Ab Initio and in-Crystal Geometry of trans-1,4-Dibromo1,4-dicarboxymethylcyclohexane

The structure of trans-1,4-dibromo-1,4-dicarboxymethylcyclohexane (I) has been determined by single crystal x-ray diffraction. The molecules, located on symmetry centers, are in the rigid chair conformation with the Br and COOCH₃ axial and equatorial, respectively. The molecular geometry observed in the crystal is similar to that calculated for the isolated molecule using ab initio calculations performed at the HF/6-31(d) level. A peculiar arrangement of the carboxymethyl substituents, along with short contacts involving the Br atoms, seem to play a role in the stabilization of the crystalline structure.     

Enantioselective allylation of α,β-unsaturated aldehydes with allyltrichlorosilane catalyzed by METHOX

α,β-Unsaturated aldehydes 6a-j undergo an enantioselective allylation with allylic trichlorosilanes 2a,b in the presence of METHOX (4) as a Lewis basic catalyst (≤10 mol %) to produce the homoallylic alcohols 7a-l at good to high enantioselectivity (83-96% ee). This study shows that the reactivity scope of METHOX can be extended from aromatic to nonaromatic aldehydes.     

Polymerization in the crystalline state. VIII. Polymerization in N-carboxy anhydrides of γ-benzyl glutamate, γ-methyl glutamate,and ϵ-carbobenzoxylysine

The kinetics of the solid-state polymerization of the N-carboxy anhydrides (NCA) of the L - and racemic forms of γ-benzyl glutamate (BG), γ-methyl glutamate (MG), and ?-carbobenzoxylysine (CL) were studied as a function of temperature and aqueous vapor pressure. The reaction of the L -forms of BG and MG was characterized by an induction period, while the CL derivative reached its maximum polymerization rate at the outset of the reaction. Water vapor had only a minor effect in accelerating the reaction and reducing the chain length of the polypeptides formed. The racemic monomers were found to have different crystal structures from those of the L -isomers and the racemic MG and CL derivatives polymerized much more slowly than the corresponding optically active crystals. All polymers gave diffuse x-ray diffraction patterns. Infrared spectra of the L -polypeptides showed that they were largely in the α-helical form. The polymer derived from the racemic BG–NCA had a content of α-helical material which suggested that it consisted of polypeptides with long blocks of D and L residues.     

Evaluation of crystallization kinetics by means of DTA

The kinetics of bulk crystallization of Se_61.5Ge_{15 4}Sb_23.1 glasses was investigated from their thermal behaviour. In the thermal characterization of a glass the recrystallization temperature is highly dependent on both the rate of heating and the thermal history of the glass. Vitreous samples were prepared by quenching. From ratedependent curves it was found that the recrystallization process obeys first-order kinetics with an apparent activation enthalpy of 48±5 kcal/mole. Further analysis allows determination of both the activation enthalpy,H=90±4 kcal/mole, and the kinetic exponent of the Avrami equation,n=1.9±0.3.

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Zusammenfassung Die Kinetik der Massenkristallisation von Glas-Arten der Zusammensetzung Se_61.5Ge_15.4Sb_23.1 wurde an Hand ihres thermischen Verhaltens studiert. Bei der thermischen Charakterisireung von Glas hängt die Rekristallisationstemperatur stark sowohl von der Aufheizgeschwindigkeit als auch von der Wärmevorgeschichte des Glases ab. Glasige Proben wurden durch rasches Abkühlen hergestellt. Aus den geschwindigkeitsabhängigen Thermogrammen geht hervor, dass der Rekristallisierungsprozess der Kinetik erster Ordnung gehorcht, mit einer scheinbaren Aktivierungsenthalpie von 48±5 kcal/mol. Die weitere Analyse ermöglicht die Bestimmung sowohl der AktivierungsenthalpieH=90±4 kcal/mol als auch des kinetischen Exponentenn=1.9±0.3 der Avrami-Gleichung.

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Résumé Etude de la cinétique de la cristallisation dans la masse de verres Se_61.5Ge_15.4Sb_23.1 à partir de leur comportement thermique. La température de recristallisation dépend fortement tant de la vitesse de chauffage que de l'histoire thermique du verre. Des échantillons vitreux ont été préparés par refroidissement rapide. La recristallisation obéit à une cinétique du premier ordre, avec une enthalpie d'activation apparente de 48±5 kcal·mol^–1. Une analyse ultérieure permet de déterminer l'enthalpie d'activationH=90±4 kcal-mol^–1 ainis que l'exposant cinétiquen=1.9±0.3 de l'équation d'Avrami.

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Se_61.5Ge_15.4Sb_23.1 . , , . . , 48±5 /. H=90±4/ , n=1.9±0.3 .

