Lanczos Spintensor via the Andersson-Edgar’s Generator

For arbitrary geometries with Petrov types O, N, III, and D (empty), we construct the Andersson-Edgar’s generator for the Lanczos spinor

Ramanujan’s Tau-Function and Convolution Sums

We study certain type of convolution sums involving an arbitrary arithmetic function f, which it is applied to Ramanujan’s tau function when f coincides with the sum of divisors function.&nbsp

On the Persson-Strang’s Identity for the Legendre Polynomials

We show an alternative proof of an identity given by Persson-Strang for the well known Legendre polynomials.&nbsp

The Wijsman topology of a fuzzy metric space

[EN] We introduce and study the notions of lower Wijsman topology, upper Wijsman topology and Wijsman topology of a fuzzy metric space in the sense of Kramosil and Michalek. In particular, quasi-uniformizability, uniformizability, quasi-metrizability and metrizability of these topologies are discussed. Their relations with other hypertopologies are also analyzed. Corresponding results to the Wijsman topology of a metric space are deduced from our approach with the help of the standard fuzzy metric.J. Gutierrez Garcia acknowledges the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-02. J. Rodriguez-Lopez, S. Romaguera and M. Sanchis also acknowledge the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.Gutierrez Garcia, J.; Rodríguez López, J.; Romaguera Bonilla, S.; Sanchis, M. (2016). The Wijsman topology of a fuzzy metric space. Fuzzy Sets and Systems. 300:57-71. https://doi.org/10.1016/j.fss.2015.08.005S577130

Lanczos Potential for The Weyl Tensor

For arbitrary spacetimes with Petrov types O, N and III, we indicate general results about the  Lanczos potential for the corresponding Weyl tensor

Quasienergy spectrum and tunneling current in ac-driven triple quantum dot shuttles

The dynamics of electrons in ac driven double quantum dots have been extensively analyzed by means of Floquet theory. In these systems, coherent destruction of tunneling has been shown to occur for certain ac field parameters. In the present work we analyze, by means of Floquet theory, the electron dynamics of a triple quantum dot in series attached to electric contacts, where the central dot position oscillates. In particular, we analyze the quasienergy spectrum of this ac driven nanoelectromechanical system, as a function of the intensity and frequency of the ac field and of external dc voltages. For strong driving fields, we derive, by means of perturbation theory, analytical expressions for the quasienergies of the driven oscillator system. From this analysis we discuss the conditions for coherent destruction of tunneling (CDT) to occur as a function of detuning and field parameters. For zero detuning, and from the invariance of the Floquet Hamiltonian under a generalized parity transformation, we find analytical expressions describing the symmetry properties of the Fourier components of the Floquet states under such transformation. By using these expressions, we show that in the vicinity of the CDT condition, the quasienergy spectrum exhibits exact crossings which can be characterized by the parity properties of the corresponding eigenvectors

A COMMENT ON THE DARBOUX TRANSFORMATION

Abstract. It is known that the Darboux transformation (DT) allows us to construct isospectral potentials in the frame of the Schrödinger equation. Here we give a simple mathematical deduction for the DT

Decreased metalloproteinase production as a response to mechanical pressure in human cartilage: a mechanism for homeostatic regulation

Articular cartilage is optimised for bearing mechanical loads. Chondrocytes are the only cells present in mature cartilage and are responsible for the synthesis and integrity of the extracellular matrix. Appropriate joint loads stimulate chondrocytes to maintain healthy cartilage with a concrete protein composition according to loading demands. In contrast, inappropriate loads alter the composition of cartilage, leading to osteoarthritis (OA). Matrix metalloproteinases (MMPs) are involved in degradation of cartilage matrix components and have been implicated in OA, but their role in loading response is unclear. With this study, we aimed to elucidate the role of MMP-1 and MMP-3 in cartilage composition in response to mechanical load and to analyse the differences in aggrecan and type II collagen content in articular cartilage from maximum- and minimum-weight-bearing regions of human healthy and OA hips. In parallel, we analyse the apoptosis of chondrocytes in maximal and minimal load areas. Because human femoral heads are subjected to different loads at defined sites, both areas were obtained from the same hip and subsequently evaluated for differences in aggrecan, type II collagen, MMP-1, and MMP-3 content (enzyme-linked immunosorbent assay) and gene expression (real-time polymerase chain reaction) and for chondrocyte apoptosis (flow cytometry, bcl-2 Western blot, and mitochondrial membrane potential analysis). The results showed that the load reduced the MMP-1 and MMP-3 synthesis (p < 0.05) in healthy but not in OA cartilage. No significant differences between pressure areas were found for aggrecan and type II collagen gene expression levels. However, a trend toward significance, in the aggrecan/collagen II ratio, was found for healthy hips (p = 0.057) upon comparison of pressure areas (loaded areas > non-loaded areas). Moreover, compared with normal cartilage, OA cartilage showed a 10- to 20-fold lower ratio of aggrecan to type II collagen, suggesting that the balance between the major structural proteins is crucial to the integrity and function of the tissue. Alternatively, no differences in apoptosis levels between loading areas were found – evidence that mechanical load regulates cartilage matrix composition but does not affect chondrocyte viability. The results suggest that MMPs play a key role in regulating the balance of structural proteins of the articular cartilage matrix according to local mechanical demands

A COMMENT ON THE DARBOUX TRANSFORMATION

Abstract. It is known that the Darboux transformation (DT) allows us to construct isospectral potentials in the frame of the Schrödinger equation. Here we give a simple mathematical deduction for the DT

Deletion of the von Hippel-Lindau gene causes sympathoadrenal cell death and impairs chemoreceptor-mediated adaptation to hypoxia

Mutations of the von Hippel–Lindau (VHL) gene are associated with pheochromocytomas and paragangliomas, but the role of VHL in sympathoadrenal homeostasis is unknown. We generated mice lacking Vhl in catecholaminergic cells. They exhibited atrophy of the carotid body (CB), adrenal medulla, and sympathetic ganglia. Vhl‐null animals had an increased number of adult CB stem cells, although the survival of newly generated neuron‐like glomus cells was severely compromised. The effects of Vhl deficiency were neither prevented by pharmacological inhibition of prolyl hydroxylases or selective genetic down‐regulation of prolyl hydroxylase‐3, nor phenocopied by hypoxia inducible factor overexpression. Vhl‐deficient animals appeared normal in normoxia but survived for only a few days in hypoxia, presenting with pronounced erythrocytosis, pulmonary edema, and right cardiac hypertrophy. Therefore, in the normal sympathoadrenal setting, Vhl deletion does not give rise to tumors but impairs development and plasticity of the peripheral O2‐sensing system required for survival in hypoxic conditions