Effective Prüfer angles and relative oscillation criteria

We present a streamlined approach to relative oscillation criteria based on effective Prüfer angles adapted to the use at the edges of the essential spectrum.Based on this we provided a new scale of oscillation criteria for general Sturm-Liouville operators which answer the question whether a perturbation inserts a finite or an infinite number of eigenvalues into an essential spectral gap. As a special case we recover and generalize the Gesztesy-Ünal criterion (which works below the spectrum and contains classical criteria by Kneser, Hartman, Hille, and Weber) and the well-known results by Rofe-Beketov including the extensions by Schmidt.     

Orthogonal similarity of a real matrix and its transpose

Any square matrix over a field is similar to its transpose and any square complex matrix is similar to a symmetric complex matrix. We investigate the situation for real orthogonal (respectively complex unitary) similarity.     

On the zero set of semi-invariants for regular modules over tame canonical algebras

We investigate sets of the common zeros of non-constant semi-invariants for regular modules over canonical algebras. In particular, we show that if the considered algebra is tame then for big enough vectors these sets are complete intersections.     

Equations ax = c and xb = d in rings and rings with involution with applications to Hilbert space operators

This paper reviews the equations ax = c and xb = d from a new perspective by studying them in the setting of associative rings with or without involution. Results for rectangular matrices and operators between different Banach and Hilbert spaces are obtained by embedding the ‘rectangles’ into rings of square matrices or rings of operators acting on the same space. Necessary and sufficient conditions using generalized inverses are given for the existence of the hermitian, skew-hermitian, reflexive, antireflexive, positive and real-positive solutions, and the general solutions are described in terms of the original elements or operators. New results are obtained, and many results existing in the literature are recovered and corrected.     

Geometry of 2×2 Hermitian matrices II

Let Z be a field of characteristic ≠2, D be a quaternion division algebra over Z and have a nonstandard involution of the first kind. The fundamental theorem of geometry of 2× 2 Hermitian matrices over D are proved. Thus, if D is a quaternion division algebra over Z with an involution of the first kind, then the fundamental theorem of geometry of 2× 2 Hermitian matrices over D are obtained.     

α -正规函数的一些积分准则

对 0<α <∞, N^α 是开单位圆盘 D 上满足 sup _{z∈ D}(1-|z|²)^α f^# (z)<∞ 的亚纯函数类, 其中 f^# (z)=|f'(z)|/(1+|f(z)|²) 是 f 的球面导数. 该文给出了 D 上的 α -正规函数类的一些积分准则, 并用 Bergman-Carleson 测度的形式予以表示.     

α N-O turn induced by fluorinated α-aminoxy diamide: synthesis and conformational studies

Two α-aminoxy diamides with fluorinated side chains were synthesized. Their secondary structures characterization was carried out by ¹H NMR, and IR spectrometries as well as X-ray crystallography studies. α N-O turn secondary structures are adopted insusceptibly by side-chain-fluorinated α-aminoxy residues. Thus the fluorinated α-aminoxy diamide can be a potential residue as a biological tracer to be incorporated into aminoxy peptides.     

Research on preparing compact bulk nanocomposite Nd2Fe14B/α-Fe magnetic materials by hot extrusion

In this paper, compact bulk nanocomposite Nd₂Fe₁₄B/α-Fe magnetic materials were prepared by hot extrusion of amorphous and nanocrystalline powders, which were prepared by high-energy ball-milling (HEBM) of the Nd₂Fe₁₄ B-type hard magnetic phase with 20 vol% of α-Fe as soft magnetic phase. The extrusion temperature has important influence on magnetic properties and microstructure of magnetic materials. The results show that the grain size of Nd₂Fe₁₄B and α-Fe phase increases steadily with increasing extrusion temperature. Furthermore, optimal extrusion temperature of 1223 K occurs, at which the highest magnetic properties and relative density can be obtained.     

B位Co掺杂对Sr14C24O41的结构和电输运的影响

采用固相反应法制备了系列Sr14（Cu1-xCox）24O41（x=0,0.02,0.06,0.1,0.14,0.18）的样品,X-射线衍射结果显示所有样品均为单相,且Co的掺杂几乎不改变样品的晶格常数,电子衍射和X-射线光电子能谱的测量结果证实Co替代的是链上的Cu原子;电输运的测量显示,Co掺杂样品表现为半导体行为,且渡越温度T随掺杂量的增加逐渐减小.