On the direct parallel solution of systems of linear equations: New algorithms and systolic structures

The paper presents two new algorithms for the direct parallel solution of systems of linear equations. The algorithms employ a novel recursive doubling technique to obtain solutions to an nth-order system in n steps with no more than 2n(n −1) processors. Comparing their performance with the Gaussian elimination algorithm (GE), we show that they are almost 100% faster than the latter. This speedup is achieved by dispensing with all the computation involved in the back-substitution phase of GE. It is also shown that the new algorithms exhibit error characteristics which are superior to GE. An n(n + 1) systolic array structure is proposed for the implementation of the new algorithms. We show that complete solutions can be obtained, through these single-phase solution methods, in 5n−log2n−4 computational steps, without the need for intermediate I/O operations.

Formative time lags in nitrogen, oxygen and dry air In crossed electric and magnetic fields

Formative time lags in nitrogen, oxygen, and dry air are measured with and without a magnetic field over a range of gas pressures (0.05 ' p ' 20.2 torr 5 kPa to 2 MPa, electric field strengths (1.8xO14 EEs 60xlO V m l) and magnetic field strengths (85xl0-4 < B ' 16x10-2 Tesla). For experiments below the Paschen minimum, the electrodes are designed to ensure that breakdown occurs over longer gaps and for experiments above the Paschen minimum, a coaxial cylindrical system is employed. The experimental technique consists of applying pulse voltages to the gap at various constant values of E/p and B/p and measuring the time lags from which the formative time lags are separated. In the gases studed, formative time lags decrease on application of a magnetic field at a given pressure for conditions below the Paschen minimum. The voltages at which the formative time lags remain the same without and with magnetic fields are determined, and electron molecule collision frequencies (v/p) are determined using the Effective Reduced Electric Field [EREF] concept. With increasing ratio of E/p in crossed fields, v/p decreases in all the three gases. Measurements above the Paschen minimum yield formative time lags which increase on application of a magnetic field. Formative time lags in nitrogen in ExB fields are calculated assuming an average collision frequency of 8.5x109 sec-1 torr 1. It is concluded that the EREF concept can be applied to explain formative time lags in ExB fields.

Preparation, structure, and magnetic properties of isostructural La3MAlS7 and La3MFeS7 (M = Mg, Mn, Fe, Co, Ni, or Zn)

A series of quaternary metal sulfides of the general formula La3MM′S7 (M = Mn, Fe, Co; M′ = Al and M = Mg, Mn, Fe, Co, Ni; M′ = Fe) consisting of linear chains of face shared MS6 octahedra and isolated M′S4 tetrahedra has been prepared and studied. The aluminium compounds La3MAlS7 (M = Mn, Fe, Co) exhibit linear chain antiferromagnetism. Magnetic behavior of other La3MFeS7 sulfides has been examined in detail. The magnetic susceptibility of La3MgFeS7 shows that tetrahedral site Fe3+ undergoes a transition from Image to S = 2 spin state around 150 K.

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

Push-pull ethylenes: the structures of 3-(2-imidazolidinylidene)-2,4-pentanedione (I), C8H12N2O2, and 3-(1,3-dimethyl-2-imidazolidinylidene)-2,4-pentanedione trihydrate (II), C10H16N2O2.3H2O

