Related papers: A New Approach to Examine q-Steiner Systems
This article describes our invention of a new poetic form based on projective geometry. In doing this we also explore the 'what ifs' in mathematics and poetry which spark the creative processes of poet and mathematician. In other words,…
Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new…
Let $D_{m,n}^r$ and $P_{m,n}^r$ denote the subschemes of $\mathbb{P}^{mn-1}$ given by the $r\times r$ determinants (respectively the $r\times r$ permanents) of an $m\times n$ matrix of indeterminates. In this paper, we study the geometry of…
The paper deals with a particular type of a projective ring plane defined over the ring of double numbers over Galois fields, R\_{\otimes}(q) \equiv GF(q) \otimes GF(q) \cong GF(q)[x]/(x(x-1)). The plane is endowed with (q^2 + q + 1)^2…
We consider the problem to determine which blow-ups along subvarieties in products of two projective spaces are log Fano. By describing the nef cones of such blow-ups with special centers, we give a partial classification result. For each…
A common feature of most numerically optimized stellarator geometries is the presence of sharp ridges on outer flux surfaces, irrespective of the rotational transform. Despite their importance, an analytical theory for their existence has…
This paper is concerned with a nonlinear fractional Sch\"ordinger system in $\mathbb{{R}}$ with intraspecies interactions $a_{i}>0 \ (i=1,2)$ and interspecies interactions $\beta \in\mathbb{{R}}$. We study this system by solving an…
In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the…
In the presence of direct trajectories connecting source and drain contacts, the conductance of a quantum dot may exhibit resonances of the Fano type. Since Fano resonances result from the interference of two transmission pathways, their…
A novel scheme is presented for fault-tolerant quantum computation based on the cluster model. Some relevant logical cluster states are constructed in concatenation by post-selection through verification, without necessity of recovery…
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…
A $q$-ary $t$-$(n,w,\lambda)$ design is a collection $\mathcal{A}$ of vectors of weight $w$ in $\mathbb{F}_{q}^{n}$ with the property that every vector of weight $t$ in $\mathbb{F}_{q}^{n}$ is contained in exactly $\lambda$ members of…
We demonstrate a fully-tunable multi-state Fano system in which remotely-implemented quantum states interfere with each other through their coupling to a mutual continuum. On tuning these resonances near coincidence a robust avoided…
A tunable microwave scattering device is presented which allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. We observe a non-monotonic evolution of resonance parameters that is explained…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to $2$-designs, and have applications in constructions for…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground…
We describe the Fano asymmetry by expanding the transmission amplitude with respect to states with point spectra (discrete eigenstates), including not only bound states but also resonant states with complex eigenvalues. We first introduce a…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…