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Completing Einstein’s Spacetime

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DOI: 10.4236/jmp.2016.715175    21,569 Downloads   22,459 Views   Citations

ABSTRACT

The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.

1. Introduction

The present work is a quite comprehensive review of E-Infinity theory [1] - [60] in high energy physics and cosmology which addresses a fundamental question in the very nature of the geometry and topology of spacetime [60] - [402] . Spacetime is four-dimensional manifold with three spatial and one time dimension [403] [404] [405] [406] . There is nothing very surprising nor deviating from our everyday experience in this picture which goes back to the beginning of modern physics [407] - [419] . In other words, Einstein’s spacetime is truly conventional except for two minor details, which on closer examination turns out to be truly profound. The deceptively simple twist is that in Einstein’s theory space and time are linked together to a spacetime and that at large scales spacetime acquires a curvature linking mass and gravity with the geometry of the Universe [4] - [80] [403] - [410] .

The starting point of our criticism of Einstein’s preceding conception, which we accept in principle, is again a deceptively simple one. Our point is that Einstein did not dwell on the nature of spacetime at the very small scales [406] . On the other hand at very small scales our inability to give a watertight definition for what a point is becoming critical while the very small scale is also where quantum mechanics becomes very important in fact indispensable for high energy physics let alone quantum gravity [1] [13] [411] . Our solution in the present work is equally disarmingly straightforward. We simply insist that Einstein’s spacetime remain self-affine to four-dimensional manifold on all scales down to a point like “infinitesimally” small spacetime “point” which naturally cannot be a classical point but rather a “Cantorian” point. This means a point which upon “magnification” i.e. upon increasing the resolution of our “observation” turns ours to be not a point but an entire Cantor set with uncountably infinitely many points and so on ad infinitum [1] - [50] . The analysis to be presented in the next section shows that the requirement of “geometrical” gauge invariance [1] - [80] [406] [412] of Einstein’s D - 4 leads to a new fractal-like dimension where. From there we proceed to show how this result connects with Witten’s M-Theory spacetime [158] [413] as well as explaining the mystery of the Dark Energy and Dark Matter of the Cosmos [4] - [70] [158] .

2. Analysis. Geometrical Gauge Invariance

The simple picture of self-similar fractal-like space which we will propose here is all what we need [1] - [10] . Thus to ensure a quasi-geometrical gauge invariance [412] , [415] is all what is required to convert Einstein’s 4D spacetime to a 4D spacetime on all scales. Our analytical tool to do that is the marvelous classical mathematical “technique” known in the literature as continued fraction. This means that our space should be 4D inside 4D and so on like an infinite arrangement of Russian Dolls [3] each with D = 4 so that at the end we find that our dimension is given by

(1)

Summing this infinite “series” one finds a little surprise namely that our new total dimension is equal to 4 plus the golden mean to the power of three. In other words D is [1] - [158]

(2)

The same neat result could be obtained using the bijection formula of E-Infinity theory [1] - [10] or more conventionally using Von Neumann-Connes’ dimensional function of Non-commutative geometry [414] .

An important and revealing property of the new spacetime is that union and intersection of “wave” and “particle” lead to the same result which is the quintessence of the wave-particle duality of quantum mechanics [403] [409] . Thus with the wave given by while the particle is characterized by one finds the un-normed probability to be [1] - [80] [158]

(3)

and similarly

(4)

In other words we find the classical indistinguishability or fuzziness condition of Cantorian quantum physics to be validated and reflected into the Hausdorff dimension which fully explains the paradoxical outcome of the famous two-slit experiment with quantum particles. Next we examine the relevance of the present result for Witten’s M-Theory [158] [207] [413] as well as the major cosmological riddle of Dark Energy and Dark Matter [10] - [80] [158] .

3. Witten’s M-Theory, Dark Energy and the Isomorphic Length of Super-Symmetric Penrose Tiling Universe

It may come to some as an unexpected surprise initiating some deep thinking that can lead to a fractal version of the D = 11 of the wizard of Theoretical Physics E. Witten [413] [416] and particularly his M-theory and the five brane in eleven dimensions model. To find Witten’s D from it needs to be golden mean scaled twice. That way we find [1] - [20] [158]

(5)

Amazingly this is exactly equivalent to making D = 11 a geometrically gauge invariant spacetime exactly as we did with Einstein’s D = 4 spacetime to obtain. Thus using the same continued fraction procedure we find:

(6)

where is nothing but Hardy’s quantum entanglement of two quantum particles [82] . The preceding connection to Hardy’s quantum entanglement [41] leads us to speculate on whether could be used in determining the ordinary and thus the dark energy density of the cosmos [28] - [90] . It turns out that this hunch is correct and we will attempt to explain it in what follows.

4. The Dark Energy Density of the Universe

We recall that a simple dimension is a basically bosonic space which needs a spin half degree of freedom to accommodate fermions. Consequently is the fermionic counterpart of. It just happened to be a dimension identical to the fractal Kaluza-Klein space D = 5 [45] [92] . A few minutes of clear thinking would easily convince us that a space which is super symmetric must possess a dimension which results from the intersection of the bosonic spacetime with the fermionic space That means

(7)

where.

Consequently the isomorphic length of this super symmetric space is exactly equal to that of the fractal version of Witten’s M-theory [158] .

(8)

Now we know that the Einstein spacetime D = 4 is isotropic and consequently the isomorphic diameter is unity and therefore the isometric radius i.e. isomorphic length is one half. Inserting in E (Einstein), one finds [158]

(9)

Consequently the Dark Energy density of the Universe must be [22] - [85] :

(10)

This means the measurable ordinary energy of the Universe is about 4.5% while the corresponding Dark Energy density is a staggering 95.5% in full agreement with cosmic measurements and observations as well as all our previous analyses [4] - [90] .

It is remarkable and noteworthy to register in the present context the agreement between the present derivation and the K3-Kähler topology [16] [417] used in deriving the same result namely

(11)

and

(12)

5. Discussion and Conclusion

Again and again the Golden Mean appears unexpectedly in theoretical quantum physics at crucial points [11] such as the probability of quantum entanglement for two particles as well as the dimensional function of a non-commutative Penrose-Connes Universe [1] [3] [414] . The present work shows that this particular phenomenon is intimately linked to the completion of Einstein’s space time via extending it to a gauge invariant manifold with rather than D = 4 where is the said golden mean. The simplest way to calculate this is to use the classical marvelous simple mathematical procedure of continuous fraction. In this way we can neatly show in analogous way that the dimension of the fractal universe of Kaluza-Klein theory is rather than D = 5 and similarly D for a fractal M-theory is rather than D = 11 [158] . From there we arrive to the accurate ordinary and dark energy density of the universe in a relatively short way indeed. In addition equipped with the preceding insight the remarkable connection of our result to the topology of K3-Kähler and Conway’s isomorphic length on one side and our gauge invariant Einstein’s spacetime on the other was amply demonstrated and instructively used in the same context namely that of Dark Energy density of the Universe [22] - [90] .

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

El Naschie, M. (2016) Completing Einstein’s Spacetime. Journal of Modern Physics, 7, 1972-1994. doi: 10.4236/jmp.2016.715175.

