Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

This paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

Riemann–Hilbert approach for a Schrödinger-type equation with nonzero boundary conditions

In this paper, we focus on investigating a nonlinear Schrödinger-type equation with nonzero boundary at infinity. An appropriate two-sheeted Riemann surface is introduced to map the original spectral parameter [Formula: see text] into a single-valued parameter [Formula: see text]. Starting from the Lax pair of the Schrödinger-type equation, we derive its Jost solutions with nonzero boundary conditions, and further analyze the asymptotic behaviors, analyticity, the symmetries of the Jost solutions and the corresponding spectral matrix. An associated matrix Riemann–Hilbert (RH) problem associated with the problem of nonzero boundary conditions is subsequently presented, and a formulae of [Formula: see text]-soliton solutions for the Schrödinger-type equation by solving the matrix RH problem. As an application of the [Formula: see text]-soliton formulae, we present two kinds of one-soliton solutions and three kinds of two-soliton solutions according to different distributions of spectral parameters, and dynamical features of those solutions are also further analyzed.

The presence of microbial contamination and biofilms at a beer can filling production line

Contamination of beer arises in 50% of all events at the late stages of production, the filling area. Hereby, biofilms, being consortia of microorganisms embedded in a matrix composed of extracellular polymeric substances, play a critical role. To date, most studies have focused on the presence of (biofilm forming) microorganisms within this filling environment. Our aim was to characterize the microbial status as well as the presence of possible biofilms at a can filling line for beer by determining the presence of microorganisms and their associated matrix components (carbohydrates, proteins and extracellular DNA (eDNA)). Targeted qPCR confirmed the presence of microorganisms at ten sites during operation and three after cleaning (from 23 sites respectively). The evaluation of carbohydrates, eDNA and proteins showed that 16 sites were positive for at least one component during operation and four after cleaning. We identified one potential biofilm hotspot, namely the struts below the filler, harboring high loads of bacteria and yeast, eDNA, carbohydrates and proteins. The protein pattern was different than that of beer. This work deepens our understanding of biofilms and microorganisms found at the filling line of beer beverages at sites critical for production.

Riemann–Hilbert problems of a nonlocal reverse-time six-component AKNS system of fourth order and its exact soliton solutions

We investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann–Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix.

Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity

We improve upon the local bound in the depth aspect for sup-norms of newforms on $D^\times$, where $D$ is an indefinite quaternion division algebra over ${\mathbb {Q}}$. Our sup-norm bound implies a depth-aspect subconvexity bound for $L(1/2, f \times \theta _\chi )$, where $f$ is a (varying) newform on $D^\times$ of level $p^n$, and $\theta _\chi$ is an (essentially fixed) automorphic form on $\textrm {GL}_2$ obtained as the theta lift of a Hecke character $\chi$ on a quadratic field. For the proof, we augment the amplification method with a novel filtration argument and a recent counting result proved by the second-named author to reduce to showing strong quantitative decay of matrix coefficients of local newvectors along compact subsets, which we establish via $p$-adic stationary phase analysis. Furthermore, we prove a general upper bound in the level aspect for sup-norms of automorphic forms belonging to any family whose associated matrix coefficients have such a decay property.

Determination of the Most Stable Configuration Pair(s) of the Constituent Matrix Shells and the Set of Most Stable Configurations of the Corresponding Matrix Shell System

The present article addresses the issue of determining the most stable configuration pair(s) of a Matrix Shell, and thereby, of determining the set of most stable configurations of the associated Matrix Shell System. The problem is resolved using the criteria of spectral proximity w.r.t. the Ordered Eigenspectrum of a defined Baseline Matrix (both for Individual constituent Matrix Shells and the Matrix Shell System) and quantified in terms of an appropriate Proximity Function, the article presents the analytic expressions of the Matrix Shell Baseline elements, corresponding to A n A n A n A n (0,2 ), (0,2 1), (1,2 ), (1,2 1)   and A t n A t n ( ,2 ), ( ,2 1)  where t  2 , type Matrix Shells and defines the Baseline Matrices in terms of these Baseline elements, the article then provides a mathematical framework to determine the most stable Configuration pair(s) of constituent Matrix Shells and the set of most stable configurations of the Matrix Shell System and concludes with demonstration of the working of the presented framework through hypothetical examples based case studies

On diagonal quasi-free automorphisms of simple Cuntz-Krieger algebras

We show that an outer action of a finite abelian group on a simple Cuntz-Krieger algebra is strongly approximately inner in the sense of Izumi if the action is given by diagonal quasi-free automorphisms and the associated matrix is aperiodic. This is achieved by an approximate cohomology vanishing-type argument for the canonical shift restricted to the relative commutant of the set of domain projections of the canonical generating isometries in the fixed point algebra.