Estimation of Gini Index within Pre-Specied Error Bound

Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size methods cannot simultaneously achieve both the specified confidence coefficient and specified width. We develop a purely sequential procedure for interval estimation of Gini index with a specified confidence coefficient and a fixed margin of error. Optimality properties of the proposed method, namely first order asymptotic efficiency and asymptotic consistency are proved. All theoretical results are derived without assuming any specific distribution of the data

Inner multipliers and Rudin type invariant subspaces

Let $\mathcal{E}$ be a Hilbert space and $H^2_{\mathcal{E}}(\mathbb{D})$ be the $\mathcal{E}$-valued Hardy space over the unit disc $\mathbb{D}$ in $\mathbb{C}$. The well known Beurling-Lax-Halmos theorem states that every shift invariant subspace of $H^2_{\mathcal{E}}(\mathbb{D})$ other than $\{0\}$ has the form $\Theta H^2_{\mathcal{E}_*}(\mathbb{D})$, where $\Theta$ is an operator-valued inner multiplier in $H^\infty_{B(\mathcal{E}_*, \mathcal{E})}(\mathbb{D})$ for some Hilbert space $\mathcal{E}_*$. In this paper we identify $H^2(\mathbb{D}^n)$ with $H^2(\mathbb{D}^{n-1})$-valued Hardy space $H^2_{H^2(\mathbb{D}^{n-1})}(\mathbb{D})$ and classify all such inner multiplier $\Theta \in H^\infty_{\mathcal{B}(H^2(\mathbb{D}^{n-1}))}(\mathbb{D})$ for which $\Theta H^2_{H^2(\mathbb{D}^{n-1})}(\mathbb{D})$ is a Rudin type invariant subspace of $H^2(\mathbb{D}^n)$.Comment: 8 page

Comparative analysis of the biochemical parameters among the three Prakriti individuals having Type 2 diabetes mellitus

242-249The occurrence of multi-organ affecting Type 2 diabetes mellitus is increasing day by day that consequently becomes a serious threat to public health. According to Ayurveda, individual’s basic constitution (Prakriti) describes its predisposition and prognosis to disease status and also the treatment for disease but no detailed studies carried out yet on diabetic individuals of three Prakriti groups on biochemical aspects. This study was conducted with twelve patients in each three Prakriti groups having Type 2 diabetes mellitus to determine the differences of some anthropometrical and biochemical parameters amongst them. Clinical profiling and various biochemical parameters of liver and kidney, lipid profiles and anti-oxidant enzymes were assayed. Significant differences were observed amongst the subjects belonging in different Prakriti groups. Differences in liver function enzymes and kidney function parameters and lipid profiles revealed that the subjects of Kapha and Pitta Prakriti were predominant groups. Glycosylated haemoglobin percentage was higher in Pitta Prakriti individuals. The screening process of the study indicated that diabetic individuals mostly belong to the Pitta and Kapha Prakriti groups of which Kapha Prakriti was more prone to hepatic and renal disorder and Pitta Prakriti was more susceptible towards cardiac disorder due to their diabetic complications

A Mitogen-activated Protein Kinase cascade module, MKK3-MPK6 and MYC2, is involved in blue light-mediated seedling development in Arabidopsis

Mitogen-activated protein kinase (MAPK) pathways are involved in several signal transduction processes in eukaryotes. Light signal transduction pathways have been extensively studied in plants; however, the connection between MAPK and light signaling pathways is currently unknown. Here, we show that MKK3-MPK6 is activated by blue light in a MYC2-dependent manner. MPK6 physically interacts with and phosphorylates a basic helix-loop-helix transcription factor, MYC2, and is phosphorylated by a MAPK kinase, MKK3. Furthermore, MYC2 binds to the MPK6 promoter and regulates its expression in a feedback regulatory mechanism in blue light signaling. We present mutational and physiological studies that illustrate the function of the MKK3-MPK6-MYC2 module in Arabidopsis thaliana seedling development and provide a revised mechanistic view of photomorphogenesis

