ALBERT

Notes: The Su(3) limit intrinsic states in the interacting boson model (IBM) are given by the group theoretical method. A method to calculate the physical states from the intrinsic states is given. Using this method, the physical states of the SU(3) limit ground state band are given completely. Some preliminary results are also obtained for beta and gamma band states. The wavefunctions obtained are expressed in terms of the five building blocks of the IBM wave functions belonging to Sun, Zhang, and Feng. In the SU(3) limit it is found that the building block T+d, which represents three d bosons coupled to zero angular momentum, appears even in the ground state band wavefunctions. The wavefunctions have very interesting physical implications.

Notes: We present new and useful "external potential" forms of the two-body Dirac equations of constraint dynamics for combined scalar, vector, pseudoscalar, pseudovector, and tensor interactions. These equations have potential applications in two-body problems for bound states in meson spectroscopy and phase shift analysis in nucleon–nucleon scattering. Toward this end, we derive their coupled Schrödinger-like forms using matrix techniques and obtain the corresponding radial equations to these forms from scalar and vector spherical harmonic decompositions. © 1998 American Institute of Physics.

Notes: : Pressure is increasing in the western United States to reallocate water from irrigated agriculture to other competitive uses. Since water is normally allocated through water rights and not necessarily by the price system, the question of economic efficiency is a continual concern. Study results show that returns per acre-foot of water used in western irrigation are quite high and are closely tied to the livestock industry. Returns per acre-foot of water used for crops ranged from $60 to $1,500. When water was used to support livestock, returns per acre-foot ranged from $100 to $600. Clearly, losses of water supply that reduced irrigation production could also lower farm income significantly. Estimated returns also show what alternative uses would have to pay for water under competitive market conditions. Production elasticities are also shown for various states.

Notes: The feasibility of doing multiloop calculations in the noncovariant light-cone gauge nμAaμ=0, n2=0, is investigated by evaluating various Feynman integrals arising in a two-loop Yang–Mills self-energy. Application of a consistent prescription for (q ⋅ n)−1 is essential.

Notes: Acclimation of photosynthesis to growth at elevated CO2 concentration varies markedly between species. Species functionally classified as stress-tolerators (S) and ruderals (R), are thought to be incapable, or the least capable, of responding positively in terms of growth to elevated [CO2]. Is this pattern of response also apparent in leaf photosynthesis of wild S- and R-strategists? Acclimatory loss of a photosynthetic and growth response to elevated [CO2] is assumed to reflect limitation on capacity to utilize additional photosynthate. The doubling of pre-industrial global [CO2] is expected to coincide with a 3 °C increase in mean temperature which could stimulate growth; will photosynthetic capacity at elevated [CO2] be greater when the concurrent temperature increase is simulated? Five species from natural grassland of NW Europe and of contrasting ecological strategy were grown in hemispherical greenhouses, environmentally controlled to track the external microclimate. Within a replicated design, plants were grown at (i) current ambient [CO2] and temperature, (ii) elevated [CO2] (ambient + 340 μmol mol–1) and ambient temperature, (iii) ambient [CO2] and elevated temperature (ambient + 3 °C), or (iv) elevated [CO2] and elevated temperature. After 75–104 days, the CO2 response of light-saturated rates of photosynthesis (Asat) was analysed in controlled-environment cuvettes in a field laboratory. There was no acclimatory loss of photosynthetic capacity with growth in elevated [CO2] or elevated temperature over this period in Poa alpina (S), Bellis perennis (R) or Plantago lanceolata (mixed C-S-R strategist), and a significant (P ??bl 0.05) increase in capacity in Helianthemum nummularium (S) and Poa annua (R). Photosynthetic rates of leaves grown and measured in elevated [CO2] were therefore significantly higher than rates for leaves grown and measured in ambient [CO2], for all species. With the exception of Poa alpina, stomatal conductance and stomatal limitation on Asat showed no acclimatory response to growth in elevated [CO2].Carboxylation efficiency, determined from the initial slope of the response of Asat to intercellular CO2 concentration was significantly increased by elevated [CO2] and elevated temperature in H.nummularium, implying a possible increase in in vivo RubisCO activity. Increased carboxylation efficiency of this species was also reflected by an increase in the CO2- and light-saturated rates of photosynthesis, indicating an increased capacity for regeneration of the primary CO2 acceptor in photosynthesis. The results show that R-strategists and slow-growing S-strategists, are inherently capable of large increases in leaf photosynthetic capacity with growth in elevated [CO2] in contrast to expectations from growth studies. With the exception of P.annua, where there was a significant negative interaction between CO2 and temperature, concurrent increase in growth temperature had little effect on this pattern of response.

Notes: Let there be several identical deposits of an exhaustible, non-renewable resource, the working of each deposit entailing a set-up cost but no other costs. It is found that the optimal path of extraction dictates that the deposits must be removed in strict sequence with discontinuities of marginal benefit at transition points. Moreover, the average rate of increase of marginal benefit is less than the rate of interest. These results embellish Hotelling's rule relating to optimal methods of resource extraction.