematician renowned for her exceptional contributions to the fields of mathematics, particularly in geometry and dynamical systems. Born on May 3, 1977, in Tehran, Iran, she became the first woman and the first Iranian to win the prestigious Fields Medal in 2014, often considered the highest honor in mathematics.

In astrodynamics, the "sphere of influence" (SOI) refers to the region around a celestial body within which that body exerts a dominant gravitational influence on an object, such as a spacecraft, compared to the influence of other gravitational bodies. The concept is crucial for trajectory planning and navigation in space, as it helps determine when to consider the gravitational effects of a particular body.