Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Fluidity, Permeability And Antioxidant Behavior Of Model Membranes Incorporated With Alpha-Tocopherol And Vitamin-E Acetate

Magnetic resonance studies reveal a marked difference between the binding of α-tocopherol and that of the corresponding acetate (vitamin E acetate) with dipalmitoylphosphatidylcholine (DPPC) vesicles. This is reflected in differences in the phase-transition curves of the DPPC vesicles incorporated with the two compounds, as well as in the 13C relaxation times and line widths. A model for the incorporation of these molecules in lipid bilayers has been suggested. α-Tocopherol binds strongly with the lipids, possibly through a hydrogen bond formation between the hydroxyl group of the former and one of the oxygen atoms of the latter. The possibility of such a hydrogen bond formation is excluded in vitamin E acetate, which binds loosely through the normal hydrophobic interaction. The model for lipid-vitamin interaction explains the in vitro decomposition of H2O2 by α-tocopherol. α-Tocopherol in conjuction with H2O2 can also act as a free-radical scavenger in the lipid phase. The incorporation of α-tocopherol and vitamin E acetate in DPPC vesicles enhances the permeability of lipid bilayers for small molecules such as sodium ascorbate.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Mandatory nap times and group napping patterns in child care: An observational study

Policy provision for naps is typical in child care settings, but there is variability in the practices employed. One practice that might modify children’s early sleep patterns is the allocation of a mandatory nap time in which all children are required to lie on their beds without alternate activity permitted. There is currently limited evidence of the effects of such practices on children’s napping patterns. This study examined the association between duration of mandatory nap times and group-level napping patterns in child care settings. Observations were undertaken in a community sample of 113 preschool rooms with a scheduled nap time (N = 2,114 children). Results showed that 83.5% of child care settings implemented a mandatory nap time (range = 15–145 min) while 14.2% provided alternate activities for children throughout the nap time period. Overall, 31% of children napped during nap times. Compared to rooms with ≤ 30 min of mandatory nap time, rooms with 31–60 min and > 60 min of mandatory nap time had a two-and-a-half and fourfold increase, respectively, in the proportion of children napping. Nap onset latency did not significantly differ across groups. Among preschool children, exposure to longer mandatory nap times in child care may increase incidence of napping.

Analysis of human immunodeficiency virus type 1 drug resistance in children receiving nucleoside analogue reverse-transcriptase inhibitors plus nevirapine, nelfinavir, or ritonavir (Pediatric AIDS Clinical Trials Group 377)

In Pediatric AIDS Clinical Trials Group 377, antiretroviral therapy-experienced children were randomized to 4 treatment arms that included different combinations of stavudine, lamivudine (3TC), nevirapine (Nvp), nelfinavir (Nfv), and ritonavir (Rtv). Previous treatment with zidovudine (Zdv), didanosine (ddI), or zalcitabine (ddC) was acceptable. Drug resistance ((R)) mutations were assessed before study treatment (baseline) and at virologic failure. Zdv(R), ddI(R), and ddC(R) mutations were detected frequently at baseline but were not associated with virologic failure. Children with drug resistance mutations at baseline had greater reductions in virus load over time than did children who did not. Nvp(R) and 3TC(R) mutations were detected frequently at virologic failure, and Nvp(R) mutations were more common among children receiving 3-drug versus 4-drug Nvp-containing regimens. Children who were maintained on their study regimen after virologic failure accumulated additional Nvp(R) and 3TC(R) mutations plus Rtv(R) and Nfv(R) mutations. However, Rtv(R) and Nfv(R) mutations were detected at unexpectedly low rates.

