The calculus of fractal interpolation functions

Barnsley, Michael F.; Harrington, A. N.

doi:10.1016/0021-9045(89)90080-4

Cited by 221 publications

(115 citation statements)

References 2 publications

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“…By using IFS collage theorem, can perform transformation checking to a given set and paste the results in model. Barnsley and Harrington [16] proposed another model to assist IFS, called fractal interpolation theory. By using, this method can perform deterministic iteration to any point and can get the attractor.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Another constant size cipher text policy was proposed in [15], encryption and decryption techniques are not efficient; in that case, security was reduced to encrypt and decrypt the file. Next, security scheme was proposed [16] based on decisional Bilinear Diffie-Hellman problem. This scheme worked for, policy must be same of attributes in a private key, and had a high secure decryption technique.…”

Section: Model Descriptionmentioning

confidence: 99%

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An Authenticated, Secure Virtualization Management System in Cloud Computing

Kumar

Umamaheswari

2017

Asian J Pharm Clin Res

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Cloud computing is one of the trending technologies that provide boundless virtualized resources to the internet users as an important services through the internet while providing the privacy and security. Using these cloud services, internet users get many parallel computing resources at low cost. It predicted that till 2016, revenues from the online business management spent $4 billion for data storage. Cloud is an open-source platform structure, so it is having more chances to malicious attacks. Privacy, confidentiality, and security of stored data are primary security challenges in cloud computing. In cloud computing, "virtualization" is one of the techniques dividing memory into different blocks. In most of the existing systems, there is only single authority in the system to provide the encrypted keys. To fill the few security issues, this paper proposed a novel authenticated trust security model for secure virtualization system to encrypt the files. The proposed security model achieves the following functions: (1) allotting the VM security monitor model for each virtual machine and (2) providing secret keys to encrypt and decrypt information by symmetric encryption. The contribution is a proposed architecture that provides a workable security that a cloud service provider can offer to its consumers. Detailed analysis and architecture design presented to elaborate security model. Keywords:Cloud computing, Authentication, Encryption, Confidentiality, Virtualization. INTRODUCTIONDistributed systems as an area of research have seen a high growing progress for the past few years, driven by the use of new use cases to technical improvements. Cloud computing [1] is one such a famous model that has progressed from the adopting of utility computing, service oriented architectures, and virtualization. In other words, cloud is a storage remote location. Cloud can provide the services over private or public networks, i.e., local area network, metropolitan area network, wide area network, and virtual private network. Cloud computing refers to manipulating, accessing, and configuring the software and hardware resources remotely. Cloud computing is featured by those users who can easily utilize the platforms [2], for example, operating systems and middleware services, infrastructure, for example, networks, servers, and storages, and software's. In cloud computing service environments, two users play vital role: Cloud service providers and cloud users or consumers. One side, cloud provider maintains the huge computing services in their large server centers [2] to cloud users on the rent-usage basis. On the other side, there are cloud consumers use services from cloud owner to deploy their applications. First, a consumer will check the services, those services are suitable for their applications, and then, consumer sends a request for services to a cloud owner. When the cloud owner receives the user requests, will assign the required resources to the user as a cast of guest virtual machines (VMs) [3]. Then, the c...

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Section: Model Descriptionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

An Authenticated, Secure Virtualization Management System in Cloud Computing

Kumar

Umamaheswari

2017

Asian J Pharm Clin Res

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“…In view of their diverse applications, there has been steadily increasing interest in the theory of fractal functions, and it still continues to be a hot topic of research. Following the publication of Fractals Everywhere [2], a beautiful exposition of IFS theory, fractal functions and their applications, various related issues such as calculus, Holder continuity, convergence, stability, smoothness, determination of scaling parameters, and perturbation error have been investigated in the literature [3][4][5][6][7][8][9][10][11][12][13]. The concept of smooth FIFs has been used to generalize the traditional splines [14][15][16][17][18] and to demonstrate that the interaction of classical numerical methods with fractal theory provides new interpolation schemes that supplement the existing ones.…”

Section: Prologuementioning

confidence: 99%

Fractal Functions in Interpolation and Approximation: A Bird's-Eye View

AKB¹

2014

J Appl Computat Math

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This article is targeted to provide a brief and coarse discussion on theory of fractal functions and their recent developments including some of the researches of the authors. Materials on fractal functions provided by this paper is not claimed to be exhaustive, but is intended to be read before or in parallel with technical papers available in the literature on this subject. We have made an earnest attempt to supply an overall flavor of the subject of univarite fractal approximation and useful source of links to assist a novice and perhaps to an expert in fractal functions too.

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“…They have been developed both in theory and applications by many authors; see for example [25,40,89,90,95,101,108,109,120]. They provide an alternative view on wavelets, [40,53].…”

Section: Fractal Continuationmentioning

confidence: 99%

“…In this section we précis a natural generalization of analytic continuation. Generalizing [13,19,25], we first define (analytic) fractal function. The following theorem is an amalgam of some results proved in [37].…”

Section: Fractal Continuationmentioning

confidence: 99%

Developments in fractal geometry

Barnsley¹,

Vince²

2013

Bull. Math. Sci.

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Iterated function systems have been at the heart of fractal geometry almost from its origins. The purpose of this expository article is to discuss new research trends that are at the core of the theory of iterated function systems (IFSs). The focus is on geometrically simple systems with finitely many maps, such as affine, projective and Möbius IFSs. There is an emphasis on topological and dynamical systems aspects. Particular topics include the role of contractive functions on the existence of an attractor (of an IFS), chaos game orbits for approximating an attractor, a phase transition to an attractor depending on the joint spectral radius, the classification of attractors according to fibres and according to overlap, the kneading invariant of an attractor, the Mandelbrot set of a family of IFSs, fractal transformations between pairs of attractors, tilings by copies of an attractor, a generalization of analytic continuation to fractal functions, and attractor-repeller pairs and the Conley "landscape picture" for an IFS.

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The calculus of fractal interpolation functions

Cited by 221 publications

References 2 publications

An Authenticated, Secure Virtualization Management System in Cloud Computing

An Authenticated, Secure Virtualization Management System in Cloud Computing

Fractal Functions in Interpolation and Approximation: A Bird's-Eye View

Developments in fractal geometry

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