scholarly journals Data Visualization Using Rational Trigonometric Spline

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Uzma Bashir ◽  
Jamaludin Md. Ali
Keyword(s):  
Data Visualization ◽  
The Other ◽  
Shape Features ◽  
Shape Parameters ◽  
Shape Preserving ◽  
Numerical Examples ◽  
Data Points ◽  
Trigonometric Spline ◽  
The Given

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

scholarly journals C1Rational Quadratic Trigonometric Interpolation Spline for Data Visualization

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Shengjun Liu ◽  
Zhili Chen ◽  
Yuanpeng Zhu
Keyword(s):  
Trigonometric Interpolation ◽  
Data Sets ◽  
Order Of Approximation ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Shape Preserving ◽  
Shape Preserving Interpolation ◽  
Trigonometric Spline ◽  
The Given ◽  
Data Constraints

A newC1piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated asO(h3). Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

scholarly journals Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ayser Nasir Hassan Tahat ◽  
Abd Rahni Mt Piah ◽  
Zainor Ridzuan Yahya
Keyword(s):  
Numerical Experiments ◽  
Smooth Curve ◽  
The Other ◽  
Data Interpolation ◽  
Shape Parameters ◽  
Interpolation Scheme ◽  
Shape Preserving ◽  
Curve Interpolation ◽  
Two Parameters

A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness isC1. The outputs from a number of numerical experiments are presented.

Cubic TP B-Spline Curves with a Shape Parameter

2013 ◽  
Vol 11 ◽  
pp. 59-72 ◽  
Author(s):  
Mridula Dube ◽  
Reenu Sharma
Keyword(s):  
Tensor Product ◽  
Shape Parameter ◽  
Control Points ◽  
Shape Parameters ◽  
Special Shape ◽  
B Spline ◽  
Control Polygon ◽  
Spline Curves ◽  
Trigonometric Spline ◽  
The Given

In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS

2012 ◽  
Vol 12 (04) ◽  
pp. 1250028
Author(s):  
MRIDULA DUBE ◽  
REENU SHARMA
Keyword(s):  
Trigonometric Polynomial ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curve ◽  
Control Polygon ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Polynomial Curve ◽  
Trigonometric Spline ◽  
The Given

Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

Stresses in a Perforated Wedge

1973 ◽  
Vol 40 (3) ◽  
pp. 759-766 ◽  
Author(s):  
Chih-Bing Ling ◽  
Chang-Ming Hsu
Keyword(s):  
Boundary Conditions ◽  
Circular Hole ◽  
Stress Function ◽  
The Other ◽  
Numerical Examples ◽  
Biharmonic Functions ◽  
Method Of Solution ◽  
The Given ◽  
Infinite Wedge

This paper presents a method of solution for an infinite wedge containing a symmetrically located circular hole. The solution is formulated separately according to the given in-plane edge tractions being even or odd with respect to the axis of the wedge. In either case, the stress function is constructed as the sum of four parts of biharmonic functions, two in the form of integrals and the other two in the form of series, in addition to a basic stress function for an otherwise unperforated wedge. The four parts as a whole give no traction along the edges and no stress at infinity of the wedge. Together with the basic stress function, the boundary conditions of no traction at the rim of hole are adjusted. Complex expressions are used in adjusting the boundary conditions. Finally, numerical examples are given for illustration.

scholarly journals New Iterative Method: An Application for Solving Fractional Physical Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Fractional Order ◽  
Small Perturbation ◽  
The Other ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
The Given ◽  
New Iterative Method

The new iterative method with a powerful algorithm is developed for the solution of linear and nonlinear ordinary and partial differential equations of fractional order as well. The analysis is accompanied by numerical examples where this method, in solving them, is used without linearization or small perturbation which con…firm the power, accuracy, and simplicity of the given method compared with some of the other methods.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

