Construction and decoding of BCH codes over chain of commutative rings

In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0 ⊂ K1 ⊂···⊂ Kt−1 ⊂ Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗ i and K∗ i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗ i and K∗ i for each i, where 0 ≤ i ≤ t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

A note on units of finite local rings in an ascending chain

In this paper we present matrices over unitary finite commutative local rings connected through an ascending chain of containments, whose elements are units of the corresponding rings in the chain such that the McCoy ranks are the largest ones.

Achiral lanthanide alkyl complexes bearing N,O multidentate ligands. Synthesis and catalysis of highly heteroselective ring-opening polymerization of rac-lactide

Alkane elimination reactions of amino-amino-bis(phenols) H2L1-4, Salan H2L5, and methoxy-beta-diimines HL6,7 with lanthanide tris(alkyl) s, Ln(CH2SiMe3)(3)(THF)(2) (Ln = Y, Lu), respectively, afforded a series of lanthanide alkyl complexes 1-8 with the release of tetramethylsilane. Complexes 1-6 are THF-solvated mono( alkyl) s stabilized by O, N, N, O-tetradentate ligands. Complexes 1-3 and 5 adopt twisted octahedral geometry, whereas 4 contains a tetragonal bipyramidal core. Bearing a monoanionic moiety L-6 (L-7), complex 7 ( 8) is a THF-free bis(alkyl). In complex 7, the O, N, N-tridentate ligand combined with two alkyl species forms a tetrahedral coordination core. Complexes 1, 2, and 3 displayed modest activity but high stereoselectivity for the polymerization of rac-lactide to give heterotactic polylactide with the racemic enchainment of monomer units P-r ranging from 0.95 to 0.99, the highest value reached to date. Complex 5 exhibited almost the same level of activity albeit with relatively low selectivity. In contrast, dramatic decreases in activity and stereoselectivity were found for complex 4. The Salan yttrium alkyl complex 6 was active but nonselective. Bis(alkyl) complexes 7 and 8 were more active than 1-3 toward polymerization of rac-LA, however, to afford atactic polylactides due to di-active sites. The ligand framework, especially the "bridge" between the two nitrogen atoms, played a significant role in governing the selectivity of the corresponding complexes via changing the geometry of the metal center.

Units of F5kD10

2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.

The Behavior of Hydroxyl Units of Synthetic Goethite and its Dehydroxylated Product Hematite

The behavior of the hydroxyl units of synthetic goethite and its dehydroxylated product hematite was characterized using a combination of Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) during the thermal transformation over a temperature range of 180-270 degrees C. Hematite was detected at temperatures above 200 degrees C by XRD while goethite was not observed above 230 degrees C. Five intense OH vibrations at 3212-3194, 1687-1674, 1643-1640, 888-884 and 800-798 cm(-1), and a H2O vibration at 3450-3445 cm(-1) were observed for goethite. The intensity of hydroxyl stretching and bending vibrations decreased with the extent of dehydroxylation of goethite. Infrared absorption bands clearly show the phase transformation between goethite and hematite: in particular. the migration of excess hydroxyl units from goethite to hematite. Two bands at 536-533 and 454-452 cm(-1) are the low wavenumber vibrations of Fe-O in the hematite structure. Band component analysis data of FTIR spectra support the fact that the hydroxyl units mainly affect the a plane in goethite and the equivalent c plane in hematite.

The rationale for using microscopic units of a donor matrix in cartilage defect repair

The efficacy of existing articular cartilage defect repair strategies are limited. Native cartilage tissue forms via a series of exquisitely orchestrated morphogenic events spanning through gestation into early childhood. However, defect repair must be achieved in a non-ideal microenvironment over an accelerated time-frame compatible with the normal life of an adult patient. Scaffolds formed from decellularized tissues are commonly utilized to enable the rapid and accurate repair of tissues such as skin, bladder and heart valves. The intact extracellular matrix remaining following the decellularization of these relatively low-matrix-density tissues is able to rapidly and accurately guide host cell repopulation. By contrast, the extraordinary density of cartilage matrix limits both the initial decellularization of donor material as well as its subsequent repopulation. Repopulation of donor cartilage matrix is generally limited to the periphery, with repopulation of lacunae deeper within the matrix mass being highly inefficient. Herein, we review the relevant literature and discuss the trend toward the use of decellularized donor cartilage matrix of microscopic dimensions. We show that 2-µm microparticles of donor matrix are rapidly integrate with articular chondrocytes, forming a robust cartilage-like composites with enhanced chondrogenic gene expression. Strategies for the clinical application of donor matrix microparticles in cartilage defect repair are discussed.

Accurate placement of a pelvic binder improves reduction of unstable fractures of the pelvic ring

The aim of this study was to assess the accuracy of placement of pelvic binders and to determine whether circumferential compression at the level of the greater trochanters is the best method of reducing a symphyseal diastasis. Patients were identified by a retrospective review of all pelvic radiographs performed at a military hospital over a period of 30 months. We analysed any pelvic radiograph on which the buckle of the pelvic binder was clearly visible. The patients were divided into groups according to the position of the buckle in relation to the greater trochanters: high, trochanteric or low. Reduction of the symphyseal diastasis was measured in a subgroup of patients with an open-book fracture, which consisted of an injury to the symphysis and disruption of the posterior pelvic arch (AO/OTA 61-B/C). We identified 172 radiographs with a visible pelvic binder. Five cases were excluded due to inadequate radiographs. In 83 (50%) the binder was positioned at the level of the greater trochanters. A high position was the most common site of inaccurate placement, occurring in 65 (39%). Seventeen patients were identified as a subgroup to assess the effect of the position of the binder on reduction of the diastasis. The mean gap was 2.8 times greater (mean difference 22 mm) in the high group compared with the trochanteric group (p < 0.01). Application of a pelvic binder above the level of the greater trochanters is common and is an inadequate method of reducing pelvic fractures and is likely to delay cardiovascular recovery in these seriously injured patients.

