ORIGINAL_ARTICLE
Carter–Penrose diagrams and differential spaces
In this paper it is argued that a Carter–Penrose diagram can be viewed as a differential space.
http://cjms.journals.umz.ac.ir/article_1630_be06a4b7c8df9de007d8c0757b4aab9c.pdf
2016-10-01T11:23:20
2018-10-21T11:23:20
47
53
10.22080/cjms.2017.1630
Carter–Penrose diagram
Conformal diagram
Differential spaces
Krzysztof
Drachal
k.drachal@mini.pw.edu.pl
true
1
Faculty of Mathematics and Information Science
Warsaw University of Technology, Poland
Faculty of Mathematics and Information Science
Warsaw University of Technology, Poland
Faculty of Mathematics and Information Science
Warsaw University of Technology, Poland
LEAD_AUTHOR
[1] G. D. Birkhoff and R.E. Langer, Relativity and Modern Physics, Harvard University Press, Cambridge MA, 1923.
1
[2] G. B¨orner, The Early Universe, Facts and Fiction, Springer, Berlin, 2003.
2
[3] S. Carroll, Spacetime and Geometry, Addison Wesley, Boston MA, 2004.
3
[4] Deepmala and L.N. Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, Facta Universitatis (Niˇs) Ser. Math. Inform. 30 (2015), 753-764.
4
[5] R. D’Inverno, Introducing Einstein’s Relativity, Oxford University Press, Oxford, 1992.
5
[6] K. Drachal, Advantages of generalizing manifold model in mechanics and cosmology, In M. Lieskovsk´y and M. Mokryˇs, (eds.), Proceedings in Advanced Research in Scientific Areas, The 1st Virtual International Conference, 1451-1453, EDIS – Publishing Institution of the University of ˇZilina, ˇZilina, 2012.
6
[7] K. Drachal, Introduction to d–spaces, Math. Aeterna 3(2013), 753-770.
7
[8] K. Drachal, Differential spaces and cosmological models, In S. Badura, M. Mokryˇs, and A. Lieskovsk´y, (eds.), Proceedings in Scientific Conference, SCIECONF 2014, 376-380, EDIS – Publishing Institution of the University of ˇZilina, ˇZilina, 2014.
8
[9] K. Drachal, Differential spaces and spacetime singularities: a current perspective, In press.
9
[10] G. F. R. Ellis and B. G. Schmidt, Classification of singular space–times, Gen. Rel. Grav. 10(1979), 989-997.
10
[11] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space–Time, Cambridge University Press, Cambridge, 1973.
11
[12] P. G. Fre, Gravity, a Geometrical Course, Springer, Berlin, 2013.
12
[13] M. Heller and W. Sasin, Structured spaces and their application to relativistic physics, J. Math. Phys. 36(1995), 3644-3662.
13
[14] J. T. Jebsen, ¨ Uber die allgemeinen kugelsymmetrischen L¨osungen der Einsteinschen Gravitationsgleichungen im Vakuum, Ark. Mat. Ast. Fys. 15(1921), 1-9.
14
[15] S. Krasnikov, Quasiregular singularities taken seriously, Preprint, arXiv:0909.4963.
15
[16] E. Minguzzi and M. Sanchez, The causal hierarchy of spacetimes, In H. Baum and D. Alekseevsky, (eds.), Recent Developments in Pseudo–Riemannian Geometry, 299-358, Eur. Math. Soc. Publ. House, Z¨urich,
16
[17] V. N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Indian Institute of Technology, Roorkee, 2007.
17
[18] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman and Company, New York, 1973.
18
[19] Z. Odrzyg´o´zd´z, Geometrical Properties of Quasi–regular Singularities, Warsaw University of Technology, Warsaw, 1996.
19
[20] A. R. Parry, A survey of spherically symmetric spacetimes, Anal. Math. Phys. 4(2014), 333-375.
20
[21] L. I. Piscoran and V. N. Mishra, Projectively flatness of a new class of (a,b)-metrics, Georgian Math. Journal, In press. [22] R. Sikorski, Abstract covariant derivative, Colloq. Math. 18(1967), 251-272.
21
[23] R. Sikorski, Differential modules, Colloq. Math. 24(1972), 45-79.
22
[24] J. ´ Sniatycki, Orbits of families of vector fields on subcartesian spaces, Ann. Inst. Fourier 53(2003), 2257-2296.
23
[25] J. ´ Sniatycki, Differential Geometry of Singular Spaces and Reduction of Symmetry, Cambridge University Press, Cambridge, 2013.
24
[26] R. M. Wald, General Relativity, The University of Chicago Press, Chicago IL, 1984.
