Effect of fluid forces on rotor stability of centrifugal compressors and pumps

A simple two dimensional model for calculating the rotordynamic effects of the impeller force in centrifugal compressors and pumps is presented. It is based on potential flow theory with singularities. Equivalent stiffness and damping coefficients are calculated for a machine with a vaneless volute formed as a logarithmic spiral. It is shown that for certain operating conditions, the impeller force has a destablizing effect on the rotor

On the growth of the Betti sequence of the canonical module

We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.Comment: 12 pages. version 2: includes omitted author contact informatio

Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(\Omega) where the self-adjointness is defined relative to L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when \Omega=I\times\Omega_2 and I is an open interval. We then apply the results to the case when \Omega is a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that {e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.B

Redshift-distance Survey of Early-type Galaxies: The D_n-sigma Relation

In this paper R-band photometric and velocity dispersion measurements for a sample of 452 elliptical and S0 galaxies in 28 clusters are used to construct a template D_n-sigma relation. This template relation is constructed by combining the data from the 28 clusters, under the assumption that galaxies in different clusters have similar properties. The photometric and spectroscopic data used consist of new as well as published measurements, converted to a common system, as presented in a accompanying paper. The resulting direct relation, corrected for incompleteness bias, is log{D_n} =1.203 log{sigma} + 1.406; the zero-point has been defined by requiring distant clusters to be at rest relative to the CMB. This zero-point is consistent with the value obtained by using the distance to Virgo as determined by the Cepheid period-luminosity relation. This new D_n-sigma relation leads to a peculiar velocity of -72 (\pm 189) km/s for the Coma cluster. The scatter in the distance relation corresponds to a distance error of about 20%, comparable to the values obtained for the Fundamental Plane relation. Correlations between the scatter and residuals of the D_n-sigma relation with other parameters that characterize the cluster and/or the galaxy stellar population are also analyzed. The direct and inverse relations presented here have been used in recent studies of the peculiar velocity field mapped by the ENEAR all-sky sample.Comment: 46 pages, 20 figures, and 7 tables. To appear in AJ, vol. 123, no. 5, May 200

Spectral reciprocity and matrix representations of unbounded operators

Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian. These operators are discrete analogues of the classical conformal Laplacians and Hamiltonians from statistical mechanics. For an infinite discrete set $X$, we consider operators acting on Hilbert spaces of functions on $X$, and their representations as infinite matrices; the focus is on $\ell^2(X)$, and the energy space $\mathcal{H}_{\mathcal E}$. In particular, we prove that these operators are always essentially self-adjoint on $\ell^2(X)$, but may fail to be essentially self-adjoint on $\mathcal{H}_{\mathcal E}$. In the general case, we examine the von Neumann deficiency indices of these operators and explore their relevance in mathematical physics. Finally we study the spectra of the $\mathcal{H}_{\mathcal E}$ operators with the use of a new approximation scheme.Comment: 20 pages, 1 figure. To appear: Journal of Functional Analysi