Non-Euler–Lagrangian Pareto-optimality Conditions for Dynamic Multiple Criterion Decision Problems

In this paper the problem of verifying the Pareto-optimality of a given solution to a dynamic multiple-criterion decision (DMCD) problem is investigated. For this purpose, some new conditions are derived for Pareto-optimality of DMCD problems. In the literature, Pareto-optimality is characterized by means of Euler-Lagrangian differential equations. There exist problems in production and inventory control to which these conditions cannot be applied directly (Song 1997). Thus, it is necessary to explore new conditions for Pareto-optimality of DMCD problems. With some mild assumptions on the objective functionals, we develop necessary and/or sufficient conditions for Pareto-optimality in the sprit of optimization theory. Both linear and non-linear cases are considered.     

Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

Reservoir operations optimization via fuzzy criterion decision processes

In this paper, we propose the treatment of complex reservoir operation problems via our newly developed tool of fuzzy criterion decision processes. This novel approach has been shown to be a more flexible and useful analysis tool especially when it is desirable to incorporate an expert’s knowledge into the decision models. Additionally, it has been demonstrated that this form of decision models will usually result in an optimal solution, which guarantees the highest satisfactory degree. We provide a practical exemplification procedure for the models presented as well as an application example.     

Quantitative measurement of collagen methylation by capillary electrophoresis

Collagen methylation has been exploited in various applications involving living cells. We have observed correlation between the collagen methylation with the rate of cell proliferation in three-dimensional (3-D) microenvironment. To quantify the degree of collagen methylation, we have developed a capillary zone electrophoresis method. Using a polyvinyl alcohol-coated fused-silica capillary and UV detection at 200 nm, we have optimized pH and separated the native collagen into three major bands in phosphate buffer (50 mM, pH 2.5) with 0.05% hydroxypropylmethylcellulose. Under these conditions, the methylated collagens were separated into four major bands, which changed with different methylation reaction conditions. We propose an index to quantify the degree of collagen methylation that also correlates with their effects on cell proliferation.     

Transition-state effects in acid-catalyzed aryl epoxide hydrolyses

The hydronium ion-catalyzed hydrolyses of 5-methoxyindene 1,2-oxide and of 6-methoxy-1,2,3,4-tetrohydronaphthalene-1,2-epoxide were each found to yield 75-80% of cis diol and only 20-25% of trans diol as hydrolysis products. The relative stabilities of the cis and trans diols in each system were determined by treating either cis or trans diols with perchloric acid in water solutions and following the approach to an equilibrium cis/trans mixture as a function of time. These studies establish that the trans diol in each system is more stable than the corresponding cis diol. Thus, acid-catalyzed hydrolysis of each epoxide, which proceeds via a carbocation intermediate, yields the less stable cis diol as the major product. Transition-state effects, presumably of a hydrogen-bonding nature, selectively stabilize the transition state for attack of water on the intermediate 2-hydroxy-1-indanyl carbocation leading to the less stable cis diol in this system. Transition-state effects must also be responsible for formation of the less stable cis diol as the major product in the acid-catalyzed hydrolysis of 5-methoxy-1,2,3,4-tetrahydronaphthalene 1,2-epoxide. However, in this system steric effects at the transition state may be more important than hydrogen bonding in determining the cis/trans diol product ratio. The synthesis of 5-methoxyindene 1,2-oxide and a study of its rate of reaction as a function of pH in water and dioxane-water solutions are reported. Both an acid-catalyzed reaction leading to only diol products and a pH-independent reaction yielding 71% of 5-methoxy-2-indanone and 29% of diols are observed; the half-life of its pH-independent reaction in water is only 2.4 s.     

Optically switchable liquid crystal photonic structures

Photo-optic materials offer the possibility of light controlled photonic devices, intelligent and environmentally adaptive optical materials. One strategy for creating these materials is the combination of structure formation through holographic photopolymerization and the variable optical properties of liquid crystals. Holographically patterned, polymer stabilized liquid crystals (HPSLCs) have proven to be useful optical materials. By incorporating photo-optic, azobenzene-derived liquid crystal blends into such material systems, we have generated practical photoresponsive optical materials.     

Fourier multipliers of Lipschitz spaces

Let G denote an infinite, compact, metrizable, 0-dimensional, Abelian group. The following are characterized: (i) the multipliers from one Lipschitz space Lip(α, p; G) to another Lipschitz space Lip(β, q; G) for 0 < α < β < ∞ and 1 ? p, q ? ∞; and (ii) the multipliers from Lip(α, p; G) to Lip(β, q; G) for 0 < β ? α < ∞ and 1 < q ? 2 ? p < ∞. Two special cases of (i), namely the case q = ∞ and the case p = 1, were obtained by the authors in an earlier publication (1981). A. Zygmund (J. Math. Mech.8 (1959), 889–895) and T. Mizuhara (Tôhoku Math. J.24 (1972), 263–268) have characterized the multipliers of certain Lipschitz spaces defined on the circle group.     

