Papers by Srijanani Anurag Prasad
arXiv (Cornell University), Jun 11, 2012
The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal... more The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function depends on the interpolation data. In this note, the effect of insertion of data on the related IFS and the Coalescence Hidden-variable Fractal Interpolation Function is studied.
arXiv (Cornell University), Aug 26, 2021
In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and s... more In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the unit square and triangle, which were already studied. This paper mainly deals with the construction of quadrilateral labyrinth fractal and studying its topological properties.
arXiv (Cornell University), Jan 17, 2012
In the present paper, multiresolution analysis arising from Coalescence Hidden-variable Fractal I... more In the present paper, multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is accomplished. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(\mathbb{R})than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). In our approach, the vector space of CHFIFs is introduced, its dimension is determined and Riesz bases of vector subspaces Vk, k \in \mathbb{Z}, consisting of certain CHFIFs in L2(\mathbb{R}) \cap C0(\mathbb{R}) are constructed. As a special case, for the vector space of CHFIFs of dimension 4, orthogonal bases for the vector subspaces Vk, k \in \mathbb{Z}, are explicitly constructed and, using these bases, compactly supported continuous orthonormal wavelets are generated.
arXiv (Cornell University), Jan 17, 2012
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for ... more In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of nature or outcomes of scientific experiments that reveal one or more structures embedded in to another. In the construction of SFIF, an IFS is chosen from a pool of several IFSs at each level of iteration leading to implementation of the desired randomness and variability in fractal interpolation of the given data. Further, an expository description of our investigations on the integral, the smoothness and determination of conditions for existence of derivatives of an SFIF is given in the present work.
arXiv (Cornell University), Jun 19, 2012
In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. T... more In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation through which FIF is constructed. By this method, it is shown that the FIF belongs to Lipschitz class of order δ, (0 < δ ≤ 1), under certain conditions on free parameters. The second method is via Fourier transform of FIF. This approach gives the λ-regularity, (0 < λ), of FIF under certain conditions on free parameters. Fourier transform of a FIF is also derived in this paper to facilitate the approach of wavelet transform of a FIF via Fourier transform.
International Journal of Computational Mathematics, Dec 11, 2014
Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions... more Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is developed. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in 2 (R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). Our approach consists of introduction of the vector space of CHFIFs, determination of its dimension and construction of Riesz bases of vector subspaces V , ∈ Z, consisting of certain CHFIFs in 2 (R) ∩ 0 (R).
Chaos Solitons & Fractals, 2023
In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sier... more In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sierpiński gaskets. Further, we collect some results regarding smoothness of the constructed FIF. We prove, in particular, that the FIF are Hölder functions under specific conditions. In the final section, we obtain some bounds on the fractal dimension of FIF.
Chaos, Solitons & Fractals
In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sier... more In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sierpiński gaskets. Further, we collect some results regarding smoothness of the constructed FIF. We prove, in particular, that the FIF are Hölder functions under specific conditions. In the final section, we obtain some bounds on the fractal dimension of FIF.
arXiv (Cornell University), Jun 19, 2012
In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. T... more In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation through which FIF is constructed. By this method, it is shown that the FIF belongs to Lipschitz class of order δ, (0 < δ ≤ 1), under certain conditions on free parameters. The second method is via Fourier transform of FIF. This approach gives the λ-regularity, (0 < λ), of FIF under certain conditions on free parameters. Fourier transform of a FIF is also derived in this paper to facilitate the approach of wavelet transform of a FIF via Fourier transform.
arXiv (Cornell University), Jun 11, 2012
The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal... more The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function depends on the interpolation data. In this note, the effect of insertion of data on the related IFS and the Coalescence Hidden-variable Fractal Interpolation Function is studied.
Spectrum of a Self-Affine Measure with Four-Element Digit Set
Fractals
Let [Formula: see text] and [Formula: see text] be an expansive matrix. In this paper, we have pr... more Let [Formula: see text] and [Formula: see text] be an expansive matrix. In this paper, we have proved that there exists [Formula: see text] such that the set [Formula: see text] is an orthonormal basis of [Formula: see text] for a matrix which has all even entries. Also, we have found a spectrum [Formula: see text] of [Formula: see text] for some specific [Formula: see text] and [Formula: see text].