The acquisition of Hungarian recursive PPs

2018 ◽  
Vol 4 (1) ◽  
pp. 105-123
Author(s):  
Ágnes Langó-Tóth
Keyword(s):  
Language Acquisition ◽  
Functional Element ◽  
The Other ◽  
Functional Head ◽  
Experiment Subject ◽  
The Given

Abstract In this study an experiment is presented on how Hungarian children interpret two word orders of recursive PPs (subject-PP-verb and PP-subject-verb order). According to the research of Roeper (2011) and Hollebrandse and Roeper (2014), children tend to give conjunctive interpretation to multiple embedded sentences at the beginning of language acquisition. This interpretation later turns into an adult-like, recursive interpretation. Our aim is to discover (i) whether Hungarian children start with conjunction as well, and whether (ii) the apparently more salient functional head lévő appearing in Hungarian recursive PPs can help them to acquire the correct, recursive interpretation early. We also want to find out whether (iii) the word orders in recursive PPs have an influence on the acquisition of children. In this paper two experiments are presented conducted with 6 and 8-year-olds and adults, in which the participants were asked to choose between two pictures. One of the pictures depicted recursive and the other one depicted conjunctive interpretation of the given sentence. In the first experiment subject-PP-verb order was tested, but in the second one sentences were tested with PP-subject-verb order. We will claim that lévő, which is (arguably) a more salient Hungarian functional element than -i, does not help children to acquire the embedded reading of recursive sentences, because both of them are overt functional heads. However, the two types of word orders affect the acquisition of recursive PPs. PP-subject-verb order is easier to compute because the order of the elements in the sentences and the order of the elements in the pictures matches.

Growth Characteristics of Activated Sludges Acclimated to para-Nitrophenol in Batch and Continuous Modes

1994 ◽  
Vol 29 (7) ◽  
pp. 327-333
Author(s):  
Y. Matsui ◽  
F. Yamaguchi ◽  
Y. Suwa ◽  
Y. Urushigawa
Keyword(s):  
Growth Characteristics ◽  
The Other ◽  
Operational Mode ◽  
Continuous Mode ◽  
Relative Resistance ◽  
Batch Mode ◽  
The Given ◽  
Operational Modes ◽  
Very High ◽  
Sensitive Group

Activated sludges were acclimated to p-nitrophenol (PNP) in two operational modes, a batch and a continuous. The operational mode of the PNP acclimation of activated sludges strongly affected the physiological characteristics of predominant microorganisms responsible for PNP degradation. Predominant PNP degraders in the sludge in batch mode (Sludge B) had lower PNP affinity and were relatively insensitive to PNP concentration. Those of the sludge in continuous mode (Sludge C), on the other hand, had very high PNP affinity and were sensitive to PNP. MPN enumeration of PNP degraders in sludge B and C using media with different PNP concentrations (0.05, 0.2,0.5 and 2.0 mM) supported the above results. Medium with 0.2 mM of PNP did not recover PNP degraders in sludge C well, while it recovered PNP degraders in sludge B as well as the medium with 0.05 mM did. When switching from one operational mode to the other, the predominant population in sludge B shifted to the sensitive group, but that of sludge C did not shift at the given loading of PNP, showing relative resistance to inhibitive concentration.

Giving and Promising

2018 ◽  
Author(s):  
Jean-Yves Lacoste ◽  
Oliver O’Donovan
Keyword(s):  
The Other ◽  
Face To Face ◽  
Present Experience ◽  
The World ◽  
The Given

Giving and promise must be thought together. Being-in-the world entails being-with the other, who is both “given” and bearer of a gift promised. But any disclosure may be understood as a gift; it is not anthropomorphic to speak of “self-giving” with a wider reference than person-to-person disclosure. Which implies that no act of giving can exhaust itself in its gift. Present experience never brings closure to self-revealing. Yet giving is crystallized into “the given,” the closure of gift. “The given” is what it is, needing no gift-event to reveal it. But the given, too, is precarious, and can be destabilized when giving brings us face to face with something unfamiliar. Nothing appears without a promise of further appearances, and God himself can never be “given.”

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