Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential

We consider d-dimensional Brownian motion in a scaled Poissonian potential and the principal Dirichlet eigenvalue (ground state energy) of the corresponding Schr?dinger operator. The scaling is chosen to be of critical order, i.e. it is determined by the typical size of large holes in the Poissonian cloud. We prove existence of a phase transition in dimensions d≥ 4: There exists a critical scaling constant for the potential. Below this constant the scaled infinite volume limit of the corresponding principal Dirichlet eigenvalue is linear in the scale. On the other hand, for large values of the scaling constant this limit is strictly smaller than the linear bound. For d > 4 we prove that this phase transition does not take place on that scale. Further we show that the analogous picture holds true for the partition sum of the underlying motion process. Received: 10 December 1999 / Revised version: 14 July 2000/?Published online: 15 February 2001     

Market Power Issues in Bid-Based Hydrothermal Dispatch

The objective of this work is to investigate market power issues in bid-based hydrothermal scheduling. Initially, market power was simulated with a single stage Cournot–Nash equilibrium model. In this static model the equilibrium was calculated analytically. It was shown that the total production of N strategic agents is smaller than the least-cost solution by a factor of (N/(N+1)). Market power analysis for multiple stages was then carried through a stochastic dynamic programming scheme, where the decision in each stage and state is the Cournot–Nash equilibrium of a multi-agent game. Case studies with data taken from the Brazilian system are presented.     

Some Normal Cryptogroups as Semigroups of Isomorphisms

Given a Clifford semigroup G, we construct special G-operands L and R which we term conformai. Certain suboperands of L and R we call threads and fix some special G-isomorphisms, which we term coherent, of threads in R onto threads in L. On the set of all coherent G-isomorphisms of threads in L onto threads in R we define a sandwich-type multiplication. When we restrict our threads to be cyclic suboperands of L and R, this construction produces a normal cryptogroup which we represent as $ S=[Y;S_{\alpha},\chi_{{\alpha},{\beta}}] $ -Without any restriction on the threads this produces a semigroup isomorphic with a remarkable ideal of the translational hull of S. Conversely, given a strong semilattice of completely simple semigroups, satisfying certain conditions, we can represent it isomorphically as indicated above.     

A novel methodological approach for δ18O analysis of sugars using gas chromatography-pyrolysis-isotope ratio mass spectrometry

Although the instrumental coupling of gas chromatography-pyrolysis-isotope ratio mass spectrometry (GC-Py-IRMS) for compound-specific δ¹⁸O analysis has been commercially available for more than a decade, this method has been hardly applied so far. Here we present the first GC-Py-IRMS δ¹⁸O results for trimethylsilyl-derivatives of plant sap-relevant sugars and a polyalcohol (glucose, fructose, sucrose, raffinose and pinitol). Particularly, we focus on sucrose, which is assimilated in leaves and which is the most important transport sugar in plants and hence of utmost relevance in plant physiology and paleoclimate studies. Replication measurements of sucrose standards and concentration series indicate that the GC-Py-IRMS δ¹⁸O measurements are not stable over time and that they are amount (area) dependent. We, therefore, suggest running sample batch replication measurements in alternation with standard concentration series of reference material. This allows for carrying out (i) a drift correction, (ii) a calibration against reference material and (iii) an amount (area) correction. Tests with ¹⁸O-enriched water do not provide any evidence for oxygen isotope exchange reactions affecting sucrose and raffinose. We present the first application of GC-Py-IRMS δ¹⁸O analysis for sucrose from needle extract (soluble carbohydrate) samples. The obtained δ¹⁸O_{sucrose/ Vienna Standard Mean Ocean Water (VSMOW)} values are more positive and vary in a wider range (32.1–40.1 ‰) than the δ¹⁸O_{bulk/ VSMOW} values (24.6–27.2 ‰). Furthermore, they are shown to depend on the climate parameters maximum day temperature, relative air humidity and cloud cover. These findings suggest that δ¹⁸O_sucrose of the investigated needles very sensitively reflects the climatically controlled evaporative ¹⁸O enrichment of leaf water and thus highlights the great potential of GC-Py-IRMS δ¹⁸O_sucrose analysis for plant physiology and paleoclimate studies.     

