An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Minimal truncations of supersingular p-divisible groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Evaluation of the quantity of Fe3+ in spinels for obtaining the oxygen fugacities in xenoliths.

The analysis by electron microprobe allows the evaluation of the quantity of Fe3+ ih spinels with considerable errors. The use of a correction equation which is based on a the calibration of analyses with an electron microprobe in relation to those carried out with Mossbauer spectroscopy gives more precise evaluations of Fe3+. In fact, it allows a calculation of the oxygen fugacity in peridotitic xenoliths. The obtained results show that peridotites of the French Central Massif crystallised under oxygen fugacities which were higher than those of the Moroccan Anti-Atlas.

The optimum quantity of money: Theory and evidence

In this paper we propose a simple and general model for computing the Ramsey optimal inflation tax, which includes several models from the previous literature as special cases. We show that it cannot be claimed that the Friedman rule is always optimal (or always non--optimal) on theoretical grounds. The Friedman rule is optimal or not, depending on conditions related to the shape of various relevant functions. One contribution of this paper is to relate these conditions to {\it measurable} variables such as the interest rate or the consumption elasticity of money demand. We find that it tends to be optimal to tax money when there are economies of scale in the demand for money (the scale elasticity is smaller than one) and/or when money is required for the payment of consumption or wage taxes. We find that it tends to be optimal to tax money more heavily when the interest elasticity of money demand is small. We present empirical evidence on the parameters that determine the optimal inflation tax. Calibrating the model to a variety of empirical studies yields a optimal nominal interest rate of less than 1\%/year, although that finding is sensitive to the calibration.

A minimal set of coordinates for describing humanoid shoulder motion

The kinematics of the anatomical shoulder are analysed and modelled as a parallel mechanism similar to a Stewart platform. A new method is proposed to describe the shoulder kinematics with minimal coordinates and solve the indeterminacy. The minimal coordinates are defined from bony landmarks and the scapulothoracic kinematic constraints. Independent from one another, they uniquely characterise the shoulder motion. A humanoid mechanism is then proposed with identical kinematic properties. It is then shown how minimal coordinates can be obtained for this mechanism and how the coordinates simplify both the motion-planning task and trajectory-tracking control. Lastly, the coordinates are also shown to have an application in the field of biomechanics where they can be used to model the scapulohumeral rhythm.

Cross-country data on the quantity of schooling: a selective survey and some quality measures

We survey a number of papers that have focused on the construction of cross-country data sets on average years of schooling. We discuss the construction of the different series, compare their profiles and construct indicators of their information content. The discussion focuses on a sample of OECD countries but we also provide some results for a large non-OECD sample.

Minimal doses of hydroxyurea for sickle cell disease

The use of hydroxyurea (HU) can improve the clinical course of sickle cell disease. However, several features of HU treatment remain unclear, including the predictability of drug response and determination of adequate doses, considering positive responses and minimal side effects. In order to identify adequate doses of HU for treatment of sickle cell disease, 10 patients, 8 with sickle cell anemia and 2 with Sß thalassemia (8SS, 2Sß), were studied for a period of 6 to 19 months in an open label dose escalation trial (10 to 20 mg kg-1 day-1). Hemoglobin (Hb), fetal hemoglobin (Hb F) and mean corpuscular volume (MCV) values and reticulocyte, neutrophil and platelet counts were performed every two weeks during the increase of the HU dose and every 4 weeks when the maximum HU dose was established. Reduction in the number of vasoocclusive episodes was also considered in order to evaluate the efficiency of the treatment. The final Hb and Hb F concentrations, and MCV values were significantly higher than the initial values, while the final reticulocyte and neutrophil counts were significantly lower. There was an improvement in the concentration of Hb (range: 0.7-2.0 g/dl) at 15 mg HU kg-1 day-1, but this concentration did not increase significantly when the HU dose was raised to 20 mg kg-1 day-1. The concentration of Hb F increased significantly (range: 1.0-18.1%) when 15 mg HU was used, and continued to increase when the dose was raised to 20 mg kg-1 day-1. The final MCV values increased 11-28 fl (femtoliters). However, reticulocyte (range: 51-205 x 109/l) and neutrophil counts (range: 9.5-1.3 x 109/l) obtained at this dose were significantly lower than those obtained with 15 mg kg-1 day-1. All patients reported a decrease in frequency or severity of vasoocclusive episodes. These results suggest that a hydroxyurea dose of 15 mg kg-1 day-1 seems to be adequate for treatment of sickle cell disease in view of the minimal side effects observed and the improvement in laboratory and clinical parameters.

Letter to S.D. Woodruff stating the total quantity of timber plank in the Port Robinson Bridge at Chippawa

Letter to S.D. Woodruff stating the total quantity of timber plank in the Port Robinson Bridge at Chippawa. This is signed by Fred Holmes, Oct. 6, 1857.

List showing the quantity of excavation from lot no.5 to Marshville Culvert

List showing the quantity of excavation from lot no.5 to Marshville Culvert, n.d.

Chart of approximate quantity of excavation in slides in the deep cut

Chart of approximate quantity of excavation in slides in the deep cut, July 1, 1848.

Abstract of quantity of excavation for lock no.12

Abstract of quantity of excavation for lock no.12, July 4, 1854.

General return (copy) showing the quantity of each article transported on the Welland Canal during the year ending January 5th 1857 (Port Robinson)

General return (copy) showing the quantity of each article transported on the Welland Canal during the year ending January 5th 1857 (Port Robinson) (2 pages), 1857.

General return showing the quantity of each article transported on the Welland Canal during the year ending 1857 and the amount of tolls collected thereon (Port of Maitland)

General return showing the quantity of each article transported on the Welland Canal during the year ending 1857 and the amount of tolls collected thereon (Port of Maitland) (2 page, printed blank), 1857.

General return showing the quantity of each article transported on the Welland Canal during the year ending December 31st, 1858

General return showing the quantity of each article transported on the Welland Canal during the year ending December 31st, 1858 and the amount of tolls collected thereon (Port of Maitland). This is signed by William Turner, collector (2 page, printed blank), 1858.

General return showing the quantity of each article transported on the Welland Canal during the year ending on the 31st of December 1858

General return showing the quantity of each article transported on the Welland Canal during the year ending on the 31st of December 1858 and the tolls collected thereon (office at Port Robinson) (2 pages), 1858.