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.     

A unified small-signal simulation algorithm for SMPS

The small-signal behavior of a frequency controlled resonant converter is modeled as an equivalent pulsewidth modulation (PWM) converter. By this model, a recently developed simulation algorithm for PWM converter is modified to simulate both the open-loop and closed-loop small-signal behavior. Experimental results show that this approach is accurate and efficient.     

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.     

Surface-Degenerate Semiconductor Photocatalysis for Efficient Water Splitting without Sacrificial Agents via a Reticular Chemistry Approach

The production of green hydrogen through photocatalytic water splitting is crucial for a sustainable hydrogen economy and chemical manufacturing. However, current approaches suffer from slow hydrogen production (<70 μmol ⋅ g_cat⁻¹ ⋅ h⁻¹) due to the sluggish four-electrons oxygen evolution reaction (OER) and limited catalyst activity. Herein, we achieve efficient photocatalytic water splitting by exploiting a multifunctional interface between a nano-photocatalyst and metal–organic framework (MOF) layer. The functional interface plays two critical roles: (1) enriching electron density directly on photocatalyst surface to promote catalytic activity, and (2) delocalizing photogenerated holes into MOF to enhance OER. Our photocatalytic ensemble boosts hydrogen evolution by ≈100-fold over pristine photocatalyst and concurrently produces oxygen at ideal stoichiometric ratio, even without using sacrificial agents. Notably, this unique design attains superior hydrogen production (519 μmol ⋅ g_cat⁻¹ ⋅ h⁻¹) and apparent quantum efficiency up to 13-fold and 8-fold better than emerging photocatalytic designs utilizing hole scavengers. Comprehensive investigations underscore the vital role of the interfacial design in generating high-energy photoelectrons on surface-degenerate photocatalyst to thermodynamically drive hydrogen evolution, while leveraging the nanoporous MOF scaffold as an effective photohole sink to enhance OER. Our interfacial approach creates vast opportunities for designing next-generation, multifunctional photocatalytic ensembles using reticular chemistry with diverse energy and environmental applications.     

Increasing structure dimensionality of copper(I) complexes by varying the flexible thioether ligand geometry and counteranions

This work focuses on the systematic investigation of the influences of pyrimidine-based thioether ligand geometries and counteranions on the overall molecular architectures. A N-containing heterocyclic dithioether ligand 2,6-bis(2-pyrimidinesulfanylmethyl)pyridine (L1) and three structurally related isomeric bis(2-pyrimidinesulfanylmethyl)benzene (L2-L4) ligands have been prepared. On the basis of the self-assembly of CuX (X = I, Br, Cl, SCN, or CN) and the four structurally related flexible dithioether ligands, we have synthesized and characterized 10 new metal-organic entities, Cu4(L1)2I4 1, Cu4(L1)2Br4 2, [Cu2(L2)2I2.CH3CN]n 3, [Cu(L3)I]n 4, [Cu(L3)Br]n 5, [Cu(L3)CN]n 6, [Cu(L4)CN]n 7, [Cu2(L4)I2]n 8, [Cu2(L4)(SCN)2]n 9, and [[Cu6I5(L4)3](BF4).H2O]n 10, by elemental analyses, IR spectroscopy, and X-ray crystallography. Single-crystal X-ray analyses show that the 10 Cu(I) complexes possess an increasing dimensionality from 0D (1 and 2) to 1D (3-5) to 2D (6-9) to 3D (10), which indicates that the ligand geometry takes an essential role in the framework formation of the Cu(I) complexes. The influence of counteranions and pi-pi weak interactions on the formation and dimensionality of these coordination polymers has also been explored. In addition, the photoluminescence properties of Cu(I) coordination polymers 4-10 in the solid state have been studied.     

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.     

Tetrapyrrole derivatives substituted with ferrocenylethynyl moieties. synthesis and electrochemical studies

Up to eight redox-active ferrocenyl units have been incorporated, through the unsaturated ethynyl linkers, on the periphery of a series of cyclic tetrapyrrole derivatives including zinc(II) phthalocyanine and 2,3-naphthalocyanine, and nickel(II) meso-diphenylporphyrin. The synthesis of the former two macrocycles 4 and 7 involves the Sonogashira coupling reaction of ferrocenylethyne with 4,5-dichlorophthalonitrile (1) or 6,7-dibromonaphthalonitrile (5), respectively, followed by a base-promoted cyclization. The meso-bis(ferrocenylethynyl)porphyrin 11 has been prepared from the dibromo analogue 10 also by a palladium-catalyzed coupling reaction. These novel macrocyclic compounds have been spectroscopically and electrochemically characterized. As revealed by cyclic voltammetry, the ferrocenyl moieties appear to be electrochemically independent in these complexes and there is no significant electronic coupling among the iron(II) centers.