The influence of the first integrals and the rolling resistance model on tippe top inversion

Nonlinear Dynamics - In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is...     

Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

Mechanism and rate constants of the CH2 + CH2CO reactions in triplet and singlet states: A theoretical study

Ab initio and density functional CCSD(T)-F12/cc-pVQZ-f12//B2PLYPD3/6-311G** calculations have been performed to unravel the reaction mechanism of triplet and singlet methylene CH₂ with ketene CH₂CO. The computed potential energy diagrams and molecular properties have been then utilized in Rice–Ramsperger–Kassel–Marcus-Master Equation (RRKM-ME) calculations of the reaction rate constants and product branching ratios combined with the use of nonadiabatic transition state theory for spin-forbidden triplet-singlet isomerization. The results indicate that the most important channels of the reaction of ketene with triplet methylene lead to the formation of the HCCO + CH₃ and C₂H₄ + CO products, where the former channel is preferable at higher temperatures from 1000 K and above. In the C₂H₄ + CO product pair, the ethylene molecule can be formed either adiabatically in the triplet electronic state or via triplet-singlet intersystem crossing in the singlet electronic state occurring in the vicinity of the CH₂COCH₂ intermediate or along the pathway of CO elimination from the initial CH₂CH₂CO complex. The predominant products of the reaction of ketene with singlet methylene have been shown to be C₂H₄ + CO. The formation of these products mostly proceeds via a well-skipping mechanism but at high pressures may to some extent involve collisional stabilization of the CH₃CHCO and cyclic CH₂COCH₂ intermediates followed by their thermal unimolecular decomposition. The calculated rate constants at different pressures from 0.01 to 100 atm have been fitted by the modified Arrhenius expressions in the temperature range of 300–3000 K, which are proposed for kinetic modeling of ketene reactions in combustion. © 2018 Wiley Periodicals, Inc.     

Identification and Directed Development of Non‐Organic Catalysts with Apparent Pan‐Enzymatic Mimicry into Nanozymes for Efficient Prodrug Conversion

Nanozymes, nanoparticles that mimic the natural activity of enzymes, are intriguing academically and are important in the context of the Origin of Life. However, current nanozymes offer mimicry of a narrow range of mammalian enzymes, near‐exclusively performing redox reactions. We present an unexpected discovery of non‐proteinaceous enzymes based on metals, metal oxides, 1D/2D‐materials, and non‐metallic nanomaterials. The specific novelty of these findings lies in the identification of nanozymes with apparent mimicry of diverse mammalian enzymes, including unique pan‐glycosidases. Further novelty lies in the identification of the substrate scope for the lead candidates, specifically in the context of bioconversion of glucuronides, that is, human metabolites and privileged prodrugs in the field of enzyme‐prodrug therapies. Lastly, nanozymes are employed for conversion of glucuronide prodrugs into marketed anti‐inflammatory and antibacterial agents, as well as “nanozyme prodrug therapy” to mediate antibacterial measures.     

Electrochemical methods for analysing and controlling charge transfer at the electrode–tissue interface

There have been rapid advances in the development of new materials for use in electrode–tissue interfacing. The development of conducting polymers, conducting hydrogels, carbon nanotubes, graphene and other conducting materials has provided a rich landscape for controlling charge transfer at the electrode–tissue interface and hence to monitor and manipulate cell behaviour. These materials have been used in tissue-engineered constructs to direct and control cell proliferation, growth and differentiation. However, their translation to clinical devices has been less successful. In this review, the use of electroanalytical techniques to develop an understanding of charge transfer at the electrode–tissue interface is discussed. In particular, the impact of solution and electrode conditions on charge injection capacity is demonstrated. The importance of standardised testing methods and the correlation of electrochemical and electrophysiological performance show the limitations of empirical studies and help define key electrode properties for clinical devices. The development of a sound theoretical basis for charge transfer at this increasingly important interface is being advocated to improve clinical outcomes and device lifetime and reduce power usage.     

“Printing” DNA Strand Patterns on Small Molecules with Control of Valency,Directionality, and Sequence

The incorporation of synthetic molecules as corner units in DNA structures has been of interest over the last two decades. In this work, we present a facile method for generating branched small molecule‐DNA hybrids with controllable valency, different sequences, and directionalities (5′–3′) using a “printing” process from a simple 3‐way junction structure. We also show that the DNA‐imprinted small molecule can be extended asymmetrically using polymerase chain reaction (PCR) and can be replicated chemically. This strategy provides opportunities to achieve new structural motifs in DNA nanotechnology and introduce new functionalities to DNA nanostructures.     

Fluorescent core-shell polymer particles containing luminophore dyes: synthesis and optical response to acetone

Monodisperse dye-containing crosslinked particles are promising for application in novel optical chemical sensors due to their intrinsic sensitivity. However, preparation of these particles in aqueous media still remains a challenge, since luminophores inhibit radical processes or else cannot embed into polymer chains because of difference in monomer reactivity ratios. In this work, novel dye-containing monodisperse crosslinked particles were prepared and characterized. In order to obtain dye-containing monodisperse crosslinked particles, we studied seed copolymerization of styrene in the presence of divinylbenzene. The influence of nature and concentration of the used comonomers and co-solvents on shape, size distributions and surface characteristics of the particles formed was investigated. Shapes and diameters of the particles were analyzed by DLS, TEM and SEM. The data of SEM and optical spectroscopy studies demonstrated that the synthesized particles were able to self-assemble into thin-film three-dimensional ordered structures. Finally, the structures under study are promising for development of sensor devices with optical response to acetone.     

Aqueous Electrochemical Reduction of Carbon Dioxide and Carbon Monoxide into Methanol with Cobalt Phthalocyanine

Conversion of CO₂ into valuable molecules is a field of intensive investigation with the aim of developing scalable technologies for making fuels using renewable energy sources. While electrochemical reduction into CO and formate are approaching industrial maturity, a current challenge is obtaining more reduced products like methanol. However, literature on the matter is scarce, and even more for the use of molecular catalysts. Here, we demonstrate that cobalt phthalocyanine, a well‐known catalyst for the electrochemical conversion of CO₂ to CO, can also catalyze the reaction from CO₂ or CO to methanol in aqueous electrolytes at ambient conditions of temperature and pressure. The studies identify formaldehyde as a key intermediate and an unexpected pH effect on selectivity. This paves the way for establishing a sequential process where CO₂ is first converted to CO which is subsequently used as a reactant to produce methanol. Under ideal conditions, the reaction shows a global Faradaic efficiency of 19.5 % and chemical selectivity of 7.5 %.     

The maximum size of short character sums

The Ramanujan Journal - In the present note, we prove new lower bounds on large values of character sums $$\varDelta (x,q):=\max _{\chi \ne \chi _0} \big \vert \sum _{n\le x} \chi (n)\big \vert $$...