Discrete facility location with nonlinear diseconomies in fixed costs

A discrete facility location problem is formulated where the total fixed cost for establishing the facilities includes a component that is a nonlinear function of the number of facilities being established. Some theoretical properties of the solution are derived when this fixed cost is a convex nondecreasing function of the number of facilities. Based on these properties an efficient bisection heuristic is developed where at each iteration, the classical uncapacitated facility location and/or m-median subproblems are solved using available efficient heuristics.     

On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1))

A quantum algebraU _{p, q} (,H,X _±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardU _{p, q}(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU _{p, q}(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU _{p, q}(,H,X _±) leads to the super-Hopf algebraU _{p, q}(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU _{p, q}(sh(1)) and its universal -matrix.     

Finite-dimensional quantum mechanics of a particle

This paper analyzes the possible implications of interpreting the finitedimensional representations of canonically conjugate quantum mechanical position, and momentum operators of a particle consistent with Weyl's form of Heisenberg's commutation relation as the actual position, and momentum operators of the particle when it is confined to move within a finite spatial domain, and regarding the application of current quantum mechanical formalism based on Heisenberg's relation to such a situation as an asymptotic approximation. In the resulting quantum mechanical formalism the discrete and finite position and momentum spectra of a particle depend on its rest mass and the spatial domain of confinement. Such a finite-dimensional quantum mechanics may be very suitable for describing the physics of particles confined to move within very small regions of space.     

In vivo (31)P MRS study of skeletal muscle metabolism in patients with postpolio residual paralysis

The muscle metabolism of at-rest patients with varying degrees of postpolio residual paralysis (PPRP) was studied and compared with that of controls using in vivo phosphorus magnetic resonance spectroscopy. The phosphocreatine (PCr)/inorganic phosphate (Pi) and PCr/adenosine triphosphate ratios were lower in patients than in controls. Reduction in PCr/Pi suggests abnormalities in oxidative phosphorylation. A significant increase was observed in the phosphomonoester/PCr ratio in patients, indicating the accumulation of intermediary compounds of the glycolytic pathway. Furthermore, the phosphodiester/PCr ratio was also significantly increased in patients. In general, the observed changes in metabolite ratios were found to be related to the degree of residual paralysis, suggesting that metabolic changes are secondary to chronic neurogenic processes. These metabolic alterations appear to be the possible cause of energy deficit and underlying muscle fatigue in PPRP patients. The present results provide an insight into the metabolic impairment and degree of muscle damage in patients with PPRP.     

The dependence of ultrasound contrast agents backscatter on acoustic pressure: theory versus experiment

Experimental investigations have not fully explored the interaction between ultrasound beams and microbubble contrast agents. Moreover theoretical investigations have not solved the problem of the microbubble oscillation. A simple in-vitro system based on a commercial scanner (ATL UM9) was used to insonate (3 MHz transmission) diluted contrast suspensions of Definity and Quantison at different acoustic pressures (0.27-1.52 MPa). The experimental data were referred to a blood mimicking fluid in order to extract an estimate of their scattering cross-section. The results were compared with the solutions of the three main bubble oscillatidn models, Rayleigh-Plesset, Herring and Gilmore. Non-linear solutions of the above models were produced numerically using the Mathematica Package Software. The experiments showed that both agents provided a linear increase in scattering cross-section with increasing acoustic pressure. The thick shelled Quantison provided an increasing number of scatterers with increasing acoustic pressure, which proved that free bubbles leaked out of the shell. At high acoustic pressures both Quantison and Definity scattering cross-sections were almost identical, and were probably that of a free bubble. The Rayleigh-Plesset model provided a scattering cross-section almost independent of acoustic pressure. On the contrary the scattering cross-sections calculated by the Herring and Gilmore models solutions displayed a definite dependence on acoustic pressure of an order higher than one, which is slightly higher than the order of dependence exhibited by the experimental data. However, the increase of the experimentally measured scattering cross-section with acoustic pressure was sharper than the calculated one by the above two models. This is most probably due to the fact that the models simulated damped and not free bubble oscillations. In conclusion the Rayleigh-Plesset model was inadequate in describing the bubble oscillations even at small diagnostic acoustic pressures. The Herring and Gilmore models could simulate the dependence of the scattering cross-section of encapsulated microbubbles on acoustic pressure. However the contribution of free bubble oscillations has still to be modelled.     

Mössbauer study of a ferromagnetic metallic glass: Fe74Co10B16

Amorphous Fe₇₄Co₁₀B₁₆ (METGLAS 2605CO) has been studied in the temperature range of 77 K – 700 K by Mössbauer spectroscopy. Its crystallization temperature is found to be 665 ± 5 K and Curie temperature is estimated to be 760±10 K. The observed rapid decrease in reduced hyperfine fields can be explained well by Handrich's model for amorphous ferromagnets if one assumes a temperature dependent δ, a measure of fluctuations in the exchange interactions in such solids.     

On the estimation of second moment for organic compounds in wide-line pmr: analysis of group geometry

Neutron diffraction data available in the literature have been analyzed statistically to arrive at the ideal geometry for the commonly occurring groups, NH ₄ ⁺ , NH ₃ ⁺ , CH₃, CH₂, and CH; this has yielded optimum experimental values for the bond length and bond angle parameters. They are: N-H distance of 1.030 Å in both NH ₄ ⁺ and NH ₃ ⁺ groups, H-N-H angle of 109.47° and 108.1° respectively in NH ₄ ⁺ and NH ₃ ⁺ and 110.8° for the corresponding X-N-H angle in –NH ₃ ⁺ . For CH₃, CH₂, and CH groups the bond length C-H is 1.090 Å, while the H-C-H and X-C-H angles are respectively 108.2° and 110.5° in CH₃ and 107.2° and 109.3° in CH₂. The importance of using precise values of both bond lengths and bond angles for the ideal geometry when estimating theoretical second moments is emphasized.Contribution No. 564 from the Department of Crystallography and Biophysics, University of Madras, Guindy Campus, Madras-600025, India.