"Binyamin Amirà" does not appear to be a widely recognized term, name, or phrase in my training data up until October 2023. It's possible that it could refer to a specific individual, a brand, or a concept that isn't well-documented or that has emerged recently.

The "Biographical Encyclopedia of Astronomers" is a comprehensive reference work that provides biographical entries on notable astronomers throughout history. It includes detailed information about their lives, contributions to the field of astronomy, discoveries, and the contexts in which they worked. Typically, it includes not only well-known figures but also lesser-known astronomers, giving a broad overview of the history of the discipline.

Andreu Mas-Colell is a prominent Spanish economist known for his contributions to economic theory, particularly in the fields of microeconomics, game theory, and auction theory. He has published extensively and is recognized for his work on the foundations of economic mechanisms and the mathematical underpinnings of economic models. In addition to his research contributions, Mas-Colell has held significant academic and administrative positions.

Bipolar electrochemistry is a technique in electrochemistry that involves the use of bipolar electrodes to facilitate electrochemical reactions. A bipolar electrode (BPE) is unique in that it has two distinct regions: one that is positively polarized (anodic) and another that is negatively polarized (cathodic).

The Bismuth Phosphate process is a method used in the field of hydrometallurgy for the extraction and purification of certain metals, particularly uranium and thorium. This process involves the precipitation of bismuth phosphate (BiPO₄) from a solution containing these metals. ### Key Steps of the Process: 1. **Solution Preparation**: The process begins with the preparation of an aqueous solution that contains the metal ions of interest, typically uranium or thorium.

A bisymmetric matrix is a square matrix that is symmetric with respect to both its main diagonal and its anti-diagonal (the diagonal from the top right to the bottom left).

The ADM formalism, or Arnowitt-Deser-Misner formalism, is a mathematical framework used in general relativity, particularly for the formulation of Einstein's field equations in the context of canonical gravity. It was developed by Richard Arnowitt, Stanley Deser, and Charles Misner in the 1960s.

Bjørn Gjevik is a Norwegian figure known for his work in the field of music, particularly as a pianist and composer. He may also be involved in various artistic or educational endeavors related to music.

Something analogous to a group isomorphism, but that preserves whatever properties the given algebraic object has. E.g. for a field, we also have to preserve multiplication in addition to addition.

Other common examples include isomorphisms of vector spaces and field. But since both of those two are much simpler than groups in classification, as they are both determined by number of elements/dimension alone, see:we tend to not talk about isomorphisms so much in those contexts.

Like isomorphism, but does not have to be one-to-one: multiple different inputs can have the same output.

The image is as for any function smaller or equal in size as the domain of course.

This brings us to the key intuition about group homomorphisms: they are a way to split out a larger group into smaller groups that retains a subset of the original structure.

As shown by the fundamental theorem on homomorphisms, each group homomorphism is fully characterized by a normal subgroup of the domain.

Ultimate explanation by Ciro Santilli: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Links group homomorphism and the quotient group via normal subgroups.

Minimum number of elements in a generating set of a group.

You select a generating set of a group, and then you name every node with them, and you specify:

Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the

How to build it: math.stackexchange.com/questions/3137319/how-in-general-does-one-construct-a-cycle-graph-for-a-group/3162746#3162746 good answer with ASCII art. You basically just pick each element, and repeatedly apply it, and remove any path that has a longer version.

Immediately gives the generating set of a group by looking at elements adjacent to the origin, and more generally the order of each element.

TODO uniqueness: can two different groups have the same cycle graph? It does not seem to tell us how every element interact with every other element, only with itself. This is in contrast with the Cayley graph, which more accurately describes group structure (but does not give the order of elements as directly), so feels like it won't be unique.

Take the element and apply it to itself. Then again. And so on.

In the case of a finite group, you have to eventually reach the identity element again sooner or later, giving you the order of an element of a group.

The continuous analogue for the cycle of a group are the one parameter subgroups. In the continuous case, you sometimes reach identity again and to around infinitely many times (which always happens in the finite case), but sometimes you don't.