Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

Mentolabial angle and aesthetics : a quantitative investigation of idealized and normative values

BACKGROUND: This study is a quantitative evaluation of the influence of the mentolabial angle on perceived attractiveness and threshold values of desire for surgery. METHODS: The mentolabial angle of an idealized silhouette male Caucasian profile image was altered incrementally between 84° and 162°. Images were rated on a Likert scale by pretreatment orthognathic patients (n = 75), lay people (n = 75) and clinicians (n = 35). RESULTS: A mentolabial angle of approximately 107° to 118° was deemed the most attractive, with a range of up to 140° deemed acceptable. Angles above or below this range were perceived as unattractive, and anything outside the range of below 98° or above 162° was deemed very unattractive. A deep mentolabial angle (84°) or an almost flat angle (162°) was deemed the least attractive. In terms of threshold values of desire for surgery, for all groups, a threshold value of ≥162° and ≤84° indicated a preference for surgery, although clinicians were least likely to suggest surgery. The clinician group was the most consistent, and for many of the images, there was some variation in agreement between clinicians and lay people as to whether surgery is required. There was even more variability in the assessments for the patient group. CONCLUSIONS: It is recommended that in orthognathic and genioplasty planning, the range of normal variability of the mentolabial angle, in terms of observer acceptance, is taken into account as well as threshold values of desire for surgery. The importance of using patients as observers in attractiveness research is stressed

Regeneration of base-oil from waste-oil under different conditions and variables

The demand for lubricants is continuously increasing with the increase in the establishment of factories and the tremendous increase in the number of vehicles and other means of transportation. The oil consumed can be a great source of contamination if it is thrown as a waste or can be considered as a new source of energy if properly used, and all depends on methods of how oil can be reused. This study shows how to be innovative on reusing waste-oil while keeping the basic characteristics of base oil. In this experiment, a process known as acid clay is used to restore the basic characteristics of original oil. The oil-waste is collected from different places and a number of experiments are conducted under different conditions with different set of variables. The impact of these variables on the quality of the product is discussed. The possibility of restoring and reviving nearly two-thirds of the oil consumed is proved in this investigation.Key words: Waste oil, base-oil, regeneration of base-oil

Antecedents of consumer trust in mobile payment adoption

This study empirically examines the role of consumer trust and its antecedents in determining consumers’ intention to adopt mobile payment. This research proposes that consumers’ willingness to adopt mobile payment depends on their assessment of the trustworthiness of mobile service provider and vendor, their assessment of the functional reliability of mobile payment systems as well as their general disposition to trust and their cultural background, in particular, uncertainty avoidance. Data were gathered from 302 participants in Auckland, New Zealand. Results show that all five sets of trust antecedents influence the development of trust and trust is an important predictor of intention to adopt mobile payment. Both theoretical and practical implications are discussed

Optimal Siting of Electric Vehicle Charging Stations Using Pythagorean Fuzzy VIKOR Approach

Site selection for electric vehicle charging stations (EVCSs) is the process of determining the most suitable location among alternatives for the construction of charging facilities for electric vehicles. It can be regarded as a complex multicriteria decision-making (MCDM) problem requiring consideration of multiple conflicting criteria. In the real world, it is often hard or impossible for decision makers to estimate their preferences with exact numerical values. Therefore, Pythagorean fuzzy set theory has been frequently used to handle imprecise data and vague expressions in practical decision-making problems. In this paper, a Pythagorean fuzzy VIKOR (PF-VIKOR) approach is developed for solving the EVCS site selection problems, in which the evaluations of alternatives are given as linguistic terms characterized by Pythagorean fuzzy values (PFVs). Particularly, the generalized Pythagorean fuzzy ordered weighted standardized distance (GPFOWSD) operator is proposed to calculate the utility and regret measures for ranking alternative sites. Finally, a practical example in Shanghai, China, is included to demonstrate the proposed EVCS sitting model, and the advantages are highlighted by comparing the results with other relevant methods.Peer Reviewe

Congenital dysplastic hips, spinal column abnormalities, fractures and progressive neurological manifestations in Tunisian family with cockayne syndrome

We report an inbred, Tunisian family in which cousins have the definite diagnosis of Cockayne syndrome. Intervening members in this family, who are intellectually normal, though, most are manifesting complications of hip dysplasia (development of dysplastic arthrosis) and various vertebral abnormalities. We presume that these are carriers who manifest dreadful bone features rather than the clinical phenotype of Cockayne syndrome, the mode of inheritance of the abnormal gene in this family is suggesting autosomal dominant, to our knowledge the family reported with such skeletal abnormalities in association to Cockayne syndrome is the largest in comparison to the international literatures.Keywords: cockayne syndrome, skeletal abnormalitiesRésuméNous faisons un rapport sur un cas résultant de croisements entre animaux de même souche, une famille tunisiene chez laquelle les cousins avaient un diagnostic précis du syndrome de cockaye. Les membres de cette famille qui interviennent et qui sont sains intellectuellement bien que la plupart des patients manifestaient des complications de la hanche dysplasie (devéloppement d\'arthrose dysplastique) et des anomalies vertébrales. Nous supposons qu\'elles sont des porteuses qui manifestent des traits épouvantables d\'os plutôt que le phénotype clinique de syndrone de cockaye, la méthode d\'héritage de ce gêne anomalie chez cette famille pourrait être autosome dominant. Pour autant que nous sachons, la famille s\'est présentée atteinte d\'une telle anomalité squelettique en association avec le syndrome de cockaye est le plus grand par rapport à la littérature internationale.Mots clés: syndrome de cockaye, anomalité squelettiqueAnnals of African Medicine Vol. 4(2) 2005: 83–8