References

[1] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 19, 209-236.
http://dx.doi.org/10.1016/S0960-0779(03)00278-9
[2] El Naschie, M.S. (1995) Chaos, Solitons & Fractals, 4, 1235-1247.
[3] El Naschie, M.S. (2009) Chaos, Solitons & Fractals, 41, 2635-2646.
http://dx.doi.org/10.1016/j.chaos.2008.09.059
[4] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 30, 579-605.
http://dx.doi.org/10.1016/j.chaos.2006.03.030
[5] El Naschie, M.S. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 407-409.
http://dx.doi.org/10.1515/ijnsns.2006.7.4.407
[6] El Naschie, M.S. (2007) International Journal of Nonlinear Sciences and Numerical Simulation, 8, 11-20.
http://dx.doi.org/10.1515/ijnsns.2007.8.1.11
[7] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 24, 1-5.
http://dx.doi.org/10.1016/j.chaos.2004.09.001
[8] El Naschie, M.S. (1998) Chaos, Solitons & Fractals, 9, 931-933.
http://dx.doi.org/10.1016/S0960-0779(98)00077-0
[9] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 27, 843-849.
http://dx.doi.org/10.1016/j.chaos.2005.06.002
[10] El Naschie, M.S. (1997) Chaos, Solitons & Fractals, 8, 131-133.
http://dx.doi.org/10.1016/S0960-0779(96)00128-2
[11] El Naschie, M.S. (1994) Chaos, Solitons & Fractals, 4, 177-179.
http://dx.doi.org/10.1016/0960-0779(94)90141-4
[12] El Naschie, M.S. (1996) Chaos, Solitons & Fractals, 7, 499-518.
http://dx.doi.org/10.1016/0960-0779(96)00007-0
[13] El Naschie, M.S. (2014) International Journal of Astronomy and Astrophysics, 4, 80-90.
http://dx.doi.org/10.4236/ijaa.2014.41009
[14] Nottale, L. (1996) Chaos, Solitons & Fractals, 7, 877-938.
http://dx.doi.org/10.1016/0960-0779(96)00002-1
[15] Marek-Crnjac, L., El Naschie, M.S. and He, J.H. (2013) International Journal of Modern Nonlinear Theory and Application, 2, 78-88.
http://dx.doi.org/10.4236/ijmnta.2013.21A010
[16] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 25, 969-977.
http://dx.doi.org/10.1016/j.chaos.2005.02.028
[17] El Naschie, M.S. (2013) Journal of Quantum Information Science, 3, 23-26.
http://dx.doi.org/10.4236/jqis.2013.31006
[18] El Naschie, M.S. (2013) International Journal of Astronomy and Astrophysics, 3, 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024
[19] El Naschie, M.S. (2005) International Journal of Nonlinear Sciences and Numerical Simulation, 6, 331-333.
[20] El Naschie, M.S. (2013) International Journal of Astronomy and Astrophysics, 3, 483-493. http://dx.doi.org/10.4236/ijaa.2013.34056
[21] He, J.H. (2005) International Journal of Nonlinear Sciences and Numerical Simulation, 6, 343-346.
http://dx.doi.org/10.1515/IJNSNS.2005.6.4.343
[22] El Naschie, M.S. (2013) International Journal of Modern Nonlinear Theory and Application, 2, 43-54.
http://dx.doi.org/10.4236/ijmnta.2013.21005
[23] El Naschie, M.S. (2013) Journal of Quantum Information Science, 3, 121-126.
http://dx.doi.org/10.4236/jqis.2013.34016
[24] He, J.H. (2005) International Journal of Nonlinear Sciences and Numerical Simulation, 6, 93-94.
http://dx.doi.org/10.1515/IJNSNS.2005.6.2.93
[25] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 20, 917-923.
http://dx.doi.org/10.1016/j.chaos.2003.11.001
[26] El Naschie, M.S. (2013) Journal of Modern Physics, 4, 591-596.
http://dx.doi.org/10.4236/jmp.2013.45084
[27] El Naschie, M. (2014) World Journal of Mechanics, 4, Article ID: 47445.
[28] Sigalotti, L.D.G. and Mejias, A. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 467-472.
http://dx.doi.org/10.1515/IJNSNS.2006.7.4.467
[29] El Naschie, M.S. (1995) Chaos, Solitons & Fractals, 5, 1031-1032.
http://dx.doi.org/10.1016/0960-0779(95)00044-5
[30] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 29, 876-881.
http://dx.doi.org/10.1016/j.chaos.2005.12.027
[31] El Naschie, M.S. (2014) American Journal of Astronomy & Astrophysics, 2, 72-77.
http://dx.doi.org/10.11648/j.ajaa.20140206.13
[32] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 19, 1339-1344.
http://dx.doi.org/10.1016/j.chaos.2003.08.009
[33] El Naschie, M.S. and Helal, A. (2013) International Journal of Astronomy and Astrophysics, 3, 318-343.
http://dx.doi.org/10.4236/ijaa.2013.33037
[34] Iovane, G. (2005) Chaos, Solitons & Fractals, 23, 351-360.
http://dx.doi.org/10.1016/j.chaos.2004.05.032
[35] El Naschie, M.S. (2014) American Journal of Astronomy & Astrophysics, 2, 34-37.
http://dx.doi.org/10.11648/j.ajaa.20140203.12
[36] El Naschie, M.S. (2007) Chaos, Solitons & Fractals, 31, 537-547.
http://dx.doi.org/10.1016/j.chaos.2006.07.001
[37] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 30, 525-531.
http://dx.doi.org/10.1016/j.chaos.2005.04.123
[38] El Naschie, M.S. (2013) International Journal of Modern Nonlinear Theory and Application, 2, 107-121.
http://dx.doi.org/10.4236/ijmnta.2013.22014
[39] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 21, 249-260.
http://dx.doi.org/10.1016/j.chaos.2003.12.001
[40] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 20, 437-450.
http://dx.doi.org/10.1016/j.chaos.2003.09.029
[41] El Naschie, M.S. (2013) Journal of Quantum Information Science, 3, Article ID: 32831.
[42] El Naschie, M.S. (2015) The Open Astronomy Journal, 8, 1-17.
http://dx.doi.org/10.2174/1874381101508010001
[43] El Naschie, M.S. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 129-132.
http://dx.doi.org/10.1515/IJNSNS.2006.7.2.129
[44] El Naschie, M.S. (2014) World Journal of Nuclear Science and Technology, 4, 216.
http://dx.doi.org/10.4236/wjnst.2014.44027
[45] El Naschie, M.S. (2013) Journal of Modern Physics, 4, Article ID: 32975.
[46] Tang, W., Li, Y., Kong, H.Y. and El Naschie, M.S. (2014) Bubbfil Nanotechnology, 1, 3-12.
