Frobenius manifolds and Frobenius algebra-valued integrable systems

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929–952, 1996), Kontsevich and Manin (Inv Math 124: 313–339, 1996). By specializing this construction, using a fixed Frobenius algebra \({\mathcal {A}},\) one can arrive at such a theory. More generally, one can apply the same idea to construct an \({\mathcal {A}}\)-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an \({\mathcal {A}}\)-valued modified Camassa–Holm equation is constructed.     

Synthesis of novel 7-aryl and 7-spiropyrazolo[4′,3′:5,6]pyrido[2,3-<Emphasis Type="BoldItalic">d</Emphasis>]pyrimidine derivatives and their study as AChE inhibitors

An efficient route for the synthesis of novel 7-aryl and 7-spiropyrazolo[4\(^{\prime }\),3\(^{\prime }\):5,6]pyrido[2,3-d]pyrimidine derivatives is described. These compounds were obtained by a cyclocondensation reaction between pyrazolopyridinediamines 4 and aldehydes 5 or cyclic ketones 6 in the presence of acetic acid as catalyst. This procedure provides the desired compounds in good yields under a simple two-step methodology. The obtained compounds were evaluated as AChE inhibitors and showed weak AChe inhibition with \(\hbox {IC}_{50} = 115{-}470 \, \upmu \hbox {M}\).     

Luminescence imaging of biological subjects during X-ray irradiations lower energy than Cerenkov-light threshold

It is commonly thought that UV or visible-light luminescence imaging of biological subjects during X-ray irradiation at the energy below 120 keV is impossible because the secondary electrons produced in this energy range do not emit Cerenkov light. Contrary to this consensus, we found UV or visible-light luminescence imaging of the subjects were possible with X-ray irradiations of this energy range. We placed one of the biological subjects in a black box; visible-light luminescence images were measured with a high-sensitivity, cooled charge coupled device (CCD) camera during X-ray irradiation at energy below 120 keV. We also conducted the imaging of air without subjects during irradiation of the same X-ray. The biological subjects emitted visible-light luminescence, and the imaging was possible with the irradiation of the X-ray below 120 keV. The luminescence images were observed in only the X-ray irradiated areas. Also air luminescence images could be obtained and the intensity of the luminescence measured from the images was proportionally increased with the exposure dose. UV or visible-light luminescence imaging of biological subjects was possible during X-ray irradiations lower energy than the Cerenkov-light threshold. The phenomenon was different from general X-ray fluorescence because wavelength of the luminescence is UV or visible-light. The luminescence imaging method is promising for estimating the irradiated area with X-ray, which could be used for interventional radiology (IVR). Also air luminescence imaging would be applied to the exposure dose distribution measurements for X-ray of diagnostic X-ray systems.     

A horn ridge waveguide DFB laser with reduced spatial hole burning for high-speed modulation

In this paper, we propose a DFB laser with a horn ridge waveguide (HRW) to suppress the longitudinal spatial hole burning (LSHB) effect in the lasers cavity, thus to reduce the rolloff at low frequency. The simulation result shows that HRW DFB lasers could significantly suppress the LSHB effect and its modulation bandwidth is increased by 14% comparing with the conventional straight ridge waveguide (RW) DFB lasers when the normalized coupling coefficient (κL) is 3.0. The calculated eye diagrams of HRW DFB lasers under direct 25 Gbps modulation have clearer opening than that of the conventional RW DFB lasers. These superior properties are due to the suppression of the LSHB effect by the HRW structure.     

Distributions of positive correlations in sectoral value added growth in the global economic network*

International trade has grown considerably during the process of globalization. Complex supply chains for the production of goods have resulted in an increasingly connected International Trade Network (ITN). Traditionally, direct trade relations between industries have been regarded as mediators of supply and demand spillovers. With increasing network connectivity the question arises if higher-order relations become more important in explaining a national sector’s susceptibility to supply and demand changes of its trading partner. In this study we address this question by investigating empirically to what extent the topological properties of the ITN provide information about positive correlations in the production of two industry sectors. We observe that although direct trade relations between industries serve as important indicators for correlations in the industries’ value added growth, opportunities of substitution for required production inputs as well as second-order trade relations cannot be neglected. Our results contribute to a better understanding of the relation between trade and economic productivity and can serve as a basis for the improvement of crisis spreading models that evaluate contagion threats in the case of a node’s failure in the ITN.     

Efficient and accurate modeling of electron photoemission in nanostructures with TDDFT

We derive and extend the time-dependent surface-flux method introduced in [L. Tao, A. Scrinzi, New J. Phys. 14, 013021 (2012)] within a time-dependent density-functional theory (TDDFT) formalism and use it to calculate photoelectron spectra and angular distributions of atoms and molecules when excited by laser pulses. We present other, existing computational TDDFT methods that are suitable for the calculation of electron emission in compact spatial regions, and compare their results. We illustrate the performance of the new method by simulating strong-field ionization of C₆₀ fullerene and discuss final state effects in the orbital reconstruction of planar organic molecules.     

Scale-invariant structure of energy fluctuations in real earthquakes

Earthquakes are obviously complex phenomena associated with complicated spatiotemporal correlations, and they are generally characterized by two power laws: the Gutenberg-Richter (GR) and the Omori-Utsu laws. However, an important challenge has been to explain two apparently contrasting features: the GR and Omori-Utsu laws are scale-invariant and unaffected by energy or time scales, whereas earthquakes occasionally exhibit a characteristic energy or time scale, such as with asperity events. In this paper, three high-quality datasets on earthquakes were used to calculate the earthquake energy fluctuations at various spatiotemporal scales, and the results reveal the correlations between seismic events regardless of their critical or characteristic features. The probability density functions (PDFs) of the fluctuations exhibit evidence of another scaling that behaves as a q-Gaussian rather than random process. The scaling behaviors are observed for scales spanning three orders of magnitude. Considering the spatial heterogeneities in a real earthquake fault, we propose an inhomogeneous Olami-Feder-Christensen (OFC) model to describe the statistical properties of real earthquakes. The numerical simulations show that the inhomogeneous OFC model shares the same statistical properties with real earthquakes.     

Enhancing energy harvesting by coupling monostable oscillators

The performance of a ring of linearly coupled, monostable nonlinear oscillators is optimized towards its goal of acting as energy harvester – through piezoelectric transduction – of mesoscopic fluctuations, which are modeled as Ornstein-Uhlenbeck noises. For a single oscillator, the maximum output voltage and overall efficiency are attained for a soft piecewise-linear potential (providing a weak attractive constant force) but they are still fairly large for a harmonic potential. When several harmonic springs are linearly and bidirectionally coupled to form a ring, it is found that counter-phase coupling can largely improve the performance while in-phase coupling worsens it. Moreover, it turns out that few (two or three) coupled units perform better than more.