Ladders and canonical varieties of completely regular semigroups

A completely regular semigroup is a (disjoint) union of its (maximal) subgroups. We consider it here with the unary operation of inversion within its maximal subgroups. Their totality \(\mathcal {C}\mathcal {R}\) forms a variety whose lattice of subvarieties is denoted by \(\mathcal {L}(\mathcal {C}\mathcal {R})\). On it, one defines the relations \(\mathbf {B}^\wedge \) and \(\mathbf {B}^\vee \) by

$$\begin{aligned} \begin{array}{lll} \mathcal {U}\ \mathbf {B}^\wedge \ \mathcal {V}&{} \Longleftrightarrow &{} \mathcal {U}\cap \mathcal {B} =\mathcal {V}\cap \mathcal {B}, \\ \mathcal {U}\ \mathbf {B}^\vee \ \mathcal {V}&{} \Longleftrightarrow &{} \mathcal {U}\vee \mathcal {B} =\mathcal {V}\vee \mathcal {B} , \end{array} \end{aligned}$$

respectively, where \(\mathcal {B}\) denotes the variety of all bands. This is a study of the interplay between the \(\cap \)-subsemilatice \(\triangle \) of \(\mathcal {L}(\mathcal {C}\mathcal {R})\) of upper ends of \(\mathbf {B}^\wedge \)-classes and their \(\mathbf {B}^\vee \)-classes. The main tool is the concept of a ladder and their \(\mathbf {B}^\vee \)-classes, an indispensable part of the important Polák’s theorem providing a construction for the join of varieties of completely regular semigroups. The paper includes the tables of ladders of the upper ends of most \(\mathbf {B}^\wedge \)-classes. Canonical varieties consist of two ascending countably infinite chains which generate most of the upper ends of \(\mathbf {B}^\wedge \)-classes.

     

Radon levels in underground workplaces – results of a nationwide survey in Italy

In Italy an extensive survey has been carried out with the aim to evaluate annual average radon concentration in underground workplaces.The survey covered 933 underground rooms located in 311 bank workplaces spread throughout in all Italian regions; at this scope the sampling was stratified random in order to be representative on national scale. The annual radon concentration was estimated by using passive radon dosemeters (NRPB/SSI type holder and CR-39 as detector): the devices were exposed for a period of about 3 months and 4 cycles were performed to cover a solar year. The radon levels in underground workplaces ranged from 27 to 4851 Bq/m³ with an overall mean value of 153 Bq/m³. As expected, radon distribution is not uniform throughout Italy: in several regions high radon annual averages have been found, confirming previous surveys.The analysis of data shows a high variability among regions and intra-region but low spread among rooms belonging to the same workplace.About 5% of underground workplaces displayed radon concentration exceeding 400 Bq/m³, and the 4.4% exceeds 500 Bq/m³, the national action level for the exposure to natural radioactivity in workplaces.     

Chebyshev model arithmetic for factorable functions

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.     

Polarization behavior of polystyrene particles under direct current and low‐frequency (<1 kHz) electric fields in dielectrophoretic systems

The relative polarization behavior of micron and submicron polystyrene particles was investigated under direct current and very low frequency (<1 kHz) alternating current electric fields. Relative polarization of particles with respect to the suspending medium is expressed in terms of the Clausius–Mossotti factor, a parameter of crucial importance in dielectrophoretic‐based operations. Particle relative polarization was studied by employing insulator‐based dielectrophoretic (iDEP) devices. The effects of particle size, medium conductivity, and frequency (10–1000 Hz) of the applied electric potential on particle response were assessed through experiments and mathematical modeling with COMSOL Multiphysics^®. Particles of different sizes (100–1000 nm diameters) were introduced into iDEP devices fabricated from polydimethylsiloxane (PDMS) and their dielectrophoretic responses under direct and alternating current electric fields were recorded and analyzed in the form of images and videos. The results illustrated that particle polarizability and dielectrophoretic response depend greatly on particle size and the frequency of the electric field. Small particles tend to exhibit positive DEP at higher frequencies (200–1000 Hz), while large particles exhibit negative DEP at lower frequencies (20–200 Hz). These differences in relative polarization can be used for the design of iDEP‐based separations and analysis of particle mixtures.