Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations

Rotational spectra of ortho-nitrotoluene (2-NT) and para-nitrotoluene (4-NT) have been recorded at low and room temperatures using a supersonic jet Fourier Transform microwave (MW) spectrometer and a millimeter-wave frequency multiplier chain, respectively. Supported by quantum chemistry calculations, the spectral analysis of pure rotation lines in the vibrational ground state has allowed to characterise the rotational energy, the hyperfine structure due to the ¹⁴N nucleus and the internal rotation splittings arising from the methyl group. For 2-NT, an anisotropic internal rotation of coupled −CH₃ and −NO₂ torsional motions was identified by quantum chemistry calculations and discussed from the results of the MW analysis. The study of the internal rotation splittings in the spectra of three NT isomers allowed to characterise the internal rotation potentials of the methyl group and to compare them with other mono-substituted toluene derivatives in order to study the isomeric influence on the internal rotation barrier.     

Iterative Suzuki‐Miyaura Cross‐coupling/Bromo‐desilylation Reaction Sequences for the Assembly of Chemically Well‐defined,Acyclic Oligopyrrole/Benzenoid Hybrids Embodying Mixed Modes of Connectivity

Syntheses of a range of chemically well‐defined oligopyrrole/benzenoid hybrids are described using tandem Suzuki‐Miyaura cross‐coupling/bromo‐desilyation reaction sequences for linking borylated pyrroles, halogenated pyrroles and/or dibromobenzenes to one another. By such means, including iterative variants, a range of all α‐linked, all β‐linked oligopyrroles as well as certain combinations thereof have been assembled, some of them for the first time. The conductivities of iodine‐treated thin films formed from certain such systems have been determined.     

Utilizing a Photocatalysis Process to Achieve a Cathode with Low Charging Overpotential and High Cycling Durability for a Li-O2 Battery

The practical applications of non-aqueous lithium-oxygen batteries are impeded by large overpotentials and unsatisfactory cycling durability. Reported here is that commonly encountered fatal problems can be efficiently solved by using a carbon- and binder-free electrode of titanium coated with TiO₂ nanotube arrays (TNAs) and gold nanoparticles (AuNPs). Ultraviolet irradiation of the TNAs generates positively charged holes, which efficiently decompose Li₂O₂ and Li₂CO₃ during recharging, thereby reducing the overpotential to one that is near the equilibrium potential for Li₂O₂ formation. The AuNPs promote Li₂O₂ formation, resulting in a large discharge capacity. The electrode exhibits excellent stability with about 100 % coulombic efficiency during continuous cycling of up to 200 cycles, which is due to the carbon- and binder-free composition. This work reveals a new strategy towards the development of highly efficient oxygen electrode materials for lithium-oxygen batteries.     

Numerical analysis of space charge effects in electron bunches at laser-driven plasma accelerators

Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can reach many kA peak current, over short distances. Space charge issues, even in transport lines as simple as a drift section, have to be carefully taken into account since they can degrade the beam quality, preventing any further application of such electron beams. We analyse the space charge effects within an electron bunch with numerical simulations in order to assess their effect on the beam. We use LPA beam parameters published in previous experimental studies. These studies can give an indication of the working point where space charge can dominate the beam dynamics and has to be taken into account in the application of such beams.     

Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems

Due to their fundamental nature and numerous applications, sphere constrained polynomial optimization problems have received a lot of attention lately. In this paper, we consider three such problems: (i) maximizing a homogeneous polynomial over the sphere; (ii) maximizing a multilinear form over a Cartesian product of spheres; and (iii) maximizing a multiquadratic form over a Cartesian product of spheres. Since these problems are generally intractable, our focus is on designing polynomial-time approximation algorithms for them. By reducing the above problems to that of determining the L ₂-diameters of certain convex bodies, we show that they can all be approximated to within a factor of Ω((log n/n) ^d/2–1) deterministically, where n is the number of variables and d is the degree of the polynomial. This improves upon the currently best known approximation bound of Ω((1/n) ^d/2–1) in the literature. We believe that our approach will find further applications in the design of approximation algorithms for polynomial optimization problems with provable guarantees.     

Failure of the Hasse principle for Enriques surfaces

We construct an Enriques surface X over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer–Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on X, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.     

An algebraic slice in the coadjoint space of the Borel and the Coxeter element

Let g be a complex simple Lie algebra and b a Borel subalgebra. The algebra Y of polynomial semi-invariants on the dual b^? of b is a polynomial algebra on rank g generators (Grothendieck and Dieudonné (1965–1967)) [16]. The analogy with the semisimple case suggests there exists an algebraic slice to coadjoint action, that is an affine translate y+V of a vector subspace of b^? such that the restriction map induces an isomorphism of Y onto the algebra R[y+V] of regular functions on y+V. This holds in type A and even extends to all biparabolic subalgebras (Joseph (2007)) [20]; but the construction fails in general even with respect to the Borel. Moreover already in type C(2) no algebraic slice exists.Very surprisingly the exception of type C(2) is itself an exception. Indeed an algebraic slice for the coadjoint action of the Borel subalgebra is constructed for all simple Lie algebras except those of types B(2m), C(n) and F(4).Outside type A, the slice obtained meets an open dense subset of regular orbits, even though the special point y of the slice is not itself regular. This explains the failure of our previous construction.     

Two-dimensional quaternion wavelet transform

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several examples of the CQWT. As an application we derive a Heisenberg type uncertainty principle for these extended wavelets.     

Infinite Random Geometric Graphs

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ? (0, 1){p \in (0, 1)} if the metric distance between the vertices is below a given threshold. For certain choices of V as a countable dense set in \mathbbRⁿ{\mathbb{R}^n} equipped with the metric derived from the L _∞-norm, it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR _n , is characterized by a geometric analogue of the existentially closed adjacency property, and we give a deterministic construction of GR _n . In contrast, we show that infinite random geometric graphs in \mathbbR²{\mathbb{R}^{2}} with the Euclidean metric are not necessarily isomorphic.