Factorizations of Matrices Over Projective-free Rings

An element of a ring $R$ is called strongly $J^{\#}$-clean provided that it can be written as the sum of an idempotent and an element in $J^{\#}(R)$ that commute. We characterize, in this article, the strongly $J^{\#}$-cleanness of matrices over projective-free rings. These extend many known results on strongly clean matrices over commutative local rings

Developing an Unnatural Amino Acid-Specific Aminoacyl tRNA Synthetase

Unnatural Amino Acids (UAAs), amino acids not present in the human genetic code, have been synthesized to have a broad range of useful properties, in this case, as metal-binders which could have drug delivery applications. In order for the cell to place a UAA into the protein, two components, a unique aminoacyl tRNA synthetase and a corresponding tRNA must be present. If an amino acid is successfully charged to the tRNA, a stop codon is suppressed and a functional protein is built with the UAA at the mutation site. Such a tRNA molecule has previously been developed, as well as many synthetases specific to UAAs. In this work, the range of UAAs which can be incorporated into proteins using the E. coli’s own machinery is expanded by the development of a novel aminoacyl tRNA synthetase. By making a library of synthetase-coding plasmid variants and performing positive and negative screenings, the binding pocket of the synthetase can be modified for specificity to a UAA while not allowing the tRNA to be charged with a natural amino acid. In this work, we are attempting to evolve new tRNA synthetases for the incorporation of metal-binding amino acids by developing the plasmid library and a screening system to find synthetase variants meeting these criteria

Strongly clean triangular matrix rings with endomorphisms

A ring R is strongly clean provided that every element in R is the sum of an idempotent and a unit that commutate. Let Tn(R; σ) be the skew triangular matrix ring over a local ring R where σ is an endomorphism of R. We show that T2(R; σ) is strongly clean if and only if for any aϵ 1+J(R); b ϵ J(R), la -rσ (b): R→ R is surjective. Further, T3(R; σ) is strongly clean if la-rσ (b); la-rσ2 (b) and lb-rσ (a)are surjective for any a ϵ U(R); b ϵ J(R). The necessary condition for T3(R; σ) to be strongly clean is also obtained. © 2015 Iranian Mathematical Society

Strongly clean matrices over power series

An n � n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) ∈ Mn (R[[x]]). We prove, in this note, that A(x) ∈ Mn (R[[x]]) is strongly clean if and only if A(0) ∈ Mn(R) is strongly clean. Strongly clean matrices over quotient rings of power series are also determined. � Kyungpook Mathematical Journal

On feckly clean rings

A ring R is feckly clean provided that for any a R there exists an element e R and a full element u R such that a = e + u, eR(1 - e) J(R). We prove that a ring R is feckly clean if and only if for any a R, there exists an element e R such that V(a) V(e), V(1 - a) V(1 - e) and eR(1 - e) J(R), if and only if for any distinct maximal ideals M and N, there exists an element e R such that e M, 1 - e N and eR(1 - e) J(R), if and only if J-spec(R) is strongly zero-dimensional, if and only if Max(R) is strongly zero-dimensional and every prime ideal containing J(R) is contained in a unique maximal ideal. More explicit characterizations are also discussed for commutative feckly clean rings. © 2015 World Scientific Publishing Company

Distribution of allele frequencies at TTN g.231054C > T, RPL27A g.3109537C > T and AKIRIN2 c.*188G > A between Japanese Black and four other cattle breeds with differing historical selection for marbling

