Periodic solutions for a nonautonomous ordinary differential equation

We consider the nonautonomous differential equation of second order x^″+a(t)x−b(t)x²+c(t)x³=0, where a(t),b(t),c(t) are T-periodic functions. This is a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of at least two positive T-periodic solutions for this equation, using coincidence degree theories.     

Mixed-Ligand Complex Formation Equilibria of Vanadium(III) with 2,2′-Bipyridine and the Amino Acids Glycine, Proline, α-Alanine and β-Alanine Studied in 3.0 mol?dm?3 KCl at 25 °C

We studied speciation of the mixed-ligand complex formation equilibria of vanadium(III) with both 2,2??-bipyridine (Bipy) and the amino acids glycine (HGly), proline (HPro), ??-alanine (H??Ala), and ??-alanine (H??Ala) by means of electromotive forces measurements emf(H) using 3.0?mol?dm^?3 KCl as the ionic medium at 25 °C. The experimental data were analyzed by means of the computational least-squares program LETAGROP, taking into account the hydrolysis of the vanadium(III) cation, the respective stability constants of the binary complexes, and the acid/base reactions of the ligands which were kept fixed during the analysis. In all four amino acid systems studied we observed the complexes [V₂O(Bipy)(B)]³⁺, [V₂O(Bipy)₂(B)₂]²⁺, [V(OH)(Bipy)(B)₂] and [V(OH)₂(Bipy)(B)], where B represents the deprotonated form of the amino acids studied in this work. The respective stability constants were determined and the species distribution diagrams as a function of pH are briefly discussed.     

The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings

Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring instantiations enlarges the scope of possible applications and favors the diversification of security assumptions. In this work, we extend the Ring-LWE problem in lattice-based cryptography to include algebraic lattices, realized through twisted embeddings. We define the class of problems Twisted Ring-LWE, which replaces the canonical embedding by an extended form. By doing so, we allow the Ring-LWE problem to be used over maximal real subfields of cyclotomic number fields. We prove that Twisted Ring-LWE is secure by providing a security reduction from Ring-LWE to Twisted Ring-LWE in both search and decision forms. It is also shown that the twist factor does not affect the asymptotic approximation factors in the worst-case to average-case reductions. Thus, Twisted Ring-LWE maintains the consolidated hardness guarantee of Ring-LWE and increases the existing scope of algebraic lattices that can be considered for cryptographic applications. Additionally, we expand on the results of Ducas and Durmus (Public-Key Cryptography, 2012) on spherical Gaussian distributions to the proposed class of lattices under certain restrictions. As a result, sampling from a spherical Gaussian distribution can be done directly in the respective number field while maintaining its format and standard deviation when seen in Zn via twisted embeddings.     

A method for calibration and validation subset partitioning

This paper proposes a new method to divide a pool of samples into calibration and validation subsets for multivariate modelling. The proposed method is of value for analytical applications involving complex matrices, in which the composition variability of real samples cannot be easily reproduced by optimized experimental designs. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. The proposed technique is illustrated in a case study involving the prediction of three quality parameters (specific mass and distillation temperatures at which 10 and 90% of the sample has evaporated) of diesel by NIR spectrometry and PLS modelling. For comparison, PLS models are also constructed by full cross-validation, as well as by using the Kennard-Stone and random sampling methods for calibration and validation subset partitioning. The obtained models are compared in terms of prediction performance by employing an independent set of samples not used for calibration or validation. The results of F-tests at 95% confidence level reveal that the proposed technique may be an advantageous alternative to the other three strategies.     

Online collaborative mind mapping in a mathematics teacher education program: a study on student interaction and knowledge construction

The inclusion of alternative and multimodal methods for online interaction and knowledge construction in mathematics teacher education is still an incipien     

Ion exchange equilibria between glass and molten salts

It is shown that interaction between the ions undergoing ion exchange leads to a sigmoidal equilibrium curve. A negative interaction in the glass causes the ratio of concentration of the two ions to be more nearly equal to unity in the glass than it is in the molten salt. It is further shown that the Rothmund-Kornfeld parameter is a measure of the non-ideality of the system. A value of the parameter greater than unity indicates a negative interaction energy.     

Gravitomagnetic Effect and Spin-Torsion Coupling

We study the gravitomagnetic effect in the context of absolute parallelism with the use of a modified geodesic equation via a free parameter b. We calculate the time difference in two atomic clocks orbiting the Earth in opposite directions and find a small correction due to the coupling between the torsion of space time and the internal structure of atomic clocks measured by the free parameter.     

Application of a fractional factorial design for the determination of cadmium by ETA-AAS in different atomization systems

A multivariate study was applied to the investigation of the variables affecting the cadmium sensitivity in a graphite furnace, with and without platform atomization or matrix modifier. The results indicated that, depending on the atomization system used, the factors studied (drying, ashing, atomization, calibration curve) exert an influence on the analysis. The interactions between the factors were also analyzed.     

Polyesters from Macrolactones Using Commercial Lipase NS 88011 and Novozym 435 as Biocatalysts

The demand for environmentally friendly products allied with the depletion of natural resources has increased the search for sustainable materials in chemical and pharmaceutical industries. Polyesters are among the most widely used biodegradable polymers in biomedical applications. In this work, aliphatic polyesters (from globalide and ω-pentadecalactone) were synthesized using a new commercial biocatalyst, the low-cost immobilized NS 88011 lipase (lipase B from Candida antarctica immobilized on a hydrophobic support). Results were compared with those obtained under the same conditions using a traditional, but more expensive, commercial biocatalyst, Novozym 435 (lipase B from C. antarctica immobilized on Lewatit VP OC). When NS 88011 was used in the polymerization of globalide, longer reaction times (240 min)—when compared to Novozym 435—were required to obtain high yields (80–90 wt%). However, higher molecular weights were achieved. When poly(ω-pentadecalactone) was synthesized, high yields and molecular weights (130,000 g mol^?1) were obtained and the enzyme concentration showed strong influence on the polyester properties. This is the first report describing NS 88011 in polymer synthesis. The use of this cheaper enzymatic preparation can provide an alternative for polyester synthesis via enzymatic ring-opening polymerization.     

Mercury determination by CV-AAS in wastewater and sewage sludge from a stabilization pond system

The mercury concentrations in wastewater and sewage sludge of a stabilization pond system have been evaluated. The system is built by three parallel facultative ponds followed by two systems of three maturation ponds in series. The samples of wastewater and sludge were digested using nitric acid and placed into a Parr-type bomb for 4 h at 110 degrees C. Mercury was measured by Cold Vapour Atomic Absorption Spectrometry (CV-AAS) at 253.7 nm with sodium tetrahydroborate as reductant. The methodologies were checked with an USEPA quality control sample, a standard reference material from NIST and with another method of mineralization (cold mineralization) showing good results. Concentrations of mercury in wastewater between 1.47 +/- 0.75 microgl(-1) have been found at the entrance of the system and 0.74 +/- 0.0 microgl(-1) at the exit, while in sludge the results were between 0.29 +/- 0.12 microgkg(-1) in the facultative pond and 0.04 +/- 0.02 microgkg(-1) in the second maturation pond (exit).