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.

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.

Optimization of Inlet Ring Groove Arrangement for Suppression of Unstable Flow in a Centrifugal Impeller

2005 ◽  
Author(s):  
Masahiro Ishida ◽  
Daisaku Sakaguchi ◽  
Hironobu Ueki
Keyword(s):  
Flow Rate ◽  
The Other ◽  
Centrifugal Impeller ◽  
Shape Parameters ◽  
Unstable Flow ◽  
Ring Groove ◽  
Flow Rates ◽  
Small Flow ◽  
Specific Speed ◽  
Large Flow

An optimization of the inlet ring groove arrangement has been pursued in the present study for obtaining better impeller characteristics and a wider operation range at both small and large flow rates in a high specific speed type centrifugal impeller with inducer. The effects of the shape parameters with respect to the inlet ring groove on the impeller characteristic and the flow incidence were analyzed mainly based on numerical simulations, but also compared to the experimental results. At small flow rates, a significant improvement in the impeller characteristic is achieved due to reduction in the excessive-positive flow incidence by optimizing both location and width of the rear groove near the inducer tip throat. On the other hand, the impeller characteristic is improved at large flow rates by implementing the corner radius at the rear groove edge and by placing another front ring groove in the suction pipe. As a result, by the optimized configuration of the front and rear ring grooves, the unstable flow range of the test impeller can be reduced by about 50% without deterioration of the impeller characteristic even at the 125% flow rate.

Development of Advanced CNC Interpolation Algorithm With Consideration of Command and Dynamic Errors

2015 ◽  
Author(s):  
Meng-Shiun Tsai ◽  
Ying-Che Huang
Keyword(s):  
The Other ◽  
Contour Error ◽  
Interpolation Algorithm ◽  
Interpolation Scheme ◽  
Error Equation ◽  
The Past ◽  
Cnc Interpolation ◽  
Dynamic Errors ◽  
Simulation Results ◽  
The Given

In this paper, an integrated acceleration/deceleration with dynamics interpolation scheme is proposed to confine the maximum contour error at the junction of linear junction. The dynamic contour error equation is derived analytically and then it is utilized for the interpolation design. Based on the derived formulations which could predict the command and dynamic errors, the advanced interpolation design could adjust the connecting velocity of the two blocks to confine the overall contour errors under the given tolerance. Simulation results validate the proposed algorithm can achieve higher accurate trajectory as compared to the other interpolation algorithm proposed in the past.

Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

2021 ◽  
pp. 2150002
Author(s):  
Guimin Yang ◽  
Yuanguo Zhu
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Numerical Experiments ◽  
Critical Value ◽  
The Other ◽  
Options Pricing ◽  
Underlying Asset ◽  
Pricing Problems ◽  
Fractional Differential ◽  
The One

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

scholarly journals Modifications to Kozeny–Carman model to enhance petrophysical relationships

2017 ◽  
Author(s):  
Amir M. S. Lala
Keyword(s):  
Grain Size ◽  
Pore Size ◽  
The Other ◽  
Shaly Sand ◽  
Two Parameters ◽  
Log Linear

Abstract. The most commonly used relationship relates permeability to porosity, grain size, and tortuosity is Kozeny–Carman formalism. When it is used to estimate the permeability behavior versus porosity, the other two parameters (the grain size and tortuosity) are usually kept constant. Here, we investigate the deficiency of the Kozeny–Carman assumption and offer alternative derived equations for the Kozeny–Carman equation, including equations where the grain size is replaced with the pore size and with varying tortuosity. We also introduced relationships for the permeability of shaly sand reservoir that answer the approximately linear permeability decreases in the log-linear permeability-porosity relationships in datasets from different locations.

Smooth curve interpolation

1969 ◽  
Vol 9 (1) ◽  
pp. 69-77 ◽  
Author(s):  
C. H. Woodford
Keyword(s):  
Smooth Curve ◽  
Curve Interpolation

Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series

2019 ◽  
Vol 150 (4) ◽  
pp. 1853-1870 ◽  
Author(s):  
R. I. Dmytryshyn
Keyword(s):  
Power Series ◽  
Continued Fractions ◽  
Numerical Experiments ◽  
The Other ◽  
Independent Variables ◽  
Classical Algorithm ◽  
Multiple Power ◽  
The One ◽  
The Given ◽  
Multiple Power Series

AbstractIn the paper the correspondence between a formal multiple power series and a special type of branched continued fractions, the so-called ‘multidimensional regular C-fractions with independent variables’ is analysed providing with an algorithm based upon the classical algorithm and that enables us to compute from the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional regular C-fraction with independent variables. A few numerical experiments show, on the one hand, the efficiency of the proposed algorithm and, on the other, the power and feasibility of the method in order to numerically approximate certain multivariable functions from their formal multiple power series.

scholarly journals Re-semantization of A. Pushkin’s poetry in the creative work of V. Kosenko (on the example of “The Five Romances”, op. 20)

2018 ◽  
Vol 50 (50) ◽  
pp. 89-102
Author(s):  
Duangui Wang
Keyword(s):  
Slow Motion ◽  
The Other ◽  
Literary Translation ◽  
Time Space ◽  
Free Translation ◽  
The One ◽  
The Individual ◽  
Two Parameters ◽  
Love Language ◽  
Poetic Composition

