Discrepancy of Fractions with Divisibility Constraints

We provide bounds for the absolute discrepancy of sequences of fractions with denominators streaming in a given arithmetic progression and satisfying divisibility constraints. Supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.     

On the vanishing of higher syzygies of curves. II

Mathematische Zeitschrift -     

The cyber infrastructure initiative for rheology

A new cyber infrastructure for rheology (CIR) has the potential of integrating the diverse rheological knowledge of experts around the world. In a multi-disciplinary effort, experts in specialized topics of rheology began to write CIR-modules that seamlessly merge into a general code so that it can be used by a wide range of engineers and scientists. At the center of CIR is a platform operating system that connects a wide range of dedicated software modules. These CIR-modules perform calculations and return the corresponding results to a central graphics screen. The computer platform allows the detailed analysis of experimental data, the communication of data, and the prediction of rheological material functions from a wide range of theories in rheology. Rheologists can access each other’s experimental results, make predictions with each other’s theories and simulate with each other’s computer codes. Through such collaboration, seemingly disparate theories and experimental observations can be linked and taken to their limits, thereby leading to unexpected insights and new questions. Beyond the pool of experts, CIR will draw industrial users into the rheology discussion. Easy-to-use CIR-tools will allow industrial rheologists to adjust rapidly to the changing needs and the pressure to obtain short-term solutions in a competitive environment. CIR has the potential of generating ideas for novel materials and novel manufacturing methods. At the same time, it will supply the tools to examine ideas quantitatively and to push these ideas even further. User-friendly methods are essential not only for research and application, but also for the teaching of rheology. We envision tools that allow a student to move seamlessly and rapidly between experimental data and the most advanced rheological theories, simulations, and modeling of applications. In-depth data analysis and evaluation of theory should become easy enough to be performed after reasonable training and without relying on over-simplifications. This will enable the student to reach a deeper understanding of rheology and to appreciate the significance that rheology has in technical applications. Even untrained talent may get introduced quickly into advanced concepts of rheology.Presented at the Annual Meeting of European Society of Rheology, Grenoble, April 2005     

Determination of the radiative lifetimes of the b1Σ+ and a1Δ states in NH by ab initio methods

Probabilities for the spin-forbidden transitions from the b¹Σ⁺ and a¹Δ states to the X³Σ^? ground state of NH have been evaluated by a first-order perturbation expansion into S-eigenfunctions Nine ³Π and ¹Π, five ¹Σ⁺ and three ³Σ^? states have been calculated by the MRD CI method at the experimental equilibrium distance of the X³Σ^? state (1.0362 Å) which cover a vertical spectral region of = 100000 cm^?1. The expansion terms of the perturbation sum are spin-orbit coupling coefficients obtained by using the Breit-Pauli one- and two-electron spin-orbit operator. The radiative lifetime of b¹Σ⁺ has been determined in the Franck-Condon approximation to be 72 ms from ab initio data and 97 ms if experimental excitation energies for the low-lying valence states are employed. Recent experiments give a somewhat shorter lifetime for the corresponding 0-0 transition of 53 ms. The lifetime is governed by the transition to the ³Σ^?_±1 level of the non-rotating molecule, borrowing its intensity mainly from the A³Π → X³Σ^? dipole transition. The second possible transition to the Ω = 0 level of the ground state is found to be weak. A similar relation of μ₁/μ₀ is expected for all the hydrogen containing isovalent molecules such as PH and AsH. The radiative lifetime of the a¹Δ state has been calculated to be = 1.7 s. Recent matrix experiments predict a gas-phase lifetime of at least 3 s. Further experimental and theoretical investigations are in progress to clarify this unusual finding that the experimentally determined lifetime is longer than that calculated theoretically.     

On fuzzy multi-valued functions part 3: Fixed-point theorem

In this paper a Fixed-Point Theorem and an application is presented.     

On fuzzy multi-valued functions part 2: Some topological properties

In this paper new topological concepts connected with fuzzy multi-valued functions theory-as presented in the first part of this work-are introduced and their properties are investigated. As will be shown in future papers these concepts and properties are indispensable in connection with the analysis of fuzzy economic systems.     

Ab initio calculation of the potential energy surface for the large-amplitude bending and symmetric stretching vibration in the electronic ground state of XeF2

A two-dimensional symmetric stretching-bending potential surface for the electronic ground state of the XeF₂ molecule has been computed by means of self-consistent field and multi-reference configuration interaction methods. At the correlated level of treatment it is found that the linear nuclear arrangement of XeF₂ with XeF bond distances close to 200 pm corresponds only to a local minimum on the potential energy surface separated from the dissociation products Xe + 2F by a high energy barrier. The results of a vibrational analysis study enable a reliable reproduction and interpretation of available experimental data concerning the infrared spectrum of the molecule.     

Studies on the reactions of selenite ion with 1,2-dimercaptoethane or thioacetic acid

The reactions are reported between selenite and 1,2-dimercaptoethane (DME) or thioacetic acid (TAA) to form moderately stable derivatives having an enhanced absorptions in the 230–360 nm region in combining molar ratios 3:2 and 4:1, respectively. Both reactions invariably yield one product corresponding to the selenium-containing derivative of DME or TAA. The formation of products is a pH dependent process. The equilibrium constants of reactions between selenite and DME or TAA were measured.     

Graph Approach to the Computation of the Homology of Continuous Maps

We introduce an efficient algorithm to compute the homomorphism induced in (relative) homology by a continous map. The algorithm is based on a cubical approximation of the map and the theory of multivalued maps. A software implementation of the algorithms introduced in this paper is available at [27].