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)

Direct retrospective comparison of adalimumab and infliximab in preventing early postoperative endoscopic recurrence after ileocaecal resection for crohn's disease: results from the MULTIPER database

Both adalimumab [ADA] and infliximab [IFX] seem to be effective in the prevention of early postoperative endoscopic recurrence [EPER] after ileocaecal resection in Crohn's disease [CD] patients. There is lack of data with direct comparison between the two agents in the postoperative scenario. The aim of this study was to compare the rates of EPER in patients treated with ADA and IFX after ileocaecal resection for CD. This was a multicentre retrospective analysis of EPER rates in CD patients after ileocaecal resections, from seven referral centres in three countries. Endoscopic recurrence was defined as Rutgeerts' score ≥ i2. The patients were allocated according to treatment to two groups: ADA or IFX. The EPER rates were compared between the two treatment groups. Among the 168 patients included in the database, 96 received anti-tumour necrosis factor [TNF] agents after resection [37 in the ADA and 59 in the IFX groups] and were included in this comparative study. The groups were comparable in all baseline characteristics, mainly age, gender, previous resections, perianal CD, and mono or combination therapy. EPER was identified in 9/37 [24.32%] in the ADA group vs 16/59 [27.12%] in the IFX group [p = 0.815]. In this retrospective direct comparison between ADA and IFX therapy after ileocaecal resection, there was no significant difference between the two anti-TNF agents in terms of EPER rates. However, prospective randomised studies are needed to confirm these data and better define the role of each agent in the prevention of EPER.

Conventional versus biological therapy for prevention of postoperative endoscopic recurrence in patients with Crohn's disease: an international, multicenter, and observational study

Postoperative endoscopic recurrence (PER) occurs in nearly 80% of patients 1 year after ileocecal resection in patients with Crohn's disease (CD). Biological agents were more effective in reducing the rates of PER in comparison with conventional therapy, in prospective trials. The aim of this study was to compare the PER rates of biological versus conventional therapy after ileocecal resections in patients with CD in real-world practice. The MULTIPER (Multicenter International Postoperative Endoscopic Recurrence) database is a retrospective analysis of PER rates in CD patients after ileocecal resection, from 7 referral centers in 3 different countries. All consecutive patients who underwent ileocecal resections between 2008 and 2012 and in whom colonoscopies had been performed up to 12 months after surgery, were included. Recurrence was defined as Rutgeerts' score ≥i2. The patients were allocated to either biological or conventional therapy after surgery, and PER rates were compared between the groups. Initially, 231 patients were evaluated, and 63 were excluded. Of the 168 patients in the database, 96 received anti-tumor necrosis factor agents and 72 were treated with conventional therapy after resection. The groups were comparable regarding age, gender, and perianal disease. There was longer disease duration, more previous resections, and more open surgical procedures in patients on biologicals postoperatively. PER was identified in 25/96 (26%) patients on biological therapy and in 24/72 (33.3%) patients on conventional therapy (P=0.310). In this retrospective observational analysis from an international database, no difference was observed between biological and conventional therapy in preventing PER after ileocecal resections in CD patients.

Theorem for series in three-parameter mittag-leffler function

The new result presented here is a theorem involving series in the three-parameter Mittag-Le er function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional di erential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Le er function.

Biological therapy for the prevention and treatment of postoperative endoscopic recurrence in Crohn's disease: time for acceptance?

In most patients, postoperative endoscopic recurrence (PER) occurs 1 year after abdominal resection for Crohn’s disease (CD). Preventing PER is essential for disease control, as most patients develop further clinical and surgical recurrences. Conventional therapy with nitroimidazoles, aminosalicylates, and immunomodulators have limited efficacy for preventing PER. Initial trials with biological therapy (infliximab and adalimumab) showed promising results in preventing PER, and the efficacy of these drugs seems higher than that with conventional therapy. The aim of this review is to outline the results of studies that used infliximab or adalimumab for preventing and treating PER in CD patients. Data with both agents are available, and a few, small prospective trials have shown the efficacy of these drugs in patients with a high risk for recurrence. We believe that, in 2013, biological agents will be better accepted for the prevention PER in CD patients, in addition to the already existing data. Larger trials are still underway, and their results will certainly determine the role of these agents in PER, which develops after bowel resection for CD.

Risk factors for postoperative endoscopic recurrence in Crohn's disease: a Brazilian observational study

Introduction: Postoperative endoscopic recurrence (PER) is the initial event after intestinal resection in Crohn’s disease (CD), and after a few years most patients present with progressive symptoms and complications related to the disease. The identification of risk factors for PER can help in the optimization of postoperative therapy and contribute to its prevention. Methods: Retrospective, longitudinal, multicenter, observational study involving patients with CD who underwent ileocolic resections. The patients were allocated into two groups according to the presence of PER and the variables of interest were analyzed to identify the associated factors for recurrence. Results: Eighty-five patients were included in the study. The mean period of the first postoperative colonoscopy was 12.8 (3–120) months and PER was observed in 28 patients (32.9%). There was no statistical difference in relation to gender, mean age, duration of CD, family history, previous intestinal resections, smoking, Montreal classification, blood transfusion, residual CD, surgical technique, postoperative complications, presence of granulomas at histology, specimen extension and use of postoperative biological therapy. The preoperative use of corticosteroids was the only variable that showed a significant difference between the groups in univariate analysis, being more common in patients with PER (42.8% vs. 21%; p = 0.044). Conclusions: PER was observed in 32.9% of the patients. The preoperative use of corticosteroids was the only risk factor associated with PER in this observational analysis.