Rigid cohomology is a relatively new and sophisticated theory in the field of arithmetic geometry, developed primarily by Bhargav Bhatt and Peter Scholze. It serves as a tool to study the properties of schemes over p-adic fields, with a focus on their rigid analytic aspects. Rigid cohomology generalizes several classical notions in algebraic geometry and offers a framework for understanding phenomena in the realm of p-adic Hodge theory.

RMIT School of Science is part of the Royal Melbourne Institute of Technology (RMIT) University in Australia. It is focused on various disciplines within the sciences, including but not limited to chemistry, environmental science, physics, and mathematics. The school aims to provide a high-quality education through innovative teaching methods, research initiatives, and collaborative projects. Students at RMIT School of Science can engage in practical learning experiences, research opportunities, and gain exposure to industry practices.

Robert A. Frosch is a notable figure in the fields of engineering, management, and research. He is best known for his role as a former Administrator of the National Aeronautics and Space Administration (NASA) from 1977 to 1981. Frosch played a significant part in overseeing various space programs during his tenure. He has also worked in the private sector and held positions in academia, contributing to advancements in technology, particularly in areas related to energy and engineering.

The small icosicosidodecahedron is a convex Archimedean solid characterized by its unique arrangement of faces, vertices, and edges. Specifically, it is composed of 62 faces: 20 regular triangles, 30 squares, and 12 regular pentagons. It has a total of 120 edges and 60 vertices.

Topochemical polymerization is a specialized method of polymerization that involves the conversion of monomers into polymers through a mechanism that is influenced by the spatial arrangement of molecules in a solid-state or crystalline form. This process typically requires that the monomers be organized in a specific geometric arrangement, allowing for direct reactions to occur without the need for solvent, heat, or other conventional polymerization conditions.

Bioplastic refers to a type of plastic that is either made from renewable biomass sources, such as plant materials, or is designed to biodegrade more easily than traditional plastics. There are two main categories of bioplastics: 1. **Bio-based Plastics**: These are primarily made from renewable resources like starch, cellulose, or polylactic acid (PLA) derived from corn or sugarcane.

The Cossee–Arlman mechanism is a theoretical framework used to explain the mechanism of polymerization in certain catalytic processes, particularly in the context of olefin polymerization. It was proposed by the chemists Cossee and Arlman in the mid-20th century. The mechanism describes the coordinated steps involved in the polymerization of alkenes (olefins) through a transition metal catalyst, typically zirconium or other metal complexes.

Ostwald's rule, also known as Ostwald's dilution law, refers to a principle in chemistry that describes the behavior of certain solutions when they are diluted. Specifically, it states that the more dilute a solution is, the more likely it is to favor the formation of the most stable form of a solute or product, often in relation to an equilibrium process.

I = PAT is an equation that represents the relationship between environmental impact (I), population (P), affluence (A), and technology (T). This formula is often used in environmental science and sustainability discussions to analyze how various factors contribute to environmental degradation and resource use. - **I (Impact)**: This refers to the environmental impact, which includes factors such as ecological footprint, carbon emissions, and resource depletion. - **P (Population)**: This represents the total number of people.

The Big \( q \)-Legendre polynomials are a generalization of the classical Legendre polynomials, which arise in various areas of mathematics, including orthogonal polynomial theory and special functions. The \( q \)-analog of mathematical concepts replaces conventional operations with ones that are compatible with the \( q \)-calculus, often leading to new insights and applications, particularly in combinatorial contexts, statistical mechanics, and quantum algebra.

Biocapacity refers to the capacity of an ecosystem to regenerate biological materials and to provide resources and services. It reflects the ability of the Earth's ecosystems to produce renewable resources, such as food, timber, and fibers, and to absorb waste, particularly carbon emissions.

Biological exponential growth refers to a pattern of population growth where the number of individuals in a population increases rapidly over time under ideal environmental conditions. This phenomenon occurs when resources are abundant and environmental factors do not limit reproduction and survival. Key characteristics of biological exponential growth include: 1. **Rapid Growth Rate**: When conditions are favorable, populations can grow at a constant rate, resulting in a doubling of the population size over regular intervals.

Immigration reduction in the United States refers to policies and measures aimed at decreasing the number of immigrants entering or residing in the country. Advocates of immigration reduction argue that limiting immigration can help protect jobs for native-born Americans, reduce strain on public services, enhance national security, and preserve cultural identity. Key aspects of immigration reduction include: 1. **Policy Changes**: This may involve changing visa availability, imposing stricter eligibility criteria for immigration, or enhancing border enforcement measures.

In biology, a growth curve is a graphical representation that shows the increase in the number of cells, organisms, or biological mass over time. Growth curves can be used to analyze the growth patterns of populations, microorganisms, plants, or even different stages in the life of an individual organism. They typically depict how a biological entity grows and can include various phases, often classified into distinct stages.

Heia Norge (VG) is a feature associated with the Norwegian newspaper Verdens Gang (VG), which is one of the largest newspapers in Norway. The term "Heia Norge" translates to "Go Norway" in English and is often used in a patriotic context, especially during sporting events or national celebrations. It typically encompasses content that promotes national pride and support for Norwegian athletes, teams, or cultural events.

Populism in Europe refers to a political approach that contrasts "the people" against "the elite" and often portrays itself as a movement that represents the common people against a perceived corrupt or disconnected establishment. This phenomenon has gained significant traction in various European countries over the past few decades, particularly in response to economic dissatisfaction, immigration, globalization, and the perceived shortcomings of traditional political parties.

Qasimism is a term that generally refers to a religious or ideological approach associated with the beliefs and teachings of Qasim al-Ibn al-Hassan, a prominent figure in Shiite Islam, especially within the context of the events of Ashura and the Battle of Karbala. Followers of Qasimism typically emphasize themes such as martyrdom, sacrifice, justice, and the struggle against oppression, which are central to the narrative of Karbala and the larger Shiite tradition.

Socialism of the 21st Century is a political and economic concept that seeks to adapt traditional socialist principles to contemporary realities. It emerged notably in Latin America in the late 20th and early 21st centuries, particularly through the policies and leadership of figures such as Hugo Chávez in Venezuela, Evo Morales in Bolivia, and Rafael Correa in Ecuador.

William Jennings Bryan (1860–1925) was an American politician, orator, and lawyer who played a significant role in the Democratic Party during the late 19th and early 20th centuries. He is best known for his advocacy of populism and his support of various progressive reforms, including women's suffrage and the regulation of monopolies.

The 21st century has seen numerous contributions from Portuguese mathematicians across various fields of mathematics. Here are a few notable figures and their contributions: 1. **Artur Avila** - A prominent mathematician known for his work in dynamical systems and mathematical analysis. He was awarded the Fields Medal in 2014 for his contributions to the theory of dynamical systems and is recognized for his work on the stability of differential equations and the statistical properties of dynamical systems.