Vector spaces as unions of proper subspaces

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.Comment: 8 pages, LaTex; to appear in "Linear Algebra and its Applications

Cycle factorizations of cycle products

AbstractLet n and k1,k2,…,kn be integers with n > 1 and ki ⩾ 2 for 1 ⩽ i ⩽ n. We show that there exists a Cs-factorization of Πi=1n C2ki if and only if s = 2t with 2 ⩽ t ⩽ k1 + ··· + kn. We also settle the problem of cycle factorizations of the d-cube

Decomposing the real line into Borel sets closed under addition

We consider decompositions of the real line into pairwise disjoint Borel pieces so that each piece is closed under addition. How many pieces can there be? We prove among others that the number of pieces is either at most 3 or uncountable, and we show that it is undecidable in $ZFC$ and even in the theory $ZFC + \mathfrak{c} = \omega_2$ if the number of pieces can be uncountable but less than the continuum. We also investigate various versions: what happens if we drop the Borelness requirement, if we replace addition by multiplication, if the pieces are subgroups, if we partition $(0,\infty)$, and so on

Le contrôle de gestion et la performance du secteur public: quelle interdépendance ?

L’amélioration de la performance et la rationalisation des ressources, autant d’objectifs à atteindre pour toute organisation qui cherche à se moderniser et s’adapter aux nouveaux défis de l’environnement (mondialisation, nouvelles technologies …), et aux attentes du citoyen qui est devenu une priorité. Dans ce cadre, différents outils et méthodes de contrôle de gestion ont été adoptée par les responsables des organisations publiques dans le but de renforcer la logique de l’efficacité, de l’efficience et de la performance, ce qui s’inscrit dans le cadre du modèle du "New public management" (NPM). Ce papier porte principalement sur la relation entre la mise en place d’un système de contrôle de gestion et l’amélioration de la performance du secteur public et présente d’une façon globale les différentes théories et études empiriques qui ont démontré le lien entre l’intégration des méthodes et outils du contrôle de gestion au sein des organisations publiques et l’atteinte de la performance de cette dernière, on mettra aussi l’accent sur la particularité du secteur public, les  points de convergence et de divergence avec le secteur privé et les spécificités du contrôle de gestion dans les organisations publiques

DESIGN AND SCALE-UP OF CONTINUOUS FLOW MICRO-REACTOR

Micro-reactor systems are a promising progress in chemical engineering. The challenge is to design continuous processes enable to develop products with uniform quality and high quantity,it might be provided by using the microreactors, the industrially important production of fine chemicals is frequently characterized by low conversions and yields, while the reaction conversion using the microreactors approaches +99%, which reduces the load in the separation step. The small volume of the micro-reactor issaving the material of construction, it isalso, enhanced the mass and heat management. Microreactors were locally designed and fabricated to develop a comprehensive study of micro-reactors performance. The aim of this article is the increasing of micro-reactor productivity through a numbering-up of the number of channels and micro-reactors. Multi-channel micro-reactors consist of ten and twenty Yshaped channels areemployed. Esterification reaction of ethanol/2-ethyl hexanoic acid was taken as an example to test the developed micro-reactors, itcarried out using different designs of micro-reactors.The reactions were completed at temperature 25°C and molar ratio 1:1. The product flow rate is significantly increased (0.00028-2.5E-6 m3s-1 ). A battery of 3-parallel microreactors of twenty channels was used to produce Ethyl Hexanoate, an economic feasibility study is developed

Can age adjusted Charlson comorbidity index predict prognosis in hospitalised COVID-19 patients?

Background: Age adjusted Charlson comorbidity index (ACCI) has previously shown to predict outcome in wide range of diseases. We aim to assess if ACCI can predict 30-day all-cause mortality and need for critical care in COVID-19 patients. Methods: Prospective cohort study of hospitalised patients with confirmed COVID-19 in three acute hospitals. Patients were divided into two groups based on ACCI: Low ACCI (0-4) and high ACCI (≥ 5). Electronic case notes were analysed and results were compared. Results: 173 patients were identified, 108 (62.4%) were males, mean age was 68.4 ± 14.6 years. Median ACCI was 4 (range 0-11). 108 (62.4%) patients were in low ACCI. High ACCI had more ≥ 71 years-old patients (30.6% vs. 81.5%, p < 0.001). Low ACCI had more patients with normal renal function (78.7% vs. 44.6%, p < 0.001) and more likely to present with COVID-19 symptoms (87.0% vs. 56.9%, p < 0.001).More patients in low ACCI were transferred to critical care (42.6% vs. 3.1%, p < 0.001) and intubated (30.6% vs. 1.5%, p < 0.001). However, 30-day all-cause mortality and overall poor outcome was similar in both groups, (15.7% vs. 23.1%, p = 0.229 and 35.2% vs. 24.6%, p = 0.146, respectively). Conclusion: The outcome in COVID-19 hospitalised patients cannot be reliably predicted by ACCI

On partitions of finite vector spaces of low dimension over GF(2)

AbstractLet Vn(q) denote a vector space of dimension n over the field with q elements. A set P of subspaces of Vn(q) is a partition of Vn(q) if every nonzero vector in Vn(q) is contained in exactly one subspace of P. If there exists a partition of Vn(q) containing ai subspaces of dimension ni for 1≤i≤k, then (ak,ak−1,…,a1) must satisfy the Diophantine equation ∑i=1kai(qni−1)=qn−1. In general, however, not every solution of this Diophantine equation corresponds to a partition of Vn(q). In this article, we determine all solutions of the Diophantine equation for which there is a corresponding partition of Vn(2) for n≤7 and provide a construction of each of the partitions that exist

Place du repérage isotopique peropératoire dans la prise en charge de l’ostéome ostéoïde

L'ostéome ostéoïde est une tumeur osseuse bénigne. Le diagnostic est clinique et radiologique, et le  traitement consiste en l'exérèse chirurgicale totale avec des marges saines. Nous rapportons 05 cas d'ostéome ostéoïde opérés avec succès à l’aide d'un repérage isotopique peropératoire. Nous précisons les avantages de cette technique dans l'orientation de l'exérèse chirurgicale ainsi que la confirmation de son  caractère radical.Key words: Chirurgie, marges saines, ostéome ostéoïde, repérage isotopiqu

Technique de Blount dans le traitement des fractures supra condyliennes du coude chez l’enfant: à propos de 68 cas

La fracture de la palette humérale est la plus fréquente des fractures du coude de l’enfant. La méthode de BLOUNT, constitue une perspective thérapeutique longtemps connue. Elle consiste en une réduction sous  contrôle scopique de la fracture et une contention en hyper flexion du coude. Notre série a porté sur l’étude de 68 cas de fractures supra condyliennes chez des enfants traités dans le service des urgences chirurgicales pédiatriques de l’hôpital d’enfant de Rabat entre janvier 2009 et janvier 2012. Nous comparons nos résultats  avec les données de la littérature.Key words: Humérus, fracture supra condyliennes, enfant, traitement orthopédiqu