Schur Q-Polynomials and Kontsevich-Witten Tau Function

In this paper, we prove a conjecture of Mironov and Morozov which expresses Kontsevich-Witten tau-function as a linear combination of Schur Q-polynomials. Consequently we also give a proof for Alexandrov's conjecture that Kontsevich-Witten tau-function is a hypergeometric tau-function of the BKP hierarchy after re-scaling.Comment: 45 pages. Improved presentation for the proof of L_2 constraint, added references, corrected typo

Action of WW-type operators on Schur functions and Schur Q-functions

In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau functions of higher KdV hierarchies which satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur's Q-functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov-Morozov's formula, which express the Br\'{e}zin-Gross-Witten and Kontsevich-Witten tau-functions as linear combinations of Q-functions with simple coefficients respectively.Comment: 31 pages. Added an application for Kontsevich-Witten mode

Action of Virasoro operators on Hall-Littlewood polynomials

In this paper, we prove formulas for the action of Virasoro operators on Hall-Littlewood polynomials at roots of unity.Comment: 20 page

Q-Polynomial expansion for Brezin-Gross-Witten tau-function

In this paper, we prove a conjecture of Alexandrov that the generalized Brezin-Gross-Witten tau-functions are hypergeometric tau functions of BKP hierarchy after re-scaling. In particular, this shows that the original BGW tau-function, which has enumerative geometric interpretations, can be represented as a linear combination of Schur Q-polynomials with simple coefficients.Comment: 27 pages. arXiv admin note: text overlap with arXiv:2103.1431

SODs involved in the hormone mediated regulation of H 2 O 2 content in Kandelia obovata root tissues under cadmium stress

Abstract(#br)Cadmium (Cd) pollution in mangrove wetlands has received increasing attention as urbanization expands rapidly. As a dominant mangrove species, Kandelia obovata is highly tolerant to Cd toxicity. Plant hormones and superoxide dismutase (SODs) play critical roles in the response to heavy metal stress in K. obovata roots. Although theirs important influence have been reported, the regulation mechanism between SODs and plant hormones in Cd detoxification by K. obovata roots remains limited. Here, we investigated relationships among SOD, plant hormones, and Cd tolerance in K. obovata roots exposed to Cd. We found that Cd was retained in the epidermis and exodermis of roots, and the epidermis and exodermis had highest hydrogen peroxide (H 2 O 2 ) content and SOD activity. Similarly, SOD isozymes also exhibited distinct activity in the different parts of root. Overexpressed KoCSD3 and KoFSD2 individually in Nicotiana benthamiana revealed that different SOD members contributed to H 2 O 2 content regulation by promote the activity of downstream antioxidant enzymes under Cd treatment. In addition, assays on the effects of hormones showed that increased endogenous indole-3-acetic acid (IAA) was observed in the cortex and stele, whereas the abscisic acid (ABA) content was enhanced in the epidermis and exodermis in roots during Cd treatment. The results of exogenous hormones treatment indicated that KoFSD2 upregulated under ABA and IAA treatment, but KoCSD3 only induced by ABA stimulation. Taken together, our results reveal the relationship between SODs and plant hormones, which expands the knowledge base regarding KoSODs response to plant hormones and mediating H 2 O 2 concentration under Cd stress

SODs involved in the hormone mediated regulation of H2O2 content in Kandelia obovata root tissues under cadmium stress.

Cadmium (Cd) pollution in mangrove wetlands has received increasing attention as urbanization expands rapidly. As a dominant mangrove species, Kandelia obovata is highly tolerant to Cd toxicity. Plant hormones and superoxide dismutase (SODs) play critical roles in the response to heavy metal stress in K. obovata roots. Although theirs important influence have been reported, the regulation mechanism between SODs and plant hormones in Cd detoxification by K. obovata roots remains limited. Here, we investigated relationships among SOD, plant hormones, and Cd tolerance in K. obovata roots exposed to Cd. We found that Cd was retained in the epidermis and exodermis of roots, and the epidermis and exodermis had highest hydrogen peroxide (H2O2) content and SOD activity. Similarly, SOD isozymes also exhibited distinct activity in the different parts of root. Overexpressed KoCSD3 and KoFSD2 individually in Nicotiana benthamiana revealed that different SOD members contributed to H2O2 content regulation by promote the activity of downstream antioxidant enzymes under Cd treatment. In addition, assays on the effects of hormones showed that increased endogenous indole-3-acetic acid (IAA) was observed in the cortex and stele, whereas the abscisic acid (ABA) content was enhanced in the epidermis and exodermis in roots during Cd treatment. The results of exogenous hormones treatment indicated that KoFSD2 upregulated under ABA and IAA treatment, but KoCSD3 only induced by ABA stimulation. Taken together, our results reveal the relationship between SODs and plant hormones, which expands the knowledge base regarding KoSODs response to plant hormones and mediating H2O2 concentration under Cd stress

