Mac Lane's planarity criterion, also known as the "Mac Lane's formation", is a combinatorial condition used to determine whether a graph can be embedded in the plane without any edges crossing. Specifically, the criterion states that a graph is planar if and only if it does not contain a specific type of subgraph as a "minor.

The Parry–Sullivan invariant is a concept in the field of dynamical systems and statistical mechanics, particularly related to the study of interval exchanges and translations. It is associated with the study of the dynamics of certain classes of transformations, particularly those that exhibit specific structural and statistical properties. The invariant itself is often connected to topological and measure-theoretic characteristics of systems that exhibit a certain type of symmetry or recurrence.

Barbara L. Osofsky is a prominent figure in the field of law, particularly known for her contributions to the field of legal education and health law. She has been recognized for her work in various legal areas, including her advocacy for legal issues related to health and medicine. Her writings and research often focus on the intersection of law, ethics, and public health. If you were looking for specific information or a different context regarding Barbara L. Osofsky, please provide more details!

Bjarni Jónsson is a name that can refer to different individuals, but without additional context, it is difficult to determine exactly who you're referring to. If you're asking about a notable person, it could be an Icelandic figure, as Bjarni Jónsson is a common name in Iceland. There may be athletes, academics, or artists by that name.

Chiungtze C. Tsen is a notable figure in the fields of mathematics and education, particularly known for her contributions to mathematical research and her role in academia. She has published research in various mathematical topics and has been involved in educational initiatives aimed at improving mathematics education.

D. S. Malik is an author known for his contributions to the field of computer science and programming. He is particularly recognized for his textbooks related to programming languages, data structures, and algorithms. One of his notable works is "Data Structures Using C," which is widely used in academic settings to teach data structures through the C programming language.

Dave Bayer is an American mathematician known for his work in various areas of mathematics, including algebra and combinatorics. He is also recognized for his contributions to mathematical education and outreach. Bayer has published numerous papers and is involved in promoting mathematical understanding through teaching and public engagement.

Donald S. Passman is an American entertainment attorney known for his expertise in the music industry. He has represented a variety of high-profile artists, songwriters, and music publishers. Passman is well-known for his book "All You Need to Know About the Music Business," which provides insights into the complexities of the music industry, including contracts, rights, and the various roles within the music business.

As of my last update in October 2023, there is no widely known figure by the name Ellen Kirkman in popular culture, history, or current events. It's possible that she could be a private individual or a subject relevant to a niche area not widely recognized.

Ada Lovelace refers to Augusta Ada King, Countess of Lovelace, who is often credited as one of the first computer programmers. She was born on December 10, 1815, and was the daughter of the famous poet Lord Byron. Lovelace is known for her work on Charles Babbage's early mechanical general-purpose computer, the Analytical Engine.

Adam Harper could refer to different individuals depending on the context, including professionals in various fields such as academia, music, or other industries. Without additional information about the specific Adam Harper you are asking about, it's challenging to provide a precise answer.

In computer science, "adaptation" can refer to several concepts depending on the context in which it is used. Here are a few common interpretations: 1. **Software Adaptation**: This involves modifying software to function in a new environment or to meet new requirements. This can include changes in the software itself, such as code modifications or updates, or could involve adjusting how the software interacts with other systems or hardware.

Additive combinatorics is a branch of mathematics that studies combinatorial properties of integers, particularly focusing on additive structures within sets of numbers. It explores how subsets of integers can be analyzed using tools from both combinatorics and number theory, often involving questions about sums, differences, and other additive operations. Key topics in additive combinatorics include: 1. **Sumsets**: The study of sets formed by the sums of elements from given sets.

An **additive polynomial** is a polynomial that satisfies a specific property related to addition.

An **adelic algebraic group** is a concept that arises in the context of algebraic groups and number theory, particularly in the study of rational points and arithmetic geometry. To explain it more precisely, we first need to understand what an algebraic group is and then what "adelic" means in this context. ### Algebraic Groups An **algebraic group** is a group that is also an algebraic variety.

The Fraňková–Helly selection theorem is a result in the field of functional analysis and topology, specifically concerning the selection of points from family of sets. It builds upon the classical Helly's theorem, which deals with finite intersections of convex sets in Euclidean spaces. The Fraňková–Helly selection theorem provides conditions under which one can extract a sequence from a family of sets that converges in a certain sense.

ADITYA is a tokamak, which is a device designed to confine plasma using magnetic fields in order to achieve controlled nuclear fusion. It is a part of India's efforts in fusion research and is primarily developed by the Institute for Plasma Research (IPR) in Gandhinagar, Gujarat.

Adolf Wüllner is a name associated with a historical figure, specifically a German composer, conductor, and music educator who was active primarily in the late 19th and early 20th centuries. He is known for his works in choral and orchestral music, contributing to the musical landscape of his time.

Vera W. de Spinadel is an Argentine mathematician known for her work in the fields of mathematics education and the history and philosophy of mathematics. She has contributed significantly to the study and promotion of mathematical thinking and pedagogy. In addition to her academic work, she has been involved in various initiatives aimed at improving mathematics education and understanding.

Audio electronics refers to the branch of electronics that deals with the generation, manipulation, and transmission of sound signals. This field encompasses various devices and technologies used to create, record, amplify, and play back audio. Key components and concepts in audio electronics include: 1. **Microphones:** Devices that convert sound waves into electrical signals. Different types include dynamic, condenser, ribbon, and lavalier microphones. 2. **Amplifiers:** Electronic devices that increase the power of audio signals to drive speakers.