A numerical method for nonconvex multi-objective optimal control problems

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.     

Synthesis and Spectrophotometric PH Sensing Applications of Poly-2-[4-(diethylaminophenyl)imino]-5-nitro-phenol and its Schiff Base Monomer for Two Different PH Ranges

Poly-2-[4-(diethylaminophenyl)imino]-5-nitro-phenol (PEAPINP) and 2-[4-(diethylaminophenyl)imino]-5-nitro-phenol (EAPINP) were prepared as new pH sensors. Spectrophotometric and spectrofluorometric response of the novel sensors in various p^H values were investigated. EAPINP has the ability to respond linearly at alkaline P^H values, 8 to 9, and can be utilized in absorption and wavelength radiometric methods. PEAPINP has the ability to respond linearly at lower pH values, 6 to 7, and can be used as an alternative pH sensor in this range. The new sensors are yellow-colored in acidic and neutral media and red-colored in alkaline P^Hs. With their colorimetric responses at different pH ranges EAPINP and PEAPINP can be used to develop color-tunable P^H sensors.     

Syntheses and pH sensing applications of imine-coupled phenol and polyphenol species derived from 2-amino-4-nitrophenol

Developing of new generation optical polymeric pH sensors has increasing importance due to their stable structures. Available polymeric sensors for different pH ranges are already needed. In the present study new kinds of monomeric and polymeric absorption pH sensors (HBANP and PHBANP) derived from 2-amino-4-nitrophenol were prepared. The novel sensors were investigated in various pH values using spectrophotometric, spectrofluorometric, and electrochemical techniques. The sensors showed sigmoidal correlations vs. pH range in optical measurements. These correlations were improved as mathematical formula to obtain the solution pH. HBANP and PHBANP differed from each other by response fields. HBANP had a sharp absorption increase between the pH of 6.5→7.5 while PHBANP spectrophotometrically responded at lower pHs. HBANP was colorless in acidic pHs, yellow-colored in neutral media and red-colored in alkaline pHs. With its colorimetric responses in various pHs HBANP can be used to develop color-tunable pH sensors. Electrochemical oxidation peak potentials and currents also particularly changed in various pHs.     

Variations of microhardness with solidification parameters and electrical resistivity with temperature for Al-Cu-Ag eutectic alloy

Al-Cu-Ag eutectic alloy was directionally solidified upwards with different growth rates (1.83-498.25 μm/s) at a constant temperature gradient (8.79 K/mm) and with different temperature gradients (3.99-8.79 K/mm) at a constant growth rate (8.30 μm/s) by using a Bridgman type directional solidification apparatus. The dependence of microhardness (HV) on the growth rate (V), temperature gradient (G) and microstructure parameter (λ) were found to be HV = k₁ V^0.10, HV = k₂ G^0.13 and HV = k₃ λ^−0.22, respectively. The electrical resistivity of the Al-Cu-Ag eutectic cast alloy increases linearly with the temperature in the range of 300-780 K. The enthalpy of fusion and specific heat change during melting for same alloy were also determined to be 223.8 J/g, and 0.433 J/g K, respectively by a differential scanning calorimeter from heating curve during the transformation from eutectic solid to eutectic liquid.     

Determination of the Unknown Cauchy Data in a Linear Parabolic Problem from the Measured Data at the Final Time

The problem of determining the initial value u(x, 0) = μ ₀(x) in the parabolic equation u _t = (k(x)u _x (x, t)) _x + F(x, t) from the final overdetermination μ _T (x) = u(x, T) is formulated. It is proved that the Fréchet derivative of the cost functional ${{J(\mu_0) = \|\mu_T(x) - u(x, T)\|_0^2}}$ can be formulated via the solution of the adjoint parabolic problem. Lipschitz continuity of the gradient is proved. The existence of a quasisolution of the considered inverse problem is proved. A monotone iteration scheme is obtained based on the gradient method.     

Spectral properties of some regular boundary value problems for fourth order differential operators

In this paper we consider the problem $\begin{gathered} y^{iv} + p_2 (x)y'' + p_1 (x)y' + p_0 (x)y = \lambda y,0 < x < 1, \hfill \\ y^{(s)} (1) - ( - 1)^\sigma y^{(s)} (0) + \sum\limits_{l = 0}^{s - 1} {\alpha _{s,l} y^{(l)} (0) = 0,} s = 1,2,3, \hfill \\ y(1) - ( - 1)^\sigma y(0) = 0, \hfill \\ \end{gathered} $ where λ is a spectral parameter; p _j (x) ∈ L ₁(0, 1), j = 0, 1, 2, are complex-valued functions; α _s;l , s = 1, 2, 3, $l = \overline {0,s - 1} $ , are arbitrary complex constants; and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established in the case α _3,2 + α _1,0 ≠ α _2,1. It is proved that the system of root functions of this spectral problem forms a basis in the space L _p (0, 1), 1 < p < ∞, when α _3,2+α _1,0 ≠ α _2,1, p _j (x) ∈ W ₁ ^j (0, 1), j = 1, 2, and p ₀(x) ∈ L ₁(0, 1); moreover, this basis is unconditional for p = 2.     

On lifting singular curves

The aim of this note is to lift singular curves of a certain type to characteristic zero. The liftings are obtained as suitable pushouts and the corresponding relative jacobians are identified as rigidifed Picard functors.     

Orientation in Nematic Liquid Crystals Doped with Orange Dyes and Effect of Carbon Nanoparticles

研究了掺杂两种分散染料橙的向列型液晶E7的性质以及碳纳米粒子(单壁碳纳米管或富勒烯C₆₀)的影响. 两种分散染料橙11和13具有较高的溶解度和有序参数,被作为掺杂剂同时使用. 与掺杂单染料相比,同时加入两种染料橙使液晶的有序参数明显提高. 与纯液晶相比,掺杂可引起向列相向各向同性相转变温度的升高.     

NEURAL MODELS FOR THE BROADSIDE-COUPLED V-SHAPED MICROSHIELD COPLANAR WAVEGUIDES

This article presents a new approach based on multilayered perceptron neural networks (MLPNNs) to calculate the odd-and even-mode characteristic impedances and effective permittivities of the broadside-coupled V-shaped microshield coplanar waveguides (BC-VSMCPWs). Six learning algorithms, bayesian regulation (BR), Levenberg-Marquardt (LM), quasi-Newton (QN), scaled conjugate gradient (SCG), resilient propagation (RP), and conjugate gradient of Fletcher-Powell (CGF), are used to train the MLPNNs. The neural results are in very good agreement with the results reported elsewhere. When the performances of neural models are compared with each other, the best and worst results are obtained from the MLPNNs trained by the BR and CGF algorithms, respectively.