25
[27] J. Watts, Differential spaces, vector fields, and orbit–type stratifications, Preprint, arXiv:1104.4084
26
ORIGINAL_ARTICLE
Special Bertrand Curves in semi-Euclidean space E4^2 and their Characterizations
In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand curves by means of the {κ,τ,(σ-ε_{t}ε_{T}ε_{N}κ)} functions of the curves in E4^2.
http://cjms.journals.umz.ac.ir/article_1632_2994a402a942b5f3e9e976c8bfc69a0f.pdf
2016-10-01T11:23:20
2018-10-21T11:23:20
54
67
10.22080/cjms.2017.1632
Semi-Euclidean spaces
Quaternionic frame
Quaternionic
Bertrand curves
Faik
BABADAG
faik.babadag@kku.edu.tr
true
1
Kırıkkale Unıversty
Kırıkkale Unıversty
Kırıkkale Unıversty
LEAD_AUTHOR
ORIGINAL_ARTICLE
Impulsive integrodifferential Equations and Measure of noncompactness
This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.
http://cjms.journals.umz.ac.ir/article_1634_e8eb18b21a9f45fe9124e50b2a6d894c.pdf
2017-01-03T11:23:20
2018-10-21T11:23:20
68
84
10.22080/cjms.2017.1634
Impulsive integrodifferential equations
nonlocal conditions
Hausdorff measure of noncompactness
fixed point theorem
convex-power condensing map
Alireza
Valipour Baboli
a.valipour@umz.ac.ir
true
1
Department of Mathematics, College of Basic Sciences, Karaj Branch,
Islamic Azad Univercity, Alborz, Iran.
Department of Mathematics, College of Basic Sciences, Karaj Branch,
Islamic Azad Univercity, Alborz, Iran.
Department of Mathematics, College of Basic Sciences, Karaj Branch,
Islamic Azad Univercity, Alborz, Iran.
LEAD_AUTHOR
M.B.
Ghaemi
mghaemi@iust.ac.ir
true
2
Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad Univercity, Alborz, Iran.
Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad Univercity, Alborz, Iran.
Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad Univercity, Alborz, Iran.
AUTHOR
ORIGINAL_ARTICLE
Anti-synchronization and synchronization of T-system
In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T-systems. The adaptive and nonlinear control schemes are used for the synchronization and anti-synchronization. The stability of these schemes is derived by Lyapunov Stability Theorem. Firstly, the synchronization and anti-synchronization are applied to systems with known parameters, then to systems in which the drive and response systems have one unknown parameter. Numerical simulations show the effectiveness and feasibility of the proposed methods.
http://cjms.journals.umz.ac.ir/article_1661_67c5ef899710d02fd42d5ba6ad0b6a6a.pdf
2016-10-01T11:23:20
2018-10-21T11:23:20
85
97
10.22080/cjms.2016.1661
Lyapunov stability
Chaos
Control
Anti-Synchronization
Synchronization
Bashir
Naderi
b_naderi@pnu.ac.ir
true
1
Department of Mathematics, Payame Noor University, POBOX 19395-3697 Tehran, Iran
Department of Mathematics, Payame Noor University, POBOX 19395-3697 Tehran, Iran
Department of Mathematics, Payame Noor University, POBOX 19395-3697 Tehran, Iran
LEAD_AUTHOR
Hossein
Kheiri
h-kheiri@tabrizu.ac.ir
true
2
University of Tabriz, Tabriz, Iran
University of Tabriz, Tabriz, Iran
University of Tabriz, Tabriz, Iran
AUTHOR
Aghileh
Heydari
a_heidari@pnu.ac.ir
true
3
Department of Mathematics, Payame Noor University, I. R. of Iran
Department of Mathematics, Payame Noor University, I. R. of Iran
Department of Mathematics, Payame Noor University, I. R. of Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Some Results for the Jacobi-Dunkl Transform in the Space $L^{p}(\mathbb{R},A_{\alpha,\beta}(x)dx)$
In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.
http://cjms.journals.umz.ac.ir/article_1631_77f108f2dc8bdc10d01f80291334a83d.pdf
2016-10-01T11:23:20
2018-10-21T11:23:20
98
105
10.22080/cjms.2017.1631
Jacobi-Dunkl operator
Jacobi-Dunkl transform
generalized Jacobi- Dunkl translation
S.
El ouadih
salahwadih@gmail.com
true
1
Department of Mathematics, Faculty of Sciences A¨ın Chock, University Hassan II, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences A¨ın Chock, University Hassan II, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences A¨ın Chock, University Hassan II, Casablanca, Morocco
LEAD_AUTHOR
R.
Daher
true
2
Department of Mathematics, Faculty of Sciences A¨ın Chock, University Hassan II, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences A¨ın Chock, University Hassan II, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences A¨ın Chock, University Hassan II, Casablanca, Morocco
AUTHOR