(I): Mr= 168, triclinic, P1, Z=2, a= 5.596 (2), b = 6.938 (3), c = 10.852 (4) A, ~t= 75.64 (3), fl= 93.44 (3), ),= 95.47 (3) °, V= 406.0A 3, Din= 1.35 (by flotation using carbon tetrachloride and n-hexane), D x= 1.374 Mg m -3, g(Mo Kct, 2 = 0.7107 A) = 1.08 cm -l, _F(000) = 180, T= 293 K. (II): Mr= 250, triclinic, P1, Z= 2, a = 7.731(2), b=8.580(2), c=11.033(3)A, a= 97-66 (2), fl= 98.86 (2), y= 101.78 (2) °, V= 697.5 A 3, D m = 1.18 (by flotation using KI solution), Dx= 1.190Mgm -3, g(MoKa, 2=0.7107A)= 1.02 cm -1, F(000) = 272, T= 293 K. Both structures were solved by direct methods and refined to R = 4.4% for 901 reflexions for (I) and 5.7% for 2001 reflexions for (II). The C=C bond distances are 1.451 (3) A in (I) and 1.468 (3)A in (II), quite significantly longer than the C=C bond in ethylene [1.336 (2).~; Bartell, Roth, Hollowell, Kuchitsu & Young (1965). J. Chem. Phys. 42, 2683-2686]. The twist angle about the C=C bond in (II) is 72.9 (5) ° but molecule (I) is essentially planar, the twist angle being only 4.9 (5) ° .

The structures of the ammonium halides

A comparison with the alkali halides suggests that all the ammonium halides should occur in the NaCl centre-of-mass structure. Experimentally, at room temperature and atmospheric pressure, only NH4I crystallizes in this structure, while NH4F is found in the ZnO structure, and NH4C1 and NH4Br occur in the CsCl structure. We show that a distributed charge on the NH4+ ion can explain these structures. Taking charges of + 0.2e on each of the five atoms in NH4+, as suggested by other studies, we have recomputed the Madelung energy in the cases of interest. A full ionic theory including electrostatic, van der Waals and repulsive interactions then explains the centre-of-mass structures of all the four ammonium halides. The thermal and pressure transitions are also explained reasonably well. The calculated phase diagram of NH4F compares well with experiment. Barring the poorly understood NH4F(II) phase, which is beyond the scope of this work, the other features are in qualitative agreement. In particular, the theory correctly predicts a pressure transition at room temperature from the ZnO structure directly to the CsCl structure without an intermediate NaCl phase. A feature of our approach is that we do not need to invoke hydrogen bonding in NH4F.

Determination of the magnetic moment by QCD sum rules

The magnetic moment of the Λ hyperon is calculated using the QCD sum-rule approach of Ioffe and Smilga. It is shown that μΛ has the structure μΛ=(2/3(eu+ed+4es)(eħ/2MΛc)(1+δΛ), where δΛ is small. In deriving the sum rules special attention is paid to the strange-quark mass-dependent terms and to several additional terms not considered in earlier works. These terms are now appropriately incorporated. The sum rule is analyzed using the ratio method. Using the external-field-induced susceptibilities determined earlier, we find that the calculated value of μΛ is in agreement with experiment.

Magnetic properties of quasi-two-dimensional La2NiO4

Magnetic susceptibility studies on single crystals of nearly stoichiometric La2NiO4 with the applied field both parallel and perpendicular to the c axis show a transition at 204 K below which two-dimensional canted antiferromagnetic order seems to exist. This oxide also undergoes a transition from isotropic to anisotropic susceptibility near 100 and 250 K.

Gluon-field contribution in QCD sum rules for the magnetic moments of the nucleons

The Wilson coefficient corresponding to the gluon-field strength GμνGμν is evaluated for the nucleon current correlation function in the presence of a static external electromagnetic field, using a regulator mass Λ to separate the high-momentum part of the Feynman diagrams. The magnetic-moment sum rules are analyzed by two different methods and the sensitivity of the results to variations in Λ are discussed.

