Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

From the UV to the static-field limit: rates and scaling laws of intense-field ionization of helium

We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The data are obtained from full-dimensionality integrations of the helium-laser time-dependent Schrödinger equation. Comparison is made with our previously obtained data at 390 nm and 780 nm. We show that scaling laws introduced by Parker et al extend unmodified from the near-infrared limit into the UV limit. Static-field ionization rates of helium are also obtained, again from time-dependent full-dimensionality integrations of the helium Schrödinger equation. We compare the static-field ionization results with those of Scrinzi et al and Themelis et al, who also treat the full-dimensional helium atom, but with time-independent methods. Good agreement is obtained.

An Investigation into the Dissolution Properties of Celecoxib Melt Extrudates: Understanding the Role of Polymer Type and Concentration in Stabilizing Supersaturated Drug Concentrations

In this study, the dissolution properties of celecoxib (CX) solid dispersions manufactured from Eudragit 4155F and polyvinylpyrrolidone (PVP) were evaluated. Hot-melt extrusion (HME) technology was used to prepare amorphous solid dispersions of drug/polymer binary systems at different mass ratios. The drug concentrations achieved from the dissolution of PVP and Eudragit 4155F solid dispersions in phosphate buffer, pH 7.4 (PBS 7.4) were significantly greater than the equilibrium solubility of CX (1.58 µg/mL). The degree of supersaturation increased significantly as the polymer concentration within the solid dispersion increased. The maximum drug concentration achieved by PVP solid dispersions did not significantly exceed the apparent solubility of amorphous CX. The predominant mechanism for achieving supersaturated CX concentrations in PBS 7.4 was attributed to stabilization of amorphous CX during dissolution. Conversely, Eudragit 4155F solid dispersions showed significantly greater supersaturated drug solutions particularly at high polymer concentrations. For example, at a drug/polymer ratio of 1:9, a concentration of 100 µg/mL was achieved after 60 min that was stable (no evidence of drug recrystallization) for up to 72 h. This clearly identifies the potential of Eudragit 4155F to act as a solubilizing agent for CX. These findings were in good agreement with the results from solubility performed using PBS 7.4 in which Eudragit 4155F had been predissolved. In these tests, Eudragit 4155F significantly increased the equilibrium solubility of CX. Solution 1H NMR spectra were used to identify drug/polymer interactions. Deshielding of CX aromatic protons (H-1a and H-1b) containing the sulfonamide group occurred as a result of dissolution of Eudragit 4155F solid dispersions, whereas deshielding of H-1a protons and shielding of H-1b protons occurred as a result of the dissolution of PVP solid dispersions. In principle, it is reasonable to suggest that the different drug/polymer interactions observed give rise to the variation in dissolution observed for the two polymer/drug systems.

Theoretical and experimental correlations of gas dissolution, diffusion, and thermodynamic properties in determination of gas permeability and selectivity in supported ionic liquid membranes

Supported ionic liquid membranes (SILMs) has the potential to be a new technological platform for gas/organic vapour separation because of the unique non-volatile nature and discriminating gas dissolution properties of room temperature ionic liquids (ILs). This work starts with an examination of gas dissolution and transport properties in bulk imidazulium cation based ionic liquids [C_nmim][NTf2] (n = 2.4, 6, 8.10) from simple gas H₂, N₂, to polar CO₂, and C₂H₆, leading to a further analysis of how gas dissolution and diffusion are influenced by molecular specific gas-SILMs interactions, reflected by differences in gas dissolution enthalpy and entropy. These effects were elucidated again during gas permeation studies by examining how changes in these properties and molecular specific interactions work together to cause deviations from conventional solution–diffusion theory and their impact on some remarkably contrasting gas perm-selectivity performance. The experimental perm-selectivity for all tested gases showed varied and contrasting deviation from the solution–diffusion, depending on specific gas-IL combinations. It transpires permeation for simpler non-polar gases (H₂, N₂) is diffusion controlled, but strong molecular specific gas-ILs interactions led to a different permeation and selectivity performance for C₂H₆ and CO₂. With exothermic dissolution enthalpy and large order disruptive entropy, C₂H₆ displayed the fastest permeation rate at increased gas phase pressure in spite of its smallest diffusivity among the tested gases. The C₂H₆ gas molecules “peg” on the side alkyl chain on the imidazulium cation at low concentration, and are well dispersed in the ionic liquids phase at high concentration. On the other hand strong CO₂-ILs affinity resulted in a more prolonged “residence time” for the gas molecule, typified by reversed CO₂/N₂ selectivity and slowest CO₂ transport despite CO₂ possess the highest solubility and comparable diffusivity in the ionic liquids. The unique transport and dissolution behaviour of CO₂ are further exploited by examining the residing state of CO₂ molecules in the ionic liquid phase, which leads to a hypothesis of a condensing and holding capacity of ILs towards CO₂, which provide an explanation to slower CO₂ transport through the SILMs. The pressure related exponential increase in permeations rate is also analysed which suggests a typical concentration dependent diffusion rate at high gas concentration under increased gas feed pressure. Finally the strong influence of discriminating and molecular specific gas-ILs interactions on gas perm-selectivity performance points to future specific design of ionic liquids for targeted gas separations.

