120 research outputs found
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
where 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 there exists such that the
Hausdorff dimension of is at least . We also provide a
Diophantine condition on that guarantees the existence of
such that the dimension of is positive. Finally, for some
multidimensional rotations on \T^d, , we construct smooth
so that the Hausdorff dimension of 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 with periodically placed
linear barriers of length . We prove that the set of ergodic
directions is always uncountable. Moreover, if 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
Sex determination based on the analysis of a contemporary Polish populationâs 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 CTâs (627 female; 52.3%). The mean age of the group was 43.5 ± 17.4 years â no age difference between sexes was noted (p = 0.37). All of the performed measurements were significantly (p < 0.0001) larger in males than in females. The mathematical formula based on the âorale-spina nasalis posteriorâ (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
Determination of nitrogen dioxide, sulfur dioxide, ozone, and ammonia in ambient air using the passive sampling method associated with ion chromatographic and potentiometric analyses
Concentrations of nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3), and ammonia (NH3) were determined in the ambient air of Al-Ain city over a year using the passive sampling method associated with ion chromatographic and potentiometric detections. IVL samplers were used for collecting nitrogen and sulfur dioxides whereas Ogawa samplers were used for collecting ozone and ammonia. Five sites representing the industrial, traffic, commercial, residential, and background regions of the city were monitored in the course of this investigation. Year average concentrations of â€59.26, 15.15, 17.03, and 11.88 Όg/m3 were obtained for NO2, SO2, O3, and NH3, respectively. These values are lower than the maxima recommended for ambient air quality standards by the local environmental agency and the world health organization. Results obtained were correlated with the three meteorological parameters: humidity, wind speed, and temperature recorded during the same period of time using the paired t test, probability p values, and correlation coefficients. Humidity and wind speed showed insignificant effects on NO2, SO2, O3, and NH3 concentrations at 95% confidence level. Temperature showed insignificant effects on the concentrations of NO2 and NH3 while significant effects on SO2 and O3 were observed. Nonlinear correlations (R2ââ€â0.722) were obtained for the changes in measured concentrations with changes in the three meteorological parameters. Passive samplers were shown to be not only precise (RSDââ€â13.57) but also of low cost, low technical demand, and expediency in monitoring different locations
Modeling of static friction in closed-loop kinematic chainsâUniqueness and parametric sensitivity problems
The role of open-air inhalatoria in the air quality improvement in spa towns
Objectives: The present study was aimed at evaluating microbiological contamination of air in Ciechocinek and InoÂwroÂcĆaw â Polish lowland spa towns. Additionally, the impact of open-air inhalatoria on the quality of air was evaluated. Material and Methods: Air samples were collected seasonally in the urban areas, in the recreation areas and in the vicinity of inhalatoria in both towns using impaction. The numbers of mesophilic bacteria, staphylococci, hemolytic bacteria and actinomycetes were determined on media according to the Polish Standard PN-86/Z-04111/02. The number of moulds was determined on media according to the Polish Standard PN-86/Z-04111/03. Results: While the highest numbers of microorganisms were noted at the sites located in the urban areas, the lowest numbers were noted in the vicinity of the open-air inhalatoria. In all the investigated air samples the values of bioaerosol concentrations were below the recommended TLVs (†5000 CFUĂmâ3 for both bacteria and fungi in outdoor environments). Location of the sampling site was invariably a decisive factor in determining the number of microorganisms in the air. Conclusions: The aerosol which is formed in the open-air inhalatoria has a positive influence on microbiological air quality. Owing to a unique microclimate and low air contamination, Ciechocinek and InowrocĆaw comply with all necessary requirements set for health resorts specializing in treating upper respiratory tract infections
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