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

Preliminary phonological analysis of the Limi dialect of Humla Bhotia

The purpose of this research was to analyse the phonological system of the Limi dialect of Humla Bhotia. Humla Bhotia is a Tibeto-Burman language that is spoken by approximately 4000 5000 people in the far northwestern Humla province of the Kingdom of Nepal. The language has not previously been the subject of analysis. The data base for this thesis was collected on two different dialects of Humla Bhotia in Kathmandu, the capital of Nepal, from February to May 2000. I had three language informants who speak Humla Bhotia as their mother tongue. One of the informants speaks the Upper Humla dialect and the other two informants speak the Limi dialect. In this thesis I have concentrated on the phonology of the dialect of Limi but occasionally I also make reference to the Upper Humla dialect. The Limi data base consists of 600 words elicited in isolation, sentences where words have been checked for consonantal and pitch variation, and five texts comprising 117 sentences. Firstly, I have studied the geographical location, population and dialects of Humla Bhotia. Five dialects were identified: Limi, Upper Humla, La Yakba, Nyinba and Humli Khyampa. Information on the dialect areas is based on the accounts of seven mother tongue speakers of the language and on Nancy Levine s (1988) anthropological research of the ethnic group Nyinba. Secondly, I have analysed the phonological system of Limi from the viewpoint of American stucturalism much along the lines followed by Pike 1966 [1947] ja 1967 [1948]. In defining the prosodic elements I have also used acoustic analysis. In the Limi dialect there are 7 vowel phonemes. No vowel clusters occur within the same syllable. In this preliminary analysis 29 contrastive plosives, 8 affricates and 5 6 fricatives were found. The data also revealed 4 nasal phonemes, two rhotic phonemes, one lateral phoneme and two central approximants. Further research is however called for to check the phonemic status of these segments. Four contrastive prosodic elements were encountered: nasalisation, length, phonation type and pitch movement. There are two contrastive types of phonation: tense and lax. Many words were found with a third type of phonation, modal phonation. How modal phonation relates to the prosodic system is unclear at this stage and is therefore left for further research to determine. There are two contrastive pitch movement tonemes: a rising toneme and falling toneme. The falling toneme occurs in free variation with a level pitch contour. Rising appears to be linked with lax phonation and falling with tense phonation.

Intake, growth and carcass characteristics of lambs consuming low digestible hay and cereal grain

The influence of barley and oat grain supplements on hay dry matter intake (DMI), carcass components gain and meat quality in lambs fed a low quality basal diet was examined. Thirty five crossbred wether lambs (9 months of age) were divided into four groups. After adaptation to a basal diet of 85% oat hay and 15% lucerne hay for one week, an initial group of 11 was slaughtered. The weights of carcass components and digesta-free empty body weight (EBW) of this group was used to estimate the weight of carcass components of the other three experimental groups at the start of the experiment. The remaining three groups were randomly assigned to pens and fed ad libitum the basal diet alone (basal), basal with 300 g air dry barley grain (barley), basal with 300 g air dry oat grain (oat). Supplements were fed twice weekly (i.e., 900 g on Tuesday and 1200 g on Friday). After 13 weeks of feeding, animals were slaughtered and, at 24 h post-mortem meat quality and subcutaneous fat colour were measured. Samples of longissimus muscle were collected for determination of sarcomere length and meat tenderness. Hay DMI was reduced (P<0.01) by both barley and oat supplements. Lambs fed barley or oat had a higher and moderate digestibility of DM, and a higher intake of CP (P<0.05) and ME (P<0.01) than basal lambs. Final live weight of barley and oat lambs was higher (P<0.05) than basal, but this was not reflected in EBW or hot carcass weight. Lambs fed barley or oat had increases in protein (P<0.01) and water (P<0.001) in the carcass, but fat gain was not changed (P>0.05). There were no differences in eye muscle area or fat depth (total muscle and adipose tissue depth at 12th rib, 110 mm from midline; GR) among groups. The increased levels of protein and water components in the carcass of barley and oat fed lambs, associated with improved muscle production, were small and did not alter (P>0.05) any of the carcass/meat quality attributes compared to lambs fed a low quality forage diet. Feeding barley or oat grain at 0.9–1% of live weight daily to lambs consuming poor quality hay may not substantially improve carcass quality, but may be useful in maintaining body condition of lambs through the dry season for slaughter out of season

