On the instructional model of a blended learning program for developing mathematical knowledge for teaching

ZDM – Mathematics Education - Blended learning, which combines face-to-face workshops with self-directed online learning, is becoming a good alternative in designing and deploying...     

Liouville Type Theorems for Elliptic Equations with Gradient Terms

In this paper we obtain Liouville type theorems for nonnegative supersolutions of the elliptic problem ${-\Delta u + b(x)|\nabla u| = c(x)u}$ in exterior domains of ${\mathbb{R}^N}$ . We show that if lim ${{\rm inf}_{x \longrightarrow \infty} 4c(x) - b(x)^2 > 0}$ then no positive supersolutions can exist, provided the coefficients b and c verify a further restriction related to the fundamental solutions of the homogeneous problem. The weights b and c are allowed to be unbounded. As an application, we also consider supersolutions to the problems ${-\Delta u + b|x|^{\lambda}|{\nabla} u| = c|x|^{\mu} u^p}$ and ${-\Delta u + be^{\lambda |x|}|\nabla u| = ce^{\mu |x|}u^p}$ , where p > 0 and λ, μ ≥ 0, and obtain nonexistence results which are shown to be optimal.     

Effect of support and pre-treatment conditions on Pt-Sn catalysts: application to nitrate reduction in water

The effect of the support (activated carbon or titanium dioxide) on the catalytic activity and selectivity to nitrogen of Pt-Sn catalysts in nitrate reduction was studied. The effects of the preparation conditions and the Pt:Sn atomic ratio were also evaluated. It was observed that the support plays an important role in nitrate reduction and that different preparation conditions lead to different catalytic activities and selectivities. Generally, the catalysts supported on activated carbon were less active but more selective to nitrogen than those supported on titanium dioxide. The monometallic Pt catalyst is active for nitrate reduction only when supported on titanium dioxide, which is explained by the involvement of the support in the reaction mechanism. The catalysts were characterized by different techniques, and significant changes on metal chemical states were observed for the different preparation conditions used. Only metallic Pt and oxidized Sn were observed at low calcination and reduction temperatures, but some metallic Sn was also present when high temperatures were used, being also possible the formation of Pt-Sn alloys.     

Structure and properties of one-dimensional heterobimetallic polymers containing dicyanoaurate and dirhodium(II) fragments

The synthesis and characterization of compound [Rh(2)(O(2)CEt)(4)(H(2)O)(2)] (1) and one-dimensional heterobimetallic polymers K(n){Rh(2)(O(2)CEt)(4)[Au(CN)(2)]}(n) (2) and K(n){Rh(2)(O(2)CMe)(4)[Au(CN)(2)]}(n)·4nH(2)O (3), constructed from dirhodiumtetracarboxylato units, [Rh(2)(O(2)CR)(4)](+), and dicyanoaurate, [Au(CN)(2)](-), fragments are described. In both compounds 2 and 3 the resulting polymeric chains are nonlinear and have in common similar structural parameters, although the solid state supramolecular arrangement is very different. These structural differences explain the fact that complex 2 displays aurophilic interactions while this type of interactions are absent in complex 3. As a result, compound 2 shows rich blue luminescent properties whereas compound 3 is not luminescent. The electrical conductivity in solid state of compounds 2 and 3 is also studied.     

Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in \mathbb R ^3

We consider the polynomial vector fields of arbitrary degree in $\mathbb R ^3$ R 3 having the 2-dimensional algebraic torus $$\begin{aligned} \mathbb T ^2(l,m,n)=\{(x,y,z)\in \mathbb R ^3 : (x^{2l}+y^{2m}-r^2)^2+z^{2n}-1=0\}, \end{aligned}$$ T 2 ( l , m , n ) = { ( x , y , z ) ∈ R 3 : ( x 2 l + y 2 m - r 2 ) 2 + z 2 n - 1 = 0 } , where $l,m$ l , m , and $n$ n positive integers, and $r\in (1,\infty )$ r ∈ ( 1 , ∞ ) , invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on $\mathbb T ^2(l,m,n)$ T 2 ( l , m , n ) . Furthermore, we analyze when these invariant meridians or parallels are limit cycles.     

Luminescent Thermochromism of 2D Coordination Polymers Based on Copper(I) Halides with 4‐Hydroxythiophenol

Solvothermal reactions between copper(I) halides and 4‐mercaptophenol give rise to the formation of three coordination polymers with general formula [Cu₃X(HT)₂]_n (X=Cl, 1 ; Br, 2 ; and I, 3 ). The structures of these coordination polymers have been determined by X‐ray diffraction at both room‐ and low temperature (110 K), showing a general shortening in Cu?S, Cu?X and Cu?Cu bond lengths at low temperatures. 1 and 2 are isostructural, consisting of layers in which the halogen ligands act as μ₃‐bridges joining two Cu1 and one Cu2 atoms whereas in 3 the iodine ligands is as μ₄‐mode but the layers are quasi‐isostructural with 1 or 2 . These compounds show a reversible thermochromic luminescence, with strong orange emission for 1 and 2 , but weaker for 3 at room temperature, whereas upon cooling at 77 K 1 and 2 show stronger yellow emission, and 3 displays stronger green emission. DFT calculations have been used to rationalize these observations. These results suggest a high potential for this novel and promising stimuli‐responsive materials.     