X-ray Studies on Crystalline Complexes Involving Amino Acids and Peptides. XIII. Effect of Chirality on Molecular Aggregation: The Crystal Structures of L-Arginine D-Aspartate and L-Arginine D-Glutamate Trihydrate

The crystal structures of (1) L-arginine D-asparate, C6HIsN40~.C4H6NO4 [triclinic, P1, a=5.239(1), b=9.544(1), c=14.064(2)A, a=85"58(1), /3=88.73 (1), ~/=84.35 (1) °, Z=2] and (2) L-arginine D-glutamate trihydrate, C6H15N40~-.CsHsNO4.3H20 [monoclinic, P2~, a=9.968(2), b=4.652(1), c=19.930 (2) A, fl = 101.20 (1) °, Z = 2] have been determined using direct methods. They have been refined to R =0.042 and 0.048 for 2829 and 2035 unique reflections respectively [I>2cr(I)]. The conformations of the two arginine molecules in the aspartate complex are different from those observed so far in the crystal structures of arginine, its salts and complexes. In both complexes, the molecules are organized into double layers stacked along the longest axis. The core of each double layer consists of two parallel sheets made up of main-chain atoms, each involving both types of molecules. The hydrogen bonds within each sheet and those that interconnect the two sheets give rise to EL-, DD- and DE-type head-to-tail sequences. Adjacent double layers in (1) are held together by side-chain-side-chain interactions whereas those in (2) are interconnected through an extensive network of water molecules which interact with sidechain guanidyl and carboxylate groups. The aggregation pattern observed in the two LD complexes is fundamentally different from that found in the corresponding EL complexes.

Electrical, structural and magnetic properties of polyaniline/pTSA-TiO2 nanocomposites

Polyaniline (PANI)/para-toluene sulfonic acid (pTSA) and PANI/pTSA-TiO2 composites were prepared using chemical method and characterized by infrared spectroscopy (IR), powder X-ray diffraction (XRD), scanning electron microscopy (SEM). The electrical conductivity and magnetic properties were also measured. In corroboration with XRD, the micrographs of SEM indicated the homogeneous dispersion of TiO nanoparticles in bulk PANI/pTSA matrix. Conductivity of the PANI/pTSA-TiO2 was higher than the PAN[/pTSA, and the maximum conductivity obtained was 9.48 (S/cm) at 5 wt% of TiO2. Using SQUID magnetometer, it was found that PANI/pTSA was either paramagnetic or weakly ferromagnetic from 300 K down to 5 K with H-C approximate to 30 Oe and M-r approximate to 0.015 emu/g. On the other hand,PANI/pTSA-TiO2 was diamagnetic from 300 K down to about 50 K and below which it was weakly ferromagnetic. Furthermore, a nearly temperature-independent magnetization was observed in both the cases down to 50 K and below which the magnetization increased rapidly (a Curie like susceptibility was observed). The Pauli susceptibility (chi(pauli)) was calculated to be about 4.8 X 10(-5) and 1.6 x 10(-5)emug(-1) Oe(-1) K for PANI/pTSA and PANI/pTSA-TiO2, respectively.

Chemical synthesis and structure elucidation of bovine K-casein (1-44)

The caseins (αs1, αs2, β, and κ) are phosphoproteins present in bovine milk that have been studied for over a century and whose structures remain obscure. Here we describe the chemical synthesis and structure elucidation of the N-terminal segment (1–44) of bovine κ-casein, the protein which maintains the micellar structure of the caseins. κ-Casein (1–44) was synthesised by highly optimised Boc solid-phase peptide chemistry and characterised by mass spectrometry. Structure elucidation was carried out by circular dichroism and nuclear magnetic resonance spectroscopy. CD analysis demonstrated that the segment was ill defined in aqueous medium but in 30% trifluoroethanol it exhibited considerable helical structure. Further, NMR analysis showed the presence of a helical segment containing 26 residues which extends from Pro8 to Arg34. This is the first report which demonstrates extensive secondary structure within the casein class of proteins.

