Random sampling within the framework of a multivariate principal-agent approach

In this paper, we analyze a specific class of principal-agent models which seems to be sufficiently general to cover applications in environmental economics with upstream-downstream problems as an example. In our basic model, the observation outcome is ann-dimensional random vectorx and only the first and second moments ofx are common knowledge. We study the effects of random sampling in the presence of costly signals. For this purpose, we assume that the principal and the agent use a simple statistical procedure, i.e. their contract will be based on the mean of a random sample with sampling costs dependent on the sample size. It is shown that there exists an optimal sample size. We investigate the relationship between the optimal sample size, the marginal sampling costs, and the agent's risk aversion.     

On measures integrating all functions of a given vector lattice

LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f1}:fE}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsfE is (E)--smooth iffX is (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively.     

Algebraic properties of discrete box splines

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.     

The hyperbolic n-space as a graph in Euclidean (6n−6)-space

We construct for each n2 an isometric C-imbedding HⁿE^6n–6 of the n-dim. hyperbolic space into the Euclidean space E^6n–6 whose image is the graph of a C-map RⁿR^5n–6. This generalizes a well known result of D. Blanusa 1955 (the case n=2).     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

Siliceous spicules in marine demosponges (example Suberites domuncula)

All metazoan animals comprise a body plan of different complexity. Since--especially based on molecular and cell biological data--it is well established that all metazoan phyla, including the Porifera (sponges), evolved from a common ancestor the search for common, basic principles of pattern formation (body plan) in all phyla began. Common to all metazoan body plans is the formation of at least one axis that runs from the apical to the basal region; examples for this type of organization are the Porifera and the Cnidaria (diploblastic animals). It seems conceivable that the basis for the formation of the Bauplan in sponges is the construction of their skeleton by spicules. In Demospongiae (we use the model species Suberites domuncula) and Hexactinellida, the spicules consist of silica. The formation of the spicules as the building blocks of the skeleton, starts with the expression of an enzyme which was termed silicatein. Spicule growth begins intracellularly around an axial filament composed of silicatein. When the first layer of silica is made, the spicules are extruded from the cells and completed extracellularly to reach their the final form and size. While the first steps of spicule formation within the cells are becoming increasingly clear, it remains to be studied how the extracellularly present silicatein strings are formed. The understanding of especially this morphogenetic process will allow an insight into the construction of the amazingly diverse skeleton of the siliceous sponges; animals which evolved between two periods of glaciations, the Sturtian glaciation (710-680 MYA) and the Varanger-Marinoan ice ages (605-585 MYA). Sponges are--as living fossils--witnesses of evolutionary trends which remained unique in the metazoan kingdom.     

Broadly tunable dual-wavelength light source for coherent anti-Stokes Raman scattering microscopy

The signal and idler beams from a picosecond, synchronously pumped optical parametric oscillator (OPO) provide the two colors necessary for coherent anti-Stokes Raman scattering (CARS) microscopy. The OPO provides a continuously tunable frequency difference between the two beams over a broad range of Raman shifts (100-3700 cm(-1)) by varying the temperature of a single nonlinear crystal. The near-infrared output (900-1300 nm) allows for deep penetration into thick samples and reduced nonlinear photodamage. Applications of this light source to in vivo cell and ex vivo tissue imaging are demonstrated.     

Uniform Field Re-entrant Cylindrical TE$$_{01\text {U}}$$ Cavity for Pulse Electron Paramagnetic Resonance Spectroscopy at Q-band

Uniform field (UF) resonators create a region-of-interest, where the sample volume receives a homogeneous microwave magnetic field (\(B_1\)) excitation. However, as the region-of-interest is increased, resonator efficiency is reduced. In this work, a new class of uniform field resonators is introduced: the uniform field re-entrant cylindrical TE\(_{\text {01U}}\) cavity. Here, a UF cylindrical TE\(_{\text {01U}}\) cavity is designed with re-entrant fins to increase the overall resonator efficiency to match the resonator efficiency maximum of a typical cylindrical TE\(_{011}\) cavity. The new UF re-entrant cylindrical TE\(_{\text {01U}}\) cavity is designed for Q-band (34 GHz) and is calculated to have the same electron paramagnetic resonance (EPR) signal intensity as a TE\(_{011}\) cavity, a 60% increase in average resonator efficiency \(\Lambda _\mathrm{ave}\) over the sample, and has a \(B_1\) profile that is 79.8% uniform over the entire sample volume (98% uniform over the region-of-interest). A new H-type T-junction waveguide coupler with inductive obstacles is introduced that increases the dynamic range of a movable short coupler while reducing the frequency shift by 43% during over-coupling. The resonator assembly is fabricated and tested both on the bench and with EPR experiments. This resonator provides a template to improve EPR spectroscopy for pulse experiments at high frequencies.