A wide range of mathematical ideas could be used to develop and justify a formula for calculating the area of trapezoid. Those ideas lead to different strategies for finding out area of trapezoid that we classify in three groups: decomposing, enclosing and transforming strategies. Those strategies should be part of mathematics content knowledge for teaching. In this study we trace a change in structure of mathematics content knowledge of nine pre-service mathematics teachers as a result of using GeoGebra applets that visualize different approaches in finding out the area of trapezoid. We argue that engaging pre-service mathematics teachers to develop and justify formula for calculating the area of trapezoid using GeoGebra applets is a worth task that enhances pre-service mathematics teachers’ content knowledge for teaching. Our experiment confirmed that the use of Geogebra encourage pre-service mathematics teachers to uncover new ideas that lead them towards clearer justifications and easier way of proving formula for area of trapezoid. Keywords: Area of trapezoid, GeoGebra, content knowledge for teaching

Prion diseases are dementing illnesses with poorly defined neuropsychological features. This is probably because the most common form, sporadic Creutzfeldt‐Jakob disease, is often rapidly progressive with pervasive cognitive decline making detailed neuropsychological investigation difficult. This study, which includes patients with inherited, acquired (iatrogenic and variant) and sporadic forms of the disease, is the only large‐scale neuropsychological investigation of this patient group ever undertaken and aimed to define a neuropsychological profile of human prion diseases.

Two-dimensional semiconductors such as MoS2 are an emerging material family with wide-ranging potential applications in electronics, optoelectronics, and energy harvesting. Large-area growth methods are needed to open the way to applications. Control over lattice orientation during growth remains a challenge. This is needed to minimize or even avoid the formation of grain boundaries, detrimental to electrical, optical, and mechanical properties of MoS2 and other 2D semiconductors. Here, we report on the growth of high-quality monolayer MoS2 with control over lattice orientation. We show that the monolayer film is composed of coalescing single islands with limited numbers of lattice orientation due to an epitaxial growth mechanism. Optical absorbance spectra acquired over large areas show significant absorbance in the high-energy part of the spectrum, indicating that MoS2 could also be interesting for harvesting this region of the solar spectrum and fabrication of UV-sensitive photodetectors. Even though the interaction between the growth substrate and MoS2 is strong enough to induce lattice alignment via van der Waals interaction, we can easily transfer the grown material and fabricate devices. Local potential mapping along channels in field-effect transistors shows that the single-crystal MoS2 grains in our film are well connected, with interfaces that do not degrade the electrical conductivity. This is also confirmed by the relatively large and length-independent mobility in devices with a channel length reaching 80 μm.

The ultralow thermal conductivity $\kappa$ observed experimentally in intentionally roughened silicon nanowires (SiNWs) is reproduced in phonon Monte Carlo simulations with exponentially correlated real-space rough surfaces similar to measurement [J. Lim, K. Hippalgaonkar, S. C. Andrews, A. Majumdar, and P. Yang, Nano Lett. 12, 2475 (2012)]. Universal features of thermal transport are revealed by presenting $\kappa$ as a function of the normalized geometric mean free path $\bar\lambda$ ($0<\bar\lambda<1$); the diffusive (Casimir) limit corresponds to $\bar\lambda=1/2$. $\kappa$ vs $\bar\lambda$ is exponential at low-to-moderate roughness (high $\bar\lambda$), where internal scattering randomly interrupts phonon bouncing across the SiNW, and linear at high roughness (low $\bar\lambda$), where multiple scattering events at the same surface results in ultralow, amorphous-limit thermal conductivity.

Ceratomegilla ( Adaliopsis ) alpina (Villa & Villa, 1835) is a Pleistocene glacial relict with disjunctive distribution in high mountain areas of the Alps, Carpathians and the Bulgarian mountains, where it inhabits mountain meadows from 800 to 2.000 m a.s.l. (Fürsch 1967, Haviar 2003, Kovar 2007). Two ssp. are recognized, Ceratomegilla alpina alpina Villa & Villa, 1835, restricted to the Alps (Austria, France, Italy, Liechtenstein and Switzerland), and Ceratomegilla alpina redtenbacheri Capra, 1928 with a wider distribution, including Austria, Bulgaria, Germany, Poland, Romania, Slovakia and Ukraina (Kovar 2007, Canepari 2013). In comparison with C. a. alpina , C. a. redtenbacheri is characterized by smaller humeral red spot reaching half of elytra width and without sub-humeral black spot; posterior spot roundish or square (never stripe shaped); body more convex and less pointed posteriorly (Capra 1928). Travnik C. a. Sampling site “Travnik

The aim of this study was to analyze one year survival outcome of the patients with sleep apnea in acute stroke in order to type and localisation of lesion. Patients and Methods: It was analyzed 110 patients with acute stroke (AS) and verified sleep apnea, treated at Department of Neurology, University Clinical Center Tuzla in the period December 2009 thorough may 2010. Acute stroke has been verified either by computerized tomography or magnetic resonance imaging of the brain. Average age was 65.13±9.27 years and it was 65 (59%) men. Number of participants with no apnea in control group was the same as well as sex distribution, with average age 64±8.69 years. Results: One year after acute stroke survived 78 (84.8%) patients out of 92 with apnea and ischemic stroke (IS). Otherwise, 13 (72.2%) patients survived out of 18 with hemorrhagic stroke (HS). Without apnea 88 (95.7%) patients who survived had IS and 16 (88.9%) HS. Survival of patients with IS and without apnea is significantly better than in patients with IS and apnea (X2=5.46, p=0.02). Survival of patients with HS with/without apnea is not significantly different. Majority (51/87.9%) of 58 patients with apnea who survived had lesions at two or more locations. Otherwise, 12 (100%) patients out of 12 without apnea who survived had lesion in frontal lobe. Survival of patients with/without apnea is not statisticaly different in order to location of lesion. Concerning the side of stroke 23 (85.5%) patients with apnea who survived had lesion(s) in left hemisphere but this difference is not significant. Patients without apnea 48 (96%) had lesion(s) at both sides. Conclusion: Survival of patients without apnea in ischemic stroke is significantly better than in patients with apnea. Survival in patients with/without apnea in hemorrhagic stroke has no statistical difference. Localization and side of lesion do not have influence on survival.