Temporal freedom in mathematical thought: A philosophical–empirical enquiry

This paper seeks to introduce and elaborate on the notion of ‘temporal freedom’ in the context of mathematical thinking.The intention is to merge a philosophical and empirical discussion on this topic, and findings will be presented from a qualitative study in which 29 high-school students were invited to explore the symmetry group of a square during clinical interviews. The data indicate how the interviewees – who were given the opportunity to freely explore an unseen mathematical system – repeatedly brought past and future together in a tangible present during their investigations. In doing so they were exceptionally successful in engaging with advanced abstract algebra, far beyond what might have been expected at the outset.By using empirical data to exemplify an otherwise highly philosophical discussion, I hope to draw explicit attention to the temporal aspect of the human mind in mathematical action which instructional methods frequently fail to recognise, value and utilise.     

Lanthanum trilactate: Vibrational spectroscopic study − infrared/Raman spectroscopy

In this study lanthanum trilactate was prepared by neutralization reaction of lactic acid and lanthanum oxide, purified and identified by X-ray powder diffraction. Infrared spectra (Mid-IR region 4000–650 cm⁻¹) and Raman spectra (Stokes region 4000–100 cm⁻¹) of the high quality crystalline samples have been recorded and presented for the first time. For comparison DFT calculations were performed using Gaussian 09 D.01 and agreement between predicted and measured spectral data has been achieved. Acquired information can be utilized for substance identification for example in various industrial applications or in biological systems.     

(3S,4S)-4-氨基-3-羟基-6-甲基庚酸的合成

价廉易得的L-亮氨酸先以苄基同时保护氨基及羧基得(S)-2-(二苄胺基)-4-甲基戊酸苄酯,进而在碱性条件下与乙腈发生亲核取代反应得(S)-4-(二苄胺基)-6-甲基-3-氧代庚腈,再经硼氢化钠选择性还原羰基得(3S,4S)-4-(二苄胺基)-3-羟基-6-甲基庚腈,用双氧水氧化得(3S,4S)-4-(二苄胺基)-3-羟基-6-甲基庚酸,最后在Pd(OH)2/C-H2作用下脱掉苄基得到(3S,4S)-4-氨基-3-羟基-6-甲基庚酸,即(3S,4S)-statine。整个合成路线总产率为33.6%。     

Flavonoid glycosides from Persea caerulea. Unraveling their interactions with SDS‐micelles through matrix‐assisted DOSY,PGSE, mass spectrometry,and NOESY

Two flavonoid glycosides derived from rhamnopyranoside ( 1 ) and arabinofuranoside ( 2 ) have been isolated from leaves of Persea caerulea for the first time. The structures of 1 and 2 have been established by ¹H NMR, ¹³C NMR, and IR spectroscopy, together with LC–ESI–TOF and LC–ESI–IT MS spectrometry. From the MS and MS/MS data, the molecular weights of the intact molecules as well as those of quercetin and kaempferol together with their sugar moieties were deduced. The NMR data provided information on the identity of the compounds, as well as the α and β configurations and the position of the glycosides on quercetin and kaempferol. We have also explored the application of sodium dodecyl sulfate (SDS) normal micelles in binary aqueous solution, at a range of concentrations, to the diffusion resolution of these two glycosides, by the application of matrix‐assisted diffusion ordered spectroscopy (DOSY) and pulse field gradient spin echo (PGSE) methodologies, showing that SDS micelles offer a significant resolution which can, in part, be rationalized in terms of differing degrees of hydrophobicity, amphiphilicity, and steric effects. In addition, intra‐residue and inter‐residue proton–proton distances using nuclear Overhauser effect build‐up curves were used to elucidate the conformational preferences of these two flavonoid glycosides when interacting with the micelles. By the combination of both diffusion and nuclear Overhauser spectroscopy techniques, the average location site of kaempferol and quercetin glycosides has been postulated, with the former exhibiting a clear insertion into the interior of the SDS‐micelle, whereas the latter is placed closer to the surface. Copyright © 2016 John Wiley & Sons, Ltd.     

Intermolecular Stetter reaction of aromatic aldehydes with (E)-(2-nitrovinyl)cyclohexane induced by N-heterocyclic carbene and thiourea

Intermolecular Stetter reaction of aromatic aldehydes with (E)-(2-nitrovinyl)cyclohexane catalyzed by thiazolium A has been developed. The reaction rate and efficiency are profoundly impacted by the presence of thiourea B. The reaction affords moderate to good yields of the Stetter product. Some factors influencing yield were discussed.     