[47] Iovane, G. and Benedetto, E. (2005) International Journal of Nonlinear Sciences and Numerical Simulation, 6, 357-370.
http://dx.doi.org/10.1515/IJNSNS.2005.6.4.357
[48] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 22, 1-11.
http://dx.doi.org/10.1016/j.chaos.2004.01.015
[49] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 22, 495-511.
http://dx.doi.org/10.1016/j.chaos.2004.02.028
[50] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 27, 297-330.
http://dx.doi.org/10.1016/j.chaos.2005.04.116
[51] Iovane, G. (2005) Chaos, Solitons & Fractals, 25, 775-779.
http://dx.doi.org/10.1016/j.chaos.2005.02.024
[52] El Naschie, M.S. and Marek-Crnjac, L. (2012) International Journal of Modern Nonlinear Theory and Application, 1, 118-124.
http://dx.doi.org/10.4236/ijmnta.2012.14018
[53] El Naschie, M.S. (2000) Chaos, Solitons & Fractals, 11, 1149-1162.
http://dx.doi.org/10.1016/S0960-0779(99)00185-X
[54] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 30, 622-628.
http://dx.doi.org/10.1016/j.chaos.2006.04.042
[55] El Naschie, M.S. (2013) Journal of Modern Physics and Applications, 2014, 2.
[56] El Naschie, M.S. (2013) Journal of Modern Physics, 4, 1417-1428.
http://dx.doi.org/10.4236/jmp.2013.410170
[57] El Naschie, M.S. (2013) Journal of Modern Physics, 4, 354-356.
http://dx.doi.org/10.4236/jmp.2013.43049
[58] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 16, 353-366.
http://dx.doi.org/10.1016/S0960-0779(02)00440-X
[59] El Naschie, M.S. (2014) Journal of Quantum Information Science, 4, 284-291.
http://dx.doi.org/10.4236/jqis.2014.44023
[60] El Naschie, M.S. (1993) Journal of the Franklin Institute, 330, 199-211.
http://dx.doi.org/10.1016/0016-0032(93)90030-X
[61] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 18, 401-420.
http://dx.doi.org/10.1016/S0960-0779(03)00098-5
[62] El-Ahmady, A.E. (2007) Chaos, Solitons & Fractals, 31, 1272-1278.
http://dx.doi.org/10.1016/j.chaos.2005.10.112
[63] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 24, 447-457.
http://dx.doi.org/10.1016/j.chaos.2004.09.071
[64] El Naschie, M.S. (2014) World Journal of Condensed Matter Physics, 4, 74-77.
http://dx.doi.org/10.4236/wjcmp.2014.42011
[65] El Naschie, M.S. (2014) Problems of Nonlinear Analysis in Engineering Systems, 20, 79-98.
[66] El Naschie, M.S. (2014) Journal of Quantum Information Science, 4, 83-91.
http://dx.doi.org/10.4236/jqis.2014.42008
[67] Helal, M.A., Marek-Crnjac, L. and He, J.H. (2013) Open Journal of Microphysics, 3, 141-145. http://dx.doi.org/10.4236/ojm.2013.34020
[68] El Naschie, M.S. (2007) Chaos, Solitons & Fractals, 32, 911-915.
http://dx.doi.org/10.1016/j.chaos.2006.08.014
[69] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 202-211.
http://dx.doi.org/10.1016/j.chaos.2007.05.006
[70] El Naschie, M.S. (2014) Open Journal of Fluid Dynamics, 4, 15-17.
[71] El Naschie, M.S. (2016) Quantum Matter, 5, 1-4.
http://dx.doi.org/10.1166/qm.2016.1247
[72] El Naschie, M.S. (2015) Advances in Pure Mathematics, 5, 560-570.
http://dx.doi.org/10.4236/apm.2015.59052
[73] El Naschie, M.S. (2007) International Journal of Nonlinear Sciences and Numerical Simulation, 8, 445-450.
http://dx.doi.org/10.1515/IJNSNS.2007.8.3.445
[74] Marek-Crnjac, L. and He, J. (2013) International Journal of Astronomy and Astrophysics, 3, 464-471.
http://dx.doi.org/10.4236/ijaa.2013.34053
[75] El Naschie, M.S. (1997) COBE Satellite Measurement, Cantorian Space and Cosmic Strings. Chaos, Solitons & Fractals, 8, 847-850.
http://dx.doi.org/10.1016/S0960-0779(97)00084-2
[76] El Naschie, M.S. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 97-100.
http://dx.doi.org/10.1515/ijnsns.2006.7.1.97
[77] El Naschie, M.S. (2015) World Journal of Condensed Matter Physics, 5, 249-260.
http://dx.doi.org/10.4236/wjcmp.2015.54026
[78] El Naschie, M.S. (2014) Journal of Modern Physics, 5, 743-750.
[79] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 26, 257-261.
http://dx.doi.org/10.1016/j.chaos.2004.12.024
[80] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 25, 759-764.
http://dx.doi.org/10.1016/j.chaos.2004.12.010
[81] El Naschie, M.S. (1998) Chaos, Solitons & Fractals, 9, 913-919.
http://dx.doi.org/10.1016/S0960-0779(97)00165-3
[82] El Naschie, M.S. (2013) Journal of Modern Physics and Applications, 2, 88-96.
[83] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 24, 941-946.
http://dx.doi.org/10.1016/j.chaos.2004.10.001
[84] El Naschie, M.S. (2014) International Journal of Astronomy and Astrophysics, 4, 332-339.
http://dx.doi.org/10.4236/ijaa.2014.42027
[85] El Naschie, M.S. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 119-128.
http://dx.doi.org/10.1515/IJNSNS.2006.7.2.119
[86] El Naschie, M.S. (1998) International Journal of Theoretical Physics, 37, 2935-2951.
http://dx.doi.org/10.1023/A:1026679628582
[87] El Naschie, M.S. (2013) Open Journal of Microphysics, 3, 64-70.
http://dx.doi.org/10.4236/ojm.2013.33012
[88] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 320-322.
http://dx.doi.org/10.1016/j.chaos.2007.06.110
[89] Iovane, G. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 155-162.
http://dx.doi.org/10.1515/IJNSNS.2006.7.2.155
[90] El Naschie, M.S. (2014) Open Journal of Philosophy, 4, 157-159.
http://dx.doi.org/10.4236/ojpp.2014.42022
[91] El Naschie, M.S. (2007) Chaos, Solitons & Fractals, 32, 427-430.
http://dx.doi.org/10.1016/j.chaos.2006.09.016
[92] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 37, 16-22.
http://dx.doi.org/10.1016/j.chaos.2007.09.079
[93] El Naschie, M.S. (2015) Open Journal of Applied Sciences, 5, 313-324.
http://dx.doi.org/10.4236/ojapps.2015.57032
[94] He, J.H. (2007) International Journal of Nonlinear Sciences and Numerical Simulation, 8, 1-4.
