Search results for "Geometry"
showing 10 items of 4487 documents
Systematische Analyse der Geometrie eines definierten Kontrastmittelbolus - Implikationen für die kontrastmittelverstärkte 3D-MR-Angiographie thoraka…
2005
Purpose: Little is known about the dispersion of a defined contrast bolus during its passage through the heart and pulmonary vasculature. The purpose of this study was to analyze factors influencing a defined contrast bolus for ce-MRA of thoracic vessels. Materials and Methods: For analysis of bolus geometry, an ECG-gated saturation-recovery Turbo-Flash sequence with a TI of 20 msec was used. It was acquired axially at the level of the pulmonary trunc, so that with one data acquisition a curve analysis was possible in the ascending and descending aorta, and in the pulmonary trunc. Twenty-nine patients received 3 ml of Gd-DTPA diluted with saline to a total of 20 ml. Contrast injection was d…
Association of Arsenic Exposure With Cardiac Geometry and Left Ventricular Function in Young Adults
2019
Background: Arsenic exposure has been related to numerous adverse cardiovascular outcomes. The aim of this study was to investigate the cross-sectional and prospective association between arsenic exposure with echocardiographic measures of left ventricular (LV) geometry and functioning. Methods: A total of 1337 young adult participants free of diabetes mellitus and cardiovascular disease were recruited from the SHFS (Strong Heart Family Study). The sum of inorganic and methylated arsenic concentrations in urine (ΣAs) at baseline was used as a biomarker of arsenic exposure. LV geometry and functioning were assessed using transthoracic echocardiography at baseline and follow-up. Results: Mea…
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.…
Application of the star-product method to the angular momentum quantization
1992
We define a *-product on ℝ3 and solve the polarization equation f*C=0 where C is the Casimir of the coadjoint representation of SO(3). We compute the action of SO(3) on the space of solutions. We then examine the case of non-zero eigenvalues of C, in order to find finite-dimensional representations of SO(3). Finally, we compute \(\sqrt C *\sqrt C \) as an asymptotic series of C. This gives an explanation of the use of the star square root of C in a paper by Bayen et al. instead of its natural square root.
Convergence in discrete Cauchy problems and applications to circle patterns
2005
A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.
The Cauchy problem in hybrid metric-Palatini f(X)-gravity
2013
The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it \`{a} la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be {\it well-formulated} and, furthermore, can be {\it well-…
Exact treatment of linear difference equations with noncommutative coefficients
2007
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
Exact treatment of operator difference equations with nonconstant and noncommutative coefficients
2013
We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.
A note on the higher order strain and stress tensors within deformation gradient elasticity theories: Physical interpretations and comparisons
2016
Abstract Higher order strain and stress tensors encompassed within gradient elasticity theories are discussed with a particular concern to the physical meaning of double and triple stresses. A single rule is shown to hold for the physical interpretation of the indices of a higher order stress tensor both within distortion gradient and strain gradient theories, whereas the analogous Mindlin’s rule holds only within distortion gradient theories. Double and triple stresses are discussed separately with the aid of simple illustrative examples. A corrigendum to a previous paper by the author (IJSS 50 (2013) 3749–3765) is also presented.
Mixed-ligand copper(ii)–sulfonamide complexes: effect of the sulfonamide derivative on DNA binding, DNA cleavage, genotoxicity and anticancer activity
2013
Four ternary complexes, [Cu(L1)2(bipy)] (1) [HL1 = N-(6-chlorobenzo[d]thiazol-2-yl)-4-methylbenzenesulfonamide], [Cu(L2)2(bipy)] (2) [HL2 = N-(benzo[d]thiazol-2-yl)-4-methylbenzenesulfonamide], [Cu(L3)2(bipy)]·1/2H2O (3) [HL3 = N-(5,6-dimethylbenzo[d]thiazol-2-yl)-4-methylbenzenesulfonamide] and [Cu(L4)2(bipy)] (4) [HL4 = N-(5,6-dimethylbenzo[d]thiazol-2-yl)benzenesulfonamide], were prepared and then characterized by X-ray crystallography, spectroscopy and magnetic measurements. Whereas the molecular structure of 1 and 2 consists of a discrete monomeric copper(II) species with a distorted square planar geometry, that of 3 and 4 consists of two independent molecules. In 3, both molecules pre…