Mapping the Outer Edge of the Young Stellar Cluster in the Galactic Center

We present new near-infrared spectroscopic observations of the outer edges of the young stellar cluster around the supermassive black hole at the Galactic center. The observations show a break in the surface-density profile of young stars at approximately 13 arcsec (0.52 pc). These observations spectroscopically confirm previous suggestions of a break based on photometry. Using Gemini North's Near-Infrared Integral Field Spectrometer (NIFS) we are able to detect and separate early- and late-type stars with a 75% completeness at Ks = 15.5. We sample a region with radii between 7" to 23" (0.28 pc to 0.92 pc) from Sgr A*, and present new spectral classifications of 144 stars brighter than Ks = 15.5, where 140 stars are late-type (> 1 Gyr) and only four stars are early-type (young, 4-6 Myr). A broken power-law fit of the early-type surface-density matches well with our data and previously published values. The projected surface-density of late-type stars is also measured and found to be consistent with previous results. We find that the observed early-type surface-density profile is inconsistent with the theory of the young stars originating from a tightly bound infalling cluster, as no significant trail of young stars is found at radii above 13". We also note that either a simple disk instability criterion or a cloud-cloud collision could explain the location of the outer edge, though we lack information to make conclusive remarks on either alternative. If this break in surface-density represents an edge to the young stellar cluster it would set an important scale for the most recent episode of star formation at the Galactic center.Comment: 17 pages, 11 figures, 3 tables, ApJ accepte

12CO emission from EP Aqr: Another example of an axi-symmetric AGB wind?

The CO(1-0) and (2-1) emission of the circumstellar envelope of the AGB star EP Aqr has been observed using the IRAM PdBI and the IRAM 30-m telescope. The line profiles reveal the presence of two distinct components centered on the star velocity, a broad component extending up to ~10 km/s and a narrow component indicating an expansion velocity of ~2 km/s. An early analysis of these data was performed under the assumption of isotropic winds. The present study revisits this interpretation by assuming instead a bipolar outflow nearly aligned with the line of sight. A satisfactory description of the observed flux densities is obtained with a radial expansion velocity increasing from ~2 km/s at the equator to ~10 km/s near the poles. The angular aperture of the bipolar outflow is ~45 deg with respect to the star axis, which makes an angle of ~13 deg with the line of sight. A detailed study of the CO(1-0) to CO(2-1) flux ratio reveals a significant dependence of the temperature on the star latitude, smaller and steeper at the poles than at the equator at large distances from the star. Under the hypothesis of radial expansion and of rotation invariance about the star axis, the effective density has been evaluated in space as a function of star coordinates. Evidence is found for an enhancement of the effective density in the northern hemisphere of the star at angular distances in excess of ~3" and covering the whole longitudinal range. The peak velocity of the narrow component is observed to vary slightly with position on the sky, a variation consistent with the model and understood as the effect of the inclination of the star axis with respect to the line of sight. While the phenomenological model presented here reproduces well the general features of the observations, significant differences are also revealed, which would require a better spatial resolution to be properly described.Comment: accepted for publication in Astronomy & Astrophysic

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

New convolutions associated with the Mellin transform and their applications in integral equations

In this paper, we introduce two new convolutions associated with the Mellin transform which exhibit factorization properties upon the use of certain weight functions. This is applied to the solvability analysis of classes of integral equations. In particular, we present sufficient conditions for the solvability of an integral equation and a system of integral equations of convolution type.publishe

New convolutions weighted by Hermite functions and their applications

We introduce eight new convolutions weighted by multi-dimensional Hermite functions, prove two Young-type inequalities, and exhibit their applications in different subjects. One application consists in the study of the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are here obtained.publishe

New convolutions for an oscillatory integral operator on the half-line

The main purpose of this work is to present three new convolutions for oscillatory integral operators defined on the positive half-line and in the framework of L1 Lebesgue spaces. Therefore, such new functions introduced by the new convolutions will have factorization properties when considering the oscillatory integral operators under consideration. Moreover, some fundamental and operational properties of the mentioned integral operator are also studied in the first part of the paper.publishe

On integral operators and equations generated by cosine and sine Fourier transforms

In this paper, we study some properties of a class of integral operators that depends on the cosine and sine Fourier transforms. In particular, we will exhibit properties related with their invertibility, the spectrum, Parseval type identities and involutions. Moreover, a new convolution will be proposed and consequent integral equations will be also studied in detail. Namely, we will characterize the solvability of two integral equations which are associated with the integral operator under study. Moreover, under appropriate conditions, the unique solutions of those two equations are also obtained in a constructive way.publishe

Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case

By means of Riemann boundary value problems and of certain convenient systems of linear algebraic equations, this paper deals with the solvability of a class of singular integral equations with rotations and degenerate kernel within the case of a coefficient vanishing on the unit circle. All the possibilities about the index of the coefficients in the corresponding equations are considered and described in detail, and explicit formulas for their solutions are obtained. An example of application of the method is shown at the end of the last section