The Voorhoeve index is a measure used in health economics and decision analysis to evaluate the efficiency of health interventions by comparing the cost-effectiveness ratios of different health care options. Originally developed by the Dutch economist Jan Voorhoeve, it allows for the prioritization of health interventions based on their ability to improve health outcomes per unit of cost.

Conformal mappings are a class of functions in mathematics, particularly in complex analysis, that preserve angles locally. A function \( f \) is said to be conformal at a point if it is holomorphic (complex differentiable) at that point and its derivative \( f' \) is non-zero. This property ensures that the mapping preserves the shapes of infinitesimally small figures (though not necessarily their sizes).

A Dirichlet space is a type of Hilbert space that arises in the study of Dirichlet forms and potential theory. These spaces have applications in various areas of analysis, including the theory of harmonic functions and partial differential equations. A Dirichlet space can be defined as follows: 1. **Function Space**: A Dirichlet space is typically formed from a collection of functions defined on a domain, often a subset of Euclidean space or a more general manifold.

Partial fractions is a technique commonly used in algebra to break down rational functions into simpler fractions that can be more easily integrated or manipulated. In the context of complex analysis, the method can also be applied to simplify integrals of rational functions, particularly when dealing with complex variables. ### What is Partial Fraction Decomposition?

Goodman's conjecture is a hypothesis in the field of combinatorial geometry, proposed by the mathematician Jesse Goodman in 1987. The conjecture deals with the arrangement of points in the plane and relates to the number of convex polygons that can be formed by connecting those points.

Hilbert's inequality is a fundamental result in the field of functional analysis and it relates to the boundedness of certain linear operators. There are various forms of Hilbert's inequalities, but one of the most well-known is the one dealing with the summation of sequences.

In complex analysis, an isolated singularity is a point at which a complex function is not defined or is not analytic, but is analytic in some neighborhood around that point, except at the singularity itself.

In mathematical analysis, particularly in the theory of partial differential equations and functional analysis, a pseudo-zero set typically refers to a set of points where a function behaves in a certain way that is "near" to being zero but doesn't necessarily equate to zero everywhere on the set. The term is not universally defined across all areas of mathematics, so its exact meaning can vary based on the context in which it is used.

Cauchy's functional equation is a well-known functional equation given by: \[ f(x + y) = f(x) + f(y) \] for all real numbers \(x\) and \(y\). This equation describes a function \(f\) that satisfies the property that the value of the function at the sum of two arguments is equal to the sum of the values of the function at each argument.

The **domain** of a function is the set of all possible input values (or "arguments") for which the function is defined. In other words, it includes all the values you can use as inputs without causing any mathematical inconsistencies, such as division by zero or taking the square root of a negative number.

A **local diffeomorphism** is a mathematical concept from differential geometry that describes a type of smooth map between two differentiable manifolds (or smooth manifolds).

An amenable Banach algebra is a specific type of Banach algebra that possesses a certain property related to its representations and, intuitively speaking, its "size" or "complexity." The concept of amenability can be traced back to the theory of groups, but it has been extended to abstract algebraic structures such as Banach algebras.

BK-space generally refers to a specific type of topological space in the context of topology and functional analysis. The term "BK-space" often denotes a **Banach-Knaster space**, which is a certain type of topological vector space that can be endowed with the properties of completeness and other characteristics typical to Banach spaces.

Borchers algebra refers to a mathematical framework introduced by Daniel Borchers in the context of quantum field theory. It arises notably in the study of algebraic quantum field theory (AQFT), where the focus is on the algebraic structures that underpin quantum fields and their interactions. In Borchers algebra, one typically deals with specific types of algebras constructed from the observables of a quantum field theory. These observables are collections of operators associated with physical measurements.

The Cramér–Wold theorem is a result in probability theory that provides a characterization of multivariate normal distributions. It states that a random vector follows a multivariate normal distribution if and only if every linear combination of its components is normally distributed. More formally, let \( X = (X_1, X_2, \ldots, X_n) \) be a random vector in \( \mathbb{R}^n \).

The Cohen–Hewitt factorization theorem is an important result in the field of functional analysis, particularly in the study of commutative Banach algebras and holomorphic functions. The theorem essentially deals with the factorization of elements in certain algebras, specifically those elements that have a suitable structure, such as being the spectrum of a compact space.

The Eberlein–Šmulian theorem is a result in functional analysis that characterizes weak*-compactness in the dual space of a Banach space. Specifically, it provides a criterion for when a subset of the dual space \( X^* \) (the space of continuous linear functionals on a Banach space \( X \)) is weak*-compact.

An enveloping von Neumann algebra is a concept from the field of functional analysis, specifically in the context of operator algebras. To understand this concept, we first need to clarify what a von Neumann algebra is. A **von Neumann algebra** is a *-subalgebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator.

The Fifth-order Korteweg–De Vries (KdV) equation is a mathematical model that extends the classical KdV equation, which is used to describe shallow water waves and other dispersive wave phenomena.

Friedrichs's inequality is a fundamental result in the field of functional analysis and partial differential equations. It provides a way to control the norm of a function in a Sobolev space by the norm of its gradient. Specifically, it is often used in the context of Sobolev spaces \( W^{1,p} \) and \( L^p \) spaces.