On modular k-free sets

Let $n$ and $k$ be integers. A set $A\subset\mathbb{Z}/n\mathbb{Z}$ is $k$-free if for all $x$ in $A$, $kx\notin A$. We determine the maximal cardinality of such a set when $k$ and $n$ are coprime. We also study several particular cases and we propose an efficient algorithm for solving the general case. We finally give the asymptotic behaviour of the minimal size of a $k$-free set in $\left[ 1,n\right]$ which is maximal for inclusion

Entity Matching for Digital World: A Modern Approach using Artificial Intelligence and Machine Learning

Entity matching is the field of research solving the problem of identifying similar records which refer to the same real-world entity In today s digital world business organizations deal with large amount of data like customers vendors manufacturers etc Entities are spread across various data sources and failure to correlate two records as one entity can lead to confusion Relationships and patterns would be missed Aggregations and calculations won t make any sense It is a significant data integration effort that often arises when data originate from different sources In such scenarios we understand the situation by linking records and then track entities from a person to a product etc There is appreciable value in integrating the data silos across various industrie

Time-Dependent Stresses From Fluid Extraction and Diffusion With Applications to Induced Seismicity

Over recent decades, it has become clear that the extraction of fluids from underground reservoirs can be linked to seismicity and aseismic deformation around producing fields. Using a simple model with uniform fluid extraction from a reservoir, Segall (1989, “Earthquakes Triggered by Fluid Extraction,” Geology, 17(10), pp. 942–946) illustrated how poroelastic stresses resulting from fluid withdrawal may be consistent with earthquake focal mechanisms surrounding some producing fields. Since these stress fields depend on the spatial gradient of the change in pore fluid content within the reservoir, both quantitative and qualitative predictions of the stress changes surrounding a reservoir may be considerably affected by assumptions in the geometry and hydraulic properties of the producing zone. Here, we expand upon the work of Segall (1989, “Earthquakes Triggered by Fluid Extraction,” Geology, 17, pp. 942–946 and 1985, “Stress and Subsidence Resulting From Subsurface Fluid Withdrawal in the Epicentral Region of the 1983 Coalinga Earthquake,” J. Geophys. Res. Solid Earth, 90, pp. 6801–6816) to provide a quantitative analysis of the surrounding stresses resulting from fluid extraction and diffusion in a horizontal reservoir. In particular, when considering the diffusion of fluids, the spatial pattern and magnitude of imposed stresses is controlled by the ratio between the volumetric rate of fluid extraction and the reservoir diffusivity. Moreover, the effective reservoir length expands over time along with the diffusion front, predicting a time-dependent rotation of the induced principal stresses from relative tension to compression along the ends of the producing zone. This reversal in perturbed principal stress directions may manifest as a rotation in earthquake focal mechanisms or varied sensitivity to poroelastic triggering, depending upon the criticality of the pre-existing stress state and fault orientations, which may explain inferred rotations in principal stress directions associated with some induced seismicity

Time-Dependent Stresses From Fluid Extraction and Diffusion With Applications to Induced Seismicity

Over recent decades, it has become clear that the extraction of fluids from underground reservoirs can be linked to seismicity and aseismic deformation around producing fields. Using a simple model with uniform fluid extraction from a reservoir, Segall (1989, “Earthquakes Triggered by Fluid Extraction,” Geology, 17(10), pp. 942–946) illustrated how poroelastic stresses resulting from fluid withdrawal may be consistent with earthquake focal mechanisms surrounding some producing fields. Since these stress fields depend on the spatial gradient of the change in pore fluid content within the reservoir, both quantitative and qualitative predictions of the stress changes surrounding a reservoir may be considerably affected by assumptions in the geometry and hydraulic properties of the producing zone. Here, we expand upon the work of Segall (1989, “Earthquakes Triggered by Fluid Extraction,” Geology, 17, pp. 942–946 and 1985, “Stress and Subsidence Resulting From Subsurface Fluid Withdrawal in the Epicentral Region of the 1983 Coalinga Earthquake,” J. Geophys. Res. Solid Earth, 90, pp. 6801–6816) to provide a quantitative analysis of the surrounding stresses resulting from fluid extraction and diffusion in a horizontal reservoir. In particular, when considering the diffusion of fluids, the spatial pattern and magnitude of imposed stresses is controlled by the ratio between the volumetric rate of fluid extraction and the reservoir diffusivity. Moreover, the effective reservoir length expands over time along with the diffusion front, predicting a time-dependent rotation of the induced principal stresses from relative tension to compression along the ends of the producing zone. This reversal in perturbed principal stress directions may manifest as a rotation in earthquake focal mechanisms or varied sensitivity to poroelastic triggering, depending upon the criticality of the pre-existing stress state and fault orientations, which may explain inferred rotations in principal stress directions associated with some induced seismicity

