In-trees and plane embeddings of outerplanar graphs

A notion of anin-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.This research was partially supported by the grant RP.I.09, from the Institute of Informatics, University of Warsaw. Hospitality of the Institute of Datalogy, University of Copenhagen where this research has been completed is gratefully acknowledged.     

Comparison theorems for diffusion processes

We prove comparison theorems for diffusion processes onR ^d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential operator.     

The E(4) Πu state in K2 and its perturbations

The E(4) ¹Π_u←X ¹Σ⁺_g band system of the K₂ molecule is investigated by the technique of Doppler-free optical–optical double resonance polarization spectroscopy. The observed vibrational levels v=0 to 9 of the E state are subject to numerous rotational perturbations by the neighboring 4 ³Π_u, 4 ¹Σ⁺_u, and 5 ³Σ⁺_u electronic states. By using deperturbation methods, the potential curves of the 4 ¹Π_u and 4 ³Π_u states are determined as well as some properties of the 4 ¹Σ⁺_u and 5 ³Σ⁺_u state potentials. The results are compared with predictions of ab initio calculations.     

A novel approach to the rapid determination of amoxicillin in human plasma by solid phase microextraction and liquid chromatography

A new approach to the rapid determination of amoxicillin (AMO) in human plasma followed by solid phase microextraction (SPME) fiber coatings based on conducting polymers (polypyrrole and polythiophene) and high performance liquid chromatography (HPLC) has been described. The porous structures of the electrochemically deposited polymer coatings have been characterized by scanning electron microscopy (SEM). The experimental parameters relating to the extraction efficiency of the SPME fibers such as pH, extraction time and desorption conditions (solvents, time) were studied and selected. The SPME/HPLC-UV method was linear over a working range of 1-50 μg ml(-1). The inter-day accuracy (expressed as coefficients of variations, CVs) was less than 15% and precision (expressed as the relative standard deviations, RSDs) with percentage values was less than 5.9%. Amoxicillin was found to be stable in the human plasma at room temperature (20 °C) within 8 hours. The developed method was successfully applied to the analysis of real human plasma samples. The limit of detection and limit of quantification for amoxicillin in plasma were 1.21 μg ml(-1) and 3.48 μg ml(-1), respectively.     

Information Theories with Adversaries,Intrinsic Information,and Entanglement

There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I_M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions. It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.     

Quantum Hall ferrimagnetism in lateral quantum dot molecules

We demonstrate the existence of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from the Hartree-Fock configuration interaction method as a function of electron number N and magnetic field B. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong interdot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between nu=2 and nu=1.