Strings from position-dependent noncommutativity

We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PTlike symmetries, i.e.antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two dimensional space is string like, i.e.having a fundamental length in one direction beyond which a resolution is impossible. Subsequently we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.Comment: 11 pages, Late

Leçons apprises de la gestion des épidémies de la maladie à virus Ebola en République Démocratique du Congo de 2007 à 2017: Lessons learned from the management of Ebola outbreaks in the Democratic Republic of Congo from 2007 to 2017

Context and objective. DRC’s ecosystem provides conditions that are favorable to the occurrence of zoonotic diseases at the human-animal interface including Ebola virus disease (EVD). Because the level of lethality of EVD is high, the present study focuses on the epidemics that occurred in Mweka (2007 and 2008), Isiro (2012), Boende (2014) and Likati (2017) with a view to assess the response components during each outbreak and to identify those with relevant impact on the scale of the epidemic. Methods. An analytical retrospective study of secondary data collected during the management of the five aforementioned EVD epidemics in DRC was conducted.Charecteristics of each outbreak were described based on descriptive statistics, and univariate analyzes of each response component were conducted in relation to lethality. Results. A total of 422 cases were recorded with 282 deaths or 66.8% lethality. The vast majority of cases are in the 15 to 49 age group. The female sex is the most represented. Among all the elements of the answer, in a univariate model, the deployment of the mobile laboratory (p = 0.002), the functionality of the commissions (p =0.001), the deployment of a multidisciplinary team and the powerful surveillance system (p = 0.001) are significantly associated with lethality. Conclusion. Rapid deployment of the mobile laboratory in the field, deployment of multidisciplinary teams, efficient functionality of the commissions and a functional monitoring system significantly reduced the fatality rate. Contexte et objectifs. La RDC a un écosystème favorable à la survenue des maladies d’origine zoonotique à l’interface homme-animal dont la maladie à virus Ebola (MVE). Face à une létalité reconnue être élevée pour cette dernière, cette étude s’est focalisée sur les épidémies survenues à Mweka (2007 et 2008), à Isiro (2012), à Boende (2014) et à Likati (2017) afin de décrire les différents éléments de réponse mis en place lors de chacune de ces épidémies et identifier ceux qui ont une influence significative sur l’ampleur de l’épidémie. Méthodes. Une étude documentaire analytique sur les données secondaires recueillies lors de la gestion de ces cinq épidémies de la MVE survenues en RDC. Les statistiques descriptives ont été réalisées pour caractériser chaque épidémie. Les analyses univariées de chaque élément de réponse ont été menées en rapport avec la létalité. Résultats. Un total de 422 cas a été enregistré avec 282 décès soit 66,8 % de létalité. La grande majorité de cas se trouve dans la tranche d’âge de 15 à 49 ans. Le sexe féminin est le plus représenté. Parmi tous les éléments de la réponse, dans un modèle univarié, le déploiement du laboratoire mobile (p=0,002), la fonctionnalité des commissions (p=0,001), le déploiement d’une équipe multidisciplinaire et le système de surveillance performant (p=0,001) sont associés significativement à la létalité. Conclusion. Le déploiement rapide du laboratoire mobile sur le terrain, le déploiement des équipes multidisciplinaires, la bonne fonctionnalité des commissions et le système de surveillance fonctionnel ont permis de réduire significativement la létalité

Post-Newtonian equation for the energy levels of a Dirac particle in a static metric

We study first the Hamiltonian operator H corresponding to the Fock-Weyl extension of the Dirac equation to gravitation. When searching for stationary solutions to this equation, in a static metric, we show that just one invariant Hermitian product appears natural. In the case of a space-isotropic metric, H is Hermitian for that product. Then we investigate the asymptotic post-Newtonian approximation of the stationary Schroedinger equation associated with H, for a slow particle in a weak-field static metric. We rewrite the expanded equations as one equation for a two-component spinor field. This equation contains just the non-relativistic Schroedinger equation in the gravity potential, plus correction terms. Those "correction" terms are of the same order in the small parameter as the "main" terms, but are numerically negligible in the case of ultra-cold neutrons in the Earth's gravity.Comment: 12pt LaTeX, 17 pages. v2: version accepted for publication in Phys.Rev.D: comments on scalar product changed, using a recent paper; discussion of PN expansions simplified (no change of units any more); numerical estimates for ultra-cold neutrons in the Earth's gravit

Some remarks on quasi-Hermitian operators

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally we discuss their application in the so-called pseudo-Hermitian quantum mechanics.Comment: 18page

Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

Deaf, Dumb, and Chatting Robots, Enabling Distributed Computation and Fault-Tolerance Among Stigmergic Robot

