Aeroelastic stability of coupled flap-lag motion of hingeless helicopter blades at arbitrary advance ratios

Equations for large amplitude coupled flap-lag motion of a hingeless elastic helicopter blade in forward flight are derived. Only a torsionally rigid blade excited by quasi-steady aerodynamic loads is considered. The effects of reversed flow together with some new terms due to radial flow are included. Using Galerkin's method the spatial dependence is eliminated and the equations are linearized about a suitable equilibrium position. The resulting system of homogeneous periodic equations is solved using multivariable Floquet-Liapunov theory, and the transition matrix at the end of the period is evaluated by two separate methods. Computational efficiency of the two numerical methods is compared. Results illustrating the effects of forward flight and various important blade parameters on the stability boundaries are presented

On a generalization of Lie(kk): a CataLAnKe theorem

We define a generalization of the free Lie algebra based on an $n$-ary commutator and call it the free LAnKe. We show that the action of the symmetric group $S_{2n-1}$ on the multilinear component with $2n-1$ generators is given by the representation $S^{2^{n-1}1}$, whose dimension is the $n$th Catalan number. An application involving Specht modules of staircase shape is presented. We also introduce a conjecture that extends the relation between the Whitehouse representation and Lie($k$).Comment: 14 page

Walking With God: Realism, Fanaticism, and the Future of Jewish Law

Since the mid-twentieth century, converging factors have enabled haredi (“ultra-orthodox”) Jews to exert considerable influence on more moderate forms of observant Judaism. In the area of Jewish law, this has led to a shift from rabbinic realism, characterized by contextual and lenient rulings, to fanaticism, which views stringency as the only authentic mode of Jewish legal interpretation. This paper examines two historically moderate communities particularly affected by haredization: modern Orthodoxy in America and Sephardic Judaism in Israel. From these case studies, it will become clear that without significant efforts to revive and promote a middle-of-the-road approach, observant Judaism will continue to be dominated by fundamentalist views

Review of Bug Music: How Insects Gave Us Rhythm and Noise

Review of Bug Music: How Insects Gave Us Rhythm and Noise, by David Rothenberg. This book proposes that the human sense of rhythm derived in part from insect sounds

A new presentation for Specht modules with distinct parts

We obtain a new presentation for Specht modules whose conjugate shapes have strictly decreasing parts by introducing a linear operator on the space generated by column tabloids. The generators of the presentation are column tabloids and the relations form a proper subset of the Garnir relations of Fulton. The results in this paper extend earlier results of the authors and Stanley on Specht modules of staircase shape.Comment: 14 pages. This article generalizes Theorem 2.4 of arXiv:1710.00376. V2:small changes and correction

Isoform-specific subcellular localization and function of protein kinase A identified by mosaic imaging of mouse brain.

Protein kinase A (PKA) plays critical roles in neuronal function that are mediated by different regulatory (R) subunits. Deficiency in either the RIβ or the RIIβ subunit results in distinct neuronal phenotypes. Although RIβ contributes to synaptic plasticity, it is the least studied isoform. Using isoform-specific antibodies, we generated high-resolution large-scale immunohistochemical mosaic images of mouse brain that provided global views of several brain regions, including the hippocampus and cerebellum. The isoforms concentrate in discrete brain regions, and we were able to zoom-in to show distinct patterns of subcellular localization. RIβ is enriched in dendrites and co-localizes with MAP2, whereas RIIβ is concentrated in axons. Using correlated light and electron microscopy, we confirmed the mitochondrial and nuclear localization of RIβ in cultured neurons. To show the functional significance of nuclear localization, we demonstrated that downregulation of RIβ, but not of RIIβ, decreased CREB phosphorylation. Our study reveals how PKA isoform specificity is defined by precise localization

Explaining the Electroweak Scale and Stabilizing Moduli in M Theory

In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification. This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions. One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass. We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.Comment: 73 pages, 39 figures, Minor typos corrected, Figures and References adde

Action of the Symmetric Group on the Free LAnKe: A CataLAnKe Theorem

We initiate a study of the representation of the symmetric group on the multilinear component of an n-ary generalization of the free Lie algebra, which we call a free LAnKe. Our central result is that the representation of the symmetric group S2n−1 on the multilinear component of the free LAnKe with S2n−1 generators is given by an irreducible representation whose dimension is the nth Catalan number. This leads to a more general result on eigenspaces of a certain linear operator. A decomposition, into irreducibles, of the representation of S3n−2 on the multilinear component the free LAnKe with 3n − 2 generators is also presented. We also obtain a new presentation of Specht modules of shape λ, where λ has strictly decreasing column lengths, as a consequence of our eigenspace result

Non-minimal couplings in two dimensional gravity: a quantum investigation

We investigate the quantum effects of the non-minimal matter-gravity couplings derived by Cangemi and Jackiw in the realm of a specific fermionic theory, namely the abelian Thirring model on a Riemann surface of genus zero and one. The structure and the strength of the new interactions are seen to be highly constrained, when the topology of the underlying manifold is taken into account. As a matter of fact, by requiring to have a well-defined action, we are led both to quantization rules for the coupling constants and to selection rules for the correlation functions. Explicit quantum computations are carried out in genus one (torus). In particular the two-point function and the chiral condensate are carefully derived for this case. Finally the effective gravitational action, coming from integrating out the fermionic degrees of freedoom, is presented. It is different from the standard Liouville one: a new non-local functional of the conformal factor arises and the central charge is improved, depending also on the Thirring coupling constant. This last feature opens the possibility of giving a new explicit representation of the minimal series in terms of a fermionic interacting model.Comment: Latex, 41 Page