Phosphonate‐Modified UiO‐66 Brønsted Acid Catalyst and Its Use in Dehydra‐Decyclization of 2‐Methyltetrahydrofuran to Pentadienes

Phosphorus‐modified all‐silica zeolites exhibit activity and selectivity in certain Brønsted acid catalyzed reactions for biomass conversion. In an effort to achieve similar performance with catalysts having well‐defined sites, we report the incorporation of Brønsted acidity to metal–organic frameworks with the UiO‐66 topology, achieved by attaching phosphonic acid to the 1,4‐benzenedicarboxylate ligand and using it to form UiO‐66‐PO₃H₂ by post‐synthesis modification. Characterization reveals that UiO‐66‐PO₃H₂ retains stability similar to UiO‐66, and exhibits weak Brønsted acidity, as demonstrated by titrations, alcohol dehydration, and dehydra‐decyclization of 2‐methyltetrahydrofuran (2‐MTHF). For the later reaction, the reported catalyst exhibits site‐time yields and selectivity approaching that of phosphoric acid on all‐silica zeolites. Using solid‐state NMR and deprotonation energy calculations, the chemical environments of P and the corresponding acidities are determined.     

Birational modifications of surfaces via unprojections

We describe elementary transformations between minimal models of rational surfaces in terms of unprojections. These do not fit into the framework of Kustin–Miller unprojections as introduced by Papadakis and Reid, since we have to leave the world of projectively Gorenstein varieties. Also, our unprojections do not depend on the choice of the unprojection locus only, but need extra data corresponding to the choice of a divisor on this unprojection locus.     

Routes to vibrational chaos in triatomic molecules

Analysis of both classical and quantum calculations on LiNC and LiCN shows the onset of vibrational chaos is closely associated with the degree of bending excitation. Conversely quasiperiodic stretching states persist above the barrier to isomerization. Classical studies on O₃ give similar results. In the light of these results we re-interpret the high-energy vibrational data on O₃ and HCN and suggest that the observed regular stretching states probably are embedded in the chaotic region. We discuss the importance of mode coupling by the potential.     

Approximating disjoint-path problems using packing integer programs

In a packing integer program, we are given a matrix $A$ and column vectors $b,c$ with nonnegative entries. We seek a vector $x$ of nonnegative integers, which maximizes $c^{T}x,$ subject to $Ax \leq b.$ The edge and vertex-disjoint path problems together with their unsplittable flow generalization are NP-hard problems with a multitude of applications in areas such as routing, scheduling and bin packing. These two categories of problems are known to be conceptually related, but this connection has largely been ignored in terms of approximation algorithms. We explore the topic of approximating disjoint-path problems using polynomial-size packing integer programs. Motivated by the disjoint paths applications, we introduce the study of a class of packing integer programs, called column-restricted. We develop improved approximation algorithms for column-restricted programs, a result that we believe is of independent interest. Additional approximation algorithms for disjoint-paths are presented that are simple to implement and achieve good performance when the input has a special structure.Work partially supported by NSERC OG 227809-00 and a CFI New Opportunities Award. Part of this work was done while at the Department of Computer Science, Dartmouth College and partially by NSF Award CCR-9308701 and NSF Career Award CCR-9624828.This work was done while at the Department of Computer Science, Dartmouth College and partially supported by NSF Award CCR-9308701 and NSF Career Award CCR-9624828.     

The Huggins band of ozone: unambiguous electronic and vibrational assignment

The Huggins band of ozone is investigated by means of exact dynamics calculations using a new (diabatic) potential energy surface for the (1)B(2) state. The remarkable agreement with the measured spectrum strongly suggests that the Huggins band is due to the two C(s) potential wells of the (1)B(2) state. The vibrational assignment, based on the nodal structure of wave functions, supports the most recent experimental assignment.     

On the étale Descent Problem for Topological Cyclic Homology and Algebraic K-Theory

We investigate étale descent properties of topological Hochschild and cyclic homology. Using these properties we deduce a general injectivity result for the descent map in algebraic K-theory, and show that algebraic K-theory has étale descent for rings of integers in unramified and tamely ramified p-adic fields.     

Asset and liability modelling for participating policies with guarantees

We study the problem of asset and liability management of participating insurance policies with guarantees. We develop a scenario optimization model for integrative asset and liability management, analyze the tradeoffs in structuring such policies, and study alternative choices in funding them. The nonlinearly constrained optimization model can be linearized through closed form solutions of the dynamic equations. Thus large-scale problems are solved with standard methods. We report on an empirical analysis of policies offered by Italian insurers. The optimized model results are in general agreement with current industry practices. However, some inefficiencies are identified and potential improvements are highlighted.     

Rigidochromism by imide functionalisation of an aminomaleimide fluorophore

Fluorescent dyes that exhibit high solid state quantum yields and sensitivity to the mechanical properties of their local environment are useful for a wide variety of applications, but are limited in chemical diversity. We report a trityl-functionalised maleimide that displays rigidochromic behaviour, becoming highly fluorescent when immobilised in a solid matrix, while displaying negligible fluorescence in solution. Furthermore, the dye''s quantum yield is shown to be sensitive to the nature of the surrounding matrix. Computational studies reveal that this behaviour arises from the precise tuning of inter- and intramolecular noncovalent interactions. This work expands the diversity of molecules exhibiting solid state environment sensitivity, and provides important fundamental insights into their design.

In this study, by systematic tuning of imide substituent a maleimides dye with sensitivity to its solid-state environment was investigated.