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THE RIESZ DECOMPOSITION THEOREM FOR SKEW SYMMETRIC OPERATORS
Zhu, Sen,Zhao, Jiayin Korean Mathematical Society 2015 대한수학회지 Vol.52 No.2
An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.
ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES
Sen Zhu 대한수학회 2015 대한수학회지 Vol.52 No.6
An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular op- erator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew sym- metric triangular operators, which is based on the geometric relationship between eigenvectors.
ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES
ZHU, SEN Korean Mathematical Society 2015 대한수학회지 Vol.52 No.6
An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.
OPERATORS SIMILAR TO NORMALOID OPERATORS
Sen Zhu,Chun Guang Li 대한수학회 2011 대한수학회지 Vol.48 No.6
In this paper, the authors investigate the structure of opera-tors similar to normaloid and transloid operators. In particular, we char-acterize the interior of the set of operators similar to normaloid (transloid,respectively) operators. This gives a concise spectral condition to deter-mine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact pertur-bation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.
THE RIESZ DECOMPOSITION THEOREM FOR SKEW SYMMETRIC OPERATORS
Sen Zhu,Jiayin Zhao 대한수학회 2015 대한수학회지 Vol.52 No.2
An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.
OPERATORS SIMILAR TO NORMALOID OPERATORS
Zhu, Sen,Li, Chun Guang Korean Mathematical Society 2011 대한수학회지 Vol.48 No.6
In this paper, the authors investigate the structure of operators similar to normaloid and transloid operators. In particular, we characterize the interior of the set of operators similar to normaloid (transloid, respectively) operators. This gives a concise spectral condition to determine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact perturbation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.
Sen Li,Yang Zou,Xue-Liang Zhang,Ping Wang,Xiao-Qing Chen,Xing-Quan Zhu 대한기생충학열대의학회 2020 The Korean Journal of Parasitology Vol.58 No.6
Giardia lamblia is a common enteric pathogen associated with diarrheal diseases. There are some reports of G. lamblia infection among different breeds of cattle in recent years worldwide. However, it is yet to know whether cattle in Jiangxi province, southeastern China is infected with G. lamblia. The objectives of the present study were to investigate the prevalence and examine the multilocus genotypes of G. lamblia in cattle in Jiangxi province. A total of 556 fecal samples were collected from 3 cattle breeds (dairy cattle, beef cattle, and buffalo) in Jiangxi province, and the prevalence and genotypes of G. lamblia were determined by the nested PCR amplification of the beta-giardin (bg) gene. A total of 52 samples (9.2%) were positive for G. lamblia. The highest prevalence of G. lamblia was detected in dairy cattle (20.0%), followed by that in beef cattle (6.4%), and meat buffalo (0.9%). Multilocus sequence typing of G. lamblia was performed based on sequences of the bg, triose phosphate isomerase and glutamate dehydrogenase loci, and 22, 42, and 52 samples were amplifiable, respectively, forming 15 MLGs. Moreover, one mixed G. lamblia infection (assemblages A and E) was found in the present study. Altogether, 6 novel assemblage E subtypes (E41*-E46*) were identified for the first time. These results not only provided baseline data for the control of G. lamblia infection in cattle in this southeastern province of China, but also enriched the molecular epidemiological data and genetic diversity of G. lamblia in cattle.
Jing Zhu,Jun-xia Yu,Jia-dong Chen,Jie-sen Zhang,Jia-qi Tang,Yuan-lai Xu,Yue-fei Zhang,Ru-an Chi 한국화학공학회 2017 Korean Journal of Chemical Engineering Vol.34 No.6
A modified sugarcane bagasse (SCB) fixed bed column was used to remove Pb2+ from aqueous solution. To determine the optimal condition for Pb2+ separation, Ca2+ was chosen as the model interfering ion, and effects of Ca2+ and Pb2+ initial concentration ratio (C0 Ca : C0 Pb) on the adsorption of Pb2+ were investigated. Results showed that adsorption amount ratio of Ca2+ and Pb2+ (qe Ca : qe Pb) had a good linear relationship with C0 Ca : C0 Pb. Mass ratio of Pb2+ absorbed on the modified SCB was higher than 95% at C0 Ca : C0 Pb<1.95, illustrating that Pb2+ could be selectively removed from aqueous solution. To verify that, simulated waste water containing co-ions of K+, Na+, Cd2+ and Ca2+ was treated, and results showed that the equilibrium amount of Pb2+, K+, Na+, Cd2+ and Ca2+ adsorbed was 134.14, 0.083, 0.058, 1.28, and 1.28mg g−1, respectively, demonstrating that the modified SCB could be used to remove Pb2+ from aqueous solution in the investigated range.
( Fuquan Zhu ),( Huajun Wang ),( Liping Yang ),( Changguo Li ),( Sen Wang ) 한국인터넷정보학회 2020 KSII Transactions on Internet and Information Syst Vol.14 No.8
With the wide application of hyperspectral images, it becomes more and more important to compress hyperspectral images. Conventional recursive least squares (CRLS) algorithm has great potentiality in lossless compression for hyperspectral images. The prediction accuracy of CRLS is closely related to the correlations between the reference bands and the current band, and the similarity between pixels in prediction context. According to this characteristic, we present an improved CRLS with adaptive band selection and adaptive predictor selection (CRLS-ABS-APS). Firstly, a spectral vector correlation coefficient-based k-means clustering algorithm is employed to generate clustering map. Afterwards, an adaptive band selection strategy based on inter-spectral correlation coefficient is adopted to select the reference bands for each band. Then, an adaptive predictor selection strategy based on clustering map is adopted to select the optimal CRLS predictor for each pixel. In addition, a double snake scan mode is used to further improve the similarity of prediction context, and a recursive average estimation method is used to accelerate the local average calculation. Finally, the prediction residuals are entropy encoded by arithmetic encoder. Experiments on the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) 2006 data set show that the CRLS-ABS-APS achieves average bit rates of 3.28 bpp, 5.55 bpp and 2.39 bpp on the three subsets, respectively. The results indicate that the CRLS-ABS-APS effectively improves the compression effect with lower computation complexity, and outperforms to the current state-of-the-art methods.