Ri-continua and hyperspaces

AbstractIt is proved that if a continuum X contains an Ri-continuum for some iϵ{1,2,3}, then the hyperspaces 2x and C(X) contain Ri-continua, therefore they are not contractible. Moreover, 2x has no confluent Whitney map. Some examples concerning this subject are given and som

Dark matter and dark energy as a effects of Modified Gravity

We explain the effect of dark matter (flat rotation curve) using modified gravitational dynamics. We investigate in this context a low energy limit of generalized general relativity with a nonlinear Lagrangian ${\cal L}\propto R^n$, where $R$ is the (generalized) Ricci scalar and $n$ is parameter estimated from SNIa data. We estimate parameter $\beta$ in modified gravitational potential $V(r) \propto -\frac{1}{r}(1+(\frac{r}{r_c})^{\beta})$. Then we compare value of $\beta$ obtained from SNIa data with $\beta$ parameter evaluated from the best fitted rotation curve. We find $\beta \simeq 0.7$ which becomes in good agreement with an observation of spiral galaxies rotation curve. We also find preferred value of $\Omega_{m,0}$ from the combined analysis of supernovae data and baryon oscillation peak. We argue that although amount of "dark energy" (of non-substantial origin) is consistent with SNIa data and flat curves of spiral galaxies are reproduces in the framework of modified Einstein's equation we still need substantial dark matter. For comparison predictions of the model with predictions of the $\Lambda$CDM concordance model we apply the Akaike and Bayesian information criteria of model selection.Comment: Lectures given at 42nd Karpacz Winter School of Theoretical Physics: Ladek, Poland, 6-11 Feb 200

Reduction for natural operators on projectable connections

AbstractWe present a very simple proof of a general reduction for natural operators on torsion free projectable classical linear connections.</jats:p

Projective Fra\"{\i}ss\'{e} limits of trees

We continue study of projective Fra\"{\i}ss\'e limit developed by Irvin, Panagiotopoulos and Solecki. We modify the ideas of monotone, confluent, and light mappings from continuum theory as well as several properties of continua so as to apply to topological graphs. As the topological realizations of the projective Fra\"{\i}ss\'e limits we obtain the dendrite $D_3$ as well as quite new, interesting continua for which we do not yet have topological characterizations

Mould walls inclination and dendritic morphology of CMSX-4 blades airfoils

The airfoils of single-crystalline turbine blades were studied. The blades made of industrial CMSX-4 superalloy were obtained by the Bridgman technique. Five different withdrawal rates (1–5 mm/min) were used. Series of as-cast samples were prepared by cutting the airfoils at different distances from the blade root. The metallographic sections, prepared for each cutting planes, were subjected to scanning electron microscopy observations and Laue diffraction studies. Macrostructure images of whole area of airfoil cross-sections were obtained by stitching several obtained SEM images. Morphology of dendrites in different area of cross-sections were analysed. The crystal orientation of each sample were determined by analysis of Laue pattern. It was found that the morphology of dendrites changes in the area, where the dendrite growth is limited by inclined mould walls

Characterization of casting defects in the single crystal turbine blade airfoil

In the paper turbine blades made from single crystal CMSX-4 superalloy were investigated by X-ray diffraction methods (topography, -scan mapping) complemented by scanning electron microscopy observations. By the X-ray diffraction topography method several misorientation defects were visualized as well as dendrites arrangement. It was discussed that tip of the airfoil and thin walled area of the turbine blades located near the trailing edge can accumulate more growth defects than other airfoil part, due to the complex shape of the mould

The projective Fra\"{\i}ss\'{e} limit of the class of all connected finite graphs with confluent epimorphisms

We show that the class of finite connected graphs with confluent epimorphism is a projective Fra\"{\i}ss\'e class and we investigate the continuum obtained as the topological realization of the projective Fra\"{\i}ss\'e limit. This continuum was unknown before. We show that it is indecomposable, but not hereditarily indecomposable, one-dimensional, Kelley, pointwise self-homeomorphic, but not homogeneous. It is hereditarily unicoherent and each point is the top of the Cantor fan. Moreover, the universal solenoid, the universal pseudo-solenoid, and the pseudo-arc may be embedded in it

Crystal perfection studies of single crystal superalloy turbine blades by X-Ray diffraction methods