Speciation of heavy metals in paddy soils from selected areas in Kedah and Penang, Malaysia

This study was carried out with the intention of evaluating heavy metal contamination in cultivated paddy areas. The speciation of heavy metals in paddy soils was determined in order to gain insight regarding their origin and distribution in soils. Five sampling sites were randomly selected from Kedah (Yan, Kota Setar, Kubang Pasu district) and Penang (Bumbung Lima district), where the soils constituted marine alluvial deposits. A site in Langkawi, where organic paddy farming is practised was used as the control. The sequential extraction method was adopted in order to obtain the four heavy metal fractions namely the easily leachable and ion exchange (ELFE), acid reducible (AR), oxidizable organic (OO) and resistant (RR) fractions. This study shows that the soil samples were clayey (82 to 96% of grain size <63 μm), fairly high in organic carbon (6.54 to 8.71%) and slightly acidic (pH 4.92 to 5.12). Heavy metal content in the soils varied widely and occurred in the following decreasing order of Fe>Mn>Cr>Cd>Pb>Zn>Cu. Heavy metals such as Pb, Cu, Cr and Zn predominantly occurred in the insoluble form (RR fraction), with the oxides of Fe and Mn incorporated into the clay minerals. Although, the fertilizers and pesticides studied contained low amounts of heavy metals, the elevated amount of amount of Mn and Cd in the soils (ELFE fraction) could possibly be attributed to the longterm and repeated application of these materials to the cultivated paddy areas.Key words: Heavy metals, paddy soil, pesticide, fertilizer

The Pattern of Histologically-Proven Acute Post-infectious Glomerulonephritis in Tunisian Adults Seen in 1976 - 2004

Introduction: Acute post-infectious glomerulonephritis (APIGN) is uncommon in adults. It is widely recognized that the prognosis of APIGN is good in children. There is however little information about its long-term prognosis in adults.Methods: Between December 1976 and October 2004, 148 adult cases of APIGN were managed in our center. We retrospectively reviewed these patients’ records and evaluated their clinical course and outcome.Results: The mean age of studied patients was 36±15 years, and the male to female ratio was 2.3. The most common site of preceding infection was the respiratory tract (68.8%). At presentation, 89.2% had nephritic syndrome and 9.4% had rapidly progressive glomerulonephritis.Proteinuria was observed in 99.3%, hematuria in 95.3%, peripheral edema in 89.2% and hypertension in 81.8%. Most patients (60.7%) had acute kidney injury and four patients (2.7%) required dialysis. Renal biopsy showed diffuse endocapillary proliferative glomerulonephritis in 88.8% of patients, associated with extracapillary proliferation in 12%. After a median follow-up of 2.5 year, only two patients died and 16.12% of patients hadpersistent clinical and/or biological abnormality. Chronic kidney disease was noted in 10 patients (6.75%) including four patients (2.7%) who progressed to end-stage renal disease. Poor prognostic factors included nephrotic range proteinuria, extracapillary proliferation in renal biopsy,acute kidney injury and the need for dialysis.Conclusion: In this cohort of patients, APIGN progressed to chronic kidney disease in less than 10% of patients

Hereditary sensory and autonomic neuropathies: types II, III, and IV

The hereditary sensory and autonomic neuropathies (HSAN) encompass a number of inherited disorders that are associated with sensory dysfunction (depressed reflexes, altered pain and temperature perception) and varying degrees of autonomic dysfunction (gastroesophageal reflux, postural hypotention, excessive sweating). Subsequent to the numerical classification of four distinct forms of HSAN that was proposed by Dyck and Ohta, additional entities continue to be described, so that identification and classification are ongoing. As a group, the HSAN are rare diseases that affect both sexes. HSAN III is almost exclusive to individuals of Eastern European Jewish extraction, with incidence of 1 per 3600 live births. Several hundred cases with HSAN IV have been reported. The worldwide prevalence of HSAN type II is very low. This review focuses on the description of three of the disorders, HSAN II through IV, that are characterized by autosomal recessive inheritance and onset at birth. These three forms of HSAN have been the most intensively studied, especially familial dysautonomia (Riley-Day syndrome or HSAN III), which is often used as a prototype for comparison to the other HSAN. Each HSAN disorder is likely caused by different genetic errors that affect specific aspects of small fiber neurodevelopment, which result in variable phenotypic expression. As genetic tests are routinely used for diagnostic confirmation of HSAN III only, other means of differentiating between the disorders is necessary. Diagnosis is based on the clinical features, the degree of both sensory and autonomic dysfunction, and biochemical evaluations, with pathologic examinations serving to further confirm differences. Treatments for all these disorders are supportive