Orthonormal Coalescence Hidden-Variable Fractal Interpolation Functions
Analysis, Probability and Mathematical Physics on Fractals, 2020
Fractals, May 15, 2014
In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is in... more In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown that, for an equidistant partition points of [x 0 , x N ], the interpolating Cubic Spline SFIF g σ (x) ≡ g (0) σ (x) and their derivatives g (j) σ (x) converge respectively to the data generating function y(x) ≡ y (0) (x) and its derivatives y (j) (x) at the rate of h 2−j+ǫ (0 < ǫ < 1), j = 0, 1, 2, as the norm h of the partition of [x 0 , x N ] approaches zero. The convergence results for Cubic Spline SFIF found here show that any desired accuracy can be achieved in the approximation of a regular data generating function and its derivatives by a Cubic Spline SFIF and its corresponding derivatives.
In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is in... more In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown that, for an equidistant partition points of [x 0 , x N ], the interpolating Cubic Spline SFIF g σ (x) ≡ g (0) σ (x) and their derivatives g (j) σ (x) converge respectively to the data generating function y(x) ≡ y (0) (x) and its derivatives y (j) (x) at the rate of h 2−j+ǫ (0 < ǫ < 1), j = 0, 1, 2, as the norm h of the partition of [x 0 , x N ] approaches zero. The convergence results for Cubic Spline SFIF found here show that any desired accuracy can be achieved in the approximation of a regular data generating function and its derivatives by a Cubic Spline SFIF and its corresponding derivatives.
In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. T... more In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation through which FIF is constructed. By this method, it is shown that the FIF belongs to Lipschitz class of order δ, (0 < δ ≤ 1), under certain conditions on free parameters. The second method is via Fourier transform of FIF. This approach gives the λ-regularity, (0 < λ), of FIF under certain conditions on free parameters. Fourier transform of a FIF is also derived in this paper to facilitate the approach of wavelet transform of a FIF via Fourier transform.
The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal... more The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function depends on the interpolation data. In this note, the effect of insertion of data on the related IFS and the Coalescence Hidden-variable Fractal Interpolation Function is studied.
In the present paper, multiresolution analysis arising from Coalescence Hiddenvariable Fractal In... more In the present paper, multiresolution analysis arising from Coalescence Hiddenvariable Fractal Interpolation Functions (CHFIFs) is accomplished. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L 2 (R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). In our approach, the vector space of CHFIFs is introduced, its dimension is determined and Riesz bases of vector subspaces V k , k ∈ Z, consisting of certain CHFIFs in L 2 (R) C 0 (R) are constructed. As a special case, for the vector space of CHFIFs of dimension 4, orthogonal bases for the vector subspaces V k , k ∈ Z, are explicitly constructed and, using these bases, compactly supported continuous orthonormal wavelets are generated.
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for ... more In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of the nature or outcomes of scientific experiments that reveal one or more structures embedded in to another. In the construction of SFIF, an IFS is chosen from a pool of several IFS at each level of iteration leading to implementation of the desired randomness and variability in fractal interpolation of the given data. Further, an expository description of our investigations on the integral, the smoothness and determination of conditions for existence of derivatives of a SFIF is given in the present work.
Super Coalescence Hidden-Variable Fractal Interpolation Functions
Fractals, 2021
In this paper, a new notion of super coalescence hidden-variable fractal interpolation function (... more In this paper, a new notion of super coalescence hidden-variable fractal interpolation function (SCHFIF) is introduced. The construction of SCHFIF involves choosing an IFS from a pool of several non-diagonal IFS at each level of iteration. Further, the integral of a SCHFIF is studied and shown to be a SCHFIF passing through a different set of interpolation data.
arXiv: Dynamical Systems, 2012
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for ... more In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of nature or outcomes of scientific experiments that reveal one or more struc- tures embedded in to another. In the construction of SFIF, an IFS is chosen from a pool of several IFSs at each level of iteration leading to implementation of the desired randomness and variability in fractal interpolation of the given data. Further, an expository description of our investigations on the integral, the smoothness and determination of conditions for existence of derivatives of an SFIF is given in the present work.
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Papers by Srijanani Anurag Prasad