An explicit upper bound for the least prime ideal in the Chebotarev density theorem

Lagarias, Montgomery, and Odlyzko proved that there exists an effectively computable absolute constant $A_1$ such that for every finite extension $K$ of ${\mathbb{Q}}$, every finite Galois extension $L$ of $K$ with Galois group $G$ and every conjugacy class $C$ of $G$, there exists a prime ideal $\mathfrak{p}$ of $K$ which is unramified in $L$, for which $\left[\frac{L/K}{\mathfrak{p}}\right]=C$, for which $N_{K/{\mathbb Q}}\,\mathfrak{p}$ is a rational prime, and which satisfies $N_{K/{\mathbb Q}}\,{\mathfrak{p}} \leq 2 {d_L}^{A_1}$. In this paper we show without any restriction that $N_{K/{\mathbb Q}}\,{\mathfrak{p}} \leq {d_L}^{12577}$ if $L \neq {\mathbb Q}$, using the approach developed by Lagarias, Montgomery, and Odlyzko.Comment: This paper will appear at Annales de l'institut Fourie

Ultrahigh-efficiency solution-processed simplified small-molecule organic light-emitting diodes using universal host materials

Although solution processing of small-molecule organic light-emitting diodes (OLEDs) has been considered as a promising alternative to standard vacuum deposition requiring high material and processing cost, the devices have suffered from low luminous efficiency and difficulty of multilayer solution processing. Therefore, high efficiency should be achieved in simple-structured small-molecule OLEDs fabricated using a solution process. We report very efficient solution-processed simple-structured small-molecule OLEDs that use novel universal electron-transporting host materials based on tetraphenylsilane with pyridine moieties. These materials have wide band gaps, high triplet energy levels, and good solution processabilities; they provide balanced charge transport in a mixed-host emitting layer. Orange-red (similar to 97.5 cd/A, similar to 35.5% photons per electron), green (similar to 101.5 cd/A, similar to 29.0% photons per electron), and white (similar to 74.2 cd/A, similar to 28.5% photons per electron) phosphorescent OLEDs exhibited the highest recorded electroluminescent efficiencies of solution-processed OLEDs reported to date. We also demonstrate a solution-processed flexible solid-state lighting device as a potential application of our devices.

Fumarate Reductase Activity Maintains an Energized Membrane in Anaerobic Mycobacterium tuberculosis

Oxygen depletion of Mycobacterium tuberculosis engages the DosR regulon that coordinates an overall down-regulation of metabolism while up-regulating specific genes involved in respiration and central metabolism. We have developed a chemostat model of M. tuberculosis where growth rate was a function of dissolved oxygen concentration to analyze metabolic adaptation to hypoxia. A drop in dissolved oxygen concentration from 50 mmHg to 0.42 mmHg led to a 2.3 fold decrease in intracellular ATP levels with an almost 70-fold increase in the ratio of NADH/NAD+. This suggests that re-oxidation of this co-factor becomes limiting in the absence of a terminal electron acceptor. Upon oxygen limitation genes involved in the reverse TCA cycle were upregulated and this upregulation was associated with a significant accumulation of succinate in the extracellular milieu. We confirmed that this succinate was produced by a reversal of the TCA cycle towards the non-oxidative direction with net CO2 incorporation by analysis of the isotopomers of secreted succinate after feeding stable isotope (13C) labeled precursors. This showed that the resulting succinate retained both carbons lost during oxidative operation of the TCA cycle. Metabolomic analyses of all glycolytic and TCA cycle intermediates from 13C-glucose fed cells under aerobic and anaerobic conditions showed a clear reversal of isotope labeling patterns accompanying the switch from normoxic to anoxic conditions. M. tuberculosis encodes three potential succinate-producing enzymes including a canonical fumarate reductase which was highly upregulated under hypoxia. Knockout of frd, however, failed to reduce succinate accumulation and gene expression studies revealed a compensatory upregulation of two homologous enzymes. These major realignments of central metabolism are consistent with a model of oxygen-induced stasis in which an energized membrane is maintained by coupling the reductive branch of the TCA cycle to succinate secretion. This fermentative process may offer unique targets for the treatment of latent tuberculosis

Precore Mutation of Hepatitis B Virus May Contribute to Hepatocellular Carcinoma Risk: Evidence from an Updated Meta-Analysis

BACKGROUND: Studies focused on the correlation of mutations in the genome of Hepatitis B Virus (HBV) like Pre-S mutation, Basal Core promoter (BCP), Enhancer II (EnhII), especially Precore mutation, with the risk of hepatocellular carcinoma (HCC) have triggered stiff controversies. With an increasing number of studies in this field recently, we conducted this meta-analysis to appraise the correlations. METHODS: We searched the commonly used databases both in English and Chinese till February 1(st), 2012. Meta-analysis was performed in fixed/random-effects models using STATA 10.0. Publication bias was examined through Egger's test and Begg's funnel plot. RESULTS: In total, 85 case-control studies were included involving 16745 HBV-infected patients, of whom 5781 had HCC. Statistically significant correlations were observed in Precore mutation G1896A (OR = 1.46, 95% confidence interval [CI] = 1.15-1.85, P(OR) = 0.002), G1899A (OR = 3.13, 95%CI = 2.38-4.13, P(OR)<0.001) and Pre-S mutation especially Pre-S1 deletion (OR = 2.94, 95%CI = 2.22 to 3.89) and Pre-S2 deletion (OR = 3.02, 95%CI = 2.03 to 4.50). Similar correlation existed between BCP double mutation A1762T/G1764A, T1753V, C1653T and HCC. In subgroup analysis, the Asians, genotype C or HBeAg positive patients with certain above mutations may be more susceptible to HCC. Besides, the mutations like G1896A and BCP double mutation may be associated with the progression of the liver diseases. CONCLUSIONS: Precore mutation G1896A, G1899A, deletions in Pre-S region as well as the other commonly seen mutations correlated with the increased risk of HCC, especially in Asians and may predict the progression of the liver disease

Littoral Cell Angioma (LCA) Associated with Liver Cirrhosis

A littoral cell angioma (LCA) is a rare benign vascular tumor of the spleen. A 60-year-old man, with multiple nodules in imaging study and liver cirrhosis graded as Child-Pugh classification class A, was transferred for splenomegaly. A thrombocytopenia was found on hematological evaluation. Because there was no evidence of hematological and visceral malignancy, a splenectomy was performed for a definitive diagnosis. The histological and immunohistochemical features of the splenic specimens were consistent with a LCA. After the splenectomy, the thrombocytopenia recovered to the normal platelet count. There has been no previous report of a LCA combined with liver cirrhosis. Herein, the first case of a LCA in Korea, diagnosed and treated by a splenectomy, is reported