Search results for "Geometry"
showing 10 items of 4487 documents
Adhesive papillae ofAscidia malacaswimming larvae: investigations on their sensory function
1999
Summary Swimming larvae of Ascidia malaca bear, in the anterior region of cephalenteron, three adhesive papillae through which they can attach to a substratum prior to metamorphosis. The ultrastructural investigations described in the present work have mainly revealed the presence of three cell types constituting the papillae: (a) collocytes, (b) axial columnar cells, (c) sensory cells. Collocytes, whose ultrastructure is typical of secretory cells, form the adhesive secretion. The ultrastructural observations of the axial columnar cells are insufficient to explain their function. Probably this cell type plays a supporting role though some sensory function cannot be excluded due to the pres…
Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems
2021
In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.
Regional and experiential differences in surgeon preference for the treatment of cervical facet injuries: a case study survey with the AO Spine Cervi…
2021
Abstract Purpose The management of cervical facet dislocation injuries remains controversial. The main purpose of this investigation was to identify whether a surgeon’s geographic location or years in practice influences their preferred management of traumatic cervical facet dislocation injuries. Methods A survey was sent to 272 AO Spine members across all geographic regions and with a variety of practice experience. The survey included clinical case scenarios of cervical facet dislocation injuries and asked responders to select preferences among various diagnostic and management options. Results A total of 189 complete responses were received. Over 50% of responding surgeons in each region…
Local symmetries of digital contours from their chain codes
1996
In this work symmetry is evaluated as a numeric feature for each point of a contour, using only the positions of a local vicinity of points. A measurement is defined, named as Local Symmetric Deficiency (LSD), so that the lower this quantity is, the higher the symmetry will be in the local region considered. This approach is very simple and it is based on a suitable manipulation of the chain code of the curve. Its computational cost is very low and it has the advantages of a parallel algorithm, since values for LSD can be computed for each point independently.
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.