Quantum turbulence is a phenomenon that occurs in superfluid systems, particularly in liquid helium at very low temperatures. It is the quantum analog of classical turbulence, which involves chaotic and irregular fluid motion. In superfluids, the behavior of the fluid is governed by quantum mechanics rather than classical mechanics. As a result, quantum turbulence exhibits unique characteristics. It typically arises when a superfluid is subjected to a flow that exceeds a critical velocity, leading to the formation of quantized vortices.

A superfluid film refers to a thin layer of superfluid, a state of matter characterized by the complete absence of viscosity, allowing it to flow without dissipating energy. Superfluidity typically occurs in certain liquids, such as helium-4 and helium-3, at very low temperatures.

Fawwaz T. Ulaby is a prominent figure in the fields of electrical and computer engineering, particularly known for his work in electromagnetics and microwave engineering. As of my last knowledge update in October 2023, he has held academic positions, including serving as a professor and administrator at various institutions, notably at the University of Michigan. Ulaby has made significant contributions to research and education in areas such as remote sensing, radar, and the interaction of electromagnetic waves with various materials.

A "squircle" is a geometric shape that is a combination of a square and a circle. It has rounded corners, making it appear softer than a square while maintaining the general outline of a square. The term is commonly used in design, particularly in user interface design and graphics, where it's used to create visually appealing shapes that fit into a modern aesthetic.

The ATS theorem, also known as the Aharonov–Bohm theorem, is a fundamental result in quantum mechanics that illustrates the importance of electromagnetic potentials in the behavior of charged particles, even in regions where the electric and magnetic fields are zero.

The Brezis–Gallouët inequality is an important result in functional analysis and partial differential equations, particularly in the context of Sobolev spaces. It provides a bound for a certain type of functional involving the fractional Sobolev norms. Specifically, the inequality can be stated as follows: Let \( n \geq 1 \) and \( p \in (1, n) \).

Günther Frei may refer to a person, but without additional context, it's unclear who exactly you mean, as it is a name that could belong to various individuals. If you are referring to a specific person, providing more context would help clarify. For example, is he known for contributions in a specific field like sports, science, or arts?

In the context of matter, "phase" refers to a distinct form or state that a substance can take, characterized by its physical properties and the arrangement and behavior of its particles. The most commonly recognized phases of matter are: 1. **Solid**: In solids, particles are closely packed together in a fixed arrangement, which gives solids a definite shape and volume. The particles vibrate in place but do not move freely.

L. Gustave du Pasquier is a notable figure in the field of economics, particularly known for his contributions to the analysis of economic policy and the implications of government decisions on market dynamics. His work often involves the interaction between economic theory and practical government applications, focusing on the effects of regulations, taxation, and public spending on economic performance.

The Bender–Knuth involution is a combinatorial technique used in the enumeration of certain types of objects, specifically in the context of permutations and their associated structures. The technique was introduced by Edward A. Bender and Donald M. Knuth in the study of permutations with specific constraints, particularly permutations that can be represented with certain kinds of diagrams or structures.

Hall algebra is a mathematical structure that arises in the context of category theory and representation theory, particularly in the study of representations of finite groups and combinatorial structures. It is named after Philip Hall, who introduced the concept of Hall systems in the 1930s. At its core, Hall algebra is built on the idea of Hall pairs, which are certain collections of subsets of a finite set that satisfy specific combinatorial properties.

The Jucys-Murphy elements are a set of operators that arise in the theory of symmetric groups and representations of the symmetric group algebra. They are named after the mathematicians Alexander Jucys and J. D. Murphy, who introduced them in the context of representation theory.

The Kronecker coefficient is a combinatorial invariant associated with representations of symmetric groups. It is defined in the context of the representation theory of finite groups, particularly in relation to the decomposition of the tensor product of two representations.

The Littlewood–Richardson rule is a combinatorial rule used in the representation theory of symmetric groups and in the theory of Schur functions, which are important topics in algebraic combinatorics and mathematical physics.

Maclaurin's inequality is a result in mathematical analysis that relates to the behavior of convex functions.

Monk's formula is a mathematical formula used in the context of combinatorial optimization and scheduling, particularly in the analysis of certain types of resource allocation problems. However, the term "Monk's formula" might not be widely recognized in every mathematical or scientific community, and it may refer to different concepts depending on the context.

Newton's inequalities refer to a set of inequalities that relate the power sums of non-negative real numbers to the elementary symmetric sums of those numbers.

A Newton polygon is a geometric tool used in number theory and algebraic geometry, particularly in the study of polynomials and algebraic equations. It provides a way to analyze the behavior of a polynomial function at various points and helps in determining the properties of its roots, as well as understanding the multiplicity of these roots.

Schubert polynomials are a family of polynomials that arise in algebraic geometry, combinatorics, and representation theory. They are particularly important in the study of the cohomology of Grassmannians and the Schubert calculus.