The loss of carbon dioxide from activated perbenzoate anions in the gas phase : Unimolecular rearrangement via epoxidation of the benzene ring

The unimolecular reactivities of a range of perbenzoate anions (X-C6H5CO3-), including the perbenzoate anion itself (X=H), nitroperbenzoates (X=para-, meta-, ortho-NO2), and methoxyperbenzoates (X=para-, meta-OCH3) were investigated in the gas phase by electrospray ionization tandem mass spectrometry. The collision-induced dissociation mass spectra of these compounds reveal product ions consistent with a major loss of carbon dioxide requiring unimolecular rearrangement of the perbenzoate anion prior to fragmentation. Isotopic labeling of the perbenzoate anion supports rearrangement via an initial nucleophilic aromatic substitution at the ortho carbon of the benzene ring, while data from substituted perbenzoates indicate that nucleophilic attack at the ipso carbon can be induced in the presence of electron-withdrawing moieties at the ortho and para positions. Electronic structure calculations carried out at the B3LYP/6311++G(d,p) level of theory reveal two competing reaction pathways for decarboxylation of perbenzoate anions via initial nucleophilic substitution at the ortho and ipso positions, respectively. Somewhat surprisingly, however, the computational data indicate that the reaction proceeds in both instances via epoxidation of the benzene ring with decarboxylation resulting-at least initially-in the formation of oxepin or benzene oxide anions rather than the energetically favored phenoxide anion. As such, this novel rearrangement of perbenzoate anions provides an intriguing new pathway for epoxidation of the usually inert benzene ring.

Using the factors that have a positive impact on the retention of low socioeconomic students to prepare accelerated enrolled nurses for the science units of a nursing degree : a practice report

At a campus in a low socioeconomic (SES) area, our University allows enrolled nurses entry into the second year of a Bachelor of Nursing, but attrition is high. Using the factors, described by Yorke and Thomas (2003) to have a positive impact on the attrition of low SES students, we developed strategies to prepare the enrolled nurses for the pharmacology and bioscience units of a nursing degree with the aim of reducing their attrition. As a strategy, the introduction of review lectures of anatomy, physiology and microbiology, was associated with significantly reduced attrition rates. The subsequent introduction of a formative website activity of some basic concepts in bioscience and pharmacology, and a workshop addressing study skills and online resources, were associated with a further reduction in attrition rates of enrolled nursing students in a Bachelor of Nursing.

Flexibility of the furanose ring in nucleic acids: a compilation of crystal data

A compilation of crystal structure data on deoxyribo- and ribonucleosides and their higher derivatives is presented. The aim of this paper is to highlight the flexibility of deoxyribose and ribose rings. So far, the conformational parameters of nucleic acids constituents of ribose and deoxyribose have not been analysed separately. This paper aims to correlate the conformational parameters with the nature and puckering of the sugar. Deoxyribose puckering occurs in the C2′ endo region while ribose puckering is observed both in the C3′ endo and C2′ endo regions. A few endocyclic and exocyclic bond angles depend on the puckering and the nature of the sugar. The majority of structures have an anti conformation about the glycosyl bond. There appears to be a puckering dependence on the torsion angle about the C4′---C5′ bonds. Such stereochemical information is useful in model building studies of polynucleotides and nucleic acids.

Dual-frequency characteristics of Minkowski-square ring antennas

Fractal Minkowski curves to design a compact dual-frequency microstrip ring antenna are proposed. Sides of a square ring have been selectively replaced with first and second iterations of the generalised fractal geometry to design a smaller antenna with dual-frequency operation. This behaviour has been explained based on current distributions on the antenna structure. Measured results compare well with electromagnetic simulations.

A norbornadiene–cyclobutadiene cycloaddition cascade: novel intramolecular σ2+π2 trapping of a cyclobutane ring

Norbornadiene and 1,2-bismethoxycarbonylcyclobutadiene furnish a novel heptacyclic system 3(whose X-ray crystal structure has been determined)and an annulated pterodactylane derivative 4 in a single step.

Performance of a pipelined ring algorithm for Fast Fourier Transform on transputer arrays

In this paper a pipelined ring algorithm is presented for efficient computation of one and two dimensional Fast Fourier Transform (FFT) on a message passing multiprocessor. The algorithm has been implemented on a transputer based system and experiments reveal that the algorithm is very efficient. A model for analysing the performance of the algorithm is developed from its computation-communication characteristics. Expressions for execution time, speedup and efficiency are obtained and these expressions are validated with experimental results obtained on a four transputer system. The analytical model is then used to estimate the performance of the algorithm for different number of processors, and for different sizes of the input data.

Spiroannulation of a cyclopentane ring. Synthesis of spiro[4.n](n+5)alk-2-en-1-ones

A methodology based on Claisen rearrangement-Wacker oxidation and intramolecular aldol condensation strategy starting from cyclic ketones leading to spiro[4.n](n+5)alk-2-en-1-ones has been developed. Thus one-pot Claisen rearrangement of the alkyl alcohols 6a-c furnished the aldehydes 8a-c, which on regiospecific oxidation using Wacker conditions generated the keto-aldehydes 9a-c. Finally, intramolecular aldol condensation transformed the keto-aldehydes 9a-c into spiroannulated products 10a-c.