Keywords: HermiteâHadamard type inequality, (α, m)-convex function, ... is valid for all x, y â [0,b] and t â [0,1], then we say that f(x) is m-convex on [0,b].
Nov 3, 2011 - We can denote the derivatives of the functions using additional indices, ... For simplicity we shorten the differentiation notation so that. âi = â.
MHF4U – Final Exam Review. 1. Rational Functions. 1. Find the vertical and
horizontal asymptotes for f x x x. ( ) = +. −. 2. 3. 2. 2. Given: f x x x x x. ( ) = −. −. +. 2
. 3.
Mar 31, 2012 - AbstractâIn this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi- dimension. We find ...
all real rational functions R(x) of fixed degree n find the best approximation to the pulse function in the uniform ... We will give an overview of the Chebyshev construction for polynomials; for a detailed ..... model as η â âη (mod L). Howeve
Feb 9, 2005 - resultant output spectrum comprises just 2n spectral elements. ... (measuring) any specific qubit configuration is as small as possible, ... Moreover, the set of all LC-equivalent graphs form an LC-orbit. ... characterise and analyse th
In this Appendix we list the 69 non-vanishing contact terms associated to the two-indices LFs of Sec. 3.4. We use the notation λα. mnX1(Y1)X2(Y2), where.
Jurnal Pengukuran Kualiti dan Analisis. HARMONIC FUNCTIONS DEFINED BY ... Ditunjukkan bahawa syarat pekali ini adalah perlu apabila fungsi berpekali ...
Feb 15, 1994 - gramming to the case of nonsmooth multi-objective programming ... In the differentiable case, Jeyakumar and Mond [3] defined a vector invexity ...
2] H. Alzer, A note on Hadamard's inequalities, C.R. Math. Rep. Acad. .... 72] P. M. Vasi c, I. B. Lackovi c and D. M. Maksimovi c, Note on convex functions IV: On-.
Mar 19, 2017 - brated Hadwiger classification theorem establishes a complete ..... (Rn) is dense in Conv(Rn) and use the Moreau-Yosida approximation.
Nov 15, 2017 - 2Department of Mathematics, Longyan University, Longyan, Fujian 364012, China. Correspondence should be addressed to Shan-He Wu; ...
In the paper, the authors introduce a new notion â(s, QC)-convex function on the co- ordinatesâ ...... J Appl Anal Comput 6(1):171â178. doi:10.11948/2016014.
Feb 20, 2013 - Keywords: convex combination; barycenter; convex function; Jensen's inequality; ... to insert the quasi-arithmetic means into this implication.
vex and alpha-convex functions of hyperbolic complex and of dual complex ...... for x = 0, and simple calculations show that a (SU)-Galilean convex function f,.
2. • Find the domains of rational functions. • Find the vertical and horizontal
asymptotes of graphs of rational functions. • Analyze and sketch graphs of
rational ...
Target: On completion of this worksheet you should be able to sketch a rational
graph. To sketch the graph of a rational function we need to find where in cuts the
...
Use your graphing calculator to help you to draw the following graphs on this ...
learn the differences between the four different cases of rational functions. ...
graphs. 1. y = m < n so y = 0 is the horizontal 2. y = m = n so y = is the. 1 x+3. 2
G Consider the rational functions in the table below. a. Check the types of discontinuities each function has. f(x) = x(
Nov 4, 1999 - arXiv:math/9911030v1 [math.AG] 4 Nov 1999 ... aim is to answer these questions for the multivariate hypergeometric functions ... Throughout this paper we use the multi-exponent notation âu = âs j=1 â ...... For u â N6, the.
This is the initial introduction to the concept of a rational function. ... graphing capabilities, data collection devic
graph of f will cross the x-axis at (â2,0), as shown in Figure 4. Note that the rational function (9) is already reduc
TIPS4RM: MHF4U: Unit 2 – Rational Functions. 2008. 1. Unit 2: Rational
Functions. MHF4U. Lesson Outline. Big Picture. Students will: • identify and use
key ...
Jun 3, 1997 - 12.2 Pisarenko modeling problem . ... Polynomials can be seen as rational functions whose poles are all xed at in nity. For the orthogonal ...
Satu skema interpolasi lengkung berdasarkan fungsi asas Ball teritlak yang telah dibina oleh pengarang menggunakan fungsi Ball teritlak kuintik nisbah cebis ...
