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  • 1
    Electronic Resource
    Electronic Resource
    An operator analysis for the Schrödinger, Klein–Gordon, and Dirac equations with a Coulomb potential (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 858-866 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An operator analysis is presented that provides a unified treatment of the Schrödinger (S), Klein–Gordon (KG), and Dirac (D) equations with a Coulomb potential. The analysis uses energy shift operators that factorize an appropriate radial equation. This radial equation is based on standard results and a recent formulation of the Dirac–Coulomb problem [J. Y. Su, Phys. Rev. A 32, 3251 (1985)]. The shift operators yield energy eigenvalues and a formula that contains normalized, radial coordinate-space wave functions for the S, KG, and D equations. Formulas that contain expectation values for the S, KG, and D equations are obtained by applying the hypervirial theorem and the Hellmann–Feynman theorem to the radial equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528353
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  • 2
    Electronic Resource
    Electronic Resource
    Factorizations of vector operators for the isotropic harmonic oscillator in an angular momentum basis (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2650-2654 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The factorization of four vector operators, D±(ω) and D±(−ω), which occur in a representation-independent, spectrum-generating algebra for the three-dimensional, isotropic harmonic oscillator in an angular momentum basis, is considered (ω is the angular frequency of the oscillator). The D±(ω) are quantum-mechanical analogs of the classical vectors (1(minus-plus)iLˆ×)Fc (ω), where Fc(ω)=−Mωr×L+pL is constant in a frame rotating with angular velocity ωLˆ. It is shown that these four vector operators can be factorized in two different ways to yield operators that, apart from their dependence on a constant of the motion (L2), are linear in either p or r. In this way 20 abstract operators are obtained. The properties of these operators are discussed: (i) Twelve are ladder operators for the quantum numbers l, and l and m, in the eigenkets ||lm〉 of L2 and Lz. In linearized, differential form six of these operators are ladder operators for the spherical harmonics in the coordinate representation, while the other six are the corresponding operators in the momentum representation. (ii) The remaining eight operators factorize linear combinations of the Hamiltonian and the dimension operator. In linearized, differential form four of these operators are ladder operators for energy and angular momentum in the radial part of the coordinate-space wave functions, while the other four are the corresponding operators in the momentum representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527757
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  • 3
    Electronic Resource
    Electronic Resource
    Canopy structure, light microclimate and leaf gas exchange of Quercus coccifera L. in a Portuguese macchia: measurements in different canopy layers and simulations with a canopy model (1986)
    Springer
    Trees 1 (1986), S. 25-41 
    Details
    ISSN: 1432-2285
    Keywords: Canopy structure ; Quercus coccifera ; Photosynthesis ; Transpiration ; Simulation model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The structural characteristics of a diverse array of Quercus coccifera canopies were assessed and related to measured and computed light attenuation, proportion of sunlit foliage, foliage temperatures, and photosynthesis and diffusive conductance behavior in different canopy layers. A canopy model incorporating all components of shortwave and longwave radiation, and the energy balance, conductance, and CO2 and H2O exchanges of all leaf layers was developed and compared with measurements of microclimate and gas exchange in canopies in four seasons of the year. In the denser canopies with a leaf area index (LAI) greater than 5, there is little sunlit foliage and the diffuse radiation (400–700 nm) is attenuated to 5% or less of the global radiation (400–700 nm) incident on the top of the canopy. Foliage of this species is nonrandomly distributed with respect to azimuth angle, and within each canopy layer, foliage azimuth and inclination angles are correlated. A detailed version of the model which computed radiation interception and photosynthetic light harvesting according to these nonrandom distributions indicated little difference in whole-canopy gas exchange from calculations of the normal model, which assumes random azimuth orientation. The contributions of different leaf layers to canopy gas exchange are not only a function of the canopy microclimate, but also the degree to which leaves in the lower layers of the canopy exhibit more shade-leaf characteristics, such as low photosynthetic and respiratory capacity and maximal conductance. On cloudless days, the majority of the foliage in a canopy of 5.4 LAI is shaded —70%–90% depending on the time of year. Yet, the shaded foliage under these conditions is calculated to contribute only about one-third of the canopy carbon gain. This contribution is about the same as that of the upper 13% of the canopy foliage. Computed annual whole-canopy carbon gain and water use are, respectively, 60% and 100% greater for a canopy of 5 LAI than for one of 2 LAI. Canopy water-use efficiency is correspondingly less for the canopy of 5 LAI than for that of 2 LAI, but most of this difference is apparent during the cool months of the year, when moisture is more abundant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00197022
