ISSN (Print): 2333-4878

ISSN (Online): 2333-4886

Editor-in-Chief: Vishwa Nath Maurya

Website: http://www.sciepub.com/journal/AMP

   

Article

The Existence and Stability of Inclusion Equations Type of Stochastic Dynamical System Driven by Mixed Fractional Brownian Motion in a Real Separable Hilbert Space

1Department of Mathematics, College of Education Almustansryah University


Applied Mathematics and Physics. 2017, 5(1), 1-10
doi: 10.12691/amp-5-1-1
Copyright © 2017 Science and Education Publishing

Cite this paper:
Salah H Abid, Sameer Q Hasan, Zainab A Khudhur. The Existence and Stability of Inclusion Equations Type of Stochastic Dynamical System Driven by Mixed Fractional Brownian Motion in a Real Separable Hilbert Space. Applied Mathematics and Physics. 2017; 5(1):1-10. doi: 10.12691/amp-5-1-1.

Correspondence to: Sameer  Q Hasan, Department of Mathematics, College of Education Almustansryah University. Email: dr.sameer_kasim @yahoo.com

Abstract

In this paper we presented The existence and stability of inclusion equations type of stochastic dynamical system driven by mixed fractional Brownian motion in a real separable Hilbert space with an illustrative example.

Keywords

References

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Article

Periodicity of Generalized Fibonacci-like Sequences

1“Dianet”, Laboratory of Digital Technologies, Moscow, Russia


Applied Mathematics and Physics. 2017, 5(1), 11-18
doi: 10.12691/amp-5-1-2
Copyright © 2017 Science and Education Publishing

Cite this paper:
Alexander V. Evako. Periodicity of Generalized Fibonacci-like Sequences. Applied Mathematics and Physics. 2017; 5(1):11-18. doi: 10.12691/amp-5-1-2.

Correspondence to: Alexander  V. Evako, “Dianet”, Laboratory of Digital Technologies, Moscow, Russia. Email: evakoa@mail.ru

Abstract

Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence Fn+2=A+BFn+1+CFn. It is shown that this sequence is periodic with period T>2, if C= -1, |B|<2.

Keywords

References

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[5]  Evako, A., Kopperman, R. and Mukhin, Y., Dimensional properties of graphs and digital spaces. Journal of Mathematical Imaging and Vision, 6 (1996) 109-119.
 
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[6]  Evako, A., Classification of digital n-manifolds. Discrete Applied Mathematics. 181 (2015) 289-296.
 
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Article

Graph Theoretical Models of Closed n-Dimensional Manifolds: Digital Models of a Moebius Strip, a Projective Plane a Klein Bottle and n-Dimensional Spheres

1“Dianet”, Laboratory of Digital Technologies, Moscow, Russia


Applied Mathematics and Physics. 2017, 5(1), 19-27
doi: 10.12691/amp-5-1-3
Copyright © 2017 Science and Education Publishing

Cite this paper:
Alexander V. Evako. Graph Theoretical Models of Closed n-Dimensional Manifolds: Digital Models of a Moebius Strip, a Projective Plane a Klein Bottle and n-Dimensional Spheres. Applied Mathematics and Physics. 2017; 5(1):19-27. doi: 10.12691/amp-5-1-3.

Correspondence to: Alexander  V. Evako, “Dianet”, Laboratory of Digital Technologies, Moscow, Russia. Email: evakoa@mail.ru

Abstract

This paper presents discretization schemes for building graph theoretical models of n-dimensional continuous objects with the same topological properties as their continuous counterparts. An LCL collection of n-cells in Euclidean space is introduced and investigated. The digital model of a continuous n-dimensional object is the intersection graph of an LCL cover of the object. We prove that the digital model of a continuous closed n-dimensional manifold is a digital closed n-dimensional manifold. It is shown that the digital model of a continuous n-dimensional sphere is a digital n-sphere with at least 2n+2 points, the digital model of a continuous projective plane is a digital projective plane with at least eleven points and the digital model of a continuous Klein bottle is the digital Klein bottle with at least sixteen points.

Keywords

References

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[3]  Eckhardt, U., Latecki, L.: Topologies for the digital spaces Z2 and Z3, Computer Vision and Image Understanding, 90 (2003), 295-312.
 
[4]  Evako, A., Kopperman, R., Mukhin, Y., Dimensional properties of graphs and digital spaces, Journal of Mathematical Imaging and Vision, 6 (1996) 109-119
 
[5]  Evako, A., Topological properties of closed digital spaces. One method of constructing digital models of closed continuous surfaces by using covers, Computer Vision and Image Understanding, 102 (2006) 134-144
 
Show More References
[6]  Evako, A., Classification of digital n-manifolds, Discrete Applied Mathematics, 181 (2015) 289-296.
 
[7]  Evako, A., Topology Preserving Discretization Schemes for Digital Image Segmentation and Digital Models of the Plane, Open Access Library Journal, 1: e566, (2014).
 
[8]  Evako, A., Topological properties of the intersection graph of covers of n-dimensional surfaces, Discrete Mathematics, 147 (1995) 107-120.
 
[9]  Evako, A., Characterizations of simple points, simple edges and simple cliques of digital spaces: One method of topology-preserving transformations of digital spaces by deleting simple points and edges, Graphical Models, 73 (2011) 1-9.
 
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[11]  Ivashchenko, A., Contractible transformations do not change the homology groups of graphs, Discrete Math., 126 (1994) 159-170.
 
[12]  Ivashchenko, A., Representation of smooth surfaces by graphs. Transformations of graphs which do not change the Euler characteristic of graphs, Discrete Math., 122 (1993) 219-233.
 
[13]  Kong, T., Saha, P., Rosenfeld A., Strongly normal sets of contractible tiles in N dimensions. Pattern Recognition, 40(2) (2007) 530-543.
 
[14]  Lu, W., and Wu, F., Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle, Phys. Rev., E 63 (2001) 026107.
 
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