Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces

New convolutions for quadratic-phase Fourier integral operators and their applications

We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann-Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations

Hyers-Ulam-Rassias stability of nonlinear integral equations through the Bielecki metric

We analyse different kinds of stabilities for classes of nonlinear integral equations of Fredholm and Volterra type. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and Hyers-Ulam stabilities for those integral equations. Finite and infinite intervals are considered as integration domains. Those sufficient conditions are obtained based on the use of fixed point arguments within the framework of the Bielecki metric and its generalizations. The results are illustrated by concrete examples

Quantizing higher-spin gravity in free-field variables

We study the formulation of massless higher-spin gravity on AdS$_3$ in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for $W_N$ CFT's: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical $W_N$ charges. Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of $W_\infty[\lambda]$. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate $W_N$ primaries, to all orders in the large central charge expansion.Comment: 31 pages + appendices. V2: typos corrected, reference adde

Disentangling astroglial physiology with a realistic cell model in silico

Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. Our simulations suggest that currents generated by glutamate transporters or K+ channels have negligible distant effects on membrane voltage and that individual astrocytes can successfully handle extracellular K+ hotspots. We show how intracellular Ca2+ buffers affect Ca2+ waves and why the classical Ca2+ sparks-and-puffs mechanism is theoretically compatible with common readouts of astroglial Ca2+ imaging

Transport through a strongly coupled graphene quantum dot in perpendicular magnetic field

We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of around 4.5 meV. We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level. Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.Comment: 6 pages, 4 figure

Cell walls of the dimorphic fungal pathogens Sporothrix schenckii and Sporothrix brasiliensis exhibit bilaminate structures and sloughing of extensive and intact layers

This work was supported by the Fundação Carlos Chagas de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), grants E-26/202.974/2015 and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), grants 229755/2013-5, Brazil. LMLB is a senior research fellow of CNPq and Faperj. NG acknowledged support from the Wellcome Trust (Trust (097377, 101873, 200208) and MRC Centre for Medical Mycology (MR/N006364/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Diffraction from polygonal-conical screens, an operator approach

The aim of this work is to construct explicitly resolvent operators for a class of boundary value problems in diffraction theory. These are formulated as boundary value problems for the three-dimensional Helmholtz equation with Dirichlet or Neumann conditions on a plane screen of polynomial-conical form (including unbounded and multiply-connected screens), in weak formulation. The method is based upon operator theoretical techniques in Hilbert spaces, such as the construction of matrical coupling relations and certain orthogonal projections, which represent new techniques in this area of applications. Various cross connections are exposed, particularly considering classical Wiener-Hopf operators in So\-bo\-lev spaces as general Wiener-Hopf operators in Hilbert spaces and studying relations between the crucial operators in game. Former results are extended, particularly to multiply-connected screens