THE EFFECT OF VARYING COSMIC-RAY IONIZATION RATES ON DARK CLOUD CHEMISTRY

We investigate the effects of varying the cosmic ray ionization rate in chemical models of dense interstellar clouds. In the absence of such ionization, a scenario which may be applicable to dark cloud cores, we find that chemi-ionization is able to drive a limited ion-neutral chemistry. Models of clouds in starburst galaxies, which may have enhanced cosmic ray fluxes, are also investigated and enable an upper limit to be derived for the cosmic ray ionization rate in M82. The derived value, which is about 700 times the typical value for Galactic molecular clouds, is in good agreement with that necessary to explain the recent observations of C I in this galaxy.

Order Flow and the Monetary Model of Exchange Rates: Evidence from a Novel Data Set

We propose an exchange rate model that is a hybrid of the conventional specification with monetary fundamentals and the Evans–Lyons microstructure approach. We estimate a model augmented with order flow variables, using a unique data set: almost 100 monthly observations on interdealer order flow on dollar/euro and dollar/yen. The augmented macroeconomic, or “hybrid,” model exhibits greater in-sample stability and out of sample forecasting improvement vis-à-vis the basic macroeconomic and random walk specifications.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Li II, Be III, B IV and C V

We report calculations for energy levels, radiative rates and electron impact excitation rates for transitions in He-like Li II, Be III, B IV and C V. grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Collision strengths have been averaged over a Maxwellian velocity distribution and the effective collision strengths so obtained are reported over a wide temperature range up to 10(6) K. Comparisons have been made with similar data obtained from the flexible atomic code (FAC) to highlight the importance of resonances, included in calculations from darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, particularly for weak transitions and at low energies, have also been discussed. Additionally, lifetimes are also listed for all calculated levels of the above four ions.

Energy levels, radiative rates and electron impact excitation rates for transitions in Si XII, Si XIII and Si XIV

In this paper, we report calculations of energy levels, radiative rates and electron impact excitation rates for transitions in Li-like Si XII, He-like Si XIII and H-like Si XIV. The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 24 levels of Si XII, 49 levels of Si XIII and 25 levels of Si XIV, belonging to the n≤5 configurations. Collision strengths have been averaged over a Maxwellian electron velocity distribution and the effective collision strengths so obtained are reported over a wide temperature range below 107 K. Comparisons have been made with similar data obtained from the flexible atomic code (fac) to highlight the importance of resonances, included in calculations from darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, particularly for weak transitions and at low energies, are also discussed. Additionally, lifetimes are listed for all calculated levels of the above three ions, although no measurements are available with which to compare.

Energy levels, radiative rates and electron impact excitation rates for transitions in H-like N VII, O VIII, F IX, Ne X and Na XI

We report calculations of energy levels, radiative rates and electron impact excitation rates for transitions in H-like N VII, O VIII, F IX, Ne X and Na XI. The general-purpose relativistic atomic structure package (grasp) is adopted for calculating energy levels and radiative rates, while the Dirac atomic R-matrix code (DARC) and the flexible atomic code (FAC) are used for determining the collision strengths and subsequently the excitation rates. Oscillator strengths, radiative rates and line strengths are listed for all E1, E2, M1 and M2 transitions among the lowest 25 levels of the above five ions. Collision strengths have been averaged over a Maxwellian velocity distribution, and the effective collision strengths so obtained are reported over a wide temperature range below 10(7) K. Additionally, lifetimes are also given for all the calculated energy levels of the above five ions.

Energy levels, radiative rates and electron impact excitation rates for transitions in Li-like N V, F VII, Ne VIII and Na IX

In this paper, we report calculations of energy levels, radiative rates and electron impact excitation rates for transitions in Li-like N V, F VII, Ne VIII and Na IX. The general-purpose relativistic atomic structure package (GRASP) is adopted for calculating energy levels and radiative rates, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (DARC) and the flexible atomic code (FAC) are used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 24 levels of N V, F VII, Ne VIII and Na IX. Collision strengths have been averaged over a Maxwellian velocity distribution and the effective collision strengths so obtained are reported over a wide temperature range below 10(6.6) K. Additionally, lifetimes are also reported for all calculated levels of the above four ions.