Dangling and hydrolyzed ligand arms in [Mn3] and [Mn6] coordination assemblies: synthesis, characterization, and functional activity

Two flexible, branched, and sterically constrained di- and tripodal side arms around a phenol backbone were utilized in ligands H3L1 and H5L2 to isolate {Mn6} and {Mn3} coordination aggregates. 2,6-Bis{(1-hydroxy-2-methylpropan-2-ylimino)methyl}-4-methylphenol (H3L1) gave trinuclear complex [Mn3(μ-H2L1)2(μ1,3-O2CCH3)4(CH3OH)2](ClO4)2·4CH3OH (1), whereas 2,6-bis[{1-hydroxy-2-(hydroxymethyl)butan-2-ylimino}methyl]-4-methylphenol (H5L2) provided hexanuclear complex [Mn6(μ4-H2L2)2(μ-HL3)2(μ3-OH)2(μ1,3-O2CC2H5)4](ClO4)2·2H2O (2). Binding of acetates and coordination of {H2L1}− provided a linear MnIIIMnIIMnIII arrangement in 1. A MnIII6 fused diadamantane-type assembly was obtained in 2 from propionate bridges, coordination of {H2L2}3–, and in situ generated {HL3}2–. The magnetic characterization of 1 and 2 revealed the properties dominated by intramolecular anti-ferromagnetic exchange interactions, and this was confirmed using density functional theory calculations. Complex 1 exhibited field-induced slow magnetic relaxation at 2 K due to the axial anisotropy of MnIII centers. Both the complexes show effective solvent-dependent catechol oxidation toward 3,5-di-tert-butylcatechol in air. The catechol oxidation abilities are comparable from two complexes of different nuclearity and structure

MKKK20 works as an upstream triple-kinase of MKK3-MPK6-MYC2 module in Arabidopsis seedling development

The mitogen-activated protein kinase (MAPK) cascade is involved in several signal transduction processes in eukaryotes. Here, we report a mechanistic function of MAP kinase kinase kinase 20 (MKKK20) in light signal transduction pathways. We show that MKKK20 acts as a negative regulator of photomorphogenic growth at various wavelengths of light. MKKK20 not only regulates the expression of light signaling pathway regulatory genes but also gets regulated by the same pathway genes. The atmyc2 mkkk20 double mutant analysis shows that MYC2 works downstream to MKKK20 in the regulation of photomorphogenic growth. MYC2 directly binds to the promoter of MKKK20 to modulate its expression. The protein-protein interaction study indicates that MKKK20 physically interacts with MYC2, and this interaction likely suppresses the MYC2-mediated promotion of MKKK20 expression. Further, the protein phosphorylation studies demonstrate that MKKK20 works as the upstream kinase of MKK3-MPK6-MYC2 module in photomorphogenesis

Simulation and extended range prediction of monsoon intraseasonal oscillations in NCEP CFS/GFS version 2 framework

The present study investigates the role of ocean-atmosphere coupling in improving the simulation and extended range prediction skill of the monsoon intraseasonal oscillations (MISOs) using the NCEP CFS (version 2) vis-Ã -vis its atmospheric component GFS (version 2) forced with bias-corrected sea-surface temperature (SST) derived from CFS. Though the CFS free-run analysis shows dry bias over Indian land as compared to GFS, the interactive air-sea coupling in CFS has considerably improved the simulation of large-scale dynamical fields, SST-rainfall relationship, and the northward propagation of the MISOs with respect to GFS. However, the improvement of MISO simulation in CFS over GFS has not necessarily guaranteed the improvement of real-time extended range prediction during 2011 and 2012. CFS shows better skill over GFS (forced with bias-corrected CFS derived SST) at pentad lead 4. The phases of MISOs are better predicted in GFS and the amplitude prediction skill is marginally improved in CFS. The present study also advocates the need of probabilistic category (active, normal or break) forecast at extended range