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.     

Extended Rees algebras and mixed multiplicities

Partially supported by the general research fund at the University of Kansas     

Miscibility of polyester/nitrocellulose blends: A DSC and FTIR study

The miscibility of polyester/nitrocellulose blends was investigated by differential scanning calorimetry and Fourier-transform infrared (FTIR) spectroscopy. Two nitrocelluloses (NC) derived from wood and having different nitrogen contents (12.62 and 13.42%) were used. On the basis of the glass transition temperature criterion, poly(?-caprolactone) (PCL), poly(valerolactone), poly(ethylene adipate), and poly(butylene adipate) are miscible with nitrocellulose, whereas poly(α-methyl α-propyl β-propiolactone) and poly(α-methyl β-proiolactone) are immiscible. The T_g versus composition curves of PCL/NC blends do not follow a monotone function but exhibit a singular point at a critical PCL volume fraction of 0.51 for NC-1342 and 0.45 for NC-1262 in agreement with Kovacs' theory. A shift of 17 cm^-1 of the carbonyl stretching band was observed with PCL/NC blends and is taken as evidence for hydrogen bonding interaction between the PCL carbonyl group and NC hydroxyl group. The frequency difference between the free hydroxyl absorbance and the absorbances of the hydrogen-bonded species was found to be 85 cm^-1 in pure NC and 125 cm^-1 in PCL/NC blends; it indicates that the average strength of this interaction is stronger than the corresponding self-associated hydrogen bonding in pure NC. The presence of a dipole-dipole interaction between the nitrate-ester groups of NC and the carbonyl groups of the polyesters is reported. The relative strength of the hydrogen bonding and dipole-dipole interactions is discussed and correlated with polymer miscibility.     

Photothermal microanalysis of thermal discontinuities in metallic samples

Modeling the behavior of a protective coating during a thermal shock not only requires the knowledge of its own thermophysical characteristics, but also those of the coating–substrate discontinuity. According to its nature, this discontinuity can be modeled as a zero-thickness interface (thermal contact resistance) or a finite thickness layer (thermal third body). This paper presents an experimental device and two associated thermal transfer models developed in view of the microscale characterization of such discontinuities.     

Sur les automorphismes analytiques des variétés hyperboliques

Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism.     

Quantitative analysis of imazamox herbicide in environmental water samples by capillary electrophoresis electrospray ionization mass spectrometry

Capillary electrophoresis-mass spectrometry (CE-MS) with an electrospray ionization interface was applied for the quantitative analysis of imazamox pesticide in well water, potable water, and pond water. The detector response for imazamox was determined to be linear over the concentration range of 50-1 ng/ml. The limits of quantitation and detection of the method were determined to be 200 and 20 ng/l for imazamox compound in each type of water sample, respectively. The total sample preparation and CE-MS analysis time was under 2 h.     

New example of a non-heme mononuclear iron(IV) oxo complex. Spectroscopic data and oxidation activity

The green complex S=1 [(TPEN)FeO]2+ [TPEN=N,N,N',N'-tetrakis(2-pyridylmethyl)ethane-1,2-diamine] has been obtained by treating the [(TPEN)Fe]2+ precursor with meta-chloroperoxybenzoic acid (m-CPBA). This high-valent complex belongs to the emerging family of synthetic models of Fe(IV)=O intermediates invoked during the catalytic cycle of biological systems. This complex exhibits spectroscopic characteristics that are similar to those of other models reported recently with a similar amine/pyridine environment. Thanks to its relative stability, vibrational data in solution have been obtained by Fourier transform infrared. A comparison of the Fe=O and Fe=(18)O wavenumbers reveals that the Fe-oxo vibration is not a pure one. The ability of the green complex to oxidize small organic molecules has been studied. Mixtures of oxygenated products derived from two- or four-electron oxidations are obtained. The reactivity of this [FeO]2+ complex is then not straightforward, and different mechanisms may be involved.     

A single crystal study of eight-layer barium managanese oxide,BaMnO3

A single crystal study of hydrothermally prepared eight-layer BaMnO₃ has been carried out which confirms the (Zhdanov notation) 121121 layer stacking scheme for the BaO₃ layers. The MnO₆ octahedra share faces in strings of four, and these strings are connected to each other by corner sharing. The compound has an hexagonal unit cell of dimensions a = 5.667 ± 0.003 and c = 18.738 ± 0.009 Å, probable space group $\text{P6}{}_3\text{mmc}\text{, Z = 8}$. Its structure has been determined from 352 independent reflections, of which 242 were considered observed, collected manually by a counter technique and refined to a conventional R value of 0.079.