Covariant derivative of the curvature tensor of pseudo-K\"ahlerian manifolds

It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary group exists on a pseudo-K\"ahlerian manifold; instead of the Weyl tensor one obtains the Bochner tensor. In the present paper, the known decomposition with respect to the pseudo-orthogonal group of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition with respect to the pseudo-unitary group of the covariant derivative of the curvature tensor for pseudo-K\"ahlerian manifolds is obtained. This defines natural classes of spaces generalizing locally symmetric spaces and Einstein spaces. It is shown that the values of the covariant derivative of the curvature tensor for a non-locally symmetric pseudo-Riemannian manifold with an irreducible connected holonomy group different from the pseudo-orthogonal and pseudo-unitary groups belong to an irreducible module of the holonomy group.Comment: the final version accepted to Annals of Global Analysis and Geometr

Genetically engineered protein in hydrogels tailors stimuli-responsive characteristics

A hybrid material that integrates genetically engineered proteins within hydrogels capable of producing a stimulus-responsive action mechanism was analyzed. Parametric studies were undertaken to understand the relationship between the extent of responsive swelling and the amounts of crosslinker and protein used to prepare the hydrogel. The stimuli-responsive hydrogel exhibited three specific swelling stages in response to various ligands offering additional fine-tuned control over a conventional two-stage swelling hydrogel. The prepared material was used in the sensing, and subsequent gating and transport of biomolecules across a polymer network, demonstrating its potential application in microfluidics and miniaturized drug-delivery systems.close15113

Self-assembling of Thermo-Responsive Block Copolymers: Structural, Thermal and Dielectric Investigations

Plethora of amphiphilic polymers and copolymers have been synthesized that form self-assembled structures in aqueous media, resembling the assemblies of biopolymers invented by nature. Such polymeric systems serve as stimuli-responsive materials, i.e. they respond to small external changes in the environmental conditions, which is a common process for biopolymers in living organisms. Temperature is the most widely used stimulus in environmentally responsive polymer systems. Thermoresponsive polymers have attracted much research interest because of their potential applications, which include rheological control additives, thermal affinity separation, controlled drug release, gene therapy and regenerative medicine. On the other hand, they represent model systems for many biological systems, for example for the investigation of the interaction between peptide-like groups and solvents and, thus, for the study of protein stability in aqueous solutions. In this chapter, we provide a comprehensive view on recent investigations on the micellar aggregation and the thermoresponsive behavior of amphiphilic model polymers. Firstly, we will present general characteristics of the thermoresponsive behavior of macromolecules and discuss in more detail their applications with biomedical interest. Next, we will focus on the experimental investigation of thermoresponsive polymers and present, briefly, research outcomes concerning the properties of the well-studied poly(N-isopropylacrylamide) (PNIPAM) polymer. Then, we will present results with respect to the thermoresponsive behavior of a rat her new class of polymers based on the nonionic poly(methoxy diethylene glycol acrylate) (PMDEGA) polymer. Copolymers with various architectures, namely diblock, triblock and star block copolymers are studied, as well as a PMDEGA homopolymer as reference. To that aim, complementary methods were applied, such as small-angle X-ray (SAXS), differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS). Seeking for understanding of fundamental aspects of the macromolecular thermoresponsive behavior, we present, in a comparative way, results obtained on PNIPAM- and PMDEGA-based systems. Characteristic differences between the two series of polymeric solutions are worked out, concerning the self-organization, the width and hysteresis of the transition, and the chain conformat ions during the demixing phase transition