Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases

A Linear Programming Approach for Molecular QSAR analysis

Small molecules in chemistry can be represented as graphs. In a quantitative structure-activity relationship (QSAR) analysis, the central task is to find a regression function that predicts the activity of the molecule in high accuracy. Setting a QSAR as a primal target, we propose a new linear programming approach to the graph-based regression problem. Our method extends the graph classification algorithm by Kudo et al. (NIPS 2004), which is a combination of boosting and graph mining. Instead of sequential multiplicative updates, we employ the linear programming boosting (LP) for regression. The LP approach allows to include inequality constraints for the parameter vector, which turns out to be particularly useful in QSAR tasks where activity values are sometimes unavailable. Furthermore, the efficiency is improved significantly by employing multiple pricing

Rotationally-Driven Fragmentation for the Formation of the Binary Protostellar System L1551 IRS 5

Either bulk rotation or local turbulence is widely invoked to drive fragmentation in collapsing cores so as to produce multiple star systems. Even when the two mechanisms predict different manners in which the stellar spins and orbits are aligned, subsequent internal or external interactions can drive multiple systems towards or away from alignment thus masking their formation process. Here, we demonstrate that the geometrical and dynamical relationship between the binary system and its surrounding bulk envelope provide the crucial distinction between fragmentation models. We find that the circumstellar disks of the binary protostellar system L1551 IRS 5 are closely parallel not just with each other but also with their surrounding flattened envelope. Measurements of the relative proper motion of the binary components spanning nearly 30 yr indicate an orbital motion in the same sense as the envelope rotation. Eliminating orbital solutions whereby the circumstellar disks would be tidally truncated to sizes smaller than are observed, the remaining solutions favor a circular or low-eccentricity orbit tilted by up to $\sim$25$^\circ$ from the circumstellar disks. Turbulence-driven fragmentation can generate local angular momentum to produce a coplanar binary system, but which bears no particular relationship with its surrounding envelope. Instead, the observed properties conform with predictions for rotationally-driven fragmentation. If the fragments were produced at different heights or on opposite sides of the midplane in the flattened central region of a rotating core, the resulting protostars would then exhibit circumstellar disks parallel with the surrounding envelope but tilted from the orbital plane as is observed.Comment: Accepted for publication in Ap

Spiral Arms, Infall, and Misalignment of the Circumbinary Disk from the Circumstellar Disks in the Protostellar Binary System L1551 NE

postprin

VIRGO sensitivity to binary coalescences and the Population III black hole binaries

We analyze the properties of VIRGO detector with the aim of studying its ability to search for coalescing black hole binaries. We focus on the remnants of the Population III stars, which currently should be massive black holes ($\sim 100-1000 M_\odot$), some of them bound in binary systems. The coalescence of such binaries due to emission of gravitational waves may be currently observable. We use a binary population synthesis to model the evolution of Population III binaries. We calculate the signal to noise ratios of gravitational waves emitted by the system in each of the coalescence phase: inspiral, merger and ringdown, and provide simple formulae for the signal to noise ratio as a function of masses of the binaries. We estimate the detection rates for the VIRGO interferometer and also compare them with the estimates for the current LIGO. We show that these expected rates are similar to, or larger than the expected rates from coalescences of Population I and II compact object binaries.Comment: sumbitted to A&