On Hausdorff dimension of the set of closed orbits for a cylindrical transformation

We deal with Besicovitch's problem of existence of discrete orbits for transitive cylindrical transformations $T_\varphi:(x,t)\mapsto(x+\alpha,t+\varphi(x))$ where $Tx=x+\alpha$ is an irrational rotation on the circle \T and \varphi:\T\to\R is continuous, i.e.\ we try to estimate how big can be the set D(\alpha,\varphi):=\{x\in\T:|\varphi^{(n)}(x)|\to+\infty\text{as}|n|\to+\infty\}. We show that for almost every $\alpha$ there exists $\varphi$ such that the Hausdorff dimension of $D(\alpha,\varphi)$ is at least $1/2$. We also provide a Diophantine condition on $\alpha$ that guarantees the existence of $\varphi$ such that the dimension of $D(\alpha,\varphi)$ is positive. Finally, for some multidimensional rotations $T$ on \T^d, $d\geq3$, we construct smooth $\varphi$ so that the Hausdorff dimension of $D(\alpha,\varphi)$ is positive.Comment: 32 pages, 1 figur

Ergodic directions for billiards in a strip with periodically located obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\R\times [0,h]$ with periodically placed linear barriers of length $0<\lambda<h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda/h\in(0,1)$ is rational the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.Comment: The article is complementary to arXiv:1109.458

Coexistence of posterior cerebral circulation anatomical variations andbasilar artery aneurysms : case-control study

Background: The anatomy of arteries supplying blood to the brain often varies among the population. It applies particularly to posterior cerebral circulation. The impact of its anatomy variabilities on the formation of intracranial aneurysms has not been determined yet. The aim was to find out if posterior cerebral circulation anatomy variations coexist with basilar artery aneurysms (BAAs). We retrospectively analyzed 27 patients with BAA and a group of 30 patients matched by gender and age but without BAA. In both groups together most (66.67%) of patients were female and the average age was 59.75 ± 10.91. All of the patients had Computed Tomography performed. We assessed the occurrence of BAA, basilar artery (BA) diameter, vertebral artery (VA) diameter, posterior cerebral artery (PCA) diameter, and if patients had hypoplastic VA or PCA. Results: The presence of right VA hypoplasia significantly increased the risk of BAA occurrence (48.15% vs. 16.67%; p = 0.011). The occurrence of hypoplastic VA on either side was significantly associated with the risk of BAA formation (59.26% vs. 26.67%; p = 0.013). Patients with BAA had slightly larger left PCA diameter 1cm after division (1.96 ± 0.51 vs. 1.64 ± 0.42; p = 0.014) in comparison to those without BAA. Additionally, hypoplastic right PCA occurred more often in patients with BAA (22.22% vs. 0%; p = 0.022). Conclusions: We can conclude that the anatomy of PCA and VA affects the occurrence of BAA. Hypoplastic VA, the presence of wider left PCA and hypoplastic right PCA may be factors that coexist with BAA occurrence

Kratkotrajno niskotemperaturno nitriranje austenitnog čelika 316L

The AISI 316L austenitic steel after glow discharge nitriding at temperature of T = 673 K and duration of τ=14,4 ks, for two different variants of specimen arrangement in the glow-discharge chamber was investigated. In order to assess the effectiveness of nitriding process, the surface layers profile analysis examination, surface hardness and hardness profile examination, the analysis of surface layer structures and corrosion resistance tests were performed. It has been found that application of a booster screen effects in a nitrogen diffusion depth increment into the 316L austenitic steel surface, what results in the surface layer thickness escalation.Ispitani su uzorci od AISI 316L austenitni čelik tretirani na dva raziličita načina u komori za nitriranje nakon nitriranja na temperaturi T=673 K u trajanju τ=14,4 s. Kako bi procijenili efikasnost procesa nitriranja provedena je analiza profila površinskog sloja, ispitana je površinska tvrdoća kao i tvrdoća profila, te analiza strukture površinskog sloja i ispitivanje korozijske otpornosti. Pronađena je primjena efekta pojačane podrške u povećanju dubine difuzije kod nitriranja u površinu austenitnog čelika 316L, što rezultira povećanje debljine površinskog sloja

CEReS -Co-processing of Coal Mine & Electronic Wastes: Novel Resources for a Sustainable Future

International audienceMany coal mines produce waste which causes acid mine drainage (AMD) potentially resulting in severe environmental damage. This drainage can be treated, but most wastes will continue to produce such drainage for hundreds of years. Therefore, longer term, permanent solutions are needed. At the same time, the pace of technological development means most electrical and electronic equipment becomes obsolete within a matter of years. This results in the generation of vast and growing quantities of electronic waste (e-waste) every year. Where this cannot be recycled, it must be discarded. CEReS was a 3.2 M€ RFCS-funded project comprising eight partners from five countries. It targeted the development of a co-processing approach to treat these waste streams to produce metals and other valuable products, while eliminating their environmental impact. This brings together two waste streams from opposite ends of the supply chain (for which no alternative treatment option exists); turning each into a novel resource in a single, coherent 'grave-to-cradle' process. This industrial ecology approach is key to supporting a circular economy while securing the sustainable supply of critical raw materials. The project successfully elaborated a novel co-processing flow-sheet comprising: (i) the accelerated weathering of AMD-generating coal production wastes to generate a biolixiviant; (ii) the pyrolysis and catalytic cracking of low-grade PCBs to produce hydrocarbon fuel, a halogen brine a Cu-rich char; (iii) the leaching of base metals from the char using the biolixiviant; (iv) the reuse of the stabilised coal wastes; and (v) the recovery of valuable metal while concentrating precious and critical metals into enriched substrates. These individual process units were demonstrated individually at lab-pilot scale. The data were then used to validate the entire flow-sheet in an integrated process simulator. Finally an LCA approach was used to demonstrate the environmental benefits of the CEReS process over the status quo

Sex determination based on the analysis of a contemporary Polish population’s palatine bones: a computed tomography study of 1,200 patients

Background: The aims of the present study were to assess whether the hard palate reveals any measurable sex-related differences, and to create a mathematical model which would differentiate between males and females using hard palate measurements alone. Materials and methods: The present study was conducted on 1,200 archived sinus computed tomography (CT) scans. Each cranial measurement was taken twice by the same observer, and in cases of any discrepancies, the mean of the two values was recorded. Twenty per cent of randomly chosen samples were re-measured by an observer who did not partake in assessing the samples the first time. Logistic regression was used to derivate two mathematical formulas which would calculate the probability of a skull being male. Results: The studied group comprised 1,200 head CT’s (627 female; 52.3%). The mean age of the group was 43.5 ± 17.4 years — no age difference between sexes was noted (p = 0.37). All of the performed measurements were significantly (p &lt; 0.0001) larger in males than in females. The mathematical formula based on the “orale-spina nasalis posterior” (O-SNP) distance alone had a reliability rate of 68.35%. The equation based on the depth of the right greater palatine canal (GPC), the O-SNP distance and the anterior width of the palatal arch (AWPA) had a reliability rate of 78.37%. Conclusions: The most prominent sexually dimorphic parameters were the O-SNP, the GPC depth and the AWPA. The mathematical models presented in the current study can be used to successfully distinguish between sexes during forensic examination.

Ergodic infinite group extensions of geodesic flows on translation surfaces

We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that certain concrete staircases, covers of square-tiled surfaces, are not ergodic in almost every direction. In contrast we show the almost sure ergodicity of other concrete staircases. An appendix provides a combinatorial approach for the study of square-tiled surfaces