The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in Cn\mathbb{C}^{n}

We prove that the multiplier algebra of the Drury-Arveson Hardy space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal space, thus generalizing the famous Corona Theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach space result: the Besov-Sobolev space $B_{p}^{\sigma}$ has the "baby corona property" for all $\sigma \geq 0$ and $1<p<\infty$. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.Comment: v1: 70 pgs; v2: 73 pgs.; introduction expanded, clarified. v3: 73 pgs.; restriction in main result removed (see 9.2), arguments expanded (see 8.1.1). v4: 74 pgs.; systematic arithmetic misprints fixed on pgs. 37-48. v5: 76 pgs.; incorrect embedding corrected via Proposition 4. v6: 80 pgs.; main result extended to vector-valued setting. v7: 82 pgs.; typos removed

Estimation of Cutoff Values of Cotinine in Urine and Saliva for Pregnant Women in Poland

Setting appropriate cutoff values and the use of a highly sensitive analytical method allow for correct classification of the smoking status. Urine-saliva pairs samples of pregnant women in the second and third trimester, and saliva only in the first trimester were collected. Offline SPE and LC-ESI-MS/MS method was developed in the broad concentration range (saliva 0.4–1000 ng/mL, urine 0.8–4000 ng/mL). The mean recoveries were 3.7±7.6% for urine and 99.1±2.6% for saliva. LOD for saliva was 0.12 ng/mL and for urine 0.05 ng/mL; LOQ was 0.4 ng/mL and 0.8 ng/mL, respectively. Intraday and interday precision equaled, respectively, 1.2% and 3.4% for urine, and 2.3% and 6.4% for saliva. There was a strong correlation between salivary cotinine and the uncorrected cotinine concentration in urine in the second and third trimesters of pregnancy. The cutoff values were established for saliva 12.9 ng/mL and urine 42.3 ng/mL or 53.1 μg/g creatinine with the ROC curve analysis. The developed analytical method was successfully applied to quantify cotinine, and a significant correlation between the urinary and salivary cotinine levels was found. The presented cut-off values for salivary and urinary cotinine ensure a categorization of the smoking status among pregnant women that is more accurate than self-reporting

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Bioethical committees and data protection issues in Poland

In Poland there are only Regional Bioethical Committees. Unlike most EU countries Poland has no coordinating centre on bioethics for human research. However, the Ministry of Health and Welfare has established a Bioethics Appeals Committee

Estimation of Saliva Cotinine Cut-Off Points for Active and Passive Smoking during Pregnancy-Polish Mother and Child Cohort (REPRO_PL)

A reliable assessment of smoking status has significant public health implications and is essential for research purposes. The aim of this study was to determine optimal saliva cotinine cut-off values for smoking during pregnancy. The analyses were based on data from 1771 women from the Polish Mother and Child Cohort. Saliva cotinine concentrations were assessed by high performance liquid chromatography coupled with tandem mass spectrometry (HPLC-ESI + MS/MS). The saliva cotinine cut-off value for active smoking was established at 10 ng/mL (sensitivity 96%, specificity 95%) and for passive smoking at 1.5 ng/mL (sensitivity 63%, specificity 71%). About 5% of the self-reported non-smoking women were classified as smokers based on the cotinine cut-off value. Significantly more younger, single, and less educated self-reported non-smokers had a cotinine concentration higher than 10 ng/mL compared to those who were older, married, and who had a university degree. Close to 30% of the non-smokers who indicated that smoking was not allowed in their home could be classified as exposed to passive smoking based on the cut-off value. The study suggests that self-reported smoking status is a valid measure of active smoking, whereas in the case of passive smoking, a combination of questionnaire data and biomarker verification may be required

Lost and Found, or about Henryk Gotlib’s "Polish War-Time Triptych" and its Changing Fate

English verion. Original issue: “Archiwum Emigracji” 2015, no. 1–2 (22–23)https://apcz.umk.pl/AE/article/view/AE.2015.01

An explicit formula for the Berezin star product

We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.Comment: 19 pages, to appear in Lett. Math. Phy

The relationship between macroeconomic variables and stock market indices: evidence from Central and Eastern European countries

