Temperature dependence of macrobending loss in all-fiber bend loss edge filter

A theoretical model for macrobending-induced temperature dependent loss (TDL) for a standard singlemode fiber (SMF28) with dual coating layers is presented, with good agreement demonstrated between theoretical calculations and experimental results. The impact of temperature on two examples of an all-fiber based edge filter is also investigated theoretically and experimentally and using the developed model, it is shown that it is possible to predict the impact of temperature variations on an all-fiber based edge filter.     

Pricing of catastrophe insurance options written on a loss index with reestimation

We propose a valuation model for catastrophe insurance options written on a loss index. This kind of options distinguishes between a loss period [0,T₁], during which the catastrophes may happen, and a development period [T₁,T₂], during which losses entered before T₁ are reestimated. Here we suppose that the underlying loss index is given by a time inhomogeneous compound Poisson process before T₁ and that losses are reestimated by a common factor given by an exponential time inhomogeneous Lévy process after T₁. In this setting, using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options written on this kind of index.     

Novel type of isoprenoid membrane anchors: an investigation of binding properties with dipalmitoylphosphatidylcholine vesicles

In this work, we present a new type of amphiphilic membrane‐anchoring agents that can be easily obtained by the Diels‐Alder reaction between terpene myrcene and N‐substituted maleimides. The interaction between the compounds and small unilamellar dipalmitoylphosphatidylcholine vesicles was investigated using infrared spectroscopy, microgravimetry, and turbidimetry. The ability of the compounds to embed in the phospholipid membrane was shown to be strongly dependent on the charge of their polar group. The insertion of the compounds studied into the lipid bilayer did not lead to disruption of the dipalmitoylphosphatidylcholine vesicles up to the highest tested drug to lipid molar ratio of 0.5 to 0.6. Low lipid solubilization ability of the compounds as well as their rigid nonplanar structure makes them an interesting alternative to the common membrane‐anchoring structural motifs.     

Germanium microsphere high-Q resonator

In this Letter, the fabrication and characterization of a microsphere resonator from the semiconductor germanium is demonstrated. Whispering gallery modes are excited in a 46 μm diameter germanium microsphere resonator using evanescent coupling from a tapered silica optical fiber with a waist diameter of 2 μm. Resonances with Q factors as high as 3.8×10(4) at wavelengths near 2 μm are observed. Because of their ultrahigh optical nonlinearities and extremely broad transparency window, germanium microsphere resonators offer the potential for optical processing devices, in particular at long wavelengths, such as around 2 μm.     

Variational splines for the numerical solution of singular differential equations

The numerical parametrization method (PM), originally created for optimal control problems, is specificated for classical calculus of variation problems that arise in connection with singular implicit (IDEs) and differential-algebraic equations (DAEs). The PM for IDEs is based on representation of the required solution as a spline with moving knots and on minimization of the discrepancy functional with respect to the spline parameters. Such splines are named variational splines. For DAEs only finite entering functions can be represented by splines, and the functional under minimization is the discrepancy of the algebraic subsystem. The first and the second derivatives of the functionals are calculated in two ways – for DAEs with the help of adjoint variables, and for IDE directly. The PM does not use the notion of differentiation index, and it is applicable to any singular equation having a solution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polarization dependence of an edge filter based on singlemode–multimode–singlemode fibre

The polarization dependent loss (PDL) of a singlemode–multimode–singlemode (SMS) fibre structure used as an edge filter is presented. Minor errors in the fabrication process for the SMS fibre structure can introduce SMS fibre core offsets. The PDL due to lateral and rotational core offsets is investigated numerically and experimentally. It is shown that small core offsets are necessary to achieve low PDL for an SMS fibre based edge filter. It is also demonstrated that when lateral core offsets are unavoidable, the PDL of a SMS edge filter can still be minimized by introducing a rotational core offset of 90^°.     

On the invertibility of seasonally adjusted series

This paper examines the implications of the seasonal adjustment by an ARIMA model based (AMB) approach in the context of seasonal fractional integration. According to the AMB approach, if the model identified from the data contains seasonal unit roots, the adjusted series will not be invertible that has serious implications for the posterior analysis. We show that even if the ARIMA model identified from the data contains seasonal unit roots, if the true data generating process is stationary seasonally fractionally integrated (as it is often found in economic data), the AMB seasonal adjustment produces dips in the periodogram at seasonal frequencies, but the adjusted series still can be approximated by an invertible process. We also perform a small Monte Carlo study of the log-periodogram regression with tapered data for negative seasonal fractional integration. An empirical application for the Spanish economy that illustrates our results is also carried out at the end of the article.     

Monochrome symmetric subsets of colored groups

In (Electron. J. Combin. 10 (2003); http://www.combinatorics.org/volume-10/Abstracts/v1oi1r28.html), the first author (Yuliya Gryshko) asked three questions. Is it true that every infinite group admitting a 2-coloring without infinite monochromatic symmetric subsets is either almost cyclic (i.e., have a finite index subgroup which is cyclic infinite) or countable locally finite? Does every infinite group G include a monochromatic symmetric subset of any cardinal <|G| for any finite coloring? Does every uncountable group G such that |B(G)|< |G| where B(G)={xG:x²=1}, admit a 2-coloring without monochromatic symmetric subsets of cardinality |G|? We answer the first question positively. Assuming the generalized continuum hypothesis (GCH), we give a positive answer to the second question in the abelian case. Finally, we build a counter-example for the third question and we give a necessary and sufficient condition for an infinite group G to admit 2-coloring without monochromatic symmetric subsets of cardinality |G|. This generalizes some results of Protasov on infinite abelian groups (Mat. Zametki 59 (1996) 468–471; Dopovidi NAN Ukrain 1 (1999) 54–57).     

Radicals of some semigroup algebras

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups (βS,□), where S is a cancellative, countable, abelian semigroup and βS is its Stone–?ech semigroup compactification. In particular, we wish to determine the radical of ? ^?1(β?).     

Aldol-type transformations of levoglucosenone-derived medium-sized keto lactones

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