Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

Effect of Thermal Processing on the Metabolic Components of Black Beans on Ultra-High-Performance Liquid Chromatography Coupled with High-Field Quadrupole-Orbitrap High-Resolution Mass Spectrometry

An ultra-high-performance liquid chromatography coupled with high-field quadrupole-orbitrap mass spectrometry (UHPLC-QE-MS) histological platform was used to analyze the effects of two thermal processing methods (cooking and steaming) on the nutritional metabolic components of black beans. Black beans had the most amino acids, followed by lipids and polyphenols, and more sugars. Multivariate statistical analysis indicated that heat processing significantly affected the metabolic component content in black beans, with effects varying among different components. Polyphenols, especially flavonoids and isoflavones, were highly susceptible. A total of 197 and 210 differential metabolites were identified in both raw black beans and cooked and steamed black beans, respectively. Cooking reduced the cumulative content of amino acids, lipids, polyphenols, sugars, and nucleosides, whereas steaming reduced amino acid and lipid content, slightly increased polyphenol content, and significantly increased sugar and nucleoside content. Our results indicated that metabolic components were better retained during steaming than cooking. Heat treatment had the greatest impact on amino acids, followed by polyphenols, fatty acids, sugars, and vitamins, indicating that cooking promotes the transformation of most substances and the synthesis of a few. The results of this study provide a basis for further research and development of nutritional products using black beans.     

ZnSe薄膜的化学反应辅助热壁外延法生长及特性研究

本文通过将新型化学气相反应促进剂Zn(NH4)3Cl5引入到热壁外延系统中,以二元素单质Zn和Se为原料,直接在Si(111)衬底上生长了高质量的ZnSe晶体薄膜,薄膜成分接近理想化学计量比。研究了主要工艺参数对薄膜生长形貌和性能的影响。采用SEM、AFM、EDS和PL谱技术研究了生长的ZnSe薄膜的形貌、成分和发光特性。研究结果表明,热壁温度和生长时间是影响ZnSe薄膜形貌的主要因素;气相反应促进剂在薄膜生长和调节成分方面扮演了关键角色,Zn(NH4)3Cl5的存在使得Zn(g)和Se2(g)合成ZnSe晶体的反应转变为气固非一致反应,从而更容易获得近乎理想化学计量比的ZnSe薄膜。ZnSe薄膜在氦镉激光激发下,室温下PL谱由近带边发射和(VZn-ClSe)组合的SA发光组成,而在飞秒激光激发下,仅在481nm处显示出强烈的双光子发射峰。     

Röntgenographische Strukturuntersuchung geschmolzener Magnesium-Blei Legierungen

Abstract

Um Aufschluß über die Atomanordnung in geschmolzenen Magnesium-Blei Legierungen zu erhalten, wurden rontgenographische Strukturuntersuchungen durchgeführt.     

The Novikov Conjecture for Low Degree Cohomology Classes

We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C* _r (, )-bundle and connection, which can be used to construct a C* _r (, )-index that lies in the Grothendieck group of C* _r (, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem.     

On Potentially Abelian Geometric Representations

The finiteness is proved of the set of isomorphism classes of potentially abelian geometric Galois representations with a given set of data. This is a special case of the finiteness conjecture of Fontaine and Mazur.     

Differentiators and the geometry of polynomials

In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer.     

Witten Solution for the Gelfand–Dikii Hierarchy

We derive formulas making it possible to calculate the Taylor expansion coefficients of the string solution for the Gelfand–Dikii hierarchy. According to the Witten conjecture, these coefficients coincide with the Mumford–Morita–Miller intersection numbers (correlators) of stable cohomology classes for the moduli space of n-spin bundles on Riemann surfaces with punctures.     

The Chern Conjecture for Affinely Flat Manifolds Using Combinatorial Methods

An affine manifold is a manifold with a flat affine structure, i.e. a torsion-free flat affine connection. We slightly generalize the result of Hirsch and Thurston that if the holonomy of a closed affine manifold is isomorphic to amenable groups amalgamated or HNN-extended along finite groups, then the Euler characteristic of the manifold is zero confirming an old conjecture of Chern. The technique is from Kim and Lee's work using the combinatorial Gauss–Bonnet theorem and taking the means of the angles by amenability. We show that if an even-dimensional manifold is obtained from a connected sum operation from K(, 1)s with amenable fundamental groups, then the manifold does not admit an affine structure generalizing a result of Smillie.