Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dampings

In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They ?rst show that under the observability of a scalar equation, Kalman’s rank condition is su?cient for the uniqueness of solution to a complex system of elliptic equations with mixedobservations. The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures. Some classic models are presented to illustrate the ?eld of applications of the abstract theory.     

Some Results on the Optimal Matching Problem for the Jacobi Model

Potential Analysis - We establish some exact asymptotic results for a matching problem with respect to a family of beta distributions. Let X1,…,Xn be independent random variables with common...     

Construction of long MDS self-dual codes from short codes

In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed.     

A cost-scaling algorithm for minimum-cost node-capacitated multiflow problem

Mathematical Programming - Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (A refined Gomory–Chvátal closure for polytopes...     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

STABILITY AND BIFURCATION OF A STAGE-STRUCTURED PREDATOR-PREY MODEL INCORPORATING A CONSTANT PREY REFUGE

A stage-structured predator-prey model incorporating a constant prey refuge is proposed in this paper. The stability analysis of the equilibria is carried out. We also study Hopf bifurcations occurring at the positive equilibrium by choosing a suitable time delay as bifurcating parameter.     

Highly reusable chitosan-stabilized Fe-ZnO immobilized onto fiberglass cloth and the photocatalytic degradation properties in batch and loop reactors

The new design of the photocatalytic reactor is crucial to study for improving compatibility and scaling up the operation. A compatible loop photocatalytic reactor has been designed and used for rhodamine B decomposition. The photocatalysts were either ZnO or Fe-ZnO immobilized onto fiberglass cloth. The ZnO catalyst exhibited high crystallinity with or without Fe as the dopant. The crystallite size increased with the presence of Fe in the lattices. Most of the crystal parameters matched the standard ZnO data, and the cluster size was comparable to most reported studies. Diffuse Reflectance Spectroscopy (DRS) analysis confirmed the photon absorption shifted to the visible light range. The Fe dopant decreased the ZnO bandgap, and SEM-EDS confirmed the catalysts adhered to the fiberglass surface. The volume, thickness of the substrate solution, and reaction temperature influenced the photocatalytic-degradation rate. The photocatalytic degradation rate was higher under sunlight than ultraviolet irradiation. The reaction rate was lower in the batch reactor than in the loop reactor. The photocatalytic reaction almost completely mineralized RhB and changed the red solution to colorless. The immobilized photocatalyst has been reused more than 50 times without significantly decreasing the catalytic activity.     

Hypersurfaces in nearly Kaehler manifold $$\pmb {\mathbb {S}}^{\varvec{3}}\varvec{\times } \pmb {\mathbb {S}}^{\varvec{3}}$$

In this paper, we initiate the study of contact and minimal hypersurfaces in nearly Kaehler manifold \({\mathbb {S}}^3\times {\mathbb {S}}^3\) with a conformal vector field. There are three almost contact metric structures on a hypersurface of \({\mathbb {S}}^3\times {\mathbb {S}}^3\), and we will give some important properties of them. Besides, we study the influence of the conformal vector field on the almost contact metric structures and use it to characterize the hypersurfaces in \({\mathbb {S}}^3\times {\mathbb {S}}^3\).     

THE APPLICATION OF RANDOM MATRICES IN MATHEMATICAL PHYSICS

In this paper, we introduce the application of random matrices in mathematical physics including Riemann-Hilbert problem, nuclear physics, big data, image processing, compressed sensing and so on. We start with the Riemann-Hilbert problem and state the relation between the probability distribution of nontrivial zeros and the eigenvalues of the random matrices. Through the random matrices theory, we derive the distribution of Neutron width and probability density between energy levels. In addition, the application of random matrices in quantum chromo dynamics and two dimensional Einstein gravity equations is also present in this paper.