http://dx.doi.org/10.1515/IJNSNS.2007.8.1.1
[95] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 19, 689-697.
http://dx.doi.org/10.1016/S0960-0779(03)00337-0
[96] El Naschie, M.S. (2014) Journal of Applied Mathematics and Physics, 2, 634-638.
http://dx.doi.org/10.4236/jamp.2014.27069
[97] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 23, 1091-1098.
http://dx.doi.org/10.1016/j.chaos.2004.08.001
[98] He, J.H. (2006) Chaos, Solitons & Fractals, 28, 285-289.
http://dx.doi.org/10.1016/j.chaos.2005.08.001
[99] He, J.H. and Marek-Crnjac, L. (2013) IJMNTA, 2, 55-59.
[100] El Naschie, M.S. (1998) Biosystems, 46, 41-46.
http://dx.doi.org/10.1016/S0303-2647(97)00079-8
[101] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 23, 1521-1525.
http://dx.doi.org/10.1016/j.chaos.2004.09.003
[102] El Naschie, M.S. (2001) Chaos, Solitons & Fractals, 12, 969-988.
http://dx.doi.org/10.1016/S0960-0779(00)00263-0
[103] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 30, 1025-1033.
http://dx.doi.org/10.1016/j.chaos.2006.05.088
[104] El Naschie, M.S. (2013) Journal of Physics, 2, 18-23.
[105] El Naschie, M.S., Marek-Crnjac, L., Helal, M.A. and He, J.H. (2014) Applied Mathematics, 5, 1780-1790.
[106] Sigalotti, L.D.G. and Mejias, A. (2006) Chaos, Solitons & Fractals, 30, 521-524.
http://dx.doi.org/10.1016/j.chaos.2006.03.005
[107] Castro, C., El-Naschie, M.S. and Granik, A. (2000) Why We Live in 3+ 1 Dimensions. CERN Document Server. (No. hep-th/0004152).
[108] Crnjac, L.M. and El Naschie, M.S. (2013) Journal of Modern Physics, 4, 31-38.
[109] El Naschie, M.S. (2016) Journal of Quantum Information Science, 6, 1-9.
http://dx.doi.org/10.4236/jqis.2016.61001
[110] El Naschie, M.S. (1993) Chaos, Solitons & Fractals, 3, 89-98.
http://dx.doi.org/10.1016/0960-0779(93)90042-Y
[111] El Naschie, M.S. (1995) Computers & Mathematics with Applications, 29, 103-110.
http://dx.doi.org/10.1016/0898-1221(95)00062-4
[112] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 16, 637-649.
http://dx.doi.org/10.1016/S0960-0779(02)00489-7
[113] El Naschie, M.S. (2014) Journal of Electromagnetic Analysis and Applications, 6, 233-237.
http://dx.doi.org/10.4236/jemaa.2014.69023
[114] El Naschie, M.S. (2013) American Journal of Modern Physics, 2, 357-361.
http://dx.doi.org/10.11648/j.ajmp.20130206.23
[115] El Naschie, M.S. (2015) Natural Science, 7, 210-225.
http://dx.doi.org/10.4236/ns.2015.74024
[116] Castro, C. (2000) Chaos, Solitons & Fractals, 11, 1663-1670.
http://dx.doi.org/10.1016/S0960-0779(00)00018-7
[117] El Naschie, M.S. (2014) International Journal of Modern Nonlinear Theory and Application, 3, 1-5.
http://dx.doi.org/10.4236/ijmnta.2014.31001
[118] El Naschie, M.S. (2004) International Journal of Modern Physics E, 13, 835-849.
http://dx.doi.org/10.1142/S0218301304002429
[119] El Naschie, M.S. (2000) Chaos, Solitons & Fractals, 11, 1459-1469.
http://dx.doi.org/10.1016/S0960-0779(99)00194-0
[120] El Naschie, M.S. (2014) Journal of Applied Mathematics and Physics, 2, 803-806.
http://dx.doi.org/10.4236/jamp.2014.28088
[121] El Naschie, M.S. (2001) Chaos, Solitons & Fractals, 12, 539-549.
http://dx.doi.org/10.1016/S0960-0779(00)00187-9
[122] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 23, 711-726.
http://dx.doi.org/10.1016/j.chaos.2004.06.048
[123] El Naschie, M.S. (2015) Journal of Modern Physics, 6, 1321-1333.
http://dx.doi.org/10.4236/jmp.2015.69137
[124] Iovane, G. and Giordano, P. (2007) Chaos, Solitons & Fractals, 32, 896-910.
http://dx.doi.org/10.1016/j.chaos.2005.11.097
[125] He, J. H., Liu, Y., Xu, L. and Yu, J.Y. (2007) Chaos, Solitons & Fractals, 32, 1096-1100.
http://dx.doi.org/10.1016/j.chaos.2006.07.045
[126] Chen, W. (2006) Chaos, Solitons & Fractals, 28, 923-929.
http://dx.doi.org/10.1016/j.chaos.2005.08.199
[127] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 29, 803-807.
http://dx.doi.org/10.1016/j.chaos.2006.01.012
[128] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 37, 662-668.
http://dx.doi.org/10.1016/j.chaos.2008.01.018
[129] El Naschie, M.S. (2015) World Journal of Nano Science and Engineering, 5, 57-67.
http://dx.doi.org/10.4236/wjnse.2015.53008
[130] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 24, 899-905.
http://dx.doi.org/10.1016/j.chaos.2004.11.003
[131] El Naschie, M.S. (2015) Open Journal of Philosophy, 5, 123-130.
http://dx.doi.org/10.4236/ojpp.2015.51014
[132] El Naschie, M.S. (2014) Journal of Modern Physics and Applications, 2014, 6.
[133] Marek-Crnjac, L. and El Naschie, M.S. (2013) Applied Mathematics, 4, 22-29.
http://dx.doi.org/10.4236/am.2013.411A2005
[134] Nottale, L. (1999) Chaos, Solitons & Fractals, 10, 459-468.
http://dx.doi.org/10.1016/S0960-0779(98)00195-7
[135] El Naschie, M.S. (2013) International Journal of Modern Nonlinear Theory and Application, 2, 167-169.
http://dx.doi.org/10.4236/ijmnta.2013.23023
[136] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 25, 935-939.
http://dx.doi.org/10.1016/j.chaos.2005.02.029
[137] He, J.H. (2007) Chaos, Solitons & Fractals, 32, 1645-1648.
http://dx.doi.org/10.1016/j.chaos.2006.08.015
[138] Gottlieb, I., Agop, M., Ciobanu, G. and Stroe, A. (2006) Chaos, Solitons & Fractals, 30, 380-398.
http://dx.doi.org/10.1016/j.chaos.2005.11.018
[139] El Naschie, M.S. (2015) American Journal of Nano Research and Application, 3, 66-70.
[140] Gottlieb, I., Agop, M. and Jarcǎu, M. (2004) Chaos, Solitons & Fractals, 19, 705-730.
http://dx.doi.org/10.1016/S0960-0779(03)00244-3
[141] El Naschie, M.S. (2009) Chaos, Solitons & Fractals, 41, 2725-2732.
http://dx.doi.org/10.1016/j.chaos.2008.10.001