We investigate ways for the exchange of information (explicit communication) among deaf and dumb mobile robots scattered in the plane. We introduce the use of movement-signals (analogously to flight signals and bees waggle) as a mean to transfer messages, enabling the use of distributed algorithms among the robots. We propose one-to-one deterministic movement protocols that implement explicit communication. We first present protocols for synchronous robots. We begin with a very simple coding protocol for two robots. Based on on this protocol, we provide one-to-one communication for any system of n \geq 2 robots equipped with observable IDs that agree on a common direction (sense of direction). We then propose two solutions enabling one-to-one communication among anonymous robots. Since the robots are devoid of observable IDs, both protocols build recognition mechanisms using the (weak) capabilities offered to the robots. The first protocol assumes that the robots agree on a common direction and a common handedness (chirality), while the second protocol assumes chirality only. Next, we show how the movements of robots can provide implicit acknowledgments in asynchronous systems. We use this result to design asynchronous one-to-one communication with two robots only. Finally, we combine this solution with the schemes developed in synchronous settings to fit the general case of asynchronous one-to-one communication among any number of robots. Our protocols enable the use of distributing algorithms based on message exchanges among swarms of Stigmergic robots. Furthermore, they provides robots equipped with means of communication to overcome faults of their communication device

Impact of the Degrading Toxicity of Metallic Trace Elements on the Flora and Fauna of the Matete River in Kinshasa

This work presents the results for which the general objective pursued in this study is to assess the impact of the degrading toxicity of metallic trace elements on the flora and fauna of the Matete river in Kinshasa. This evaluation was studied through the understanding of the accumulative power of species of flora and fauna in this same ecosystem with metallic elements. In particular: Pistia stratiotes (manganese): 10.7 ± 1.1 and 236.4 × 101 ± 248.8 mg / kg, iron: from 187.5 × 101 ± 61.9 and 500.0 × 101 ± 0, 1 mg / kg, potassium: between 314.8 ± 12.1 and 119.0 × 103 ± 6981.1 mg / kg, calcium: <10 ± <0.3 and 252200 ± 1892.8 mg / kg, cobalt: <3.0 ± <0.2, nickel: <0.5 ± <0.1 and 20.6 ± 0.5 mg / kg, zinc: 1.9 ± 0.0 and 98.7 × 101 ± 0.0 mg / kg, copper: <0.5 ± <0.1 and 79.4 ± 1.2 mg / kg, aluminum: 56.3 × 101 ± 53.1 and 5229.0 × 101 ± 583, 8 mg / kg, chromium: <1.0 ± <0.1 mg / kg and 21.6 ± 4.0 mg / kg, cadmium: 2.8 ± 0.3 and 25.6 ± 0.4 mg / kg, lead: 0.5 ± 0.4 and 86.7 ± 5.5 mg / kg and for Lemna minor (manganese): 5.10 ± 0.1 and 5.80 ± 0.3 mg / kg, iron: 49.9 × 101 ± 18.8 and 6784.0 × 101 ± 709.5 mg / kg, potassium: 113.8 ± 4.4 and 2712.0 × 101 ± 98.8 mg / kg, calcium: <10 ± <0.1 and 97830 ± 2073.9 mg / kg, cobalt: <3.0 ± <0.2 mg / kg, nickel: 0.001 ± 0.00 and 0.004 ± 0.00 mg / kg, zinc : 3.12 ± 0.17 and 4.00 ± 0.82 mg / kg, copper: 0.001 ± 0.0001 and 0.006 ± 0.0004 mg / kg, aluminum: 0.02 ± 0.00 mg / kg and 0.15 ± 0.06 mg / kg, chromium: 0.001 ± 0.0001 and 0.003 ± 0.0002 mg / kg, cadmium: 0.0004 ± 0.00002 and 0.001 ± 0.00003 mg / kg, lead: 0.001 ± 0.00 and 0.004 ± 0.0002 mg / kg. On the other hand, Oreochromis niloticus (Calcium): <0.1 × 102 ± 0.3 and 25 220.0 × 101 ± 48094.1mg / kg, Iron: 10350.7 × 101 ± 5131.7 and 102158.0 × 101 ± 27182.7,Manganese: 1.815 × 101 ± 0.931mg / kg and 7.945 × 101 ± 2.131 mg / kg, Cobalt: <6.0 ± <0.0 mg / kg, Nickel: <0.501 ± <0.049 mg / kg and 61.503 ± 1.302 mg / kg, Zinc: <0.736 ± 0.015 mg / kg and 42.923 × 101 ± 3.176 mg / kg, Copper: 1.902 ± 0.007 mg / kg and 35.302 ± 0.247 mg / kg, Aluminum: 1.414 × 103 ± 70.464mg / kg and 9.493 × 103 ± 147.214 mg / kg, Chromium: <1.0001 ± <0.0408 and <1.0003 ± <0.0105, Cadmium: 0.2002 ± 0.0718 mg / kg and 19.0001 ± 0.8981mg / kg and Lead: <1, 0002 ± <0.0051 mg / kg and 3.9004 ± 0.0895 mg / kg of dry matter. One of the serious causes of their persistence is their biomagnification in the food chain. This is why the response of  Pistia stratiotes, water lettuce and Lemna minor from the nine sampling sites of the Matete river to large and / or low concentrations of metallic elements is reflected either by an inhibition of photosynthetic processes (antagonism and effect synergistic) and the instinct of certain species. However, this ecosystem offers an ecological niche low in dissolved oxygen and a nutrient-poor and toxic diet for the species that live there. In this regard, the flora of the Matete river accumulates the metallic elements in a significant way and according to the diversity of the environments and the size of the species

