Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

An estimate of the global impact of multiple scattering by clouds on outgoing long-wave radiation

Although the potential importance of scattering of long-wave radiation by clouds has been recognised, most studies have concentrated on the impact of high clouds and few estimates of the global impact of scattering have been presented. This study shows that scattering in low clouds has a significant impact on outgoing long-wave radiation (OLR) in regions of marine stratocumulus (-3.5 W m(-2) for overcast conditions) where the column water vapour is relatively low. This corresponds to an enhancement of the greenhouse effect of such clouds by 10%. The near-global impact of scattering on OLR is estimated to be -3.0 W m(-2), with low clouds contributing -0.9 W m(-2), mid-level cloud -0.7 W m(-2) and high clouds -1.4 W m(-2). Although this effect appears small compared to the global mean OLR of 240 W m(-2), it indicates that neglect of scattering will lead to an error in cloud long-wave forcing of about 10% and an error in net cloud forcing of about 20%.

Effect of hyaluronidase on ocular motility and eyelid function in sub-Tenon's anaesthesia: randomised controlled trial

Purpose: To assess the effect of hyaluronidase on eye and eyelid movements when used as an adjunct in sub-Tenon's anaesthesia. Methods: A total of 60 patients who had sub-Tenon's anaesthesia prior to phacoemulsification surgery were divided into two equal groups in a double-masked randomised controlled fashion. Of these, Group A had 4 ml lignocaine 2%, while Group B had 4ml lignocaine 2% with the addition of sodium hyaluronidase 75 IU/ml. Ocular motility, levator, and orbicularis oculi function were measured in all patients at 5 and 8 min. Levator function was scored from 0 (no function) to 3 (complete function) while orbicularis function was scored from 0 to 2. The score for ocular motility was the sum in four positions of gaze, each position scoring from 0 to 2. Results were compared using a nonparametric test. Results Group B achieved significantly better ocular and lid akinesia than Group A both at 5 and 8 min with P < 0.01. The median scores for levator function at 5 and 8 min were 2 for Group A and 0 for Group B. For orbicularis function, the median scores at both time intervals were 2 for Group A and 1 for Group B. For ocular motility, the median score for Group A at 5 min was 3 and at 8 min was 2.5; for Group B at 5 min was 0.5 and at 8 min was 0. Conclusions: The addition of hyaluronidase in sub-Tenon's anaesthesia has a significant effect in improving ocular and lid (levator and orbicularis) akinesia.

Structure, and thermal, magnetic and chemical properties of copper(II)iodoacetate monohydrate

Reaction of iodoacetic acid with cupric carbonate in water in dimmed light yields green Cu(ICH2COO)(2 center dot)H2O (1). From X-ray crystallography, it is found to be a tetra-acetato bridged copper(II) dimer with the water molecules occupying the apical positions. In thermogravimetry, the coordinated water molecules are lost in the temperature range 50-100 degrees C. From magnetic susceptibility measurements in the temperature range 300-1.8 K, the exchange coupling constant J is found to be -142(1) cm(-1) and g = 2.18(2) with the spin Hamiltonian H = -2J{S-Cu1 center dot S-Cu2}. It reacts with 2,2'-bipyridine (bpy) to yield [Cu(bpy)(2)I]I. It oxidises thiophenol to Ph-S-S-Ph under dry N-2 atmosphere.

Effect of H-bonding on the ambivalence of SCN- towards copper(II)

Condensations of 2-(2-aminoethyl)pyridine with 4-methylimidazole-5-carboxaldehyde and 1-methyl-2-imidazolecarboxaldehyde generate the tridentate N donor ligands L and L' respectively. Reactions of Cu(NCS)(2) with L and L' yield respectively CuL(SCN)(NCS) (1) containing a CuN4S core and CuL'(NCS)(2) (2) having a CuN5 core. Both the cores are square pyramidal with SCN bound in 1 at the axial position through the S end. This differential behaviour of SCN in the two complexes despite the ligands being very similar, is investigated by DFT calculations at the B3LYP/TZV level. It is found that DFT calculations predict isolation of the Cu(ligand)(NCS)(2) species for both the ligands L and L'. Presence of an offsetting intermolecular H-bonding between the N atom of the thiocyanate and the N-H proton of the ligand L of an adjacent molecule makes the binding of SCN via the S end feasible in 1 resulting in the H-bonded-dimer Cu2L2(SCN)(2)(NCS)(2). The strength of the H-bond is estimated as 27.1 kJ mol (1) from the DFT calculations. The question of such H-bonding does not arise with L' as it lacks in a similar H atom. Dimeric 1 represents a case of two non-interacting spins. (C) 2008 Elsevier B. V. All rights reserved.

