On codimension two flats in Fermat-type arrangements

In the present note we study certain arrangements of codimension $2$ flats in projective spaces, we call them "Fermat arrangements". We describe algebraic properties of their defining ideals. In particular, we show that they provide counterexamples to an expected containment relation between ordinary and symbolic powers of homogeneous ideals.Comment: 9 page

Posebnosti metalurške industrije za implementaciju Lean principa

The ideal balance between innovating and effective financing is provided by the Lean principles. The basic principle of Lean is to eliminate the wastes and to increase the effi ciency of production processes. The objective of this article is to define the basic specifics of metallurgical production, to analyze the classical sources of wastes (Ohno’s seven wastes) from the point of view of the identified specifics and to propose the priorities for their elimination in metallurgical production.Idealnu ravnotežu između inovacije I djelotvornog financiranja osigurava se Lean principima. Osnovni princip Lean-a je kako smanjiti gubitke i kako povećati učinkovitost proizvodnih procesa. Cilj ovog članka je definirati osnovne specifičnosti metalurške proizvodnje kako bi analizirali klasične izvore gubitaka (Ohnovih sedam gubitaka) i to s točke gledišta identificiranih specifičnosti i predložiti prioritete za otklanjanje gubitaka u metalurškoj proizvodnji

From faeces to ecology and behaviour: non-invasive microsatellite genotyping as a means to study wild otters (lutra lutra)

The threatened Eurasian otter (Lutra lutra) is of high conservation concern because of its earlier massive decline and range contractions, its important role as a top predator in its ecosystem, and because of its current increase and expansion in Germany that evokes conflicts with humans living on aquaculture. To understand the population dynamic and hence the current spread and to be able to manage it, we require knowledge that is either unavailable, not well understood, or has to be checked whether it also applies to fish pond systems, the main otter habitat in the Upper Lusatia that is the main source population for the recent expansion in Saxony, Germany. For this purpose, I used non-invasive genetic CMR methods to gain information about actual population sizes, population dynamic parameters, marking behaviour, and spatial use of one source population in Eastern Germany. To make this method more efficient, especially for otter scats, I first optimised the required genetic methods to receive high success rates and low genotyping errors rates (Chapter two). Following this, I applied non-invasive genetic CMR to the first sampling year (2006) to demonstrate pitfalls and risks of this method and present a road map in which I offer solutions for the outlined problems (Chapter three). This road map is not only valid for otters, but is written as a general guideline when using non-invasively collected samples with low quality. Finally, I used this road map to obtain reliable estimates and information on population size, sex ratio, and marking behaviour (Chapter four), as well as survival, temporary migration, dispersal, and spatial use (Chapter five) over six sampling years (2006–2012). Chapter six completes the thesis by first giving an overview of the conducted research, followed by a synthesis of the four key findings and a discussion about limitations and methodological constraints. The chapter closes with suggestions for further research and for otter conservation

Evaluation of benefits resulting from innovation of input raw materials dosing process in sintering

Production of blast furnace sinter is among the processes with the highest energy and material requirements. Fuel consumption is especially significant cost item here. The presence of grate sintered in charge, i.e. return sinter from 12 to 22 mm in size, can have fundamental impact on the technical and economic indicators of the sintering process. Grate sinter can be used as a foundation layer under the sintering mixture, to increase air permeability of charge and to improve the gas-dynamic conditions. The article analyzes the impact of grate sinter on the sintering process, based on an analysis of the acquired production indicators within the scope of the research in question

Life-Time Covariation of Major Cardiovascular Diseases: A 40-Year Longitudinal Study and Genetic Studies

BACKGROUND: It is known that certain cardiovascular diseases (CVD) are associated, like atrial fibrillation and stroke. However, for other CVDs, the links and temporal trends are less studied. In this longitudinal study, we have investigated temporal epidemiological and genetic associations between different CVDs. METHODS: The ULSAM (Uppsala Longitudinal Study of Adult Men; 2322 men aged 50 years) has been followed for 40 years regarding 4 major CVDs (incident myocardial infarction, ischemic stroke, heart failure, and atrial fibrillation). For the genetic analyses, publicly available data were used. RESULTS: Using multistate modeling, significant relationships were seen between pairs of all of the 4 investigated CVDs. However, the risk of obtaining one additional CVD differed substantially both between different CVDs and between their temporal order. The relationship between heart failure and atrial fibrillation showed a high risk ratio (risk ratios, 24-26) regardless of the temporal order. A consistent association was seen also for myocardial infarction and atrial fibrillation but with a lower relative risk (risk ratios, 4-5). In contrast, the risk of receiving a diagnosis of heart failure following a myocardial infarction was almost twice as high as for the reverse temporal order (risk ratios, 16 versus 9). Genetic loci linked to traditional risk factors could partly explain the observed associations between the CVDs, but pathway analyses disclosed also other pathophysiological links. CONCLUSIONS: During 40 years, all of the 4 investigated CVDs were pairwise associated with each other regardless of the temporal order of occurrence, but the risk magnitude differed between different CVDs and their temporal order. Genetic analyses disclosed new pathophysiological links between CVDs

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric