A heuristic algorithm for two-machine re-entrant shop scheduling

This paper considers the problem of sequencing n jobs in a two‐machine re‐entrant shopwith the objective of minimizing the maximum completion time. The shop consists of twomachines, M1 and M2 , and each job has the processing route (M1 , M2 , M1 ). An O(n log n)time heuristic is presented which generates a schedule with length at most 4/3 times that ofan optimal schedule, thereby improving the best previously available worst‐case performanceratio of 3/2.

Three-machine shop scheduling with partially ordered processing routes

This paper considers the problem of sequencing n jobs in a three-machine shop with the objective of minimising the maximum completion time. The shop consists of three machines, M1,M2 and M_{3}. A job is first processed on M1 and then is assigned either the route (M2,M_{3}) or the route (M_{3},M2). Thus, for our model the processing route is given by a partial order of machines, as opposed to the linear order of machines for a job shop, or to an arbitrary sequence of machines for an open shop. The main result is on O(nlog n) time heuristic, which generates a schedule with the makespan that is at most 5/3 times the optimum value.

Radiative lifetimes of metastable states of negative ions

We present a technique for measuring the radiative lifetimes of metastable states of negative ions that involves the use of a heavy-ion storage ring. The method has been applied to investigate the radiative decay of the np3 2P1/2 levels of Te–(n=5) and Se–(n=4) and the 3p3 2D state of Si– for which the J=3/2 and 5/2 levels were unresolved. All of these states are metastable and decay primarily by emission of E2 and M1 radiation. Multi Configuration Dirac-Hartree-Fock calculations of rates for the transitions in Te– and Se– yielded lifetimes of 0.45 s and 4.7 s, respectively. The measured values agree well with these predicted values. In the case of the 2D state of Si–, however, our measurement was only able to set a lower limit on the lifetime. The upper limit of the lifetime that can be measured with our apparatus is set by how long the ions can be stored in the ring, a limit determined by the rate of collisional detachment. Our lower limit of 1 min for the lifetime of the 2D state is consistent with both the calculated lifetimes of 162 s for the 2D3/2 level and 27.3 h for the 2D5/2 level reported by O'Malley and Beck and 14.5 h and 12.5 h, respectively, from our Breit-Pauli calculations.

Electron impact excitation of Ar XVII

Energies for the lowest 49 levels among the 1s(2) and 1snl (n = 2-5) configurations of Ar XVII have been calculated using the GRASP code of Dyall et al. (1989, Comput. Phys. Comm., 55, 424). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Furthermore, collision strengths have also been calculated for all the 1176 transitions among the above 49 levels using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2005, Comput. Phys. Commun., in preparation), over a wide energy range up to 580 Ryd. Resonances have been resolved in the threshold region, and effective collision strengths have been obtained over a wide temperature range up to log T-e = 7.2 K. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 0.1%, whereas results for other parameters are probably accurate to better than 20%.

Radiative rates, collision strengths and effective collision strengths for transitions in Mo XXXIV

Radiative rates for electric dipole (E I), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the lowest 60 fine-structure levels of the (1s(2)) 2S(2)2p(5), 2s2p(6), and 2S(2)2p(4)3l configurations of F-like Mo XXXIV have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed over a wide energy range below 3200Ry, using the Dirac Atomic R-matrix Code. Resonances have been resolved in a fine energy mesh in order to calculate the effective collision strengths. Results for radiative rates and excitation rates are presented for all transitions, and for collision strengths for transitions from the lowest three levels to the higher lying levels. The accuracy of the present data is assessed to be similar to 20%.

Energy levels and radiative rates for transitions in Ar XIII, Ar XIV and Ar XV

Energies for 524 levels of Ar XIII, 460 levels of Ar XIV and 156 levels of Ar XV have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 1%, whereas results for other parameters are probably accurate to better than 20%. Additionally, the level lifetimes derived from our radiative rates are in excellent agreement with measured values.

Energy levels and transition probabilities for nitrogen-like Fe xx

Energies of the 700 lowest levels in Fe XX have been obtained using the multiconfiguration Dirac-Fock method. Configuration interaction method on the basis set of transformed radial orbitals with variable parameters taking into account relativistic corrections in the Breit-Pauli approximation was used to crosscheck our presented results. Transition probabilities, oscillator and line strengths are presented for electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transitions among these levels. The total radiative transition probabilities from each level are also provided. Results are compared with data compiled by NIST and with other theoretical work.

Relativistic allowed and forbidden transition probabilities for fluorine-like Fe XVIII

Energy levels and the corresponding transition probabilities for allowed and forbidden transitions among the levels of the ground configuration and first 23 excited configurations of fluorine-like Fe XVIII have been calculated using the multiconfigurational Dirac-Fock GRASP code. A total of 379 lowest bound levels of Fe XVIII is presented, and the energy levels are identified in spectroscopic notations. Transition probabilities, oscillator strengths and line strengths for electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transitions among these 379 levels are also presented. The calculated energy levels and transition probabilities are compared with experimental data.

