In algebra, particularly in the context of group theory and ring theory, the term "center" refers to a specific subset of a mathematical structure that has particular properties. 1. **Center of a Group**: For a group \( G \), the center of \( G \), denoted as \( Z(G) \), is defined as the set of elements in \( G \) that commute with every other element of \( G \).

A Cauchy sequence is a sequence of elements in a metric space (or a normed vector space) that exhibits a particular convergence behavior, focusing on the distances between its terms rather than on their actual limits.

Besides of course sexual selection, considering in this section only "formal learning" activities.

Consider e.g. the 2020 University of Oxford, where many many people are taking courses without any laboratory work (and also without much use at all) like literature and history, and they are paying about 9k pounds/year for it: how much it costs to study at the University of Oxford?.

Basically all of this could be done online from books.

Laboratories are impossible however, because expendables of every experiment you do cost from hundreds to thousands of dollars, not to mention crazy upfront equipment costs.

For this reason, the brick and mortar aspect universities should focus exclusively on laboratories, and ensuring that the students with the most relevant knowledge (which can be readily obtained online) get access to those laboratories. Students should of course fully master every aspect of theory pertinent to their experiments. principal investigators should hand pick whichever criteria they want to select their students, possibly based partly on exam as a service if they find it a useful metric.

Furthermore, the use of laboratories should put great focus on novel research. A lot of laboratory instruction could be done from video of an experiments. As much as possible, we should use laboratories for novel research. Related: Section "Videos of all key physics experiments".

In the context of Wikipedia, a "stub" refers to an article that is incomplete or lacking in detail and therefore needs expansion. "Applied mathematics stubs" specifically refer to articles related to applied mathematics that have been identified as needing more comprehensive information. Applied mathematics is a branch of mathematics that deals with mathematical methods and techniques that are typically used in practical applications in science, engineering, business, and other fields.

The inverse limit (or projective limit) is a concept in topology and abstract algebra that generalizes the notion of taking a limit of sequences or families of objects. It is particularly useful in the study of topological spaces, algebraic structures, and their relationships.

In theoretical physics, particularly in the context of gauge theories and string theory, the term "bifundamental representation" refers to a specific type of representation of a gauge group that is associated with two distinct gauge groups simultaneously. For example, consider two gauge groups \( G_1 \) and \( G_2 \). A field (or representation) that transforms under both groups simultaneously is said to be in the bifundamental representation.

Bendixson's inequality is a result in the theory of dynamical systems, particularly in the study of differential equations. It provides a criterion for the non-existence of periodic orbits in certain types of planar systems. In more detail, Bendixson's inequality applies to a continuous, planar vector field given by a differential equation.

Arity is a concept that refers to the number of arguments or operands that a function or operation takes. It's commonly used in mathematics and programming to describe how many inputs a function requires to produce an output. For example: - A function with an arity of 0 takes no arguments (often referred to as a constant function). - A function with an arity of 1 takes one argument (e.g., a unary function).

In the context of machine learning and natural language processing, the term "embedding problem" can refer to several related concepts, primarily revolving around the challenge of representing complex data in a form that can be effectively processed by algorithms. Here are some key aspects: 1. **Embedding Vectors**: In machine learning, "embedding" typically refers to the transformation of high-dimensional data into a lower-dimensional vector space. This is crucial for enabling efficient computation and understanding relationships between data points.

The additive inverse of a number is the value that, when added to that number, results in zero. In mathematical terms, for any number \( a \), its additive inverse is \( -a \).

The additive identity is a concept in mathematics that refers to a number which, when added to any other number, does not change the value of that number. In the set of real numbers (as well as in many other mathematical systems), the additive identity is the number \(0\).

A bilinear form is a mathematical function that is bilinear in nature, meaning it is linear in each of its arguments when the other is held fixed.

An absolutely convex set is a concept from functional analysis and convex geometry.

In abstract algebra, a branch of mathematics that deals with algebraic structures, theorems serve as fundamental results or propositions that have been rigorously proven based on axioms and previously established theorems. Here are some significant theorems and concepts in abstract algebra: 1. **Group Theory Theorems**: - **Lagrange's Theorem**: In a finite group, the order (number of elements) of any subgroup divides the order of the group.

Ternary operations, also known as ternary conditional operators or ternary expressions, refer to operations that take three operands. In programming, the most common example of a ternary operation is the ternary conditional operator, which is often used as a shorthand for an `if-else` statement. ### Ternary Conditional Operator The syntax typically appears as follows: ```plaintext condition ?

Petru Gaugaș does not seem to be a widely recognized name or term based on the information available up to October 2023. It's possible that he could be a local figure, a person involved in a specific field, a fictional character, or something else that has gained prominence since then.

Pius Nwankwo Okeke does not appear to be a widely recognized figure based on the available data up to October 2023. It's possible that he could be a private individual, a professional in a specific field, or someone who has gained recognition after that date. If you provide more context or specify the area in which you're interested (such as academia, politics, sports, etc.

Rabia Salihu Sa'id does not seem to be a widely recognized figure or concept as of my last knowledge update in October 2023. It’s possible that Rabia Salihu Sa'id could refer to a person who has gained prominence after this date or is known in specific regional or professional contexts.

As of my last update in October 2023, there is no widely recognized entity, concept, or notable figure specifically known as "Stepan Beril." It’s possible that you might be referring to something more current or niche that hasn’t gained significant coverage.