Coercive Inequalities on Metric Measure Spaces

We study coercive inequalities on finite dimensional metric spaces with probability measures which do not have volume doubling property. This class of inequalities includes Poincar\'e and Log-Sobolev inequality. Our main result is proof of Log-Sobolev inequality on Heisenberg group equipped with either heat kernel measure or "gaussian" density build from optimal control distance. As intermediate results we prove so called U-bounds

Extended Rate, more GFUN

We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some enhancements to render our package efficient. Thus we extend and complement Christian Krattenthaler's program Rate, the parts concerned with guessing of Bruno Salvy and Paul Zimmermann's GFUN, the univariate case of Manuel Kauers' Guess.m and Manuel Kauers' and Christoph Koutschan's qGeneratingFunctions.m.Comment: 26 page

Classification of finite congruence-simple semirings with zero

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We also investigate those subsemirings further, addressing e.g. the question of isomorphy.Comment: 16 page

Placental pathology: its impact on explaining prenatal and perinatal death

This review considers six main situations in which pathologists are expected to report and interpret placental messages for obstetricians, neonatologists and, indirectly, parents: (1) abortion is the body's corrective response to the embryonic defect suggested by malformed chorionic villi; (2) infection causing chorionic villous inflammation is specific and haematogenous; pathogen identification is mandatory, in contrast to chorioamnionitis caused by increased local immunosuppression allowing indiscriminate bacterial entry; (3) prematurity and (4) intrauterine growth restriction are often associated with pregnancy-specific disease (pre-eclampsia) or pre-existing maternal conditions (systemic lupus); parental studies may improve outcome in subsequent pregnancies; (5) intrauterine death near term is often due to placental dysmaturity featuring a severely reduced number of syncytiocapillary membranes; it accounts for the death in utero of 3 in 1000 pregnancies; detection helps to minimise recurrence in subsequent pregnancies; (6) twins are best confirmed as monozygous by the absence of chorionic tissue in the dividing membranes; most monochorionic twins have vascular connections whose detailed analysis is requested only if there are inter-twin differences in growth and colour. From a formal point of view, many more bits of pathology than discussed in this review can be found in placentas and, with the advances in ultrasonography, might even be seen prior to birth. The extent of such a disturbance might ultimately affect fetal growth, which is amenable to prenatal detection offering the chances for an appropriate management. In contrast, dysmaturity is a great challenge as no predictive tests are as yet availabl

On the rank of semimodules over semirings

In this paper we investigate conditions on a semiring $S$ such that there are semimodules over $S$ with bases of different length. This includes and generalizes corresponding results on rings, in particular one due to P. Dubreil