6 - Wikipedia
6 is the smallest integer which is not an exponent of a prime number, making it the smallest integer greater than 1 for which there does not exist a finite field of that size.
Symmetric Bush-type generalized Hadamard matrices and association schemes
We define Bush-type generalized Hadamard matrices over abelian groups and construct symmetric Bush-type generalized Hadamard matrices over the additive group of finite field $\mathbb{F}_q$, $q$ a prime power. We then show and study an association sch...
Mechanical Properties of the Meninges: Large Language Model Assisted Systematic Review of…
Accurate constitutive models and corresponding mechanical property values for the meninges are important for predicting mechanical damage to brain tissue due to traumatic brain injury. The meninges are often oversimplified in current finite element (...
An unstructured finite element model for incompressible two-phase flow based on a monolith…
We present a robust numerical method for solving incompressible, immiscible two-phase flows. The method extends the monolithic phase conservative level set method with embedded redistancing by Quezada de Luna et al. [38] and a semi-implicit high-orde...
Entropy and chirality in sphinx tilings
As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and ri...
jakesgordon/javascript-state-machine
A javascript finite state machine library (⭐ 8755)
Optimal Subpattern Assignment Metric for Multiple Tracks (OSPAMT Metric)
In this paper, we propose a new metric which measures the distance between two finite sets of tracks (a track is a path of either a real or estimated target). This metric is based on the same principle as the Optimal Subpattern Assignment (OSPA) metr...
Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions
Given a finite group $ G $, we study certain regular subgroups of the group of permutations of $ G $, which occur in the classification theories of two types of algebraic objects: skew left braces with multiplicative group isomorphic to $ G $ and Hop...
The Hermitian null-range of a matrix over a finite field
Let $q$ be a prime power. For $u=(u_1,\dots ,u_n), v=(v_1,\dots ,v_n)\in \mathbb {F}_{q^2}^n$ let $\langle u,v\rangle := \sum _{i=1}^{n} u_i^qv_i$ be the Hermitian form of $\mathbb {F} _{q^2}^n$. Fix an $n\times n$ matrix $M$ over $\mathbb {F} _{q^2}...
Realizing algebraic 2-complexes by cell complexes
The realization theorem asserts that for a finitely presented group G, the D(2) property and the realization property are equivalent as long as G satisfies a certain finiteness condition. We show that the two properties are in fact equivalent for all...
Cluster lens reconstruction using only observed local data -- an improved finite-field inv…
Gravitational light deflection can distort the images of distant sources by its tidal effects. The population of faint blue galaxies is at sufficiently high redshift so that their images are distorted near foreground clusters, with giant luminous a...
Model and Program Repair via SAT Solving
We consider the following \emph{model repair problem}: given a finite Kripke structure $M$ and a specification formula $η$ in some modal or temporal logic, determine if $M$ contains a substructure $M'$ (with the same initial state) that satisfies...
Computing monomial bases in Lie theory using OSCAR
In this survey, we present a detailed guide on using the computer algebra system OSCAR to compute monomial bases for simple, finite-dimensional modules of simple, complex Lie algebras. We will also demonstrate how to determine monomial bases for the...
The Sandpile Group of a Cone Over a Bi-Coconut Tree
The sandpile group of a connected graph is a finite abelian group whose cardinality is the number of spanning trees in the graph. We compute the spanning tree number and sandpile group structure for the cone over a bi-coconut tree, generalizing work...
A simple finite delayed multi-type branching process for infectious disease modeling
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce offspring d...
D-Optimal Input Design for Nonlinear FIR-type Systems:A Dispersion-based Approach
Optimal input design is an important step of the identification process in order to reduce the model variance. In this work a D-optimal input design method for finite-impulse-response-type nonlinear systems is presented. The optimization of the deter...
On a bound of Cocke and Venkataraman
Let G be a finite group with exactly k elements of largest possible order m. Let q(m) be the product of gcd(m,4) and the odd prime divisors of m. We show that |G|\le q(m)k^2/φ(m) where φdenotes Euler's totient function. This strengthens a recent re...
A fake Klein bottle with bubble
We resolve the question of the existence of a finite 2-complex with the same fundamental group and Euler characteristic as a Klein bottle with a bubble, but homotopically distinct to it....
Real-time computation of bio-heat transfer in the fast explicit dynamics finite element al…
Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical algorithm well...
Computation of a 30750-Bit Binary Field Discrete Logarithm
This paper reports on the computation of a discrete logarithm in the finite field $\mathbb F_{2^{30750}}$, breaking by a large margin the previous record, which was set in January 2014 by a computation in $\mathbb F_{2^{9234}}$. The present computati...