A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

Mechatronic design of a fast and long range 4 degrees of freedom humanoid neck

This paper describes the mechatronic design of a humanoid neck. To research human machine interaction, the head and neck combination should be able to approach the human behavior as much as possible. We present a novel humanoid neck concept that is both fast, and has a long range of motion in 4 degrees of freedom (DOFs). This enables the head to track fast objects, and the neck design is suitable for mimicking expressions. The humanoid neck features a differential drive design for the lower 2 DOFs resulting in a low moving mass and the ability to use strong actuators. The performance of the neck has been\ud optimized by minimizing backlash in the mechanisms, and by using gravity compensation. Two cameras in the head are used for scanning and interaction with the environment

Study of Magnetic Excitation in Singlet-Ground-State Magnets CsFeCl3_3 and RbFeCl3_3 by Nuclear Magnetic Relaxation

The temperature dependences of spin-lattice relaxation time $T_1$ of $^{133}$Cs in CsFeCl$_3$ and $^{87}$Rb in RbFeCl$_3$ were measured in the temperature range between 1.5 K and 22 K, at various fields up to 7 T applied parallel (or perpendicular) to the c-axis, and the analysis was made on the basis of the DCEFA. The mechanism of the nuclear magnetic relaxation is interpreted in terms of the magnetic fluctuations which are characterized by the singlet ground state system. In the field region where the phase transition occurs, $T_1^{-1}$ exhibited the tendency of divergence near $T_{\rm N}$, and this feature was ascribed to the transverse spin fluctuation associated with the mode softening at the $K$-point. It was found that the damping constant of the soft mode is remarkably affected by the occurrence of the magnetic ordering at lower temperature, and increases largely in the field region where the phase transition occurs.Comment: 12 pages, 18 figures, submitted to J. Phys. Soc. Jp

Lattice Diagram Polynomials and Extended Pieri Rules

The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\mu$ is a partition of $n+1$, we denote by $\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the (French) Ferrers diagram of $\mu$. We set $\Delta_{\mu/ij}=\det \| x_i^{p_j}y_i^{q_j} \|_{i,j=1}^n$, where $(p_1,q_1),... ,(p_n,q_n)$ are the cells of $\mu/ij$, and let ${\bf M}_{\mu/ij}$ be the linear span of the partial derivatives of $\Delta_{\mu/ij}$. The bihomogeneity of $\Delta_{\mu/ij}$ and its alternating nature under the diagonal action of $S_n$ gives ${\bf M}_{\mu/ij}$ the structure of a bigraded $S_n$-module. We conjecture that ${\bf M}_{\mu/ij}$ is always a direct sum of $k$ left regular representations of $S_n$, where $k$ is the number of cells that are weakly north and east of $(i,j)$ in $\mu$. We also make a number of conjectures describing the precise nature of the bivariate Frobenius characteristic of ${\bf M}_{\mu/ij}$ in terms of the theory of Macdonald polynomials. On the validity of these conjectures, we derive a number of surprising identities. In particular, we obtain a representation theoretical interpretation of the coefficients appearing in some Macdonald Pieri Rules.Comment: 77 pages, Te

A 3D radiative transfer framework: VII. Arbitrary velocity fields in the Eulerian frame

A solution of the radiative-transfer problem in 3D with arbitrary velocity fields in the Eulerian frame is presented. The method is implemented in our 3D radiative transfer framework and used in the PHOENIX/3D code. It is tested by comparison to our well- tested 1D co-moving frame radiative transfer code, where the treatment of a monotonic velocity field is implemented in the Lagrangian frame. The Eulerian formulation does not need much additional memory and is useable on state-of-the-art computers, even large-scale applications with 1000's of wavelength points are feasible

The Rise Times of High and Low Redshift Type Ia Supernovae are Consistent

We present a self-consistent comparison of the rise times for low- and high-redshift Type Ia supernovae. Following previous studies, the early light curve is modeled using a t-squared law, which is then mated with a modified Leibundgut template light curve. The best-fit t-squared law is determined for ensemble samples of low- and high-redshift supernovae by fitting simultaneously for all light curve parameters for all supernovae in each sample. Our method fully accounts for the non-negligible covariance amongst the light curve fitting parameters, which previous analyses have neglected. Contrary to Riess et al. (1999), we find fair to good agreement between the rise times of the low- and high-redshift Type Ia supernovae. The uncertainty in the rise time of the high-redshift Type Ia supernovae is presently quite large (roughly +/- 1.2 days statistical), making any search for evidence of evolution based on a comparison of rise times premature. Furthermore, systematic effects on rise time determinations from the high-redshift observations, due to the form of the late-time light curve and the manner in which the light curves of these supernovae were sampled, can bias the high-redshift rise time determinations by up to +3.6/-1.9 days under extreme situations. The peak brightnesses - used for cosmology - do not suffer any significant bias, nor any significant increase in uncertainty.Comment: 18 pages, 4 figures, Accepted for publication in the Astronomical Journal. Also available at http://www.lbl.gov/~nugent/papers.html Typos were corrected and a few sentences were added for improved clarit