The projective translation equation and rational plane flows. I

Let X=(x,y). A plane flow is a function F(X,t): R^2*R->R^2 such that F(F(X,s),t)=F(X,s+t) for (almost) all real numbers x,y,s,t (the function F might not be well-defined for certain x,y,t). In this paper we investigate rational plane flows which are of the form F(X,t)=f(Xt)/t; here f is a pair of rational functions in 2 real variables. These may be called projective flows, and for a description of such flows only the knowledge of Cremona group in dimension 1 is needed. Thus, the aim of this work is to completely describe over R all rational solutions of the two dimensional translation equation (1-z)f(X)=f(f(Xz)(1-z)/z). We show that, up to conjugation with a 1-homogenic birational plane transformation (1-BIR), all solutions are as follows: a zero flow, two singular flows, an identity flow, and one non-singular flow for each non-negative integer N, called the level of the flow. The case N=0 stands apart, while the case N=1 has special features as well. Conjugation of these canonical solutions with 1-BIR produce a variety of flows with different properties and invariants, depending on the level and on the conjugation itself. We explore many more features of these flows; for example, there are 1, 4, and 2 essentially different symmetric flows in cases N=0, N=1, and N>=2, respectively. Many more questions will be treated in the second part of this work.Comment: 54 pages, 6 figures. Final version before proof

Health related quality of life in patients with multiple myeloma undergoing a double transplantation

Objectives: To investigate the subjective well-being of patients with newly diagnosed multiple myeloma who were treated in a tandem transplantation programme. Methods: Fifty-one patients participated in the prospective, longitudinal questionnaire study. The EORTC QLQ-C30 and the EuroQol-5D were administered 2 wk after completion of vincristine, adriamycin and dexamethason/vincristine, adriamycin and methyl prednison (VAD/VAMP) chemotherapy, both at hospital discharge after treatment with high-dose melphalan (HDM) and 1 month after this hospital discharge, at hospital admission, at the day of hospital discharge for peripheral stem cell transplantation (PSCT) and at 6 and 12 months following discharge after PSCT. Results: Overall, patients' functioning improved during treatment and follow-up, with significant decreases shortly following PSCT. Shortly after HDM and PSCT, patients reported a considerable increase in levels of soreness in the mouth (+ 26/ + 36 points on a scale ranging form 0 to 100; P < 0.01), change of taste (+ 23/ + 21 points; P < 0.05/ NS), nausea/vomiting (+ 26

Ground-state properties of tubelike flexible polymers

In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects

Synthesis of pseudo-disaccharide analogues of lipid A: haptens for the generation of antibodies with glycosidase activity towards lipid A

Bio-organic Synthesi

Multi-basin depositional framework for moisture-balance reconstruction during the last 1300 years at Lake Bogoria, central Kenya Rift Valley

Multi-proxy analysis of sediment cores from five key locations in hypersaline, alkaline Lake Bogoria (central Kenya Rift Valley) has allowed reconstruction of its history of depositional and hydrological change during the past 1300years. Analyses including organic matter and carbonate content, granulometry, mineralogical composition, charcoal counting and high-resolution scanning of magnetic susceptibility and elemental geochemistry resulted in a detailed sedimentological and compositional characterization of lacustrine deposits in the three lake basins and on the two sills separating them. Thesepalaeolimnological data were supplemented with information on present-day sedimentation conditions based on seasonal sampling of settling particles and on measurement of physicochemical profiles through the water column. A new age model based on Pb-210, Cs-137 and C-14 dating captures the sediment chronology of this hydrochemically complex and geothermally fed lake. An extensive set of chronological tie points between the equivalent high-resolution proxy time series of the five sediment sequences allowed transfer of radiometric dates between the basins, enabling interbasin comparison of sedimentation dynamics through time. The resulting reconstruction demonstrates considerable moisture-balance variability through time, reflecting regional hydroclimate dynamics over the past 1300years. Between ca 690 and 950AD, the central and southern basins of Lake Bogoria were reduced to shallow and separated brine pools. In the former, occasional near-complete desiccation triggered massive trona precipitation. Between ca 950 and 1100AD, slightly higher water levels allowed the build-up of high pCO(2) leading to precipitation of nahcolite still under strongly evaporative conditions. Lake Bogoria experienced a pronounced highstand between ca 1100 and 1350AD, only to recede again afterwards. For a substantial part of the time between ca 1350 and 1800AD, the northern basin was probably disconnected from the united central and southern basins. Throughout the last two centuries, lake level has been relatively high compared to the rest of the past millennium. Evidence for increased terrestrial sediment supply in recent decades, due to anthropogenic soil erosion in the wider Bogoria catchment, is a reason for concern about possible adverse impacts on the unique ecosystem of Lake Bogoria

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting