Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

SK1-like functors for division algebras

We investigate the group valued functor G(D) = D*/F*D' where D is a division algebra with center F and D' the commutator subgroup of D*. We show that G has the most important functorial properties of the reduced Whitehead group SK1. We then establish a fundamental connection between this group, its residue version, and relative value group when D is a Henselian division algebra. The structure of G(D) turns out to carry significant information about the arithmetic of D. Along these lines, we employ G(D) to compute the group SK1(D). As an application, we obtain theorems of reduced K-theory which require heavy machinery, as simple examples of our method.

Multiplicative spectra of Banach spaces

The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.

Crystallization and preliminary X-ray diffraction analysis of naphthalene dioxygenase from Rhodococcus sp strain NCIMB 12038

The three-component naphthalene dioxygenase (NDO) enzyme system carries out the first step in the aerobic degradation of naphthalene to (+)-cis-(1R,2S)-dihydroxy-1,2-dihydronaphthalene by Rhodococcus sp. strain NCIMB 12038. The terminal oxygenase component (naphthalene 1,2-dioxygenase) that catalyzes this reaction belongs to the aromatic ring hydroxylating dioxygenase family and has been crystallized. These enzymes utilize a mononuclear nonheme iron centre to catalyze the addition of dioxygen to their respective substrates. In this reaction, two electrons, two protons and a dioxygen molecule are consumed. The Rhodococcus enzyme has only 33 and 29% sequence identity to the corresponding alpha- and beta-subunits of the NDO system of Pseudomonas putida NCIMB 9816-4, for which the tertiary structure has been reported. In order to determine the three-dimensional structure of the Rhodococcus NDO, diffraction-quality crystals have been prepared by the hanging-drop method. The crystals belongs to space group P2(1)2(1)2(1), with unit-cell parameters a = 87.5, b = 144, c = 185.6 Angstrom, alpha = beta = gamma = 90degrees, and diffract to 2.3 Angstrom resolution.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Characterization, crystallization and preliminary X—ray diffraction analysis of acutohaemolysin, a haemolytic toxin from Agkistrodon acutus venom

Acutohaemolysin, a phospholipase A2 (PLA2) from the venom of the snake Agkistrodon acutus, has been isolated and purified to homogeneity by anion-exchange chromatography on a DEAE-Sepharose column followed by cation-exchange chromatography on a CM-Sepharose column. It is an alkaline protein with an isoelectric point of 10.5 and is comprised of a single polypeptide chain of 13 938 Da. Its N-terminal amino-acid sequence shows very high similarity to Lys49-type PLA2 proteins from other snake venoms. Although its PLA2 enzymatic activity is very low, acutohaemolysin has a strong indirect haemolytic activity and anticoagulant activity. Acutohaemolysin crystals with a diffraction limit of 1.60 Å were obtained by the hanging-drop vapour-diffusion method. The crystals belong to the space group C2, with unit-cell parameters a = 45.30, b = 59.55, c = 46.13 Å, [beta] = 117.69°. The asymmetric unit contains one molecule

165/183 GHz FSS for the MetOp Second Generation Microwave Sounder Instrument

This paper reports the design of a Frequency Selective Surface (FSS) which simultaneously allows transmission of 175.3 – 191.3 GHz radiation and rejection from 164 - 167 GHz with a loss <0.5 dB for TE wave polarization at 45° incidence. The state-of-the art filter consists of three air spaced perforated screens with unit cells that are composed of nested resonant slots. The FSS satisfies the stringent electromagnetic performance requirements for signal demultiplexing in the quasi-optical feed train of the Microwave Sounder (MWS) instrument which is under development for the MetOp-SG mission.

C∗-Segal algebras with order unit

We introduce the notion of a (noncommutative) C *-Segal algebra as a Banach algebra (A, {norm of matrix}{dot operator}{norm of matrix} A) which is a dense ideal in a C *-algebra (C, {norm of matrix}{dot operator}{norm of matrix} C), where {norm of matrix}{dot operator}{norm of matrix} A is strictly stronger than {norm of matrix}{dot operator}{norm of matrix} C onA. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C *-Segal algebras with order unit is determined.

Extravascular lung water indexed to predicted body weight is a novel predictor of intensive care unit mortality in patients with acute lung injury

Objectives: Acute lung injury and the acute respiratory distress syndrome are characterized by noncardiogenic pulmonary edema, which can be assessed by measurement of extravascular lung water. Traditionally, extravascular lung water has been indexed to actual body weight (mL/kg). Because lung size is dependent on height rather than weight, we hypothesized indexing to predicted body weight may be a better predictor of mortality in acute lung injury/acute respiratory distress syndrome.

PANEL DATA UNIT ROOT TEST WITH FIXED TIME DIMENSION

The consideration of the limit theory in which T is fixed and N is allowed to go to infinity improves the finite-sample properties of the tests and avoids the imposition of the relative rates at which T and N go to infinity.

Specific Newborn Individualized Developmental Care and Assessment Program movements are associated with acute pain in preterm infants in the neonatal intensive care unit

The Newborn Individualized Developmental Care and Assessment Program (NIDCAP) is widely used in neonatal intensive care units and comprises 85 discrete infant behaviors, some of which may communicate infant distress. The objective of this study was to identify developmentally relevant movements indicative of pain in preterm infants.

Loss-of-Mains Protection System by Application of Phasor Measurement Unit Technology with Experimentally Assessed Threshold Settings

Loss-of-mains protection is an important component of the protection systems of embedded generation. The role of loss-of-mains is to disconnect the embedded generator from the utility grid in the event that connection to utility dispatched generation is lost. This is necessary for a number of reasons, including the safety of personnel during fault restoration and the protection of plant against out-of-synchronism reclosure to the mains supply. The incumbent methods of loss-of-mains protection were designed when the installed capacity of embedded generation was low, and known problems with nuisance tripping of the devices were considered acceptable because of the insignificant consequence to system operation. With the dramatic increase in the installed capacity of embedded generation over the last decade, the limitations of current islanding detection methods are no longer acceptable. This study describes a new method of loss-of-mains protection based on phasor measurement unit (PMU) technology, specifically using a low cost PMU device of the authors' design which has been developed for distribution network applications. The proposed method addresses the limitations of the incumbent methods, providing a solution that is free of nuisance tripping and has a zero non-detection zone. This system has been tested experimentally and is shown to be practical, feasible and effective. Threshold settings for the new method are recommended based on data acquired from both the Great Britain and Ireland power systems.

Synergy Between an Improved Covariate Unit Root Test and Cross-sectionally Dependent Panel Data Unit Root Tests, with two Applications

This paper proposes the use of an improved covariate unit root test which exploits the cross-sectional dependence information when the panel data null hypothesis of a unit root is rejected. More explicitly, to increase the power of the test, we suggest the utilization of more than one covariate and offer several ways to select the ‘best’ covariates from the set of potential covariates represented by the individuals in the panel. Employing our methods, we investigate the Prebish-Singer hypothesis for nine commodity prices. Our results show that this hypothesis holds for all but the price of petroleum.