Thomas Bauer

The influence of hormone replacement therapy (HRT) on serum leptin concentration in postmenopausal women

OBJECTIVE This study aimed to evaluate the influence of hormone replacement therapy (HRT), the estradiol concentration and body mass index (BMI, kg/m(2)) on the serum leptin concentration in postmenopausal women. SUBJECTS AND METHODS 352 healthy postmenopausal women (mean age, 60.9 +/- 8.5 years) participated in this comparative study. 71 (30%) women (mean age 55.9 +/- 8.3 years) had taken HRT, while 281 (70%) women (mean age, 59.1 +/- 10.6 years) had not. Baseline characteristics -age, weight, height, BMI (greater than or = 25 or <25), follicle stimulating hormone, estradiol, and leptin values-were compared in the two groups. In a second analysis to evaluate the influence of HRT, estradiol concentrations, and BMI on leptin concentrations, these data were analysed in women allocated to one of four groups: (a) postmenopausal women not on HRT with a BMI <25 (n = 130); (b) postmenopausal women not on HRT with a BMI greater than or = 25 (n = 151); (c) postmenopausal women on HRT with a BMI<25 (n = 48); and (d) postmenopausal women on HRT with a BMI greater than or = 25 (n = 23). Leptin concentrations were subsequently analysed in relation to BMI and age and BMI and estradiol concentrations to determine any independent effect of these variables. RESULTS The women taking HRT had a significantly lower mean age, weight, BMI and follicle stimulating hormone concentration than those who were not taking HRT. Furthermore, they had a higher mean height and serum estradiol value, but a significantly lower serum leptin concentration. After controlling for BMI, neither the use of HRT nor the estradiol concentration was found to be related to the leptin value (group (a) versus (c) and group (b) versus (d)), but there were significant differences in leptin concentrations between HRT users with BMI greater than or = 25 and BMI <25 and between women not taking HRT with BMI greater than or = 25 and BMI <25 (groups (a) versus (b) and (c) versus (d)). Furthermore, women with a BMI greater than or = 25 had significantly higher leptin concentrations than women with a BMI<25, irrespective of the HRT use. CONCLUSIONS Leptin concentrations are significantly higher in obese postmenopausal women than in their non-obese counterparts. Serum leptin concentrations are not influenced by HRT use or estradiol concentrations. Further studies are needed to elucidate the role of HRT and estrogen on serum leptin concentrations.

Negative curves on algebraic surfaces

We study curves of negative self-intersection on algebraic surfaces. Our main result shows there exist smooth complex projective surfaces X, related to Hilbert modular surfaces, such that X contains reduced, irreducible curves C of arbitrarily negative self-intersection C 2 . Previously the only known examples of surfaces for which C 2 was not bounded below were in positive characteristic, and the general expectation was that no examples could arise over the complex numbers. Indeed, we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field, and thus our complex examples require a different approach.

Higher order embeddings of abelian varieties

The strongest notion is k-jet ampleness; it implies k-very ampleness (cf. [BeSo2, Proposition 2.2]) which of course implies k-spannedness. For k = 0 or k = 1 all the three notions are equivalent and correspond to global generation resp. very ampleness. In this note we give criteria for k-jet ampleness of line bundles on abelian varieties. A naive way to obtain such a criterion is as follows: According to [BeSo2, Corollary 2.1] a tensor product of k very ample line bundles is always k-jet ample. Now on an abelian variety, by the generalization of Lefschetz’ classical theorem [LB,

The Effect of Age, Sex Hormones, and Bone Turnover Markers on Calcaneal Quantitative Ultrasonometry in Healthy German Men

