Reducing subspaces for Toeplitz operators on the polydisk

Yanyue Shi,Yufeng Lu 대한수학회 2013 대한수학회보 Vol.50 No.2

In this note, we completely characterize the reducing sub- spaces of TzN 1 zM 2 on A2 α(D2) where α> −1 and N,M are positive in- tegers with N ≠ M, and show that the minimal reducing subspaces of TzN 1 zM 2 on the unweighted Bergman space and on the weighted Bergman space are different.

Comparing of backfat microRNAomes of Landrace and Neijiang pig by high-throughput sequencing

Yanyue Li 한국유전학회 2021 Genes & Genomics Vol.43 No.5

Background MicroRNAs (miRNAs) could regulate the expression of target genes and play important roles in modulation of various metabolic processes. Nevertheless, little is known about the backfat microRNAome (miRNAome) of the Neijiang pig. Objectives The primary objective of this study was to analyse miRNAomes of Landrace and Neijiang pig backfat (LPB and NPB resp.). Furthermore, investigating diferentially expressed miRNAs participating in lipid metabolism and mining potential biomarker for Neijiang pig breeding. Methods Here we used the Landrace pig with diferent metabolic characteristics as a control to analyse the Neijiang pigspecifc backfat miRNAome. A comprehensive analysis of miRNAomes was performed by deep sequencing. Results Small RNA sequencing identifed 326 unique miRNAs, 280 were co-expressed in both libraries. Only 11 and 35 miRNAs were specifcally expressed in LPB and NPB respectively. Sixty seven diferentially expressed miRNAs were identifed by IDEG6. MiR-1-3p were identifed that may participate in lipid metabolism. Furthermore, qPCR results revealed that lower expression of miR-1-3p in NPB could increase the expression of LXRα, which is an enzyme important for the synthesis and accumulation of lipid. The double luciferase report experiment suggested that LXRα was the direct target gene of miR-1-3p. In short, miR-1-3p could modulate the synthesis and accumulation of lipid by target LXRα. It may be a potential marker for pig breeding. Conclusion Our investigation has delineated the diferent miRNAs expression patterns of LPB and NPB, which may help understand the regulatory mechanisms of miRNAs in the lipid metabolism, and provide potential biomarkers for Neijiang pig breeding.

Design of reverse osmosis networks for multiple freshwater production

Yanyue Lu,Anping Liao,Yangdong Hu 한국화학공학회 2013 Korean Journal of Chemical Engineering Vol.30 No.5

Reverse osmosis (RO) desalination, which produces multiple freshwater from seawater, has been studied in this work. An optimization method based on process synthesis has been applied to design the RO system. First, a simplified superstructure that contains all the feasible design for this desalination problem has been presented. In this structural representation, the stream split ratios and the logical expressions of stream mixing were employed, which can make the mathematical model easy to handle. Then, the membrane separation units employing the spiral wound reverse osmosis elements were described by using a pressure vessel model, which takes into account the pressure drop and the concentration changes in the membrane channel. The optimum design problem can be formulated as a mixedinteger non-linear programming (MINLP) problem, which minimizes the total annualized cost of the RO system. The cost equation relating the capital and operating cost to the design variables, as well as the structural variables, has been introduced in the objective function. The problem solution includes the optimal streams distribution, the optimal system structure and the operating conditions. The design method could also be used for the optimal selection of membrane element type in each stage and the optimal number of membrane elements in each pressure vessel. The effectiveness of this design methodology has been demonstrated by solving a desalination case. The comparisons with common industrial approach indicated that the integrative RO system proposed in this work is more economical, which can lead to significant capital cost and energy saving and provide an economically attractive desalination scheme.

REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK

Shi, Yanyue,Lu, Yufeng Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2

In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.

Reducing subspaces of a class of multiplication operators

Bin Liu,Yanyue Shi 대한수학회 2017 대한수학회보 Vol.54 No.4

Let $M_{z^N}$($N\in \mathbb{Z}_+^d$) be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n: n\in \mathbb{Z}_+^d\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that $d=2$, we find all the minimal reducing subspaces of $M_{z^N}(N=(N_1,N_2), N_1\neq N_2)$ on weighted Bergman space $A_\alpha^2(\mathbb{B}_2)(\alpha>-1)$ and Hardy space $H^2(\mathbb{B}_2)$, and characterize the structure of $\mathcal{V}^*(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

Comparison of stomach microRNA transcriptomes of Tibetan and Yorkshire pigs by deep sequencing

Wen‑kui Sun,Yanyue Li,Chi Cheng,Yi‑hui Chen,Kai Zeng,Xiaohui Chen,Yiren Gu,Rui Liu,Xuebin Lv,Rong Gao 한국유전학회 2018 Genes & Genomics Vol.40 No.9

MiRNAs regulate the expression of target genes in diverse cellular processes and hence play important roles in different physiological processes, yet little is known about the stomach microRNAome (miRNAome) of the Tibetan pig. The objective of this experiment was to investigate differentially expressed stomach miRNAs participating in digestion. Firstly, we isolated total RNA by Trizol reagent from three Tibetan and three Yorkshire purebred pigs stomach samples at 90-day-old. Secondly, a comprehensive analysis of Tibetan and Yorkshire pig stomach miRNAomes was performed by small RNA sequencing in the Illumina HiSeq 2000 system. Finally, SYBR Green Real-time RT-PCR was performed to validate the differentially expressed miRNAs. We identified 318 unique miRNAs, 260 were co-expressed in both libraries, 17 and 31 miRNAs were specifically expressed in Tibetan and Yorkshire pigs respectively. Fifty six differentially expressed miRNAs were identified by the identifying differentially expressed genes 6 (IDEG6). Kyoto encyclopedia of genes and genomes analysis revealed that some of the differentially expressed miRNAs were associated with protein and fat digestion. Two differentially expressed miRNAs (miR-214-3p and ssc-un39) participating in the digestion of lipid were identified. Additionally, qRT-PCR results suggested that a higher expression of miR-214-3p in the Tibetan pig stomach could lead to relatively lower expression of calcium-dependent phospholipase A2, which is an enzyme important for the digestion of glycerol phospholipid. This study has delineated the different stomach miRNAs expression patterns of Tibetan and Yorkshire pigs, which would help explain the regulatory mechanisms of miRNAs in digestion of Tibetan pigs, and contribute to utilize a the unique digestion merits of Tibetan pig in future porcine hybridization breeding.

REDUCING SUBSPACES OF A CLASS OF MULTIPLICATION OPERATORS

Liu, Bin,Shi, Yanyue Korean Mathematical Society 2017 대한수학회보 Vol.54 No.4

Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

The Hyponormal Toeplitz operators on the vector valued Bergman space

Yufeng Lu,Puyu Cui,Yanyue Shi 대한수학회 2014 대한수학회보 Vol.51 No.1

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ 2 h∞ ⓧ Mn×n on L2 a(D, Cn). In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ ∈ h∞ ⓧ Mn×n on L2 a(D, Cn).

REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK

Mohammed Albaseer,Yufeng Lu,Yanyue Shi 대한수학회 2015 대한수학회보 Vol.52 No.5

In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator TzN 1- zM2 on the Bergman space A2(D2), where N and M are positive integers.

THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE

Lu, Yufeng,Cui, Puyu,Shi, Yanyue Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.