<p>Abstract</p> <p>Background</p> <p>Marbling defined by the amount and distribution of intramuscular fat, so-called <it>Shimofuri</it>, is an economically important trait of beef cattle in Japan. Our previous study detected 3 single nucleotide polymorphisms (SNPs), <it>g.231054C > T</it>, <it>g.3109537C > T </it>and <it>c.*188G > A</it>, respectively, in the 5' flanking region of the <it>titin </it>(<it>TTN</it>), the 5' flanking region of the <it>ribosomal protein L27a </it>(<it>RPL27A</it>) and the 3' untranslated region of the <it>akirin 2 </it>genes (<it>AKIRIN2</it>), which have been considered as positional functional candidates for the genes responsible for marbling, and showed association of these SNPs with marbling in Japanese Black beef cattle. In the present study, we investigated the allele frequency distribution of the 3 SNPs among the 5 cattle breeds, Japanese Black, Japanese Brown, Japanese Shorthorn, Holstein and Brown Swiss breeds.</p> <p>Findings</p> <p>We genotyped the <it>TTN g.231054C > T</it>, <it>RPL27A g.3109537C > T </it>and <it>AKIRIN2 c.*188G > A </it>SNPs by polymerase chain reaction-restriction fragment length polymorphism method, using 101 sires and 1,705 paternal half sib progeny steers from 8 sires for Japanese Black, 86 sires and 27 paternal half sib progeny steers from 3 sires for Japanese Brown, 79 sires and 264 paternal half sib progeny steers from 14 sires for Japanese Shorthorn, 119 unrelated cows for Holstein, and 118 unrelated cows for Brown Swiss breeds. As compared to the frequencies of the <it>g.231054C > T T</it>, <it>g.3109537C > T T </it>and <it>c.*188G > A A </it>alleles, associated with high marbling, in Japanese Black breed that has been subjected to a strong selection for high marbling, those in the breeds, Japanese Shorthorn, Holstein and Brown Swiss breeds, that have not been selected for high marbling were null or lower. The Japanese Brown breed selected slightly for high marbling showed lower frequency than Japanese Black breed in the <it>g.3109537C > T T </it>allele, whereas no differences were detected between the 2 breeds in the frequencies of the <it>g.231054C > T T </it>and <it>c.*188G > A A </it>alleles.</p> <p>Conclusions</p> <p>Based on this finding, we hypothesized that the pressure of the strong selection for high marbling in Japanese Black breed has increased the frequencies of the <it>T</it>, <it>T </it>and <it>A </it>alleles at the <it>TTN g.231054C > T</it>, <it>RPL27A g.3109537C > T </it>and <it>AKIRIN2 c.*188G > A </it>SNPs, respectively. This study, together with the previous association studies, suggested that the 3 SNPs may be useful for effective marker-assisted selection to increase the levels of marbling.</p

Movement of the external ear in human embryo

Introduction: External ears, one of the major face components, show an interesting movement during craniofacial morphogenesis in human embryo. The present study was performed to see if movement of the external ears in a human embryo could be explained by differential growth. Methods: In all, 171 samples between Carnegie stage (CS) 17 and CS 23 were selected from MR image datasets of human embryos obtained from the Kyoto Collection of Human Embryos. The three-dimensional absolute positio

A Hybrid 3D/2D Field Response Calculation for Liquid Argon Detectors with PCB Based Anode Plane

Liquid Argon Time Projection Chamber (LArTPC) technology is commonly utilized in neutrino detector designs. It enables detailed reconstruction of neutrino events with high spatial precision and low energy threshold. Its field response (FR) model describes the time-dependent electric currents induced in the anode-plane electrodes when ionization electrons drift nearby. An accurate and precise FR is a crucial input to LArTPC detector simulations and charge reconstruction. Established LArTPC designs have been based on parallel wire planes. It allows accurate and computationally economic two-dimensional (2D) FR models utilizing the translational symmetry along the direction of the wires. Recently, novel LArTPC designs utilize electrodes formed on printed circuit board (PCB) in the shape of strips with through holes. The translational symmetry is no longer a good approximation near the electrodes and a new FR calculation that employs regions with three dimensions (3D) has been developed. Extending the 2D models to 3D would be computationally expensive. Fortuitously, the nature of strips with through holes allows for a computationally economic approach based on the finite-difference method (FDM). In this paper, we present a new software package "pochoir" that calculates LArTPC field response for these new strip-based anode designs. This package combines 3D calculations in the volume near the electrodes with 2D far-field solutions to achieve fast and precise field response computation. We apply the resulting FR to simulate and reconstruct samples of cosmic-ray muons and $^{39}$Ar decays from a Vertical Drift (VD) detector prototype operated at CERN. We find the difference between real and simulated data within 5 %. Current state-of-the-art LArTPC software requires a 2D FR which we provide by averaging over one dimension and estimate that variations lost in this average are smaller than 7 %.Comment: 16 pages, 12 figure