缺项算子矩阵的谱补

设H和K为可分复Hiblert空间,对定义在Hilbert空间H K上的2×2阶算子矩阵MX=ACXB,其中A∈B(H),B∈B(K),C∈B(K,H)给定,当X取遍B(H,K)中的算子时,给出了所有MX的谱之交集及在一定条件下MX的谱分布情况.

关于谱补算子对的刻画

Ｈｉｌｂｅｒｔ空间上的算子对（Ａ，Ｂ）∈Ｌ（Ｈ）×Ｌ（Ｋ，Ｈ）是谱补算子对，是指对复平面Ｃ上的任一非空紧集Ｄ，都存在算子对（Ｘ，Ｙ）∈Ｌ（Ｈ，Ｋ）×Ｌ（Ｋ），使得以（Ａ，Ｂ）为第一行，（Ｘ，Ｙ）为第二行的算子矩阵ＭＡ，Ｂ（Ｘ，Ｙ）∈Ｌ（ＨＫ）的谱是Ｄ．文中研究了谱补算子对的性质，给出了若干等价条件，并证明了谱补算子对等价于可控算子对．

2×2上三角算子矩阵的一类谱补问题

设H,K为Hilbert空间,MC=A C0 B是定义在HK上的2×2上三角缺项算子矩,对于给定的A,B本文得到了一些关于MC的谱补的一些结果.

关于某类2×2缺项算子矩阵的谱补

对于Hilbert空间上的2×2缺项算子矩阵和，我们刻画了它们所有补的谱的交集与并集，也给出了缺项算式矩阵具有补T＝满足X和Y是紧算子使得σ（T）Ω的充分必要条件，其中Ω是复平面上包含零点的非空开集，且具有每个连通分支是单通的．这个结论也被应用于讨论连续（或离散）时间无限维线性系统的指数（或幂）稳定性问题．

一类缺项算子矩阵的谱补问题

对于Hilbert空间上的2×2算子矩阵，其中A∈B（H），C∈B（K，H），D∈B（H，K）给定，当X取遍B（K）中算子时，我们给出所有Nx的谱之交集和并集的刻画．

中年进补餐谱

寒冷的季节，谁不希望自已的身心都是暖洋洋的呢。你以为只有大鱼大肉才会给身体带来热量吗？那未免有些偏颇。事实上，蔬菜同样会给需要温暖的你添上“冬天里的一把火”。

鄭氏《詩譜》考原

佚書《毛詩譜》是鄭玄《詩經》學中不可或缺的組成部分。鄭氏《詩譜》主要由《譜》序、《譜》文和《譜》表構成,《譜》表是《詩譜》的核心。唐人所撰《毛詩正義》引録《譜》序和《譜》文,並對《譜》表加以描述,但未保留原表。《詩譜》亡佚後,《譜》表的主要内容以及《譜》序、《譜》文可據《正義》大致恢復,《譜》表之體式則成爲《詩譜》復原的關鍵。北宋歐陽修以《詩譜》殘本爲基礎作《詩譜補亡》,具備《譜》表,但又羼入了私見。以歐氏《詩譜補亡》版本及後來諸家所製《譜》表之體式爲基礎,裁之以《毛詩》經義、鄭學原義及《正義》對《譜》表的描述,鄭氏《譜》表之體式始得尋繹。在此基礎上,辨析《譜》表内容之疑義,兼及《譜》題,鄭氏《詩譜》原貌始得概見。

Signal-purity-spectrum-based colored deconvolution

Signal to noise ratio （SNR） and resolution are two important but contradictory characteristics used to evaluate the quality of seismic data. For relatively preserving SNR while enhancing resolution, the signal purity spectrum is introduced, estimated, and used to define the desired output amplitude spectrum after deconvolution. Since a real reflectivity series is blue rather than white, the effects of white reflectivity hypothesis on wavelets are experimentally analyzed and color compensation is applied after spectrum whitening. Experiments on real seismic data indicate that the cascade of the two processing stages can improve the ability of seismic data to delineate the geological details.

