A modulus-based formulation for the vertical linear complementarity problem

Numerical Algorithms - We introduce a modulus-based formulation for vertical linear complementarity problems (VLCPs) with an arbitrary number ? of matrices. This formulation can be used to...     

A Matrix Model with a Singular Weight and Painlevé III

We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional p-Laplacean operator with measurable coefficients. We introduce a natural function class where we solve the Dirichlet problem, and prove basic and optimal nonlinear Wolff potential estimates for solutions. These are the exact analogs of the results valid in the case of local quasilinear degenerate equations established by Boccardo and Gallouët (J Funct Anal 87:149–169, 1989, Partial Differ Equ 17:641–655, 1992) and Kilpeläinen and Malý (Ann Scuola Norm Sup Pisa Cl Sci (IV) 19:591–613, 1992, Acta Math 172:137–161, 1994). As a consequence, we establish a number of results that can be considered as basic building blocks for a nonlocal, nonlinear potential theory: fine properties of solutions, Calderón–Zygmund estimates, continuity and boundedness criteria are established via Wolff potentials. A main tool is the introduction of a global excess functional that allows us to prove a nonlocal analog of the classical theory due to Campanato (Ann Mat Pura Appl (IV) 69:321–381, 1965). Our results cover the case of linear nonlocal equations with measurable coefficients, and the one of the fractional Laplacean, and are new already in such cases.     

Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems

Numerical Algorithms - In this paper, we generalize modulus-based matrix splitting methods to a class of horizontal nonlinear complementarity problems (HNCPs). First, we write the HNCP as an...     

Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory

We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2N+kappa as N-->infinity, where kappa and kappa are determined explicitly. In an important class of systems, kappa is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for kappa therefore provides an explicit formula for the central charge.     

Projected Splitting Methods for Vertical Linear Complementarity Problems

Journal of Optimization Theory and Applications - In this paper, we generalize the projected Jacobi and the projected Gauss–Seidel methods to vertical linear complementarity problems (VLCPs)...     

Influence of anions in silver supramolecular frameworks: structural characteristics and sorption properties

The complexation of a preorganized thioether-functionalized bis(pyrazolyl)methane ligand (L) with silver precursors produces supramolecular structures organized at two hierarchical levels: [AgL](6)(X)(6) metal-organic cyclic hexamers and their organization in 3D architectures. The cyclic toroidal hexamers of 22-26 ? external diameter are found to be stable already in solution before self-assembly into the crystalline state. In the 3D lattice, the hexameric building block are arranged in different highly symmetric space groups as a function of a variety of anions (cubic Fd3 with PF(6)(-) or BF(4)(-) and rhombohedral R3 with CF(3)SO(3)(-) or NO(3)(-)) and form cavities with the geometrical shapes of Platonic solids (tetrahedron and octahedron) that can be occupied by a variety of solvent molecules. Upon evacuation, cubic crystals can produce stable frameworks with permanent porosity, which can absorb reversibly several vapors, CO(2) and CH(4).     

Modulus-based matrix splitting methods for horizontal linear complementarity problems

Numerical Algorithms - In this paper, we extend modulus-based matrix splitting iteration methods to horizontal linear complementarity problems. We consider both standard and accelerated methods and...     

Using high pressure to prepare polymorphs of the Ba2Co(1-x)Zn(x)S3 (0 ≤ x ≤ 1.0) compounds

In this work, high pressure was used as a tool to induce structural transition and prepare metastable polymorphs of ternary sulfides. Structural transformations under high pressure of compounds belonging to the Ba(2)Co(1-x)Zn(x)S(3) (0 ≤ x ≤ 1.0) series were studied using X-ray diffraction and electron microscopy. All members of the Ba(2)Co(1-x)Zn(x)S(3) series show the Ba(2)CoS(3)-type one-dimensional structure, but, after heating under pressure, the Ba(2)CoS(3) compound (x = 0) separates into BaS and the two-dimensional BaCoS(2-δ) (δ ≈ 0), while Ba(2)Co(1-x)Zn(x)S(3) compounds with x ≥ 0.25 maintain their one-dimensional features but rearrange into polymorphs showing the Ba(2)MnS(3)-type structure. All structural transformations can be linked to shortening in interchain metal-metal distances caused by the high pressure, and the role of the zinc in preventing loss of one-dimensionality is discussed.     

Selective and Reversible Solvent Uptake in Tetra-4-(4-pyridyl)phenylmethane-based Supramolecular Organic Frameworks

The dynamic behavior of supramolecular organic frameworks (SOFs) based on the rigid tetra-4-(4-pyridyl)phenylmethane ( TPPM) organic tecton has been elucidated through 3D electron diffraction, X-ray powder diffraction and differential scanning calorimetry (DSC) analysis. The SOF undergoes a reversible single-crystal-to-single-crystal transformation when exposed to vapours of selected organic solvents, moving from a closed structure with isolated small voids to an expanded structure with solvated channels along the b axis. The observed selectivity is dictated by the fitting of the guest in the expanded SOF, following the degree of packing coefficient. The effect of solvent uptake on TPPM solid-state fluorescence was investigated, evidencing a significant variation in the emission profile only in the presence of chloroform.