Bounding the dimensions of rational cohomology groups

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations where the dimension of a rational cohomology group for $G$ can be bounded by a constant times the dimension of the coefficient module. We then demonstrate how our results can be applied to obtain effective bounds on the first cohomology of the symmetric group. We also show how, for finite Chevalley groups, our methods permit significant improvements over previous estimates for the dimensions of second cohomology groups.Comment: 13 page

Quantum function algebras as quantum enveloping algebras

Inspired by a result in [Ga], we locate two $k[q,q^{-1}]$-integer forms of $F_q[SL(n+1)]$, along with a presentation by generators and relations, and prove that for $q=1$ they specialize to $U({\mathfrak{h}})$, where ${\mathfrak{h}}$ is the Lie bialgebra of the Poisson Lie group $H$ dual of $SL(n+1)$; moreover, we explain the relation with [loc. cit.]. In sight of this, we prove two PBW-like theorems for $F_q[SL(n+1)]$, both related to the classical PBW theorem for $U({\mathfrak{h}})$.Comment: 27 pages, AMS-TeX C, Version 3.0 - Author's file of the final version, as it appears in the journal printed version, BUT for a formula in Subsec. 3.5 and one in Subsec. 5.2 - six lines after (5.1) - that in this very pre(post)print have been correcte

Review Essay

Midway was one of the most decisive naval battles of all time. It was a battle that should have been won by the Japanese but wasn’t. Future American writers would dub it an incredible or miraculous victory, based on the superiority of the Japanese and the widely held perception before the battle that the Imperial Japa- nese Navy was invincible

Set and Drift: Doctrine MattersWhy the Japanese Lost at Midway

Dallas Isom’s article “The Battle of Midway: Why the Japanese Lost” [Naval War College Review, Summer 2000, pp. 60–100] is laudable for its use of Japanese sources and for the interesting points it raises. In particular, we applaud Isom’s interviews with Japanese survivors, which contribute new and useful informa- tion regarding Japanese aircraft rearmament procedures. This new data is cru- cial to building an accurate account of the events that transpired aboard the Japanese carriers on the morning of 4 June 1942

Test–retest reliability of multidimensional dyspnea profile recall ratings in the emergency department: a prospective, longitudinal study

BACKGROUND: Dyspnea is among the most common reasons for emergency department (ED) visits by patients with cardiopulmonary disease who are commonly asked to recall the symptoms that prompted them to come to the ED. The reliability of recalled dyspnea has not been systematically investigated in ED patients. METHODS: Patients with chronic or acute cardiopulmonary conditions who came to the ED with dyspnea (N = 154) completed the Multidimensional Dyspnea Profile (MDP) several times during the visit and in a follow-up visit 4 to 6 weeks later (n = 68). The MDP has 12 items with numerical ratings of intensity, unpleasantness, sensory qualities, and emotions associated with how breathing felt when participants decided to come to the ED (recall MDP) or at the time of administration (“now” MDP). The recall MDP was administered twice in the ED and once during the follow-up visit. Principal components analysis (PCA) with varimax rotation was used to assess domain structure of the recall MDP. Internal consistency reliability was assessed with Cronbach’s alpha. Test–retest reliability was assessed with intraclass correlation coefficients (ICCs) for absolute agreement for individual items and domains. RESULTS: PCA of the recall MDP was consistent with two domains (Immediate Perception, 7 items, Cronbach’s alpha = .89 to .94; Emotional Response, 5 items; Cronbach’s alpha = .81 to .85). Test–retest ICCs for the recall MDP during the ED visit ranged from .70 to .87 for individual items and were .93 and .94 for the Immediate Perception and Emotional Response domains. ICCs were much lower for the interval between the ED visit and follow-up, both for individual items (.28 to .66) and for the Immediate Perception and Emotional Response domains (.72 and .78, respectively). CONCLUSIONS: During an ED visit, recall MDP ratings of dyspnea at the time participants decided to seek care in the ED are reliable and sufficiently stable, both for individual items and the two domains, that a time lag between arrival and questionnaire administration does not critically affect recall of perceptual and emotional characteristics immediately prior to the visit. However, test–retest reliability of recall over a 4- to 6-week interval is poor for individual items and significantly attenuated for the two domains

On dual canonical bases

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type $A$. The construction of a basis for the coordinate algebra of the $n\times n$ quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a basis of quantum SL(n) is obtained by setting the quantum determinant to one. This basis turns out to be equivalent to the dual canonical basis

Spin Excitations in BaFe1.84Co0.16As2 Superconductor Observed by Inelastic Neutron Scattering

Superconductivity appears to compete against the spin-density-wave in Fe pnictides. However, optimally cobalt doped samples show a quasi-two-dimensional spin excitation centered at the (0.5, 0.5, L) wavevector, "the spin resonance peak", that is strongly tied to the onset of superconductivity. By inelastic neutron scattering on single crystals we show the similarities and differences of the spin excitations in BaFe1.84Co0.16As2, with respect to the spin excitations in the high-temperature superconducting cuprates. As in the cuprates the resonance occurs as an enhancement to a part of the spin excitation spectrum which extends to higher energy transfer and higher temperature. However, unlike in the cuprates, the resonance peak in this compound is asymmetric in energy.Comment: 12 pages, 6 figures; PACS # 74.70.-b, 74.20.Mn, 78.70.Nx, 74.25.Ha; corrected discussion of figures in tex