Intermolecular Vibrational Energy Transfers in Melts and Solutions

Resonant and nonresonant intermolecular vibrational energy transfers in Gdm- SCN/KSCN=1/1, GdmSCN/KS^13CN=1/1 and GdmSCN/KS^13C^15N=1/1 mixed crystals in melts and in aqueous solutions are studied with the two dimensional infrared spectroscopy. The energy transfers in the samples are slower with a larger energy donor/acceptor gap, independent of the Raman spectra. The energy gap dependences of the nonresonant energy transfers cannot be described by the phonon compensation mechanism. Instead, the experi- mental energy gap dependences can be quantitatively described by the dephasing mechanism. Temperature dependences of resonant and nonresonant energy transfer rates in the melts are also consistent with the prediction of the dephasing mechanism. The series of results suggest that the dephasing mechanism can be dominant not only in solutions, but also in melts （pure liquids without solvents）, only if the molecular motions （translations and rotations） are much faster than the nonresonant energy transfer processes.

Analysis of the hotspots and trends in traditional Chinese medicine immunomodulation research based on bibliometrics

Objective To analyze the intellectual structure,hotspots and trends of traditional Chinese medicine(TCM)in immune regulation research.Methods The data were extracted from the Web of Science Core Collection(WoSCC)and the China National Knowledge Infrastructure(CNKI)and verified by two experienced TCM researchers.The time of literature retrieval is up to 2020.CiteSpace 5.7.R1 and Microsoft Excel 2016 were used for the statistical analysis and bibliometric diagrams,including the co-occurrence network of authors,institutions,countries,keywords,references,dual-map overlays of journals and citation bursts,etc.Results A total of 12270 publications related to TCM in immune regulation were included.The annual number of publications has increased in this field.There was close cooperation of countries and institutions,while the distribution of scholars was scattered.China was the core of the cooperation network.The dual-map overlays analysis of journals showed that core and marginal fields had increased.The keywords and references analysis showed that network pharmacology,metabolism and cancer were the most high-frequency keywords with high-intensity bursts.Conclusion TCM in immune regulation has attracted wider attention,with multi-country,multi-field,multi-disciplinary and multi-level research developing toward informatization.Network pharmacology,metabolism and cancer may be the focus of future research in this field.

First-Principles Study of Ca3Sc2Si3O12： Ce3＋ Phosphors

Charge compensation plays a very important role in modifying the local atomic structure and moreover the spectroscopic property of an isolated luminescent center, and so has been widely adopted in phosphor designs. In this work, we carry out first-principles calculations on various cases of Ce3＋ centers in Ca3Sc2Si3O12 by considering the effects of the charge com- pensations related to N3-, Sc3＋, Mn2＋, Mg2＋, and Na＋. Firstly, the local structures around Ce3＋ are optimized by using density functional theory calculations with supercell model. The 4f→5d transition energies of Ce3＋ are then obtained from the CASSCF/CASPT2/RASSI-SO calculations performed on Ce3＋-centered embedded clusters. The calculated energies support the previous assignments of the experimental spectra. Especially, a previously unclear peak is identified to be caused by Sc3＋ substituting Si4＋. The results show that the first-principles calculations can be used as an effective tool for predicting and interpreting spectroscopic properties of the phosphors.

Improving the resolution of seismic traces based on the secondary time-frequency spectrum

The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time-frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform （ST） and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time frequency spectrum. Second, using the secondary time frequency spectrum, we design a two- dimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time- fi＇equency-space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio （SNR）.