Journal of Quality Measurement and Analysis Jurnal Pengukuran Kualiti dan Analisis
JQMA 5(1) 2009,65-74
RATIONAL GENERALISED BALL FUNCTIONS FOR CONVEX INTERPOLATING CURVES (Fungsi Ball Teritlak Nisbah untuk Lengkung Interpolasi Cembung) SAMSUL ARIFFIN ABDUL KARIM & ABD RAHNI MT PIAH
ABSTRACT A curve interpolation scheme based on the generalised Ball basis functions which has been developed by the authors uses piecewise rational quintic generalised Ball functions to visualise scientific data. In fact, this scheme uses a rational generalised Ball with quartic numerator and linear denominator, which involves shape parameters. In this paper, we discuss an interpolation problem for convex data. The two parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. We examine the convexity-preserving properties of this rational interpolant to a given data set. Based on the analysis, the degree of smoothness attained is C 1. Some numerical results are presented. Keywords: Visualisation; interpolation; rational generalised Ball; convexity; continuity ABSTRAK Satu skema interpolasi lengkung berdasarkan fungsi asas Ball teritlak yang telah dibina oleh pengarang menggunakan fungsi Ball teritlak kuintik nisbah cebis demi cebis untuk menampakkan data saintifik. Malahan, skema ini sebenarnya menggunakan fungsi nisbah Ball teritlak dengan pengangka kuartik dan penyebut linear, yang melibatkan parameter bentuk. Dalam makalah ini, masalah interpolasi untuk data cembung dibincang. Dua parameter, dalam pentakrifan penginterpolasi nisbah, telah dikekang untuk mengekalkan bentuk data. Sifat kekal-cembung penginterpolasi nisbah ini diteliti terhadap set data yang diberikan. Berdasarkan analisis, darjah kelicinan yang dicapai adalah C 1. Beberapa keputusan berangka dipersembahkan. Kata kunci: Penampakan; interpolasi; Ball teritlak nisbah; kecembungan; keselanjaran References Ball A.A. 1974. CONSURF Part I: Introduction to conic lofting tile. Computer Aided Design 6(4):243-249. Brodlie K.W. & Butt S. 1991. Preserving convexity using piecewise cubic interpolation. Computers & Graphics 15(1):15-23. Clements J.C. 1990. Convexity-preserving piecewise rational cubic interpolation. SIAM J. Numer. Anal. 27(4):1016-1023. Dejdumrong N. 2007. A shape preserving verification technique for parametric curves. In Computer Graphics, Imaging and Visualisation, Techniques and Applications. Bangkok, Thailand. Delbourgo R. 1989. Shape-preserving interpolation to convex data by rational functions with quadratic numerator and linear denominator. IMA Journal of Numerical Analysis 9:123-136. Delbourgo R. & Gregory J.A. 1985. Shape-preserving piecewise rational interpolation. SIAM J. Sci. & Stat. Comput. 6: 967-976. Delgado J. & Pena J.M. 2003. A shape preserving representation with an evaluation algorithm of linear complexity. Computer Aided Geometric Design 20(1): 1-10. Duan Q., Djidjeli K., Price W.G. & Twizell E.H. 2003. Constrained control and approximation properties of a rational interpolating curve. Information Sciences 152:181-194. Fiorot J.C. & Tabka J. 1991. Shape preserving C 2 cubic polynomial interpolating splines. Mathematics of Computation 57(195): 291-298. Hu S.M., Wang G.Z. & Jin T.G. 1996. Properties of two generalised Ball curves. Computer Aided Design 28: 125133.
Karim S.A.A. & Piah A.R.M. 2007. A rational quartic generalised Ball for the visualisation of monotonic data. Preprint. Phien H.N. & Dejdumrong N. 2000. Efficient algorithms for Bézier curves. Computer Aided Geometric Design 17(3):247-250. Said H.B. 1989. Generalised Ball curve and its recursive algorithm. ACM Transactions on Graphics 8(4):360-371. Sarfraz M. 2002. Visualisation of positive and convex data by a rational cubic spline interpolation. Information Sciences 146: 239-254. Tian M., Zhang Y., Zhu J. & Duan Q. 2005. Convexity-preserving piecewise rational cubic interpolation. Journal of Information & Computational Science 2 (4):799-803. Wang Q. & Tan J. 2004. Rational quartic involving shape parameters. Journal of Information & Computational Science 1(1):127-130.
