Search results for "Approx"

Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence

2022

We consider the Navier problem-Delta(2)(k,p)u(x)=f(x,u(x), del u(x), Delta u(x)) in Omega, u vertical bar(partial derivative Omega) =Delta u vertical bar(partial derivative Omega) = 0,driven by the sign-changing (degenerate) Kirchhoff type p(x)-biharmonic operator, and involving a (del u, Delta u)-dependent nonlinearity f. We prove the existence of solutions, in weak sense, defining an appropriate Nemitsky map for the nonlinearity. Then, the Brouwer fixed point theorem assessed for a Galerkin basis of the Banach space W-2,W-p(x)(Omega)boolean AND W-0(1,p(x))(Omega) leads to the existence result. The case of nondegenerate Kirchhoff type p(x)-biharmonic operator is also considered with respec…

A comparative study of the atomic and electronic structure of F centers in ferroelectric KNbO3: Ab initio and semi-empirical calculations

1998

Abstract The linear muffin-tin-orbital method combined with density functional theory (in a local density approximation) and the semi-empirical method of the intermediate neglect of the differential overlap (INDO) based on the Hartree-Fock formalism are used for the supercell study of the F centers (O vacancy with two electrons) in cubic and orthorhombic ferroelectric KNbO3 crystals. The two electrons are found to be considerably delocalized even in the ground state of the defect. Their wave functions extend over the two Nb atoms closest to the O vacancy and over other nearby atoms. Thus, the F center in KNbO3 resembles much more electron defects in the partly covalent SiO2 crystal (the so-…

The microscopic theory of diffusion-controlled defect aggregation

1998

Abstract The kinetics of diffusion-controlled aggregation of primary Frenkel defects ( F and H centers) in irradiated CaF 2 crystals is theoretically studied. Microscopic theory is based on the discrete-lattice formalism for the single defect densities (concentrations) and the coupled joint densities of similar and dissimilar defects treated in terms of the Kirkwood superposition approximation. Conditions and dynamics of the efficient F center aggregation during crystal heating after irradiation are analyzed.

From Nerode's congruence to Suffix Automata with mismatches

2009

AbstractIn this paper we focus on the minimal deterministic finite automaton Sk that recognizes the set of suffixes of a word w up to k errors. As first result we give a characterization of the Nerode’s right-invariant congruence that is associated with Sk. This result generalizes the classical characterization described in [A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. Chen, J. Seiferas, The smallest automaton recognizing the subwords of a text, Theoretical Computer Science, 40, 1985, 31–55]. As second result we present an algorithm that makes use of Sk to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text, where r is the…

Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes

2006

A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…

On approximating curves associated with nonexpansive mappings

2011

Let X be a Banach space with metric d. Let T, N : X → X be a strict d-contraction and a d-nonexpansive map, respectively. In this paper we investigate the properties of the approximating curve associated with T and N. Moreover, following [3], we consider the approximating curve associated with a holomorphic map f : B → α B and a ρ-nonexpansive map M : B → B, where B is the open unit ball of a complex Hilbert space H, ρ is the hyperbolic metric defined on B and 0 ≤ α < 1. We give conditions on f and M for this curve to be injective, and we show that this curve is continuous.

Using the dglars Package to Estimate a Sparse Generalized Linear Model

2015

dglars is a publicly available R package that implements the method proposed in Augugliaro et al. (J. R. Statist. Soc. B 75(3), 471-498, 2013) developed to study the sparse structure of a generalized linear model (GLM). This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method. The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve. dglars is a publicly available R package that implements the method proposed in Augugliaro et al. (J. R. Statist. Soc. B 75(3), 471-498, 2013) developed to study the sparse structure of a generalized linear model (GLM). This method, call…

Modern taurine cattle descended from small number of near-eastern founders.

2012

Archaeozoological and genetic data indicate that taurine cattle were first domesticated from local wild ox (aurochs) in the Near East some 10,500 years ago. However, while modern mitochondrial DNA (mtDNA) variation indicates early Holocene founding event(s), a lack of ancient DNA data from the region of origin, variation in mutation rate estimates, and limited application of appropriate inference methodologies have resulted in uncertainty on the number of animals first domesticated. A large number would be expected if cattle domestication was a technologically straightforward and unexacting region-wide phenomenon, while a smaller number would be consistent with a more complex and challengin…

Weierstraß’s Approximation Theorem (1885) and his 1886 lecture course revisited

2015

The paper provides new insight into the origins of Weierstras’s 1886 lecture course on the foundations of function theory and of the mimeographed lecture notes connected to this course which were published by the author in German in 1988. A short overview of the content of the lecture course is given; the central role that Weierstras’s famous approximation theorem of 1885 played in it is emphasized. The paper uses archival material recently discovered at the Institut Mittag-Leffler in Djursholm.

2021

The domestication and spreading of grapevine as well as the gene flow history had been described in many studies. We used a high-quality 7k SNP dataset of 1,038 Eurasian grape varieties with unique profiles to assess the population genetic diversity, structure, and relatedness, and to infer the most likely migration events. Comparisons of putative scenarios of gene flow throughout Europe from Caucasus helped to fit the more reliable migration routes around the Mediterranean Basin. Approximate Bayesian computation (ABC) approach made possible to provide a response to several questions so far remaining unsolved. Firstly, the assessment of genetic diversity and population structure within a we…