On spectra of algebras over ultranormed fields

Algebras over ultranormed fields are studied. Conditions under which spectra of such algebras are non-void are investigated. For this purpose extensions of fields are considered.     

On Weyl’s Theorem for Functions of Operators

Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl's theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl's theorem for f(T).     

Components Analysis of Biochar Based on Near Infrared Spectroscopy Technology

This study aims to establish a rapid quantitative analysis method for biochar based on near infrared spectroscopy (NIRS) technology. Near infrared spectra of 163 samples in the 10000–3800 cm^–1 (1000–2632 nm) range were collected, and the contents of fixed carbon (FC), volatile matter (VM) and ash of samples were also analyzed. A partial least square (PLS) model for FC, VM and Ash was established after the model spectral ranges were optimized, the optimal factors were determined, and the raw spectra were pretreated by multiple scatter correction and second derivative (MSC + SD) method. Finally, the prediction performance of predictive model was evaluated. The results showed that the PLS model had a good prediction ability, and the predicted coefficient R²_p of actual values vs prediction values for FC, VM and ash were 0.9423, 0.9517 and 0.9265, respectively. Root mean square error of prediction (RMSEP) was 0.1074, 0.1201 and 0.1243, and ratios of prediction to deviation (RPD) were 3.51, 4.28 and 2.03, respectively. The PLS model had good accuracy and precision for both of FC and VM, and could be used as a quantitative method for FC and VM contents analysis. Nevertheless, PLS model need to improve the precision for Ash analysis according to RPD value. This method provides a fast and effective technical means for the quantitative analysis of biochar components.     

Unit gain graphs with two distinct eigenvalues and systems of lines in complex space

Since the introduction of the Hermitian adjacency matrix for digraphs, interest in so-called complex unit gain graphs has surged. In this work, we consider gain graphs whose spectra contain the minimum number of two distinct eigenvalues. Analogously to graphs with few distinct eigenvalues, a great deal of structural symmetry is required for a gain graph to attain this minimum. This allows us to draw a surprising parallel to well-studied systems of lines in complex space, through a natural correspondence to unit-norm tight frames. We offer a full classification of two-eigenvalue gain graphs with degree at most 4, or with multiplicity at most 3. Intermediate results include an extensive review of various relevant concepts related to lines in complex space, including SIC-POVMs, MUBs and geometries such as the Coxeter-Todd lattice, and many examples obtained as induced subgraphs by employing a technique parallel to the dismantling of association schemes. Finally, we touch on an innovative application of simulated annealing to find examples by computer.     

单块磁悬浮系统磁体和超导体的厚度优化

研究了磁铁厚度和YBCO超导体厚度对悬浮力的大小及系统动态特性的影响,通过分析得出磁悬浮系统中磁体和超导体厚度的最优值。通过悬浮力测试系统测得超导块尺寸为φ30mm×18mm时四块不同厚度的磁体的悬浮力以及磁体尺寸为φ30mm×10mm时六块不同厚度的YBCO超导体的悬浮力的大小;并在振动实验台上测试了上述情况下的振动特性。对动态曲线进行频谱分析,最终得出最优组合,从而对磁悬浮系统的磁体和超导体厚度进行了优化。     

Spectral Polarimeters Based on Integrated Acousto-Optical Ti:LiNbO3 TE-TM Converters

An integrated Ti:LiNbO3 acousto-optical TE-TM converter followed by a polarizer was used to realize a wavelength-selective polarimeter. The stop-band attenuation was shown to increase to > 28 dB when more mode converters were integrated on a chip. Based on this experience, a four-stage demonstration unit was built, and polarimetric spectra as well as the time evolution of the state of polarization were measured. Finally, a simple optical spectrum analyzer is proposed.     

Spectral problem for branching chain quantum graph

Branching chain of rings as a quantum graph is considered. We use the transfer matrix method to obtain the spectral equation. The existence of bound states is proved. The discrete spectrum of the Schrödinger operator for the system is described. We find the dependence of the eigenvalues positions on the branching angle.     

近红外差谱法选择信息区提高同分异构体预测模型准确度

以短波近红外光谱法定量检测了二甲苯三种同分异构体混合溶液中各自的体积相对含量。分别采用全光谱、截取具有高相关系数的波段和差谱法选择光谱差异大的波段三种不同的建模方式建立偏最小二乘回归 (Partial L east- Squares Regression)预测模型并对被预测样品进行了相互验证 (Cross Validation)。实验表明 ,采用差谱法选择光谱差异大的波段建立的预测模型显著地克服了同分异构体光谱之间的相似性 ,其预测准确度优于前两者。     

Microwave spectrum, tunneling motions, and quadrupole coupling hyperfine structure of ethylene diamine

New transitions are measured in the microwave spectrum of two conformers of the non-rigid ethylene diamine (CH₂NH₂-CH₂NH₂) molecule using both molecular beam Fourier transform and stark modulation spectroscopy. Ab initio calculations are carried out to obtain geometries and energies for several stationary points of the potential energy surface and to gain quantitative information on the tunneling paths along which the molecule tunnels. The microwave data are reproduced using an IAM-like approach which accounts for the rotational dependence of the tunneling splitting corresponding to the interconversion large amplitude motion. For one of the conformers, the results of this analysis are consistent with the ones obtained through ab initio calculations. Hyperfine patterns are analyzed with the help of a theoretical approach accounting for the large amplitude motion effects and for hyperfine matrix elements within and between tunneling sublevels.