A {\mathsf{D}}-induced duality and its applications

This paper attempts to extend the notion of duality for convex cones, by basing it on a prescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified conic ordering, defined by a convex cone , and the inner-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the -induced duality in the paper. We further introduce the notion of -induced polar sets within the same framework, which can be viewed as a generalization of the -induced dual cones and is convenient to use for some practical applications. Properties of the extended duality, including the extended bi-polar theorem, are proven. Furthermore, attention is paid to the computation and approximation of the -induced dual objects. We discuss, as examples, applications of the newly introduced -induced duality concepts in robust conic optimization and the duality theory for multi-objective conic optimization. Research supported in part by the Foundation ‘Vereniging Trustfonds Erasmus Universiteit Rotterdam’ in The Netherlands, and in part by Hong Kong RGC Earmarked Grants CUHK4174/03E and CUHK418406.     

Peptide-mediated blood-brain barrier transport of polymersomes

A polymeric nanocarrier: Polymersomes tagged with a dodecamer peptide that recognizes gangliosides GM1 and GT1b are shown to cross the blood-brain barrier, both in an in?vitro model and in?vivo. The combination of polymeric vesicles with a small GM1-binding peptide and GM1/GT1b gangliosides as targeting sites for blood-brain barrier transport is unprecedented.     

Core–shell and gradient morphology polymer particles analyzed by X‐ray photoelectron spectroscopy: Effect of monomer feed order

The synthesis of composite latex particles possessing core–shell and gradient morphologies, respectively, using seeded starve‐fed semibatch emulsion polymerization of styrene (St) and methyl methacrylate (MMA) is presented. The focus is on the effect of the monomer feed order on the particle morphology development. The particle morphology is assessed using a novel approach which entails comparing the experimental surface composition as a function of polymerization time (particle growth) obtained by X‐ray photoelectron spectroscopy with the predicted surface composition using a mass balance mathematical model. Both types of composite latexes (core–shell and gradient) feature changes with polymerization time in the oxygen/carbon surface composition which enables one to track the morphology development. Differential scanning calorimetry is also implemented to analyze the extent of phase separation. The monomer feed order is shown to play a crucial role—under the present conditions, gradient and core–shell particles are obtained if the feed order is St/MMA (St fed first), but not if the feed order is reversed. These findings illustrate that thermodynamic factors are important, given that thermodynamically it is more favorable for MMA‐rich chains to occupy the oil–water interface to reduce the interfacial tension. Systems where St is the second stage monomer lead to mixed structures rather than the targeted core–shell or gradient morphology with St‐rich chains at the particle surface. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2513–2526     

On a geometrical construction of the multipler rule

In this paper we make a contribution to the theory of necessary conditions for optimization problems. Tikhomirov has given in [T] a unified necessary condition for mixed (smooth-convex) problems. In this paper we develop the smooth case, one of the two building blocks. We offer a new, geometrical construction giving a necessary condition under minimal assumptions.     

Magnetoelectric effect in cobalt ferrite-barium titanate composites and their electrical properties

CoFe₂O₄-BaTiO₃ composites were prepared using conventional ceramic double sintering process with various compositions. Presence of two phases in the composites was confirmed using X-ray diffraction. The dc resistivity and thermoemf as a function of temperature in the temperature range 300 K to 600 K were measured. Variation of dielectric constant (ɛ′) with frequency in the range 100 Hz to 1 MHz and also with temperature at a fixed frequency of 1 kHz was studied. The ac conductivity was derived from dielectric constant (ɛ′) and loss tangent (tan δ). The nature of conduction is discussed on the basis of small polaron hopping model. The static value of magnetoelectric conversion factor has been studied as a function of magnetic field.     

Introduction to duality in optimization theory

A systematic exposition of duality theory is given on what appears to be the optimal level of generality. A condition is offered which implies that the ideal of duality theory is achieved. For the case of linear programming, our approach leads to two novel features. In the first place, primal and dual LP-problems and complementarity conditions are defined canonically, without choosing a matrix form. In the second place, without deriving the explicit form of the dual problem, we show that the following well-known fact implies that the condition mentioned above holds: the polyhedral set property is invariant under linear maps. We give a new quick algorithmic proof of this fact.The author would like to thank Jan Boone for his helpful comments on a preliminary version of this paper.