Minimal half-spaces and external representation of tropical polyhedra

We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements which appeared in the tropical literature, and disproving a conjecture of F. Block and J. Yu. We also establish an analogue of the Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently represented internally (in terms of extreme points and rays) or externally (in terms of half-spaces containing it). A canonical external representation of a polyhedron turns out to be provided by the extreme elements of its tropical polar. We characterize these extreme elements, showing in particular that they are determined by support vectors.Comment: 19 pages, 4 figures, example added with a new figure, figures improved, references update

Submonolayer Quantum Dots for High Speed Surface Emitting Lasers

We report on progress in growth and applications of submonolayer (SML) quantum dots (QDs) in high-speed vertical-cavity surface-emitting lasers (VCSELs). SML deposition enables controlled formation of high density QD arrays with good size and shape uniformity. Further increase in excitonic absorption and gain is possible with vertical stacking of SML QDs using ultrathin spacer layers. Vertically correlated, tilted or anticorrelated arrangements of the SML islands are realized and allow QD strain and wavefunction engineering. Respectively, both TE and TM polarizations of the luminescence can be achieved in the edge-emission using the same constituting materials. SML QDs provide ultrahigh modal gain, reduced temperature depletion and gain saturation effects when used in active media in laser diodes. Temperature robustness up to 100 °C for 0.98 μm range vertical-cavity surface-emitting lasers (VCSELs) is realized in the continuous wave regime. An open eye 20 Gb/s operation with bit error rates better than 10−12has been achieved in a temperature range 25–85 °Cwithout current adjustment. Relaxation oscillations up to ∼30 GHz have been realized indicating feasibility of 40 Gb/s signal transmission

Non-exponential decay in quantum field theory and in quantum mechanics: the case of two (or more) decay channels

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between $t$ and $t+dt.$ An important quantity is the ratio of the probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity $\Gamma_{1}/\Gamma_{2}$, where $\Gamma_{1}$ and $\Gamma_{2}$ are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value $\Gamma_{1}/\Gamma_{2}$ and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case.Comment: 32 pages, 10 figures. To appear in "Foundations of Physics

Analysis of Articles on Education and Instructional Technologies (Scopus)

© 2020. All Rights Reserved. It is an indisputable fact that technology is a part of our lives. It is known that research and education technologies are concentrated. By examining the articles and dissertations published in the field, the scope, strengths and weaknesses of the studies were determined. An important gap has been filled in to guide researches what kind of studies may be needed in the future. Many studies for this purpose were found in the literature. However, since similar studies dealing with educational technologies are outdated, this study is considered important in terms of gathering current research trends and results. The aim of this study is to analyse the articles published in the Scopus database on educational technologies and instructional technologies, thematically and methodologically. The study was designed by adopting a case study from qualitative research models. The sample has not been determined for postgraduate dissertations to be included in the study, and it was aimed to reach the whole universe. In this context, all articles have been accessed through the library system of the university in the Scopus database included. The keywords ‘educational technologies’ and ‘instructional technologies’ were used in the article search. The document types have been examined by year, by country, by authors, by field research and by place of publication

Analysis of Articles on Education and Instructional Technologies (Scopus)

It is an indisputable fact that technology is a part of our lives. It is known that research and education technologies are concentrated. By examining the articles and dissertations published in the field, the scope, strengths and weaknesses of the studies were determined. An important gap has been filled in to guide researches what kind of studies may be needed in the future. Many studies for this purpose were found in the literature. However, since similar studies dealing with educational technologies are outdated, this study is considered important in terms of gathering current research trends and results. The aim of this study is to analyse the articles published in the Scopus database on educational technologies and instructional technologies, thematically and methodologically. The study was designed by adopting a case study from qualitative research models. The sample has not been determined for postgraduate dissertations to be included in the study, and it was aimed to reach the whole universe. In this context, all articles have been accessed through the library system of the university in the Scopus database included. The keywords ‘educational technologies’ and ‘instructional technologies’ were used in the article search. The document types have been examined by year, by country, by authors, by field research and by place of publication. © 2020. All Rights Reserved

Effects of hyperhomocysteinemia on the platelet-driven contraction of blood clots

Hyperhomocysteinemia (HHcy) is associated with thrombosis, but the mechanistic links between them are not understood. We studied effects of homocysteine (Hcy) on clot contraction in vitro and in a rat model of HHcy. Incubation of blood with exogenous Hcy for 1 min enhanced clot contraction, while 15-min incubation led to a dose-dependent suppression of contraction. These effects were likely due to direct Hcy-induced platelet activation followed by exhaustion, as revealed by an increase in fibrinogen-binding capacity and P-selectin expression determined by flow cytometry. In the blood of rats with HHcy, clot contraction was enhanced at moderately elevated Hcy levels (10-50 µM), while at higher Hcy levels (>50 µM), the onset of clot contraction was delayed. HHcy was associated with thrombocytosis combined with a reduced erythrocyte count and hypofibrinogenemia. These data suggest that in HHcy, platelets get activated directly and indirectly, leading to enhanced clot contraction that is facilitated by the reduced content and resilience of fibrin and erythrocytes in the clot. The excessive platelet activation can lead to exhaustion and impaired contractility, which makes clots larger and more obstructive. In conclusion, HHcy modulates blood clot contraction, which may comprise an underappreciated pro- or antithrombotic mechanism