Finite Schur filtration dimension for modules over an algebra with Schur filtration

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.Comment: 22 pages; final versio

A Review of Natural Plants as Sources of Substances for Cleaner Leather Tanning Technologies

The stringent environmental regulations and compliance regarding leather tanning has compelled leather industry to seek alternative cleaner ingredients that have the capacity to minimize or prevent pollution caused by hazardous chemicals. Practical measures have so far involved replacing the current use of synthetic chemicals such as chromium salts, dyes, fatliquors and surfactants or minimizing their usage by incorporating agrobased organic components. Numerous papers have documented the use of different plant extracts at different stages of leather processing such as tanning, retanning, dyeing and fatliquoring. This present article details the specific plants and the leather processing stage at which they are applied and eventually the quality of the resulting leather. This article attempts to compile a considerable number of investigations published on physical properties of leather that is processed using natural plants. It has been shown that there are striking similarities in leather properties of leather processed using natural plants and using synthetic chemicals. This could help in compiling a database that details works on natural plants, stages of application and the corresponding physical properties which could provide a crucial assistance to research focusing on environmental protection and physical properties of leather which would in turn improve the quality of the resulting leather

The ATF6-Met [67] Val substitution is associated with increased plasma cholesterol levels

Objective— Activating transcription factor 6 (ATF6) is a sensor of the endoplasmic reticulum stress response and regulates expression of several key lipogenic genes. We used a 2-stage design to investigate whether ATF6 polymorphisms are associated with lipids in subjects at increased risk for cardiovascular disease (CVD). Methods and Results— In stage 1, 13 tag-SNPs were tested for association in Dutch samples ascertained for familial combined hyperlipidemia (FCHL) or increased risk for CVD (CVR). In stage 2, we further investigated the SNP with the strongest association from stage 1, a Methionine/Valine substitution at amino-acid 67, in Finnish FCHL families and in subjects with CVR from METSIM, a Finnish population-based cohort. The combined analysis of both stages reached region-wide significance (P=9x10–4), but this association was not seen in the entire METSIM cohort. Our functional analysis demonstrated that Valine at position 67 augments ATF6 protein and its targets Grp78 and Grp94 as well as increases luciferase expression through Grp78 promoter. Conclusions— A common nonsynonymous variant in ATF6 increases ATF6 protein levels and is associated with cholesterol levels in subjects at increased risk for CVD, but this association was not seen in a population-based cohort. Further replication is needed to confirm the role of this variant in lipids. We report the association of the ATF6-methionine [67]valine amino-acid substitution with plasma cholesterol levels. Association analyses in 2674 subjects and functional data suggest that the ATF6 gene may influence cholesterol levels in subjects at increased risk to develop cardiovascular disease

Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

Producing valid statistics when legislation, culture, and medical practices differ for births at or before the threshold of survival: Report of a European workshop

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Two-Loop Polarization Contributions to Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We calculate radiative-recoil corrections of order $\alpha^2(Z\alpha)(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.Comment: 15 pages, 11 figure

5-dim Superconformal Index with Enhanced En Global Symmetry

The five-dimensional $\mathcal{N}=1$ supersymmetric gauge theory with Sp(N) gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes with $N_f$ D8-branes on top of a single O8 orientifold plane in Type I' theory. This theory is known to be superconformal at the strong coupling limit with the enhanced global symmetry $E_{N_f+1}$ for $N_f\le 7$. In this work we calculate the superconformal index on $S^1\times S^4$ for the Sp(1) gauge theory by the localization method and confirm such enhancement of the global symmetry at the superconformal limit for $N_f\le 5$ to a few leading orders in the chemical potential. Both perturbative and (anti)instanton contributions are present in this calculation. For $N_f=6,7$ cases some issues related the pole structure of the instanton calculation could not be resolved and here we could provide only some suggestive answer for the leading contributions to the index. For the Sp(N) case, similar issues related to the pole structure appear.Comment: 70 pages, references added, published versio

M5-branes from gauge theories on the 5-sphere

We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S^3. With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N) gauge group also completely agrees with the supergravity index on AdS_7 x S^4.Comment: 44 pages, 1 figure, v4: ref added, clarified weak/strong coupling behaviors of large N free energy, minor improvements, version to be published in JHE

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.Comment: 30 pages, 4 figures. v2: typo corrected, references adde