New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations, are obtained using the exp_a function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.     

Off‐grid DoA estimation method of wideband signals

In this paper, an off‐grid direction of arrival (DoA) estimation method is proposed for wideband signals. This method is based on the sparse representation (SR) of the array covariance matrix. Similar to the time domain DoA estimation methods, the correlation function of the sources was assumed to be the same and known. A new measurement vector is obtained using the lower‐left triangular elements of the covariance matrix. The DoAs are estimated by quantizing the entire range of continuous angle space into discrete grid points. However, the exact DoAs may be located between two grid points; therefore, this estimation has errors. The accuracy of DoA estimation is improved by the minimization of the difference between the new measurement vector and its estimated values. Simulation results revealed that the proposed method can enhance the DoA estimation accuracy of wideband signals.     

Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

Achieving Rich and Active Alkaline Hydrogen Evolution Heterostructures via Interface Engineering on 2D 1T‐MoS2 Quantum Sheets

Large‐scale production of hydrogen from water‐alkali electrolyzers is impeded by the sluggish kinetics of hydrogen evolution reaction (HER) electrocatalysts. The hybridization of an acid‐active HER catalyst with a cocatalyst at the nanoscale helps boost HER kinetics in alkaline media. Here, it is demonstrated that 1T–MoS₂ nanosheet edges (instead of basal planes) decorated by metal hydroxides form highly active ${\text{edge}}_{{\text{1T‐MoS}}_{\text{2}}}$/ ${\text{edge}}_{\text{Ni}{(\text{OH})}_{\text{2}}}$ heterostructures, which significantly enhance HER performance in alkaline media. Featured with rich ${\text{edge}}_{{\text{1T‐MoS}}_{\text{2}}}$/ ${\text{edge}}_{\text{Ni}{(\text{OH})}_{\text{2}}}$ sites, the fabricated 1T–MoS₂ QS/Ni(OH)₂ hybrid (quantum sized 1T–MoS₂ sheets decorated with Ni(OH)₂ via interface engineering) only requires overpotentials of 57 and 112 mV to drive HER current densities of 10 and 100 mA cm^?2, respectively, and has a low Tafel slope of 30 mV dec^?1 in 1 m KOH. So far, this is the best performance for MoS₂‐based electrocatalysts and the 1T–MoS₂ QS/Ni(OH)₂ hybrid is among the best‐performing non‐Pt alkaline HER electrocatalysts known. The HER process is durable for 100 h at current densities up to 500 mA cm^?2. This work not only provides an active, cost‐effective, and robust alkaline HER electrocatalyst, but also demonstrates a design strategy for preparing high‐performance catalysts based on edge‐rich 2D quantum sheets for other catalytic reactions.     

Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

Molecular structure and granule morphology of native and heat‐moisture‐treated pinhão starch

Pinhão seed is an unconventional source of starch and the pines grow up in native forests of southern Latin America. In this study, pinhão starch was adjusted at 15, 20 and 25% moisture content and heated to 100, 110 and 120 °C for 1 h. A decrease in λ max (starch/iodine complex) was observed as a result of increase in temperature and moisture content of HMT. The ratio of crystalline to amorphous phase in pinhão starch was determined via Fourier transform infra red by taking 1045/1022 band ratio. A decrease in crystallinity occurred as a result of HMT. Polarised light microscopy indicated a loss of birefringence of starch granules under 120 °C at 25% moisture content. Granule size distribution was further confirmed via scanning electron microscopy which showed the HMT effects. These results increased the understanding on molecular and structural properties of HMT pinhão starch and broadened its food and nonfood industrial applications.     

Effect of gums on viability and β‐galactosidase activity of Lactobacillus spp. in milk drink during refrigerated storage

The viability and β‐galactosidase activity of four Lactobacillus strains in milk drink containing gums during 28 days of refrigerated storage at 4 °C were assessed. The population of Lactobacillus rhamnosus GGB101 and Lactobacillus rhamnosus GGB103 were maintained, whereas the population of Lactobacillus reuteri DSM20016 and Lactobacillus reuteri SD2112 significantly decreased. The recommended level of 6 log CFU g^?1 was exceeded for all tested trains throughout storage. The highest viable number of Lactobacillus rhamnosus GGB103 (8.76 ± 0.03 log CFU mL^?1) was obtained in the product containing carrageenan–maltodextrin. The addition of guar–locust bean–carrageenan led to 20‐fold increase in the level of β‐galactosidase activity for L. rhamnosus GGB101 (1208 ± 2.12 Miller units mL^?1) compared to the control (61 ± 2.83 Miller units mL^?1). Our results suggested that gums could be added to milk to improve viability and enhance β‐galactosidase activity of Lactobacillus.