On the least common multiple of qq-binomial coefficients

In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack 1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, where ${n\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page

Magnetotransport in the CeIrIn5{_5} system: The influence of antiferromagnetic fluctuations

We present an overview of magnetotransport measurements on the heavy-fermion superconductor CeIrIn$_5$. Sensitive measurements of the Hall effect and magnetoresistance (MR) are used to elucidate the low temperature phase diagram of this system. The normal-state magnetotransport is highly anomalous, and experimental signatures of a pseudogap-like precursor state to superconductivity as well as evidence for two distinct scattering times governing the Hall effect and the MR are observed. Our observations point out the influence of antiferromagnetic fluctuations on the magnetotransport in this class of materials. The implications of these findings, both in the context of unconventional superconductivity in heavy-fermion systems as well as in relation to the high temperature superconducting cuprates are discussed

Carrier mobility and scattering lifetime in electric double-layer gated few-layer graphene

We fabricate electric double-layer field-effect transistor (EDL-FET) devices on mechanically exfoliated few-layer graphene. We exploit the large capacitance of a polymeric electrolyte to study the transport properties of three, four and five-layer samples under a large induced surface charge density both above and below the glass transition temperature of the polymer. We find that the carrier mobility shows a strong asymmetry between the hole and electron doping regime. We then employ ab-initio density functional theory (DFT) calculations to determine the average scattering lifetime from the experimental data. We explain its peculiar dependence on the carrier density in terms of the specific properties of the electrolyte we used in our experiments.Comment: 6 pages, 3 figure

Noncommutative gravity: fuzzy sphere and others

Gravity on noncommutative analogues of compact spaces can give a finite mode truncation of ordinary commutative gravity. We obtain the actions for gravity on the noncommutative two-sphere and on the noncommutative ${\bf CP}^2$ in terms of finite dimensional $(N\times N)$-matrices. The commutative large $N$ limit is also discussed.Comment: LaTeX, 13 pages, section on CP^2 added + minor change

Relief network design problem (RNDP): A scoping review, challenges, and opportunities

The Relief Network Design Problem (RNDP) is particularly important in emergency management. Any uncertain factors caused by natural disasters, the equity measurement in network design, and the adequate analysis of relief behavior will affect the efficiency of the relief network. This paper provides a comprehensive basis to support this view. The scope of the review allowed for exploring all existing literature on RNDP, where screening for titles, abstracts, keywords, and main contents, a total of 629 relevant articles are preserved. To construct the review work, existing research perspectives on the Relief Logistics Network Design Problem (RLNDP) as well as the Relief Transport Network Design Problem (RTNDP) are addressed, and their research focus and main research approaches are discussed. The existing studies on RNDP seem to be reached a bottleneck on how to design a humanitarian relief network. Hence, this paper contributes to the existing body of knowledge by summarizing the literature in the field, identifying gaps, analyzing future challenges, and providing solutions for future research. Specifically, this review reveals that while a large number of studies have considered uncertainty in the network design, they have not considered it at both the management level and the residents' level. In addition, equity is often mentioned, but the definition of humanitarian equity is unclear, as most studies consider equity at the management level. In real disaster relief scenarios, people do not only wait for relief, but self-evacuation is also a main behavior in the relief process, yet there are few studies that consider it in the network design. This review also emphasizes the relief network design structure problem, and the interdependence and coupling of the relief infrastructure transport or logistics facility network with other networks, such as the electric network, energy network, etc., deserves to be focused. In summary, five valuable research highlights are proposed based on a review of the existing literature: (1) Explore uncertainties from both the government management and disaster victim perspectives and integrate them into network design approaches. (2) Define and consider relief equity from both the government management and disaster victim perspectives. (3) Analyze self-evacuation behavior in the emergency relief phase and explore how it affects RNDP. (4) Optimize the transfer point location and relief routing from the perspective of management and humanitarian equity. (5) Strengthen the resilience of disaster relief interdependent network

Soil Carbon in Agroforestry Systems: An Unexplored Treasure?

Soil organic matter (SOM), which contains more reactive organic carbon (C) than any other single terrestrial pool, plays a major role in determining C storage in ecosystems and regulating atmospheric concentrations of carbon dioxide (CO2)^1^. Agroforestry, the practice of growing trees and crops in interacting combinations on the same unit of land^2^, primarily by resource-poor smallholder farmers in developing countries, is recognized as a strategy for soil carbon sequestration (SCS) under the Clean Development Mechanism (CDM) of the Kyoto Protocol^3^. The understanding about C storage and dynamics under agroforestry systems (AFS), however, is minimal. Our studies under various AFS in diverse ecological conditions in five countries showed that tree-based agricultural systems, compared to treeless systems, stored more C in deeper soil layers up to 1 m depth under comparable conditions. More C is stored in soil near the tree than away from the tree; higher SOC content is associated with higher species richness and tree density; and C3 plants (trees) contribute to more C in the silt- + clay-sized (<53 µm) fractions that constitute more stable C, than C4 plants, in deeper soil profiles4 - 8. These results provide clear indications of the possibilities for climate change mitigation through SCS in AFS, and opportunities for economic benefit - through carbon trading - to millions of smallholder farmers in developing countries

A precursor state to unconventional superconductivity in CeIrIn5{_5}

We present sensitive measurements of the Hall effect and magnetoresistance in CeIrIn${_5}$ down to temperatures of 50 mK and magnetic fields up to 15 T. The presence of a low temperature coherent Kondo state is established. Deviations from Kohler's rule and a quadratic temperature dependence of the cotangent of the Hall angle are reminiscent of properties observed in the high temperature superconducting cuprates. The most striking observation pertains to the presence of a \textit{precursor} state--characterized by a change in the Hall mobility--that appears to precede the superconductivity in this material, in similarity to the pseudogap in the cuprate high $T_c$ superconductors.Comment: 4 figure

Cardiovascular risk stratification in familial hypercholesterolaemia

Familial hypercholesterolaemia (FH) is a common autosomal-dominant disorder in most European countries. Patients with FH are characterised by a raised level of low-density lipoprotein cholesterol and a high risk of premature coronary heart disease (CHD). Currently there is no consensus regarding the clinical utility to predict future coronary events or testing for the presence of subclinical atherosclerotic disease in asymptomatic patients with FH. Family screening of patients with FH as recommended by the UK National Institute of Health and Care Excellence guideline would result in finding many young individuals with a diagnosis of FH who are clinically asymptomatic. The traditional CHD risk scores, that is, the Framingham score, are insufficient in risk prediction in this group of young individuals. In addition, a better understanding of the genetic aetiology of the FH phenotype and CHD risk in monogenic FH and polygenic hypercholesterolaemia is needed. Non-invasive imaging methods such as carotid intima-media thickness measurement might produce more reliable information in finding high-risk patients with FH. The potential market authorisation of novel therapeutic agents such as PCSK9 monoclonal inhibitors makes it essential to have a better screening programme to prioritise the candidates for treatment with the most severe form of FH and at higher risk of coronary events. The utility of new imaging techniques and new cardiovascular biomarkers remains to be determined in prospective trials