Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Synthesis and cytotoxicity of new 2-oxo-7-phenyl-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid amides

Abstract

The synthesis and anticancer activity evaluation of new thiazolo[4,5-b]pyridine-5-carboxylic acid amides is described. The structures of the synthesized compounds were confirmed by spectroscopic data and a single crystal X-ray diffraction analysis for 2.4. The synthesized compounds were screened for their in vitro anticancer activity according to US NCI protocols. The most active 7-(4-fluorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.2 and 7-(4-chlorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.5 were screened for their cytotoxicity effects on C6 Rat glioma cells and U373 Human glioblastoma astrocytoma cells which revealed promising results comparable to temozolamide as reference control according MTT assay data.     

复杂换热网络MINLP中的非线性特性分析

针对复杂换热网络MINLP问题,本文应用多维函数渐变法探索和分析了连续变量和整型变量引起的网络性能非线性和非凸特性。研究表明,当系统规模增大时,不但连续变量的叠加效应将增加系统的非线性,整型变量将使得非线性特性更为严重。     

三维荧光光谱的特征区域选择方法

将数学中的二元凸函数判定和数据挖掘中的聚类分析方法结合,提出了针对三维荧光的光谱区域选择方法,并利用此种方法从光谱图中提取出含有丰富光谱信息的凸集区域。对水体中总有机碳的检测和白酒中黄曲霉素的检测进行了实验研究,实验结果表明,采用本文提出的三维荧光光谱区域选择方法提高了模型的精度,与利用全光谱所建立的回归模型相比,模型精度分别提高了6.17%和4.97%。     

Super-symmetric informationally complete measurements

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.     

A conformal mapping approach for investigating the free-boundary seepage from symmetric channels

We present a new method to investigate the two-dimensional free-boundary groundwater seepage from symmetric soil channels into a homogeneous isotropic porous medium. We use Levi–Civitá’s function to construct an integral representation for the conformal mapping of the complex potential domain onto the physical flow domain. A genetic algorithm (GA) is used to calculate the coefficients of the Maclaurin series expansion of Levi–Civitá’s function. The coordinates of the points from the channel contour, calculated by means of the integral representation, must satisfy the analytic equation of the contour. We use this condition to define the objective function of the genetic algorithm. Levi–Civitá’s function is afterwards used to calculate the seepage loss, the free lines, the streamlines, the equipotential lines, the isobars and the velocity field. Some examples illustrate the method.     

大豆油煎炸过程理化指标与LF-NMR弛豫特性的相关性研究

在对大豆油无料/薯条煎炸过程[温度:(180±5)℃,持续36 h]中的酸价(AV)、粘度(V)、吸光值(A)及总极性化合物(TPC)含量等及低场核磁共振(LF-NMR)弛豫特性(峰起始时间T21、T22、T23、相应的峰面积比例S21、S22、S23、单组份弛豫时间T2W)变化规律研究的基础上,利用多元回归分析建立了理化指标与其LF-NMR检测结果的相关性模型,并进行验证。结果表明:大豆油的酸价、TPC含量及S21峰面积均随煎炸时间的延长而线性增大,T21、T22峰起始时间及T2W则随煎炸时间的延长而线性减小(r2>0.90),粘度、吸光值随煎炸时间的延长逐渐增加并符合二项式关系(r2>0.90),而T23峰起始时间及S22、S23与煎炸时间之间无明显规律性变化。煎炸薯条后,油样的酸价、粘度、TPC含量、吸光值及S21均较无料煎炸显著增大(P<0.05),而T21、T22峰起始时间及T2W显著缩短。多元回归分析表明,酸价及TPC含量与T2W、T21,粘度与T2W,吸光值与S21间均可建立良好的相关性模型(R2>0.93)。模型验证合理可靠,可通过油样的LF-NMR检测结果有效预测其理化指标的变化。     

Formation of Glyco-Functionalized Platinum Complexes by Cross-Metathesis and Evaluation of Their Efficacy in Inhibition of Lung Tumor Cell Lines

Syntheses of carbohydrate-functionalized platinum complexes resembling presently employed cytostatics were performed. Mono-allylated sugar substrates obtained in two steps from glucose and galactose were connected with 2-allyl diethyl malonate by cross-metathesis. Following hydrogenation and acidic cleavage of the ester and alkylidene functionalities gave dicarboxylated glycoconjugates, which were transformed into their diammine platinum complexes. The antitumor activities of these platinum complexes were checked by sensitivity testing with 11 lung cancer cell lines. The novel glucose-platinum complex proved to be comparable to the drug carboplatin.