Decay chain differential equations: Solution through matrix algebra

A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. (C) 2009 Elsevier B.V. All rights reserved.

Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Shared and differential traits in the accessory olfactory bulb of caviomorph rodents with particular reference to the semiaquatic capybara

The vomeronasal system is crucial for social and sexual communication in mammals. Two populations of vomeronasal sensory neurons, each expressing G alpha i2 or G alpha o proteins, send projections to glomeruli of the rostral or caudal accessory olfactory bulb, rAOB and cAOB, respectively. In rodents, the G alpha i2- and G alpha o-expressing vomeronasal pathways have shown differential responses to small/volatile vs. large/non-volatile semiochemicals, respectively. Moreover, early gene expression suggests predominant activation of rAOB and cAOB neurons in sexual vs. aggressive contexts, respectively. We recently described the AOB of Octodon degus, a semiarid-inhabiting diurnal caviomorph. Their AOB has a cell indentation between subdomains and the rAOB is twice the size of the cAOB. Moreover, their AOB receives innervation from the lateral aspect, contrasting with the medial innervation of all other mammals examined to date. Aiming to relate AOB anatomy with lifestyle, we performed a morphometric study on the AOB of the capybara, a semiaquatic caviomorph whose lifestyle differs remarkably from that of O. degus. Capybaras mate in water and scent-mark their surroundings with oily deposits, mostly for male-male communication. We found that, similar to O. degus, the AOB of capybaras shows a lateral innervation of the vomeronasal nerve, a cell indentation between subdomains and heterogeneous subdomains, but in contrast to O. degus the caudal portion is larger than the rostral one. We also observed that four other caviomorph species present a lateral AOB innervation and a cell indentation between AOB subdomains, suggesting that those traits could represent apomorphies of the group. We propose that although some AOB traits may be phylogenetically conserved in caviomorphs, ecological specializations may play an important role in shaping the AOB.

Angiomyolipomatous hamartoma of the upper lip: A rare case in an 8-month-old child and differential diagnosis

Hamartoma is a proliferation of normal tissues that are considered endogenous to the site of occurrence. In the head and neck region, hamartomas composed of other tissues different from blood and lymphatic vessels (hemangiomas and lymphangiomas) are very uncommon. We report an unusual case of upper lip angiomyolipomatous hamartoma in an 8-month-old patient. The patient underwent surgical treatment and the 1-year follow-up revealed no signs of recurrence. Angiomyolipomatous hamartoma is a very rare condition in the paediatric population group, especially in the head and neck region. It should be considered in the differential diagnosis of congenital lesions in childhood. (C) 2010 European Association for Cranio-Maxillo-Facial Surgery.

Differential Shh, Bmp and Wnt gene expressions during craniofacial development in mice

In this study, Bmp-4, Wnt-5a and Shh gene expressions were compared during early craniofacial development in mice by comparative non-isotopic in situ hybridization. Wild-type C57BL/6J mice were studied at various stages of embryonic development (from 8.5- to 13.5-day-old embryos - E8.5-13.5). During early odontogenesis, transcripts for Bmp-4, Shh and Wnt-5a were co-localised at the tooth initiation stage. At E8.5, Shh mRNA expression was restricted to diencephalon and pharyngeal endoderm. Before maxillae and mandible ossification, Bmp-4 and Wnt-5a signals were detected in the mesenchymal cells and around Meckel`s cartilage. During palatogenesis, Shh was expressed only in the epithelium and Wnt-5a only in the mesenchyme of the elevating palatal shelves. During tongue development, Shh expression was found in mesenchyme, probably contributing to tongue miogenesis, while Wnt-5a signal was in the epithelium, possibly during placode development and papillae formation. Taken together, these findings suggest that Bmp-4, Shh and Wnt-5a gene expressions may act together on the epithelial mesenchymal interactions occurring in several aspects of the early mouse craniofacial development, such as odontogenesis, neuronal development, maxillae and mandible ossification, palatogenesis and tongue formation. (C) 2009 Elsevier GmbH. All rights reserved.

Differential expression of galectin-3, beta-catenin, and cyclin D1 in adenoid cystic carcinoma and polymorphous low-grade adenocarcinoma of salivary glands

Background: Galectin-3 has been implicated in tumor progression of some malignancies as thyroid, prostate, and salivary gland tumors. Recently, it has been suggested that this protein may be an important mediator of the beta-catenin/Wnt pathway. Moreover, nuclear galectin-3 expression has been implicated in cell proliferation, promoting cyclin D1 activation. Thus, the present study aimed to correlate galectin-3 expression with beta-catenin and cyclin D1 expressions in adenoid cystic carcinoma (ACC) and in polymorphous low-grade adenocarcinoma (PLGA). Methods: Fifteen formalin-fixed paraffin-embedded cases of each tumor were retrieved from the files of the Surgical Oral Pathology Service at the University of Sao Paulo and the proteins were analyzed by immunohistochemistry. Results: Adenoid cystic carcinoma showed galectin-3 immunostaining mainly in the nuclei, while PLGA revealed a positive mostly cytoplasmic reaction to galectin-3 in the largest part of tumor cells. Both tumors showed intense cytoplasmic/nuclear staining for beta-catenin in majority of cases. Cyclin D1 immunoreactivity was not detected in 14/15 PLGA and showed specific nuclear staining in 10/15 cases of ACC in more than 5% of the neoplastic cells. Cyclin D1 expression was correlated with cytoplasmic and nuclear galectin-3 expression in ACC (P < 0.05). Conclusions: These results suggest that in ACC galectin-3 may play a role in cellular proliferation through cyclin D1 activation. In addition, nuclear expression of galectin-3 in ACC may be related to a more aggressive behavior of this lesion. Although beta-catenin seems to play a role in carcinogenesis in both lesions, it seems that it does not bind to galectin-3 for cyclin D1 stimulation.

