On Kropina Change of m-th Root Finsler Metrics

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.Comment: accepted in Ukrainian Mathematical Journal Volume 66, number 1, 201

On Kropina change for m-th root Finsler metrics

We study the Kropina change for m-th root Finsler metrics and establish necessary and sufficient condition under which the Kropina change of an m-th root Finsler metric is locally dually flat. Then we prove that the Kropina change of an m-th root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.Розглянуто замшу Кропіної для m-кореневих фінслерових метрик. Встановлено необхідні та достатні умови того, що заміна Кропіної для m-кореневої метрики Фінслера є локально дуально плоскою. Також доведено, що заміна Кропіної для m-кореневої метрики Фінслера є локально проективно плоскою тоді i тільки тоді, коли вона є локально мінковською

Deletion of Fibroblast Growth Factor Receptor 2 from the Peri-Wolffian Duct Stroma Leads to Ureteric Induction Abnormalities and Vesicoureteral Reflux

Purpose: Pax3cre-mediated deletion of fibroblast growth factor receptor 2 (Fgfr2) broadly in renal and urinary tract mesenchyme led to ureteric bud (UB) induction defects and vesicoureteral reflux (VUR), although the mechanisms were unclear. Here, we investigated whether Fgfr2 acts specifically in peri-Wolffian duct stroma (ST) to regulate UB induction and development of VUR and the mechanisms of Fgfr2 activity. Methods: We conditionally deleted Fgfr2 in ST (Fgfr2 ST-/- ) using Tbx18cre mice. To look for ureteric bud induction defects in young embryos, we assessed length and apoptosis of common nephric ducts (CNDs). We performed 3D reconstructions and histological analyses of urinary tracts of embryos and postnatal mice and cystograms in postnatal mice to test for VUR. We performed in situ hybridization and real-time PCR in young embryos to determine mechanisms underlying UB induction defects. Results: We confirmed that Fgfr2 is expressed in ST and that Fgfr2 was efficiently deleted in this tissue in Fgfr2 ST-/- mice at embryonic day (E) 10.5. E11.5 Fgfr2 ST-/- mice had randomized UB induction sites with approximately 1/3 arising too high and 1/3 too low from the Wolffian duct; however, apoptosis was unaltered in E12.5 mutant CNDs. While ureters were histologically normal, E15.5 Fgfr2 ST-/- mice exhibit improper ureteral insertion sites into the bladder, consistent with the ureteric induction defects. While ureter and bladder histology appeared normal, postnatal day (P) 1 mutants had high rates of VUR versus controls (75% versus 3%, p = 0.001) and occasionally other defects including renal hypoplasia and duplex systems. P1 mutant mice also had improper ureteral bladder insertion sites and shortened intravesicular tunnel lengths that correlated with VUR. E10.5 Fgfr2 ST-/- mice had decreases in Bmp4 mRNA in stromal tissues, suggesting a mechanism underlying the ureteric induction and VUR phenotypes. Conclusion: Mutations in FGFR2 could possibly cause VUR in humans. © 2013 Walker et al

Matsumoto metrics of reversible curvature

In this paper, we study the reversibility of Riemann curvature and Ricci curvature for the Matsumoto metric and prove three global results. First, we prove that a Matsumoto metric is R-reversible if and only if it is R-quadratic. Then we show that a Matsumoto metric is Ricci-reversible if and only if it is Ricci-quadratic. Finally, we prove that every weakly Einstein Matsumoto metric is Ricci-reversible

Systemic reactogenicity following homologues and heterologous prime-boost AZD1222 and BNT162b2 COVID-19 vaccination of 2862 healthcare workers compared with an unvaccinated population

During spring 2021, AZD1222 and BNT162b2 were used as prime and BNT162b2 as booster COVID-19 vaccines in Denmark. We obtained self-reported information on systemic reactogenicity day-by-day during two weeks for 2862 healthcare workers vaccinated with heterologous AZD1222 + BNT162b2 or homologous BNT162b2 + BNT162b2 regimens and compared prevalences of symptoms with unvaccinated healthcare workers. We found comparable systemic reactogenicity during the first week in the two vaccine regimens and no reactogenicity during the second week. Most of the symptoms returned to a level equal to the control population four days after booster vaccination