Phase clustering in complex networks of delay-coupled oscillators

We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution of the linear system for non-linear couplings. Taking advantage of the form of the solution, we propose a frequency adaptation rule to achieve perfect synchronization. We also propose a mean-field theory for uncorrelated random networks that proves to be pretty accurate to predict phase synchronization in real topologies, as for example, the Caenorhabditis elegans or the autonomous systems connectivity.     

$${\mathbb{Z}_2\mathbb{Z}_4}$$-linear codes: rank and kernel

A code C{{\mathcal C}} is \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given.     

Instabilities in optically pumped infrared lasers

The unstable emission of an optically pumped FIR gas laser is theoretically analysed through numerical resolution of the associated Maxwell-Bloch equations. The instability domain in the main control parameters space is determined and an example of chaotic behaviour is examined.     

Error estimates for three-dimensional Stokes problem with non-standard boundary conditions

This work is devoted to the optimal and a posteriori error estimates of the Stokes problem with some non-standard boundary conditions in three dimensions. The variational formulation is decoupled into a system for the velocity and a Poisson equation for the pressure. The velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. Next, we establish optimal a posteriori estimates.     

On the 2-adic valuation of the cardinality of elliptic curves over finite extensions of $$\mathbb {F}_{\varvec{q}} $$

In this paper we study the difference between the 2-adic valuations of the cardinalities \( \# E( \mathbb {F}_{q^k} ) \) and \( \# E( \mathbb {F}_q ) \) of an elliptic curve E over \( \mathbb {F}_q \). We also deduce information about the structure of the 2-Sylow subgroup \( E[ 2^\infty ]( \mathbb {F}_{q^k} ) \) from the exponents of \( E[ 2^\infty ]( \mathbb {F}_q ) \).     

The impact of integrated STEM professional development on teacher quality

This study of a state‐funded, 3‐year implementation of an integrated STEM professional development (PD) program for teachers from two middle schools in the midwestern U.S. examined if participants in the PD were enabled to transform their practice and perceptions of STEM. An integrated STEM approach includes a focus on the STEM disciplines, along with leveraging social studies/history and English/language arts as important context and tools for solving society’s biggest challenges. Findings in this study indicated that teachers implemented more effective STEM teaching strategies and had more positive perceptions regarding STEM overall. Further, participants became more aware of their personal needs for resources and support to teach through integrated STEM. Implications for research and practice are discussed.     

Coherence-polarization mixing in resonance gratings

We show, using rigorous diffraction theory, that resonance gratings can be used to transfer partial spatial correlation to partial polarization even if the incident light beam is fully polarized. The phenomenon is based on the fact that either of the two orthogonal polarization components can be coupled into the leaky waveguide mode, leading to a strong phase delay, while the other one is reflected without being coupled into the grating. Numerical demonstrations are based on a Gaussian Schell-model beam and a grating analysis performed by rigorous Fourier modal method.     

Investigation of Lewis Acid versus Lewis Base Catalysis in Asymmetric Cyanohydrin Synthesis

The asymmetric addition of trimethylsilyl cyanide to aldehydes can be catalysed by Lewis acids and/or Lewis bases, which activate the aldehyde and trimethylsilyl cyanide, respectively. It is not always apparent from the structure of the catalyst whether Lewis acid or Lewis base catalysis predominates. To investigate this in the context of using salen complexes of titanium, vanadium and aluminium as catalysts, a Hammett analysis of asymmetric cyanohydrin synthesis was undertaken. When Lewis acid catalysis is dominant, a significantly positive reaction constant is observed, whereas reactions dominated by Lewis base catalysis give much smaller reaction constants. [{Ti(salen)O}₂] was found to show the highest degree of Lewis acid catalysis, whereas two [VO(salen)X] (X=EtOSO₃ or NCS) complexes both displayed lower degrees of Lewis acid catalysis. In the case of reactions catalysed by [{Al(salen)}₂O] and triphenylphosphine oxide, a non‐linear Hammett plot was observed, which is indicative of a change in mechanism with increasing Lewis base catalysis as the carbonyl compound becomes more electron‐deficient. These results suggested that the aluminium complex/triphenylphosphine oxide catalyst system should also catalyse the asymmetric addition of trimethylsilyl cyanide to ketones and this was found to be the case.     

Noncovalent Axial I⋅⋅⋅Pt⋅⋅⋅I Interactions in Platinum(II) Complexes Strengthen in the Excited State

Coordination compounds of platinum(II) participate in various noncovalent axial interactions involving metal center. Weakly bound axial ligands can be electrophilic or nucleophilic; however, interactions with nucleophiles are compromised by electron density clashing. Consequently, simultaneous axial interaction of platinum(II) with two nucleophilic ligands is almost unprecedented. Herein, we report structural and computational study of a platinum(II) complex possessing such intramolecular noncovalent I⋅⋅⋅Pt⋅⋅⋅I interactions. Structural analysis indicates that the two iodine atoms approach the platinum(II) center in a “side-on” fashion and act as nucleophilic ligands. According to computational studies, the interactions are dispersive, weak and anti-cooperative in the ground electronic state, but strengthen substantially and become partially covalent and cooperative in the lowest excited state. Strengthening of I⋅⋅⋅Pt⋅⋅⋅I contacts in the excited state is also predicted for the sole previously reported complex with analogous axial interactions.     

New nucleoside analogs from 2-amino-9-(beta-D-ribofuranosyl)purine

Four novel derivatives of 2-amino-9-(beta-D-ribofuranosyl)purine (1) were synthesised and fully characterised. When 1 was reacted with chloroacetaldehyde (a), 2-chloropropanal (b), bromomalonaldehyde (c) and a mixture of chloroacetaldehyde + malonaldehyde (d), 3-(beta-D-ribofuranosyl)-imidazo-[1,2a]purine (2), 3-(beta-D-ribofuranosyl)-5-methylimidazo-[1,2a]purine (3), 3-(beta-D-ribofuranosyl)-5-formylimidazo-[1,2a]purine (4) and 9-(beta-D-ribofuranosyl)-2-(3,5-diformyl-4-methyl-1,4-dihydro-1-pyridyl)purine (5) were formed, respectively. The products were isolated, purified by chromatography and characterised by MS, complete NMR assignment as well as fluorescence and UV spectroscopy. The yields of these reactions were moderate (14-20%). The fluorescence properties differed from those of the starting compound and the quantum yields were considerably lower.