Nonlinear Variational Inequalities Depending on a Parameter

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions

Pointwise Sum of two Maximal Monotone Operators

∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone operators to the more general setting of reflexive Banach spaces. In addition, we present some conditions which imply the uniform Brézis-Crandall-Pazy condition. Afterwards, we present, as a consequence, some recent conditions which ensure the Mosco-epiconvergence of the sum of convex proper lower semicontinuous functions

Théra, Variational sum of monotone operators

The sum of (nonlinear) maximal monotone operators is reconsidered from the Yosida approximation and graph-convergence point of view. This leads to a new concept, called variational sum, which coincides with the classical (pointwise) sum when the classical sum happens to be maximal monotone. In the case of subdifferentials of convex lower semicontinuous proper functions, the variational sum is equal to the subdifferential of the sum of the functions. A general feature of the variational sum is to involve not only the values of the two operators at the given point but also their values at nearby points

Extensions of Fréchet ϵ-Subdifferential Calculus and Applications

AbstractIn this paper, we establish some calculus rules for the limiting Fréchet ϵ-subdifferentials of marginal functions and composite functions. Necessary conditions for approximate solutions of a constrained optimization problem are derived

Première observation malienne d’histoplasmose africaine disséminée à prédominance osseuse chez un enfant VIH négatif. Revue de la littérature

Endemic deep fungal infections are still under recognised diseases in daily medical practice because of their rarity in sub-Saharan area. The African histoplasmosis Histoplasma capsulatum var. duboisii (H. capsulatum duboisii) is the most frequent variety described in Mali through limited studies in adult patients, since the first case described by Catanei and Kervran (1945). Our case report is a disseminated histoplasmosis in a young 6-year-old african child. He was male and rural. The infectious localisations were mucosae, skin, lymphnodes, urinary tract and bones. Evolution has been marred by an episode of worsening of symptoms despite initial clinical improvement with ketoconazole. After healing of mucocutaneous lesions, we noticed a limitation of ampliation of both wrists. The radiographic bone lesions were lysis of the right lower end of the right radius and cubitus and fragmentation of cubital epiphysis of the same arm. Lacunes were present on the fifth right finger in metatarsus and phalanx; lacune and blowing aspect of the second phalanx of the left third finger was noted. The disseminated form of African histoplasmosis may occur in HIV-negative subject. The prognosis depends on early diagnosis and administration of appropriate and well-conducted therapy

Impact of intermittent preventive treatment with sulphadoxine-pyrimethamine targeting the transmission season on the incidence of clinical malaria in children in Mali

<p>Abstract</p> <p>Background</p> <p>Recent studies have shown that intermittent preventive malaria treatment (IPT) in infants in areas of stable malaria transmission reduces malaria and severe anaemia incidence. However in most areas malaria morbidity and mortality remain high in older children.</p> <p>Methods</p> <p>To evaluate the effect of seasonal IPT with sulphadoxine pyrimethamine (SP) on incidence of malaria disease in area of seasonal transmission, 262 children 6 months-10 years in Kambila, Mali were randomized to receive either IPT with SP twice at eight weeks interval or no IPT during the transmission season of 2002 and were followed up for 12 months. Subjects were also followed during the subsequent transmission season in 2003 to assess possible rebound effect. Clinical malaria cases were treated with SP and followed to assess the <it>in vivo </it>response during both periods.</p> <p>Results</p> <p>The incidence rate of malaria disease per 1,000 person-months during the first 12 months was 3.2 episodes in the treatment group vs. 5.8 episodes in the control group with age-adjusted Protective Efficacy (PE) of 42.5%; [95% CI 28.6%–53.8%]. When the first 16 weeks of follow up is considered age-adjusted PE was 67.5% [95% CI 55.3% – 76.6%]. During the subsequent transmission season, the incidence of clinical malaria per 1000 persons-days was similar between the two groups (23.0 vs 21.5 episodes, age-adjusted IRR = 1.07 [95% CI, 0.90–1.27]). No significant difference was detected in <it>in vivo </it>response between the groups during both periods.</p> <p>Conclusion</p> <p>Two malaria intermittent treatments targeting the peak transmission season reduced the annual incidence rate of clinical malaria by 42.5% in an area with intense seasonal transmission. This simple strategy is likely to be one of the most effectives in reducing malaria burden in such areas.</p> <p>Trial Registration</p> <p>Clinicaltrials.gov NCT00623155</p

The Recognition of and Care Seeking Behaviour for Childhood Illness in Developing Countries: A Systematic Review

Background: Pneumonia, diarrhoea, and malaria are among the leading causes of death in children. These deaths are largely preventable if appropriate care is sought early. This review aimed to determine the percentage of caregivers in low- and middle-income countries (LMICs) with a child less than 5 years who were able to recognise illness in their child and subsequently sought care from different types of healthcare providers. Methods and Findings: We conducted a systematic literature review of studies that reported recognition of, and/or care seeking for episodes of diarrhoea, pneumonia or malaria in LMICs. The review is registered with PROSPERO (registration number: CRD42011001654). Ninety-one studies met the inclusion criteria. Eighteen studies reported data on caregiver recognition of disease and seventy-seven studies on care seeking. The median sensitivity of recognition of diarrhoea, malaria and pneumonia was low (36.0%, 37.4%, and 45.8%, respectively). A median of 73.0% of caregivers sought care outside the home. Care seeking from community health workers (median: 5.4% for diarrhoea, 4.2% for pneumonia, and 1.3% for malaria) and the use of oral rehydration therapy (median: 34%) was low. Conclusions: Given the importance of this topic to child survival programmes there are few published studies. Recognition of diarrhoea, malaria and pneumonia by caregivers is generally poor and represents a key factor to address in attempts to improve health care utilisation. In addition, considering that oral rehydration therapy has been widely recommended for over forty years, its use remains disappointingly low. Similarly, the reported levels of care seeking from community health workers in the included studies are low even though global action plans to address these illnesses promote community case management. Giving greater priority to research on care seeking could provide crucial evidence to inform child mortality programmes