I. Gertner

A new efficient algorithm to compute the two-dimensional discrete Fourier transform

An algorithm is presented for computation of the two-dimensional discrete Fourier transform (DFT). The algorithm is based on geometric properties of the integers and exhibits symmetry and simplicity of realization. Only one-dimensional transformation of the input data is required. The transformations are independent; hence, parallel processing is feasible. It is shown that the number of distinct N-point DFTs needed to calculate N*N-point two-dimensional DFTs is equal to the number of linear congruences spanning the N*N grid. Examples for N=3, N=4, and N=10 are presented. A short APL code illustrating the algorithm is given. >

On the complexity of scheduling problems for parallel/pipelined machines

The problem of optimal scheduling of a job system for two dedicated processors is presented. A machine model with two functional units which can be either sequential or pipelined is considered. The complexity of optimal scheduling for a set of expressions on such machines is investigated. Some previous NP-completeness results are reviewed and several new ones are presented. For one restricted case, a polynomial-time algorithm is described and analyzed. >

Approximation algorithms for scheduling arithmetic expressions on pipelined machines

Abstract Consider a processor which can issue one instruction every machine cycle, but can use its result only d + 1 machine cycles after it has been issued. It is shown that an upper bound for the completion time of an arbitrary list schedule for arbitrary expressions, with possibly common subexpressions, on such machines is greater than the optimum by a factor of 2 − 1 (d + 1) . Then a class of scheduling algorithms, called level algorithms, is defined and analyzed. These algorithms sometimes yield bad schedules which can be made arbitrarily close to the upper bound of list schedules. By extending the leveling algorithm, using the lexicographic order criterion similar to that of Coffman-Grahams algorithm, a better result of 2 − 2 (d + 1) is derived. This bound is asymptotically tight.

Low energy X-ray and γ spectroscopy using silicon pin photodiodes

An energy resolution of 1.43 keV (FWHM) for the 59.55 keV 241Am γ-ray line at 19°C was obtained by using low-cost silicon PIN photodiodes. The dependence of energy resolution on detector and preamplifier temperature was investigated. At −40°C a FWHM of 1.04 keV was reached. Low energy Mn and Ti K X-ray spectra were also taken, and the 5.9 and 4.5 keV peaks were clearly resolved from the noise. Our measurements show that silicon PIN photodiodes are comparable in performance with the best room temperature silicon detectors which are considerably more expensive.

EXPERIMENTAL EVIDENCE FOR LONG-LIVED HEAR2+ RARE-GAS DIMERS

Abstract The first observation of long-lived doubly charged HeAr2+ rare-gas dimers is reported. These dications were obtained in charge-stripping collisions of 850 keV HeAr+ in Ar gas. The mean lifetime for spontaneous dissociation of the 3 He 40 Ar2+ isotope was determined to be larger than about 40 μs using a new experimental technique. The cross-section for collision-induced dissociation of these molecular ions in air was found to be σdiss∼2×10−15 cm2. Calculations of the vibrational state population and mean lifetimes for a few low-lying electronic states indicate that all four low-lying states are very long lived and may be populated in fast charge-stripping collisions.

Methods for measuring mean lifetimes of long lived molecular ions formed in fast collisions

Abstract The direct measurement of the mean lifetime of molecular ions in a fast-beam (0.1–1 MeV) which were produced in collisions with a thin target requires methods which are different from the ones used for metastable atomic cases. This is due to the nature of the molecular ions breakup. The kinetic energy released in the dissociation is sufficient to spread the fragments on a relatively large area on the detector plane, thus special care and appropriate detectors have to be used to ensure the detection of all fragments. Several experimental techniques to determine the mean lifetime of long lived molecular ions are described. They are based on evaluating the ratio of dissociated molecular ions to the non-dissociated ones as a function of the distance they traveled. Measurements of the mean lifetimes of the recently discovered long lived rare gas dimers, NeAr2+ and HeNe2+ are used to describe these methods.

Formation and mean lifetime measurements of the long-lived doubly charged HeNe2+ rare-gas dimer

Abstract The first observation of a long-lived doubly charged HeNe 2+ rare-gas dimer is reported. This dication was obtained in charge-stripping collisions of 900 keV HeNe + and Ar. The mean lifetime of HeNe 2+ , τ = 184 ± 32 ns, was determined by measuring the yield of its He fragments, which have dissociated after passing the analyzer, as a function of the distance between the target cell and analyzer exits. Theoretical calculations of the 1 Σ + ground state indicate no bound vibrational states for this shallow potential curve. Further calculations are needed to determine the long-lived electronic state which is most likely an excited state.

Long lived CH2+ and CD2+ dications

Abstract A search for long lived CH 2+ and CD 2+ dications formed in fast charge stripping collisions of CH + and CD + on Ar was conducted. An experimental method based on the detection of the H (or D) fragments of the dication was developed, in order to eliminate possible confusion with 13 C 2+ for the first and 14 N 2+ for the latter. The flight time of these dications through the apparatus is about 70 ns, well below the 3 μs time associated with earlier observations of CH 2+ . Our measurements indicate that no long lived states of either of these dications are formed in fast charge stripping collisions. However, this result does not exclude the possibility that long lived states, like the excited A 2 Σ + metastable state, are populated in slow charge stripping collisions.

H+ and He+ spectroscopy using silicon pin photodiodes

Abstract Silicon PIN photodiodes have been used in detecting H + and He + ions from a 1 MeV accelerator. Energy resolutions (FWHM) from 2.0 keV (at 16 keV) to 4.7 keV (at 1 MeV) for H + and from 3.4 keV (at 22 keV) to 9.8 keV (at 700 keV) for He + have been measured at room temperature. Resolution measurements over this energy range using a premium PIPS detector have also been performed. A comparison between the two detectors shows that the photodiodes exhibit better energy resolution over the whole energy range for H + , and comparable resolution for He + . It is argued that the resolution of the photodiode can be further improved by manufacturing a device with thinner entrance window.

Formation of He20 and He22+ molecules by charge exchange collisions of He2+ ions in the sub-MeV region

The six dissociation and two charge exchange channels populated by single collisions of He2+ molecular ions have been studied at 400 and 800 keV. The use of the grid method enabled the separation of undissociated and dissociated channels having equal energies and charges. Both He20 and He22+ molecules have been observed.