Tilting theory is a branch of representation theory in mathematics, particularly in the area of module theory and homological algebra. It deals with the study of "tilting objects," which are certain types of modules that allow one to construct new modules and to relate different categories of modules in a controlled manner.

Sampling risk refers to the risk that a conclusion or inference drawn from a sample may not accurately reflect the characteristics of the entire population from which the sample was taken. This concept is primarily used in statistics, audit, and research contexts.

The Ore condition, named after the Norwegian mathematician, mathematician O. Ore, refers to a set of criteria in algebra that help identify whether a certain type of ring is integrally closed. More specifically, it is used to determine whether a finitely generated commutative algebra over a field is integrally closed in its field of fractions.

Scalar multiplication is an operation involving a vector (or a matrix) and a scalar (a single number). In this operation, each component of the vector (or each entry of the matrix) is multiplied by the scalar. This operation scales the vector or matrix, effectively changing its magnitude but not its direction (for vectors, with the exception of scaling by a negative scalar, which also reverses the direction).

Scanning Transmission X-ray Microscopy (STXM) is an advanced imaging technique that combines the principles of scanning microscopy with X-ray transmission imaging. This approach allows for high-resolution imaging of material samples at the nanoscale, as well as the chemical and electronic characterization of those materials. ### Key Features of STXM: 1. **X-ray Source**: STXM typically uses synchrotron radiation, which provides highly collimated and intense beams of X-rays.

Scientific visualization is the process of representing scientific data graphically to help researchers and analysts understand complex information and draw insights from it. This field combines aspects of computer graphics, data analysis, and cognitive science to create visual representations that can reveal patterns, trends, and relationships within the data.

The Serre spectral sequence is a powerful tool in algebraic topology and homological algebra that provides a method for computing the homology (or cohomology) of a space that can be decomposed into simpler pieces, often using a fibration or a cellular decomposition. ### Overview The Serre spectral sequence arises particularly in the context of a fibration sequence, which is a type of map between topological spaces characterized by having certain lifting properties.

The SIAM Journal on Discrete Mathematics (SIDMA) is a scholarly journal published by the Society for Industrial and Applied Mathematics (SIAM). It focuses on research related to discrete mathematics, which encompasses a wide range of topics including, but not limited to, combinatorics, graph theory, algorithms, and optimization. The journal aims to disseminate high-quality research that has a significant impact on both theoretical and practical aspects of discrete mathematics.

As of my last update in October 2021, Simon Ellingsen does not appear to be a widely recognized public figure, historical figure, or concept. It's possible that he has gained prominence after that date or is known within a specific community or context not widely covered in mainstream sources.

Free will is the concept that individuals have the ability to make choices and decisions independently, without being determined by prior causes or external influences. It suggests that people can exercise control over their actions and are responsible for the consequences of those actions. Philosophically, free will has been a topic of debate for centuries and is often contrasted with determinism, the idea that all events, including human actions, are determined by preceding events according to the laws of nature.