[142] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 36, 1-17.
http://dx.doi.org/10.1016/j.chaos.2007.08.058
[143] El Naschie, M.S. (2001) Chaos, Solitons & Fractals, 12, 741-746.
http://dx.doi.org/10.1016/S0960-0779(00)00193-4
[144] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 26, 1-6.
http://dx.doi.org/10.1016/j.chaos.2005.02.031
[145] El Naschie, M.S. and Rossler, O.E. (1994) Chaos, Solitons & Fractals, 4, 307-309.
http://dx.doi.org/10.1016/0960-0779(94)90049-3
[146] Nottale, L. (1995) Chaos, Solitons & Fractals, 6, 399-410.
http://dx.doi.org/10.1016/0960-0779(95)80047-K
[147] Marek-Crnjac, L. (2009) Chaos, Solitons & Fractals, 41, 2697-2705.
http://dx.doi.org/10.1016/j.chaos.2008.10.007
[148] Marek-Crnjac, L. (2015) Natural Science, 7, 581.
http://dx.doi.org/10.4236/ns.2015.713058
[149] He, J.H. (2014) International Journal of Theoretical Physics, 53, 3698-3718.
http://dx.doi.org/10.1007/s10773-014-2123-8
[150] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 26, 665-670.
http://dx.doi.org/10.1016/j.chaos.2005.01.018
[151] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 23, 1511-1514.
http://dx.doi.org/10.1016/j.chaos.2004.08.008
[152] Agop, M., Griga, V., Ciobanu, B., Ciubotariu, C., Buzea, C.G., Stan, C. and Buzea, C. (1998) Chaos, Solitons & Fractals, 9, 1143-1181.
http://dx.doi.org/10.1016/S0960-0779(98)80005-2
[153] Giordano, P., Iovane, G. and Laserra, E. (2007) Chaos, Solitons & Fractals, 31, 1108-1117.
http://dx.doi.org/10.1016/j.chaos.2006.03.114
[154] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 24, 29-32.
http://dx.doi.org/10.1016/j.chaos.2004.09.002
[155] He, J.H. (2007) Chaos, Solitons & Fractals, 31, 782-786.
http://dx.doi.org/10.1016/j.chaos.2006.04.041
[156] Iovane, G., Giordano, P. and Salerno, S. (2005) Chaos, Solitons & Fractals, 24, 423-441.
http://dx.doi.org/10.1016/j.chaos.2004.09.068
[157] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 18, 635-641.
http://dx.doi.org/10.1016/S0960-0779(03)00007-9
[158] El Naschie, M.S. (2016) International Journal of Astronomy and Astrophysics, 6, 135.
http://dx.doi.org/10.4236/ijaa.2016.62011
[159] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 268-273.
http://dx.doi.org/10.1016/j.chaos.2007.07.036
[160] El Naschie, M.S. (2015) World Journal of Nano Science and Engineering, 5, 26.
http://dx.doi.org/10.4236/wjnse.2015.51004
[161] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 37, 346-359.
http://dx.doi.org/10.1016/j.chaos.2007.10.021
[162] El Naschie, M.S. (2015) Open Journal of Philosophy, 5, 319.
http://dx.doi.org/10.4236/ojpp.2015.56040
[163] El Naschie, M.S. (2015) International Journal of Astronomy and Astrophysics, 5, 243.
http://dx.doi.org/10.4236/ijaa.2015.54027
[164] Rössler, O.E. (1996) Chaos, Solitons & Fractals, 7, 845-852.
http://dx.doi.org/10.1016/0960-0779(95)00117-4
[165] Nottale, L. (1998) Chaos, Solitons & Fractals, 9, 1051-1061.
http://dx.doi.org/10.1016/S0960-0779(97)00190-2
[166] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 25, 531-533.
http://dx.doi.org/10.1016/j.chaos.2005.01.001
[167] Iovane, G. (2006) Chaos, Solitons & Fractals, 29, 1-22.
http://dx.doi.org/10.1016/j.chaos.2005.10.045
[168] Czajko, J. (2000) Chaos, Solitons & Fractals, 11, 1983-1992.
http://dx.doi.org/10.1016/S0960-0779(99)00091-0
[169] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 26, 673-676.
http://dx.doi.org/10.1016/j.chaos.2005.02.030
[170] Nottale, L. (1994) Chaos, Solitons & Fractals, 4, 361-388.
http://dx.doi.org/10.1016/0960-0779(94)90051-5
[171] El Naschie, M.S. (2015) Open Journal of Microphysics, 5, 11.
http://dx.doi.org/10.4236/ojm.2015.52002
[172] El Naschie, M.S. (2004) Nonlinear Sci. Lett.A, 2, 1-8.
[173] Iovane, G. (2006) Chaos, Solitons & Fractals, 28, 857-878.
http://dx.doi.org/10.1016/j.chaos.2005.08.074
[174] El Naschie, M.S. (1992) Chaos, Solitons & Fractals, 2, 91-94.
http://dx.doi.org/10.1016/0960-0779(92)90050-W
[175] Iovane, G., Gargiulo, G. and Zappale, E. (2006) Chaos, Solitons & Fractals, 27, 588-598.
http://dx.doi.org/10.1016/j.chaos.2005.05.015
[176] El Naschie, M.S. (1998) Chaos, Solitons & Fractals, 9, 1445-1471.
http://dx.doi.org/10.1016/S0960-0779(98)00120-9
[177] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 28, 1366-1371.
http://dx.doi.org/10.1016/j.chaos.2005.11.001
[178] El Naschie, M.S. (2015) Journal of Modern Physics, 6, 384.
http://dx.doi.org/10.4236/jmp.2015.64042
[179] Elnaschie, M.S. (2005) International Journal of Nonlinear Sciences and Numerical Simulation, 6, 335-342.
http://dx.doi.org/10.1515/IJNSNS.2005.6.4.335
[180] Iovane, G., Chinnici, M. and Tortoriello, F.S. (2008) Chaos, Solitons & Fractals, 35, 645-658.
http://dx.doi.org/10.1016/j.chaos.2007.07.051
[181] El Naschie, M.S. (2015) World Journal of Nano Science and Engineering, 5, 49.
http://dx.doi.org/10.4236/wjnse.2015.52007
[182] El Naschie, M.S. (2014) Advances in Pure Mathematics, 4, 641.
http://dx.doi.org/10.4236/apm.2014.412073
[183] Selvam, A.M. and Fadnavis, S. (1999) Chaos, Solitons & Fractals, 10, 1321-1334.
http://dx.doi.org/10.1016/S0960-0779(98)00150-7
[184] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 30, 636-641.
http://dx.doi.org/10.1016/j.chaos.2006.04.044
[185] He, J.H. (2006) Chaos, Solitons & Fractals, 30, 506-511.
http://dx.doi.org/10.1016/j.chaos.2005.11.033
[186] Marek-Crnjac, L. (2013) American Journal of Modern Physics, 2, 255-263.
http://dx.doi.org/10.11648/j.ajmp.20130205.14
[187] El-Ahmady, A.E. and Rafat, H. (2006) Chaos, Solitons & Fractals, 30, 836-844.
http://dx.doi.org/10.1016/j.chaos.2005.05.033
[188] El Naschie, M.S. (2016) Natural Science, 8, 152.
http://dx.doi.org/10.4236/ns.2016.83018
