The sequential differentiation and its applications in the optimal control problems

Using the sequential approach, we define a certain generalization of the operator derivative. We establish the necessary extremum condition in terms of the sequential derivative. As examples we consider the optimal control problems for systems governed by partial nonlinear differential equations of several kinds.     

Energy and NEPS of graphs

The energy of a graph is the sum of the absolute values of the eigenvalues of the graph. We study the energy of the noncomplete extended p-sum (NEPS) of the graphs, a very general composition of the graphs in which the special case is the product of graphs. We show that the energy of the product of graphs is the product of the energy of graphs, and how this result may be used to construct arbitrarily large families of noncospectral connected graphs having the same number of vertices and the same energy. Further, unlike the product, we show that the energy of any other NEPS of the graphs cannot be represented as a function of the energy of starting graphs.     

Metal Supported Zeolite for Heavy Aromatics Transalkylation Process

Aiming at improving the catalytic activity, benzene product purity, and catalyst stability during heavy transalkylation processes, strategies invoking startup procedures and catalyst system designs are summarized and discussed in this review. In particular, recent advances in the developments and catalytic performances of the on-line sulfiding technique, the selective pre-coking startup procedure, and a versatile dual-bed catalyst system design were compared and discussed.     

On product form tandem structures

This paper is written in honour to A. Hordijk. It establishes product form results for a generic and instructive multi-class tandem queue with blocking, to which A. Hordijk has directly and indirectly contributed. First, a sufficient and necessary product form characterization is provided. Next, three special cases are briefly presented. These illustrate the possibility of product forms despite finite capacity constraints (blocking), unproportional processor sharing mechanisms and resource contentions (such as for access control). The results are partially new and of interest for present-day applications. In essence these rely upon the pioneering work by A. Hordijk     

Positive self-adjoint operators generated by products of differential expressions

Under the assumption of the product τ:=l⁺l of the regular differential expression l and its adjoint l⁺, being well-formed, a complete characterization of all the positive self-adjoint extensions of the minimal operator generated by τ in terms of boundary conditions is given.     

Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints

In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form 0 ∈ G(x) + Q(x), where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the Palais-Smale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation. Dedicated to Jiří V. Outrata on the occasion of his 60th birthday. This research was partly supported by the National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the Australian Research Council under grant DP-0451168.     

Enhanced Self‐Renewal and Accelerated Differentiation of Human Fetal Neural Stem Cells Using Graphene Oxide Nanoparticles

Graphene oxide (GO) has received increasing attention in bioengineering fields due to its unique biophysical and electrical properties, along with excellent biocompatibility. The application of GO nanoparticles (GO‐NPs) to engineer self‐renewal and differentiation of human fetal neural stem cells (hfNSCs) is reported. GO‐NPs added to hfNSC culture during neurosphere formation substantially promote cell‐to‐cell and cell‐to‐matrix interactions in neurospheres. Accordingly, GO‐NP‐treated hfNSCs show enhanced self‐renewal ability and accelerated differentiation compared to untreated cells, indicating the utility of GO in developing stem cell therapies for neurogenesis.

     

Comparative Study of Osteogenic Activity of Multilayers Made of Synthetic and Biogenic Polyelectrolytes

Polyelectrolyte multilayer (PEM) coatings on biomaterials are applied to tailor adhesion, growth, and function of cells on biomedical implants. Here, biogenic and synthetic polyelectrolytes (PEL) are used for layer‐by‐layer assembly to study the osteogenic activity of PEM with human osteosarcoma MG‐63 cells in a comparative manner. Formation of PEM is achieved with biogenic PEL fibrinogen (FBG) and poly‐l ‐lysine (PLL) as well as biotinylated chondroitin sulfate (BCS) and avidin (AVI), while poly(allylamine hydrochloride) (PAH) and polystyrene sulfonate (PSS) represent a fully synthetic PEM used as a reference system here. Surface plasmon resonance measurements show highest layer mass for FBG/PLL and similar for PSS/PAH and BCS/AVI systems, while water contact angle and zeta potential measurements indicate larger differences for PSS/PAH and FBG/PLL but not for BCS/AVI multilayers. All PEM systems support cell adhesion and growth and promote osteogenic differentiation as well. However, FBG/PLL layers are superior regarding MG‐63 cell adhesion during short‐term culture, while the BCS/AVI system increases alkaline phosphatase activity in long‐term culture. Particularly, a multilayer system based on affinity interaction like BCS/AVI may be useful for controlled presentation of biotinylated growth factors to promote growth and differentiation of cells for biomedical applications.

     

Electroactive 3D Scaffolds Based on Silk Fibroin and Water‐Borne Polyaniline for Skeletal Muscle Tissue Engineering

Silk fibroin (SF) with good biocompatibility and degradability has great potential for tissue engineering. However, the SF based scaffolds lack the electroactivity to regulate the myogenic differentiation for the regeneration of muscle tissue, which is sensitive to electrical signal. Herein, a series of electroactive biodegradable scaffolds based on SF and water‐soluble conductive poly(aniline‐co‐N‐(4‐sulfophenyl) aniline) (PASA) via a green method for skeletal muscle tissue engineering are designed. SF/PASA scaffolds are prepared by vortex of aqueous solution of SF and PASA under physiological condition. Murine‐derived L929 fibroblast and C2C12 myoblast cells are used to evaluate cytotoxicity of SF/PASA scaffolds. Moreover, myogenic differentiation of C2C12 cells is investigated by analyzing the morphology of myotubes and related gene expression. These results suggest that electroactive SF/PASA scaffolds with a suitable microenvironment, which can enhance the myogenic differentiation of C2C12 cells, have a great potential for skeletal muscle regeneration.