An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition

In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by developing an adaptive operator compression scheme and a multiresolution matrix factorization algorithm which achieve nearly optimal performance on both complexity and well-posedness. To develop our adaptive operator compression and multiresolution matrix factorization methods, we first introduce a novel notion of energy decomposition for SPD matrix $A$ using the representation of energy elements. The interaction between these energy elements depicts the underlying topological structure of the operator. This concept of decomposition naturally reflects the hidden geometric structure of the operator which inherits the localities of the structure. By utilizing the intrinsic geometric information under this energy framework, we propose a systematic operator compression scheme for the inverse operator $A^{-1}$. In particular, with an appropriate partition of the underlying geometric structure, we can construct localized basis by using the concept of interior and closed energy. Meanwhile, two important localized quantities are introduced, namely, the error factor and the condition factor. Our error analysis results show that these two factors will be the guidelines for finding the appropriate partition of the basis functions such that prescribed compression error and acceptable condition number can be achieved. By virtue of this insight, we propose the patch pairing algorithm to realize our energy partition framework for operator compression with controllable compression error and condition number

A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition component by integrating the multiresolution framework into the implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm

Poly[diaqua­bis(μ3-1H-benzimidazole-5,6-dicarboxyl­ato-κ4 N 3:O 5,O 5′:O 6)bis­(μ2-1H,3H-benzimidazolium-5,6-dicarboxyl­ato-κ3 O 5,O 5′:O 6)digadolinium(III)]

In the title complex, [Gd2(C9H4N2O4)2(C9H5N2O4)2(H2O)2]n, two of the benzimidazole-5,6-dicarboxyl­ate ligands are pro­ton­ated at the imidazole groups. Each GdIII ion is coordinated by six O atoms and one N atom from five ligands and one water mol­ecule, displaying a distorted bicapped trigonal-prismatic geometry. The GdIII ions are linked by the carboxyl­ate groups and imidazole N atoms, forming a layer parallel to (001). These layers are further connected by O—H⋯O and N—H⋯O hydrogen bonds into a three-dimensional supra­molecular network

Nano-Ag on vanadium dioxide. II. Thermal tuning of surface plasmon resonance

Thermal tuning of the localized surface plasmon resonance (LSPR) of Ag nanoparticles on a thermochromic thin film of VO2 was studied experimentally. The tuning is strongly temperature dependent and thermally reversible. The LSPR wavelength lambda(SPR) shifts to the blue with increasing temperature from 30 to 80 degrees C, and shifts back to the red as temperature decreases. A smart tuning is achievable on condition that the temperature is controlled in a stepwise manner. The tunable wavelength range depends on the particle size or the mass thickness of the metal nanoparticle film. Further, the tunability was found to be enhanced significantly when a layer of TiO2 was introduced to overcoat the Ag nanoparticles, yielding a marked sensitivity factor Delta lambda(SPR)/Delta n, of as large as 480 nm per refractive index unit (n) at the semiconductor phase of VO2. (c) 2008 American Institute Of Physics

Hemi(4,4′-bipyridinium) hexa­fluorido­phosphate bis­(4-amino­benzoic acid) 4,4′-bipyridine monohydrate

In the title compound, 0.5C10H10N2 2+·PF6 −·C10H8N2·2C7H7NO2·H2O, the cation is located on a center of symmetry. The crystal structure is determined by a complex three-dimensional network of inter­molecular O—H⋯O, O—H⋯N, N—H⋯N and N—H⋯F hydrogen bonds. π–π stacking inter­actions between neighboring pyridyl rings are also present; the centroid–centroid distance is 3.643 (5) Å. The hexa­fluoridophosphate anion is disordered over two positions with site-occupancy factors of ca 0.6 and 0.4

Monte Carlo Hamiltonian - From Statistical Physics to Quantum Theory

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we present a recently developed approach: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach.Comment: StatPhys-Taiwan-1999, 6 pages, LaTeX using elsart.cl

Poly[[aqua­(μ2-oxalato)(μ2-2-oxido­pyridinium-3-carboxylato)dysprosium(III)] monohydrate]

In the title complex, {[Dy(C6H4NO3)(C2O4)(H2O)]·H2O}n, the DyIII ion is coordinated by seven O atoms from two 2-oxidopyridinium-3-carboxylate ligands, two oxalate ligands and one water mol­ecule, displaying a distorted bicapped trigonal-prismatic geometry. The carboxyl­ate groups of the 2-oxidopyridinium-3-carboxylate and oxalate ligands link dysprosium metal centres, forming layers parallel to (100). These layers are further connected by inter­molecular O—H⋯O hydrogen-bonding inter­actions involving the coordin­ated water mol­ecules, forming a three-dimensional supra­molecular network. The uncoordinated water mol­ecule is involved in N—H⋯O and O—H⋯O hydrogen-bonding inter­actions within the layer