Matchings in graphs of odd regularity and girth

We establish lower bounds on the matching number of graphs of given odd regularity d$d$ and odd girth g$g$, which are sharp for many values of d$d$ and g$g$. For d=g=5$d=g=5$, we characterize all extremal graphs.     

Iteration-complexity of first-order penalty methods for convex programming

This paper considers a special but broad class of convex programming problems whose feasible region is a simple compact convex set intersected with the inverse image of a closed convex cone under an affine transformation. It studies the computational complexity of quadratic penalty based methods for solving the above class of problems. An iteration of these methods, which is simply an iteration of Nesterov’s optimal method (or one of its variants) for approximately solving a smooth penalization subproblem, consists of one or two projections onto the simple convex set. Iteration-complexity bounds expressed in terms of the latter type of iterations are derived for two quadratic penalty based variants, namely: one which applies the quadratic penalty method directly to the original problem and another one which applies the latter method to a perturbation of the original problem obtained by adding a small quadratic term to its objective function.     

Structural and optical spectroscopy of LiNbO3:Tm nanocrystals embedded in a SiO2 glass matrix

Transparent SiO₂:Li₂O:Nb₂O₅ glass doped with Tm³⁺ has been prepared by the sol–gel method, and heat-treated in air (HT) at temperatures between 500 and 800 °C. X-ray diffraction (XRD) patterns and Raman spectroscopy show SiO₂ and LiNbO₃ phases in samples HT above 650 °C, and a NbTmO₄ phase for T > 750 °C. The XRD SEM analysis show increasing particle size and number with the increase of HT temperature. Intra-4f¹² transitions due to Tm³⁺ ion dispersed in the matrix are observed in samples with T > 650 °C. The luminescence is dominated by the ¹G₄ → ³F₄ (～650 nm), ¹D₂ → ³F₃ (～780 nm), ³H₄ → ³H₆ (～800 nm), ³H₅ → ³H₆ (～1200 nm) and ³H₄ → ³F₄ (～1500 nm) transitions under resonant excitation to the ion levels.     

A liquid chromatography coupled to quadrupole–time-of-flight–mass spectrometry (LC–QTOF–MS) method for identification analysis of saponins from Quillaja saponaria bark extracts in foot-and-mouth disease vaccines: Development,validation and applicability

Saponins from Quillaja saponaria have been commonly used as immunomodulatory adjuvants in foot-and-mouth disease vaccines (FMDVs). However, due to the lack of consensus over the possible exacerbation of local inflammatory responses in cattle and its economic impacts, their use has been discouraged by Brazilian authorities. A qualitative method intended to determine the presence of saponins from Q. saponaria bark extracts in FMDVs was developed and validated. Instrumental analysis was performed using an liquid chromatography (LC) coupled to a quadrupole–time-of-flight–mass spectrometry (TOF-MS) system. The method was validated according to the International Conference on Harmonization Harmonized Tripartite Guideline Q2 (R1) and Brazilian Ministry of Agriculture, Livestock and Food Supply Analytical Quality Assurance Guidelines. Validation parameters were determined and considered suitable to the established criteria. The validated method has been applied in routine analysis in the National Agricultural Laboratory at Rio Grande do Sul (LANAGRO-RS). All results obtained were in agreement with the vaccine's composition described by the manufacturer. The method is easy and adequate for analysis in routine laboratories. To the best of the authors' knowledge, this is the first report of a method which intends to investigate the presence of saponins from Q. saponaria bark extracts in veterinary vaccines.     

A note on chain-based semi-Heyting algebras

We determine the number of non-isomorphic semi-Heyting algebras on an n-element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non-isomorphic semi-Heyting chains of a given size in some important subvarieties of the variety of semi-Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers $A(n,m)$ of non-isomorphic semi-Heyting chains with n elements such that removing the mth element ($1<m<n$) we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi-Heyting chain with $n-1$ elements can be extended to a n element semi-Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers $A(n,m)$ that provides some extra information.     

Essential oil from the leaves of Xylopia langsdorfiana (Annonaceae) as a possible spasmolytic agent

Xylopia langsdorfiana A. St.-Hil. &Tul. (Annonaceae) is popularly known in the northeast of Brazil as ‘pimenteira da terra’, and an essential oil (XL-OE) was extracted from its leaves. Since Xylopia species are cited in folk medicine and diterpenes from X. langsdorfiana have spasmolytic activity, this study aimed to investigate a possible spasmolytic action of XL-OE on smooth muscle models. XL-OE (243 and 729 μg/mL) showed low pharmacologic efficacy on guinea pig trachea and rat aorta and uterus. However, in guinea pig ileum, XL-OE (27–729 μg/mL) inhibited carbachol or histamine-induced phasic contractions (1 μM) in a significant and concentration-dependent manner. In addition, XL-OE (81 μg/mL) reduced fluorescence intensity in ileal myocytes stimulated by histamine, indicating a decrease in cytosolic calcium concentration, which could explain the spasmolytic activity. Thus, XL-OE proved to be a promising natural product to be used in gastrointestinal diseases acting by modulating the cytosolic calcium concentration.