Biorthogonal Quantum Systems

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+\nu)^2+\sum_{k>0}\mu_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.Comment: 34 pages, 5 eps figures; references added and other changes made to conform to journal versio

Potential Conservation Laws

We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.Comment: 36 pages, extended versio

Utilisation et gestion des pesticides en cultures maraîchères : cas de la zone de Nkolo dans la province du Kongo Central, République démocratique du Congo

Objectifs: L’objectif de cette étude est d’évaluer les connaissances et les pratiques des maraîchers de Nkolo et ses environs quant à l’utilisation des pesticides.Méthodologie et Résultats: Une enquête a été réalisée auprès des 46 maraîchers. Le questionnaire a porté sur les pesticides utilisés, la dose appliquée, la préparation des solutions des pesticides, la fréquence d’application, la protection des maraîchers pendant l’usage des pesticides, la durée avant récolte (DAR), la gestion d’emballages des pesticides et les caractéristiques socio-professionnelles des maraîchers. Les résultats ont montrés que le maraîchage est généralement pratiqué par les hommes (93% contre 7% de femmes), et concerne principalement la culture des légumes fruits (tomate, aubergine et poivron). Les pesticides sont systématiquement appliqués, notamment les fongicides et les insecticides, à titre préventif et fréquemment à intervalle de 7 jours (saison pluvieuse) et 14 jours (saison sèche). Un à neuf pesticides différents peuvent être utilisés par cycle de culture, et sont généralement mélangés et appliqués en une fois à l’aide d’un pulvérisateur. Le dosage des pesticides et la DAR varient largement suivant les maraîchers. La majorité de maraîchers n’a pas suivi une formation sur les pesticides (83%), ne se protège pas adéquatement pendant l’usage des pesticides (72%) et abandonne les emballages des pesticides au champ (46%).Conclusion et applications des résultats: Les maraîchers de Nkolo et ses environs n’ont généralement pas une bonne connaissance des pesticides et ne respectent pas les recommandations des fabricants. L’application systématique des pesticides sans tenue de protection appropriée les met en contact régulier avec les pesticides et les expose à l’intoxication aux pesticides. Le manque de maîtrise de dosage des pesticides peut accroître le risque de résistance des ravageurs et pathogènes aux pesticides. En vue de réduire le risque d’intoxication des maraîchers et consommateurs des légumes, et de la pollution de l’environnement, il est d’ores et déjà, urgent et important de promouvoir la formation des maraîchers de Nkolo pour une utilisation judicieuse des pesticides.Mots clés: Pesticides, cultures maraîchères, pratiques culturales, enquête, Nkolo (RD Congo)English Title: Pesticides use and management in the vegetable crops at Nkolo in Kongo Central Province in the western DR CongoEnglish AbstractObjectives: Pesticides are systematically applied in vegetable crops at Nkolo (in Kongo Central province in the western DR Congo) in order to provide crop protection and improve the yield. This study aimed at assessing the knowledges and practices of gardeners in relation to of pesticides use.Methodology and Results: Forty-six gardeners were interviewed. The questionnaire focused on the pesticides types, solution procedures, application rate and frequency, gardener protective equipment, and the pre-harvest intervals. Socio-professional traits of gardeners were also recorded. Majority of gardeners was male (93% vs 7% of women). Pesticides, especially fungicides and insecticides are systematically applied, based on preventive application and generally in 7 (dry season) and 14 (rain season) days of intervals. Depending on the gardener, 1 to 9 pesticides are used per crop cycle. All the pesticides are generally mixed and applied together on the crops using a manual sprayer. Application rate and pre-harvest intervals varied with gardeners. Most of them do not have been trained on pesticide use (83%), do not use protective equipment (72%) and abandon pesticide containers in the field (46%).Conclusion and application of results: Gardeners in Nkolo and surroundings have poor knowledges on pesticides use and do not use it properly. Systematically application of pesticides without proper protective equipment result in regular contact of gardener with pesticides and exposes them to pesticide poisoning. Furthermore, improper pesticides use should increase the risk of pest resistance in the long term use. In order to mitigate the risk of poisoning for gardeners and consumers, and environmental pollution in Nkolo and surroundings, there is an urgent need to promote proper use of pesticides.Keywords: Pesticides, vegetables crops, agricultural practices, survey, Nkolo (DR Congo