[189] Selvam, A.M. and Fadnavis, S. (1999) Chaos, Solitons & Fractals, 10, 1577-1582.
http://dx.doi.org/10.1016/S0960-0779(98)00209-4
[190] He, J.H. and Marek-Crnjac, L. (2013) Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 130-137.
[191] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 99-103.
http://dx.doi.org/10.1016/j.chaos.2007.05.005
[192] El Naschie, M.S. (2007) International Journal of Nonlinear Sciences and Numerical Simulation, 8, 195-198.
http://dx.doi.org/10.1515/ijnsns.2007.8.2.195
[193] El Naschie, M.S. (2009) Chaos, Solitons & Fractals, 41, 869-874.
http://dx.doi.org/10.1016/j.chaos.2008.04.013
[194] El Naschie, M.S. (1994) Chaos, Solitons & Fractals, 4, 1235-1247.
http://dx.doi.org/10.1016/0960-0779(94)90034-5
[195] Özgür, C. (2008) Chaos, Solitons & Fractals, 38, 1373-1377.
http://dx.doi.org/10.1016/j.chaos.2008.03.016
[196] He, J.H. (2007) Chaos, Solitons & Fractals, 34, 727-729.
http://dx.doi.org/10.1016/j.chaos.2006.04.052
[197] Castro, C. (2001) Chaos, Solitons & Fractals, 12, 101-104.
http://dx.doi.org/10.1016/S0960-0779(00)00196-X
[198] Rami, E.N.A. (2009) Chaos, Solitons & Fractals, 42, 84-88.
http://dx.doi.org/10.1016/j.chaos.2008.10.031
[199] Babchin, A.J. and El Naschie, M.S. (2015) World Journal of Condensed Matter Physics, 6, 1.
http://dx.doi.org/10.4236/wjcmp.2016.61001
[200] He, J.H. (2008) Chaos, Solitons & Fractals, 36, 542-545.
http://dx.doi.org/10.1016/j.chaos.2007.07.093
[201] Nagasawa, M. (1996) Chaos, Solitons & Fractals, 7, 631-643.
http://dx.doi.org/10.1016/0960-0779(95)00115-8
[202] Iovane, G., Giordano, P. and Laserra, E. (2004) Chaos, Solitons & Fractals, 22, 975-983.
http://dx.doi.org/10.1016/j.chaos.2004.04.019
[203] El Naschie, M.S. (2015) Natural Science, 7, 287.
http://dx.doi.org/10.4236/ns.2015.76032
[204] Ord, G.N. (1997) Chaos, Solitons & Fractals, 8, 727-741.
http://dx.doi.org/10.1016/S0960-0779(96)00059-8
[205] Agop, M., Paun, V. and Harabagiu, A. (2008) Chaos, Solitons & Fractals, 37, 1269-1278.
http://dx.doi.org/10.1016/j.chaos.2008.01.006
[206] El Naschie, M.S., Marek-Crnjac, L., He, J.H. and Helal, M.A. (2013) Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 3-10.
[207] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 26, 247-254.
http://dx.doi.org/10.1016/j.chaos.2005.01.016
[208] Nottale, L. (2005) Chaos, Solitons & Fractals, 25, 797-803.
http://dx.doi.org/10.1016/j.chaos.2004.11.071
[209] El Naschie, M.S. (2007) Chaos, Solitons & Fractals, 32, 893-895.
http://dx.doi.org/10.1016/j.chaos.2006.09.055
[210] Saniga, M. (2001) Chaos, Solitons & Fractals, 12, 2127-2142.
http://dx.doi.org/10.1016/S0960-0779(00)00183-1
[211] El Naschie, M.S. (1995) Quantum Measurement, Information, Diffusion and Cantorian Geodesies. Quantum Mechanics, Diffusion and Chaotic Fractals, Pergamon Press, Oxford.
[212] Mejias, A., Sigalotti, L.D.G., Sira, E. and De Felice, F. (2004) Chaos, Solitons & Fractals, 19, 773-777.
http://dx.doi.org/10.1016/S0960-0779(03)00273-X
[213] Munceleanu, G.V., Paun, V.P., Casian-Botez, I. and Agop, M. (2011) International Journal of Bifurcation and Chaos, 21, 603-618.
http://dx.doi.org/10.1142/S021812741102888X
[214] Ho, M.E.N. and Giuseppe Vitiello, M.W. (2015) Global Journal of Science Frontier Research, 15, No. 1-A.
[215] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 17, 989-1001.
http://dx.doi.org/10.1016/S0960-0779(03)00006-7
[216] El Naschie, M.S. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 1-6.
http://dx.doi.org/10.1515/IJNSNS.2006.7.1.1
[217] Castro, C., Granik, A. and El Naschie, M.S. (2000) Why We Live in 3 Dimensions. arXiv preprint hep-th/0004152.
[218] Selvam, A.M. (2005) A General Systems Theory for Chaos, Quantum Mechanics and Gravity for Dynamical Systems of All Space-Time Scales. arXiv preprint physics/0503028.
[219] Iovane, G. and Benedetto, E. (2006) Chaos, Solitons & Fractals, 30, 269-277.
http://dx.doi.org/10.1016/j.chaos.2005.11.005
[220] Goldfain, E. (2005) Chaos, Solitons & Fractals, 23, 701-710.
http://dx.doi.org/10.1016/j.chaos.2004.05.020
[221] El Naschie, M.S. (2016) Journal of Modern Physics, 7, 729.
http://dx.doi.org/10.4236/jmp.2016.78069
[222] El Naschie, Μ.S. (2007) International Journal of Nonlinear Sciences and Numerical Simulation, 8, 5-10.
http://dx.doi.org/10.1515/IJNSNS.2007.8.1.5
[223] El Naschie, M.S. (2009) Chaos, Solitons & Fractals, 41, 2787-2789.
http://dx.doi.org/10.1016/j.chaos.2008.10.011
[224] El Naschie, M.S. (2016) World Journal of Condensed Matter Physics, 6, 63.
http://dx.doi.org/10.4236/wjcmp.2016.62009
[225] El Naschie, M.S. (2015) American Journal of Nano Research and Applications, 3, 33-40.
[226] El Naschie, M.S. (2000) Chaos, Solitons & Fractals, 11, 2391-2395.
http://dx.doi.org/10.1016/S0960-0779(99)00209-X
[227] Stakhov, A. and Rozin, B. (2005) Chaos, Solitons & Fractals, 26, 677-684.
http://dx.doi.org/10.1016/j.chaos.2005.01.057
[228] He, J.H. (2009) Chaos, Solitons & Fractals, 42, 2754-2759.
http://dx.doi.org/10.1016/j.chaos.2009.03.182
[229] El Naschie, M.S. (2016) International Journal of Astronomy and Astrophysics, 6, 56.
http://dx.doi.org/10.4236/ijaa.2016.61005
[230] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 25, 545-548.
http://dx.doi.org/10.1016/j.chaos.2005.01.009
[231] Sidharth, B.G. (2003) Chaos, Solitons & Fractals, 18, 197-201.
http://dx.doi.org/10.1016/S0960-0779(02)00632-X
[232] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 22, 1199-1209.
http://dx.doi.org/10.1016/j.chaos.2004.04.026
[233] El Naschie, M.S. (1999) Chaos, Solitons & Fractals, 10, 1955-1965.
http://dx.doi.org/10.1016/S0960-0779(99)00030-2
