Browsing by Author "Tas, K"

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Chemometric Calibration Based on the Wavelet Transform for the Quantitative Resolution of Two-Colorant Mixtures
(Editura Acad Romane, 2005) Baleanu, Dumitru; Dinç, E; Baleanu, D; Taş, Kenan; Üstundag, O; Tas, K; 56389; 4971; Matematik
In this study we proposed a wavelet transform (WT) followed by two chemometric techniques for the quantitative determination of sunset yellow (SUN) and tartrazine (TAR) in their market samples. Absorbances of the concentration set formed by TAR and SUN mixtures were measured between 335-575 nm at 480 points with 0.5 nm intervals and their absorbance values as absorbance data vectors were transferred into the wavelets domain. A continuous wavelet transform (CWT) was applied, to the absorbance data. The obtained CWT-coefficients (x-block) and concentration set (y-block) were used for the construction of the principal component regression (VCR) and partial least squares (PLS) calibrations. Good results were reported for the application of the combining wavelets and chemometric tools in the determination of colorants in samples.
Citation - WoS: 9
Citation - Scopus: 13
The Convolution of Functions and Distributions
(Academic Press inc Elsevier Science, 2005) Tas, K; Fisher, B; 4971
The non-commutative convolution f * g of two distributions f and g in V is defined to be the limit of the sequence {(f tau(n)) * g}, provided the limit exists, where {tau(n)} is a certain sequence of functions in D converging to 1. It is proved that vertical bar x vertical bar(lambda) * (sgnx vertical bar x vertical bar(mu)) = 2 sin(lambda pi/2)cos(mu pi/2)/sin[(lambda+mu)pi/2] B(lambda+1, mu+1) sgn x vertical bar x vertical bar(lambda+mu+1), for -1 < lambda + mu < 0 and lambda, mu not equal -1, -2,..., where B denotes the Beta function. (c) 2005 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
On the Commutative Product of Distributions
(Korean Mathematical Soc, 2006) Tas, K; Fisher, B; 4971
The commutative products of the distributions x(r) ln(p) vertical bar x vertical bar and x(-r-1) ln(q) vertical bar x vertical bar and of sgn x x(r) ln(P) vertical bar x vertical bar and sgn x x(-r-1) ln(q) vertical bar x vertical bar are evaluated for r = 0, +/- 1, +/- 2,... and p, q = 0, 1, 2,....
Citation - WoS: 5
Citation - Scopus: 5
On the Composition of the Distributions X^-1 Ln|x| and X+^r
(Taylor & Francis Ltd, 2005) Fisher, B; Tas, K; 4971
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function (x). The distribution (x(+)(r))(-1) ln \x(+)(r)\ is evaluated for r = 1, 2.....
Citation - WoS: 3
Citation - Scopus: 1
On the Non-Commutative Neutrix Product of the Distributions X^r Ln^p | X | and X^-s
(Taylor & Francis Ltd, 2005) Tas, K; Fisher, B; 4971
The non-commutative neutrix product of the distributions x(r) ln(P) \x\ and x(-s) is evaluated for r - s -2. -3,..../ p = 1, 2,....
Citation - WoS: 5
Retracted: on the Composition of the Distributions X+^λ and X+^μ (Retracted Article. See Vol. 330, Pg. 1494 2007)
(Academic Press inc Elsevier Science, 2006) Tas, K; Fisher, B; 4971
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function delta(x). The distributions (x(+)(mu) )(+)(lambda) are evaluated for lambda < 0, mu > 0 and lambda, lambda mu not equal -1, -2.... (c) 2005 Elsevier Inc. All rights reserved.