Detection and analysis of knee osteoarthritis in mice with gene expression profile

When gene expression profile is used for gene detection,the probe on the chip can emit fluorescence with different wavelengths.Under the action of confocal laser scanner,a clear gene change image can be obtained,by which the gene changes of the sample to be tested can be observed directly.First,the knee osteoarthritis(KOA)models of mice are established by the method of collateral ligament and meniscus resection(MLI-OA).Then,Bushen Huoxue formula is given by gavage,and ribonucleic acid(RNA)is routinely extracted and purified.Finally,the gene expression changes of KOA tissues of mice are detected by Agilent SurePrint G3 Mouse GE V2.0 gene expression profile.The results show that Bushen Huoxue formula has significant regulation effect on gene expression of KOA tissue.Among the genes with significant up-regulation effect of Bushen Huoxue formula,there are 56 genes of traditional Chinese medicine(TCM)groups up-regulated more than twice compared with model groups.Among the genes with significant down-regulation effect,there are 119 genes of TCM groups down-regulated more than twice compared with model groups.The experimental results indicate that Bushen Huoxue formula may promote the metabolism of arthritic factors and delay cartilage degeneration to treat KOA by regulating genes that are currently unknown in the pathological process of KOA.

COMPENSATION FOR THE EFFECTS OF MUTUAL COUPLING ON THE PERFORMANCE OF ADAPTIVE ARRAYS

Using the Method of Moments(MoM) and the spectral method, the effect of mutual coupling on the performance of adaptive arrays is compensated. First, the MoM is used to compute the behavior of the array, where the accurate analytical model and odd numbers of piecewise sinusoids are applied. Then the covariance matrix with mutual coupling being taken into account is analyzed, and the expression for the weight of the Least Mean Square(LMS) algorithm with mutual coupling being compensated is given. Finally, the method given in this letter is tested on an example.

Analysis of Multi-ingredient Food Supplements by Fingerprint HPTLC Approach

The increase of import/export of every kind of herbal products calls urgently for adequate controls. Analysis of herbal food supplement （botanicals） is a difficult task, like in the composition determination of a multi-ingredient product, where several botanical drugs were used. Actually, this is an important argument in consideration of health security. The authors reported the results of an analytical approach based on HPTLC （high performance thin layer chromatography） fingerprints comparison and tailored to determine the composition of marketed multi-ingredient botanicals. The method gave positive data in case of the presence of 3-5 species, whereas difficulties were recorded when the number of plants is increased.

Differential gene expression profile of Buyanghuanwu decoction in rats with ventricular remodeling post-myocardial infarction

OBJECTIVE: To investigate the effect of Buyanghuanwu decoction(BYHWD) on gene expression in ventricular remodeling post-myocardial infarction in rats.METHODS: Animal models of myocardial infarction were established by permanent ligation of the left anterior descending coronary artery. Echocardiography measurements were performed after the treatment of BYHWD(18 g·kg-1 collagen was observ·d-1) for 90 days.Myocardialed by mallory trichrome staining. Capillary density was quantified by using Factor rentially expⅧre immunohistochemical staining.Diffessed genes were explored by a short-read sequencing technology combined with a tag-based digital gene expression profiling(DGE)system. Real-time quantitative polymerase chain reaction detecting system(q PCR) was used to validate the sequencing results. After assembling the gene information from Sham, model and BYHWD groups, we constructed three DGE libraries based on each group. The sequencing of three libraries generated 66 000-73 000 unique tags, which were mapped to reference sequences for annotation of expressed genes.RESULTS: Among them, 511 and 352 differentially expressed genes were found in comparison with sham/model and model/BYHWD, respectively. Fifty-five genes exhibited reversed direction of gene expression differences between Sham/Model and Model/BYHWD groups. We found that transforming growth factor beta receptor-1, junctophilin-2,monocyte chemotactic protein 1, neuropeptide Y,arachidonate 5-Lipoxygenase, arachidonate 15-Lipoxygenase were significantly modulated, which suggested the involvement of these genes in BYHWD treatment.CONCLUSION: The DGE profiling data provide comprehensive gene expression information at the transcriptional level that could facilitate our understanding of the pharmacological mechanisms of BYHWD in ventricular remodeling post-myocardial infarction.