Different Kinds Of Curves Research Articles

A Generalized Cubic Exponential B-Spline Scheme with Shape Control

In this paper, a generalized cubic exponential B-spline scheme is presented, which can generate different kinds of curves, including the conics. Such a scheme is obtained by generalizing the cubic exponential B-spline scheme based on an iteration from the generation of exponential polynomials and a suitable function with two parameters μ and ν. By changing the values of μ and ν, the sensitivity of the shape of the subdivision curve to the initial control value v0 can be changed and different kinds of curves can then be obtained by adjusting the value of v0. For this new scheme, we show that, with any admissible choice of μ and ν, it owns the same smoothness order and support as the cubic exponential B-spline scheme. Besides, based on a different iteration and another suitable function, we construct a similar nonstationary scheme to generate more curves with different shapes and show the role of iterations and suitably chosen functions in the construction and analysis of such schemes. Several examples are given to illustrate the performance of our new schemes.

Optimal Coordination of Overcurrent Relays inRadial Electrical Distribution Networks

Short-circuits can cause irreversible damage toelectrical system, pose a risk to the lives of humans and animals,and can set off fires on any surface in contact with the conductors.To reduce the time in which the electrical installation remainsunder the effects of a short-circuit, protection devices arenecessary. One of the most important functions of these devices isthe time overcurrent protection. The main objective of this workis to propose a solution for an automatic parameterization of thetime overcurrent protection in radial power distributionnetworks. The proposed method uses a genetic algorithm andexplores the different kinds of curves presented in each protectiondevice. The proposed method was tested in a real electricaldistribution network and obtained feasible and good solutions forthe coordination problem.

Fourier-based multi-scale representation and progressive transmission of cartographic curves on the internet

ABSTRACTAutomatic generation of multi-scale representations from the same spatial data source has been the research focus in map generalization for a long time. Based on the Fourier technique, this paper proposes a continuous, multi-scale representation model for progressive transformation of cartographic curves on the Internet. In our method, all the curves, whether closed or open, are depicted as periodical functions which are further expressed as Fourier series. The convergence degrees of the Fourier series are explored for different kinds of curves, and truncating frequencies are derived based on the similarity between the original and reconstructed curves. Using information theory and the Radical Law in cartography, the relationship between map scales and Fourier frequencies is established. Based on the proposed multi-scale model, we also introduce the principles and implementation of a progressive transmission method. Our method is evaluated using the contours from a topographic map. The results show that our model is a valid approach to multi-scale representation of cartographic curves.

Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.

Geometric Motion Control for a Kinematically Redundant Robotic Chain: Application to a Holonomic Mobile Manipulator

AbstractFor kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end‐effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end‐effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail. © 2003 Wiley Periodicals, Inc.

Gas transmission properties of polyvinyl chloride (PVC) films studied under subambient and ambient conditions for modified atmosphere packaging applications

AbstractThis study was undertaken to determine the gas transmission properties of three polyvinyl chloride (PVC) films mostly used as overwrap for fresh produce under subambient and ambient conditions (5–40°C). Three different kinds of curves or groups of data are presented: gas transmission rates, activation energy measurements and the permeability coefficient. Hydrophobic by nature, the PVCs are not affected in their gas transmission properties (O2, CO2) by the moisture level. Reliable gas transmission data were obtained with method variability (≤9%) over a wide range of temperature. Regression constants, activation energies for prediction equations and permeability ratios (CO2/O2) are presented for the three films. Greater uniformity in test procedures, and the presentation of permeability data normalized to 1 μm instead of 1 mil would simplify comparative studies within and between countries, laboratory services and from the scientific literature. More research is needed to study the wide variety of polymers available under subambient conditions.

Colloid characterization by sedimentation field-flow fractionation. III. Emulsions

The successful application of sedimentation field-flow fractionation (sedimentation FFF) to the characterization of monodisperse and polydisperse particle populations was extended to the determination of the droplet size distribution (DSD) of emulsions. The theory and advantages of sedimentation FFF are briefly reviewed, and it is shown quite generally that the centrifugal field is not sufficiently strong to cause droplet distortion, aggregation, or other similar disturbances. Two different sets of experiments, applied to two commercial emulsions used for intravenous nutrition, are described. The safflower oil emulsion, subjected primarily to self-consistency tests, was shown to yield virtually identical raw DSD curves despite changes in field strength, sample size, flow velocity, and instrumental systems. For the soybean oil emulsion, a detector response correction factor was obtained by dissolution of the emulsion. It was shown that changes in the manufactured emulsion product could be followed by directly observing changes in the fractogram, or by noting changes in the DSD curves. The conditions under which the different kinds of curves can be used for comparative purposes were outlined.

Examples of geoelectric surveys

The Introduction deals briefly with the general principles underlying geoelectric methods of surveying and gives a simple formula for the apparent resistivity at a given depth below the surface in a homogeneous medium. The two problems of interpreting the different kinds of curves obtained from field measurements and of determining the depth of the associated geological anomalies are discussed.In Section 1.2 the electrical equipment and field procedure are briefly described.Three particular anomalies are considered in Section 1.3. These are:(i) Parallel strata as illustrated by the boulder-clays which overlie the chalk of the Holderness Plain, East Yorkshire.(ii) Inclined strata which occur where the water-table reaches the surface on the slopes of the Mendip Hills, Somerset.(iii) A cavern in the limestone rocks at Pen Park near Filton, Bristol.In Sections 2, 3 and 4 respectively, the relevant equations, the geoelectric measurements and graphs together with their interpretations are discussed. The equation for inclined strata is deduced in a form comparable with the previously published equations for parallel strata and a spherical cavity. These latter are stated in Sections 2 and 4 respectively, and their derivation is given in the Appendix.From the graphs in Section 2 it is concluded that no ancient Humber estuary existed in the chalk beneath the boulder-clays, but the presence of an interglacial gravel separating two deposits of boulder-clays is established.In Section 3 the water-table is located and is found to emerge along a line of springs which coincides with the edge of the conglomerate deposited by the ancient Triassic sea.The deductions made from the graphs of Section 4 were verified by subsequent excavations which led to the rediscovery of Pen Park Hole.In the Appendix the derivation of the equations for a homogeneous medium, for parallel strata and for a buried sphere are given, together with theoretical relationships for calculating the depths of these particular anomalies.

DARK ADAPTATION IN AGRIOLIMAX

A method is described which measures the excitation of Agriolimax by light, during the progress of light adaptation, by assuming that the orientating effect of continuous excitation is expressed as a directly proportionate tension difference in the orienting muscles of the two sides of the body. The tendency toward establishment of such a tension difference is caused to work against a similar geotropic effect at right angles to the phototropic one. This enables one to study the kinetics of light adaptation, and of dark adaptation as well. The situation in the receptors is adequately described by the paradigm See PDF for Equation similar to that derived by Hecht for the differential sensitivity of various forms, but with the difference that the "dark" reaction is not only "bimolecular" but also autocatalysed by the reaction product S. The progress of dark adaptation is reflected (1) in the recovery of the amplitude of the orientation and (2) in the rates of light adaptation at different levels of the recovery; each independently supports these assumptions, for which the necessary equations have been provided. These equations also account for the relative variabilities of the angles of orientation, and, more significantly, for the two quite different kinds of curves of dark adaptation which are obtained in slightly different types of tests.