STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Comparison of Two Rotary Systems in Root Canal Preparation Regarding Disinfection

Introduction: The aim of the present study was to determine the disinfection of preparations carried out by using the Protaper or MTwo system in canals infected with Enterococcus faecalis. Methods: Twenty-eight distobuccal canals of upper molars were used, in which the canals were sterilized after being enlarged to #20 file and then contaminated with an inoculation of a culture of E. faecalis. After the incubation period, bacterial samples were collected and were seeded on plates for analysis of colony-forming units (CFU)/mL. The teeth were divided into 2 groups according to the rotary system used for instrumentation; 2 noninstrumented teeth served as the control group. Then bacterial samples were collected and were seeded on plates for analysis of CFU/mL again. The data obtained were evaluated by the Wilcoxon and Mann-Whitney U tests. Results: Bacterial reduction was 81.94% and 84.29%, respectively, in Pro Taper and Mtwo systems, and there was no statistically significant difference (P > .05). Conclusions: Both systems, Pro Taper and Mtwo, reduced the amount of bacteria in the mechanical disinfection of the root canal system, demonstrating that they are suitable for this purpose. (J Endod 2010;36:1238-1240)

Two-dimensional electron states bound to an off-plane donor in a magnetic field

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Two-dimensional QSAR studies on arylpiperazines as high-affinity 5-HT(1A) receptor ligands

5-HT(1A) receptor plays an important role in the delayed onset of antidepressant action of a class of selective serotonin reuptake inhibitors. Moreover, 5-HT(1A) receptor levels have been shown to be altered in patients suffering from major depression. In this work, hologram quantitative structure-activity relationship (HQSAR) studies were performed on a series of arylpiperazine compounds presenting affinity to the 5-HT(1A) receptor. The models were constructed with a training set of 70 compounds. The most significant HQSAR model (q(2) = 0.81, r(2) = 0.96) was generated using atoms, bonds, connections, chirality, and donor and acceptor as fragment distinction, with fragment size of 6-9. Predictions for an external test set containing 20 compounds are in good agreement with experimental results showing the robustness of the model. Additionally, useful information can be obtained from the 2D contribution maps.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

Automated two-dimensional separation flow system with electrochemical preconcentration, stripping, capillary electrophoresis and contactless conductivity detection for trace metal ion analysis

This paper describes the automation of a fully electrochemical system for preconcentration, cleanup, separation and detection, comprising the hyphenation of a thin layer electrochemical flow cell with CE coupled with contactless conductivity detection (CE-C(4)D). Traces of heavy metal ions were extracted from the pulsed-flowing sample and accumulated on a glassy carbon working electrode by electroreduction for some minutes. Anodic stripping of the accumulated metals was synchronized with hydrodynamic injection into the capillary. The effect of the angle of the slant polished tip of the CE capillary and its orientation against the working electrode in the electrochemical preconcentration (EPC) flow cell and of the accumulation time were studied, aiming at maximum CE-C(4)D signal enhancement. After 6 min of EPC, enhancement factors close to 50 times were obtained for thallium, lead, cadmium and copper ions, and about 16 for zinc ions. Limits of detection below 25 nmol/L were estimated for all target analytes but zinc. A second separation dimension was added to the CE separation capabilities by staircase scanning of the potentiostatic deposition and/or stripping potentials of metal ions, as implemented with the EPC-CE-C(4)D flow system. A matrix exchange between the deposition and stripping steps, highly valuable for sample cleanup, can be straightforwardly programmed with the multi-pumping flow management system. The automated simultaneous determination of the traces of five accumulable heavy metals together with four non-accumulated alkaline and alkaline earth metals in a single run was demonstrated, to highlight the potentiality of the system.

Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.