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  • 4
    Electronic Resource
    Electronic Resource
    Rapid field determination of photosynthetic capacity of cut spruce twigs (Picea abies) at saturating ambient CO2 (1986)
    Springer
    Trees 1 (1986), S. 70-77 
    Details
    ISSN: 1432-2285
    Keywords: Forest decline ; Photosynthetic capacity ; Picea abies ; Stomatal conductance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Routine field determination of the parameters characterizing the activity of the photosynthetic apparatus is often difficult when attached branches of tall trees have to be used for gas exchange measurement. If severed twigs could be used, determining these parameters would be greatly facilitated. Because stomatal conductance changes when twigs or leaves are detached, CO2 assimilation is usually altered. Thus, measurements made at ambient CO2 concentration fail to accurately assess the activity of the photosynthetic apparatus because photosynthetic rates greatly depend on the supply of carbon dioxide. However, when photosynthetic carboxylation reactions are saturated by increased CO2 partial pressure in the mesophyll, CO2 assimilation rates no longer depend on instantaneous stomatal conductance, as shown by gas exchange measurements of spruce (Picea abies) twigs prior to and following detachment. Because net photosynthesis following detachment at saturating CO2 remains constant for a minimum of 15 min, photosynthetic measurements of severed twigs may be reliable. This length of time is sufficient for detaching and recutting the twig, assembling a portable minicuvette system, re-establishing steady-state conditions with the gas analyser system, and reading the data over a reasonable period of time. The method described measures the maximal photosynthetic CO2 assimilation of spruce needles of a single age-class from detached spruce twigs under the following conditions: saturating light, saturating external CO2-partial pressure, standardized temperature and air humidity in the field. The method is applicable as a routine procedure to characterize the status of the photosynthetic apparatus of spruce trees that may be damaged in the process of forest decline.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00197027
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  • 5
    Electronic Resource
    Electronic Resource
    Stomatal conductance and transpiration of the two faces of Acacia phyllodes (1987)
    Springer
    Trees 1 (1987), S. 110-122 
    Details
    ISSN: 1432-2285
    Keywords: Phyllodes ; Stomatal conductance ; Transpiration ; Water potential ; Acacia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The daily course of stomatal conductance and transpiration was monitored on each separate face of vertical phyllodes of various acacias. The selected phyllodes had a north-south orientation so that one side faced eastwards and the other westwards. The principal measurements were made on Acacia longifolia and A. melanoxylon in Portugal in late summer and autumn, and additional measurements were made on A. ligulata and A. melanoxylon in Australia. In Portugal, irrespective of soil moisture status, conductance showed on early morning maximum with a subsequent gradual decline and sometimes a subsidiary peak in the late afternoon. Maximum conductances appeared to be a function of soil moisture status, whereas the decline in conductance in the late morning and afternoon was correlated with changes in phyllode-to-air vapour pressure deficits rather than changes in phyllode water status. The relationship of transpiration to phyllode water potential did not appear to be influenced by soil moisture status, although transpiration was less in drier soils and in the afternoons, this latter factor contributing to a marked hysteresis in the relationship. The opposing faces of the phyllodes exhibited a high degree of synchrony, showing parallel stomatal opening and closing, despite their large differences in irradiance. Stomatal conductance tended to be higher on the eastern faces in the morning and lower in the afternoon. In A. longifolia the daily average of relative conductance was much the same for both faces, but in A. melanoxylon that of the eastern face was higher and was retained even when the normal orientation of the phyllodes was reversed by turning them through 180°. Synchrony must be achieved by the stomata of both sides responding to common environmental or endogenous signals which are perceived by both surfaces with equal sensitivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00203579
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  • 6
    Electronic Resource
    Electronic Resource
    Photosynthetic performance, chloroplast pigments, and mineral content of various needle age classes of spruce (Picea abies) with and without the new flush: an experimental approach for analysing forest decline phenomena (1989)
    Springer
    Trees 3 (1989), S. 161-172 
    Details
    ISSN: 1432-2285