Towards the development of a Cavendish banana resistant to race 4 of fusarium wilt: gamma irradiation of micropropagated Dwarf Parfitt (Musa spp., AAA group, Cavendish subgroup)

'Dwarf parfitt', an extra-dwarf Cavendish cultivar with resistance to subtropical race 4 fusarium oxysporum f. sp. cubense 9Foc), was gamma irradiated at a dose of 20 Gy and putative mutants were recovered with improved agronomic characteristics. Further screening of putative mutants for improved yield and fruit size, as well as a degree of resistence to fusarium wilt, led to the selection of a line (DPM25) with improved productivity when grown on soils infested with subtropical race 4 Foc. DPM25 was equal to the industry standard, 'Williams', in every agronomic trait measured and it consistently showed a lower incidence of fusarium wilt. Further improvement of field resistance to race 4 Foc is needed in DPM25 and further cycles of mutation induction and selction is an option discussed.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Grower group case study on new farming practices in the Herbert region, Australia

Growers working together have proven to be a successful method for improving the utilization of farm resources and accelerating the adoption of the Sugar Yield Decline Joint Venture principles (SYDJV). The Pinnacle Precision Farming Group was formed in 2004 with the aim to bring together the ideas, knowledge and resources of growers in the Herbert region. Along with their common interest in controlled traffic, minimal tillage and crop rotations, the grower group utilize a farm machinery contractor to provide some of their major farming operations. This paper provides an insight into the changes made by the Pinnacle Precision Farming Group and their journey to adopt the new farming system practices. This paper also details the changes made by the group machinery contractor and a comparison of the old and new farming systems used by a group member. A focus point of the document is the impact of the new farming system on the economic, social and environmental components of the farming business. Analysis of the new farming system with a legume crop rotation revealed an increase in the farm gross margin by AU$22 024 and, in addition, a reduction in tractor operation time by 38% across the whole farm. This represents a return on marginal capital of 14.68 times the original capital outlay required by the group member. Using the new farming system without a legume crop will still improve the group members whole of farm gross margin by AU$6 839 and reduce tractor operation time by 43% across the whole farm. The Pinnacle Precision Farming group recognize the need to continually improve their farming businesses and believe that the new farming system principles are critical for the long term viability of the industry. [U$1 = AU$1.19].

Phosphorus nutrition and tolerance of cotton to water stress: II. Water relations, free and bound water and leaf expansion rate

In previous experiments, increased leaf-Phosphorus (P) content with increasing P supply enhanced the individual leaf expansion and water content of fresh cotton leaves in a severely drying soil. In this paper, we report on the bulk water content of leaves and its components, free and bound water, along with other measures of plant water status, in expanding cotton leaves of various ages in a drying soil with different P concentrations. The bound water in living tissue is more likely to play a major role in tolerance to abiotic stresses by maintaining the structural integrity and/or cell wall extensibility of the leaves, whilst an increased amount of free water might be able to enhance solute accumulation, leading to better osmotic adjustment and tolerance to water stress, and maintenance of the volumes of sub-cellular compartments for expansive leaf growth. There were strong correlations between leaf-P%, leaf water (total, free and bound water) and leaf expansion rate (LER) under water stress conditions in a severely drying soil. Increased soil-P enhanced the uptake of P from a drying soil, leading to increased supply of osmotically active inorganic solutes to the cells in growing leaves. This appears to have led to the accumulation of free water and more bound water, ultimately leading to increased leaf expansion rates as compared to plants in low P soil under similar water stress conditions. The greater amount of bound and free water in the high-P plants was not necessarily associated with changes in cell turgor, and appears to have maintained the cell-wall properties and extensibility under water stressed conditions in soils that are nutritionally P-deficient.