Study on factors affecting fruit development of seedless ponkan cultivar Huagan No.4

[Objective] Ponkan (Citrus reticulata Blanco.) is one of the main Mandarins cultivars in China. Huagan No.4 is a new seedless cultivar selected from a bud sport of Jing'an ponkan, with improved fruit quality. However, the cultivar has the problems of low fruiting rate and slow fruit development, limiting its industrial deployment. Therefore, it is important to clarify the key factors affecting the fruit size of seedless ponkan for high-quality production. [Methods] Huagan No.4 (HG4) and Huagan No.2 (HG2) were used as test materials. The paraffin section was used for observing the fruit development, sequencing transcriptome was performed to detect the difference of the gene expression between the two varieties. [Results] The observation of the equatorial surface of young fruits from 5 to 45 (DAF) revealed that the number of cell layers in the white pericarp of HG4 was more than HG2 on 5 DAF, but consistently less than HG2 from 15 to 45 DAF. The morphology of HG4 and HG2 was also observed during the cell division stage, and the white pericarp cell density of both continued to decrease from 5 to 45 DAF. The cell density of HG4 was consistently larger than HG2 from 15 to 45 DAF, and the significant difference was found on 35 DAF. The fruit transverse longitudinal diameters were measured at 30 day intervals starting on 80 DAF and it were found to be consistently and significantly smaller in HG4 than HG2. The plant endogenous hormone IAA, GA3 and Zeatin contents in young fruits of HG2 and HG4 showed an overall increase followed by a decrease from 15 days before flowering (DBF) to 45 DAF. The IAA contents of HG4 and HG2 were 117.08 ng·g-1 and 290.21 ng·g-1, respectively, on 45 DAF, the different was significant. The GA3 content of HG2 peaked at 2.27 ng·g-1 on 25 DAF, while the GA3 content of HG4 was only 0.90 ng·g-1, with significant differences. The GA3 and Zeatin contents of HG2 were higher than those of HG4 on 25 and 45 DAF. The differentially expressed genes were screened using the Citrus clementina genome with the criteria of p-value 1, and were functionally analyzed. Among the 173 differential genes identified, the transcription factors encoding the genes were screened. Three ERF transcription factors (Ciclev10005820m, Ciclev10005863m, Ciclev10021265m), two MADS (Ciclev10016394m, Ciclev10032489m), one GRF (Ciclev10025855m), and an ADAP (Ciclev10025985m) were screened by homologous sequence analysis with Arabidopsis transcription factors. These seven genes might be involved in the regulation of HG4 fruit development. Meanwhile, the homologous genes of YUC related to the auxin synthesis pathway of HG4 (CmYUC10, CmYUC11), genes of GA20ox related to the gibberellin (CmGA20ox1, CmGA20ox5), and genes of the cytokinin CmIPT2 were found to have an overall low level of expression in comparison with HG2, which was in accordance with the results of the plant endogenous hormone content measurement. The CmGA20ox5 was consistent with the relative expression levels of the GA20ox1 on 25 and 45 DAF. The expressions were significantly lower in HG4 than HG2, suggesting that gibberellin would have a greater possible influence on HG4 fruit development. In addition, the statistical analysis revealed that the average thickness of bearing base shoots with a diameter corresponding to HG4 fruit transverse diameters 70 mm were 2.15 mm, 2.59 mm, and 2.97 mm, respectively. It was found that the thickness was positively correlated with the size of the fruits. The proportion of large fruits with a transverse diameter >70 mm was as great as 40% for fruits siting on the upper part of the tree, whereas only 4% for lower part. [Conclusion] The low expression of hormone metabolic pathway genes affected hormone contents in HG4 fruits during early development period, which might lead to the inherent causes of smaller fruits. The thickness of HG4 bearing base shoots with a diameter and fruiting site would also be a important factor affecting its fruit dimensions