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Algebraic Geometry
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
Before defining algebraic curves we need to introduce the space where they are defined. Let K be a perfect field and K¯ it's algebraic closure. The n-dimensional projective space ℙKn over K is defined as follows ℙn(K¯)={(x0,…,xn)|}xi∈K¯, such that at least one xi≠0}/~
Sedimentation in Reservoir and Measurement
Published in Kumkum Bhattacharyya, Vijay P. Singh, Reservoir Sedimentation, 2019
Kumkum Bhattacharyya, Vijay P. Singh
Sediment sampling through perfect field techniques can generate a poor yield estimate if the sampling session does not coincide with major sediment-transporting events. For filling the data gap, the pump samplers are used to automatically pump water from the river into sample bottles, when the river stage or turbidity rises. The pump sampler obtains the concentration at a single depth at a single location which is not a representative of the entire cross section. Emerging sampling methods include the use of a linear, integrated solid-state tube (LISST) laser technology sampler, for example, to measuring suspended sediment concentration and grain size up to 0.5 mm simultaneously (Morris 2016a).
Two-dimensional Waves
Published in Jakob J Stamnes, Waves in Focal Regions, 2017
We also see from figure 13.6 that the central lobe of the non-perfect field is generally more narrow than that of the perfect field and that the amount of energy contained in the side lobes, compared with that in the central lobe, is larger in the case of a non-perfect field. Thus the change from a perfect incident wave to a non-perfect one produces the same general type of results as the application of a central obscuration (see figure 12.40(a)), i.e. we get a narrower central lobe at the expense of throwing more energy into the side lobes.
FTF: a quick surveying approach for constructing high resolution digital surface model for road elements
Published in Geomatics, Natural Hazards and Risk, 2020
Abdullah Kamel, Yehia Miky, Ahmed El Shouny
Good and correct office work starts from the field. The perfect field work is the work that describes all the surveying points correctly and consistently and uses a special code that allows connecting points with lineworks representing the same ground features. Field measurements obtained with proper description and coding are consistent with the nature of ground features that will contribute to the reduction of long hours of office drafting work. The survey team should prepare the description library and the codes to be used in the land survey which provide automatically through the survey database a rapid translation of lineworks that can be adjusted and customized with predefined styles into figures. The linework code is a text command entered after the description of the point. It is handled in accordance with the FTF method to refer to the start and endpoints of lineworks and to the creation of additional lines associated with them. In order to create linear features using points connected to each other, it is necessary to determine where the line starts and ends, whether straight or curved. The guidance for executing these geometric orders is done through specific codes that correspond to the set of lineworks codes defined in the relevant software, as shown in Table 1, to draw those ground features within the drawing file. The lineworks interface is the translator between the field work language and the Civil3D language.
Sympathetic cooling in two-species ion crystals in a Penning trap
Published in Journal of Modern Optics, 2018
S. Schmidt, T. Murböck, Z. Andelkovic, G. Birkl, K. König, W. Nörtershäuser, R. C. Thompson, M. Vogel
A Penning trap provides confinement of charged particles such as ions by a superposition of a static homogeneous magnetic field along the trap’s central axis with a static electric quadrupole potential [2,3]. The former provides radial trapping on account of the Lorentz force, while the latter confines the ions in a harmonic potential well along the axis. Under ideal trapping conditions, i.e. for perfect field geometry, an ion performs a motion that is the superposition of three independent oscillatory motions, two in the radial plane (perturbed cyclotron and magnetron motions) and one in the axial direction [16]. The frequencies of these motions are labelled , and , respectively. They typically obey a hierarchy with . For a ion in the present trap at a trapping voltage of V and a magnetic field strength of T, these frequenciesare kHz, kHz and MHz.
An ontology-based hybrid methodology for image synthesis and identification with convex objects
Published in The Imaging Science Journal, 2018
Nanfei Sun, Jian (Denny) Lin, Michael Yu-Chi Wu
As we have already described how to do image synthesis for right prisms in part 1, in this section our major task is to decompose the complex object to rectangle cuboids (A subset of right prisms) with proper number, position and orientation. Because most geometry shapes of buildings are composited by multiple rectangle cuboids in orthogonal relationships, this is a perfect field for our study to start with.