The aim of the study was to investigate the relationship between selected macroeconomic variables and the values of representative stock market indices for Central and Eastern European countries in the period Q1 2004 - Q4 2021. The results, based on the Johansen cointegration test, revealed that the selected macroeconomic variables have an impact on the value of stock market indices on the long term. These results are attributed to the importance of the state of the macroeconomic environment for stable business activity. The reason for this is that macroeconomic stability provides better grounds for predicting the development of the market situation and fiscal and monetary policy. The application of VECM estimations and the Granger causality test indicate that the selected macroeconomic variables affect the values of European stock market indices on the long term rather than on the short term. These findings may reflect the expectations of subjects and/or the consequences of policy measures, whose the impacts can only be estimated and may manifest with a significant delay

Zgubiony–znaleziony czyli o „Polskim tryptyku wojennym” Henryka Gotliba i jego zmiennych losach

LOST—FOUND: ON THE VICISSITUDES OF HENRYK GOTLIB’S POLISH WAR TRIPTYCH The article discusses the interesting and complicated history of the Polish War Triptych, that is the three monumental paintings (Warszawa, wrzesień 1939; Powrót Mickiewicza do Krakowa and Stabat Mater) created by Henryk Gotlib during the Second World War in London. The works were transferred to Poland in 1948 in order to celebrate the establishment of the Polish United Workers’ Party, however, for political reasons they were considered lost. The paintings were rediscovered and first exhibited in Poland only in 1966, two months before Gotlib’s death. The paintings are exceptional not only because they offer a unique perspective on the subject but also because they include portraits of the most eminent Polish immigrants in London, e.g. of Marek Żuławski and Feliks Topolski

Fish consumption patterns and hair mercury levels in children and their mothers in 17 EU countries

The toxicity of methylmercury (MeHg) in humans is well established and the main source of exposure is via the consumption of large marine fish and mammals. Of particular concern are the potential neurodevelopmental effects of early life exposure to low-levels of MeHg. Therefore, it is important that pregnant women, children and women of childbearing age are, as far as possible, protected from MeHg exposure.Within the European project DEMOCOPHES, we have analyzed mercury (Hg) in hair in 1799 mother–child pairs from 17 European countries using a strictly harmonized protocol for mercury analysis. Parallel, harmonized questionnaires on dietary habits provided information on consumption patterns of fish and marine products. After hierarchical cluster analysis of consumption habits of the mother–child pairs, the DEMOCOPHES cohort can be classified into two branches of approximately similar size: one with high fish consumption (H) and another with low consumption (L). All countries have representatives in both branches, but Belgium, Denmark, Spain, Portugal and Sweden have twice as many or more mother–child pairs in H than in L. For Switzerland, Czech Republic, Hungary, Poland, Romania, Slovenia and Slovakia the situation is the opposite, with more representatives in L than H.There is a strong correlation (r=0.72) in hair mercury concentration between the mother and child in the same family, which indicates that they have a similar exposure situation. The clustering of mother–child pairs on basis of their fish consumption revealed some interesting patterns. One is that for the same sea fish consumption, other food items of marine origin, like seafood products or shellfish, contribute significantly to the mercury levels in hair. We conclude that additional studies are needed to assess and quantify exposure to mercury from seafood products, in particular. The cluster analysis also showed that 95% of mothers who consume once per week fish only, and no other marine products, have mercury levels 0.55 µg/g. Thus, the 95th percentile of the distribution in this group is only around half the US-EPA recommended threshold of 1 µg/g mercury in hair. Consumption of freshwater fish played a minor role in contributing to mercury exposure in the studied cohort.The DEMOCOPHES data shows that there are significant differences in MeHg exposure across the EU and that exposure is highly correlated with consumption of fish and marine products. Fish and marine products are key components of a healthy human diet and are important both traditionally and culturally in many parts of Europe. Therefore, the communication of the potential risks of mercury exposure needs to be carefully balanced to take into account traditional and cultural values as well as the potential health benefits from fish consumption. European harmonized human biomonitoring programs provide an additional dimension to national HMB programs and can assist national authorities to tailor mitigation and adaptation strategies (dietary advice, risk communication, etc.) to their country’s specific requirements