Peixoto's Theorem for vector fields on S2 with impasse points

The structural stability of vector fields with impasse regular curves on S2 is studied and a version of Peixoto's Theorem is established. Moreover a global analysis of normal forms of the constrained systems. A(x).ẋ=F(x),x∈R3,A∈M(3),F:R3→R3 in the Poincaré ball (i.e. in the compactification of R3 with the sphere S2 of the infinity) is made. © 2013 Elsevier Masson SAS.

STEAP1 protein overexpression is an independent marker for biochemical recurrence in prostate carcinoma

Aims: To investigate the prognostic value of expression levels of the genes STEAP1 and STEAP2, and of STEAP1 protein, in prostate carcinomas (PCa). Methods and results: STEAP1 and STEAP2 transcript levels were evaluated by RT-qPCR in samples from 35 PCa, 24 adjacent non-neoplastic prostate (AdjP) tissues, five cases of benign prostatic hyperplasia (BPH), and two histologically normal prostates (N). STEAP1 expression was assessed by immunohistochemistry in samples from 198 PCa, 76 AdjP, 22 BPH, and two N. The findings were compared with clinical and pathological parameters and patient outcome. STEAP1 and STEAP2 transcript analysis showed no differences between the groups tested. Although not significant, higher STEAP1 mRNA levels were detected in tumours with high Gleason scores and in patients who presented with biochemical recurrence (BCR). STEAP1 overexpression was detected in PCa, and was significantly associated with high-grade Gleason scores, seminal vesicle invasion, BCR, and worse outcome (metastasis or PCa-specific death). STEAP1 overexpression was significantly associated with shorter BCR-free survival. Multivariate analysis revealed that STEAP1 is an independent marker for BCR. Conclusions: These findings provide evidence that STEAP1 is a biomarker of worse prognosis in PCa patients. © 2013 John Wiley & Sons Ltd.

Ki-67 and CD100 immunohistochemical expression is associated with local recurrence and poor prognosis in soft tissue sarcomas, respectively

Soft tissue sarcomas (STSs) are a heterogeneous group of mesenchymal tumors of >50 subtypes. However, STSs represent <1% of types of cancer. Despite this low frequency, the disease is aggressive and treatment, when possible, is based on traditional chemotherapies. A number of cases of resistance to adjuvant therapies have been reported. Metastases are commonly identified in STS patients during diagnosis and the development of effective clinical parameters is crucial for correct management of the disease. The use of biological markers in cancer is a useful tool to determine patient prognosis. Ki--67 is a protein marker for proliferation of somatic cells and is widely used in prognostic studies of various types of tumor, including STSs. Cluster of differentiation 100 (CD100) is a member of the semaphorin family. The family was initially described as axon guidance molecules important for angiogenesis, organogenesis, apoptosis and neoplasia. CD100 was previously utilized as a prognostic factor in tumors and also in STSs. In the present study, protein expression of Ki--67 and CD100 was analyzed by immunohistochemistry in samples of STS patients of the Barretos Cancer Hospital (Barretos, Brazil) to establish prognostic criteria of the disease. Results demonstrate a correlation between CD100 expression and poor prognosis, consistent with a previous study. Moreover, the expression of Ki-67 was identified to correlate with presence of local or locoregional recurrence. To the best of our knowledge, no large casuistic study has revealed this correlation between Ki--67 and local recurrence in STSs. The use of Ki--67 and CD100 as markers in clinical pathological analysis may be suitable as a prognostic criterion in disease progression.

Polinômios ortogonais em várias variáveis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of clinical therapy and nutritional counseling on the recurrence of urolithiasis

PURPOSE: To evaluate the influence of combined clinical therapy and nutritional guidance on the recurrence of urolithiasis. METHODS: From our registry of patients with recurrent urolithiasis we selected 57 who had at least 5-years of follow-up. We collected 24h urine samples in order to analyze Ca, Na, uric acid, citrate, oxalate, and Mg concentrations and to assess urine volume. Patients filled out a clinical questionnaire before treatment, and abdominal radiographs and/or ultrasound were performed both before treatment and during the follow-up period. During follow-up, specific and individualized dietary advice was given based on the individual's metabolic disorders. Patients also received specific pharmacological treatment for their metabolic alterations. Outcome measures were metabolites in urine and the urolith recurrence rate. Pre- and post- intervention values were compared using tests as appropriate. RESULTS: Fifty six of the patients were male and the majority of patients were overweight. The mean BMI was 27 kg/m2. Urinary excretion of calcium, uric acid and sodium decreased significantly over the five year follow-up period. The number of uroliths that formed during the 5-year follow-up also decreased significantly compared to pre-treatment values. CONCLUSION: Individualized dietary advice combined with pharmacological treatment significantly reduces long-term urolithiasis recurrence.

Multifractality, stickiness, and recurrence-time statistics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Invasive head and neck cutaneous squamous cell carcinoma: clinical and histopathological characteristics, frequency of local recurrence and metastasis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A simple application of implicit function theorem

In this note we show that the roots of a polynomial are C∞ depend of the coefficients. The main tool to show this is the Implicit Function Theorem.

Tsukamoto s Theorem in Characteristic two

In this paper it is proved that hermitian forms over quaternion division algebras over local fields of characteristic two are classified by their dimension and discriminant.

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Square of the Error Octonionic Theorem and Hypercomplex Fourier Series

The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.

Thick braneworlds and the Gibbons-Kallosh-Linde no-go theorem in the Gauss-Bonnet framework

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)