Influence of a halide ion on ribbons of water pentamer

Reactions of CuF2, CuCl2 center dot 2H(2)O and CuBr2 with 2,2'-dipyridylamine (HDPA) in water at room temperature using Cu: HDPA = 2: 1 mol yield [Cu(HDPA) (H2O)(2)F]F center dot 3H(2)O (1), Cu(HDPA) Cl-2 (2) and [Cu(HDPA) Br-2 (3) respectively. The structures of 2 and 3 are isostructural in spacegroup C-2 with cell dimensions; for 2, a = 14.702(8), b = 7.726(2), c = 4.829(6) angstrom, beta = 96.68(8)degrees and for 3, a = 14.2934(8), b = 7.9057(6), c = 5.1982(5) angstrom, beta = 94.049(7)degrees. In the X-ray crystal structure, the complex 1 is found to contain tapes of water pentamers. Our DFT calculations at the B3LYP/LanL2DZ level show that the reaction Cu(HDPA)X-2 + 2H(2)O = [Cu(HDPA)(H2O)(2)X]X is most exothermic in the gas phase when X- = F-, i.e., the tendency of water uptake is maximum for Cu(HDPA) F-2. It seems that the exothermicities of the aquations of Cu(HDPA) Cl-2 and Cu(HDPA) Br-2 are not sufficient to stabilise the type of ribbons of water observed in 1 and consequently water is eschewed when X- = Cl- or Br-.

Use of HNO3 as the source of NO to prepare a nitric oxide complex of ruthenium

Reaction of cis-Ru(bisox)(2)Cl-2, where bisox is 4,4,4',4'-tetramethyl-2,2'-bisoxazoline, with HNO3 in 1 : 4 molar proportion in boiling water under N-2 atmosphere and subsequent addition of an excess of NaClO4 center dot H2O yields [Ru(bisox)(HL)(NO)](ClO4)(NO3) (1). HL is a hydrolysed form of bisox where one of the oxazoline rings opens up. X-Ray crystallography shows that 1 contains an octahedral RuN5O core. HL binds the metal through an imino N, an amide N and an alcoholic O atom. Reaction of cis-Ru(bisox)(2)Cl-2 with an excess of NaNO2 in water gives cis-Ru(bisox)(2)(NO2)(2) (2). On acidification by HClO4 in methanol, 2 is smoothly converted to cis-[Ru(bisox)(2)(NO2)(NO)](ClO4)(2) (3) due to equilibrium (1).

Development of novel brush-type chiral stationary phases based on terpenoid selectors: HPLC evaluation and theoretical investigation of enantioselective binding interactions

The terpenoid chiral selectors dehydroabietic acid, 12,14-dinitrodehydroabietic acid and friedelin have been covalently linked to silica gel yielding three chiral stationary phases CSP 1, CSP 2 and CSP 3, respectively. The enantiodiscriminating capability of each one of these phases was evaluated by HPLC with four families of chiral aromatic compounds composed of alcohols, amines, phenylalanine and tryptophan amino acid derivatives and beta-lactams. The CSP 3 phase, containing a selector with a large friedelane backbone is particularly suitable for resolving free alcohols and their derivatives bearing fluorine substituents, while CSP 2 with a dehydroabietic architecture is the only phase that efficiently discriminates 1, 1'-binaphthol atropisomers. CSP 3 also gives efficient resolution of the free amines. All three phases resolve well the racemates of N-trifluoracetyl and N-3,5-dinitrobenzoyl phenylalanine amino acid ester derivatives. Good enantioseparation of beta-lactams and N-benzoyl tryptophan amino acid derivatives was achieved on CSP 1. In order to understand the structural factors that govern the chiral molecular recognition ability of these phases, molecular dynamics simulations were carried out in the gas phase with binary diastereomeric complexes formed by the selectors of CSP 1 and CSP 2 and several amino acid derivatives. Decomposition of molecular mechanics energies shows that van der Waals interactions dominate the formation of the diastereomeric transient complexes while the electrostatic binding interactions are primarily responsible for the enantioselective binding of the (R)- and (S)-analytes. Analysis of the hydrogen bonds shows that electrostatic interactions are mainly associated with the formation of N-(HO)-O-...=C enantio selective hydrogen bonds between the amide binding sites from the selectors and the carbonyl groups of the analytes. The role of mobile phase polarity, a mixture of n-hexane and propan-2-ol in different ratios, was also evaluated through molecular dynamics simulations in explicit solvent. (c) 2006 Elsevier Ltd. All rights reserved.

