Infinitely many singular interactions on noncompact manifolds

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004).     

Computation of critical exponents for two-dimensional ising model on a cellular automaton

Static critical exponents for the two-dimensional Ising model are computed on a cellular automaton. The analysis of the data within the framework of the finite-size scaling theory reproduces their well-established values.     

Reaktionen cyclischer Oxalylverbindungen, 34. Mitt.: Synthese von Dibenzoylacet-N-carboxyalkylamiden und semiempirische Rechnungen zur Keto-Enol Tautomerie

Summary 4-Benzoyl-5-phenylfuran-2,3-dione (1) and the urethanes2 combine under loss of carbon monoxide yielding the open chain dibenzoylacetic acid derivatives3 and4. 3a, b only can be cyclized to the oxazinone5. The keto-enole tautomerism3 4 is further investigated with aid of semiempirical quantum chemical calculations, based upon the molecular geometry of3a, deduced from an X-ray study.

Frau Univ. Prof. Dr. Helga Wittmann mit den besten Wünschen zum 70. Geburtstag gewidmet.     

New Copper（Ⅱ） and Nickel（Ⅱ） Complexes of 4-Morpholinoacetophenone Thiosemicarbazone： Structural, Electrochemical and Antimicrobial Studies

4-Morpholinoacetophenone thiosemicarbazone, MAPT, and its nickel（Ⅱ） and copper（Ⅱ） complexes have been prepared and characterized by elemental analysis, magnetic susceptibility, spectral methods （FT-IR, ^1H NMR） and cyclic voltammetry. Electrochemical behaviors of the complexes have been studied by cyclic voltammetry in DMF media showing metal centered reduction processes for both of them. The redox properties, nature of the electrode processes and the stability of the complexes were discussed. [Cu（MAPT）2]Cl2 complex shows Cu（Ⅱ）/Cu（Ⅰ） couple and quasi-reversible wave associated with the Cu（Ⅲ）/Cu（Ⅱ） process. The reduction/oxidation potential values depend on the structures of complexes. Also, the antimicrobial activities of these complexes were determined against S. aureus, E. coli and B. subtilis.     

Electrochemical Investigation of Heavy Metal Ion Transfer Across the Water/1,2‐Dichloroethane Interface Assisted by 9‐Ethyl‐3‐Carbazolecarboxaldehyde‐Thiosemicarbazone

The transfer of heavy metal ions across the polarized water/1,2‐dichloroethane (1,2‐DCE) interface assisted by 9‐ethyl‐3‐carbazolecarboxaldehyde‐thiosemicarbazone (ECCAT) in the 1,2‐DCE phase has been studied by cyclic voltammetry. Voltammetric waves of Pb(II) and Cd(II) ions were reversible and quasi‐reversible, respectively, whereas that of Hg(II) and Zn(II) ion were irreversible. The voltammogram of Cu(II) ion showed a two‐step wave, however the nature of the transfer could not be satisfactorily evaluated by analyzing the cyclic voltammetric data. When Ni(II) and Co(II) was used no peak was visible under the experimental conditions used in this study. The dependence of the half‐wave potentials of Pb(II) and Cd(II) ions on the ligand concentration reveals that their ion‐transfer is assisted by the formation of 1:3 metal‐ECCAT complex in 1,2‐DCE. The over‐all association constants of [Pb(ECCAT)₃]²⁺ and [Cd(ECCAT)₃]²⁺ complexes in DCE‐phase have been determined to be log β =14.03 and log β =15.44, respectively.     

Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the galilean space

In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G₃. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G₃.     

The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space

We study the singularities of Galilean distance and Galilean height functions intrinsically related to Frenet frame along a curve embedded into Galilean space. We establish the relationships between singularities of the functions and geometric invariants under the action of Galilean group of curves which are deeply related to the order of contact with Galilean helices.     

Call center service process analysis: Bayesian parametric and semi-parametric mixture modeling

The main focus of the call center research has been on models that assume all input distributions are known in queuing theory which gives birth to staffing and the estimation of operating characteristics. Studies investigating uncertainty of the input distributions and its implications on call center management are scarce. This study attempts to fill this gap by analyzing the call center service distribution behavior by using Bayesian parametric and semi-parametric mixture models that are capable of exhibiting non-standard behavior such as multi-modality, skewness and excess kurtosis motivated by real call center data. The study is motivated by the observation that different customer profiles might require different agent skill sets which can create additional sources of uncertainty in the behavior of service distributions. In estimating model parameters, Markov chain Monte Carlo methods such as the Gibbs sampler and the reversible jump algorithms are presented and the implications of using such models on system performance and staffing are discussed.