Reflectance anisotropy spectra of the diamond (100)-(2x1) surface: evidence of strongly bound surface state excitons

We compare the results of ab initio calculations with measured reflection anisotropy spectra and show that strongly bound surface-state excitons occur on the clean diamond (100) surface. These excitons are found to have a binding energy close to 1 eV, the strongest ever observed at a semiconductor surface. Important electron-hole interaction effects on the line shape of the optical transitions above the surface-state gap are also found.     

Reaction of carbonyl compounds with dimethyl 3-ketoglutarate. Synthesis of bicyclic furan derivatives

Acid catalyzed reaction of cyelododecane-1,2-dione VI with dimethyl,3-ketoglutarate II led to the formation of methyl (E)-6,7,8,9,10,11,12,13-octahydro-3-(methoxycarbonyl)cyclododeca-[b]furan-2-aeetate IX, presumably formed through the dihydrodihydroxy furan VIII. This dihydrofuran intermediate VIII was shown to be characteristic of the reaction of 2-substituted carbonyl-compounds with 11 for both α-chlorocyclohexanone and α-chlorocyclopentanone furnished furans XVIa and XX, respectively, when treated with 11. The effect of dihydrodihydroxy-furan intermediates on the course of such reactions is discussed.     

Global homeomorphisms and covering projections on metric spaces

For a large class of metric spaces with nice local structure, which includes Banach–Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We first obtain a general condition in terms of a path continuation property. As a consequence, we deduce several conditions in terms of path- liftings involving a generalized derivative, and in particular we obtain an extension of Hadamard global inversion theorem in this context. Next we prove that, in the case of quasi-isometric mappings, some of these sufficient conditions are also necessary. Finally, we give an application to the existence of global implicit functions. O. Gutú and J. A. Jaramillo were supported in part by D.G.E.S. (Spain) Grant BFM2003-06420.     

Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CVaR cost constraints

Using a Monte Carlo framework, we analyze the risks and rewards of moving from an unfunded defined benefit pension system to a funded plan for German civil servants, allowing for alternative strategic contribution and investment patterns. In the process we integrate a Conditional Value at Risk (CVaR) restriction on overall plan costs into the pension manager’s objective of controlling contribution rate volatility. After estimating the contribution rate that would fully fund future benefit promises for current and prospective employees, we identify the optimal contribution and investment strategy that minimizes contribution rate volatility while restricting worst-case plan costs. Finally, we analyze the time path of expected and worst-case contribution rates to assess the chances of reduced contribution rates for current and future generations. Our results show that moving toward a funded public pension system can be beneficial for both civil servants and taxpayers.     

Global inversion theorems via coercive functionals on metric spaces

Let X$X$ and Y$Y$ be metric spaces. We give sufficient metric conditions for a local homeomorphism f:X→Y$f:X\to Y$ to be a global one. We achieve this by means of auxiliary coercive functionals; several expected global inversion theorems are obtained by choosing different functionals.     

Generalizations of some conjectures of Sun on the relations between N(a, b, c, d; n) and T(a, b, c, d; n)

The Ramanujan Journal - We derive some new finite sums involving the sequence $$s_{2}\left( n\right) ,$$ the sum-of-digits of the expansion of n in base 2. These functions allow us to generalize...     

Asymptotic properties of solutions to some nonlinear integral equations of convolution type

For a class of nonlinear integral equations of convolution type we give necessary and sufficient conditions for the boundedness of nonnegative solutions. Moreover, conditions for the solution to converge asymptotically to a determined limit are obtained.     

Some modular relations for Ramanujan’s function k(q)=r(q)r^2(q^2)

In both his second and lost notebooks, Ramanujan introduced and studied a function \(k(q)=r(q)r^2(q^2)\) , where \(r(q)\) is the Rogers–Ramanujan continued fraction. Ramanujan also recorded five beautiful relations between the Rogers–Ramanujan continued fraction \(r(q)\) and the five continued fractions \(r(-q)\) , \(r(q^2)\) , \(r(q^3)\) , \(r(q^4)\) , and \(r(q^5)\) . Motivated by those relations, we present some modular relations between \(k(q)\) and \(k(-q)\) , \(k(-q^2)\) , \(k(q^3)\) , and \(k(q^5)\) in this paper.