A Hecke character (or Hecke character of the second kind) is a particular type of character associated with algebraic number fields and arithmetic functions. More specifically, these characters arise in the study of modular forms and algebraic K-theory.

Rprop, or Resilient Backpropagation, is a variant of the backpropagation algorithm used for training artificial neural networks. It was designed to address some of the issues associated with standard gradient descent methods, particularly the sensitivity to the scale of the parameters and the need for careful tuning of the learning rate. ### Key features of Rprop: 1. **Individual Learning Rates**: Rprop maintains a separate learning rate for each weight in the network.

SLUB is a memory allocator used in the Linux kernel. It is designed to efficiently manage memory in the kernel space, particularly for allocating and freeing memory for objects and data structures used by the kernel. SLUB stands for "SLAB Allocator with Unordered Lists," and it is one of several memory allocation mechanisms in the Linux kernel, the others being SLAB and SLOB. The SLUB allocator was introduced to improve performance, scalability, and memory usage compared to its predecessors.

The Riemann Xi function, denoted as \(\Xi(s)\), is a special function closely related to the Riemann zeta function \(\zeta(s)\). It is defined to facilitate the analysis of the zeros of the zeta function, especially in the context of the Riemann Hypothesis.

The Shimizu L-function is a type of L-function associated with a certain class of automorphic forms, particularly those arising from the theory of modular forms and automorphic representations. Specifically, it is related to the study of automorphic forms over several variables and is often connected to the theory of multiple zeta values and their generalizations.

The term **special values of L-functions** refers to specific evaluations of L-functions at certain points, typically integers or half-integers. These special values have significant implications in number theory, particularly in relation to various conjectures and theorems involving number theory, algebraic geometry, and representation theory.

Polygon triangulation is the process of dividing a polygon into triangles, which are simpler geometric shapes. This is useful in various fields such as computer graphics, geographical information systems (GIS), and computational geometry because triangles are easier to work with for tasks like rendering, mesh generation, and mathematical computations.

Julius von Mayer (1814–1878) was a German physicist and one of the key figures in the development of the concept of energy conservation in physics. He is best known for formulating the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed from one form to another. Mayer's work laid the foundation for the understanding of the relationship between different forms of energy, such as heat and mechanical work.

"On the Equilibrium of Heterogeneous Substances" is a seminal work by the physicist and chemist J. Willard Gibbs, published in 1876. This work is renowned for its foundational contributions to the field of thermodynamics and physical chemistry, particularly in the context of phase equilibria.

The term "level of free convection" typically refers to the degree or intensity of free convection occurring in a fluid. Free convection, also known as natural convection, occurs when fluid motion is caused by the buoyancy forces that arise due to density differences in the fluid, often due to temperature gradients. When a fluid is heated, it becomes less dense and tends to rise, while cooler, denser fluid descends.

A satellite tornado is a term used to describe a smaller tornado that forms in close proximity to a larger, stronger parent tornado. These satellite tornadoes usually occur in the vicinity of the main vortex and are often seen rotating around it. They can develop from the same thunderstorm or supercell that produces the primary tornado, and while they are typically weaker than the main tornado, they can still cause damage.

De Boor's algorithm is a computational method used for evaluating B-spline curves and surfaces efficiently. It was developed by Carl de Boor in 1972 and is a generalization of the more specific Cox-de Boor algorithm for evaluating B-splines. B-splines are a family of piecewise-defined polynomials that are used extensively in computer graphics, computer-aided design (CAD), and numerical analysis.

Gal’s accurate tables refer to a set of mathematical tables created by the Danish astronomer and mathematician, Niels Bohr Gal, in the early 20th century. These tables are specifically designed for accurate calculations in celestial mechanics, such as determining the positions of celestial objects or calculating the orbits of planets and moons.

Exome sequencing is a genomic technology that focuses on sequencing the exome, which is the part of the genome that consists of coding regions of genes. These regions, known as exons, are the portions of the DNA that are transcribed into messenger RNA (mRNA) and ultimately translated into proteins. The exome represents about 1-2% of the entire human genome but contains the majority of known disease-related variants.

The Henderson limit is a concept in the field of biochemistry and physiology, referring to a threshold beyond which an enzyme reaction can no longer proceed at an increasing rate due to saturation of the enzyme's active sites. More specifically, the Henderson limit is often associated with the behavior of enzymes or substrates in a reaction, where the rate of reaction plateaus despite increases in substrate concentration.

URA3 is a gene commonly used as a selectable marker in yeast genetic and molecular biology studies, particularly in Saccharomyces cerevisiae (baker's yeast). The URA3 gene encodes an enzyme called orotidine-5'-phosphate decarboxylase, which is involved in the pyrimidine biosynthetic pathway.

Carol S. Woodward is a prominent figure known for her contributions to education and research, particularly in the field of behavior analysis and special education. She has focused on improving the educational experiences and outcomes for students with disabilities. Her work often emphasizes evidence-based practices and interventions that support students in various educational settings.

Hendrik Wade Bode (1905–1982) was an influential American engineer and mathematician, well-known for his contributions to the fields of control systems engineering, signal processing, and telecommunications. He is particularly recognized for developing the Bode plot, a graphical method for analyzing the frequency response of linear time-invariant systems, which is widely used in control theory and engineering to design and analyze systems.

Nancy Kopell is a noted American mathematician, renowned for her contributions to the fields of dynamical systems, nonlinear dynamics, and mathematical biology. She has done significant work in understanding neural networks and synchronization phenomena, particularly in relation to rhythmic activities in the brain. Kopell has made contributions to the study of how different rhythms can interact, which has implications for understanding various neurological conditions. She has also been recognized for her efforts in promoting mathematics education and outreach, particularly to encourage diversity in the sciences.