On Panja-Prasad conjecture

In the present paper we shall investigate the Waring's problem for upper triangular matrix algebras. The main result is the following: Let $n\geq 2$ and $m\geq 1$ be integers. Let $p(x_1,\ldots,x_m)$ be a noncommutative polynomial with zero constant term over an infinite field $K$. Let $T_n(K)$ be the set of all $n\times n$ upper triangular matrices over $K$. Suppose $1<r<n-1$, where $r$ is the order of $p$. We have that $p(T_n(K))+p(T_n(K))=J^r$, where $J$ is the Jacobson radical of $T_n(K)$. If $r=n-2$, then $p(T_n(K))=J^{n-2}$. This gives a definitive solution of a conjecture proposed by Panja and Prasad.Comment: 22 pages. This version has corrected some minor errors in the first version. Comments are welcome. arXiv admin note: text overlap with arXiv:2305.1173

Effects of insecticides with different modes of action in the control of banana weevils (Cosmopolites sordidus) in Cameroon

The aim of the study was to evaluate the use of insecticides with different modes of action on banana borer weevil. Insecticides with different modes of action were administered to banana weevils (Cosmopolites sordidus) in small containers (1 litre by volume) with perforated lids and monitored in the laboratory at room temperature and pressure. The insecticides were also applied on plantain plants (Musa sapientum) in a field trial following five treatments, each replicated three times arranged in a complete randomized block design. The laboratory and field results revealed that Counter® - organophosphate with active ingredient Terbuphos (Hangzhou Tianlong Biotechnology Co., Ltd, China) and Regent® - phenyl pyrazole with active ingredient fipronyl (Kalyani Industries PVT Ltd, China) were very effective (100% mortality) in the control of banana weevil. Insector® - neonicotinoid with active ingredient imidaclopride (Heydchem Limited, China) showed a moderate effect (&lt;20%) in the control of the weevil while Bromorex® (botanical, with pepper and chilli extracts as active ingridients) proved to be a poor insecticide against this weevil. Bromorex® also showed low non-mortality effects on the weevils with a high rate of egg laid and larvae emergence (17.3±4.5 and 1.6±0.4 respectively). Insector®, Regent® and Counter® completely inhibited larvae emergence from eggs.Key words: insecticide, efficacy, Cosmopolites sordidus, Banan

Effet de l’engrais organique biojadi sur les populations d’insectes visitant le palmier a huile

Le palmier à huile est une culture oléagineuse importante à l’échelle mondiale en raison de son rendement élevé parfois dû à l’utilisation de fertilisants. Cependant, l’utilisation des engrais organiques peut influer sur les populations d’insectes visitant les plantations de palmier à huile. Cette étude vise à évaluer l’effet de l’engrais biojadi sur les populations d’insectes du palmier à huile. Le dispositif utilisé est un bloc de Fisher à quatre répétitions et trois traitements. L’inventaire de la faune entomologique réalisée dans les différents traitements a révélé la présence des insectes ravageurs, pollinisateurs et prédateurs. Le groupe des insectes pollinisateurs et ravageurs ont été présents de la même manière sur les parcelles T1, T2, T3 car aucune différence significative n’a été observée entre ces traitements. Cependant, le nombre d’insectes prédateurs a été plus élevé au niveau du traitement T3 qu’au niveau des traitements T1 et T2. La pullulation des prédateurs réduit considérablement l’abondance des pollinisateurs et ravageurs. L’engrais organique biojadi peut être recommandé. Cependant, l’application de cet engrais doit être faite de manière continue pour pouvoir maximiser son effet sur de long terme. Mot clés : Effet, engrais organique biojadi, insectes, palmier à huile &nbsp;English Title: Effect of Biojadi organic fertilizer on insect populations visiting oil palm Oil palm is an important oilseed crop worldwide because of its high yield sometimes due to the use of fertilizers. However, the use of organic&nbsp; fertilizers can affect insect populations visiting oil palm plantations. This study aims at evaluating the effect of biojadi fertilizer on oil palm insect populations. The device used is a Fisher block with four replicates and three treatments. The inventory of the entomological fauna carried out in the different treatments revealed the presence of insect pests, pollinators and predators. The group of pollinating insects and pests were present in the same way on plots T1, T2, T3 because no significant difference was observed between these treatments. However, the number of predatory insects was higher in the T3 treatment than in the treatments T1 and T2. The proliferation of predators significantly reduces the abundance of pollinators and pests. Biojadi organic fertilizer can be recommended. However, the application of this fertilizer must be done continuously to maximize its long-term effect. Keywords: Effect, biojadi organic fertilizer, insect populations, oil pal

Risk Factors for Diarrhea in Children Under Five Years of Age Residing in Peri-Urban Communities in Cochabamba, Bolivia

This study examined the relationship between childhood diarrhea prevalence and caregiver knowledge of the causes and prevention of diarrhea in a prospective cohort of 952 children \u3c 5 years of age in Cochabamba, Bolivia. The survey of caregiver knowledge found that more than 80% of caregivers were unaware that hand washing with soap could prevent childhood diarrhea. Furthermore, when asked how to keep food safe for children to eat only 17% of caregivers reported hand washing before cooking and feeding a child. Lack of caregiver awareness of the importance of practices related to hygiene and sanitation for diarrhea prevention were significant risk factors for diarrheal disease in this cohort. The knowledge findings from this study suggest that health promotion in these communities should put further emphasis on increasing knowledge of how water treatment, hand washing with soap, proper disposal of child feces, and food preparation relate to childhood diarrhea prevention

On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interaction

We consider the 3D quantum BBGKY hierarchy which corresponds to the $N$-particle Schr\"{o}dinger equation. We assume the pair interaction is $N^{3\beta -1}V(N^{\beta}\bullet).$ For interaction parameter $\beta \in(0,\frac23)$, we prove that, as $N\rightarrow \infty ,$ the limit points of the solutions to the BBGKY hierarchy satisfy the space-time bound conjectured by Klainerman-Machedon in 2008. This allows for the application of the Klainerman-Machedon uniqueness theorem, and hence implies that the limit is uniquely determined as a tensor product of solutions to the Gross-Pitaevski equation when the $N$-body initial data is factorized. The first result in this direction in 3D was obtained by T. Chen and N. Pavlovi\'{c} (2011) for $\beta \in (0,\frac14)$ and subsequently by X. Chen (2012) for $\beta\in (0,\frac27]$. We build upon the approach of X. Chen but apply frequency localized Klainerman-Machedon collapsing estimates and the endpoint Strichartz estimate in the estimate of the potential part to extend the range to $\beta\in (0,\frac23)$. Overall, this provides an alternative approach to the mean-field program by Erd\"os-Schlein-Yau (2007), whose uniqueness proof is based upon Feynman diagram combinatorics.Comment: v2, final version for Journal of the European Mathematical Society. v1 is a less technical versio