In the paper the crystal structure of single crystal CMSX-4 blade casts, applied in high pressure turbine of aircraft engines was analyzed. The longitudinal section of blade, cast at withdrawal rate of 3 mm/min was used as a sample. During the conducted research, following X-ray diffraction methods were applied: EFG -scan, Auleytner X-ray topography and analysis of diffraction reflex profile (“rocking curve”). The authors determined crystal orientation in entire blade casts on the basis of set criterion concerning values of angle — deviation of [001] direction from the direction of cast withdrawal. Conclusions concerning the crystal structure quality of the blade were drawn based on results from three different research methods. Local changes in crystal orientation on the surface of blade cast, also areas with significant structure defect degree and the presence of internal stresses were characterized

Myocardial contractility improvement after coronary artery by-pass grafting in a 1-year observation: The role of myocardial viability assessment

Background: Left ventricular (LV) contractility impairment in coronary artery disease patients may be the effect of heart muscle hibernation due to chronic ischemia. Revascularization is the only method to restore contractile function in these patients. The time and degree of LV function improvement have not been precisely determined, and the published data are discordant. The aim of our study was to evaluate the time of myocardial contractility recovery after surgical revascularization in patients with systolic LV dysfunction in relation to the results of echocardiography stress tests. Methods: The study included 50 patients with multivessel coronary artery disease and decreased left ventricular ejection fraction (LVEF < 40%) qualified for coronary artery by-pass grafting. The intervention was preceded by rest echocardiography, low dose dobutamine stress test (5-10 &#181;g/kg/min) and by low dose dipyridamole stress test (0.24 mg/kg during 4 min) performed on the next day. Consecutive rest echocardiograms were performed immediately after the intervention and after 3, 6 and 12 months. LVEF and the index of left ventricular contractility (WMSI, wall motion score index) were evaluated at each examination. Results: During 1-year follow-up after coronary artery by-pass grafting (CABG), significant improvement in LV systolic function was observed (LVEF increased, WSMI reduced), with major changes occurring over the first 6 months. The correlation of echocardiography parameters (EF, WMSI) at stress tests and during 1-year follow-up showed that the strongest relationship exists between the change in WMSI both in dobutamine and dipyridamole stress tests and the improvement in WMSI observed after 6 months. Conclusions: LV function improvement after CABG in patients with systolic LV dysfunction was most pronounced 3 to 6 months after the intervention. Both types of stress tests are characterized by similar diagnostic value for assessing LV myocardial viability. WMSI calculated during stress was identified to have the strongest prognostic value. (Cardiol J 2007; 14: 246-251

The value of dobutamine stress echocardiography in predicting clinical improvement following coronary artery bypass grafting in patients with left ventricular systolic dysfunction

Background: Recent years have seen an increasing number of patients with multivessel coronary artery disease and left ventricular systolic dysfunction being qualified for cardiac surgery. Identification of patients who are likely to benefit most from revascularisation procedures poses a considerable problem. The aim of the study was to assess the value of dobutamine stress echocardiography in predicting the clinical course following coronary artery bypass grafting (CABG) in patients with ischaemic left ventricular dysfunction. Methods: Fifty patients with multivessel coronary artery disease and reduced left ventricular ejection fraction (LVEF < 40%) who were qualified for CABG were included in the study. Resting echocardiography and a small-dose (5&#8211;10 &#181;g/kg/min) dobutamine test were performed before the procedure. Subsequent tests were repeated after the procedure and at 3.6 and 12 months. A combined endpoint of death, repeat hospitalisations, NYHA stage, severity of angina and left ventricular systolic function was evaluated. Results: Two factors were found to affect the prognosis adversely following CABG in both univariate and multivariate analysis: a history of hypertension (p = 0.039, OR 4.9, 95% CI 1.4-17.1) and lack of improvement in contractility in at least 4 segments during the dobutamine test (p = 0.0003, OR 37.2, 95% CI 6.3-218.4). An improvement in contractility in at least 4 segments of the left ventricle is the most important prognostic factor. Conclusions: The results of the dobutamine stress test have a more potent prognostic value than clinical or demographic parameters in predicting clinical improvement. Patients with negative results of the test represent the group with the gravest prognosis. (Cardiol J 2007; 14: 174-179