Formulation of the problem. In the chamber-vocal genre, the composer exists in two images: he is both the interpreter of the poetic composition and the author of a new synthetic music and poetic composition. The experience of the style analysis of one of the best examples of Ukrainian vocal lyrics of the first third of the 20th century shows that the cycle op. 20 characterizes the mature style of the composer, which was formed, on the one hand, under the influence of European Romanticism. On the other hand, the essence of the Ukrainian “branch” of the Western European song-romance (“solo-singing”) is revealed by the prominent national song-romance intonation, filled with not only a romantic worldview, but also with some personal sincerity, chastity, intimate involvement with the great in depth and simplicity poetry line, read from the individual position of the musician. The paradox is as follows. Although Pushkin’s poetry is embodied in a “holistic adequacy” (A. Khutorskaya), and the composer found the fullest semantic analogue of the poetic source, however, in terms of translating the text into the Ukrainian language, the musical semantics changes its intonation immanence, which naturally leads to inconsistency of the listeners’ position and ideas about the style of Russian romance. We are dealing with inter-specific literary translation: Pushkin’s discourse creates the Ukrainian romance style and system of figurative thinking. The purpose of the article is to reveal the principle of re-semantization of the intonation-figurative concept of the vocal composition by V. Kosenko (in the context of translating Pushkin’s poetry into the Ukrainian language) in light of the theory of interspecific art translation. Analysis of recent publications on the topic. Among the most recent studies of Ukrainian musicology, one should point out the dissertation by G. Khafizova (Kyiv, 2017), in which the theory of modelling of the stylistic system of the vocal composition as an expression of Pushkin’s discourse is described. The basis for the further stylistic analysis of V. Kosenko’s compositions is the points from A. Hutorska’s candidate’s thesis; she develops the theory of interspecific art translation. The types of translation of poetry into music are classified according to two parameters. The exact translation creates integral adequacy, which involves the composer’s finding a maximally full semantic analogue of the poetic source. The free translation is characterized by compensatory, fragmentary, generalized-genre adequacy. Presenting the main material. The Zhitomir period for Viktor Kosenko was the time of the formation of his creative style. Alongside the lyrical imagery line, the composer acquired one more – dramatic, after his mother’s death. It is possible that the romances on the poems of A. Pushkin are more late reflection of this tragic experience (op. 20 was created in 1930). “I Loved You” opens the vocal cycle and has been dedicated by A. V. Kosenko. The short piano introduction contains the intonation emblem of the love-feeling wave. The form of the composition is a two part reprising (А А1) with the piano Introduction and Postlude. The semantic culmination is emphasized by the change of metro-rhythmic organization 5/4 (instead of 4) and the plastic phrase “as I wish, that the other will love you” sounding in the text. Due to these melodies (with national segments in melo-types, rhythm formulas and harmony) V. Kosenko should be considered as “Ukrainian Glinka”, the composer who introduced new forms and “figures” of the love language into the romantic “intonation dictionary”. In general, V. Kosenko’s solo-singing represents the Ukrainian analogue of Pushkin’s discourse – the theme of love. The melos of vocal piece “I Lived through My Desires” is remembered by the broad breath, bright expression of the syntactic deployment of emotion. On the background of bass ostinato, the song intonation acquires a noble courage. This solo-singing most intermediately appeal to the typical examples of the urban romance of Russian culture of the 19th century. “The Raven to the Raven” – a Scottish folk ballad in the translation by A. Pushkin. V. Kosenko as a profound psychologist, delicately transmits the techniques of versification, following each movement of a poetic phrase, builds stages of the musical drama by purely intonation means. The semantics of a death is embodied through the sound imaging of a black bird: a marching-like tempo and rhythm of the accompaniment, with a characteristic dotted pattern in a descending motion (like a raven is beating its wings). The middle section is dominated by a slow-motion perception of time space (Andante), meditative “freeze” (size 6/4). The melody contrasts with the previous section, its profile is built on the principle of descending move: from “h1” to “h” of the small octave (with a stop on S-harmony), which creates a psychologically immersed state, filled by premonition of an unexpected tragedy. In general, the Ukrainian melodic intonation intensified the tragic content of the ballad by Pushkin. The musical semantics of V. Kosenko’s romances is marked by the dependence on the romantic “musical vocabulary”, however, it is possible to indicate and national characteristics (ascending little-sixth and fifth intervals, which is filled with a gradual anti-movement; syllabic tonic versification, and other). Conclusion. The romances (“solo-singings”) by V. Kosenko belongs to the type of a free art translation with generalized-genre adequacy. There is a re-semantization of poetic images due to the national-mental intonation. Melos, rhythm, textural presentation (repetitions), stylization of different genre formulas testify to the rare beauty of Kosenko’s vocal style, spiritual strength and maturity of the master of Ukrainian vocal culture. Entering the “Slavic song area”, the style of Ukrainian romance, however, is differenced from the Russian and common European style system of figurative and intonation thinking (the picture of the world).

Closed-Form Synthesis of Force-Generating Planar Four-Bar Linkages

1995 ◽  
Author(s):  
R. Randall Soper ◽  
Michael Scardina ◽  
Paul Tidwell ◽  
Charles Reinholtz ◽  
Michael A. Lo Presti
Keyword(s):  
Closed Form ◽  
The Other ◽  
Design Parameters ◽  
Synthesis Methods ◽  
Function Generator ◽  
Mechanical Advantage ◽  
Nonlinear Mechanical ◽  
Two Parameters ◽  
Selection Of ◽  
Weight Force

Abstract This paper presents a technique for synthesizing four-bar linkages to produce a specified resisting force or torque. The resisting energy is provided by a weight acting on the other grounded link. The linkage serves as a nonlinear mechanical advantage function generator. Force and velocity synthesis methods have been extensively discussed in the literature. The general approach, however, has been to assume that the specified force or velocity occurs at a prescribed position. This results in the loss of design parameters that are being used unnecessarily to control position. In this application, force input to the linkage is specified as a function of only the input link position and the magnitude and direction of the weight force. Mechanical advantage synthesis can be achieved at as many as seven precision points. The method presented in this paper allows free selection of two parameters and viewing one infinity of solutions.

Sign in / Sign up

Export Citation Format

Share Document