Related papers: New necessary conditions for (negative) Latin squa…

We consider a general class of infinite dimensional reversible differential systems. Assuming a non resonance condition on the linear frequencies, we construct for such systems almost invariant pseudo norms that are closed to Sobolev-like…

Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for…

Many studies collect data that can be considered as a realization of a point process. Included are medical imaging data where photon counts are recorded by a gamma camera from patients being injected with a gamma emitting tracer. It is of…

An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear PDEs and systems of PDEs, necessary and sufficient conditions…

In this paper we investigate some new problems in additive combinatorics. Our problems mainly involve permutations (or circular permutations) $n$ distinct numbers (or elements of an additive abelian group) $a_1,\ldots,a_n$ with adjacent…

Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…

We prove that if $B$ is a $p$-block with non-trivial defect group $D$ of a finite $p$-solvable group $G$, then $\ell(B) < p^r$, where $r$ is the sectional rank of $D$. We remark that there are infinitely many $p$-blocks $B$ with non-Abelian…

Relating a set of variables X to a response y is crucial in chemometrics. A quantitative prediction objective can be enriched by qualitative data interpretation, for instance by locating the most influential features. When high-dimensional…

In this paper, we extend the investigation of four-dimensional partially alternative algebras $\mathcal A$ initiated in \cite{HNT}. The partial alternativity condition, a natural generalization of the alternativity axiom, broadens the class…

Every Latin square of prime power order $q$ is uniquely described by a local permutation polynomial (LPP) in the polynomial ring $\mathbb{F}_q[x,y]$. Despite this equivalence, one may find in the literature only some preliminary results on…

To explaine the matter-antimatter asymmetry, a supersymmetric extention of the standard model is proposed where baryon and lepton numbers are local gauged(BLMSSM), and exotic superfields are introduced when gauge group is enlarged to…

Let $\alpha\in \mathbb{R}\setminus\mathbb{Q}$ and $\beta\in \mathbb{R}$ be given. Suppose that $a_1,\ldots,a_s$ are distinct positive integers that do not contain a reduced residue system modulo $p^2$ for any prime $p$. We prove that there…

Let $(G,+)$ be an abelian group and consider a subset $A \subseteq G$ with $|A|=k$. Given an ordering $(a_1, \ldots, a_k)$ of the elements of $A$, define its {\em partial sums} by $s_0 = 0$ and $s_j = \sum_{i=1}^j a_i$ for $1 \leq j \leq…

We show that partial dynamical symmetries (PDS) can occur at critical-points of quantum phase transitions, in which case, underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several…

Recently, Glasby, Praeger, and Xia asked for necessary and sufficient conditions for the `Jordan partition' $\lambda(m,n,p)$ to be standard. Previously we gave such conditions when $p$ is any odd prime. Here we give such conditions when…

This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…

This paper introduces a randomized variation of the alternating least squares (ALS) algorithm for rank reduction of canonical tensor formats. The aim is to address the potential numerical ill-conditioning of least squares matrices at each…

Let $p \geq 5$ be a prime, $N$ be an integer not divisible by $p$, $\bar\rho_0$ be a reducible, odd and semi-simple representation of $G_{\mathbb{Q},Np}$ of dimension $2$ and $\{\ell_1,\cdots,\ell_r\}$ be a set of primes not dividing $Np$.…

In this note we prove the non-existence of two types of partial difference sets in Abelian groups of order 216. This finalizes the classification of parameters for which a partial difference set of size at most 100 exists in an Abelian…

Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…