Development and validation of a RP-HPLC method for Roflumilast and its degradation products

Roflumilast is a phosphodiesterase type 4 inhibitor that is administered orally as a long-term, in the clinical treatment of chronic obstructive pulmonary disease and asthma. Launched in 2010 for the European market, it currently does not have an official monograph. Here, a reproducible gradient RP-HPLC method was developed and validated for the separation and determination of Roflumilast in the presence of its six major degradation products. Separation was performed on a C₁₈ analytical column (250?×?4.6?mm, 5?µm) with a mobile phase-A of ACN and a phase-B of ammonium acetate buffer (5?mM, pH 4.2) containing triethylamine (0.5% v/v). The most effective RP-HPLC gradient program was determined to be 0/80, 35/10, 36/80, 40/80 (time in minutes/% mobile phase-B). The flow rate was 1.0?ml/min and the column temperature was 25°C. The success of separation of the degradation products with different chemical characteristics was obtained by extending the time of the gradient, changing the proportion of the mobile phases and increasing the velocity of the flow. Two detectors were evaluated for the identification of degradation products and Roflumilast: a diode-arrary detector and a charged aerosol detector. The inability of the charged aerosol detector to dectect one of the six degradation products indicated that the method developed with RP-HPLC and the diode-array detector was more suitable for Roflumilast analysis. The method was validated according to specificity, linearity, LOD, LOQ, accuracy, precision and robustness.     

An algorithm for the determination of graphs associated to fold maps between closed surfaces

The aim of this paper is to introduce a computational tool that checks theoretical conditions in order to determine whether a weighted graph, as a topological invariant of stable maps, can be associated to stable maps without cusps (ie, fold maps) from closed surfaces to the projective plan.     

Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups

An associate inverse subsemigroup of a regular semigroup S is a subsemigroup T of S containing a least associate x* of each x ∈ S, in relation to the natural partial order ≤. In [1] the authors describe the structure of regular semigroups with an associate inverse subsemigroup, satisfying two natural conditions. In this paper we describe all *-homomorphisms and all *-congruences on such semigroups.     

Rigidity of Free Boundary Surfaces in Compact 3-Manifolds with Strictly Convex Boundary

In this paper, we obtain an analogue of Toponogov theorem in dimension 3 for compact manifolds \(M^3\) with nonnegative Ricci curvature and strictly convex boundary \(\partial M\). Here we obtain a sharp upper bound for the length \(L(\partial \Sigma )\) of the boundary \(\partial \Sigma \) of a free boundary minimal surface \(\Sigma ^2\) in \(M^3\) in terms of the genus of \(\Sigma \) and the number of connected components of \(\partial \Sigma \), assuming \(\Sigma \) has index one. After, under a natural hypothesis on the geometry of M along \(\partial M\), we prove that if \(L(\partial \Sigma )\) saturates the respective upper bound, then \(M^3\) is isometric to the Euclidean 3-ball and \(\Sigma ^2\) is isometric to the Euclidean disk. In particular, we get a sharp upper bound for the area of \(\Sigma \), when \(M^3\) is a strictly convex body in \(\mathbb {R}^3\), which is saturated only on the Euclidean 3-balls (by the Euclidean disks). We also consider similar results for free boundary stable CMC surfaces.     

Robust pair‐copula based forecasts of realized volatility

A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (p,q) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e‐markets poses some specific challenges. The large amount of real‐time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high‐frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair‐copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair‐copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine‐based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.     

Computational scheme for solving nonlinear fractional stochastic differential equations with delay

Abstract

This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation. The convergence and the numerical performance of the method are analyzed. The technique is adopted for determining the statistical indicators of stochastic responses of fractional Langevin and Mackey-Glass models with stochastic excitations.     

The degree of the bicanonical map of a surface with

In this note it is shown that, given a smooth minimal complex surface of general type with , , for which the bicanonical map is a morphism, the degree of is not 3. This completes our earlier results, showing that if is a minimal surface of general type with , such that is free, then the bicanonical map of can have degree 1, 2 or 4.

     

Pressure‐induced phase transitions in palmitic acid: C form

In this article, we report a high‐pressure Raman spectroscopy study of palmitic acid (PA, C form) from ambient pressure up to 21 GPa. The effects of hydrostatic pressure on the vibrational spectrum of PA are reported, and the data show that PA experiences a rich sequence of phase transformations. These changes in the crystal structure occur gradually as the pressure increases and they are related to the highly flexible crystalline structure. Copyright © 2011 John Wiley & Sons, Ltd.     

Strain-induced interference effects on the resonance Raman cross section of carbon nanotubes

In this Letter, we report the effects of strain on the electronic properties of single-wall carbon nanotubes. When we normalize the electronic transition energies to the corresponding values obtained for unstrained tubes, we obtain that, regardless of the tube diameter, all the data collapse onto universal curves following an n - m = constant family pattern. In the case of metallic tubes, quantum interference effects on the Raman cross section are predicted for strained tubes when the energies of the lower and the upper components have nearly the same values. Experimental evidence for the strain-induced Raman cross section changes is observed in single nanotube spectroscopy.