Search results for "geometry."
showing 10 items of 4386 documents
Infinite lie groups of point transformations leaving invariant the linear equation which describes in the hodograph plane the isentropic one-dimensio…
1991
Abstract The group analysis of the hodograph equation which is equivalent to the non-linear system of one-dimensional isentropic gas dynamics reveals the existence of infinite groups of symmetry in correspondence with particular pressure laws. These turn out to be polytropes with selected indices, as is expected, as well as a new type of pressure. In all these cases the hodograph equation can be transformed, by a suitable change of variables, into the wave equationψ ζ = 0.
On the myriad mathematical traditions of ancient greece
2002
To exert one’s historical imagination is to plunge into delicate deliberations that involve personal judgments and tastes. Historians can and do argue like lawyers, but their arguments are often made on behalf of a picture of the past, and these historical images obviously change over time. Why should the history of mathematics be any different? When we imagine the world of ancient Greek mathematics, the works of Euclid (Heath 1926), Archimedes (Heath 1897b), and Apollonius (Heath 1897a) easily spring to mind. Throughout most of the twentieth century, our dominant image of Greek mathematical traditions has been shaped by the high standards of rigor and creative achievement that are purporte…
An RF-Based Positioning Method for Tracing a Cluster of Moving Scatterers in Non-Stationary Indoor Environments
2021
Author's accepted manuscript © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This letter presents a novel iterative positioning method for tracing the body segments of a person moving indoors using radio-frequency (RF) signals. The indoor space is equipped with a multiple-input multiple-output (MIMO) communication system. The person is modelled by a cluster of …
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 …
Analysis of neuronal networks in the visual system of the cat using statistical signals
1976
If the input signals of the visual system in the cat are statistical patterns in space and time, a complete system analysis can be carried out. What counts here as a system are the neuronal networks between retina and recording site. In the case of linearity, one obtains the temporal impulse response functions at every point in the receptive field with the aid of correlation methods. The measuring time is about one minute. Some aspects of the procedure are explained in terms of examples. The method of measurement also makes it possible to determine the characteristic function of the system in time and space between different recording sites within the cortex. It is possible to specialize th…
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…
Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
2009
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.
Optimal calculation of the pair correlation function for an orthorhombic system
2012
We present a new computational method to calculate arbitrary pair correlation functions of an orthorombic system in the most efficient way. The algorithm is demonstrated by the calculation of the radial distribution function of shock compressed liquid hydrogen.