Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

Geometric collections and Castelnuovo-Mumford Regularity

The paper begins by overviewing the basic facts on geometric exceptional collections. Then, we derive, for any coherent sheaf \cF on a smooth projective variety with a geometric collection, two spectral sequences: the first one abuts to \cF and the second one to its cohomology. The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on smooth projective varieties $X$ with a geometric collection $\sigma$. We define the notion of regularity of a coherent sheaf \cF on $X$ with respect to $\sigma$. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we show that in case of coherent sheaves on \PP^n and for a suitable geometric collection of coherent sheaves on \PP^n both notions of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a smooth quadric hypersurface Q_n \subset \PP^{n+1} ($n$ odd) with respect to a suitable geometric collection and we compare it with the Castelnuovo-Mumford regularity of their extension by zero in \PP^{n+1}.Comment: To appear in Math. Proc. Cambridg

Bound, virtual and resonance SS-matrix poles from the Schr\"odinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and 4 table

Pauli spin blockade in CMOS double quantum dot devices

Silicon quantum dots are attractive candidates for the development of scalable, spin-based qubits. Pauli spin blockade in double quantum dots provides an efficient, temperature independent mechanism for qubit readout. Here we report on transport experiments in double gate nanowire transistors issued from a CMOS process on 300 mm silicon-on-insulator wafers. At low temperature the devices behave as two few-electron quantum dots in series. We observe signatures of Pauli spin blockade with a singlet-triplet splitting ranging from 0.3 to 1.3 meV. Magneto-transport measurements show that transitions which conserve spin are shown to be magnetic-field independent up to B = 6 T.Comment: 5 pages , 4 figure

Storage-ring measurement of the hyperfine induced 47Ti18+(2s 2p 3P0 -> 2s2 1S0) transition rate

The hyperfine induced 2s 2p 3P0 > 2s2 1S0 transition rate AHFI in berylliumlike 47Ti18+ was measured. Resonant electron-ion recombination in a heavy-ion storage ring was employed to monitor the time dependent population of the 3P0 state. The experimental value AHFI=0.56(3)/s is almost 60% larger than theoretically predicted.Comment: 4 pages. 3 figures, 1 table, accepted for publication in Physical Review Letter

Big data analytics for continuous assessment of astronaut health risk and its application to human-in-the-loop (HITL) related aerospace

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. The man-instrumentation-equipment-vehicle-environment ecosystem is complex in aerospace missions. Health status of the individual has important implications on decision making and performance that should be factored into assessments for probability of success/risk of failure both in offline and real-time models. To date probabilistic models have not considered the dynamic nature of health status. Big Data analytics is enabling new forms of analytics to assess health status in real-time. There is great potential to integrate dynamic health status information with platforms assessing risk and the probability of success for dynamic individualized real-time probabilistic predictive risk assessment. In this research we present an approach utilizing Big Data analytics to enable continuous assessment of astronaut health risk and show its implications for integration with HITL related aerospace mission

A comprehensive evaluation of water uptake on atmospherically relevant mineral surfaces: DRIFT spectroscopy, thermogravimetric analysis and aerosol growth measurements

The hygroscopicity of mineral aerosol samples has been examined by three independent methods: diffuse reflectance infrared Fourier transform spectroscopy, thermogravimetric analysis and differential mobility analysis. All three methods allow an evaluation of the water coverage of two samples, CaCO₃ and Arizona Test dust, as a function of relative humidity. For the first time, a correlation between absolute gravimetric measurements and the other two (indirect) methods has been established. Water uptake isotherms were reliably determined for both solids which at 298 K and 80% relative humidity exhibited similar coverages of ~4 monolayers. However, the behaviour at low relative humidity was markedly different in the two cases, with Arizona Test Dust showing a substantially higher affinity for water in the contact layer. This is understandable in terms of the chemical composition of these two materials. The mobility analysis results are in good accord with field observations and with our own spectroscopic and gravimetric measurements. These findings are of value for an understanding of atmospheric chemical processes

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty