{A Classification of Spherical Schubert Varieties in the Grassmannian}

Let $L$ be a Levi subgroup of $GL_N$ which acts by left multiplication on a Schubert variety $X(w)$ in the Grassmannian $G_{d,N}$. We say that $X(w)$ is a spherical Schubert variety if $X(w)$ is a spherical variety for the action of $L$. In earlier work we provide a combinatorial description of the decomposition of the homogeneous coordinate ring of $X(w)$ into irreducible $L$-modules for the induced action of $L$. In this work we classify those decompositions into irreducible $L$-modules that are multiplicity-free. This is then applied towards giving a complete classification of the spherical Schubert varieties in the Grassmannian

Stress analysis of 27% scale model of AH-64 main rotor hub

Stress analysis of an AH-64 27% scale model rotor hub was performed. Component loads and stresses were calculated based upon blade root loads and motions. The static and fatigue analysis indicates positive margins of safety in all components checked. Using the format developed here, the hub can be stress checked for future application

Endothermic reactions of uranium ions with N2, D2, and CD4

Journal ArticleThe assessment of new technology for isotope separation has revived an interest in the spectroscopy, properties, and reactions of uranium and its compounds. Newer methods which have been demonstrated include the use of lasers to selectively excite a particular uranium isotope with subsequent chemical or physical separation.1,2 In addition, several new electromagnetic and electrostatic schemes for separation of ions containing uranium appear promising

Cremmer-Gervais r-matrices and the Cherednik Algebras of type GL2

We give an intepretation of the Cremmer-Gervais r-matrices for sl(n) in terms of actions of elements in the rational and trigonometric Cherednik algebras of type GL2 on certain subspaces of their polynomial representations. This is used to compute the nilpotency index of the Jordanian r-matrices, thus answering a question of Gerstenhaber and Giaquinto. We also give an interpretation of the Cremmer-Gervais quantization in terms of the corresponding double affine Hecke algebra.Comment: 6 page

Functional Approach to Stochastic Inflation

We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point approximation scalar field probability distributions of various type are derived and the statistics of the inflationary-history-dependent functionals is developed.Comment: 20 pages, Preprint BROWN-HET-960, uses phyzz

Braneworld inflation from an effective field theory after WMAP three-year data

In light of the results from the WMAP three-year sky survey, we study an inflationary model based on a single-field polynomial potential, with up to quartic terms in the inflaton field. Our analysis is performed in the context of the Randall-Sundrum II braneworld theory, and we consider both the high-energy and low-energy (i.e. the standard cosmology case) limits of the theory. We examine the parameter space of the model, which leads to both large-field and small-field inflationary type solutions. We conclude that small field inflation, for a potential with a negative mass square term, is in general favored by current bounds on the tensor-to-scalar perturbation ratio rs.Comment: 11 pages, 5 figures; references updated and a few comments added; final version to appear in Phys. Rev.

Effects on Breathing of Agonists to μ-opioid or GABA\u3csub\u3eA\u3c/sub\u3e Receptors Dialyzed into the Ventral Respiratory Column of Awake and Sleeping Goats

Pulmonary ventilation (V̇I) in awake and sleeping goats does not change when antagonists to several excitatory G protein-coupled receptors are dialyzed unilaterally into the ventral respiratory column (VRC). Concomitant changes in excitatory neuromodulators in the effluent mock cerebral spinal fluid (mCSF) suggest neuromodulatory compensation. Herein, we studied neuromodulatory compensation during dialysis of agonists to inhibitory G protein-coupled or ionotropic receptors into the VRC. Microtubules were implanted into the VRC of goats for dialysis of mCSF mixed with agonists to either μ-opioid (DAMGO) or GABAA (muscimol) receptors. We found: (1) V̇I decreased during unilateral but increased during bilateral dialysis of DAMGO, (2) dialyses of DAMGO destabilized breathing, (3) unilateral dialysis of muscimol increased V̇I, and (4) dialysis of DAMGO decreased GABA in the effluent mCSF. We conclude: (1) neuromodulatory compensation can occur during altered inhibitory neuromodulator receptor activity, and (2) the mechanism of compensation differs between G protein-coupled excitatory and inhibitory receptors and between G protein-coupled and inotropic inhibitory receptors

