A Neumann problem of Ambrosetti–Prodi type

The aim of this paper is to establish an Ambrosetti–Proditype result for the problem

$$\left\{ \begin{array}{ll}-\Delta{u} = g(x, u,\nabla{u}) + t\varphi \quad {\rm in}\, \Omega,\\ \frac{\partial{u}}{\partial\eta} = 0 \qquad\qquad\qquad\quad {\rm on}\, \partial\Omega ;\end{array} \right.$$

i.e., under appropriate conditions, we will show that there exists a constant t ₀ such that the problem above has no solution if t > t ₀, at least a solution if t =  t ₀ and at least two solutions if t < t ₀. The proof is based on a combination of upper and lower solutions method and the Leray–Schauder degree.

     

Effects of Low‐Level Laser Therapy (LLLT) and Diclofenac (Topical and Intramuscular) as Single and Combined Therapy in Experimental Model of Controlled Muscle Strain in Rats

Muscle injuries represent ca 30% of sports injuries and excessive stretching of muscle causes more than 90% of injuries. Currently the most used treatments are nonsteroidal anti‐inflammatory drugs (NSAIDs), however, in last years, low‐level laser therapy (LLLT) is becoming an interesting therapeutic modality. The aim of this study was to evaluate the effect of single and combined therapies (LLLT, topical application of diclofenac and intramuscular diclofenac) on functional and biochemical aspects in an experimental model of controlled muscle strain in rats. Muscle strain was induced by overloading tibialis anterior muscle of rats. Injured groups received either no treatment, or a single treatment with topical or intramuscular diclofenac (TD and ID), or LLLT (3 J, 810 nm, 100 mW) 1 h after injury. Walking track analysis was the functional outcome and biochemical analyses included mRNA expression of COX‐1 and COX‐2 and blood levels of prostaglandin E₂ (PGE₂). All treatments significantly decreased COX‐1 and COX‐2 gene expression compared with injury group (P < 0.05). However, LLLT showed better effects than TD and ID regarding PGE₂ levels and walking track analysis (P < 0.05). We can conclude that LLLT has more efficacy than topical and intramuscular diclofenac in treatment of muscle strain injury in acute stage.     

Major and trace element characterization of prehistoric ceramic from Rezende archaeological site

Forty one ceramic fragment samples from Rezende archaeological site, Centralina city, Minas Gerais State, Brazil, were analyzed using INAA to determine the concentration of 24 chemical elements: As, Ba, Ce, Co, Cr, Cs, Eu, Fe, Hf, K, La, Lu, Na, Nd, Rb, Sb, Sc, Sm, Ta, Tb, Th, U, Yb and Zn. Three multivariate statistical methods, cluster, discriminant and principal components analysis were performed on the data set. The results showed that the large majority of the samples (94%) can be considered to be manufactured using the same source of raw material.     

Characterization of geomaterials from NE Portugal using k 0-based instrumental neutron activation analysis (k 0-INAA) and gamma spectrometry methods

The main objective of this study is the elemental characterization of geomaterial samples (??soils?? and Ra?as), collected between 2007 and 2008, in the Morais Massif, (NE Mainland of Portugal) by using two complementary techniques: instrumental neutron activation analysis (INAA) and high resolution gamma spectrometry. Samples granulometric fractions lower than 63???m were analyzed by gamma spectrometry, for artificial and natural radionuclides using HPGe detectors and by INAA, for chemical elements at the Portuguese research reactor, RPI. Statistical analysis, such as clusters analysis and Pearson correlations were applied to the obtained results. The enrichment factors were also calculated as an estimator of anthropogenic inputs in relation to the average crustal abundance. Group differentiation of Ra?as and ??soils?? is clearly shown from cluster analysis. The strong correlation factors obtained between some chemical elements corroborates the origins and the geology/mineralogy of the area studied. The combined application of both nuclear analytical techniques has shown their importance in providing useful information for the future site and repository performance and safety assessment studies.     

Glycosylation patterns of human alpha2-macroglobulin: Analysis of lectin binding by electron microscopy

Human alpha2-macroglobulin (α2M) is a 720 kDa glycoprotein that presents two ultrastructural conformations: slow (S-α2M) and fast (F-α2M). α2M acts mainly as a proteinase scavenger, but an immunomodulatory role was also proposed. This work studies the effect of desialylation and deglycosylation on the structure patterns of α2M by ultrastructural analysis of lectin-induced aggregates, which represents a new approach that had never been previously used. Transmission electron microscopy (TEM) analysis showed the loss of S-α2M conformation after deglycosylation, indicating that glycosidic side-chains contribute to the molecular stability of S-α2M. TEM proved to be an important tool to analyze the effect of biochemical changes on α2M, yielding an objective qualitative control of its morphological state. Certain carbohydrate residues did not vary between the α2M conformations, since both bound similarly ConA and WGA lectins. However, the binding of PNA and BSI-B₄ was slightly lower in F-α2M than in S-α2M. Among the neuraminidases used to desialylate both conformations of α2M that from Arthrobacter ureafaciens was the most effective. Incubation with the lectins ConA or SNA, respectively specific for mannosyl and sialyl residues, led to dose-dependent patterns of aggregation of α2M molecules, mediated by lectin binding and clearly visualized by TEM.     

Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model 1 assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2.     

Equilibrium Constant Units Revisited

The problem of the units associated with equilibrium constants is revisited. A brief survey of the arguments for and against using units with equilibrium constants is presented and the compromise solution that we have adopted in our teaching, both at the university and school level, is presented and justified.     

Microinjection molding of polyamide 6

Processing polymers by microinjection molding (μIM) generate specific constraints upon the polymer melt such as high shear stress and rapid cooling, leaving a mark upon the microstructure of the micropart. The present work compares the morphology and structure of polyamide 6 samples produced by melt extrusion and μIM. The specimens obtained were analyzed by polarized light microscopy, differential scanning calorimetry, and wide‐angle X‐ray diffraction. α and γ crystalline forms were formed in polyamide 6 samples prepared by both methods. The γ form was dominant in the skin of the microinjection molded part, with larger contribution for these samples compared with extruded samples. The conditions used in μIM lead to considerable orientation at the skin region, decreasing toward the core, while the extruded samples showed almost no orientation. The overall degree of crystallinity of the microinjection molded part was lower compared with the extruded sample. Copyright © 2014 John Wiley & Sons, Ltd.