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

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

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

Urban energy consumption and CO2 emissions in Beijing: current and future

This paper calculates the energy consumption and CO2 emissions of Beijing over 2005–2011 in light of the Beijing’s energy balance table and the carbon emission coefficients of IPCC. Furthermore, based on a series of energy conservation planning program issued in Beijing, the Long-range Energy Alternatives Planning System (LEAP)-BJ model is developed to study the energy consumption and CO2 emissions of Beijing’s six end-use sectors and the energy conversion sector over 2012–2030 under the BAU scenario and POL scenario. Some results are found in this research: (1) During 2005–2011, the energy consumption kept increasing, while the total CO2 emissions fluctuated obviously in 2008 and 2011. The energy structure and the industrial structure have been optimized to a certain extent. (2) If the policies are completely implemented, the POL scenario is projected to save 21.36 and 35.37 % of the total energy consumption and CO2 emissions than the BAU scenario during 2012 and 2030. (3) The POL scenario presents a more optimized energy structure compared with the BAU scenario, with the decrease of coal consumption and the increase of natural gas consumption. (4) The commerce and service sector and the energy conversion sector will become the largest contributor to energy consumption and CO2 emissions, respectively. The transport sector and the industrial sector are the two most potential sectors in energy savings and carbon reduction. In terms of subscenarios, the energy conservation in transport (TEC) is the most effective one. (5) The macroparameters, such as the GDP growth rate and the industrial structure, have great influence on the urban energy consumption and carbon emissions