End group polarity and block symmetry effects on cloud point and hydrodynamic diameter of thermoresponsive block copolymers

Thermoresponsive block copolymers are of interest for delivery vehicles in the body. Often an interior domain is designed for the active agent and the exterior domain provides stability in the bloodstream, and may carry a targeting ligand. There is still much to learn about how block sequence and chain end identity affect micelle structure, size, and cloud points. Here, hydrophilic oligo(ethylene glycol) methyl ether acrylate and more hydrophobic di(ethylene glycol) methyl ether methacrylate monomers were polymerized to give amphiphilic block copolymers with amphiphilic chain ends. The block sequence and chain end identity were both controlled by appropriate choice of RAFT chain transfer agents to study the effect of ‘matched’ and ‘mismatched’ chain end polarity with amphiphilic block sequence. The affect of matching or mismatching chain end polarity and block sequence was studied on the hydrodynamic diameter, cloud point, and temperature range of the chain collapse on linear di‐ and triblock copolymers and star diblock polymers. The affects of matching or mismatching chain end polarity were significant with linear diblock copolymers but more complex with triblock and star copolymers. Explanations of these results may help guide others in designing thermoresponsive block copolymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2838–2848     

Mechanism of Insertion Reactions between Silylenoid H2SiLiF and GeH3R (R =F,OH, NH2): a Theoretical Study

Theoretical investigations on the insertion reaction mechanisms of three- membered-ring silylenoid H2 Si Li F with GeH 3R(R = F, OH, NH2) have been systematically carried out by combined density functional theory(DFT) and ab initio quantum chemical calculations. The geometries of all stationary points for these reactions were optimized using the B3 LYP method and then the QCISD method was used to calculate the single-point energies. The calculated results indicate that, there are one precursor complex(Q), one transition state(TS), and one intermediate(IM) which connect the reactants and the products along the potential energy surface. The insertion reactions of three-membered-ring silylenoid with Ge H3 R proceed in a concerted manner, forming H2RSi-Ge H3 and Li F. The calculated potential energy barriers of the three reactions are 29.17, 30.90, and 54.07 k J/mol, and the reaction energies for the three reactions are –127.05, –116.91, and –103.31 k J/mol, respectively. The insertion reactions in solvents are similar to those in vacuum. Under the same situation, the insertion reactions should occur easily in the following order: GeH 3-F GeH 3-OH GeH 3-NH2. The elucidations of the mechanism of these insertion reactions provided a new mode of silicon-germanium bond formation.     

Specific Design of Titanium(IV) Phenolato Chelates Yields Stable and Accessible,Effective and Selective Anticancer Agents

Octahedral titanium(IV) complexes of phenolato hexadentate ligands were developed and showed very high stability for days in water solutions. In vitro cytotoxicity studies showed that, whereas tetrakis(phenolato) systems are generally of low activity presumably due to inaccessibility, smaller bis(phenolato)bis(alkoxo) complexes feature high anticancer activity and accessibility even without formulations, also toward a cisplatin‐resistant cell line. An all‐aliphatic control complex was unstable and inactive. A leading phenolato complex also revealed: 1) high durability in fully aqueous solutions; accordingly, negligible loss of activity after preincubation for three days in medium or in serum; 2) maximal cellular accumulation and induction of apoptosis following 24–48 h of administration; 3) reduced impact on noncancerous fibroblast cells; 4) in vivo efficacy toward lymphoma cells in murine model; 5) high activity in NCI‐60 panel, with average GI₅₀ of 4.6±2 μm . This newly developed family of Ti^IV complexes is thus of great potential for anticancer therapy.     

Generic applications of 13C‐detected NMR diffusion to formulated systems with suppression of thermal convection induced by proton decoupling

Fast and effective structural/compositional analysis on formulated systems represents one of the major challenges encountered in analytical science. ¹³C‐detected diffusion represents a promising tool to tackle the aforementioned challenges, particularly in industry. Toward exploring the generic applications of ¹³C‐detected diffusion, thermal convection induced by ¹H decoupling has been identified as a key factor that resulted in significantly reduced resolution in the diffusion dimension. Optimization of experimental parameters and utilization of double‐stimulated echo‐based pulse sequence both can effectively suppress the thermal convection caused by the ¹H decoupling, the success of which allows robust and generic applications of ¹³C‐detected diffusion to systems from mixtures of small molecules, polymer blends, and copolymers to actual complex formulated systems. The method is particularly powerful in differentiating small molecules from polymers, polymer blends from copolymers, and end‐group analysis. Copyright © 2016 John Wiley & Sons, Ltd.