[234] Dariescu, M.A., Dariescu, C. and Pîrghie, A.C. (2009) Chaos, Solitons & Fractals, 42, 247-252. http://dx.doi.org/10.1016/j.chaos.2008.11.021
[235] Maker, D. (1999) Chaos, Solitons & Fractals, 10, 31-42.
http://dx.doi.org/10.1016/S0960-0779(98)00108-8
[236] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 38, 1051-1053.
http://dx.doi.org/10.1016/j.chaos.2008.06.001
[237] Iovane, G., Laserra, E. and Giordano, P. (2004) Chaos, Solitons & Fractals, 22, 521-528.
http://dx.doi.org/10.1016/j.chaos.2004.02.026
[238] He, J.H. and Xu, L. (2009) Chaos, Solitons & Fractals, 39, 2119-2124.
http://dx.doi.org/10.1016/j.chaos.2007.06.088
[239] Naschie, M.E. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 477-482.
http://dx.doi.org/10.1515/IJNSNS.2006.7.4.477
[240] Auffray, J.P. (2014) Journal of Modern Physics, 5, 1427.
http://dx.doi.org/10.4236/jmp.2014.515144
[241] El Naschie, M.S. (2015) Journal of Quantum Information Science, 5, 24.
http://dx.doi.org/10.4236/jqis.2015.51004
[242] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 29, 871-875.
http://dx.doi.org/10.1016/j.chaos.2006.01.005
[243] El Naschie, M.S. (2006) Chaos, Solitons & Fractals, 29, 871-875.
http://dx.doi.org/10.1016/j.chaos.2006.01.005
[244] El Naschie, M.S. (2016) Journal of Quantum Information Science, 6, 57.
http://dx.doi.org/10.4236/jqis.2016.62007
[245] El-Ahmady, A.E. and Al-Hesiny, E. (2011) The International Journal of Nonlinear Science, 11, 451-458.
[246] Iovane, G. (2004) Chaos, Solitons & Fractals, 20, 657-667.
http://dx.doi.org/10.1016/j.chaos.2003.09.036
[247] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 26, 303-311.
http://dx.doi.org/10.1016/j.chaos.2005.03.004
[248] El Naschie, M.S. (2015) Natural Science, 7, 483.
http://dx.doi.org/10.4236/ns.2015.710049
[249] Marek-Crnjac, L. (2003) Chaos, Solitons & Fractals, 18, 125-133.
http://dx.doi.org/10.1016/S0960-0779(02)00587-8
[250] Marek-Crnjac, L. (2009) Chaos, Solitons & Fractals, 42, 1796-1799.
http://dx.doi.org/10.1016/j.chaos.2009.03.094
[251] Özgür, C. (2009) Chaos, Solitons & Fractals, 40, 1156-1161.
http://dx.doi.org/10.1016/j.chaos.2007.08.070
[252] Sidharth, B.G. (2002) Chaos, Solitons & Fractals, 13, 189-193.
http://dx.doi.org/10.1016/S0960-0779(00)00269-1
[253] Iovane, G. (2006) Chaos, Solitons & Fractals, 27, 618-629.
http://dx.doi.org/10.1016/j.chaos.2005.04.093
[254] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 664-667.
http://dx.doi.org/10.1016/j.chaos.2007.07.082
[255] Tanaka, Y., Mizuno, Y. and Kado, T. (2005) Chaos, Solitons & Fractals, 24, 407-422.
http://dx.doi.org/10.1016/j.chaos.2004.09.034
[256] Auffray, J.P. (2015) Journal of Modern Physics, 6, 536.
http://dx.doi.org/10.4236/jmp.2015.65058
[257] Martienssen, W. (2005) Chaos, Solitons & Fractals, 25, 805-806.
http://dx.doi.org/10.1016/j.chaos.2005.02.001
[258] Agop, M. and Vasilica, M. (2006) Chaos, Solitons & Fractals, 30, 318-323.
http://dx.doi.org/10.1016/j.chaos.2006.01.105
[259] Chen, Q. and Shi, Z. (2008) Chaos, Solitons & Fractals, 35, 323-332.
http://dx.doi.org/10.1016/j.chaos.2007.06.065
[260] Qiu, H. and Su, W. (2007) Chaos, Solitons & Fractals, 33, 1625-1634.
http://dx.doi.org/10.1016/j.chaos.2006.03.024
[261] Nottale, L. (2001) Revue de synthèse, 122, 11-25.
http://dx.doi.org/10.1007/BF02990499
[262] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 17, 631-638.
http://dx.doi.org/10.1016/S0960-0779(02)00630-6
[263] Vrobel, S. (2011) Why a Watched Kettle Never Boils.
[264] Gottlieb, I., Ciobanu, G. and Buzea, C.G. (2003) Chaos, Solitons & Fractals, 17, 789-796.
http://dx.doi.org/10.1016/S0960-0779(02)00484-8
[265] He, J.H. (2009) Chaos, Solitons & Fractals, 41, 2533-2537.
http://dx.doi.org/10.1016/j.chaos.2008.09.027
[266] Argyris, J., Ciubotariu, C.I. and Weingaertner, W.E. (2000) Chaos, Solitons & Fractals, 11, 1671-1719.
http://dx.doi.org/10.1016/S0960-0779(99)00065-X
[267] El Naschie, M.S. (2007) Chaos, Solitons & Fractals, 34, 1377-1381.
http://dx.doi.org/10.1016/j.chaos.2007.02.016
[268] Agop, M. and Craciun, P. (2006) Chaos, Solitons & Fractals, 30, 30-40.
http://dx.doi.org/10.1016/j.chaos.2006.01.006
[269] Agop, M., Ioannou, P.D. and Buzea, C.G. (2002) Chaos, Solitons & Fractals, 13, 1137-1165.
http://dx.doi.org/10.1016/S0960-0779(01)00123-0
[270] Sidharth, B.G. (2001) A Reconciliation of Electromagnetism and Gravitation. arXiv preprint physics/0110040.
[271] El-Nabulsi, A.R. (2009) Chaos, Solitons & Fractals, 42, 2924-2933.
http://dx.doi.org/10.1016/j.chaos.2009.04.004
[272] Weiss, H. and Weiss, V. (2003) Chaos, Solitons & Fractals, 18, 643-652.
http://dx.doi.org/10.1016/S0960-0779(03)00026-2
[273] Wu, G.C. and He, J.H. (2009) Chaos, Solitons & Fractals, 42, 781-783.
http://dx.doi.org/10.1016/j.chaos.2009.02.007
[274] Czajko, J. (2004) Chaos, Solitons & Fractals, 21, 261-271.
http://dx.doi.org/10.1016/j.chaos.2003.12.046
[275] Sidharth, B.G. (2002) Chaos, Solitons & Fractals, 13, 617-620.
http://dx.doi.org/10.1016/S0960-0779(01)00017-0
[276] De, A., De, U.C. and Gazi, A.K. (2011) Communications of the Korean Mathematical Society, 26, 623-634.
http://dx.doi.org/10.4134/CKMS.2011.26.4.623
[277] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 36, 521-525.
http://dx.doi.org/10.1016/j.chaos.2007.09.004
[278] Sidharth, B.G. (2000) Chaos, Solitons & Fractals, 11, 1045-1046.
http://dx.doi.org/10.1016/S0960-0779(98)00331-2
[279] El Naschie, M.S. (2001) Chaos, Solitons & Fractals, 12, 1361-1368.
http://dx.doi.org/10.1016/S0960-0779(01)00008-X
[280] Iovane, G., Laserra, E. and Tortoriello, F.S. (2004) Chaos, Solitons & Fractals, 20, 415-426.
http://dx.doi.org/10.1016/j.chaos.2003.08.004
[281] Saniga, M. (2002) Chaos, Solitons & Fractals, 13, 807-814.
