<Emphasis Type="Italic">L</Emphasis>Σ(≤ <Emphasis Type="Italic">ω</Emphasis>)-spaces and spaces of continuous functions

We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $ \mathfrak{c} $ \mathfrak{c} is an LΣ(≤ ω)-space.     

An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses

Research suggests it is difficult to learn mathematics in the fully asynchronous online (FAO) instructional modality, yet little is known about associated teaching and assessment practices. In this study, we investigate FAO mathematics assessment and feedback practices in particular consideration of both claims and findings that these practices have a powerful influence on learning.

A survey questionnaire was constructed and completed by 70 FAO undergraduate mathematics instructors, mostly from the USA, who were each asked to detail their assessment and feedback practices in a single FAO mathematics course. Alongside these questions, participants also answered the 16-item version of the Approaches to Teaching Inventory. In addition, a novel feedback framework was also created and used to examine how feedback practices may be related to participants' approaches to teaching.

Results show that assessment and feedback practices are varied and complex: in particular, we found there was not a simple emphasis on summative assessment instruments, nor a concomitant expectation these would always be invigilated. Though richer assessment feedback appears to be emphasized, evidence suggests this feedback may not be primarily directed at advancing student learning. Moreover, we found evidence of a reliance on computer--human interactions (e.g. via computer-assisted assessment systems) and further evidence of a decline in human interactions, suggesting a dynamic that is both consistent with current online learning theory and claims FAO mathematics courses are becoming commodified. Several avenues for further research are suggested.     

Complex magnetic ordering as a driving mechanism of multifunctional properties of Heusler alloys from first principles

First-principles calculations are used to study the structural, electronic and magnetic properties of (Pd, Pt)-Mn-Ni-(Ga, In, Sn, Sb) alloys, which display multifunctional properties like the magnetic shape-memory, magnetocaloric and exchange bias effect. The ab initio calculations give a basic understanding of the underlying physics which is associated with the complex magnetic behavior arising from competing ferro- and antiferromagnetic interactions with increasing number of Mn excess atoms in the unit cell. This information allows to optimize, for example, the magnetocaloric effect by using the strong influence of compositional changes on the magnetic interactions. Thermodynamic properties can be calculated by using the ab initio magnetic exchange parameters in finite-temperature Monte Carlo simulations. We present guidelines of how to improve the functional properties. For Pt-Ni-Mn-Ga alloys, a shape memory effect with 14% strain can be achieved in an external magnetic field.     

Spin-dependent and Coriolis interactions by an improved configuration interaction treatment: predissociation of excited fine structure levels of OH/OD

The state specific predissociation of OH/OD in its lowest electronically excited state (A²Σ⁺,v',N',F₁/F₂) is investigated by time dependent wave packet propagation techniques. To improve the accuracy of the potential energy curves, spin-orbit, spin-spin and rotational interactions required for the treatment, we have refined our CI techniques, using optimal orbitals for each of the electronic states. Potential energy curves, matrix elements and lifetimes of the rotational sublevels are compared with experiment and with theoretical values from multichannel scattering theory     

Avoided-crossing-based liquid-crystal photonic-bandgap notch filter

We demonstrate a highly tunable deep notch filter realized in a liquid-crystal photonic-bandgap (LCPBG) fiber. The filter is realized without inducing a long-period grating in the fiber but simply by filling a solid-core photonic-crystal fiber with a liquid crystal and exploiting avoided crossings within the bandgap of the LCPBG fiber. The filter is demonstrated experimentally and investigated using numerical simulations. A high degree of tuning of the spectral position of the deep notch is also demonstrated.     

Excited-State Dynamics of Thienoguanosine,an Isomorphic Highly Fluorescent Analogue of Guanosine

Thienoguanosine (^thG) is an isomorphic analogue of guanosine with promising potentialities as fluorescent DNA label. As a free probe in protic solvents, ^thG exists in two tautomeric forms, identified as the H1, being the only one observed in nonprotic solvents, and H3 keto–amino tautomers. We herein investigate the photophysics of ^thG in solvents of different polarity, from water to dioxane, by combining time-resolved fluorescence with PCM/TD-DFT and CASSCF calculations. Fluorescence lifetimes of 14.5–20.5 and 7–13 ns were observed for the H1 and H3 tautomers, respectively, in the tested solvents. In methanol and ethanol, an additional fluorescent decay lifetime (≈3 ns) at the blue emission side (λ≈430 nm) as well as a 0.5 ns component with negative amplitude at the red edge of the spectrum, typical of an excited-state reaction, were observed. Our computational analysis explains the solvent effects observed on the tautomeric equilibrium. The main radiative and nonradiative deactivation routes have been mapped by PCM/TD-DFT calculations in solution and CASSCF in the gas phase. The most easily accessible conical intersection, involving an out-of plane motion of the sulfur atom in the five-membered ring of ^thG, is separated by a sizeable energy barrier (≥0.4 eV) from the minimum of the spectroscopic state, which explains the large experimental fluorescence quantum yield.     

