We show the existence of weak logarithmic models for any (dicritical or not) holomorphic foliation F of (C, 0) without saddlenodes in its desingularization. The models are written in terms of a representative set of separatrices, whose equisingularity types are controlled by the Milnor number of the foliation.

A computational study of some logarithmic barrier decomposition algorithms for semi{innnite programming is presented in this paper. The conceptual algorithm is a straightforward adaptation of the logarithmic barrier cutting plane algorithm which was presented recently by den Hertog et al., to solve semi-innnite programming problems. Usually decomposition (cutting plane methods) use cutting plan...

The functional equation f(y − x) − g(xy) = h (1/x− 1/y) is solved for general solution. The result is then applied to show that the three functional equations f(xy) = f(x)+f(y), f(y−x)−f(xy) = f(1/x−1/y) and f(y−x)−f(x)−f(y) = f(1/x−1/y) are equivalent. Finally, twice differentiable solution functions of the functional equation f(y − x) − g1(x) − g2(y) = h (1/x− 1/y) are determined.

We study a class of symmetric, quasi-homothetic preferences that result in demands logarithmic in own prices when these have a negligible impact on aggregate price indices (as in monopolistic competition models). Thus marginal revenues are computationally friendly, and decreasing whenever demands are elastic. Preferences can be represented either by an additive negative exponential direct utili...

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Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial...

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and B...

We show that the graph isomorphism problem is hard under logarithmic space many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space), for every logarithmic space modular class ModkL and for the class DET of problems NC1 reducible to the determinant. These are the strongest existing hardness results for the graph isomorphism problem, and imply a randomized logarithm...

The above inequality implies a logarithmic Sobolev inequality for q. We get an explicit lower bound for the logarithmic Sobolev constant of q under the assumptions that: (i) the local specifications of q satisfy logarithmic Sobolev inequalities with constants ρi, and (ii) they also satisfy some condition expressing that the mixed partial derivatives of the Hamiltonian of q are not too large rel...