Emission properties of printed organic semiconductor lasers

We investigated the emission properties of a distributed-feedback resonator based on an organic semiconductor patterned by a novel printing technology. We observed the peak splitting of the photonic bandstructure of the periodic grating and extracted the effective refractive index of the outcoupled guided modes. The laser works at the second diffraction order, exhibiting narrow single-mode emission at 637 nm, with a threshold as low as 37 microJ/cm2. The results suggest that direct printing is a promising fabrication technique for optically confined integrated optoelectronics.     

Thiophenes as traps for benzyne. 3. Diaryl sulfides and the role of dipolar intermediates

The reactions of seven thiophenes with benzyne generated from diphenyliodonium-2-carboxylate (DPIC) under a standard set of conditions led among other products to the formation of alpha- and beta-naphthyl phenyl sulfides 2a and 2b from thiophene (1a) and of 2c and 2d from 2-methylthiophene (1b). Dithienyl sulfides 4a-f were produced from the halothiophenes 1c-g. The structures of the naphthyl sulfides were proven by comparison with authentic samples of 2a-f, thus eliminating one of two possible mechanisms of formation. The remaining mechanism involves [4+2]-cycloaddition of benzyne to thiophene or to an S-phenylthiophenium ylide 10 to give the dipolar 2:1 benzyne/thiophene adduct 8 followed by ring-opening. Stevens-like rearrangements of 11, formed from 10 by proton transfer, may also explain the origin of arylated thiophenes such as 12 and 3 found in some reactions of benzynes with thiophene.     

Considerazioni sui metodi approssimati della meçanica non-lineare

Sunto Si espone un metodo che permette di rendere rigorosi, almeno dal punto di vista delle applicazioni, i metodi di integrazione approssimata per le equazioni differenziali dei sistemi autonomi e non autonomi, a un grado di libertà, della meccanica non-lineare. A Giovanni Sansone nel suo 70^mo compleanno Sono lieto di dedicare la presente nota al prof.Giovanni Sansone che, con memorie e trattati, ha notevolmente contribuito al progresso della meccanica non-lineare (D. G).     

Design, analysis, and implementation of a multiprecision polynomial rootfinder

We present the design, analysis, and implementation of an algorithm for the computation of any number of digits of the roots of a polynomial with complex coefficients. The real and the imaginary parts of the coefficients may be integer, rational, or floating point numbers represented with an arbitrary number of digits. The algorithm has been designed to deal also with numerically hard polynomials like those arising from the symbolic preprocessing of systems of polynomial equations, where the degree and the size of the coefficients are typically huge.The algorithm is based on an adaptive strategy which automatically exploits any specific feature of the input polynomial, like its sparsity or the conditioning of its roots, in order to speed up the computation. We introduce different concepts and tools suitably designed to arrive at an adaptive implementation, such as the concepts of root neighborhood, inclusion discs and some inclusion and conditioning theorems for their determination. The main engine for shrinking the inclusion discs is the simultaneous iteration method of Ehrlich–Aberth, complemented with a suitable technique for cluster analysis that is used for getting rid of the slow convergence in case of clustered or multiple roots.The algorithm, implemented in C, relies on the GNU multiprecision package GMP and allows many options. Counting, isolating and approximating all roots in a given set are the main goals that the algorithm provides. Automatic determination of multiplicities and the detection of real or imaginary roots can be selected as well. Polynomials having coefficients with a bounded precision may be processed too. Comparisons with the polynomial rootfinders of the packages Mathematica, Mapleand Pari, performed on a wide class of test polynomials show that our algorithm is generally much faster: in most cases the speedup factor is greater than 10 and, for certain polynomials, it is greater than 1000. The MPSolve package can be downloaded from the numeralgo library of netlib.     

Exponential Times in the One-Dimensional Gross–Pitaevskii Equation with Multiple Well Potential

We present an algorithm for constructing the Wilson operator product expansion (OPE) for perturbative interacting quantum field theory in general Lorentzian curved spacetimes, to arbitrary orders in perturbation theory. The remainder in this expansion is shown to go to zero at short distances in the sense of expectation values in arbitrary Hadamard states. We also establish a number of general properties of the OPE coefficients: (a) they only depend (locally and covariantly) upon the spacetime metric and coupling constants, (b) they satisfy an associativity property, (c) they satisfy a renormalization group equation, (d) they satisfy a certain microlocal wave front set condition, (e) they possess a “scaling expansion”. The latter means that each OPE coefficient can be written as a sum of terms, each of which is the product of a curvature polynomial at a spacetime point, times a Lorentz invariant Minkowski distribution in the tangent space of that point. The algorithm is illustrated in an example.     

Plurisubharmonic geodesics and interpolating sets

Archiv der Mathematik - We apply a notion of geodesics of plurisubharmonic functions to interpolation of compact subsets of $${mathbb {C}}^n$$ . Namely, two non-pluripolar, polynomially closed,...