CBCT-guided radiotherapy for locally advanced head and cancer: dosimetric impact of weight loss on VMAT and IMRT plans for selected organs at risk structures (OARs)

Purpose: It is common for head and neck patients to be affected by time trend errors as a result of weight loss during a course of radiation treatment. The objective of this planning study was to investigate the impact of weight loss on Volumetric Modulated Arc Therapy (VMAT) as well as Intensity modulated radiation therapy (IMRT) for locally advanced head and neck cancer using automatic co-registration of the CBCT. Methods and Materials: A retrospective analysis of previously treated IMRT plans for 10 patients with locally advanced head and neck cancer patients was done. A VMAT plan was also produced for all patients. We calculated the dose–volume histograms (DVH) indices for spinal cord planning at risk volumes (PRVs), the brainstem PRVs (SC+0.5cm and BS+0.5cm, respectively) as well as mean dose to the parotid glands. Results: The results show that the mean difference in dose to the SC+0.5cm was 1.03% and 1.27% for the IMRT and VMAT plans, respectively. As for dose to the BS+0.5, the percentage difference was 0.63% for the IMRT plans and 0.61% for the VMAT plans. The analysis of the parotid gland doses shows that the percentage change in mean dose to left parotid was -8.0% whereas that of the right parotid was -6.4% for the IMRT treatment plans. In the VMAT plans, the percentages change for the left and the right parotid glands were -6.6% and -6.7% respectively. Conclusions: This study shows a clinically significant impact of weight loss on DVH indices analysed in head and neck organs at risk. It highlights the importance of adaptive radiotherapy in head and neck patients if organ at risk sparing is to be maintained.

Conformations Of Peptides Containing 1-Aminocyclohexane-Carboxylic Acid (Acc6) - Crystal-Structures Of 2 Model Peptides

The crystal structures of two peptides containing 1-aminocyclohexanecarboxylic acid (Acc6) are described. Boc-Aib-Acc6-NHMe · H2O adopts a β-turn conformation in the solid state, stabilized by an intramolecular 4 → 1 hydrogen bond between the Boc CO and methylamide NH groups. The backbone conformational angles (φAib = – 50.3°, ψAib = – 45.8°; φAcc6 = – 68.4°, ψAcc6 = – 15°) lie in between the values expected for ideal Type I or III β-turns. In Boc-Aib-Acc6-OMe, the Aib residue adopts a partially extended conformation (φAib = – 62.2°, ψAib = 143°) while the Acc6residue maintains a helical conformation (φAcc6 = 48°, ψAcc6= 42.6°). 1H n.m.r. studies in CDCl3 and (CD3)2SO suggest that Boc-Aib-Acc6-NHMe maintains the β-turn conformation in solution.

Understanding how axial loads on the spine influence segmental biomechanics for idiopathic scoliosis patients: A magnetic resonance imaging study

Background Segmental biomechanics of the scoliotic spine are important since the overall spinal deformity is comprised of the cumulative coronal and axial rotations of individual joints. This study investigates the coronal plane segmental biomechanics for adolescent idiopathic scoliosis patients in response to physiologically relevant axial compression. Methods Individual spinal joint compliance in the coronal plane was measured for a series of 15 idiopathic scoliosis patients using axially loaded magnetic resonance imaging. Each patient was first imaged in the supine position with no axial load, and then again following application of an axial compressive load. Coronal plane disc wedge angles in the unloaded and loaded configurations were measured. Joint moments exerted by the axial compressive load were used to derive estimates of individual joint compliance. Findings The mean standing major Cobb angle for this patient series was 46°. Mean intra-observer measurement error for endplate inclination was 1.6°. Following loading, initially highly wedged discs demonstrated a smaller change in wedge angle, than less wedged discs for certain spinal levels (+ 2,+1,− 2 relative to the apex, (p < 0.05)). Highly wedged discs were observed near the apex of the curve, which corresponded to lower joint compliance in the apical region. Interpretation While individual patients exhibit substantial variability in disc wedge angles and joint compliance, overall there is a pattern of increased disc wedging near the curve apex, and reduced joint compliance in this region. Approaches such as this can provide valuable biomechanical data on in vivo spinal biomechanics of the scoliotic spine, for analysis of deformity progression and surgical planning.