相关论文: A New Approach to Examine q-Steiner Systems
Q-balls are non-topological solitons in a large family of field theories. We focus on the existence of $U(1)$ gauged Q-balls for a field theory with sixth-order potential. The problem can be reduced to proving the existence of critical…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
We introduce a novel class of finite difference approximations, termed zigzag schemes, that employ a hybrid stencil that is neither symmetrical, nor fully one-sided. These zigzag schemes often enjoy more permissive stability constraints and…
The exploration of linear subspaces, particularly scattered subspaces, has garnered considerable attention across diverse mathematical disciplines in recent years, notably within finite geometries and coding theory. Scattered subspaces play…
A Kirkman triple system of order $v$, KTS$(v)$, is a resolvable Steiner triple system on $v$ elements. In this paper, we investigate an open problem posed by Doug Stinson, namely the existence of KTS$(v)$ which contain as a subdesign a…
This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of…
We present a new method to study the ground state of quantum spin systems using the Monte Carlo techniques together with restructured intermediate states which we proposed previously. Our basic idea is to obtain coefficients in the…
We develop a semiclassical method for the determination of the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N, based on the 1/N-expansion and the quantum-classical correspondence. The…
We present a uniform framework for constructing $3$-designs from $\mathrm{GL}_2(\mathbb F_q)$-invariant subspaces of $\mathbb F_q[X,Y]_k$, the space of homogeneous polynomials of degree $k$. Given such a subspace $W$, we associate a…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…
An $r$-block-coloring, simply $r$-coloring, of a Steiner triple system $\mathrm{STS}(v)$ is a partition of the block set into $r$ color classes, each color class being a partial parallel class. The chromatic index of $\mathrm{STS}(v)$,…
Experiments with both qualitative and quantitative factors occur frequently in practical applications. Many construction methods for this kind of designs, such as marginally coupled designs, were proposed to pursue some good space-filling…
The Heawood graph is the point-block incidence graph of the Fano plane (the unique Steiner triple system of order 7). We show that the minimum semidefinite rank of this graph is 10. That is, 10 is the smallest number of complex dimensions…
Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear codes…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs…
We study the geometry of the Fano schemes $\mathrm{\textbf{F}}_{k}(\mathrm{SD}_n^r)$ of the projective variety $\mathrm{SD}_n^r$ defined by the $r\times r$ minors of a symmetric $n\times n$ matrix filled with indeterminates. These schemes…
We investigate the reduced dynamics in the Markovian approximation of an infinite quantum spin system linearly coupled to a phonon field at positive temperature. The achieved diagonalization leads to a selection of the continuous family of…
Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory,…