On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua

Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density of the sum of two gamma random variables is derived. Then a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed. An explicit expression for the error bound is obtained. The proposed technique is shown to be computationally efficient, i.e. only polynomial in growth in the number of terms compared to the exponential growth of most other methods. It provides a vast improvement in accuracy and shows only logarithmic growth in the required precision. In addition, it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms. As an application, the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with N scalar fields is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio

Nonlinear dynamics of the interface of dielectric liquids in a strong electric field: Reduced equations of motion

The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly dependent functions, is possible if the ratio of the permittivities of liquids is inversely proportional to the ratio of their densities. The corresponding reduced equations for interface motion are derived. In the limit of small density ratio, these equations coincide with the well-known equations describing the Laplacian growth.Comment: 10 page

The Economic Impact of Forming a European Company

Ever since 2004 companies located in Member States of the European Economic Area have been able to opt to incorporate in a supranational legal form, the Societas Europaea. We found that companies located in Member States where the Societas Europaea offers additional legal arbitrage opportunities benefit most. Moreover, our results show that the stock price reaction is positive when the decision to incorporate as an Societas Europaea involves moving the firm's registered office and that firms are moving to jurisdictions with significantly lower corporate tax rates. Finally, we found evidence of uncertainty at the registration date but not at the time of the shareholder meeting

Noncovalent complexation of amphotericin-B with Poly(α-glutamic acid).

A noncovalent complex of amphotericin B (AmB) and poly(α-glutamic acid) (PGA) was prepared to develop a safe and stable formulation for the treatment of leishmaniasis. The loading of AmB in the complex was in the range of ∼20-50%. AmB was in a highly aggregated state with an aggregation ratio often above 2.0. This complex (AmB-PGA) was shown to be stable and to have reduced toxicity to human red blood cells and KB cells compared to the parent compound; cell viability was not affected at an AmB concentration as high as 50 and 200 μg/mL respectively. This AmB-PGA complex retained AmB activity against intracellular Leishmania major amastigotes in the differentiated THP-1 cells with an EC50 of 0.07 ± 0.03-0.08 ± 0.01 μg/mL, which is similar to Fungizone (EC50 of 0.06 ± 0.01 μg/mL). The in vitro antileishmanial activity of the complex against Leishmania donovani was retained after storage at 37 °C for 7 days in the form of a solution (EC50 of 0.27 ± 0.03 to 0.35 ± 0.04 μg/mL) and for 30 days as a solid (EC50 of 0.41 ± 0.07 to 0.63 ± 0.25 μg/mL). These encouraging results indicate that the AmB-PGA complex has the potential for further development

Optimization of growth and extracellular glucoamylase production by Candida famata isolate

Candida famata was isolated from traditional Moroccan sourdough. It exhibited high glucoamylase and biomass production. Starch induces high glucoamylase production C. famata with maximum glucoamylase activity at 5 g/L. Glucose stimulates good production in biomass but strongly inhibitsglucoamylase production. Among the sources of nitrogen tested, yeast extract and the (NH4)2HPO4 gave maximum glucoamylase and biomass after 72 h of incubation in liquid medium at 30°C, pH 5 and 105 rpm

Pressure Driven Flow of Polymer Solutions in Nanoscale Slit Pores

Polymer solutions subject to pressure driven flow and in nanoscale slit pores are systematically investigated using the dissipative particle dynamics approach. We investigated the effect of molecular weight, polymer concentration and flow rate on the profiles across the channel of the fluid and polymer velocities, polymers density, and the three components of the polymers radius of gyration. We found that the mean streaming fluid velocity decreases as the polymer molecular weight or/and polymer concentration is increased, and that the deviation of the velocity profile from the parabolic profile is accentuated with increase in polymer molecular weight or concentration. We also found that the distribution of polymers conformation is highly anisotropic and non-uniform across the channel. The polymer density profile is also found to be non-uniform, exhibiting a local minimum in the center-plane followed by two symmetric peaks. We found a migration of the polymer chains either from or towards the walls. For relatively long chains, as compared to the thickness of the slit, a migration towards the walls is observed. However, for relatively short chains, a migration away from the walls is observed.Comment: 11 pages, 13 figure

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Mesoporous Functionalized Acid Catalysts And Their Use As Environmentally Friendly Catalysts In Esterification Of Glycerols For Monoglyceride Production.

Monoglycerides are valuable compounds with wide applications as emulsifiers in food, pharmaceutical and cosmetic industries. They can be produced by esterification of glycerols with fatty acids

Residual and Past Entropies of Concomitants from Lai And Xie Extensions of Case-II of Generalized Order Statistics and its Dual

In this article, we consider a new extensions of Morgenstern family is Lai and Xie extensions and discuss their concomitants for case-II of generalized order statistics and case-II of dual generalized order statistics. Additionally, recurrence relation between moments is found for the recommended models. We have also derived the expression for the joint distribution of concomitants for case-II of generalized order statistics and its dual. The residual and past entropies are shown last