Optimal Claiming on Vehicle Insurance

Insurance companies charge reduced premiums to motorists who go through a period of one or more years without making a claim. When an accident occurs the insured frequently finds himself with the option of either making a claim and reverting to a higher premium or paying for the repair himself. Most motorists operate an informal system of "no-claim limits", whereby they only claim for repairs which exceed a certain cost.In this paper it is shown how, under reasonable assumptions regarding the rate of accidents and the distribution of repair costs, optimal no-claim limits can be determined. These minimise the long run average cost of premiums and repairs and show significant savings over the case where all claims are made. The effect of an "excess clause", whereby the insured agrees to pay a first amount of any claim is also studied, and rules for determining whether it is profitable to accept such a clause are presented in the form of a graph.     

5‐Acetyl‐2‐amino‐6‐methyl‐4‐phenyl‐4H‐pyran‐3‐carbonitrile and 2‐amino‐5‐benzoyl‐6‐methyl‐4‐phenyl‐4H‐pyran‐3‐carbonitrile acetonitrile solvate

The syntheses, X‐ray structural investigations and calculations of the conformational preferences of the carbonyl substituent with respect to the pyran ring have been carried out for the two title compounds, viz. C₁₅H₁₄N₂O₂, (II), and C₂₀H₁₆N₂O₂·C₂H₃N, (III), respectively. In both mol­ecules, the heterocyclic ring adopts a flattened boat conformation. In (II), the carbonyl group and a double bond of the heterocyclic ring are syn, but in (III) they are anti. The carbonyl group forms a short contact with a methyl group H atom in (II). The dihedral angles between the pseudo‐axial phenyl substituent and the flat part of the pyran ring are 92.7 (1) and 93.2 (1)° in (II) and (III), respectively. In the crystal structure of (II), inter­molecular N—H⋯N and N—H⋯O hydrogen bonds link the mol­ecules into a sheet along the (103) plane, while in (III), they link the mol­ecules into ribbons along the a axis.     

Direct Mannich‐Type Reactions Promoted by Frustrated Lewis Acid/Brønsted Base Catalysts

Direct Mannich‐type reactions that afford both α‐ and β‐amino esters by the reaction of a broad range of carbonyl compounds and aldimines are disclosed. The transformation is promoted by a sterically frustrated Lewis acid/Brønsted base pair, which is proposed to operate cooperatively: Within the catalyst complex, an enolate is generated that then reacts with a hydrogen‐bond‐activated imine. Noncovalent interactions between reactants and the catalyst provide selectivity and new opportunities for future catalyst design.     

Bromide control, bifurcation and activation in the Belousov-Zhabotinsky reaction

The unstirred, ferroin (Fe(phen)3(2+)) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br(-) appear red (reduced, low [Fe(phen)3(3+)]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.     

Two-photon Lee-Goldburg nuclear magnetic resonance: Simultaneous homonuclear decoupling and signal acquisition

We present NMR signals from a strongly coupled homonuclear spin system, (1)H nuclei in adamantane, acquired with simultaneous two-photon excitation under conditions of the Lee-Goldburg experiment. Small coils, having inside diameters of 0.36 mm, are used to achieve two-photon nutation frequencies of approximately 20 kHz. The very large rf field strengths required give rise to large Bloch-Siegert shifts that cannot be neglected. These experiments are found to be extremely sensitive to inhomogeneity of the applied rf field, and due to the Bloch-Siegert shift, exhibit a large asymmetry in response between the upper and lower Lee-Goldburg offsets. Two-photon excitation has the potential to enhance both the sensitivity and performance of homonuclear dipolar decoupling, but is made challenging by the high rf power required and the difficulties introduced by the inhomogeneous Bloch-Siegert shift. We briefly discuss a variation of the frequency-switched Lee-Goldburg technique, called four-quadrant Lee-Goldburg (4QLG) that produces net precession in the x-y plane, with a reduced chemical shift scaling factor of 13.     

Polarization effects in resonant nuclear scattering

Polarization phenomena are present in every radiative transition, whether it is of atomic or nuclear origin. Nuclear resonant scattering of synchrotron radiation is an ideal technique for their study because (a) the probing radiation is in a well characterized polarization state, in most cases linear, (b) the scattered radiation can be efficiently analyzed with polarization filters, and (c) synchrotron pulses are very short compared to the lifetime of a nuclear resonance, resulting in a clean signal. In the following article we describe experimental and theoretical studies of the 14.4 keV Mössbauer resonance of ⁵⁷Fe and its transitions with linear and circular polarization. After introducing the required instrumentation a formalism to calculate time dependent polarization phenomena is derived. With the help of different scattering geometries we illustrate various aspects, such as polarization mixing and selective excitation of subsets of the resonance. Perhaps the most fascinating example is the Faraday geometry where the E-vector rotates several 360^ο turns during the lifetime of the resonant scattering. A comparison of this phenomenon with the optical Faraday effect is given. New powerful synchrotron radiation sources will enable researchers to exploit polarization phenomena in nuclear resonant scattering to detect subtle changes in physically and chemically relevant systems.

     

Double Semions in Arbitrary Dimension

We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of \({d-1}\) dimensional surfaces in a d dimensional ambient space. We construct a local Hamiltonian that is a sum of commuting projectors and analyze the excitations and the ground state degeneracy. Defining a consistent set of local rules requires the sign structure of the ground state wavefunction to depend not just on the number of disconnected surfaces, but also upon their higher Betti numbers through the semicharacteristic. For odd d the theory is related to the toric code by a local unitary transformation, but for even d the dimension of the space of zero energy ground states is in general different from the toric code and for even \({d > 2}\) it is also in general different from that of the twisted \({Z_2}\) Dijkgraaf–Witten model.