Cyclotetraveratrylene and its benzene solvate

The title compound crystallizes in a solvent-free form and also includes solvent molecules. The X-ray structure analysis reveals that in the both crystal forms the cyclododecatetraene ring in the host molecules adopts a sofa conformation. The guest molecules occupy the channels formed among columns of stacked host molecules.Contribution No. 1452 of Instituto de Química, UNAM.     

Crystal structures of two substituted biphenyl derivatives: 5,5′-di t-butyl-2-2′-biphenyldiol and 5,5′-dimethyl-2,2′-biphenyldiol

5,5-Di t-butyl-2,2-biphenyldiol (I), C₂₀H₂₆O₂, crystallizes in the orthorhombic space group P2₁2₁2₁ with a = 18.243(2), b = 9.947(2), c = 9.685(3) Å, and Z = 4; 5,5-dimethyl-2,2-biphenyldiol (II), C₁₄H₁₄O₂, crystallizes in the monoclinic space group P2₁/c with a = 9.959(2), b = 7.932(3), c = 15.392(2) Å, = 105.43(2)°, and Z = 4. The aromatic rings are tilted by 52.7(1) and 43.8(1)° to each other in compounds (I) and (II), respectively. Strong intra- and inter-molecular H-bonds connect the molecules in the crystals.     

Positional disorder manifested as compositional in a pseudo‐C2‐symmetrical Pd complex

The title compound {2‐[3,5‐bis(trifluoromethyl)‐1H‐pyrazol‐1‐ylmethyl]‐6‐(3,5‐dimethyl‐1H‐pyrazol‐1‐ylmethyl)pyridine}methylpalladium(II) tetrakis[3,5‐bis(trifluoromethyl)phenyl]borate, [Pd(C₁₈H₁₈F₆N₅)][B(C₈H₃F₆)₄], crystallizes as discrete cations and anions. The cation possesses a pseudo‐twofold axis about which positional disorder of the tridentate ligand is exhibited. The four substituents on the two pyrazole rings exhibit CH₃/CF₃ disorder, while all other atoms are ordered. Thus, this disorder can be conveniently described `locally' as compositional, while `globally' for the entire tridentate ligand it is positional. The anion also exhibits typical rotational positional disorder in three of the CF₃ groups. All disordered CF₃ groups were modeled with idealized C_3v geometry.     

Nitric oxide binding and photodelivery based on ruthenium(II) complexes of 4-arylazo-3,5-dimethylpyrazole

Two fluorescent ligands, 3,5-dimethyl-4-(6'-sulfonylammonium-1'-azonaphthyl)pyrazole (dmpzn, 1) and 3,5-dimethyl-4-(4'-N,N'-dimethylaminoazophenyl)pyrazole (dmpza, 2) were obtained by condensation of ketoenolic derivatives with hydrazine. 1 and 2 formed the novel dinuclear complexes [(H(2)O)(3)ClRu(micro-L)(2)RuCl(H(2)O)(3)] (3 or 4) and [(H(2)O)(NO)Cl(2)Ru(micro-L)(2)RuCl(2)(NO)(H(2)O)] (6 or 7) (where L 1 = 2 or , respectively) which were characterized by IR, NMR and elemental analysis. The nitrosyl complexes were prepared by bubbling purified nitric oxide through methanol solutions of the corresponding ruthenium(II) chloroderivative or by reaction of the appropriate ligands with Ru(NO)Cl(3). Complexes 3 and 4 were found to bind NO, resulting in an increase in fluorescence. Ligand 1 also formed the mononuclear nitrosyl complex [Ru(NO)(bpy)(2)(dmpzn)]Cl(2) (8) which released NO in water at physiological pH and in the solid state as revealed by fluorescence and IR measurements, respectively.