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...
On the asymptotic behavior of bubble date estimators
In this study, we extend the three-regime bubble model of Pang et al. (2021) to allow the forth regime followed by the unit root process after recovery. We provide the asymptotic and finite sample justification of the consistency of the collapse date...
Reeb spaces of smooth functions on manifolds II
The Reeb space of a continuous function is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several expl...
Smooth cuspidal automorphic forms and integrable discrete series
In this paper we construct smooth cuspidal automorphic forms related to integrable discrete series of a connected semisimple Lie group with finite center for classical and adelic situation as an application of the theory of Schwartz spaces for automo...
Turn - Wikipedia
Look up turn in Wiktionary, the free dictionary. To turn is to rotate, either continuously like a wheel turns on its axle, or in a finite motion changing
Structures of G(2) type and nonintegrable distributions in characteristic p
Lately we observe: (1) an upsurge of interest (in particular, triggered by a paper by Atiyah and Witten) to manifolds with G(2)-type structure; (2) classifications are obtained of simple (finite dimensional and graded vectorial) Lie superalgebras ove...
Invariant operators on supermanifolds and Standard Models
Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was earlier o...
Optimal $\mathcal{L}_2$ discrepancy bounds for higher order digital sequences over the fin…
We show that the $\mathcal{L}_2$ discrepancy of the explicitly constructed infinite sequences of points $(\boldsymbol{x}_0,\boldsymbol{x}_1, \boldsymbol{x}_2,...)$ in $[0,1)^s$ over $\mathbb{F}_2$ introduced in [J. Dick, Walsh spaces containing smoot...
Discrete BF theory
In this work we discuss the simplicial program for topological field theories for the case of non-abelian BF theory. Discrete BF theory with finite-dimensional space of fields is constructed for a triangulated manifold (or for a manifold equipped w...
Non-uniqueness of weak solutions for a logarithmically supercritical hyperdissipative Navi…
The existence of non-unique solutions of finite kinetic energy for the three dimensional Navier-Stokes equations is proved in the slightly supercritical hyper-dissipative setting introduced by Tao. The result is based on the convex integration techni...
stranskyjan/dem-fem-coupling
Open source codes for coupling of Finite Element Method and Discrete Element Method using YADE, and OOFEM softwares. (⭐ 57)
A rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion
Adapting ideas of Daubechies and Klauder we derive a continuum path-integral formula for the time evolution generated by a spin Hamiltonian. For this purpose we identify the finite-dimensional spin Hilbert space with the ground-state eigenspace of...
Geometric Biplane Graphs I: Maximal Graphs
We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the sense tha...
Geometric Biplane Graphs II: Graph Augmentation
We study biplane graphs drawn on a finite point set $S$ in the plane in general position. This is the family of geometric graphs whose vertex set is $S$ and which can be decomposed into two plane graphs. We show that every sufficiently large point se...
Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac, cond-mat/040...
Derived equivalence, Albanese varieties, and the zeta functions of 3-dimensional varieties
We show that any derived equivalent smooth, projective varieties of dimension 3 over a finite field $\mathbb{F}_q$ have equal zeta functions. This result is an application of the extension to smooth, projective varieties over any field of Popa and Sc...
Static dipole polarizability of C70 fullerene
The electronic and vibrational contributions to the static dipole polarizability of C70 fullerene are determined using the finite-field method within the density functional formalism. Large polarized Gaussian basis sets augmented with diffuse funct...
High frequency wave packets for the Schrödinger equation and its numerical approximations
We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in Ignat, Zuazua, Numerical dis...
Geometric Property (T) and Positive Cones of Real Algebraic Roe Algebras
We give a characterization of geometric property (T) for a coarse disjoint union of finite graphs with bounded degree using the idea of noncommutative real algebraic geometry. In the proof, we define a $*$-subalgebra $I_u[X]$ of real algebraic Roe al...
Quantum Gromov-Hausdorff convergence of spectral truncations for groups with polynomial gr…
For a unital spectral triple $(\mathcal{A}, H,D)$, we study when its truncation converges to itself. The spectral truncation is obtained by using the spectral projection $P_Λ$ of $D$ onto $[-Λ,Λ]$ to deal with the case where only a finite range of...
A bimodule approach to dominant dimension
We show that a finite dimensional algebra $A$ has dominant dimension at least $n \geq 2$ if and only if the regular bimodule $A$ is $n$-torsionfree if and only if $A \cong Ω^{n}(\text{Tr}(Ω^{n-2}(V)))$ as $A$-bimodules, where $V=\text{Hom}_A(D(A),A...