The weak theory of monads

We construct a ‘weak’ version EMw(K) of Lack and Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between monads in EMw(K) and composite pre-monads in K is discussed. If K admits Eilenberg-Moore constructions for monads, we define two symmetrical notions of ‘weak liftings’ for monads in K. If moreover idempotent 2-cells in K split, we describe both kinds of weak lifting via an appropriate pseudo-functor EMw(K)→K. Weak entwining structures and partial entwining structures are shown to realize weak liftings of a comonad for a monad in these respective senses. Weak bialgebras are characterized as algebras and coalgebras, such that the corresponding monads weakly lift for the corresponding comonads and also the comonads weakly lift for the monads.     

Mathematical models for the elastic beam with structural damping

In this paper the existence, regularity and sharp estimates for the solutions of an abstract second order evolution equation are proved and applications to models of a (possibly non homogeneous) elastic beam with a frequency-proportional damping are given.     

Spectral coherent-state quantum cryptography

A novel implementation of quantum-noise optical cryptography is proposed, which is based on a simplified architecture that allows long-haul, high-speed transmission in a fiber optical network. By using a single multiport encoder/decoder and 16 phase shifters, this new approach can provide the same confidentiality as other implementations of Yuen's encryption protocol, which use a larger number of phase or polarization coherent states. Data confidentiality and error probability for authorized and unauthorized receivers are carefully analyzed.     

(Co)cyclic (Co)homology of Bialgebroids: An Approach via (Co)monads

For a (co)monad T _l on a category , an object X in , and a functor , there is a (co)simplex in . The aim of this paper is to find criteria for para-(co)cyclicity of Z ^*. Our construction is built on a distributive law of T _l with a second (co)monad T _r on , a natural transformation , and a morphism in . The (symmetrical) relations i and w need to satisfy are categorical versions of Kaygun’s axioms of a transposition map. Motivation comes from the observation that a (co)ring T over an algebra R determines a distributive law of two (co)monads and on the category of R-bimodules. The functor Π can be chosen such that is the cyclic R-module tensor product. A natural transformation is given by the flip map and a morphism is constructed whenever T is a (co)module algebra or coring of an R-bialgebroid. The notion of a stable anti-Yetter-Drinfel’d module over certain bialgebroids, the so-called  ×  _R -Hopf algebras, is introduced. In the particular example when T is a module coring of a  ×  _R -Hopf algebra and X is a stable anti-Yetter-Drinfel’d -module, the para-cyclic object Z _* is shown to project to a cyclic structure on . For a -Galois extension , a stable anti-Yetter-Drinfel’d -module T _S is constructed, such that the cyclic objects and are isomorphic. This extends a theorem by Jara and Ştefan for Hopf Galois extensions. As an application, we compute Hochschild and cyclic homologies of a groupoid with coefficients in a stable anti-Yetter-Drinfel’d module, by tracing it back to the group case. In particular, we obtain explicit expressions for (coinciding relative and ordinary) Hochschild and cyclic homologies of a groupoid. The latter extends results of Burghelea on cyclic homology of groups.     

Colloidal Surface Active Maghemite Nanoparticles for Biologically Safe CrVI Remediation: from Core‐Shell Nanostructures to Pilot Plant Development

The present study is aimed at the exploration of achievable improvements for Cr^VI ex situ and in situ water remediation by using novel naked colloidal maghemite (γ‐Fe₂O₃) nanoparticles (surface active maghemite nanoparticles, SAMNs). The reliability of SAMNs for Cr^VI binding and removal was demonstrated, and SAMN@Cr^VI complex was characterized, as well as the covalent nature of the absorption was unequivocally proved. SAMNs were structurally and magnetically well conserved after Cr^VI binding. Thus, in consideration of their affinity for Cr^VI, SAMNs were exploited in a biological model system, mimicking a real in situ application. The assay evidenced a progressive reduction of revertant colonies of Salmonella typhimurium TA100 strain, as maghemite nanoparticles concentration increased, till the complete suppression of Cr^VI mutagen effect. Finally, an automatic modular pilot system for continuous magnetic removal and recovery of Cr^VI from water is proposed. SAMNs, thanks to their colloidal, binding, and catalytic properties, represent a promising tool as a reliable nanomaterial for water remediation by Cr^VI.     

Recent Advances in Nanotechnology for the Treatment of Melanoma

Melanoma is one of the most aggressive forms of skin cancer, with few possibilities for therapeutic approaches, due to its multi-drug resistance and, consequently, low survival rate for patients. Conventional therapies for treatment melanoma include radiotherapy, chemotherapy, targeted therapy, and immunotherapy, which have various side effects. For this reason, in recent years, pharmaceutical and biomedical research has focused on new sito-specific alternative therapeutic strategies. In this regard, nanotechnology offers numerous benefits which could improve the life expectancy of melanoma patients with very low adverse effects. This review aims to examine the latest advances in nanotechnology as an innovative strategy for treating melanoma. In particular, the use of different types of nanoparticles, such as vesicles, polymers, metal-based, carbon nanotubes, dendrimers, solid lipid, microneedles, and their combination with immunotherapies and vaccines will be discussed.     

Synthesis,characterization, thermal properties and biological activity of diazine-ring containing hydrazones and their metal complexes

Journal of Thermal Analysis and Calorimetry - New coordination compounds have been synthesized by reacting Zn(II) and Co(II) nitrate or acetate in the presence of triethylamine with Schiff-base...     

The Vatican museum and the organic natural products. The Raphael’s frescoes and the “Last Judgment” by Nicolò and Giovanni

Abstract

In the second half of the 90s, alongside the restoration works of the Quattrocentisti (fifteenth century painters) in the Sistine Chapel, it also carried out the restoration of the frescoes of the Stanze di Raffaello. The results of scientific investigations conducted by the Scientific Research Laboratory of the Vatican Museums, previously presented in some assays of study, are summarised and presented in this letter to the Editor for the special issue of Natural Product Research: Natural Products in Cultural Heritage.