    Keywords: Forest decline ; Picea abies ; Mineral deficiency ; Photosynthetic performance ; Air pollution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Damage in the older needles of Norway spruce [Picea abies (L.) Karst.] in the Fichtelgebirge (NE Bavaria, FRG) appears to result primarily from nutrient imbalances rather than from direct effects of air pollutants on the mesophyll of the needles. Support for this conclusion was obtained by altering the nutrition of older needles through the removal of terminal buds on several branches from a damaged and an undamaged spruce tree in spring. Various photosynthetic parameters, as well as the chloroplast pigment and nutrient concentrations, of 1- to 3-year-old needles on manipulated branches were compared with those of branches on which the new flush was allowed to develop during the course of the growing period. Removal of terminal buds affected only the 1-year-old needles. Elimination of the new flush resulted in a higher Ca and Mn content of the needles of the undamaged tree. This treatment also resulted in an increase of the photosynthetic capacity (under saturating light and CO2 conditions), carboxylation and light use efficiency, as well as net photosynthesis under natural conditions of the 1-year-old needles on the yellow chlorotic tree. This was accompanied by higher chlorophyll concentrations and an increase in Mg, Ca, Mn, and Zn content, and no visible signs of chlorosis developed in the experiment. By contrast, the needles of twigs in which the new flush was allowed to develop exhibited reductions in mineral content in the middle of the year. This was especially true for the elements Mg and Ca, and was accompanied by needle chlorosis and a depression of the capacity of photosynthesis. Thus it appears that there is a close relationship between the development of needle damage and nutrient imbalances in spruce. The retranslocation of elements from the 1-year-old needles to the new flush seems to play a major role in the development of needle bleaching. This approach thus supports the hypothesis described above and confirms a preliminary test with a similar experimental design, which had been conducted earlier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00226652
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  • 7
    Electronic Resource
    Electronic Resource
    Stomatal aperture, photosythesis and water fluxes in mesophyll cells as affected by the abscission of leaves. Simultaneous measurements of gas exchange, light scattering and chlorphyll fluorescence (1986)
    Springer
    Planta 167 (1986), S. 554-562 
    Details
    ISSN: 1432-2048
    Keywords: Chlorophyll fluorescence ; Light scattering ; Photosynthesis ; Transpiration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Carbon dioxide exchange, transpiration, chlorophyll fluorescence and light scattering of leaves of Lycopersicom esculentum, Helianthus annuus and Arbutus unedo were measured simultaneously before and after abscission of leaves. Scattering of a weak green measuring beam was used to monitor water fluxes across the thylakoid membranes of the mesophyll. When leaves were cut under water, stomata initially closed partially and then occasionally exhibited distinct regulatory oscillations. As stomata closed, light scattering decreased indicating water influx into the mesophyll. Stomatal oscillations were accompanied, with small but noticeable phase shifts, by oscillations of water fluxes at the thylakoid level. These fluxes could be distinguished from the water fluxes accompanying light-dependent ion pumping across the thylakoids by the concomitant chlorophyll fluorescence signals. The latter record energy-dependent ion fluxes in addition to redox changes of the electron-transport chain. As stomata closed partially after cutting a leaf under water, photosynthesis decreased. In Arbutus unedo and Helianthus annuus leaves, transient stomatal closure was insufficient to account for transient inhibition of photosynthesis which appeared to be brought about by transfer of an inhibitory solute through the petiole into the mesophyll. This solute also stimulated respiration in the dark. When leaves were cut in air, stomata opened transiently (Iwanoff effect) before wilting enforced closure. Photosynthesis followed the stomatal responses, increasing during opening and decreasing during closure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00391232
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  • 8
    Electronic Resource
    Electronic Resource
    Effects of temperature at constant air dew point on leaf carboxylation efficiency and CO2 compensation point of different leaf types (1985)
    Springer
    Planta 166 (1985), S. 81-88 
    Details
    ISSN: 1432-2048
    Keywords: Carboxylation efficiency ; Compensation point (CO2) ; Photosynthesis (temperature, humidity) ; Sclerophyll ; Transpiration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The effect of temperature on photosynthesis at constant water-vapor pressure in the air was investigated using two sclerophyll species, Arbutus unedo and Quercus suber, and one mesophytic species, Spinacia oleracea. Photosynthesis and transpiration were measured over a range of temperatures, 20–39° C. The external concentration of CO2 was varied from 340 μbar to near CO2 compensation. The initial slope (carboxylation efficiency, CE) of the photosynthetic response to intercellular CO2 concentration, the CO2 compensation point (Γ), and the extrapolated rate of CO2 released into CO2-free air (R i) were calculated. At an external CO2 concentration of 320–340 μbar CO2, photosynthesis decreased with temperature in all species. The effect of temperature on Γ was similar in all species. While CE in S. oleracea changed little with temperature, CE decreased by 50% in Q. suber as temperature increased from 25 to 34° C. Arbutus unedo also exhibited a decrease in CE at higher temperatures but not as marked as Q. suber. The absolut value of R i increased with temperature in S. oleracea, while changing little or decreasing in the sclerophylls. Variations in Γ and R i of the sclerophyll species are not consistent with greater increase of respiration with temperature in the light in these species compared with S. oleracea.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00397389
