MAPLE deposition of Mn(III) metalloporphyrin thin films: Structural, topographical and electrochemical investigations

We report the deposition by MAPLE of metallized nanostructured (5,10,15,20-tetraphenyl)porphinato manganese(III) chloride thin films onto gold screen-printed electrodes, or 〈1 1 1〉 Si substrates. The deposited nanostructures were characterized by atomic force microscopy and exhibited globular structures with average diameters decreasing with laser fluence. Raman spectroscopy showed that no major decomposition appeared. We have investigated the Mn(III)-metalloporphyrin thin films by cyclic voltammetry in order to evaluate the potential bio/chemosensing activity on dopamine neurotransmitter analyte. We have found that the manganese(III)-porphyrin is appropriate as a single mediator for dopamine sensing in the specific case of gold screen-printed electrodes.     

Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

We study a non-homogeneous boundary value problem in a smooth bounded domain in R^N. We prove the existence of at least two non-negative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.     

Eigenvalue problems in Orlicz–Sobolev spaces for rapidly growing operators in divergence form

Eigenvalue problems involving the p-Laplacian and rapidly growing operators in divergence form are studied in an Orlicz–Sobolev setting. An asymptotic analysis of these problems leads to a full characterization of the spectrum of an exponential type perturbation of the Laplace operator.     

On Some Mean Value Points Defined by Divided Differences and Their Hyers–Ulam Stability

The aim of this paper is to establish some stability results involving generalized divided differences.     

The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank-one tensor u ^⊗k ∈ (ℝⁿ)^⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ  _Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn^{(k − 2)/4} , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n^{(k − 2)/4} . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ^{−1/(k − 1)}) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ^{−1/(k − 2)}) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.     

Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming

The problem of finding minima of weakly sequentially lower semicontinuous functions on reflexive Banach spaces is studied by means of convex and nonconvex subdifferentials. Finding a descent direction for a non-stationary point is a question of importance for many optimization algorithms. The existence or non-existence of such a direction is clarified through several theorems and a series of selective examples. For the general problem, a notion called radius of descent is proposed and shown to be useful for the analysis related to descent directions.     

Mathematical modeling of two-photon thermal fields in laser–solid interaction

In this paper, we have developed an analytical model to study the temperature distributions in IR optical materials heated by laser pulses. Our model takes into account the two-photon absorption (TPA). The calculations are based on a three-dimensional model of heat diffusion in solids using the integral transform method. We find out the rigorous analytical expression of the thermal field when one considers both one- and two-photon absorption. The model is valid for any laser–solid system whose interaction can be described by the generalized Beer–Lambert law. Specific results are presented for an application of the model to ZnSe sample. We find out that TPA can produce detectable temperature variation.