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

Spherical orbit closures in simple projective spaces and their normalizations

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, added references. v3: major changes due to a mistake in previous version

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

Bayesian model-independent evaluation of expansion rates of the universe

Marginal likelihoods for the cosmic expansion rates are evaluated using the `Constitution' data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an accelerated expansion, we obtain a marginal likelihood for the deceleration parameter $q_0$ peaked around zero in the spatially flat case. It is also found that the new data significantly constrains the cosmographic expansion rates, when compared to the previous analyses. These results may strongly depend on the Gaussian prior probability distribution chosen for the Hubble parameter represented by $h$, with $h=0.68\pm 0.06$. This and similar priors for other expansion rates were deduced from previous data. Here again we perform the Bayesian model-independent analysis in which the scale factor is expanded into a Taylor series in time about the present epoch. Unlike such Taylor expansions in terms of redshift, this approach has no convergence problem.Comment: To appear in Astrophysics and Space Scienc

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

Research study of some RAM antennas Final report, 18 Nov. 1964 - 18 Jun. 1965

Input impedance and radiation pattern determinations for cylindrical gap, waveguide excited and circular waveguide slot antenna array