On confining potentials and essential self-adjointness for Schr\"odinger operators on bounded domains in R^n

Let $\Omega$ be a bounded domain in $R^n$ with $C^2$-smooth boundary of co-dimension 1, and let $H=-\Delta +V(x)$ be a Schr\"odinger operator on $\Omega$ with potential V locally bounded. We seek the weakest conditions we can find on the rate of growth of the potential V close to the boundary which guarantee essential self-adjointness of H on $C_0^\infty(\Omega)$. As a special case of an abstract condition, we add optimal logarithmic type corrections to the known condition $V(x)\geq \frac{3}{4d(x)^2}$, where $d(x)=dist(x,\partial\Omega)$. The constant 1 in front of each logarithmic term in Theorem 2 is optimal. The proof is based on a refined Agmon exponential estimate combined with a well known multidimensional Hardy inequality

Matrix models for circular ensembles

We describe an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature beta. Our approach combines elements from the theory of orthogonal polynomials on the unit circle with ideas from recent work of Dumitriu and Edelman. In particular, we resolve a question left open by them: find a tri-diagonal model for the Jacobi ensemble.Comment: 28 page

CONSIDERATIONS REGARDING THE DEVELOPMENT OF NEW EQUIPMENT USED FOR HEMP HARVESTING

The important potential of cultivating hemp for fiber and cannabidiol extraction for medicinal use, makes this plant return to the attention of agronomists and medical researchers. Another strength of this plant is the potential of produced fibers to contribute to the decrease in the use of plastic in the near future, helping to reduce dependence on fossil fuels. In addition, hemp could be a more economically attractive alternative for ethanol generation or even for the production of high-strength construction materials. The paper aims to present several technologies used for hemp harvesting

REVIEW OF THE MAIN EQUIPMENT USED FOR SEPARATING CONTAMINANTS FROM WHEAT SEEDS, CLASSIFICATION ACCORDING TO THEIR FUNCTIONAL ROLE

Wheat seed cleaning require a complex set of operations to be performed in order to remove impurities from the grain mass and obtain high quality final products. These operations are carried out in a technological flow, starting from harvesting until the final processing stage, depending on the crop destination. The stages used to clean the wheat grain are usually following the operations: cleaning in aerodynamic separators, cleaning with sieves, sorting in indent cylinder separator, additional cleaning in special cleaning machines. The paper presents a synthesis of the primary processing phases of wheat seeds for the use in the food industry depending on their functional role

THE QUALITY OF THE AQUATIC ENVIRONMENT IN FISH PONDS

In our country, the most widespread growth system is the semi-intensive one with growth units represented by ponds (anthropogenic ecosystems). The semi-intensive fish culture is based on the natural productivity and / or enriched by fertilization of the anthropogenic ecosystems, respectively also on the administration of supplementary food. In fact, semi-intensive cultivation involves obtaining a fish biomass with low production costs due to the use of inexpensive inputs. The productionprofile and the way of obtaining it determine the structure and duration oftheexploitation cycle within a fish farm

ASPECTS REGARDING THE ENERGY POTENTIAL OF THE MISCANTHUS PLANT

Greenhouse gases resulting from human activities are the most significant driver of climate change. The use of renewable resources obtained by cultivating energy plants, that have the potential of replacing fossil fuels, is one of the most important approaches to reduce the consequences produced by this global climate change hazard.The paper presents information regarding the energy potential of the Miscanthus plant, that can be explored in three main directions: to produce bioethanol, biogas or solid biomass (chopped, pellets or briquettes), then use thermochemical processes for energy production

CMV matrices in random matrix theory and integrable systems: a survey

We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.Comment: Based on a talk given at the Short Program on Random Matrices, Random Processes and Integrable Systems, CRM, Universite de Montreal, 200

Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions

We consider a periodic Schroedinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from the rest of the spectrum. We study the associated localization functional introduced by Marzari and Vanderbilt, and we prove some results about the existence and exponential localization of its minimizers, in dimension d < 4. The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds.Comment: 37 pages, no figures. V2: the appendix has been completely rewritten. V3: final version, to appear in Commun. Math. Physic