Search results for " geometry"
showing 10 items of 2294 documents
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.
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…
Morphological Similarity of Channels: From Linear Erosional Features (Rill, Gully) to Alpine Rivers
2017
The geometric characteristics of incised features such as channels, rills, ephemeral gully, gully, represent the erosional transport regime and the fluvial dynamic equilibrium, and thus it is critical for the understanding of the long-term evolution of natural, agricultural, and anthropogenic landscapes. This paper examines the morphological similarity of channelized erosion in two different environments such as Alpine landscapes and cultivated hillslopes. The first dataset comprises six rivers in the Italian Alps, three in the Carnia region and three in the Dolomites, where erosion is mainly the effect of discharges with high sediment loads or landslides and debris flows. The agricultural …
Uniformization with infinitesimally metric measures
2019
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb R^2$, whose definition involves deforming lengths of curves by $\mu$. We show that if $\mu$ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a $\mu$-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.
Ferrimagnetic Heisenberg chain; influence of a random exchange interaction
1985
We report on the magnetic behavior of ‘‘rigid’’ ferrimagnetic chains isolated in bimetallic complexes of the EDTA and ‘‘flexible’’ ones obtained in the amorphous variety. As shown by LAXS, the only noteworthy difference in the amorphous state is the random distribution of bond angles between nearest neighbors within chains. The ‘‘rigid’’ bimetallic chains in CoNi(EDTA)6H2O are described in terms of Heisenberg model with an exchange coupling J=−7.5 K. The behavior of the amorphous variety somewhat differs, following the law X=AT−0.8 typical of REHAC. A classical spin chain model involving a J distribution and alternating g factors allows to explain successfully the temperature dependence of …
A Rational Design for Imidazolate-Bridged Linear Trinuclear Compounds from Mononuclear Copper(II) Complexes with 2-[((Imidazol-2-ylmethylidene)amino)…
2001
Two mononuclear copper(II) complexes with the unsymmetrical tridentate ligand 2-[((imidazol-2-ylmethylidene)amino)ethyl]pyridine (HL), [Cu(HL)(H2O)](ClO4)2.2H2O (1) and [Cu(HL)Cl2] (2), have been prepared and characterized. The X-ray analysis of 2 revealed that the copper(II) ion assumes a pentacoordinated square pyramidal geometry with an N3Cl2 donor set. When 1 and 2 are treated with an equimolecular amount of potassium hydroxide, the deprotonation of the imidazole moiety promotes a self-assembled process, by coordination of the imidazolate nitrogen atom to a Cu(II) center of an adjacent unit, leading to the polynuclear complexes [[Cu(L)(H2O)](ClO4)]n (3) and [[Cu(L)Cl].2H2O]n (4). Variab…
On fermionic shadow wave functions for strongly correlated multi-reference systems based on a single Slater determinant
2015
We demonstrate that extending the Shadow Wave Function to fermionic systems facilitates to accurately calculate strongly-correlated multi-reference systems such as the stretched H2 molecule. This development considerably extends the scope of electronic structure calculations and enables to efficiently recover the static correlation energy using just a single Slater determinant.
Fourier transform nmr investigations of organotin compounds
1980
Abstract NMR spectra have been obtained for fiteen title compounds, mainly with R = Me. Tin chemical shifts were found to lie within the expected ranges, but to vary little with R or, apparently, with change in ring size. While the magnitute of 1 (SnSe) was as predicted, the of 1 (SnTe) was more than twice as large as that previously observed for (Me 3 Sn) 2 Te. In compounds Me 6 Sn( 3 X 3 , 2 J(SnMSn) varied systematically with variations in x, but within relatively narrow limits (195-250 Hz); a much more drastic variation was observed for Me 6 Sn 3 X 2 , possibly due to bond angle changes at Sn and X.