We estimate the error of Gauss-Jacobi quadrature rule applied to a function f, which is supposed locally absolutely continuous in some Besov type spaces, or of bounded variation on [-1,1]. In the first case the error bound concerns the weighted main part phi-modulus of smoothness of f introduced by Z. Ditzian and V. Totik, while in the second case we deal with a Stieltjes integral with respect to f.

Within the framework of general relativity, we investigate the tidal acceleration of astrophysical jets relative to the central collapsed configuration ("Kerr source"). To simplify matters, we neglect electromagnetic forces throughout; however, these must be included in a complete analysis. The rest frame of the Kerr source is locally defined via the set of hypothetical static observers in the spacetime exterior to the source.

In this paper we revisit the problem of finding an orthogonal similarity transformation that puts an $n\times n$ matrix $A$ in a block upper-triangular form that reveals its Jordan structure at a particular eigenvalue $\lambda_0$. The obtained form in fact reveals the dimensions of the null spaces of $(A-\lambda_0 I)^i$ at that eigenvalue via the sizes of the leading diagonal blocks, and from this the Jordan structure at $\lambda_0$ is then easily recovered. The method starts from a Hessenberg form that already reveals several properties of the Jordan structure of $A$.

The class of Bipartite Distance Hereditary (BDH) graphs is the intersection between bipartite domino-free and chordal bipartite graphs. Graphs in both the latter classes have linearly many maximal bicliques, implying the existence of polynomial-time algorithms for computing the associated Galois lattice. Such a lattice can indeed be built in O(m?n)O(m?n)worst-case time for a domino-free graph with mm edges and nn vertices. In Apollonio et al. (2015), BDH graphs have been characterized as those bipartite graphs whose Galois lattice is tree-like.

Classical results from spectral theory of stationary linear kinetic equations are applied to efficiently approximate two physically relevant weakly nonlinear kinetic models: a model of chemotaxis involving a biased velocity-redistribution integral term, and a Vlasov-Fokker-Planck (VFP) system. Both are coupled to an attractive elliptic equation producing corresponding mean-field potentials.

ZFP57 is required to maintain the germline-marked differential methylation at imprinting control regions (ICRs) in mouse embryonic stem cells (ESCs). Although DNA methylation has a key role in genomic imprinting, several imprinted genes are controlled by different mechanisms, and a comprehensive study of the relationship between DMR methylation and imprinted gene expression is lacking. To address the latter issue, we differentiated wild-type and Zfp57-/- hybrid mouse ESCs into neural precursor cells (NPCs) and evaluated allelic expression of imprinted genes.

In this paper, we propose a new mathematical model describing the effect of phosphocitrate (PC) on sodium sulphate crystallization inside bricks. This model describes salt and water transport, and crystal formation in a one dimensional symmetry. This is a preliminary study that takes into account mathematically the effects of inhibitors inside a porous stone. To this aim, we introduce two model parameters: the crystallization rate coefficient, which depends on the nucleation rate, and the specific volume of precipitated salt.

The visual quality evaluation is one of the fundamental challenging problems in image processing. It plays a central role in the shaping, implementation, optimization, and testing of many methods. The existing image quality assessment methods centered mainly on images altered by common distortions while paying little attention to the distortion introduced by color quantization.

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a "digital twin" of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance.