Letters between Julian T. Barclay and William Kerr\u27s secretary

Letters concerning a position in the modern languages department at Utah Agricultural College

Supersymmetric quantum mechanics based on higher excited states

We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lowest m+1 states, if the superpotential is defined in terms of the (m+1)-st eigenfunction, with m=0 reserved for the ground state. It is shown that in case of the infinite 1-dim potential well nothing new emerges (the partner potential is still of P\"oschl-Teller type I, for all m), whilst in case of the 1-dim harmonic oscillator we get a new class of infinitely many partner potentials: for each m the partner potential is expressed as the sum of the quadratic harmonic potential plus rational function, defined as the derivative of the ratio of two consecutive Hermite polynomials. These partner potentials of course have m singularities exactly at the locations of the nodes of the generating (m+1)-st wavefunction. The susy formalism applies everywhere between the singularities. A systematic application of the formalism to other potentials with known spectra would yield an infinitely rich class of "solvable" potentials, in terms of their partner potentials. If the potentials are shape invariant they can be solved at least partially and new types of analytically obtainable spectra are expected. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 15 pages LaTeX file, no figures, submitted to J. Phys. A: accepted for publication

M-Dwarf Fast Rotators and the Detection of Relatively Young Multiple M-Star Systems

We have searched the Kepler light curves of ~3900 M-star targets for evidence of periodicities that indicate, by means of the effects of starspots, rapid stellar rotation. Several analysis techniques, including Fourier transforms, inspection of folded light curves, 'sonograms', and phase tracking of individual modulation cycles, were applied in order to distinguish the periodicities due to rapid rotation from those due to stellar pulsations, eclipsing binaries, or transiting planets. We find 178 Kepler M-star targets with rotation periods, P_rot, of < 2 days, and 110 with P_rot < 1 day. Some 30 of the 178 systems exhibit two or more independent short periods within the same Kepler photometric aperture, while several have three or more short periods. Adaptive optics imaging and modeling of the Kepler pixel response function for a subset of our sample support the conclusion that the targets with multiple periods are highly likely to be relatively young physical binary, triple, and even quadruple M star systems. We explore in detail the one object with four incommensurate periods all less than 1.2 days, and show that two of the periods arise from one of a close pair of stars, while the other two arise from the second star, which itself is probably a visual binary. If most of these M-star systems with multiple periods turn out to be bound M stars, this could prove a valuable way of discovering young hierarchical M-star systems; the same approach may also be applicable to G and K stars. The ~5% occurrence rate of rapid rotation among the ~3900 M star targets is consistent with spin evolution models that include an initial contraction phase followed by magnetic braking, wherein a typical M star can spend several hundred Myr before spinning down to periods longer than 2 days.Comment: 17 pages, 12 figures, 2 tables; accepted for publication in The Astrophysical Journa

Conditional Allocation of Control Rights in Venture Capital Finance

When a young entrepreneurial firm matures, it is often necessary to replace the founding entrepreneur by a professional manager. This replacement decision can be affected by the private benefits of control enjoyed by the entrepreneur which gives rise to a conflict of interest between the entrepreneur and the venture capitalist. We show that a combination of convertible securities and contingent control rights can be used to resolve this conflict efficiently. This contractual arrangement is frequently observed in venture capital finance

Asteroseismic determination of obliquities of the exoplanet systems Kepler-50 and Kepler-65

Results on the obliquity of exoplanet host stars -- the angle between the stellar spin axis and the planetary orbital axis -- provide important diagnostic information for theories describing planetary formation. Here we present the first application of asteroseismology to the problem of stellar obliquity determination in systems with transiting planets and Sun-like host stars. We consider two systems observed by the NASA Kepler Mission which have multiple transiting small (super-Earth sized) planets: the previously reported Kepler-50 and a new system, Kepler-65, whose planets we validate in this paper. Both stars show rich spectra of solar-like oscillations. From the asteroseismic analysis we find that each host has its rotation axis nearly perpendicular to the line of sight with the sines of the angles constrained at the 1-sigma level to lie above 0.97 and 0.91, respectively. We use statistical arguments to show that coplanar orbits are favoured in both systems, and that the orientations of the planetary orbits and the stellar rotation axis are correlated.Comment: Accepted for publication in ApJ; 46 pages, 11 figure

Variability in H9N2 haemagglutinin receptor-binding preference and the pH of fusion

H9N2 avian influenza viruses are primarily a disease of poultry; however, they occasionally infect humans and are considered a potential pandemic threat. Little work has been performed to assess the intrinsic biochemical properties related to zoonotic potential of H9N2 viruses. The objective of this study, therefore, was to investigate H9N2 haemagglutinins (HAs) using two well-known correlates for human adaption: receptor-binding avidity and pH of fusion. Receptor binding was characterized using bio-layer interferometry to measure virus binding to human and avian-like receptor analogues and the pH of fusion was assayed by syncytium formation in virus-infected cells at different pHs. We characterized contemporary H9N2 viruses of the zoonotic G1 lineage, as well as representative viruses of the zoonotic BJ94 lineage. We found that most contemporary H9N2 viruses show a preference for sulphated avian-like receptor analogues. However, the ‘Eastern’ G1 H9N2 viruses displayed a consistent preference in binding to a human-like receptor analogue. We demonstrate that the presence of leucine at position 226 of the HA receptor-binding site correlated poorly with the ability to bind a human-like sialic acid receptor. H9N2 HAs also display variability in their pH of fusion, ranging between pH 5.4 and 5.85 which is similar to that of the first wave of human H1N1pdm09 viruses but lower than the pH of fusion seen in zoonotic H5N1 and H7N9 viruses. Our results suggest possible molecular mechanisms that may underlie the relatively high prevalence of human zoonotic infection by particular H9N2 virus lineages