Quantification of alkali-labile phosphate groups in the plasma of Oreochromis niloticus exposed to intermittent discharges of oestrogens: effect of concentration vs. load

Vitellogenin protein (Vtg) in Oreochromis niloticus plasma has been indirectly quantified through protein-bound phosphate groups also known as alkali-labile phosphates (ALP) using a recently modified method. Such method as described in the literature was originally applied to Crucian carp and resulted in lower detection limits (3.2 μg PO₄^3–per mL). In this study, O. niloticus males were exposed to intermittent doses of oestrogens for 15 days using different concentrations (converted to loads) of 17α-ethinyloestradiol (EE2) (two different aquarium volumes), oestrone (E1) and 17β-oestradiol (E2) individually and in combination (1:1:1). The induction of physiologic and genotoxic effects in erythrocytes was investigated. For the tested oestrogen (EE2), load proved to be more relevant than concentration in determining the oestrogenicity. O. niloticus males proved to have lower ALP baseline (4.11 µg PO₄^3?/mL plasma, IQ₂₅ = 3.38; IQ₇₅ = 5.18) than other fish species, including Crucian carp, which makes it suitable for oestrogenicity detection in water. Exposure to E2, EE2 separately and in combination (1:1:1) all induced significant increases in the ALP levels at loads ≥ 0.72 μg/fish. This load was three times lower than the E1 load required to increase ALP (≥ 2.2 μg/fish). All oestrogens with loads ≥ 0.072 μg/fish caused significant increase in micronucleus frequency (≥ 2‰) compared with the control (0.1 ± 0.4‰). The study highlighted the importance of taking into account not only concentration and dose regime but also the mass load and therefore, the volume used in the experimental units, which is rarely addressed in ecotoxicity assays. Considering the good sensitivity of O. niloticus exposed to relatively low concentrations of oestrogens, the combination of the ALP method with auxiliary biomarkers (particularly micronucleus) can be used as a protocol for oestrogenicity and genotoxicity detection in different contaminated waters as part of water environmental monitoring programmes.     

Analyzing Emotion Expression in Singing via Flow Glottograms,Long-Term-Average Spectra,and Expert Listener Evaluation

BackgroundAcoustic aspects of emotional expressivity in speech have been analyzed extensively during recent decades. Emotional coloring is an important if not the most important property of sung performance, and therefore strictly controlled. Hence, emotional expressivity in singing may promote a deeper insight into vocal signaling of emotions. Furthermore, physiological voice source parameters can be assumed to facilitate the understanding of acoustical characteristics.MethodThree highly experienced professional male singers sang scales on the vowel /ae/ or /a/ in 10 emotional colors (Neutral, Sadness, Tender, Calm, Joy, Contempt, Fear, Pride, Love, Arousal, and Anger). Sixteen voice experts classified the scales in a forced-choice listening test, and the result was compared with long-term-average spectrum (LTAS) parameters and with voice source parameters, derived from flow glottograms (FLOGG) that were obtained from inverse filtering the audio signal.ResultsOn the basis of component analysis, the emotions could be grouped into four “families”, Anger-Contempt, Joy-Love-Pride, Calm-Tender-Neutral and Sad-Fear. Recognition of the intended emotion families by listeners reached accuracy levels far beyond chance level. For the LTAS and FLOGG parameters, vocal loudness had a paramount influence on all. Also after partialing out this factor, some significant correlations were found between FLOGG and LTAS parameters. These parameters could be sorted into groups that were associated with the emotion families.Conclusions(i) Both LTAS and FLOGG parameters varied significantly with the enactment intentions of the singers. (ii) Some aspects of the voice source are reflected in LTAS parameters. (iii) LTAS parameters affect listener judgment of the enacted emotions and the accuracy of the intended emotional coloring.     

Global surfaces of section in non-regular convex energy levels of Hamiltonian systems

In this paper we prove the existence of global sections of disk-type in non-regular and strictly convex energy levels of integrable and near-integrable Hamiltonian systems with two degrees of freedom. This extends a result of (Hofer et al. in Ann. Math.(2) 148(1):197–289, 1998) where the same statement is true provided the energy level is regular.     

Monte carlo simulation of diffusion-limited drug release from finite fractal matrices

How fast can drug molecules escape from a controlled matrix-type release system? This important question is of both scientific and practical importance, as increasing emphasis is placed on design considerations that can be addressed only if the physical chemistry of drug release is better understood. In this work, this problem is studied via Monte Carlo computer simulations. The drug release is simulated as a diffusion-controlled process. Six types of Menger sponges (all having the same fractal dimension, d _f = 2.727, but with different values of random walk dimension, d _w ∈ [2.028, 2.998]) are employed as models of drug delivery devices with the aim of studying the consequences of matrix structural properties (characterized by d _f and d _w ) on drug release performance. The results obtained show that, in all cases, drug release from Menger sponges follows an anomalous behavior. Finally, the influence of the matrix structural properties on the drug release profile is quantified.