相关论文: All Difference Family Structures arise from Groups
Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
Interpretation of a structure $\mathbb A$ in $\mathbb B$ allows to produce structures elementarily equivalent to $\mathbb A$ given those elementarily equivalent to $\mathbb B$. In particular, interpretation of the free group in $\mathbb N$…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…
The collection of branches (maximal linearly ordered sets of nodes) of the tree ${}^{<\omega}\omega$ (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal -- for example, any level of the tree…
Explainable machine learning methods have been accompanied by substantial development. Despite their success, the existing approaches focus more on the general framework with no prior domain expertise. High-stakes financial sectors have…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…
We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…
How does social complexity depend on population size and cultural transmission? Kinship structures in traditional societies provide a fundamental illustration, where cultural rules between clans determine people's marriage possibilities.…
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…
We extend simple opinion models to obtain stable but continuously evolving communities. Our scope is to meet a challenge raised by sociologists of generating "structures that last from non lasting entities". We achieve this by introducing…
Minimum divergence methods are popular tools in a variety of statistical applications. We consider tubular model adequacy tests, and demonstrate that the new divergences that are generated in the process are very useful in robust…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.
In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.
Differential calculus on Euclidean spaces has many generalisations. In particular, on a set $X$, a diffeological structure is given by maps from open subsets of Euclidean spaces to $X$, a differential structure is given by maps from $X$ to…
We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group…