scholarly journals Homogeneous line bundles over a toroidal group

1989 ◽  
Vol 116 ◽  
pp. 17-24 ◽  
Author(s):  
Yukitaka Abe
Keyword(s):  
Line Bundle ◽  
Lie Group ◽  
Quotient Group ◽  
Holomorphic Functions ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Complex Torus ◽  
Group 5 ◽  
Group 2

A connected complex Lie group without non-constant holomorphic functions is called a toroidal group ([5]) or an (H, C)-group ([9]). Let X be an n-dimensional toroidal group. Since a toroidal group is commutative ([5], [9] and [10]), X is isomorphic to the quotient group Cn/Γ by a lattice of Cn. A complex torus is a compact toroidal group. Cousin first studied a non-compact toroidal group ([2]).Let L be a holomorphic line bundle over X. L is said to be homogeneous if is isomorphic to L for all x ε X, where Tx is the translation defined by x ε X. It is well-known that if X is a complex torus, then the following assertions are equivalent:

scholarly journals RANK ONE CONNECTIONS ON ABELIAN VARIETIES, II

2012 ◽  
Vol 23 (12) ◽  
pp. 1250125
Author(s):  
INDRANIL BISWAS ◽  
JACQUES HURTUBISE ◽  
A. K. RAINA
Keyword(s):  
Line Bundle ◽  
Exact Sequence ◽  
Abelian Varieties ◽  
Explicit Construction ◽  
The Other ◽  
Holomorphic Line Bundle ◽  
Canonical Isomorphism ◽  
Complex Torus ◽  
Rank One

Given a holomorphic line bundle L on a compact complex torus A, there are two naturally associated holomorphic ΩA-torsors over A: one is constructed from the Atiyah exact sequence for L, and the other is constructed using the line bundle [Formula: see text], where α is the addition map on A × A, and p1 is the projection of A × A to the first factor. In [I. Biswas, J. Hurtvbise and A. K. Raina, Rank one connections on abelian varieties, Internat. J. Math.22 (2011) 1529–1543], it was shown that these two torsors are isomorphic. The aim here is to produce a canonical isomorphism between them through an explicit construction.

scholarly journals CHEN–RUAN COHOMOLOGY OF SOME MODULI SPACES, II

2010 ◽  
Vol 21 (04) ◽  
pp. 497-522 ◽  
Author(s):  
INDRANIL BISWAS ◽  
MAINAK PODDAR
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Prime Number ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Stable Vector Bundles

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and ξ → X a holomorphic line bundle such that r is not a divisor of degree ξ. Let [Formula: see text] denote the moduli space of stable vector bundles over X of rank r and determinant ξ. By Γ we will denote the group of line bundles L over X such that L⊗r is trivial. This group Γ acts on [Formula: see text] by the rule (E, L) ↦ E ⊗ L. We compute the Chen–Ruan cohomology of the corresponding orbifold.

scholarly journals Irreducible Unitary Representations Concerning Homogeneous Holomorphic Line Bundles Over Elliptic Orbits

2018 ◽  
Vol 10 (4) ◽  
pp. 62
Author(s):  
Nobutaka Boumuki ◽  
Tomonori Noda
Keyword(s):  
Line Bundle ◽  
Cross Sections ◽  
Lie Group ◽  
Vector Subspace ◽  
Line Bundles ◽  
Semisimple Lie Group ◽  
Complex Vector ◽  
Elliptic Orbits ◽  
Irreducible Unitary Representations ◽  
Holomorphic Line Bundles

In this paper we consider a homogeneous holomorphic line bundle over an elliptic adjoint orbit of a real semisimple Lie group, and set a continuous representation of the Lie group on a certain complex vector subspace of the complex vector space of holomorphic cross-sections of the line bundle. Then, we demonstrate that the representation is irreducible unitary.

