Twisted products in pseudo-Riemannian geometry

Twisted products are generalizations of warped products, namely the warping function may depend on the points of both factors. The two canonical foliations of a twisted product are mutually perpendicular and their leaves are totally geodesic, resp. totally umbilic. The main result is a decomposition theorem of de Rham type: If on a simply connected, geodesically complete pseudo-Riemannian manifoldM two foliations with the above properties are given, thenM is a twisted product.     

Optimal management and inflation protection for defined contribution pension plans

Due to the increasing risk of inflation and diminishing pension benefits, insurance companies have started selling inflation-linked products. Selling such products the insurance company takes over some or all of the inflation risk from their customers. On the other side financial derivatives which are linked to inflation such as inflation linked bonds are traded on financial markets and appear to be of increasing popularity. The insurance company can use these products to hedge its own inflation risk. In this article we study how to optimally manage a pension fund taking positions in a money market account, a stock and an inflation linked bond, while financing investments through a continuous stochastic income stream such as the plan member’s contributions. We use the martingale method in order to compute an analytic expression for the optimal strategy and express it in terms of observable market variables.     

Die Analytik von Plasmalipoproteinen des Menschen und ihre klinische Bewertung

Ohne Zusammenfassung

---

Analysis of human plasma lipoproteins and their clinical significance

     

Detection of coherent elastic neutrino scattering on nuclei, a status report for a detector development based on metastable superconductors

Summary Coherent elastic neutrino scattering on nuclei can only be detected via the recoil energy of the nucleus. We try to develop a detector based on metastable superconducting grains to detect these small recoil energies. Experiments testing some fundamental properties of a detector using metastable Sn and Cd grains are presented. In the case of Cd a sensitivity of at least 24 eV/μm³ (normalized to the volume of the grains) was achieved. We expect a still higher sensitivity if superconductors with very lowT _c are used and the quality of the grains (sphericity, size distribution, solid state properties) is improved.

---

Riassunto Lo scattering elastico coerente di neutrini su nuclei si può rilevare solo attraverso l'energia di rinculo del nucleo. Si cerca di mettere a punto un rivelatore basato su grani metastabili superconduttori per rilevare queste piccole energie di rinculo. Si presentano esperimenti per saggiare alcune proprietà fondamentali di questo rivelatore usando grani metastabili Sn e Cd. Nel caso di Cd è stata raggiunta una sensibilità di almeno 24 eV/μm⁶ (normalizzata al volume dei grani). Si prevede una sensibilità ancora piú grande se si usano superconduttori conT _c molto bassa e si migliora la qualità dei grani (sfericità, distribuzione di volume, proprietà dello stato solido).

---

Резюме Когерентное упругоерассеяние нейтрино на ядрах может быть зарегистрировано только с помоцью энергии отдачи ядра. Мы предлагаем детектирующую систему, основанную на метастабильных сверхпроводящих зернах, чтобы зарегистрировать эти малые энергии отдачи. Предлагаются эксперименты для проверки некоторых фундаментальных свойств такого детектора, с использованием метастабильных зерен Sn и Cd. В случае Cd может быть достигнута чувствительность 24 эВ/(мкм)³ (нормированная на объем зерна). Мы ожидаем еще большую чувствительность, если использовать сверхпроводники с очень низкойT _c и улучшить качество зерен (сферичность, распределение по размерам, твердотельные свойства).

     

Characterizations of pseudo-codewords of (low-density) parity-check codes

An important property of low-density parity-check codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message-passing iterative decoding and linear programming decoding, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so-called fundamental cone in Euclidean space. This cone depends upon a given parity-check matrix of a code, rather than on the code itself. We give a number of properties of this fundamental cone derived from its connection to unramified covers of the graphical models on which the decoding algorithms operate. For the class of cycle codes, these developments naturally lead to a characterization of the fundamental cone as the Newton polyhedron of the Hashimoto edge zeta function of the underlying graph.     

Coprime ordering of cyclic planar difference sets

Motivated by a question about uniform dessins d’enfants, it is conjectured that every cyclic planar difference set of prime power order m≠4 can be cyclically ordered such that the difference of every pair of neighbouring elements is coprime to the module v?m²+m+1. We prove that this is the case whenever the number ω(v) of different prime divisors of v is less than or equal to 3. To achieve this we consider a graph related to the difference set and show that it is Hamiltonian.