Quelques problèmes additifs : bases, pseudo-puissances et ensembles k-libres

Widely studied in N or Z, we are interested in additive bases in infinite abelian groups. We get some results about the functions E, X and S, which caracterize the behaviour of a basis when we remove an element. We also study the set A of pseudo s-th powers, which is an additive basis of order s+1. We wonder what is the minimal size of an additive complement of sA, that is a set B such that sA+B contains all large enough integers. With respect to this problem, we prove quite precise theorems which are tantamount to asserting that a threshold phenomenon occurs. Finally, we establish the maximal size of a k-free set in Z/nZ. The study of this quantity strongly depends on the arithmetical relative properties of n and k. That is why we use different methods depending on cases. In particular, we show a result on combinatorial trees for the general case.Habituellement étudié dans N ou Z, on s'intéresse aux bases additives dans les groupes abéliens infinis. On obtient des résultats sur les fonctions E, X et S, qui caractérisent le comportement d'une base lorsqu'on lui enlève un élément. On étudie également l'ensemble A des pseudo-puissances s-ièmes. Celles-ci forment presque sûrement une base additive d'ordre s+1. On cherche à affiner ce résultat en déterminant des compléments additifs de sA de taille minimale, c'est-à-dire des ensembles B tels que sA+B contient presque sûrement tout entier suffisamment grand. Enfin, nous montrons quelle est la taille maximale d'un ensemble k-libre dans Z/nZ. La contrainte modulaire joue ici un rôle prépondérant. Les méthodes employées sont très différentes, selon la relation arithmétique entre k et n. En particulier, nous démontrons un résultat sur des arbres combinatoires, dans l'étude du cas général

A Generalization of the Ramanujan Polynomials and Plane Trees

Generalizing a sequence of Lambert, Cayley and Ramanujan, Chapoton has recently introduced a polynomial sequence Q_n:=Q_n(x,y,z,t) defined by Q_1=1, Q_{n+1}=[x+nz+(y+t)(n+y\partial_y)]Q_n. In this paper we prove Chapoton's conjecture on the duality formula: Q_n(x,y,z,t)=Q_n(x+nz+nt,y,-t,-z), and answer his question about the combinatorial interpretation of Q_n. Actually we give combinatorial interpretations of these polynomials in terms of plane trees, half-mobile trees, and forests of plane trees. Our approach also leads to a general formula that unifies several known results for enumerating trees and plane trees.Comment: 20 pages, 2 tables, 8 figures, see also http://math.univ-lyon1.fr/~gu

Espacenet, Patentscope and Depatisnet: a comparison approach

This article is based on a presentation given at the European Patent Office Patent Information Conference (EPOPIC) that was held during 4–6 November 2014 in Warsaw, Poland. Special thanks go to the organization team of the conference from the European Patent Office and to the CITPIA Patlib Centre Team without whom this study would never have been possible.Espacenet, Patentscope and Depatisnet are known as the main multinational patent databases offered by patent authorities which are available to the public free of charge. As all three systems have substantially improved in the last few years, a comparison of their functionalities and capabilities, as discussed herein, is useful for those unfamiliar with the recent developments. In order to present the comparison, the following aspects were analysed: data coverage, search functionality, result list, bibliographic view of records and patent data export options. Case studies are presented where the search systems were compared in the field of nanotechnology. The analysis concludes that Espacenet has the best features for searching, Patentscope the best for analysis and Depatisnet the best for complex search tasks.Project "Technology Watch of Spanish Nanotechnology via its patents" (Project number: CSO2012-38801), Spanish Ministry of Education. Grupo de Investigación: SCImago-UGR (SEJ036

Addressing the challenges in antisepsis : focus on povidone iodine

Objectives: Using antiseptics in wound care can promote healing by preventing and treating infection. However, using antiseptics can present many challenges, including issues with tolerability, inactivation by organic matter and the emergence of antimicrobial resistance/cross-resistance. This review discussed the key challenges in antisepsis, focusing on povidone-iodine (PVP-I) antiseptic. Methods: Literature searches were conducted in PubMed, in January 2019, with a filter for the previous 5 years. Searches were based on the antimicrobial efficacy, antiseptic resistance, wound healing properties, and skin tolerability for the commonly used antiseptics PVP-I, chlorhexidine gluconate (CHG), polyhexanide (PHMB), and octenidine (OCT). Additional papers were identified based on author expertise. Results: When compared with CHG, PHMB and OCT, PVP-I had a broader spectrum of antimicrobial activity against Gram-negative bacteria, actinobacteria, bacterial spores, fungi and viruses, and a similar and broad spectrum of activity against Gram-positive bacteria. PVP-I was also highly effective at eradicating bacterial biofilms, which is a vitally important consideration for wound care and infection control. Despite a long history of extensive use, no resistance or cross-resistance to PVP-I has been recorded, which is in contrast with other antiseptics. Despite previous misconceptions, it has been shown that PVP-I has low allergenic properties, low cytotoxicity and can promote wound healing through increased expression of transforming growth factor beta. Conclusion: With increased understanding of the importance of tackling antimicrobial resistance and bacterial biofilms in acute and chronic wound care, alongside improved understanding of the challenges of antiseptic use, PVP-I remains a promising agent for the management of antisepsis. (c) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/