As of my last update, the following is a list of celestial objects that are considered potential dwarf planets or have been proposed as such: 1. **Pluto** - The most famous dwarf planet, located in the Kuiper Belt. 2. **Eris** - A distant object also found in the Kuiper Belt, slightly smaller than Pluto but more massive. 3. **Haumea** - Known for its elongated shape and rapid rotation, it resides in the Kuiper Belt.

Boundary value problems (BVPs) are a type of differential equation problem where one seeks solutions that satisfy specified conditions, or "boundary conditions," at certain values of the independent variable. These problems are prevalent in various fields of science and engineering, where they often arise in the context of physical systems described by differential equations.

Subharmonic functions are a class of functions that arise in the study of potential theory and various fields of mathematics, including complex analysis and partial differential equations.

Bessel potentials are a type of potential operator associated with Bessel functions, which are solutions to Bessel's differential equation. In functional analysis and partial differential equations, Bessel potentials are used to define certain types of Sobolev spaces and are closely related to the notion of fractional derivatives. The Bessel potential of order \( \alpha \) can be defined in terms of the Bessel operator.

Boggio's formula is a mathematical result used in the context of potential theory and solutions of the Poisson equation related to electrostatics. It provides a way to compute the potential (or electric field) due to point charges or other distributions under certain conditions. While there are various contexts in which the name "Boggio's formula" might arise, it is most commonly associated with the problem of determining the potential due to a point charge outside a sphere.

Cylindrical multipole moments are a mathematical representation used in physics and engineering to describe the distribution of mass, charge, or any other physical quantity in a cylindrical coordinate system. These moments help in analyzing systems with cylindrical symmetry, such as wires, cylinders, or other structures that exhibit similar symmetry properties. ### Definition and Calculation Cylindrical multipole moments extend the concept of multipole moments, which are generally used to describe the spatial distribution of charges or masses in Cartesian coordinates.

A dipole generally refers to a system that has two equal but opposite charges or magnetic poles separated by a distance. There are two main contexts in which the term "dipole" is commonly used: 1. **Electric Dipole**: In electrostatics, an electric dipole consists of two equal and opposite electric charges (positive and negative) separated by a distance.

A voltage symmetrization system is a technology or device used to equalize or balance the voltage levels across different phases or circuits in an electrical system. This is particularly important in three-phase power systems, where imbalances can lead to inefficiencies, overheating, increased losses, and premature equipment failure.

Orchidée can refer to several things depending on the context: 1. **Botany**: "Orchidée" is the French word for "orchid," a diverse and widespread family of flowering plants known for their unique and often intricate flowers. Orchids belong to the family Orchidaceae and are found in various habitats around the world.

Extremal length is a concept from the field of complex analysis and geometric topology, specifically concerning the study of Riemann surfaces and conformal mappings. It is used to measure the size of families of curves on a surface and has applications in various areas, including Teichmüller theory and the study of conformal structures. Mathematically, the extremal length of a family of curves is defined via a certain optimization problem.

The Furstenberg boundary is a concept in probability theory and dynamical systems, particularly in the study of random walks on groups and homogeneous spaces. Named after the mathematician Herbert Furstenberg, this boundary provides a way to understand the asymptotic behavior of random walks by relating them to geometric structures. In more detail, the Furstenberg boundary can be defined in the context of a probability measure on a group, often a non-abelian group.

Harmonic measure is a concept in mathematical analysis, particularly in potential theory and complex analysis. It is associated with harmonic functions, which are functions that satisfy Laplace's equation. Here are some key points to understand harmonic measure: 1. **Harmonic Functions**: A function \( u \) is harmonic in a domain if it is twice continuously differentiable and satisfies Laplace's equation, i.e., \( \nabla^2 u = 0 \).

Laplace expansion, also known as the Laplace transform, is a mathematical technique used to transform a function of time (often a signal or a system's response) into a function of a complex variable. The Laplace transform is especially useful in engineering and physics for analyzing linear time-invariant systems, particularly in control theory and circuit analysis.

The Newtonian potential, also known as the gravitational potential, describes the gravitational field generated by a mass distribution in classical physics. It is derived from Newton's law of universal gravitation and provides a way to calculate the gravitational potential energy per unit mass at a given point in space due to a mass or a distribution of mass.

Carolyne Van Vliet is not widely recognized, and there may not be extensive information available about her in popular sources.

The Poisson kernel is a fundamental concept in harmonic analysis and potential theory, particularly in the study of solutions to the Laplace equation. It is used, among other things, to express the solution to the Dirichlet problem for the unit disk.

A potential energy surface (PES) is a conceptual and mathematical representation of the potential energy of a system, typically in the context of molecular and quantum mechanics. It describes how the potential energy of a system varies with the configuration of its particles, such as the positions of atoms in a molecule.

FormMail is a script used to process web form submissions. It allows users to collect and send form data via email. Typically, FormMail is implemented using server-side languages, such as Perl, PHP, or other technologies that can handle HTTP requests and SMTP (Simple Mail Transfer Protocol) for sending emails. When users fill out a form on a website and submit it, the FormMail script captures the input, processes it, and sends it to a specified email address.

Quadrature domains are a mathematical concept related to the representation and computation of complex functions, particularly in the context of numerical analysis and function approximation. The term is often associated with the study of solutions to partial differential equations (PDEs) and can also be linked to various topics in analysis, such as potential theory and conformal mappings.

Power control generally refers to methods and techniques used to manage the power output of devices or systems, ensuring optimal performance, efficiency, and safety. The concept of power control can apply to various fields, including telecommunications, electronics, renewable energy, and more. Here are some common contexts for power control: 1. **Telecommunications**: In mobile networks, power control is essential for managing the power levels transmitted by mobile devices to maintain a good communication link with base stations.