Verified Distance Computation Between Convex Hulls of Octrees Using Interval Optimization Techniques

Distance computation is an important task in many application areas, including biomechanics, robot systems and computer games. Depending on the intended use, requirements differ. For example, in a medical context, a verified result may be of interest. In this paper we will demonstrate the use of an interval optimization algorithm for computing a verified enclosure of the minimum distance between the convex hulls of two octrees. We will also discuss runtime improvements. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Über Chalkogenolate. LXV. Untersuchungen über Thioameisensäuren 8. Kristallstruktur von Kaliumdithioformiat

On Chalkogenolates. LXV. Studies on Thioformic Acids. 8. Crystal Structure of Potassium Dithioformate Potassium dithioformate K[HCS₂] crystallizes tetragonal within the space groups I4/mem–D (no. 140). The cell dimensions are a = 10.596 and c = 7.946 Å; Z = 8. The structure contains sheets of dithioformate ions at z = 0 and 0.5 with sheets of potassium ions half way between parallel the xy-plane. The coordination number of potassium is 8, that of sulfur is 4. Structural refinements by least-squares methods came to a final R = 0.093.     

Über Chalkogenolate. 117 [1]. Untersuchungen über Guanidinodithioformiate 4. Kristall- und Molekülstruktur der Guanidinodithioameisensäure

On Chalcogenolates. 117. Studies on Guanidinodithioformates. 4. Crystal and Molecular Structure of Guanidinodithioformic Acid Guanidinodithioformic acid crystallizes with Z = 4 in the monoclinic space group P2₁ with cell dimensions a = 4.204(3) Å, b = 10.422(5) Å, c = 12.491(5) Å, β = 93.9(3)°. The crystal and molecular structure has been determined from single crystal X-ray data at 20°C and refined to a conventional R of 0.0242. The asymmetric part of the unit cell contains two molecules in the dipolar form with different conformation. The molecules have delocated double-bonds and are linked together by N? H···S hydrogen bridges.     

Über Chalkogenolate. 170. Reaktion von N,N′-Diphenylformamidin mit Kohlenstoffdisulfid 3. Kristallstruktur von Kalium-N,N′-diphenyl-N-formimidoyldithiocarbamat · Dioxan

On Chalcogenolates. 170. Reaction of N,N′-Diphenyl Formamidine with Carbon Disulfide 3. Crystal Structure of Potassium N,N′-Diphenyl N-Formimidoyl Dithiocarbamate · Dioxane The title compound K[S₂C? N(C₆H₅)? CH?NC₆H₅] · C₄H₈O₂ crystallizes with Z = 4 in the monoclinic space group P2₁/a with cell dimensions a = 10.703(2) Å, b = 18.068(3) Å, c = 10.504(3) Å, β = 100.96(3)°. The crystal structure has been determined from single crystal X-ray data measured at 20°C and refined to a conventional R of 0.052 for 4556 independent reflections (R_w = 0.054). The K⁺ cation is surrounded of one oxygen, one nitrogen, and three sulfur atoms to form a distorted trigonal bipyramid. The S₂CNCN part of the anion, which exists as E, E conformer, is plane. The dioxane molecule has chair conformation without symmetry centre.     

Synthesis and Diels-Alder Reactions of a New Kind of Chiral Dienophiles: Cyclic Vinyl-p-tolylsulfilimines

A new kind of chiral dienophiles, cyclic vinyl-p-tolylsulfilimines (2a and 2b), were obtained from the corresponding (Z)-sulfinylacrylonitriles with HBF(4) and methanol. The asymmetric Diels-Alder reaction of optically pure 2a with cyclopentadiene under mild thermal or catalyzed conditions afforded only the endo-4a adduct with complete endo and pi-facial selectivities. The ability of the sulfilimine moiety to enhance the dienophilic reactivity of the double bond is similar to that of the sulfinyl group.     

Über Chalkogenolate. 131. Untersuchungen über Rhodanine 2. Kristall- und Molekülstruktur von 5-Methylrhodanin

On Chalcogenolates. 131. Studies on Rhodanines 2. Crystal and Molecular Structure of 5-Methyl Rhodanine The title compound crystallizes with Z = 4 in the monoclinic space group P2₁/c with cell dimensions a = 6.087(1), b = 6.846(4), c = 15.336(2) Å, β = 99.85(1)°. The crystal and molecular structure has been determined from single crystal X-ray data at ?25°C and refined to a conventional R of 0.044. The structure consists of discrete 5-methyl-2-thio-4-oxo-thiazolidine molecules, which are linked together by N? H…?O hydrogen bridges. The thiazolidine ring is plane. The compound contains no located double-bonds.     

Zeros of the Whittaker function associated to Coulomb waves

The zeros in the complex z plane of the Whittaker function W_c/z,µ(z),closely related to spherical waves in the quantum-mechanicalCoulomb problem, are investigated for varying real values ofthe parameters c and µ     

Measurement of helicity-dependent photoabsorption cross sections on the neutron from 815 to 1825 MeV

Helicity-dependent total photoabsorption cross sections on the deuteron have been measured for the first time at ELSA (Bonn) in the photon energy range from 815 to 1825 MeV. Circularly polarized tagged photons impinging on a longitudinally polarized LiD target have been used together with a highly efficient 4pi detector system. The data around 1 GeV are not compatible with predictions from existing multipole analyses. From the measured energy range an experimental contribution to the GDH integral on the neutron of [33.9 +/- 5.5(stat) +/- 4.5(syst)] microb is extracted.     

Polyamide resin: A novel immunoadsorbent

A solid phase assay for radiolabeled antibody synthesizedde novo in vitro has been described (1). The solid phase consists of antigen covalently bound to bromacetyl cellulose, a useful but difficult to prepare immunoadsorbent. Herein, we describe the preparation of polyamide resin immunoadsorbent and the procedure for coupling antigen to the polymer. Data are presented that show that polyamide resin-Ag? conjugates can replace bromacetyl cellulose-Ag conjugates. The usefulness of this easily prepared and inexpensive immunoadsorbent is discussed.