Additive Riemann–Hilbert Problem in Line Bundles Over ℂℙ1

2006 ◽  
Vol 49 (1) ◽  
pp. 72-81 ◽  
Author(s):  
Roman J. Dwilewicz
Keyword(s):  
Line Bundle ◽  
Projective Space ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Hilbert Problem ◽  
Holomorphic Functions ◽  
Riemann Function ◽  
Line Bundles ◽  
Complex Projective ◽  
Riemann Hilbert Problem

AbstractIn this note we consider -problem in line bundles over complex projective space ℂℙ1 and prove that the equation can be solved for (0, 1) forms with compact support. As a consequence, any Cauchy-Riemann function on a compact real hypersurface in such line bundles is a jump of two holomorphic functions defined on the sides of the hypersurface. In particular, the results can be applied to ℂℙ2 since by removing a point from it we get a line bundle over ℂℙ1.

Morphological Changes in the Rat Granulosa Cell Surface During Differentiation Induced by Estradiol and Gonadotropins

1977 ◽  
Vol 35 ◽  
pp. 484-485
Author(s):  
P. Bagavandoss ◽  
JoAnne S. Richards ◽  
A. Rees Midgley
Keyword(s):  
Cell Surface ◽  
Granulosa Cell ◽  
Morphological Changes ◽  
Follicular Development ◽  
Female Rats ◽  
Functional Changes ◽  
Group 4 ◽  
Group 3 ◽  
Group 5 ◽  
Group 2

During follicular development in the mammalian ovary, several functional changes occur in the granulosa cells in response to steroid hormones and gonadotropins (1,2). In particular, marked changes in the content of membrane-associated receptors for the gonadotropins have been observed (1).We report here scanning electron microscope observations of morphological changes that occur on the granulosa cell surface in response to the administration of estradiol, human follicle stimulating hormone (hFSH), and human chorionic gonadotropin (hCG).Immature female rats that were hypophysectcmized on day 24 of age were treated in the following manner. Group 1: control groups were injected once a day with 0.1 ml phosphate buffered saline (PBS) for 3 days; group 2: estradiol (1.5 mg/0.2 ml propylene glycol) once a day for 3 days; group 3: estradiol for 3 days followed by 2 days of hFSH (1 μg/0.1 ml) twice daily, group 4: same as in group 3; group 5: same as in group 3 with a final injection of hCG (5 IU/0.1 ml) on the fifth day.

Ultrastructural Immunocytochemistry of Five Rat Pituitary Adenomas

1980 ◽  
Vol 38 ◽  
pp. 724-725
Author(s):  
D. J. McComb ◽  
N. Ryan ◽  
E. Horvath ◽  
K. Kovacs ◽  
E. Nagy ◽  
...  
Keyword(s):  
Pituitary Adenomas ◽  
Pituitary Tumors ◽  
Electron Microscopic ◽  
Electron Microscopic Immunocytochemistry ◽  
Transmission Electron ◽  
Rat Pituitary ◽  
Radiation Induced ◽  
Group 5 ◽  
Group 2 ◽  
Microscopic Techniques

Conventional light and electron microscopic techniques failed to clarify the cellular composition and derivation of spontaneous and induced, intrasellar and transplanted pituitary adenomas in rats (1). In the present work, electron microscopic immunocytochemistry was applied to evaluate five adenohypo-physial tumors using a technique described by Moriarty and Garner (2). Spontaneously occurring pituitary adenomas (group 1) were harvested from aging female Long-Evans rats. R-Amsterdam rats were treated with 2 x 1.0 mg estrone acetate (HogivaI) s.c. weekly for 6 months. Pituitary adenomas in excess of 30 mg were removed from these animals to make up the tumors of group 2. Groups 3 and 4 consisted of estrogen-induced autonomous transplan¬ted pituitary tumors MtT.WlO and MtT.F4. Group 5 was a radiation-induced transplanted autonomous pituitary tumor MtT.W5. The tumors of groups 3,4 and 5 were allowed to proliferate in host rats 6-8 weeks prior to removal for processing. Tissue was processed for transmission electron microscopy (glutaraldehyde fixation, OsO4 postfixation and epoxy resin embedding), and electron microscopic immunocytochemistry (3% paraformaldehyde fixation and Araldite embedding).