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  • 9
    Electronic Resource
    Electronic Resource
    Seasonal and diurnal courses of water relations of the arido-active plant Hammada scoparia in the Negev desert (1975)
    Springer
    Oecologia 21 (1975), S. 175-192 
    Details
    ISSN: 1432-1939
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The photosynthesizing branches of Hammada scoparia, one of the typical dwarf shrubs of the Negev desert, undergo a seasonal change from succulent to xeromorphic anatomy. This trend is accompanied by a marked decrease of water content and of total water Ψ plant and osmotic Ψ π plant potential. Irrigated plants do not show such transitions. The daily courses of Ψ plant and Ψ π plant showed minima around noon and a tendency for maxima before sunrise. Turgor pressure Ψ p plant reached minima around noon and became negative (until ca.-10 bars). Generally, Ψ plant decreases with increasing water vapour concentration difference between plant and air (WD) in the first half of the day, and in the second half the reversal of this trend occurs. Mostly smaller increments of Ψ plant were correlated with larger increases in WD which lead to the conclusion that stomates closed enough to maintain transpiration at a constant value. Non-irrigated and irrigated plants showed different hysteresis loops of relation between Ψ plant and WD. Regulatory reduction of transpiration appears largely independently of Ψ plant which is in spring and with irrigated plants on a high level, with non-irrigated plants in summer on a low level. In summer the continous but decreasing drop of Ψ plant with increasing WD was interpreted as caused by a change in soil or root resistance. Independent of the seasonal state and of the Ψ plant level, H. scoparia regulates its water status within limited ranges of Ψ p plant changes: the irrigated plants on a higher level, the non-irrigated on a lower level of Ψ p plant . The water contents of the tissues of H. scoparia are linearily related to Ψ plant as well as Ψ p plant . Steeper slopes with non-irrigated plants in summer than with spring palnts and with irrigated plants during the whole season signify that in the latter a certain increment in turgor pressure corresponds to a large gain in water content while in the non-irrigated summer plants it varies only little for an identical change in Ψ p plant . This behaviour of non-irrigated wild plants apparently is due to the change of the elastic properties of the tissues in the assimilating branches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00345559
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  • 10
    Electronic Resource
    Electronic Resource
    The role of air humidity and temperature in controlling stomatal resistance of Prunus armeniaca L. under desert conditions (1975)
    Springer
    Oecologia 19 (1975), S. 303-314 
    Details
    ISSN: 1432-1939
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Measurements of CO2 and water vapor exchange were performed on Prunus armeniaca L. with humidity- and temperature-controlled chambers under the climatic conditions of a desert habitat. In apricot, the stomatal response to changes in temperature and water-vapor concentration difference between leaf and air (WD) significantly determined the rates of gas exchange during the day (parts I and II). The effect of climate-controlled stomatal response on the transpiration/net photosynthesis (T/P)-ratio was analyzed and simulated using experiments conducted at constant temperature and/or humidity conditions for input parameters. The measured values of the T/P-ratio at naturally varying conditions of humidity and temperature were compared with calculated results of a model in which it was assumed, (1) that stomata and photosynthetic activity are not affected by air humidity and temperature, (2) that the stomata only respond with a constant photosynthetic activity to changes in WD, and (3) that the stomata respond to both, leaf temperature and air humidity with a constant photosynthetic activity. These simulations facilitated an analysis of the naturally observed changes in the T/P-ratio. The calculated T/P-ratios were very small if the simulation assumed that stomata only respond to WD at a constant photosynthetic activity. These low predicted values of the T/P-ratio were not obtained under natural conditions, since an increase in WD during the day was correlated with a temperature rise which tended to open stomata and change the photosynthetic activity. Humidity induced stomatal closure did appear to substantially reduce T/P-ratios. The measured T/P-ratio changed considerably during the year. The lowest T/P-ratios were obtained in the middle of the dry season at a time when stomata responded strongly to air humidity and when optimum of photosynthesis was reached at high temperatures. The daily average T/P-ratio calculated from the daily sum of P and T showed little change during the seasons. A high T/P-ratio was also observed at reduced rates of gas exchange. The T/P-ratios of apricot were compared with different species in different environments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00348106
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