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CHARACTERIZING ALMOST PERFECT RINGS BY COVERS AND ENVELOPES
Fuchs, Laszlo Korean Mathematical Society 2020 대한수학회지 Vol.57 No.1
Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫<sub>1</sub>, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.
Characterizing almost perfect rings by covers and envelopes
Laszlo Fuchs 대한수학회 2020 대한수학회지 Vol.57 No.1
Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni--Salce \cite{BS1} and Bazzoni \cite{B}, are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs--Salce \cite{FS}, showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem \ref{Ce}). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair $(\PP_1, \DD)$ (Theorem \ref{Fd}). Similar characterization is proved concerning the existence of divisible envelopes for $h$-local rings in the same class (Theorem \ref{Le}). In addition, Bazzoni's characterization {\it via} direct sums of weak-injective modules \cite{B} is extended to all commutative rings (Theorem \ref{De}). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.
Fuchs, Charles S.,Muro, Kei,Tomasek, Jiri,Van Cutsem, Eric,Cho, Jae Yong,Oh, Sang-Cheul,Safran, Howard,Bodoky, Gyorgy,Chau, Ian,Shimada, Yasuhiro,Al-Batran, Salah-Eddin,Passalacqua, Rodolfo,Ohtsu, Ats The Korean Gastric Cancer Association 2017 Journal of gastric cancer Vol.17 No.2
Purpose: To identify baseline prognostic factors for survival in patients with disease progression, during or after chemotherapy for the treatment of advanced gastric or gastroesophageal junction (GEJ) cancer. Materials and Methods: We pooled data from patients randomized between 2009 and 2012 in 2 phase III, global double-blind studies of ramucirumab for the treatment of advanced gastric or GEJ adenocarcinoma following disease progression on first-line platinum- and/or fluoropyrimidine-containing therapy (REGARD and RAINBOW). Forty-one key baseline clinical and laboratory factors common in both studies were examined. Model building started with covariate screening using univariate Cox models (significance level=0.05). A stepwise multivariable Cox model identified the final prognostic factors (entry+exit significance level=0.01). Cox models were stratified by treatment and geographic region. The process was repeated to identify baseline prognostic quality of life (QoL) parameters. Results: Of 1,020 randomized patients, 953 (93%) patients without any missing covariates were included in the analysis. We identified 12 independent prognostic factors of poor survival: 1) peritoneal metastases; 2) Eastern Cooperative Oncology Group (ECOG) performance score 1; 3) the presence of a primary tumor; 4) time to progression since prior therapy <6 months; 5) poor/unknown tumor differentiation; abnormally low blood levels of 6) albumin, 7) sodium, and/or 8) lymphocytes; and abnormally high blood levels of 9) neutrophils, 10) aspartate aminotransferase (AST), 11) alkaline phosphatase (ALP), and/or 12) lactate dehydrogenase (LDH). Factors were used to devise a 4-tier prognostic index (median overall survival [OS] by risk [months]: high=3.4, moderate=6.4, medium=9.9, and low=14.5; Harrell's C-index=0.66; 95% confidence interval [CI], 0.64-0.68). Addition of QoL to the model identified patient-reported appetite loss as an independent prognostic factor. Conclusions: The identified prognostic factors and the reported prognostic index may help clinical decision-making, patient stratification, and planning of future clinical studies.
Fuchs, Frederik,Habl, Gregor,Devecka, Michal,Kampfer, Severin,Combs, Stephanie E.,Kessel, Kerstin A. The Korean Society for Radiation Oncology 2019 Radiation Oncology Journal Vol.37 No.2
Purpose: The aim of this study was to identify volume changes and dose variations of rectum and bladder during radiation therapy in prostate cancer (PC) patients. Materials and Methods: We analyzed 20 patients with PC treated with helical tomotherapy. Daily image guidance was performed. We re-contoured the entire bladder and rectum including its contents as well as the organ walls on megavoltage computed tomography once a week. Dose variations were analyzed by means of Dmedian, Dmean, Dmax, V<sub>10</sub> to V<sub>75</sub>, as well as the organs at risk (OAR) volume. Further, we investigated the correlation between volume changes and changes in Dmean of OAR. Results: During treatment, the rectal volume ranged from 62% to 223% of its initial volume, the bladder volume from 22% to 375%. The average Dmean ranged from 87% to 118% for the rectum and 58% to 160% for the bladder. The Pearson correlation coefficients between volume changes and corresponding changes in Dmean were -0.82 for the bladder and 0.52 for the rectum. The comparison of the dose wall histogram (DWH) and the dose volume histogram (DVH) showed that the DVH underestimates the percentage of the rectal and bladder volume exposed to the high dose region. Conclusion: Relevant variations in the volume of OAR and corresponding dose variations can be observed. For the bladder, an increase in the volume generally leads to lower doses; for the rectum, the correlation is weaker. Having demonstrated remarkable differences in the dose distribution of the DWH and the DVH, the use of DWHs should be considered.
Fuchs, Hendrik,Tan, Zhaofeng,Lu, Keding,Bohn, Birger,Broch, Sebastian,Brown, Steven S.,Dong, Huabin,Gomm, Sebastian,Hä,seler, Rolf,He, Lingyan,Hofzumahaus, Andreas,Holland, Frank,Li, Xin,Liu, Ying Copernicus GmbH 2017 Atmospheric chemistry and physics Vol.17 No.1
<P>Abstract. In 2014, a large, comprehensive field campaign was conducted in the densely populated North China Plain. The measurement site was located in a botanic garden close to the small town Wangdu, without major industry but influenced by regional transportation of air pollution. The loss rate coefficient of atmospheric hydroxyl radicals (OH) was quantified by direct measurements of the OH reactivity. Values ranged between 10 and 20 s−1 for most of the daytime. Highest values were reached in the late night with maximum values of around 40 s−1. OH reactants mainly originated from anthropogenic activities as indicated (1) by a good correlation between measured OH reactivity and carbon monoxide (linear correlation coefficient R2 = 0.33) and (2) by a high contribution of nitrogen oxide species to the OH reactivity (up to 30 % in the morning). Total OH reactivity was measured by a laser flash photolysis-laser-induced fluorescence instrument (LP-LIF). Measured values can be explained well by measured trace gas concentrations including organic compounds, oxygenated organic compounds, CO and nitrogen oxides. Significant, unexplained OH reactivity was only observed during nights, when biomass burning of agricultural waste occurred on surrounding fields. OH reactivity measurements also allow investigating the chemical OH budget. During this campaign, the OH destruction rate calculated from measured OH reactivity and measured OH concentration was balanced by the sum of OH production from ozone and nitrous acid photolysis and OH regeneration from hydroperoxy radicals within the uncertainty of measurements. However, a tendency for higher OH destruction compared to OH production at lower concentrations of nitric oxide is also observed, consistent with previous findings in field campaigns in China. </P>