http://dx.doi.org/10.1016/S0960-0779(01)00056-X
[282] Nottale, L. (2001) Chaos, Solitons & Fractals, 12, 1577-1583.
http://dx.doi.org/10.1016/S0960-0779(01)00015-7
[283] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 37, 6-8.
http://dx.doi.org/10.1016/j.chaos.2007.09.057
[284] El Naschie, M.S., Olsen, S. and He, J.H. (2013) Fractal Spacetime and Noncommutative Geometry, 3, 11-20.
[285] El Naschie, M.S. (1997) Chaos, Solitons & Fractals, 8, vii-x.
http://dx.doi.org/10.1016/S0960-0779(97)88695-X
[286] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 20, 649-654.
http://dx.doi.org/10.1016/j.chaos.2003.10.010
[287] Xu, L. and Zhong, T. (2011) Nonlinear Science Letters B, 1, 10-11.
[288] Giordano, P. (2006) International Journal of Nonlinear Sciences and Numerical Simulation, 7, 451-460.
http://dx.doi.org/10.1515/IJNSNS.2006.7.4.451
[289] Nozari, K. and Mehdipour, S.H. (2009) Chaos, Solitons & Fractals, 39, 956-970.
http://dx.doi.org/10.1016/j.chaos.2007.02.018
[290] Benedetto, E. (2009) International Journal of Theoretical Physics, 48, 1603-1621.
http://dx.doi.org/10.1007/s10773-009-9933-0
[291] El Naschie, M.S. (2007) Chaos, Solitons & Fractals, 31, 521-526.
http://dx.doi.org/10.1016/j.chaos.2006.06.028
[292] Zmeskal, O., Nezadal, M. and Buchnicek, M. (2003) Chaos, Solitons & Fractals, 17, 113-119.
http://dx.doi.org/10.1016/S0960-0779(02)00412-5
[293] Castro, C. (2000) On the Four Dimensional Conformal Anomaly, Fractal Spacetime and the Fine Structure Constant. arXiv preprint physics/0010072.
[294] Marek-Crnjac, L. (2008) Chaos, Solitons & Fractals, 37, 1279-1288.
http://dx.doi.org/10.1016/j.chaos.2008.01.021
[295] Özgür, C. (2009) Chaos, Solitons & Fractals, 39, 2457-2464.
http://dx.doi.org/10.1016/j.chaos.2007.07.018
[296] Sidharth, B.G. (2001) Chaos, Solitons & Fractals, 12, 2143-2147.
http://dx.doi.org/10.1016/S0960-0779(00)00181-8
[297] Fred, Y.Y. (2009) Chaos, Solitons & Fractals, 42, 89-93.
http://dx.doi.org/10.1016/j.chaos.2008.10.030
[298] Colotin, M., Pompilian, G.O., Nica, P., Gurlui, S., Paun, V. and Agop, M. (2009) Acta Physica Polonica-Series A General Physics, 116, 157.
http://dx.doi.org/10.12693/APhysPolA.116.157
[299] Rossler, O. E., Fröhlich, D., Movassagh, R. and Moore, A. (2007) Chaos, Solitons & Fractals, 33, 770-775.
http://dx.doi.org/10.1016/j.chaos.2006.06.046
[300] El Naschie, M.S. (2004) Chaos, Solitons & Fractals, 20, 455-458.
http://dx.doi.org/10.1016/j.chaos.2003.10.008
[301] Agop, M., Ioannou, P.D., Nica, P., Buzea, C.G. and Jarcau, M. (2003) Chaos, Solitons & Fractals, 18, 1-16.
http://dx.doi.org/10.1016/S0960-0779(02)00633-1
[302] Agop, M., Ciobanu, G. and Zaharia, L. (2003) Chaos, Solitons & Fractals, 15, 445-453.
http://dx.doi.org/10.1016/S0960-0779(02)00139-X
[303] Rami, E.N.A. (2009) Chaos, Solitons & Fractals, 41, 2262-2270.
http://dx.doi.org/10.1016/j.chaos.2008.08.033
[304] Zmeskal, O., Vala, M., Weiter, M. and Stefkova, P. (2009) Chaos, Solitons & Fractals, 42, 1878-1892.
http://dx.doi.org/10.1016/j.chaos.2009.03.106
[305] Iovane, G., Bellucci, S. and Benedetto, E. (2008) Chaos, Solitons & Fractals, 37, 49-59.
http://dx.doi.org/10.1016/j.chaos.2007.09.022
[306] Goldfain, E. (2005) International Journal of Nonlinear Sciences and Numerical Simulation, 6, 351-356.
http://dx.doi.org/10.1515/ijnsns.2005.6.4.351
[307] de Felice, F., Sigalotti, L.D.G. and Mejias, A. (2004) Chaos, Solitons & Fractals, 21, 573-578.
http://dx.doi.org/10.1016/j.chaos.2003.12.091
[308] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 23, 1941-1943.
http://dx.doi.org/10.1016/j.chaos.2004.08.005
[309] Elokaby, A. (2009) Chaos, Solitons & Fractals, 41, 1616-1618.
http://dx.doi.org/10.1016/j.chaos.2008.07.003
[310] Nottale, L. (2000) Scale Relativity, Fractal Space-Time and Morphogenesis of Structures. In: Diebner, H., Druckrey, T. and Weibel, P., Eds., Sciences of the Interface, Proceedings of International Symposium in honor of O. Rössler, ZKM Karlruhe, Genista, Tübingen, p. 38.
[311] Agop, M., Ioannou, P.D., Buzea, C. and Nica, P. (2003) Chaos, Solitons & Fractals, 16, 321-338.
http://dx.doi.org/10.1016/S0960-0779(02)00413-7
[312] Rami, E.N.A. (2009) Chaos, Solitons & Fractals, 42, 377-384.
http://dx.doi.org/10.1016/j.chaos.2008.12.008
[313] El Naschie, M.S. (2000) Chaos, Solitons & Fractals, 11, 2397-2408.
http://dx.doi.org/10.1016/S0960-0779(00)00108-9
[314] El Naschie, M.S. and He, J.H. (2013) Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 106-119.
[315] Dickau, J.J. (2009) Chaos, Solitons & Fractals, 41, 2103-2105.
http://dx.doi.org/10.1016/j.chaos.2008.07.056
[316] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 684-687.
http://dx.doi.org/10.1016/j.chaos.2007.07.084
[317] Tomaschitz, R. (1997) International Journal of Bifurcation and Chaos, 7, 1847-1853.
http://dx.doi.org/10.1142/S0218127497001412
[318] Ho, M.W. (2014) Journal of the Institute of Science in Society, 62, 40-43.
[319] Sidharth, B.G. (2003) Chaos, Solitons & Fractals, 15, 593-595.
http://dx.doi.org/10.1016/S0960-0779(02)00159-5
[320] Ćirić, L.B., Jesić, S.N. and Ume, J.S. (2008) Chaos, Solitons & Fractals, 37, 781-791.
http://dx.doi.org/10.1016/j.chaos.2006.09.093
[321] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 24, 659-663.
http://dx.doi.org/10.1016/j.chaos.2004.11.002
[322] Yildiz, A., De, U. C. and Cetinkaya, A. (2011) N (k)-Quasi Einstein Manifolds Satisfying Certain Curvature Conditions. Dumlupinar University Research Fund (No: 2011-25).
[323] Sidharth, B.G. (2002) Chaos, Solitons & Fractals, 13, 1369-1370.
http://dx.doi.org/10.1016/S0960-0779(01)00114-X
[324] Tanaka, Y. (2005) Chaos, Solitons & