An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution

Producción CientíficaWe solve the Cauchy problem defined by the fractional partial differential equation [∂tt − κD]u = 0, with D the pseudo-differential Riesz operator of first order, and certain initial conditions. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse u(x, 0) by the Dirac delta distribution ϕ(x) = μδ(x) is obtained as corollary.MINECO grant MTM2014-57129-C2-1-P

Effect of root curvature on post length in the restoration of endodontically treated premolars

– Two hundred and eighteen bi-rooted maxillary premolars were examined radio graphically to determine the length from the apex at which root curvature occurred. The information may serve as a guide in determining post preparation length. The results of the study indicated that the lingual root was slightly straighter than the buccal root. The curvature of the root was on the average 6.47 mm from the apex on the buccal root and 5.18 mm from the apex on the lingual root.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75753/1/j.1600-9657.1985.tb00577.x.pd

Nonlinear Localization in Metamaterials

Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging, cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new degree of freedom for metamaterial design that allows for tuneability and multistability, properties that may offer altogether new functionalities and electromagnetic characteristics. The combination of discreteness and nonlinearity may lead to intrinsic localization of the type of discrete breather in metallic, SQUID-based, and ${\cal PT}-$symmetric metamaterials. We review recent results demonstrating the generic appearance of breather excitations in these systems resulting from power-balance between intrinsic losses and input power, either by proper initialization or by purely dynamical procedures. Breather properties peculiar to each particular system are identified and discussed. Recent progress in the fabrication of low-loss, active and superconducting metamaterials, makes the experimental observation of breathers in principle possible with the proposed dynamical procedures.Comment: 19 pages, 14 figures, Invited (Review) Chapte

Fractional dynamics pharmacokinetics–pharmacodynamic models

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics

The contribution of microlensing surveys to the distance scale

In the early nineties several teams started large scale systematic surveys of the Magellanic Clouds and the Galactic Bulge to search for microlensing effects. As a by product, these groups have created enormous time-series databases of photometric measurements of stars with a temporal sampling duration and accuracy which are unprecedented. They provide the opportunity to test the accuracy of primary distance indicators, such as Cepheids, RRLyrae stars, the detached eclipsing binaries, or the luminosity of the red clump. We will review the contribution of the microlensing surveys to the understanding of the physics of the primary distance indicators, recent differential studies and direct distance determinations to the Magellanic Clouds and the Galactic Bulge.Comment: Invited review article to appear in: `Post-Hipparcos Cosmic Candles', A. Heck & F. Caputo (Eds), Kluwer Academic Publ., Dordrecht, in press. 21 pages; uses Kluwer's crckapb.sty LaTeX style file, enclose

Morphological Differentiation May Mediate Mate-Choice between Incipient Species of Anopheles gambiae s.s.

The M and S molecular forms of Anopheles gambiae s.s. have been considered incipient species for more than ten years, yet the mechanism underlying assortative mating of these incipient species has remained elusive. The discovery of the importance of harmonic convergence of wing beat frequency in mosquito mating and its relation to wing size have laid the foundation for exploring phenotypic divergence in wing size of wild populations of the two forms. In this study, wings from field collected mosquitoes were measured for wing length and wing width from two parts of the sympatric distribution, which differ with respect to the strength of assortative mating. In Mali, where assortative mating is strong, as evidenced by low rates of hybridization, mean wing lengths and wing widths were significantly larger than those from Guinea-Bissau. In addition, mean wing widths in Mali were significantly different between molecular forms. In Guinea-Bissau, assortative mating appears comparatively reduced and wing lengths and widths did not differ significantly between molecular forms. The data presented in this study support the hypothesis that wing beat frequency may mediate assortative mating in the incipient species of A. gambiae and represent the first documentation of a morphological difference between the M and S molecular forms

Behavioral genetics and taste

This review focuses on behavioral genetic studies of sweet, umami, bitter and salt taste responses in mammals. Studies involving mouse inbred strain comparisons and genetic analyses, and their impact on elucidation of taste receptors and transduction mechanisms are discussed. Finally, the effect of genetic variation in taste responsiveness on complex traits such as drug intake is considered. Recent advances in development of genomic resources make behavioral genetics a powerful approach for understanding mechanisms of taste