Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

Two-phase MFD flows in orthogonal curvilinear coordinate system

Steady flow of an inviscid, incompressible two-phase magnetofluid with infinite electrical conductivity is treated. With one ignorable coordinate in a general orthogonal curvilinear system, general solutions of the equations, considering number densityN constant throughout the motion, are obtained.     

Molecular dynamics and structure-based virtual screening and identification of natural compounds as Wnt signaling modulators: possible therapeutics for Alzheimer’s disease

Molecular Diversity - Wnt signaling pathway is an evolutionarily conserved pathway responsible for neurogenesis, axon outgrowth, neuronal polarity, synapse formation, and maintenance....     

The finite element method with Lagrangian multipliers

Summary The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.This paper was supported by the Atomic Energy Commission under Contract No. AEC AT (40-1) 3443/4.     

Facile Synthesis of Pyrazolo[3,4‐d]pyrimidines and Pyrimido[4,5‐d]pyrimidin‐4‐one Derivatives

Pyrazolopyrimidine and pyrimidopyrimidine derivatives have shown a wide range of biological activities such as acting as A₁ adenosine receptors, kinase insert domain receptor (KDR), Rous sarcoma oncogene (Src), epidermal growth factor receptor (EGFR), antiproliferative, dihydrofolate reductase (DHFR), antimicrobial, antifungal, and lipid peroxidation. Because of this wide range of activities, we have synthesized pyrazolo[3,4‐d]pyrimidines and pyrimido[4,5‐d]pyrimidin‐4‐one derivatives.     

Dislocation driven chromium precipitation in Fe-9Cr binary alloy: a positron lifetime study

The influence of initial heat treatment on anomalous Cr precipitation within high temperature solubility region of the Fe–9Cr alloy has been investigated using positron lifetime studies. Air-quenched samples with pre-existing dislocations exhibited a distinct annealing stage in positron lifetime between 800 and 1100?K corresponding to Cr-precipitation. During this stage, Transmission Electron Microscopy showed fine precipitates of average size 4 nm, dispersed throughout the sample and from Energy-dispersive X-ray spectroscopy (EDS) analysis they are found to be Cr-enriched. The presence of dislocations is found to be responsible for Cr precipitation.     

Pore Scale Modeling of Reactive Transport Involved in Geologic CO<Subscript>2</Subscript> Sequestration

We apply a multi-component reactive transport lattice Boltzmann model developed in previous studies for modeling the injection of a CO₂-saturated brine into various porous media structures at temperatures T = 25 and 80°C. In the various cases considered the porous medium consists initially of calcite with varying grain size and shape. A chemical system consisting of Na⁺, Ca²⁺, Mg²⁺, H⁺, CO₂^°(aq){{\rm CO}_2^{\circ}{\rm (aq)}}, and Cl⁻ is considered. Flow and transport by advection and diffusion of aqueous species, combined with homogeneous reactions occurring in the bulk fluid, as well as the dissolution of calcite and precipitation of dolomite are simulated at the pore scale. The effects of the structure of the porous media on reactive transport are investigated. The results are compared with a continuum-scale model and the discrepancies between the pore- and continuum-scale models are discussed. This study sheds some light on the fundamental physics occurring at the pore scale for reactive transport involved in geologic CO₂ sequestration.     

Electro-chromatography in the study of ions

Summary Migration rate of ions increases with voltage. Nickel ion migrates in 0.5 Molar tartaric acid medium in a small well compact zone leaving no trailing and can be easily quantitatively estimated colorimetrically.Part II: Sec Z. analyt. Chem. 163, 408 (1958).     

Gradually truncated log-normal in USA publicly traded firm size distribution

We study the statistical distribution of firm size for USA and Brazilian publicly traded firms through the Zipf plot technique. Sale size is used to measure firm size. The Brazilian firm size distribution is given by a log-normal distribution without any adjustable parameter. However, we also need to consider different parameters of log-normal distribution for the largest firms in the distribution, which are mostly foreign firms. The log-normal distribution has to be gradually truncated after a certain critical value for USA firms. Therefore, the original hypothesis of proportional effect proposed by Gibrat is valid with some modification for very large firms. We also consider the possible mechanisms behind this distribution.