Dirac-Fock energy levels and transition probabilities for oxygen-like Fe XIX

Multiconfigurational Dirac-Fock calculations are reported for 656 energy levels and the 214 840 electric dipole (E I), electric quadrupole (E2) and magnetic dipole (M1) transition probabilities in oxygen-like Fe xix. The spectroscopic notations as well as the total transition probabilities from each energy level are provided. Good agreement is found with data compiled by NIST.

Energy levels and radiative rates for Li-like Ar XVI and Fe XXIV

Energy levels for transitions among the lowest 24 fine- structure levels belonging to the 1s(2)nl(n greater than or equal to 5) configurations of Li-like Ar XVI and Fe XXIV have been calculated using the fully relativistic GRASP code. Oscillator strengths, radiative rates and line strengths have also been generated among these levels for the four types of transitions: electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2). Comparisons are made for the electric dipole transitions with other available results, and the accuracy of the present data is assessed.

Energy levels, radiative rates, and excitation rates for transitions in OIV

Aims. In this paper we report calculations for energy levels, radiative rates, and excitation rates for transitions in O IV. Methods. The grasp (general-purpose relativistic atomic structure package) and FAC (flexible atomic code) were adopted for calculating energy levels and radiative rates, and the Dirac atomic R-matrix code (DARC) used to determine the excitation rates. Results. Oscillator strengths and radiative rates are reported for all E1, E2, M1, and M2 transitions among the lowest 75 levels of O IV. Additionally, lifetimes are reported for all levels and comparisons made with those available in the literature. Finally, effective collision strengths are reported for all transitions over a wide temperature range below 106 K. Comparisons are made with earlier results and the accuracy of the data is assessed.

Radiative rates and electron impact excitation rates for H-like Ar XVIII

Aims. In this paper we report on calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for
transitions among the lowest 25 levels of the n ≤ 5 configurations of H-like Ar xviii.
Methods. The general-purpose relativistic atomic structure package (grasp) andDirac atomic R-matrix code (darc) are adopted for
the calculations.
Results. Radiative rates, oscillator strengths, and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric
quadrupole (E2), and magnetic quadrupole (M2) transitions among the 25 levels. Furthermore, collision strengths and effective
collision strengths are listed for all 300 transitions among the above 25 levels over a wide energy (temperature) range up to 800 Ryd
(107.4 K).

Energy levels and radiative rates for transitions in B-like to F-like Kr ions (Kr XXXII-XXVIII)

Energy levels, radiative rates, oscillator strengths, line strengths, and lifetimes have been calculated for transitions in B-like to F-like Kr ions, Kr XXXIII-XXVIII. For the calculations, the fully relativistic GRASP code has been adopted, and results are reported for all electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the lowest 125, 236, 272, 226, and 113 levels of Kr XXXII, Kr XXXI, Kr XXX, Kr XXIX, and Kr XXVIII, respectively, belonging to the n

Energy levels, radiative rates and excitation rates for transitions in Ni XI

Aims. In this paper we report calculations for energy levels, radiative rates and excitation rates for transitions in Ni xi.
Methods. The grasp (General-purpose Relativistic Atomic Structure Package) and fac (Flexible Atomic Code) have been adopted
for calculating energy levels and radiative rates, and the Dirac Atomic R-matrix Code (darc) has been used to determine the excitation
rates.
Results. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest
250 levels of Ni xi. Additionally, lifetimes are also reported for all levels. However, results for excitation rates are presented only for
transitions among the lowest 17 levels.

The effect of simultaneous contractions of ipsilateral muscles on changes in corticospinal excitability induced by paired associative stimulation (PAS)

Consideration was given to means of increasing the reliability and muscle specificity of paired associative stimulation (PAS) by utilising the phenomenon of crossed-facilitation. Eight participants completed three separate sessions: isometric flexor contractions of the left wrist at 20% of maximum voluntary contraction (MVC) simultaneously with PAS (20s intervals; 14 min duration) delivered at the right median nerve and left primary motor cortex (MI); isometric contractions at 20% of MVC: and PAS only ( 14 min). Eight further participants completed two sessions of longer duration PAS (28 min): either alone or in conjunction with flexion contractions of the left wrist. Thirty motor potentials (MEPs) were evoked in the right flexor (rFCR) and extensor (rECR) carpi radialis muscles by magnetic stimulation of left M1 Prior to the interventions, immediately post-intervention, and 10 min post-intervention. Both 14 and 28 min of combined PAS and (left wrist flexion) contractions resulted in reliable increases in rFCR MEP amplitude, which were not present in rECR. In the PAS only conditions, 14 min of stimulation gave rise to unreliable increases in MEP amplitudes in rFCR and rECR, whereas 28 min of PAS induced small (unreliable) changes only for rFCR. These results support the conclusion that changes in the excitability of the corticospinal pathway induced by PAS interact with those associated with contraction of the muscles ipsilateral to the site of cortical stimulation. Furthermore, focal contractions applied by the opposite limb increase the extent and muscle specificity of the induced changes in excitability associated with PAS. (C) 2008 Elsevier Ireland Ltd. All rights reserved.