3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects

We present a new data structure for a set of n convex simply-shaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting—preprocess a set of n non-intersecting convex simply-shaped flat objects in 3-space, whose xy-projections are fat, for efficient vertical ray shooting queries, (ii) point enclosure—preprocess a set C of n convex simply-shaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) bounded-size range searching— preprocess a set C of n convex fat polygons, so that the k objects intersecting a “not-too-large” query polygon can be reported efficiently, and (iv) bounded-size segment shooting—preprocess a set C as in (iii), so that the first object (if exists) hit by a “not-too-long” oriented query segment can be found efficiently. For the first three problems we construct data structures of size O(λ_s(n)log³n), where s is the maximum number of intersections between the boundaries of the (xy-projections) of any pair of objects, and λ_s(n) is the maximum length of (n, s) Davenport-Schinzel sequences. The data structure for the fourth problem is of size O(λ_s(n)log²n). The query time in the first problem is O(log⁴n), the query time in the second and third problems is O(log³n + klog²n), and the query time in the fourth problem is O(log³n).

We also present a simple algorithm for computing a depth order for a set as in (i), that is based on the solution to the vertical ray shooting problem. (A depth order for , if exists, is a linear order of , such that, if K₁, K₂ and K₁ lies vertically above K₂, then K₁ precedes K₂.) Unlike the algorithm of Agarwal et al. (1995) that might output a false order when a depth order does not exist, the new algorithm is able to determine whether such an order exists, and it is often more efficient in practical situations than the former algorithm.     

Laser spectroscopic investigation of a new precursor-type polyparaphenylenevinylene

Optical, structural and morphological properties of thin films of polyparaphenylenevinylene (PPV) formed by an alkyl sulfinyl precursor route have been studied. Thin films were fabricated on an optical glass and on quartz glass either by spin-coating of the precursor solution or by layer-by-layer deposition using Langmuir–Blodgett technique. PPV precursor films were also spin-coated on gold-coated glass in order to study thin-film optical parameters by surface plasmon spectroscopy. We have been successful in forming about 40 precursor mono layers on quartz glass by Langmuir–Blodgett technique using optimized surface pressure and dipping conditions. After thermal conversion of the precursor layers good quality fluorescent PPV films of yellow colour have been obtained. Optical characterization of the films was carried out by linear absorption and emission spectroscopy, ellipsometry, and surface plasmon spectroscopy. Structural and morphological studies on the thin films were carried out by using X-ray scattering and atomic force microscopy. Wave-guided travelling-wave laser action has been achieved in a PPV film on quartz glass. The sample was transversally pumped with picosecond laser pulses (wavelength 347.15 nm, duration 35 ps). Laser emission occurred at 550 nm for pump pulse energy densities above .     

A simple low-vacuum environmental cell.

The environmental cell device discussed in this paper provides a modest low-vacuum scanning electron microscopy (SEM) capability to a standard SEM without requiring additional pumping. This environmental cell confines a volume of low vacuum in contact with the sample surface using a container that has an aperture for admitting the primary electron beam. The aperture is large enough to permit a limited field of view of the sample, and small enough to limit the outflow of gas into the SEM chamber to that which can be accommodated by the standard SEM pumping system. This environmental cell also functions as a gaseous detector device.     

A new Löwenheim-Skolem theorem

This paper establishes a refinement of the classical Löwenheim-Skolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order properties. Several consequences for Singular Cardinals Combinatorics are deduced from this.

     

Geometric algebra techniques for general relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.     

Comparison of XYZ Model Fitting Functions for 111Cd in In3La

The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal directions. The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed angular correlation spectroscopy. Three analytic approximations of the perturbation function have been developed previously, and they are evaluated in the present paper in the context of Cd jumping among In-lattice sites in In₃La.