     

Minimal Blocking Sets in PG(2, 8) and Maximal Partial Spreads in PG(3, 8)

We prove that PG(2, 8) does not contain minimal blocking sets of size 14. Using this result we prove that 58 is the largest size for a maximal partial spread of PG(3, 8). This supports the conjecture that q ²–q+ 2 is the largest size for a maximal partial spread of PG(3, q), q>7.     

Computationally tractable pairwise complexity profile

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the information to describe a system as a function of the scale at which it is observed. We present a new formulation of the complexity profile, which expands its possible application to high‐dimensional real‐world and mathematically defined systems. The new method is constructed from the pairwise dependencies between components of the system. The pairwise approach may serve as both a formulation in its own right and a computationally feasible approximation to the original complexity profile. We compare it to the original complexity profile by giving cases where they are equivalent, proving properties common to both methods, and demonstrating where they differ. Both formulations satisfy linear superposition for unrelated systems and conservation of total degrees of freedom (sum rule). The new pairwise formulation is also a monotonically nonincreasing function of scale. Furthermore, we show that the new formulation defines a class of related complexity profile functions for a given system, demonstrating the generality of the formalism. © 2013 Wiley Periodicals, Inc. Complexity 18:20–27, 2013     

A mathematical theory of strong emergence using multiscale variety

We argue conceptually and then demonstrate mathematically that it is possible to define a scientifically meaningful notion of strong emergence. A strong emergent property is a property of the system that cannot be found in the properties of the system's parts or in the interactions between the parts. The possibility of strong emergence follows from an ensemble perspective, which states that physical systems are only meaningful as ensembles rather than individual states. Emergent properties reside in the properties of the ensemble rather than of any individual state. A simple example is the case of a string of bits including a parity bit, i.e. the bits are constrained to have, e.g., an odd number of ON bits. This constraint is a property of the entire system that cannot be identified through any set of observations of the state of any or all subsystems of the system. It is a property that can only be found in observations of the state of the system as a whole. A collective constraint is a property of the system, however, the constraint is caused when the environment interacts with the system to select the allowable states. Although selection in this context does not necessarily correspond to biological evolution, it does suggest that evolutionary processes may lead to such emergent properties. A mathematical characterization of multiscale variety captures the implications of strong emergent properties on all subsystems of the system. Strong emergent properties result in oscillations of multiscale variety with negative values, a distinctive property. Examples of relevant applications in the case of social systems include various allocation, optimization, and functional requirements on the behavior of a system. Strongly emergent properties imply a global to local causality that is conceptually disturbing (but allowed!) in the context of conventional science, and is important to how we think about biological and social systems. © 2004 Wiley Periodicals, Inc. Complexity 9: 15–24, 2004     

New Red‐Emitting Tetrazine‐Phenoxazine Fluorogenic Labels for Live‐Cell Intracellular Bioorthogonal Labeling Schemes

The synthesis of a set of tetrazine‐bearing fluorogenic dyes suitable for intracellular labeling of proteins in live cells is presented. The red excitability and emission properties ensure minimal autofluorescence, while through‐bond energy‐transfer‐based fluorogenicity reduces nonspecific background fluorescence of unreacted dyes. The tetrazine motif efficiently quenches fluorescence of the phenoxazine core, which can be selectively turned on chemically upon bioorthogonal inverse‐electron‐demand Diels–Alder reaction with proteins modified genetically with strained trans‐cyclooctenes.     

On the lack of capillary Mössbauer spectroscopic effect for SnII-containing aqueous solutions trapped in corning Vycor ‘thirsty’ glass

Liquids trapped in the pores of certain silicate glasses (such as Corning Vycor ‘thirsty’ glass) were found to display frozen solutions like behavior at temperatures much higher than their actual freezing point. For example, recoilless γ-resonance absorption was observed for Mössbauer active solutes such as ¹¹⁹Sn and ⁵⁷Fe salts at room temperature (i.e., without the need of quenching). Thus capillary Mössbauer spectroscopy (CMS) proved to be a new and useful experimental tool with great potential in solution chemistry. As part of a research project concerned with the hydrolysis of Sn^II salts, we attempted to perform ¹¹⁹Sn CMS measurements for solutions containing stannous ion in a range of aqueous environments. Somewhat surprisingly, we found that under ambient conditions, Sn^II aqueous liquid solutions, both the acidic and the basic systems, are essentially CMS-silent. This can be attributed to the strong temperature dependence of Lamb–Mössbauer factor of Sn^II species, which may result in the complete disappearance of Mössbauer pattern well below room temperature. These observations can also explain why previous publications concerned with the use of CMS dealt exclusively with Sn^IV and not with Sn^II containing liquids.