Central Limit Theorems for the Shrinking Target Problem

Suppose B _i :=B(p,r _i ) are nested balls of radius r _i about a point p in a dynamical system (T,X,μ). The question of whether T ⁱ x∈B _i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if $E_{n}:=\sum_{i=1}^{n} \mu(B_{i})$ diverges then there is a quantitative rate of entry and $\lim_{n\to\infty} \frac{1}{E_{n}} \sum_{j=1}^{n} 1_{B_{i}} (T^{i} x) \to1$ for μ a.e. x∈X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form $\lim_{ n\to\infty} \frac{1}{a_{n}} \sum_{i=1}^{n} [1_{B_{i}} (T^{i} x)-\mu(B_{i})] \to N(0,1)$ (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are $a^{2}_{n} \sim E [\sum_{i=1}^{n} 1_{B_{i}} (T^{i} x)-\mu(B_{i})]^{2}$ . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.     

N,N′-Ethylene-Bridged Bis-2-Aryl-Pyrrolinium Cations to E-Diaminoalkenes: Non-Identical Stepwise Reversible Double-Redox Coupled Bond Activation Reactions

This work presents a stepwise reversible two-electron transfer induced hydrogen shift leading to the conversion of a bis-pyrrolinium cation to an E-diaminoalkene and vice versa. Remarkably, the forward and the reverse reaction, which are both reversible, follow two completely different reaction pathways. Establishing such unprecedented property in this type of processes was possible by developing a novel synthetic route towards the starting dication. All intermediates involved in both the forward and the backward reactions were comprehensively characterized by a combination of spectroscopic, crystallographic, electrochemical, spectroelectrochemical, and theoretical methods. The presented synthetic route opens up new possibilities for the generation of multi-pyrrolinium cation scaffold-based organic redox systems, which constitute decidedly sought-after molecules in contemporary chemistry.     

The notion of observable and the moment problem for $$*$$∗-algebras and their GNS representations

Letters in Mathematical Physics - We address some usually overlooked issues concerning the use of $$*$$-algebras in quantum theory and their physical interpretation. If $${\mathfrak {A}}$$ is a...     

A Zn(II) luminescent complex with a Schiff base ligand: solution,computational and solid state studies

Abstract

A new mononuclear complex of zinc(II), [Zn(HL)₂]?2DMF (H₂L = (E)-N′-((E)-(hydroxyimino)butan-2-ylidene)salicyloylhydrazide, DMF = N,N-dimethylformamide), was prepared and characterized. Single-crystal X-ray crystallography revealed a six-coordinate zinc(II) surrounded by nitrogen of the oxime function and oxygen and distal nitrogens of the acylhydrazone group. This entity also exists in solution as demonstrated by ¹H-NMR and potentiometric titrations. The computational analysis showed that the molecular orbitals involved in the main electronic transitions of the complex species in solution are centered on the ligand with negligible contribution of the metal ion. The photophysical properties of the complex were evaluated in solution and in the solid state. Luminescence studies showed that the solid has a strong emission at 550 nm with a large Stokes shift with respect to absorption. The solid state fluorescence emission is ascribed to ligand-centered and/or ligand-to-ligand charge transfer transitions, following the DFT results in solution. A comparison with a previously reported mononuclear [Zn(HL)₂] allowed the investigation of the influence of DMF molecules in the structural packing and the luminescence properties.     

Boosted feature selectors: a case study on prediction P-gp inhibitors and substrates

Feature selection is commonly used as a preprocessing step to machine learning for improving learning performance, lowering computational complexity and facilitating model interpretation. This paper proposes the application of boosting feature selection to improve the classification performance of standard feature selection algorithms evaluated for the prediction of P-gp inhibitors and substrates. Two well-known classification algorithms, decision trees and support vector machines, were used to classify the chemical compounds. The experimental results showed better performance for boosting feature selection with respect to the standard feature selection algorithms while maintaining the capability for feature reduction.     

Thermodynamics of (1-alkanol + linear monoether) systems

Densities, ρ, and speeds of sound, u, of systems formed by 1-heptanol, or 1-octanol, or 1-decanol and dibutylether have been measured at a temperature of (293.15, 298.15, and 303.15) K and atmospheric pressure using a vibrating tube densimeter and sound analyser Anton Paar model DSA-5000. The ρ and u values were used to calculate excess molar volumes, V^E, and deviations from the ideal behaviour of the thermal expansion coefficient, Δα_p and of the isentropic compressibilities, Δκ_S. The available database on molar excess enthalpies, H^E, and V^E for (1-alkanol + linear monoether) systems was used to investigate interactional and structural effects in such mixtures. The enthalpy of the OH?O bonds is lower for methanol solutions, and for the remainder systems, it is practically independent of the mixture compounds. The V^E variation with the chain length of the 1-alkanol points out the existence of structural effects for systems including longer 1-alkanols. The ERAS model is applied to the studied mixtures. ERAS represents quite accurately H^E and V^E data using parameters which consistently depend on the molecular structure.     

Amperometric Detection of Ethanol Vapors by Screen Printed Electrodes Modified by Paper Crowns Soaked with Room Temperature Ionic Liquids

A convenient assembly recently proposed for screen printed gold electrodes (SPEs) suitable for measurements in gaseous samples is here tested for the analysis of the ethanol content in alcoholic drinks. This assembly involves the use of a circular crown of filter paper, soaked in the room temperature ionic liquid (RTIL) 1-butyl-3-methylimidazolium hydrogen sulfate, which is simply placed upon a disposable screen printed cell, so as to contact the outer edge of the gold disc working electrode, as well as peripheral counter and reference electrodes. The electrical contact between the paper crown soaked in RTIL and the SPE electrode is assured by a gasket and all components are installed in a polylactic acid holder. This assembly provides a portable and disposable electrochemical platform, assembled by the easy immobilization onto a porous and inexpensive supporting material such as paper of a RTIL characterized by profitable electrical conductivity and negligible vapor pressure. The electroanalytical performance of this device was assayed for the flow injection analysis of the ethanol concentration in some real samples of wine and beer and the results obtained are compared with the alcoholic degree reported in the relevant bottle-labels, thus highlighting a substantially satisfactory agreement. Repeatable sharp peaks (RSD=6–8 %) were detected for ethanol over a wide linear range (1–20 % v/v in water) and a detection and quantitation limit of 0.55 % v/v and 1.60 % v/v were inferred for a signal-to-noise ratio of 3 and 10, respectively.     

Immunogenic Cell Death Inducing Metal Complexes for Cancer Therapy

Cancer is one of the deadliest diseases worldwide. Recent statistics have shown that metastases and tumor relapse are the leading causes of cancer-associated deaths. While traditional treatments are able to efficiently remove the primary tumor, secondary tumors remain poorly accessible. Capitalizing on this there is an urgent need for novel treatment modalities. Among the most promising approaches, increasing research interest has been devoted to immunogenic cell death inducing agents that are able to trigger localized cell death of the cancer cells as well as induce an immune response inside the whole organism. Preliminary studies have shown that immunogenic cell death inducing compounds could be able to overcome metastatic and relapsing tumors. Herein, the application of metal complexes as immunogenic cell death inducing compounds is systematically reviewed.