Small values of signed harmonic sums

For every $\tau \in \mathbb{R}$ and every integer N, let ${\mathfrak{m}}_N(\tau )$ be the minimum of the distance of τ from the sums ${\sum }_{n=1}^N{s}_n/n$, where $s_1,\dots ,s_n\in \{?1,+1\}$. We prove that ${\mathfrak{m}}_N(\tau )<\exp ?(?C{(\log ?N)}^2)$, for all sufficiently large positive integers N (depending on C and τ), where C is any positive constant less than $1/\log ?4$.     

Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods

This paper deals with the modelling of pedestrian dynamics at the entry of a metro station by means of the thermostatted kinetic theory framework. Specifically, the model depicts the time evolution of the pedestrian dynamics at the turnstiles under no panic conditions. The modelling of the microscopic interactions is based on the stochastic game theory and reflects the decision dynamics of the turnstiles pursued by pedestrians. A qualitative analysis is addressed to the equilibrium solutions by means of the classical stability theory of perturbations. Numerical simulations aim at showing the emerging behaviours captured by the model. In particular the model validation is obtained by performing a sensitivity analysis on the parameters and on the initial conditions. Further refinements and research perspective, including the modelling under panic conditions, are discussed in the last section of the paper.     

On the convergence toward nonequilibrium stationary states in thermostatted kinetic models

A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.     

Notes on local o‐minimality

We introduce and study some local versions of o‐minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chemical and Mechanical Characterization of Licorice Root and Palm Leaf Waste Incorporated into Poly(urethane-acrylate) (PUA)

A poly(urethane-acrylate) polymer (PUA) was synthesized, and a sufficiently high molecular weight starting from urethane-acrylate oligomer (UAO) was obtained. PUA was then loaded with two types of powdered ligno-cellulosic waste, namely from licorice root and palm leaf, in amounts of 1, 5 and 10%, and the obtained composites were chemically and mechanically characterized. FTIR analysis of final PUA synthesized used for the composite production confirmed the new bonds formed during the polymerization process. The degradation temperatures of the two types of waste used were in line with what observed in most common natural fibers with an onset at 270 °C for licorice waste, and at 290 °C for palm leaf one. The former was more abundant in cellulose (44% vs. 12% lignin), whilst the latter was richer in lignin (30% vs. 26% cellulose). In the composites, only a limited reduction of degradation temperature was observed for palm leaf waste addition and some dispersion issues are observed for licorice root, leading to fluctuating results. Tensile performance of the composites indicates some reduction with respect to the pure polymer in terms of tensile strength, though stabilizing between data with 5 and 10% filler. In contrast, Shore A hardness of both composites slightly increases with higher filler content, while in stiffness-driven applications licorice-based composites showed potential due to an increase up to 50% compared to neat PUA. In general terms, the fracture surfaces tend to become rougher with filler introduction, which indicates the need for optimizing interfacial adhesion.     

Isometric artifacts from polymerase chain reaction-massively parallel sequencing analysis of short tandem repeat loci: An emerging issue from a new technology?

The recent introduction of polymerase chain reaction (PCR)-massively parallel sequencing (MPS) technologies in forensics has changed the approach to allelic short tandem repeat (STR) typing because sequencing cloned PCR fragments enables alleles with identical molecular weights to be distinguished based on their nucleotide sequences. Therefore, because PCR fidelity mainly depends on template integrity, new technical issues could arise in the interpretation of the results obtained from the degraded samples. In this work, a set of DNA samples degraded in vitro was used to investigate whether PCR-MPS could generate “isometric drop-ins” (IDIs; i.e., molecular products having the same length as the original allele but with a different nucleotide sequence within the repeated units). The Precision ID GlobalFiler NGS STR panel kit was used to analyze 0.5 and 1 ng of mock samples in duplicate tests (for a total of 16 PCR-MPS analyses). As expected, several well-known PCR artifacts (such as allelic dropout, stutters above the threshold) were scored; 95 IDIs with an average occurrence of 5.9 IDIs per test (min: 1, max: 11) were scored as well. In total, IDIs represented one of the most frequent artifacts. The coverage of these IDIs reached up to 981 reads (median: 239 reads), and the ratios with the coverage of the original allele ranged from 0.069 to 7.285 (median: 0.221). In addition, approximately 5.2% of the IDIs showed coverage higher than that of the original allele. Molecular analysis of these artifacts showed that they were generated in 96.8% of cases through a single nucleotide change event, with the C > T transition being the most frequent (85.7%). Thus, in a forensic evaluation of evidence, IDIs may represent an actual issue, particularly when DNA mixtures need to be interpreted because they could mislead the operator regarding the number of contributors. Overall, the molecular features of the IDIs described in this work, as well as the performance of duplicate tests, may be useful tools for managing this new class of artifacts otherwise not detected by capillary electrophoresis technology.     

A new zirconium inorganic building brick forming metal organic frameworks with exceptional stability

Porous crystals are strategic materials with industrial applications within petrochemistry, catalysis, gas storage, and selective separation. Their unique properties are based on the molecular-scale porous character. However, a principal limitation of zeolites and similar oxide-based materials is the relatively small size of the pores, typically in the range of medium-sized molecules, limiting their use in pharmaceutical and fine chemical applications. Metal organic frameworks (MOFs) provided a breakthrough in this respect. New MOFs appear at a high and an increasing pace, but the appearances of new, stable inorganic building bricks are rare. Here we present a new zirconium-based inorganic building brick that allows the synthesis of very high surface area MOFs with unprecedented stability. The high stability is based on the combination of strong Zr-O bonds and the ability of the inner Zr6-cluster to rearrange reversibly upon removal or addition of mu3-OH groups, without any changes in the connecting carboxylates. The weak thermal, chemical, and mechanical stability of most MOFs is probably the most important property that limits their use in large scale industrial applications. The Zr-MOFs presented in this work have the toughness needed for industrial applications; decomposition temperature above 500 degrees C and resistance to most chemicals, and they remain crystalline even after exposure to 10 tons/cm2 of external pressure.     

Advances in Hybrid Composites for Photocatalytic Applications: A Review

Heterogeneous photocatalysts have garnered extensive attention as a sustainable way for environmental remediation and energy storage process. Water splitting, solar energy conversion, and pollutant degradation are examples of nowadays applications where semiconductor-based photocatalysts represent a potentially disruptive technology. The exploitation of solar radiation for photocatalysis could generate a strong impact by decreasing the energy demand and simultaneously mitigating the impact of anthropogenic pollutants. However, most of the actual photocatalysts work only on energy radiation in the Near-UV region (<400 nm), and the studies and development of new photocatalysts with high efficiency in the visible range of the spectrum are required. In this regard, hybrid organic/inorganic photocatalysts have emerged as highly potential materials to drastically improve visible photocatalytic efficiency. In this review, we will analyze the state-of-art and the developments of hybrid photocatalysts for energy storage and energy conversion process as well as their application in pollutant degradation and water treatments.     

A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.