A note on the fractional perimeter and interpolation

We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces $W^{\alpha, 1}$ of order $0 < \alpha < 1$

(2479) Proposal to conserve the name Marattia kaulfussii (Eupodium kaulfussii) against M. raddiana (Marattiaceae)

Proposal to conserve the name Marattia kaulfussii (Eupodium kaulfussii)against M. raddiana (Marattiaceae). Unless this proposal is accepted, the epithet raddiana will need to be combined under Eupodium and this will become the correctname of what is universally known as E. kaulfussii. Conservation of M. kaulfussii against M. raddiana is therefore seen as the best solution in the interest of nomenclatural stability.Fil: Arana, Marcelo Daniel. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Ciencias Naturales; ArgentinaFil: Christenhusz, MaartenJ.M.. Royal Botanic Gardens; Reino UnidoFil: Ponce, Marta Monica. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; Argentin

Residència universitària al barri del Carme a Reus

Rehabilitació d'una antiga fàbrica esclofolladora d'avellanes i nous, per adaptar-la al nou ús de residència d'estudiants al barri del Carme de Reus

Comparative Study of the Compressibility of M3V2O8 (M = Cd, Zn, Mg, Ni) Orthovanadates

We report herein a theoretical study of the high-pressure compressibility of Cd3V2O8, Zn3V2O8, Mg3V2O8, and Ni3V2O8. For Cd3V2O8, we also present a study of its structural stability. Computer simulations were performed by means of first-principles methods using the CRYSTAL program. In Cd3V2O8, we found a previously unreported polymorph which is thermodynamically more stable than the already known polymorph. We also determined the compressibility of all compounds and evaluated the different contributions of polyhedral units to compressibility. We found that the studied vanadates have an anisotropic response to compression and that the change in volume is basically determined by the compressibility of the divalent-cation coordination polyhedra. A systematic discussion of the bulk modulus of M3V2O8 orthovanadates will also be included

A decomposition by non-negative functions in the Sobolev space Wk,1W^{k, 1}

We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space $W^{k,1}(\mathbb{R}^d)$ as the difference of two non-negative functions in the same space with control of their norms

Pointwise convergence over fractals for dispersive equations with homogeneous symbol

We study the fractal pointwise convergence for the equation $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ with $s>(n-\alpha+1)/2$ the solution $u$ converges to $f$ $\mathcal{H}^\alpha$-a.e, where $\mathcal{H}^\alpha$ is the $\alpha$-dimensional Hausdorff measure. We improve upon this result depending on the dispersive strength of $P$. On the other hand, for a family of polynomials $P$ and given $\alpha$, we exploit a Talbot-like effect to construct initial data whose solutions $u$ diverge in sets of Hausdorff dimension $\alpha$. To compute the dimension of the sets of divergence, we adopt the Mass Transference Principle from Diophantine approximation. We also construct counterexamples for quadratic symbols like the saddle to show that our positive results are sometimes best possible.Comment: 54 pages, 17 figures. v3: Accepted manuscrip

Methane Drainage at the Minerales Monclova Mines in the Sabinas Coal Basin, Coahuila, Mexico

Minerales Monclova S.A. De C.V. (MIMOSA) operates five underground longwall mines in the Gassy Los Olmos Coals of the Sabinas Basin in the state of Coahuila in Northern Mexico. Because of high in-situ gas contents and high cleat and natural fracture permeability, MIMOSA has had to incorporate a system of methane drainage in advance of mining in order to safely and cost effectively exploit their reserves. In the early 1990s Resource Enterprises (REI) conducted reservoir characterization tests, numerical simulations, and Coal Mine Methane (CMM) production tests at a nearby mine property in the same basin. Using this information REI approached MIMOSA and recommended the mine-wide implementation of a degasification system that involves long in-seam directionally drilled boreholes. REI was contracted to conduct the drilling, and to date has drilled over 26,000 m (85,000 ft) of in-seam borehole in advance of mining developments, reducing gas contents significantly below in-situ values. This paper discusses the basis for the degasification program recommended at the MIMOSA mines, and presents the impact of its mine-wide application on MIMOSA\u27s mining operations over the last six years. The paper focuses on the degasification system\u27s impacts on methane emissions into mine workings, coal production, and ventilation demands. It also presents lessons learned by the degasification planners in implementing in-seam methane drainage. The paper presents actual CMM production data, measurements of methane emissions and advance rates at development sections, and mine methane liberations