First report of structurally characterized dimorph of an oxovanadium(V)-hydrazonato complex containing, VO3+ core

The orthorhombic crystalline variety (with Pbca space group) of the title complex [V2O3(L)(2)], incorporating the doubly deprotonated tridentate benzoyl hydrazone of 2-hydroxy-5-methylacetophenone has been synthesized from the decomposition of [(VO)-O-IV(L)(bipy)] complex in CH2Cl2 and structurally characterized in contrast to its recently reported monoclinic variety (with C2/c space group) obtained from the reaction of [VO(acac)(2)] with H2L in acetone.

Bidentates versus monodentates in asymmetric hydrogenation catalysis: synergic effects on rate and allosteric effects on enantioselectivity

C-1-Symmetric phosphino/phosphonite ligands are prepared by the reactions of Ph2P(CH2)(2)P(NMe2)(2) with (S)-1,11'-bi-2-naphthol (to give L-A) or (S)-10,10'-bi-9-phenanthrol (to give L-B). Racemic 10,10'-bi-9-phenanthrol is synthesized in three steps from phenanthrene in 44% overall yield. The complexes [PdCl2(L-A,L-B)] (1a,b), [PtCl2(L-A,L-B)] (2a,b), [Rh(cod)(L-A,L-B)]BF4 (3a,b) and [Rh(L-A,L-B)(2)]BF4 (4a,b) are reported and the crystal structure of la has been determined. A P-31 NMR study shows that M, a 1:1 mixture of the monodentates, PMePh2 and methyl monophosphonite L-1a (based on (S)-1,11'-bi-2-naphthol), reacts with 1 equiv of [Rh(cod)(2)]BF4 to give the heteroligand complex [Rh(cod)(PMePh2)(L-1a)]BF4 (5) and homoligand complexes [Rh(cod)(PMePh2)(2)]BF4 (6) and [Rh(cod)(L-1a)(2)]BF4 (7) in the ratio 2:1:1. The same mixture of 5-7 is obtained upon mixing the isolated homoligand complexes 6 and 7 although the equilibrium is only established rapidly in the presence of an excess of PMePh2. The predominant species 5 is a monodentate ligand complex analogue of the chelate 3a. When the mixture of 5-7 is exposed to 5 atm H-2 for 1 h (the conditions used for catalyst preactivation in the asymmetric hydrogenation studies), the products are identified as the solvento species [Rh(PMePh2)(L-1a)(S)(2)]BF4 (5'), [Rh(S)(2)(PMePh2)(2)]BF4 (6') and [Rh(S)(2)(L-1a)(2)]BF4 (7') and are formed in the same 2:1:1 ratio. The reaction of M with 0.5 equiv of [Rh(cod)(2)]BF4 gives exclusively the heteroligand complex cis-[Rh(PMePh2)(2)(L-1a)(2)]BF4 (8), an analogue of 4a. The asymmetric hydrogenation of dehydroamino acid derivatives catalyzed by 3a,b is reported, and the enantioselectivities are compared with those obtained with (a) chelate catalysts derived from analogous diphosphonite ligands L-2a and L-2b, (b) catalysts based on methyl monophosphonites L-1a and L-1b, and (c) catalysts derived from mixture M. For the cinnamate and acrylate substrates studied, the catalysts derived from the phosphino/phosphonite bidentates L-A,L-B generally give superior enantioselectivities to the analogous diphosphonites L-2a and L-2b; these results are rationalized in terms of delta/lambda-chelate conformations and allosteric effects of the substrates. The rate of hydrogenation of acrylate substrate A with heterochelate 3a is significantly faster than with the homochelate analogues [Rh(L-2a)(cod)]BF4 and [Rh(dppe)(cod)]BF4. A synergic effect on the rate is also observed with the monodentate analogues: the rate of hydrogenation with the mixture containing predominantly heteroligand complex 5 is faster than with the monophosphine complex 6 or monophosphonite complex 7. Thus the hydrogenation catalysis carried out with M and [Rh(cod)(2)]BF4 is controlled by the dominant and most efficient heteroligand complex 5. In this study, the heterodiphos chelate 3a is shown to be more efficient and gives the opposite sense of optical induction t the heteromonophos analogue