Liver, Kidney Function Tests and Oxidative Damage During and after Treatment of Salmonella typhimurium Infection in Experimental Local Rabbits

2018 ◽  
Vol 9 (4) ◽  
Author(s):  
Mustafa Salah Hasan ◽  
Ayman Barzan Abdulgafor ◽  
Maher Saber Owain ◽  
Mohammed Ali Hussein ◽  
Qusay Mohammed Aboud ◽  
...  
Keyword(s):  
Single Dose ◽  
Oxidative Damage ◽  
Salmonella Typhimurium ◽  
Infected Group ◽  
Post Treatment ◽  
Kidney Damage ◽  
Control Group ◽  
Post Inoculation ◽  
Group 5 ◽  
Group 2

This study aimed to evaluate the liver, kidney damage caused by S. typhimurium and to estimate the oxidative damage in association with this bacteria. A highly virulent isolates of S. typhimurium were obtained from the department of internal and preventive medicine/ College of Veterinary Medicine/ University of Baghdad. A twenty five local rabbits of both genders with age range (2-4 months) weeks old were used for this study, the rabbits were divided randomly into five groups each group contains 5 rabbits :- group 1: drenched orally with 5 ml of normal saline and consider as control group, group 2: were drenched orally with (5 ml) suspension which contain (5��109 CFU) of Salmonella typhimurium and regarded as infected group, group 3 were drenched orally with (5 ml) suspension which have (5��109 CFU) of Salmonella typhimurium then treated with a single dose of gentamicin alone at 0.05ml/kg (5mg/ml) orally after presence of signs (after 24hrs. post inoculation), group 4 were drenched (5 ml) suspension having (5��109 CFU) of Salmonella typhimurium then treated with a single dose of Ca-EDTA alone at 40mg/kg orally after presence of signs (after 24hrs. post inoculation) and group 5 were drenched (5 ml) suspension that contain (5��109 CFU) of Salmonella typhimurium then treated with a single dose of combined gentamicin at 0.05ml/kg (5mg/ml) orally after presence of signs (after 24hrs. post inoculation) and Ca-EDTA 40mg/kg after presence of signs (after 24hrs. post inoculation).The results of biochemical profile showed a significant increase (p less than 0.05) in ALT, creatinine and urea levels in infected group as compared with control group, while, the treated groups especially group 5 showed a significant improvement in ALT, Urea and creatinine levels which returned to relative normal levels as compared with infected group after 96hrs. post treatment. Also, the results of oxidative stress showed a significant increase in the levels of MDA in G2, G3, G4 and G5 after 48 hrs. post treatment, while the level of GSH showed a significant decrease in the level at 48hrs., both were returned to relative normal levels after 96hrs.post treatment especially in group 5.In conclusion, S. typhimurium can causing liver and kidney damage which is manifested by increase ALT, Urea and Creatinine. Also, MDA and GSH is increased due to salmonellosis.

Does Perioperative Hemoglobin A1c Level Affect the Incidence, Pattern and Mortality of Lower Extremity Amputation?

2019 ◽  
Vol 17 (4) ◽  
pp. 354-364
Author(s):  
Hassan Al-Thani ◽  
Moamena El-Matbouly ◽  
Maryam Al-Sulaiti ◽  
Noora Al-Thani ◽  
Mohammad Asim ◽  
...  
Keyword(s):  
Glycemic Control ◽  
Lower Extremity ◽  
Hazard Ratio ◽  
Lower Extremity Amputation ◽  
Group 4 ◽  
Group 3 ◽  
Group 5 ◽  
Group 2 ◽  
Extremity Amputation ◽  
Group 1