The aim of this cross-sectional study was to determine the age-dependent variations of calcaneal quantitative ultrasonometry (QUS) and the association with sex hormones and biochemical bone turnover markers in a large sample of unselected healthy German men. Bone measurements are expected to behave differently among men and women. The speed of sound (SOS), broadband ultrasound attenuation (BUA), and stiffness index (SI) of the os calcaneus were measured in 506 German men aged 20-79 yr (mean age: 45.7 yr). Additionally, follicle-stimulating hormone (FSH), luteinizing hormone (LH), estradiol, prolactin, testosterone, dehydroepiandrosterone sulfate (DHEA-S), sex hormone-binding globulin (SHBG) as well as N-terminal propeptide of human procollagen type I (PINP), C-terminal telopeptide of type I collagen (ICTP), osteocalcin, bone-specific alkaline phosphatase, and CrossLaps were measured with standardized essays and correlated with the QUS results. The QUS results comprised an overall change of 12.4%, 3.2%, and 23.2% for BUA, SOS, and SI, respectively, between the 20-29 and 70-79 yr age groups (p ≤ 0.001). The annual rate of the age-related differences was 0.33% (standard deviation [SD]: 0.31), 0.06% (SD: 0.08), and 0.53% (SD: 0.56) for BUA, SOS, and SI, respectively. Testosterone and DHEA-S were significantly associated with QUS parameters and increasing age, whereas SHBG showed an age-related increase and was inversely related with QUS values (p < 0.05). Bone turnover markers present lower values gradually, and we found a significant correlation between carboxy-terminal collagen crosslinks (CTX), osteocalcin (OC), bone alkaline phosphatase (BAP), and QUS variables (p < 0.05).

A SIMPLE PROOF FOR THE EXISTENCE OF ZARISKI DECOMPOSITIONS ON SURFACES

The decomposition D = P + N is called the Zariski decomposition of D, the divisors P and N are respectively the positive and negative parts of D. Zariski’s result has been used to study linear series on surfaces, and in the classification of surfaces (see [1, Chapt. 14] and [4, Sect. 2.3.E], as well as the references therein). We also mention that there is an extension to pseudo-effective divisors due to Fujita (see [2] and the nice account in [1]). Given an effective divisor D, Zariski’s original proof employs a rather sophisticated procedure to construct the negative part N out of those components C of D satisfying D ·C 6 0. Our purpose here is to provide a quick and simple proof, based on the idea that the positive part P can be constructed as a maximal nef subdivisor of D. This maximality condition is in the surface case equivalent to the defining condition of Nakayama’s ν-decomposition of pseudo-effective R-divisors (see the Remark below). It may be useful that this approach yields a practical algorithm for the computation of P .

Recent developments and open problems in linear series

In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of interesting problems which motivated the participants prior to the event, and examples, results and further problems which grew out of discussions during and shortly after the workshop. A lot of arguments presented here are scattered in the literature or constitute folklore. It was one of our aims to have a usable and easily accessible collection of examples and results.

Weyl and Zariski chambers on K3 surfaces

Abstract. The big cone of every K3 surface admits two natural chamber decompositions: the decomposition into Zariski chambers, and the decomposition into simple Weyl chambers. In the present paper we compare these two decompositions and we study their mutual relationship: First, we give a numerical criterion for the two decompositions to coincide. Secondly, we study the mutual inclusions of Zariski and simple Weyl chambers. Finally, we establish the fact that – even though the decompositions themselves may differ – the number of Zariski chambers always equals the number of simple Weyl chambers.

Schnittstellen bearbeiten in Schnittstellenaufgaben

Es besteht in der aktuellen Diskussion zur doppelten Diskontinuitat weitgehend Einigkeit daruber, dass sich bei vielen Studierenden die Bezuge zwischen Schulmathematik und universitarer Mathematik nicht von ganz alleine einstellen, sondern dass hierfur gezielte Schnittstellenaktivitaten erforderlich sind. Der Autor verfolgt solche Aktivitaten seit einigen Jahren im Rahmen von speziellen Ubungsaufgaben, die innerhalb eines als Schnittstellenmodul konzipierten Analysis-Moduls fur Studierende des gymnasialen Lehramts eingesetzt werden. Absicht des vorliegenden Texts ist es, aufzuzeigen, welche Ziele mit solchen Schnittstellenaufgaben verfolgt werden konnen und dies anhand von zwei Beispielaufgaben zu konkretisieren.

Zariski chambers on surfaces of high Picard number

We present an improved algorithm for the computation of Zariski chambers on algebraic surfaces. The new algorithm significantly outperforms the currently available method and therefore allows us to treat surfaces of high Picard number, where huge numbers of chambers occur. As an application, we efficiently compute the number of chambers supported by the lines on the Segre–Schur quartic.

Zariski Decomposition: A New (Old) Chapter of Linear Algebra

Abstract In a 1962 paper, Zariski introduced the decomposition theory that now bears his name. Although it arose in the context of algebraic geometry and deals with the configuration of curves on an algebraic surface, we have recently observed that the essential concept is purely within the realm of linear algebra. In this paper, we formulate Zariski decomposition as a theorem in linear algebra and present a linear algebraic proof. We also sketch the geometric context in which Zariski first introduced his decomposition.