Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A_n. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix A_n. Thus if A_n is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix A_n has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥₂. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.     

Three-dimensional visualization of diffusion flame shapes under acoustic excitation using stereoscopic imaging and reconstruction technique

Stereoscopic imaging and reconstruction technique is introduced to reconstruct the flame structures that are subject to acoustic excitation. The laminar diffusion flame under investigation was created in a cylindrical tube and excited by a loudspeaker. Stereo images were taken at a shutter speed of 1/10000^th second using a ‘stereo camera’ and the depth cue of the flame structures along the camera viewing direction were then computed using machine vision methodology. By visualizing the computed three-dimensional flame models, as well as judging the corresponding attribute such as surface gradient, the understanding of the flame and acoustic wave interaction could be improved.     

Construction of subphthalocyanine-porphyrin and subphthalocyanine-phthalocyanine heterodyads through axial coordination

The treatment of boron(III) subphthalocyanine chloride (SPcCl) with 3- or 4-hydroxypyridine in the presence of pyridine in toluene gave the corresponding boron(III) subphthalocyanine pyridinolates SPc(3-OPy) ( 1) or SPc(4-OPy) ( 2). Having a pyridyl group, these compounds could axially complex with a series of zinc(II) and ruthenium(II) porphyrins and phthalocyanines to form the corresponding subphthalocyanine-porphyrin and subphthalocyanine-phthalocyanine heterodyads. As revealed by UV-vis spectroscopy, the ground-state interaction between the two chromophores in these dyads is insignificant. The complexation processes were also studied by (1)H NMR and fluorescence spectroscopic methods, which confirmed the 1:1 binding stoichiometry. The association constants, as determined by fluorescence titration, were generally higher for the ruthenium(II) tetrapyrroles [(2.5-4.7) x 10 (4) M (-1)] than for the zinc(II) counterparts [(0.3-1.8) x 10 (4) M (-1)]. The molecular structures of the two pyridyl subphthalocyanines 1 and 2, together with three novel subphthalocyanine-porphyrin heterodyads, were also determined by X-ray diffraction analyses.     

Stress induced half-metallicity in surface defected germanium nanowires

Germanium nanowires (GeNWs) with single, double, quadruple and octuple surface dangling bonds (SDBs) are investigated using density-functional-theory calculations. We show that single SDB defected GeNWs remain semiconducting as their non-defected form while double or multiple SDB defects result in either semiconducting or metallic GeNWs, depending on the defect's locations on the surface. More importantly, we show that the electronic properties of surface defected GeNWs can also be fine-tuned by applying tensile and compressive strains. Upon the right loading, the surface defected GeNWs become half-metallic. In addition, we determine that the surface defected GeNWs can be classified into three classes: (1) GeNWs with zero magnetic moment, which are either metallic or semiconducting; (2) GeNWs with net magnetic moments equal to the number of SDBs, which are semiconducting with distinct spin-up and spin-down configurations; and (3) GeNWs with net magnetic moments significantly lower than the number of SDBs. We also find that only the defected GeNWs that fall under (3) are potentially half-metallic. Our results predict that half-metallic GeNWs can be obtained via engineering of the surface defects and the structures without the presence of impurity dopants.     

Constructing sandwich-type rare Earth double-decker complexes with N-confused porphyrinato and phthalocyaninato ligands

Reaction of the half-sandwich complexes M(III)(Pc)(acac) (M = La, Eu, Y, Lu; Pc = phthalocyaninate; acac = acetylacetonate) with the metal-free N-confused 5,10,15,20-tetrakis[(4-tert-butyl)phenyl]porphyrin (H(2)NTBPP) or its N2-position methylated analogue H(CH(3))NTBPP in refluxing 1,2,4-trichlorobenzene (TCB) led to the isolation of M(III)(Pc)(HNTBPP) (M = La, Eu, Y, Lu) or Y(III)(Pc)[(CH(3))NTBPP] in 8-15% yield. These represent the first examples of sandwich-type rare earth complexes with N-confused porphyrinato ligands. The complexes were characterized with various spectroscopic methods and elemental analysis. The molecular structures of four of these double-decker complexes were also determined by single-crystal X-ray diffraction analysis. In each of these complexes, the metal center is octa-coordinated by four isoindole nitrogen atoms of the Pc ligand, three pyrrole nitrogen atoms, and the inverted pyrrole carbon atom of the HNTBPP or (CH(3))NTBPP ligand, forming a distorted coordination square antiprism. For Eu(III)(Pc)(HNTBPP), the two macrocyclic rings are further bound to a CH(3)OH molecule through two hydrogen bonds formed between the hydroxyl group of CH(3)OH and an aza nitrogen atom of the Pc ring or the inverted pyrrole nitrogen atom of the HNTBPP ring, respectively. The location of the acidic proton at the inverted pyrrole nitrogen atom (N2) of the protonated double-deckers was revealed by (1)H NMR spectroscopy.     

Synthesis and characterization of poly(amide sulfonamide)s (PASAs)

New diamino monomers IIa – IIg were synthesized in a two-step reaction sequence starting from p-acetamidobenzenesulfonyl chloride. Solution polymerization of these monomers in DMAC with terephthaloyl or isophthaloyl chloride resulted in the formation of a series of 14 poly(amide sulfonamide)s (PASAs) in excellent yield (> 95%). The polymers have in-trinsic viscosities of 0.32–1.11 dL g^?1. Except for polymers IIIa ? p and IIId - p , all other PASAs were readily soluble in aprotic polar solvents including DMAC, DMF, and DMSO. Thermogravimetric analyses of the polymers showed moderate thermal stability with 10% weight loss being recorded in the range of 325–408°C. In addition, these polymers exhibit moderate chemical stabilities toward alkali, acidic, and chromic acid solution. © 1995 John Wiley & Sons, Inc.