Chromatic number and skewness

AbstractIn this note, we solve the problem of determing the chromatic number of planar graphs to which a certain number μ of “extra” edges are attached. We obtain a (best-possible) theorem when μ < 2k for every integer k ≥ 3. The statement of the theorem for k = 2 is the Four-Color Conjecture

Topological conformal field theories and Calabi–Yau categories

AbstractThis is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov–Witten invariants (at all genera). These Gromov–Witten type invariants depend on a Calabi–Yau A∞ category, which plays the role of the target in ordinary Gromov–Witten theory. When we use an appropriate A∞ version of the derived category of coherent sheaves on a Calabi–Yau variety, this constructs the B model at all genera. When the Fukaya category of a compact symplectic manifold X is used, it is shown, under certain assumptions, that the usual Gromov–Witten invariants are recovered. The assumptions are that open-closed Gromov–Witten theory can be constructed for X, and that the natural map from the Hochschild homology of the Fukaya category of X to the ordinary homology of X is an isomorphism

The Effect of a Sunscreen Containing Para-aminobenzoic Acid on the Systemic Immunologic Alterations Induced in Mice by Exposure to UVB Radiation

Application of a sunscreen containing para-aminobenzoic acid partially abrogated certain of the systemic immunologic alterations produced in mice by exposure to UVB (280–320 nm) radiation from sunlamp bulbs. The sunscreen reduced the degree of UVB-induced suppression of contact hypersensitivity to a chemical applied subsequently to nonirradiated skin. In addition, it reduced the frequency with which mice became susceptible to the growth of a highly antigenic, syngeneic, UVB-induced tumor following chronic treatment with UVB radiation, but this effect was not statistically significant. The tumor-susceptible state was transferred from animals treated with sunscreen and UVB radiation to lethally x-irradiated mice by injection of spleen cells. The gross morphology of the skin of mice treated with sunscreen and UVB radiation was normal but the histologic changes induced by UVB irradiation in skin were only partially abrogated by the sunscreen

Millora de l'accessibilitat al carrer de l'Alguer: escales mecàniques en construcció

Pericas, Enric;Ordóñez, Estrell

Construcció del pont de Mühlberg

Fuente Fuente, Carlos; Farrando Sicilia, Jord