Background: We hypothesized that perioperative HbA1c influenced the pattern and outcomes of Lower Extremity Amputation (LEA). Methods: A retrospective analysis was conducted for all patients who underwent LEA between 2000 and 2013. Patients were categorized into 5 groups according to their perioperative HbA1c values [Group 1 (<6.5%), Group 2 (6.5-7.4%), Group 3 (7.5-8.4%), Group 4 (8.5-9.4%) and Group 5 (≥9.5%)]. We identified 848 patients with LEA; perioperative HbA1c levels were available in 547 cases (Group 1: 18.8%, Group 2: 17.7%, Group 3: 15.0%, Group 4: 13.5% and Group 5: 34.9%). Major amputation was performed in 35%, 32%, 22%, 10.8% and 13.6%, respectively. Results: The overall mortality was 36.5%; of that one quarter occurred during the index hospitalization. Mortality was higher in Group 1 (57.4%) compared with Groups 2-5 (46.9%, 38.3%, 36.1% and 31.2%, respectively, p=0.001). Cox regression analysis showed that poor glycemic control (Group 4 and 5) had lower risk of mortality post-LEA [hazard ratio 0.57 (95% CI 0.35-0.93) and hazard ratio 0.46 (95% CI 0.31-0.69)]; this mortality risk persisted even after adjustment for age and sex but was statistically insignificant. The rate of LEA was greater among poor glycemic control patients; however, the mortality was higher among patients with tight control. Conclusion: The effects of HbA1c on the immediate and long-term LEA outcomes and its therapeutic implications need further investigation.

scholarly journals Association between serum oestradiol level on the hCG administration day and neonatal birthweight after IVF-ET among 3659 singleton live births

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yu Liu ◽  
Jing Li ◽  
Wanyu Zhang ◽  
Yihong Guo
Keyword(s):  
Birth Weight ◽  
Ovarian Stimulation ◽  
Group 4 ◽  
Group 6 ◽  
Group 3 ◽  
Group 5 ◽  
Group 2 ◽  
The Impact ◽  
Ivf Et ◽  
Group 1

AbstractOestradiol, an important hormone in follicular development and endometrial receptivity, is closely related to clinical outcomes of fresh in vitro fertilization-embryo transfer (IVF-ET) cycles. A supraphysiologic E2 level is inevitable during controlled ovarian hyper-stimulation (COH), and its effect on the outcome of IVF-ET is controversial. The aim of this retrospective study is to evaluate the association between elevated serum oestradiol (E2) levels on the day of human chorionic gonadotrophin (hCG) administration and neonatal birthweight after IVF-ET cycles. The data of 3659 infertile patients with fresh IVF-ET cycles were analysed retrospectively between August 2009 and February 2017 in First Hospital of Zhengzhou University. Patients were categorized by serum E2 levels on the day of hCG administration into six groups: group 1 (serum E2 levels ≤ 1000 pg/mL, n = 230), group 2 (serum E2 levels between 1001 and 2000 pg/mL, n = 524), group 3 (serum E2 levels between 2001 and 3000 pg/mL, n = 783), group 4 (serum E2 levels between 3001 and 4000 pg/mL, n = 721), group 5 (serum E2 levels between 4001 and 5000 pg/mL, n = 548 ), and group 6 (serum E2 levels > 5000 pg/mL, n = 852). Univariate linear regression was used to evaluate the independent correlation between each factor and outcome index. Multiple logistic regression was used to adjust for confounding factors. The LBW rates were as follows: 3.0% (group 1), 2.9% (group 2), 1.9% (group 3), 2.9% (group 4), 2.9% (group 5), and 2.0% (group 6) (P = 0.629), respectively. There were no statistically significant differences in the incidences of neonatal LBW among the six groups. We did not detect an association between peak serum E2 level during ovarian stimulation and neonatal birthweight after IVF-ET. The results of this retrospective cohort study showed that serum E2 peak levels during ovarian stimulation were not associated with birth weight during IVF cycles. In addition, no association was found between higher E2 levels and increased LBW risk. Our observations suggest that the hyper-oestrogenic milieu during COS does not seem to have adverse effects on the birthweight of offspring after IVF. Although this study provides some reference, the obstetric-related factors were not included due to historical reasons. The impact of the high estrogen environment during COS on the birth weight of IVF offspring still needs future research.

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