Perturbative Analysis of Disordered Ising Models Close to Criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion is compatible with the infinite differentiability of the free energy but does not imply its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder. MSC2000. Primary 82B44, 60K35.     

Renormalization-Group Transformations Under Strong Mixing Conditions: Gibbsianness and Convergence of Renormalized Interactions

In this paper we study a renormalization-group map: the block averaging transformation applied to Gibbs measures relative to a class of finite-range lattice gases, when suitable strong mixing conditions are satisfied. Using a block decimation procedure, cluster expansion, and detailed comparison between statistical ensembles, we are able to prove Gibbsianness and convergence to a trivial (i.e., Gaussian and product) fixed point. Our results apply to the 2D standard Ising model at any temperature above the critical one and arbitrary magnetic field.     

Graphs whose signless Laplacian spectral radius does not exceed the Hoffman limit value

For a graph matrix M, the Hoffman limit value H(M) is the limit (if it exists) of the largest eigenvalue (or, M-index, for short) of M(H_n), where the graph H_n is obtained by attaching a pendant edge to the cycle C_n-1 of length n-1. In spectral graph theory, M is usually either the adjacency matrix A or the Laplacian matrix L or the signless Laplacian matrix Q. The exact values of H(A) and H(L) were first determined by Hoffman and Guo, respectively. Since H_n is bipartite for odd n, we have H(Q)=H(L). All graphs whose A-index is not greater than H(A) were completely described in the literature. In the present paper, we determine all graphs whose Q-index does not exceed H(Q). The results obtained are determinant to describe all graphs whose L-index is not greater then H(L). This is done precisely in Wang et al. (in press) [21].     

Synthesis of Differently Protected 1‐C‐Methyl‐Ribofuranoses Intermediates for the Preparation of Biologically Active 1′‐C‐Methyl‐Ribonucleosides

Starting from D‐ribose, differently protected 1‐C‐methyl‐D‐ribofuranoses have been prepared as intermediates for the synthesis of variously modified 1′‐C‐methyl‐ribonucleosides, a class of compounds potentially endowed with interesting biological activity.     

Phase formation in mixed TiO<Subscript>2</Subscript>-ZrO<Subscript>2</Subscript> oxides prepared by sol-gel method

Pure titania, zirconia, and mixed oxides (3–37 mol.% of ZrO₂) are prepared using the sol-gel method and calcined at different temperatures. The calcined samples are characterized by Raman spectroscopy, X-ray powder diffraction, scanning electron microscopy, transmission electron microscopy, and nitrogen adsorption porosimetry. Measurements reveal a thermal stability of the titania anatase phase that slightly increases in the presence of 3–13 mol.% of zirconia. Practically, the titania anatase-rutile phase transformation is hindered during the temperature increase above 700°C. The mixed oxide with 37 mol.% of ZrO₂ treated at 550°C shows a new single amorphous phase with a surface area of the nanoparticles double with respect to the other crystalline samples and the formed srilankite structure (at 700°C). The anatase phase is not observed in the sample containing 37 mol.% of ZrO₂. The treatment at 700°C causes the formation of the srilankite (Ti_0.63Zr_0.37O_x) phase.     

Synthesis of enantiomerically pure (R)-and (S)-1-benzoyloxypropane-2,3-diol and revision of the stereochemical outcome of the Candida antarctica lipase-catalyzed benzoylation of glycerol

Enantiomerically pure (R)- and (S)-1-benzoyloxypropane-2,3-diol have been prepared from (S)-(+)-2,2-dimethyl-1,3-dioxolane-4-methanol and used as reference compounds to correct the reported stereochemical outcome of the Candida antarctica lipase (CAL)-catalyzed benzoylation of glycerol.     

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N(t) Poisson events, there are N(t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.     

Ranking vertices or edges of a network by loops: a new approach

We introduce loop ranking, a new ranking measure based on the detection of closed paths, which can be computed in an efficient way. We analyze it with respect to several ranking measures which have been proposed in the past, and are widely used to capture the relative importance of the vertices in complex networks. We argue that loop ranking is a very appropriate measure to quantify the role of both vertices and edges in the network traffic.