q-Trigonal Klein surfaces

In this paperq-trigonal Klein surfaces are introduced in a similar way to that ofq-hyperelliptic surfaces. They are characterized by means of non-Euclidean crystallographic groups (NEC groups in short). As a consequence of this characterization, given a family of Klein surfaces (orientable or not) with topological genusg andk boundary components the admissible values forq are calculated. In particular, the families for which there is no admissibleq or families with uniqueq are obtained. The authors are partially supported by DGICYT PB98 0017.     

A tauberian theorem for distributional point values

We give a tauberian theorem for boundary values of analytic functions. We prove that if is the distributional limit of the analytic function F defined in a region of the form (a, b) × (0, R), if F (x ₀ + iy)→ γ as y → 0⁺, and if f is distributionally bounded at x = x ₀, then f (x ₀) = γ distributionally. As a consequence of our tauberian theorem, we obtain a new proof of a tauberian theorem of Hardy and Littlewood. Received: 10 December 2007     

Gorenstein quivers

In this paper we characterize when the path ring associated to a quiver is Gorenstein (in the sense of Iwanaga [9]). Then, by using the notion of a Gorenstein category (cf. [2]), we extend the classes of quivers whose corresponding category of representations has finite Gorenstein global dimension. This extension includes non-noetherian quivers. E. E., S.E., and J.R.G.R., partially supported by the DGI MTM2005-03227. Estrada’s work was supported by a MEC/Fulbright grant from the Spanish Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Ciencia. Received: 28 February 2006     

Fluid-solid transition in hard hypersphere systems

In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6, and 7. We have studied the changes of the radial distribution function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states with densities above the melting point, and moved down to densities in the liquid state below the freezing point. For all the examined dimensions (including D = 3), it was observed that the height of the first minimum of the RDF changes in an almost continuous way around the freezing density and resembles a second order phase transition. With these results we propose a numerical method to estimate the freezing point as a function of the dimension D using numerical fits and semiempirical approaches. We find that the estimated values of the freezing point are very close to the previously reported values from simulations and theoretical approaches up to D = 6, reinforcing the validity of the proposed method. This was also applied to numerical simulations for D = 7 giving new estimations of the freezing point for this dimensionality.     

A model structure approach to the finitistic dimension conjectures

We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal {X}$‐dimension, for certain classes of modules $\mathcal {X}$. As an application we give a model structure approach to the finitistic dimension conjectures and present a new conceptual framework in which these conjectures can be studied.     

Antidepressant-like effect of Casimiroa pubescens root extracts

In this study, we investigated the antidepressant-like effects of the hexane (HCP), ethyl acetate (ECP) and methanol (MCP) extracts of the roots of Casimiroa pubescens Ramírez (Rutaceae) using the forced swim test (FST). In an initial experiment, each extract was orally administered to mice only once 60 min before to the FST. In a second experiment, doses were administered 24, 7 and 1 h before testing. Our results showed that the triple administration of the extracts provided a stronger effect than single administration. However, the combination of HCP at 7.5 mg/kg and imipramine (IMI) at 12.5 mg/kg showed the greatest effect. The coumarins 3-(1′,1′, dimethyl allyl)-herniarin, auraptene, 8-geranyl-oxy psoralen, isopimpinellin and the flavonoid zapotin were isolated from the extracts. The hexane extract of C. pubescens showed an antidepressant-like activity, which may inspire further studies on developing new antidepressant agents.     

Continuous symmetry numbers and entropy

Traditionally, entropy changes are corrected for rotational permutability only if the molecule is perfectly rotationally symmetric. By this approach, only a small fraction of all known molecules must be evaluated in terms of symmetry numbers, while all other molecules are totally exempt of these considerations. A general approach which encompasses all molecules, symmetric or not, is proposed here. It is based on introducing the notion of continuity to symmetry numbers and on allowing noninteger values. In the first part of the account, we provide arguments as to why continuity is needed and what difficulties one may encounter by adopting the "black-or-white" approach to symmetry. In the second part, we provide a working methodology of how to evaluate the symmetry number content of any molecule, symmetric or not. Finally, in the third part, we demonstrate the implications of this approach on entropy issues involving melting points, Jahn-Teller distortions (of fullerene) upon ionization, molecular distortion due to overcrowdedness, permutability of isotopes, and the structure of proton sponges. It is shown that continuous symmetry numbers provide entropy values, which better agree with experimental observations, and that they are capable of identifying correlations between symmetry and physical/chemical measurables.     

Designing sedative/hypnotic compounds from a novel substructural graph-theoretical approach

A novel approach to computer-aided molecular design is illustrated. This approach is based on the calculation of the spectral moments of the bond adjacency matrix of graphs representing molecular structures. Spectral moments are then expressed as linear combinations of the different sub-structures present in molecules. Two series of compounds, one containing sedative/hypnotic and the other containing different classes of drugs were used to find a discriminant function with the present approach. Several compounds from the Merck Index were identified by the model as sedative/hypnotic, five of them were found in the recent literature as possessing this activity. The critical fragments, actives and inactive ones, were detected.