Dihydrogen in cation-substituted zeolites X - an inelastic neutron scattering study

An inelastic neutron scattering (INS) study of the rotational - vibrational spectrum of dihydrogen sorbed by zeolite X having substituted sodium, calcium and zinc cations is reported. The rotational - vibrational spectrum of H-2 was observed at low energy transfer ( below ca. 25 meV, 202 cm(-1)); the vibration was that of the H-2 molecule against the binding site (H-2 - X, not H - H). The vibration frequency was proportional to the polarising power of the cation (Na+ < Ca2+ < Zn2+). Polarisation of the H-2 molecule dominated the interaction of H-2 with this binding site. The total scattering intensity was proportional to the dihydrogen dose. However the vibrational intensities became constant at ca. 0.3 wt% showing that the H-2 binding sites had saturated. Additional dihydrogen appeared as unbound or weakly bound dihydrogen exhibiting recoil.

Nitrogen donor ligands bearing N-H groups: Effect on catalytic and cytotoxic activity of molybdenum eta(3)-allyldicarbonyl complexes

Reactions of [Mo(eta(3)-C3H5)Br(CO)(2)(NCMe)(2)] with the bidentate nitrogen ligands 2-(2'-pyridyl)imidazole (L1), 2-(2'-pyridyl)benzimidazole (L2), N,N'-bis(2'-pyridinecarboxamido)-1,2-ethane (L3), and 2,2'-bisimidazole (L4) led to the new complexes [Mo(eta(3)-C3H5)Br(CO)(2)(L)] (L = L1, 1; L2, 2; L4, 4) and [{Mo(eta(3)-C3H5) Br(CO)(2)}(2)(mu-L-3)] (3). The reaction of complexes 2 and 3 with Tl[CF3SO3] afforded [Mo(eta(3)-C3H5)(CF3SO3)(CO)(2)(L2)] (2T) and [{Mo(eta(3)-C3H5)(CF3SO3)(CO)(2)}(2)(mu-L-3)] (3T). Complexes 3 and 2T were structurally characterized by single crystal X-ray diffraction, showing the facial allyl/carbonyls arrangement and the formation of the axial isomer. In 2T, two molecules are assembled in a hydrogen bond dimer. The four complexes 1-4 were tested as precursors in the catalytic epoxidation of cyclooctene and styrene, in the presence of t-butylhydroperoxide (TBHP), with moderate conversions and turnover frequencies for complexes 1-3 and very low ones for 4. The increasing number of N-H groups in the complexes seems to be responsible for the loss of catalytic activity, compared with other related systems. The cytotoxic activities of all the complexes were evaluated against HeLa cells. The results showed that compounds 1,2,4, and 2T exhibited significant activity, complexes 2 and 2T being particularly promising. (C) 2008 Elsevier B.V. All rights reserved.

