Facile Template Synthesis in the System Ni(II)-Dithiooxamide-Acetaldehyde on Gelatin-immobilized Nickel(II) Hexacyanoferrate Matrices

Template synthesis of a nickel(II) chelate with an (N'N'S'S)-donor ligand, 4'6-dimethyl-2'8-di-thio-3'7-diaza-5-oxanonanedithioamide-1'9, with a metal ion:ligand ratio of 1:1 is realized in getalin-immobilized nickel(II) hexacyanoferrate(II) matrices contacting with aqueous solutions containing dithiox-amide, acetaldehyde (pH > 10), where the latter two compounds play the role of ligand synthons. On directcontact of dithioxamide and acetaldehyde in the solution in the absence of Ni(II), the above (N,N,S,S)-donorligand does not form, and no nickel(II) chelates with this ligand can be obtained by reactions of known nickel(II) dithiooxamide complexes with acetaldehyde.     

The Laplacian and Dirac operators on critical planar graphs

On a periodic planar graph whose edge weights satisfy a certain simple geometric condition, the discrete Laplacian and Dirac operators have the property that their determinants and inverses only depend on the local geometry of the graph. We obtain explicit expressions for the logarithms of the (normalized) determinants, as well as the inverses of these operators. We relate the logarithm of the determinants to the volume plus mean curvature of an associated hyperbolic ideal polyhedron. In the associated dimer and spanning tree models, for which the determinants of the Dirac operator and the Laplacian respectively play the role of the partition function, this allows us to compute the entropy and correlations in terms of the local geometry. In addition, we define a continuous family of special discrete holomorphic functions which, via convolutions, gives a general process for constructing discrete holomorphic functions and discrete harmonic functions on critical planar graphs. Oblatum 6-III-2002 & 12-VI-2002?Published online: 6 August 2002     

Sortability of Multi-partitions

Recently, the theory of sortability of partition property has been shown to be an effective tool to prove the existence of an optimal partition with that property. In this paper, we extend the theory to multi-partition where the partition is on t types of components. We apply our results to settle an optimal assignment problem whose proof was incomplete as given in the literature.     

Incomplete data problems in X-ray computerized tomography

Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4     

Allocating Warehouse Stock in a Retail Chain

The context is that of a retail chain where stock is purchased into a central warehouse from which branch stocks are replenished. This paper considers possible methods of allocating limited warehouse stock to branches, and uses simulation to quantify the resulting benefits.     

Asymptotic expansion of the logistic midrange

Using the symbolic computation program MAPLE, we compute several terms of an asymptotic expansion for the distribution function of the logistic midrange.     

Approximation of infinite delay and Volterra type equations

Summary We consider a class of infinite delay equations of neutral type which includes Volterrra type integral und integrodifferential equations. Using abstract approximation results (cf. Trotter-Kato-type) for strongly continuous semigroups we develop an approximation scheme which is based on approximation of the system state by Laguerre (and Legendre) polynomials. Numerical examples demonstrate the feasibility of the scheme and show infinite order convergence for smooth data.Supported in part by the Air Force Office of Scientific Research under Contracts AFORS-84-0398 and AFORS-85-0303 and the National Aeronautics and Space Administration under NASA Grant NAG-1-517 and by NSF under Grant UINT-8521208Supported in part by the Air Force Office of Scientific Research under Contract AFORS-84-0398 and in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under project No. S3206