Dynamically complete markets under Brownian motion

This paper investigates how continuous-time trading renders complete a financial market in which the underlying risk process is a Brownian motion. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, has been established in the literature for single-commodity, pure-exchange economies with many heterogenous agents where the securities’ dividends as well as the agents’ utilities and endowments include flows during the trading horizon which are analytic functions. In sharp contrast, the present analysis is based upon a different mathematical argument that assumes neither analyticity nor a particular underlying economic environment. The novelty of our approach lies in deriving closed-form expressions for the dispersion coefficients of the securities’ prices. To this end, we assume only that the pricing kernels and dividends satisfy standard growth and smoothness restrictions (mild enough to allow even for options). In this sense, our sufficiency conditions apply irrespectively of preferences, endowments or other structural elements (for instance, whether or not the budget constraints include only pure exchange).

Sources and Sinks of BVOCs in a Managed Boreal Forest

<p>The ecosystem-atmosphere flux of biogenic volatile organic compounds (BVOCs) has important impacts on tropospheric oxidative capacity and the formation of secondary organic aerosols, influencing air quality and climate. In particular, this is true in managed boreal forests in the Northern Hemisphere, where BVOC emissions often dominate over anthropogenic sources of VOC.</p><p>Here we present measurements of BVOCs in a managed boreal forest located at the ICOS station Norunda in Sweden, collected using proton transfer reaction mass spectrometry (PTR-MS). This managed forest consists of a mix of Scots pine (<em>Pinus sylvestris</em>) and Norway spruce (<em>Picea abies</em>). These long-term PTR-MS measurements were collected at six heights (4m, 8.5m, 13.5m, 19m, 24.5m, and 33.5m) in the forest canopy over several periods during 2014 to 2016. Ozone concentrations were simultaneously measured in conjunction with these PTR-MS measurements. The main BVOCs investigated with the PTR-MS were isoprene, monoterpenes, methanol, acetaldehyde, and acetone. The distribution of BVOC sources and sinks in the forest canopy was explored using several Lagrangian dispersion matrix methods, including localized and continuous near-field theory. The canopy resistance and deposition velocities for ozone and the BVOCs were investigated, and the results for isoprene and monoterpene emissions were found to agree well with several standard BVOC emission algorithms. These results will have importance for constraining BVOC emission estimates from managed boreal forests in the future.</p>

Curcumin micelles entrapped in eudragit S-100 matrix: a synergistic strategy for enhanced oral delivery

Background: Therapeutic activities of curcumin (CUR) via oral administration are hampered by the lack of bioavailability due to its poor water solubility and rapid degradation in GI tract. Materials & methods: This preliminary study developed CUR micelle-eudragit S100 (EUD) dry powder (CM-EDP) spray-dried formulations. Poloxamer 407 was used as a micelle-forming agent and EUD as an entrapping matrix for protection over hydrolysis and enzymes in the GI tract. Results: The morphology of CM-EDP showed agglomeration with cratering on the surface of particles. Differential thermal analysis and x-ray diffractometry data exhibited evidence that CUR was converted into amorphous solid. An increased concentration of micelle-forming and dispersion matrix polymers resulted in a high fraction of drug being converted into the amorphous state. A significant increase in dissolution by 7–10 times was achieved compared with that of raw CUR. Conclusion: The present study disclosed the CM-EDP potency for future development of CUR oral formulation.

Adaptive estimation of UVs navigation parameters by irregular inertial-satellite measurements

PurposeThere are shortcomings of modern methods of ensuring the stability of Kalman filtration in unmanned vehicles’ (UVs) navigation systems under the condition of a priori uncertainty of the dispersion matrix of measurement interference. First, it is the absence of strict criteria for the selection of adaptation coefficients in the calculation of the a posteriori covariance matrix. Secondly, it is the impossibility of adaptive estimation in real time from the condition of minimum covariance of the updating sequence due to the necessity of its preliminary calculation.Design/methodology/approachThis paper considers a new approach to the construction of the Kalman filter adaptation algorithm. The algorithm implements the possibility of obtaining an accurate adaptive estimation of navigation parameters for integrated UVs inertial-satellite navigation systems, using the correction of non-periodic and unstable inertial estimates by high-precision satellite measurements. The problem of adaptive estimation of the noise dispersion matrix of the meter in the Kalman filter can be solved analytically using matrix methods of linear algebra. A numerical example illustrates the effectiveness of the procedure for estimating the state vector of the UVs’ navigation systems.FindingsAdaptive estimation errors are sharply reduced in comparison with the traditional scheme to the range from 2 to 7 m in latitude and from 1.5 to 4 m in longitude.Originality/valueThe simplicity and accuracy of the proposed algorithm provide the possibility of its effective application to the widest class of UVs’ navigation systems.

Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure

We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude. We scale up the diffusion–polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.

Kinematic modelling of clusters with Gaia: the death throes of the Hyades

ABSTRACT The precision of the Gaia data offers a unique opportunity to study the internal velocity field of star clusters. We develop and validate a forward-modelling method for the internal motions of stars in a cluster. The model allows an anisotropic velocity dispersion matrix and linear velocity gradient describing rotation and shear, combines radial velocities available for a subset of stars, and accounts for contamination from background sources via a mixture model. We apply the method to Gaia DR2 data of the Hyades cluster and its tidal tails, dividing and comparing the kinematics of stars within and beyond 10 pc, which is roughly the tidal radius of the cluster. While the velocity dispersion for the cluster is nearly isotropic, the velocity ellipsoid for the tails is clearly elongated with the major axis pointing towards the Galactic centre. We find positive and negative expansions at ≈2σ significance in Galactic azimuthal and vertical directions for the cluster but no rotation. The tidal tails are stretching in a direction tilted from the Galactic centre while equally contracting as the cluster in Galactic vertical direction. The tails have a shear (A) of 16.90 ± 0.92 $\mathrm{m}\, \mathrm{s}^{-1}\, \mathrm{pc}^{-1}$ and a vorticity (B) of −6.48 ± 1.15 $\mathrm{m}\, \mathrm{s}^{-1}\, \mathrm{pc}^{-1}$, values distinct from the local Oort constants. By solving the Jeans equations for flattened models of the Hyades, we show that the observed velocity dispersions are a factor of ≈2 greater than required for virial equilibrium due to tidal heating and disruption. From simple models of the mass loss, we estimate that the Hyades is close to final dissolution with only a further ≲30 Myr left.

Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data

In this contribution the fitting of a straight line to 3D point data is considered, with Cartesian coordinates xi, yi, zi as observations subject to random errors. A direct solution for the case of equally weighted and uncorrelated coordinate components was already presented almost forty years ago. For more general weighting cases, iterative algorithms, e.g., by means of an iteratively linearized Gauss–Helmert (GH) model, have been proposed in the literature. In this investigation, a new direct solution for the case of pointwise weights is derived. In the terminology of total least squares (TLS), this solution is a direct weighted total least squares (WTLS) approach. For the most general weighting case, considering a full dispersion matrix of the observations that can even be singular to some extent, a new iterative solution based on the ordinary iteration method is developed. The latter is a new iterative WTLS algorithm, since no linearization of the problem by Taylor series is performed at any step. Using a numerical example it is demonstrated how the newly developed WTLS approaches can be applied for 3D straight line fitting considering different weighting cases. The solutions are compared with results from the literature and with those obtained from an iteratively linearized GH model.