Mechanism and nanosize products of the sol-gel reaction using diphenylsilanediol and 3-methacryloxypropyltrimethoxysilane as precursors

We use a first-principles calculation and small-angle neutron scattering (SANS) to investigate the mechanism and the nanosize products of the sol-gel reaction with diphenylsilanediol (DPD) and 3-methacryloxypropyltrimethoxysilane (MEMO) precursors in synthesizing a hybrid waveguide material. It is predicted that switching between a DPD hydroxyl and a MEMO methoxy with a reaction rate of 6.8 x 10(-6) s(-1) at 300 K is the fastest process for the first reaction step, thus generating diphenylmethoxysilanol (DPM) and 3-methacryloxypropyldimethoxysilanol (MEDO) as products. However, we determine that this reaction pathway could be modified by the presence of the H2O released from a catalyst such as Ba(OH)2.H2O. Next, switching between the DPM hydroxyl and the MEDO methoxy is followed to generate diphenyldimethoxysilane (DPDM) and 3-methacryloxypropylmethoxysilanediol (MEMDO). However, condensation between a MEMDO hydroxyl and a DPDM methoxy is found to be most favorable for the third reaction step, which generates the DPDM-MEMDO dimer and CH3OH molecule as products. In a similar fashion, a DPDM methoxy of the DPDM-MEMDO dimer can condense with a MEMDO hydroxyl of the second DPDM-MEMDO dimer to increase the chain, but its reaction rate of 2.8 x 10(-11) s(-1) is predicted to be about 5 times smaller than that between a DPDM methoxy and a MEMDO hydroxyl. This implies that the reaction rate for the larger nanostructures becomes smaller. Additionally, our SANS measurements determine that the final products from our sol-gel reaction are on the nanometer scale, at sizes from 1.76 to 2.36 nm.     

Factorization of Lipschitz functions and absolute convergence of Vilenkin-Fourier series

LetG be a Vilenkin group (i.e., an infinite, compact, metrizable, zero-dimensional Abelian group). Our main result is a factorization theorem for functions in the Lipschitz spaces \(\mathfrak{L}\mathfrak{i}\mathfrak{p}\) (α,p; G). As colloraries of this theorem, we obtain (i) an extension of a factorization theorem ofY. Uno; (ii) a convolution formula which says that \(\mathfrak{L}\mathfrak{i}\mathfrak{p} (\alpha , r; G) = \mathfrak{L}\mathfrak{i}\mathfrak{p} (\beta , l; G)*\mathfrak{L}\mathfrak{i}\mathfrak{p} (\alpha - \beta , r; G)\) for 0<β<α<∞ and 1≤r≤∞; and (iii) an analogue, valid for allG, of a classical theorem ofHardy andLittlewood. We also present several results on absolute convergence of Fourier series defined onG, extending a theorem ofC. W. Onneweer and four results ofN. Ja. Vilenkin andA. I. Rubinshtein. The fourVilenkin-Rubinshtein results are analogues of classical theorems due, respectively, toO. Szász, S. B. Bernshtein, A. Zygmund, andG. G. Lorentz.     

Biomimetic pH/redox dual stimuli‐responsive zwitterionic polymer block poly(L‐histidine) micelles for intracellular delivery of doxorubicin into tumor cells

A series of pH/redox dual stimuli‐responsive poly(2‐methacryloyloxyethyl phosphorylcholine)₂₅‐block‐poly(l ‐histidine)_n (p[MPC])₂₅‐b‐p[His]_n, n = 20, 35, 50, and 75) copolymers consisting of a pH‐responsive p(His)_n block and a biocompatible phospholipid analog p(MPC) block connected by a redox‐responsive disulfide linker have been synthesized. The block copolymers are self‐assembled into uniform micelles (～100 nm) in which doxorubicin (Dox) is efficiently encapsulated. The in vitro release profile shows an enhanced release of Dox at low pH (5.0) in 10 mM glutathione (GSH). The in vitro cell viability assays performed using various cell lines show that the blank hybrid micelles have no acute or intrinsic toxicity. A pH‐dependent cytotoxicity is observed with the Dox‐loaded micelles, especially at pH 5.0. Moreover, confocal microscopy images and flow cytometry results show the pH‐dependent cellular uptake of Dox‐loaded micelles. Therefore, the Dox‐loaded micelles can be considered a good candidate for cancer therapy. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2061–2070