Differential bonds degradation of two resin-modified glass-ionomer cements in primary and permanent teeth

Objectives: To evaluate the effect of chemical degradation on bond strength of resin-modified glass-ionomer cements bonded to primary and permanent dentin. Methods: Class I cavities of permanent and primary extracted human molars were restored with two resin-modified glass-ionomer cements: Fuji 11 LC and Vitremer, and stored in water for 24 h. Half samples were immersed in 10% NaOCl aqueous solution for 5 h. Teeth were sectioned into beams and tested for microtensile bond strengths. Results were analyzed with multiple ANOVA and Tukey`s tests (p < 0.05). Analysis of debonded surfaces was performed by SEM. Results: 24 h bond strengths for Vitremer and Fuji 11 LC were similar. For Fuji 11, bond strength values were higher for primary than for permanent dentin. Vitremer bond strength was similar for both. Chemical degradation did not affect Fuji I] LC bond strength to dentin. However, decreases in bond strength were found for Vitremer groups after NaOCl immersion. Signs of glass ionomer-dentin interaction were evident by SEM analysis for Fuji 11 LC specimens. Conclusions: Vitremer and Fuji II presented similar bond strength at 24. Vitremer dentin bonds were prone to chemical degradation. Fuji II LC-dentin bonds showed typical features of glass-ionomer dentin interaction at the bonded interfaces, and were resistant to in vitro degradation. (C) 2009 Elsevier Ltd. All rights reserved.

Differential patterns of receptor activator of nuclear factor kappa B ligand/osteoprotegerin expression in human periapical granulomas: Possible association with progressive or stable nature of the lesions

Receptor activator of nuclear factor kappa B ligand (RANKL) and osteoprotegerin (OPG) are expressed in apical periodontitis, suggesting a role for these molecules during lesion development. However, the profiles of RANKL/OPG expression in periapical lesions remain unknown. In this study we investigated the patterns of RANKL and OPG mRNA expression by real-time polymerase chain reaction in human periapical granulomas (N = 44) and compared them with sites presenting characteristic bone resorbing activity: healthy (n = 14) and orthodontically stretched and compressed periodontal ligament (n = 26), healthy gingiva (n = 24), chronic gingivitis (n = 32), and chronic periodontitis (n = 34) samples. Both RANKL and OPG mRNA expression was higher in periapical granulomas when compared with healthy periodontal ligament. Distinct patterns of RANKL and OPG expression ratio were found in the granulomas and in different physiologic and pathologic conditions, with characteristic bone resorption activity potentially being indicative of the stable or progressive nature of the lesions. Lesions with radiographic image smaller than 5 mm showed higher RANKL/OPG expression than images greater than 5 mm. Periapical granulomas presented heterogeneous patterns of RANKL and OPG expression, ranging from samples with RANKL/OPG ratio similar to that seen in sites with minimal or absent bone resorption to samples with RANKL/OPG expression pattern comparable with active bone resorption sites.

Differential Production of Macrophage Inflammatory Protein-1 alpha, Stromal-Derived Factor-1, and IL-6 by Human Cultured Periodontal Ligament and Gingival Fibroblasts Challenged With Lipopolysaccharide From P. gingivalis

Background: Fibroblasts are considered important cells in periodontitis. When challenged by different agents, they respond through the release of cytokines that participate in the inflammatory process. The aim of this study is to evaluate and compare the expression and production of macrophage inflammatory protein (MIP)-1 alpha, stromal-derived factor (SDF)-1, and interleukin (IL)-6 by human cultured periodontal ligament and gingival fibroblasts challenged with lipopolysaccharide (LPS) from Porphyromonas gingivalis. Methods: Fibroblasts were cultured from biopsies of gingival tissue and periodontal ligament of the same donors and used on the fourth passage. After confluence in 24-well plates, the culture medium alone (control) or with 0.1 to 10 mu g/ml of LPS from P. gingivalis was added to the wells, and after 1, 6, and 24 hours, the supernatant and the cells were collected and analyzed by enzyme-linked immunosorbent assay and real-time polymerase chain reaction, respectively. Results: MIP-1 alpha, SDF-1, and IL-6 protein production was significantly greater in gingival fibroblasts compared to periodontal ligament fibroblasts. IL-6 was upregulated in a time-dependent manner, mainly in gingival fibroblasts (P<0.05), which secreted more MIP-1 alpha in the lowest concentration of LPS used (0.1 mu g/ml). In contrast, a basal production of SDF-1 that was inhibited with the increase of LPS concentration was detected, especially after 24 hours (P<0.05). Conclusion: The distinct ability of the gingival and periodontal ligament fibroblasts to secrete MIP-1 alpha, SDF-1, and IL-6 emphasizes that these cells may differently contribute to the balance of cytokines in the LPS-challenged periodontium. J Periodontol 2010;81:310-317.

The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.