Selenium supplementation of lactating dairy cows: effects on milk production and total selenium content and speciation in blood, milk and cheese

Forty multiparous Holstein cows were used in a 16-week continuous design study to determine the effects of either selenium (Se) source, selenised yeast (SY) (derived from a specific strain of Saccharomyces cerevisiae CNCM 1-3060) or sodium selenite (SS), or Se inclusion rate in the form of SY in the diets of lactating dairy cows on the Se concentration and speciation in blood, milk and cheese. Cows received ad libitum a total mixed ration (TMR) with a 1 : 1 forage: concentrate ratio on a dry matter (DM) basis. There were four diets (T-1 to T-4), which differed only in either source or dose of Se additive. Estimated total dietary Se for T, (no supplement), T-2 (SS), T-3 (SY) and T-4 (SY) was 0.16, 0.30, 0.30 and 0.45 mg/kg DM, respectively. Blood and milk samples were taken at 28-day intervals and at each time point there were positive linear effects of Se in the form of SY on the Se concentration in blood and milk. At day 112 blood and milk Se values for T-1 to T-4 were 177, 208, 248 and 279 +/- 6.6 and 24, 38, 57 and 72 +/- 3.7 ng/g fresh material, respectively, and indicate improved uptake and incorporation of Se from SY. In whole blood, selenocysteine (SeCys) was the main selenised amino acid and the concentration of selenomethionine (SeMet) increased with the increasing inclusion rate of SY In milk, there were no marked treatment effects on the SeCys content, but Se source had a marked effect on the concentration of SeMet. At day 112 replacing SS (T-2) with SY (T-3) increased the SeMet concentration of milk from 36 to 111 ng Se/g and its concentration increased further to 157ng Se/g dried sample as the inclusion rate of SY increased further (T-4) to provide 0.45 mg Se/kg TMR. Neither Se source nor inclusion rate affected the keeping quality of milk. At day 112 milk from T-1, T-2 and T-3 was made into a hard cheese and Se source had a marked effect on total Se and the concentration of total Se comprised as either SeMet or SeCys. Replacing SS (T-2) with SY (T-3) increased total Se, SeMet and SeCys content in cheese from 180 to 340 ng Se/g, 57 to 153 ng Se/g and 52 to 92 ng Se/g dried sample, respectively. The use of SY to produce food products with enhanced Se content as a means of meeting the Se requirements is discussed

The aetiology and treatment of developmental stammering in childhood

Developmental stammering (DS, also known as idiopathic stammering or stuttering) is a disorder of speech fluency that affects approximately 0.75% to 1% of the populations of Great Britain, Australia and America,(1-4) although a recent study puts the point prevalence figure at between 1% and 3% in the UK.(5) Prevalence is generally thought to be similar amongst communities worldwide, although there have been occasional suggestions that this figure might be lower in countries where there is less pressure on verbal acuity.(6) DS may be distinguished from neurogenic stammering, which can occur subsequent to neurological damage of various aetiologies (for example, stroke, tumour, degenerative disease) and psychogenic stammering, whose onset can be related to a significant psychological event such as bereavement. While a diagnosis of neurogenic stammering might be made in early childhood and adolescence, both neurogenic and psychogenic types are typically associated with an adult onset. DS is by far the most common form of stammering and usually develops in the pre-school years. The mean age at onset is 4 2, with 75% of cases beginning before the age of 6.(1) However, occasionally, stammering onset may be seen as late as 12 or 13 years of age.

Texture segmentation in Williams syndrome

Williams syndrome (WS) is a developmental disorder in which visuo-spatial cognition is poor relative to verbal ability. At the level of visuo-spatial perception, individuals with WS can perceive both the local and global aspects of an image. However, the manner in which local elements are integrated into a global whole is atypical, with relative strengths in integration by luminance, closure, and alignment compared to shape, orientation and proximity. The present study investigated the manner in which global images are segmented into local parts. Segmentation by seven gestalt principles was investigated: proximity, shape, luminance, orientation, closure, size (and alignment: Experiment I only). Participants were presented with uniform texture squares and asked to detect the presence of a discrepant patch (Experiment 1) or to identify the form of a discrepant patch as a capital E or H (Experiment 2). In Experiment 1, the pattern and level of performance of the WS group did not differ from that of typically developing controls, and was commensurate with the general level of non-verbal ability observed in WS. These results were replicated in Experiment 2, with the exception of segmentation by proximity, where individuals with WS demonstrated superior performance relative to the remaining segmentation types. Overall, the results suggest that, despite some atypical aspects of visuo-spatial perception in WS, the ability to segment a global form into parts is broadly typical in this population. In turn, this informs predictions of brain function in WS, particularly areas V1 and V4. (c) 2006 Elsevier Ltd. All rights reserved.