Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.     

Computation of waveguide scattering matrix near thresholds

A waveguide occupies infinite strip with one or several narrows on a two-dimensional (2D) plane and is governed by the Helmholtz equation with Dirichlet boundary condition. On the waveguide continuous spectrum, which coincides with a half-axis, a scattering matrix is defined. At each point of the continuous spectrum this matrix has finite size, which changes at thresholds. The thresholds form a sequence of positive numbers increasing to infinity. Approximate calculation of the scattering matrix in a threshold vicinity requires special treatment. We discuss and compare two methods of numerical approximation to the scattering matrix near a threshold.     

Controlled Release of Hepatocyte Growth Factor from MPEG‐b‐(PCL‐ran‐PLLA) Diblock Copolymer for Improved Vocal Fold Regeneration

An in situ‐forming gel system comprised of diblock copolymer formed from polyethylene glycol (PEG) and polycaprolactone (PCL) {MPEG‐b‐(PCL‐ran‐PLLA)} could be used in controlled drug delivery for tissue remodeling. The purpose of this study is to demonstrate favorable vocal folds (VF) regeneration by using MPEG‐b‐(PCL‐ran‐PLLA) diblock copolymers (C97L3; CL/LA ratio 97:3) incorporating hepatocyte growth factor (HGF). Gradual release of HGF from C97L3 is detected and biochemical properties of released HGF are maintained. A scar is made with microscissors on both VFs in 32 rabbits, followed by injection of HGF‐only, C97L3‐only, or HGF‐C97L3 composite gel in the left side VF, while the right side VF is left untreated. In vivo fluorescence live imaging system demonstrates that C97L3 enables the sustained release of injected HGF in the scarred VF for 12 weeks. The histological analysis shows increased glycosaminoglycan including hyaluronic acid accumulation and decreased collagen deposition. Videokymographic analysis shows more favorable vibrations of HGF‐C97L3 treated VF mucosa, compared to other treatment groups. In conclusion, the controlled HGF release helps to regulate extracellular matrix synthesis, and leads to the eventual functional improvement of the scarred VF.

     

Evaluation of a novel metal–organic framework as an adsorbent for the extraction of multiclass pesticides from coconut palm (Cocos nucifera L.): An analytical approach using matrix solid‐phase dispersion and liquid chromatography

We report the synthesis, characterization, and application of [Zn(1,4‐benzenedicarboxylate)(H₂O)₂]_n , Zn(1,4‐benzenedicarboxylate)_0.99(NH₂‐1,4‐benzenedicarboxylate)_0.01(H₂O)₂]_n , [Zn(1,4‐benzenedicarboxylate)_0.95(NH₂‐1,4‐benzenedicarboxylate)_0.05(H₂O)₂]_n , and [Zn(1,4‐benzenedicarboxylate)_0.9(NH₂‐1,4‐benzenedicarboxylate)_0.1(H₂O)₂]_n as sorbents for the extraction of multiclass pesticides from coconut palm. Liquid chromatography with ultraviolet diode array detection was used as the analysis technique, and the experiments were performed at one fortification level (0.1 μg/g). The recoveries were 47–67, 51–70, 58–72, and 64–76% for [Zn(1,4‐benzenedicarboxylate)(H₂O)₂]_n , Zn(1,4‐benzenedicarboxylate)_0.99(NH₂‐1,4‐benzenedicarboxylate)_0.01(H₂O)₂]_n , [Zn(1,4‐benzenedicarboxylate)_0.95(NH₂‐1,4‐benzenedicarboxylate)_0.05(H₂O)₂]_n , and [Zn(1,4‐benzenelate)_0.95(NH₂‐1,4‐benzenedicarboxylate)_0.05(H₂O)₂]_n , and [Zn(1,4‐benzenedicarboxylate)_0.9(NH₂‐1,4‐benzenedicarboxylate)_0.1(H₂O)₂]_n , respectively, with relative standard deviation ranging from 1 to 7% (n = 3). Detection and quantification limits were 0.01–0.05 and 0.05–0.2 μg/g, respectively, for the different pesticides studied. The method developed was linear over the range tested (0.01–10.0 μg/g) with r ² > 0.9991. A direct comparison of [Zn(1,4‐benzenedicarboxylate)_0.9(NH₂‐1,4‐benzenedicarboxylate)_0.1(H₂O)₂]_n with the commercially available neutral alumina showed that [Zn(1,4‐benzenedicarboxylate)_0.9(NH₂‐1,4‐benzenedicarboxylate)_0.1(H₂O)₂]_n was a similar extracting phase for the pesticides investigated.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Further results on generalized inverses of tensors via the Einstein product

The notion of the Moore–Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate on this theory by producing a few characterizations of different generalized inverses of tensors. A new method to compute the Moore–Penrose inverse of tensors is proposed. Reverse order laws for several generalized inverses of tensors are also presented. In addition to these, we discuss general solutions of multilinear systems of tensors using such theory.