The Effects of Lesions in the Dorsolateral Pons on the Coordination of Swallowing and Breathing in Awake Goats

The purpose of this retrospective study was to gain insight into the contribution of the dorsolateral pons to the coordination of swallowing and breathing in awake goats. In 4 goats, cannulas were chronically implanted bilaterally through the lateral (LPBN) and medial (MPBN) parabrachial nuclei just dorsal to the Kölliker–Fuse nucleus (KFN). After \u3e2 weeks recovery from this surgery, the goats were studied for 5½ h on a control day, and on separate days after receiving 1 and 10 μl injections of ibotenic acid (IA) separated by 1 week. The frequency of swallows did not change during the control and 1 μl IA studies, but after injection of 10 μl IA, there was a transient 65% increase in frequency of swallows (P \u3c 0.05). Under control conditions swallows occurred throughout the respiratory cycle, where late-E swallows accounted for 67.6% of swallows. The distribution of swallow occurrence throughout the respiratory cycle was unaffected by IA injections. Consistent with the concept that swallowing is dominant over breathing, we found that swallows increased inspiratory (TI) and expiratory (TE) time and decreased tidal volume (VT) of the breath of the swallow (n) and/or the subsequent (n + 1) breath. Injections of 10 μl IA attenuated the normal increases in TI and TE and further attenuated VT of the n breath. Additionally, E and I swallows reset respiratory rhythm, but injection of 1 or 10 μl IA progressively attenuated this resetting, suggesting a decreased dominance over respiratory motor output with increasing IA injections. Post mortem histological analysis revealed about 50% fewer (P \u3c 0.05) neurons remained in the KFN, LPBN, and MPBN in lesioned compared to control goats. We conclude that dorsolateral pontine nuclei have a modulatory role in a hypothesized holarchical neural network regulating swallowing and breathing particularly contributing to the normal dominance of swallowing over breathing in both rhythm and motor pattern generation

State-Dependent and -Independent Effects of Dialyzing Excitatory Neuromodulator Receptor Antagonists into the Ventral Respiratory Column

Unilateral dialysis of the broad-spectrum muscarinic receptor antagonist atropine (50 mM) into the ventral respiratory column [(VRC) including the pre-Bötzinger complex region] of awake goats increased pulmonary ventilation (V̇i) and breathing frequency (f), conceivably due to local compensatory increases in serotonin (5-HT) and substance P (SP) measured in effluent mock cerebral spinal fluid (mCSF). In contrast, unilateral dialysis of a triple cocktail of antagonists to muscarinic (atropine; 5 mM), neurokinin-1, and 5-HT receptors does not alter V̇i or f, but increases local SP. Herein, we tested hypotheses that 1) local compensatory 5-HT and SP responses to 50 mM atropine dialyzed into the VRC of goats will not differ between anesthetized and awake states; and 2) bilateral dialysis of the triple cocktail of antagonists into the VRC of awake goats will not alter V̇i or f, but will increase local excitatory neuromodulators. Through microtubules implanted into the VRC of goats, probes were inserted to dialyze mCSF alone (time control), 50 mM atropine, or the triple cocktail of antagonists. We found 1) equivalent increases in local 5-HT and SP with 50 mM atropine dialysis during wakefulness compared with isoflurane anesthesia, but V̇i and f only increased while awake; and 2) dialyses of the triple cocktail of antagonists increased V̇i, f, 5-HT, and SP

Tomographic imaging and scanning thermal microscopy: thermal impedance tomography

The application of tomographic imaging techniques developed for medical applications to the data provided by the scanning thermal microscope will give access to true three-dimensional information on the thermal properties of materials on a mm length scale. In principle, the technique involves calculating and inverting a sensitivity matrix for a uniform isotropic material, collecting ordered data at several modulation frequencies, and multiplying the inverse of the matrix with the data vector. In practice, inversion of the matrix in impractical, and a novel iterative technique is used. Examples from both simulated and real data are given