The 20th century saw several notable Portuguese mathematicians who made significant contributions to various fields of mathematics. Here are some prominent figures: 1. **José Champalimaud (1918-2004)**: Known more for his contributions to medicine and philanthropy, Champalimaud was also involved in mathematical research, particularly in the context of his work in medical science.

Legal positivism is a school of thought in legal philosophy that asserts that the validity of law is not connected to moral or ethical considerations but is instead determined by its sources and formal criteria. According to legal positivism, laws are rules created by human beings and are valid because they are enacted by legitimate authority or follow established procedures, rather than because they are just or moral.

Arthur P. Bochner is a prominent figure in the field of communication studies, known primarily for his work in narrative research, qualitative inquiry, and the role of storytelling in human communication. He has contributed significantly to the understanding of how narratives shape our experiences and identities. Bochner is also known for his involvement in academic publications, including editing and contributing to various journals and books that focus on the intersection of communication, culture, and personal stories.

Radiopharmaceuticals are specialized drugs that contain radioactive isotopes and are used primarily in medical imaging and therapy. They are designed for diagnostic and therapeutic purposes, particularly in nuclear medicine. ### Key characteristics: 1. **Radioactive Isotopes**: Radiopharmaceuticals consist of a radionuclide (radioactive isotope) attached to a pharmaceutical component, which can target specific organs, tissues, or cellular receptors in the body.

The notation (120132) 2003 FY128 appears to be a reference to a specific number or identifier, but its exact meaning is not clear without additional context. It could represent a variety of things depending on the field it pertains to, such as a code for a product, a financial year designation, or even a specific document or case number. - **120132** might be a part number, client ID, or some other identifier.

(145452) 2005 RN43 is a minor planet or asteroid that is part of the asteroid belt in our solar system. It was discovered on September 8, 2005. Like other asteroids, it is composed of rock and metal and orbits the Sun. The designation "145452" refers to its number in the sequential list of discovered minor planets, while "2005 RN43" is its provisional designation, indicating it was discovered in the year 2005.

(307261) 2002 MS4 is an asteroid that is part of the main belt, which is the region of space between the orbits of Mars and Jupiter where a majority of the solar system's asteroids are found. This particular asteroid was discovered in June 2002 and is classified as a "main-belt asteroid" in the asteroid catalog.

(35671) 1998 SN165 is an asteroid that is part of the main asteroid belt, which lies between the orbits of Mars and Jupiter. It was discovered on September 24, 1998, and is classified as a near-Earth object (NEO). The asteroid is named following the convention of minor planet naming, often based on various themes including characters, events, or places of significance.

(523643) 2010 TY53 is a classified asteroids and part of the larger category of near-Earth objects (NEOs). Specifically, it is a member of the Apollo group of asteroids, which are known for their orbits that bring them close to Earth's orbit.

(523671) 2013 FZ27 is a minor planet or asteroid that is part of the solar system. Specifically, it is classified as a near-Earth object (NEO), which means it has an orbit that brings it close to Earth's orbit. Discovered on March 18, 2013, it belongs to the Apollo group of asteroids, which are characterized by their orbits that cross Earth's orbit.

(574372) 2010 JO179 is a trans-Neptunian object (TNO) located in the Kuiper Belt, which is a region of the solar system beyond the orbit of Neptune. It was discovered on May 12, 2010, and is classified as a detached object, meaning its orbit is significantly influenced by gravitational interactions with nearby planets, particularly Neptune.

(523706) 2014 HF200 is a designated asteroidal object within our solar system. It is classified as a near-Earth object (NEO), specifically an Apollo-type asteroid, which means its orbit crosses that of Earth. Discovered in 2014, it has been studied for its physical characteristics, orbital parameters, and potential impact risks. As a small Solar System body, 2014 HF200 may provide insights into the formation and evolution of our solar system.

2014 SV349 is a trans-Neptunian object (TNO) located in the outer regions of our Solar System. It was discovered on September 22, 2014, during the Pan-STARRS survey. This object is classified as a "distant" Kuiper Belt Object (KBO), which means it orbits the Sun at a significant distance beyond the orbit of Neptune.

(528381) 2008 ST291 is a centaur—a type of minor planet that is situated between the asteroid and comet categories. Centaurs are typically found in the outer Solar System, between the orbits of Jupiter and Neptune. They are characterized by unstable orbits and exhibit characteristics of both asteroids and comets.

(533560) 2014 JM80 is a designation for a specific asteroid that is part of the main asteroid belt in our solar system. It was discovered in 2014 and is categorized as a member of the "Hilda" group of asteroids, which are known for their stable orbits that share similarities with Jupiter’s orbit. Asteroids like 2014 JM80 are typically small, and their characteristics can include size, orbit, and composition.

120347 Salacia is a trans-Neptunian object located in the Kuiper Belt, which is a region of the solar system beyond the orbit of Neptune filled with icy bodies and dwarf planets. Discovered in 2003, Salacia is categorized as a "dwarf planet" candidate and is one of the larger objects of its kind. Its diameter is estimated to be around 800 kilometers (approximately 500 miles), though measurements may vary.

20000 Varuna is a trans-Neptunian object and a Centaur, which means it is located in the outer region of the Solar System, beyond the orbit of Neptune. It was discovered in 1978 and is named after Varuna, a deity in Hindu mythology associated with the sky and the oceans.

The double layer potential is a concept from potential theory and is particularly relevant in the study of boundary value problems in mathematical physics, especially in the context of electrostatics and fluid dynamics. It is often used when dealing with boundary integral equations. ### Definition In a simple sense, the double layer potential is a way to represent a distribution of surface charges on a boundary in an n-dimensional space.

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.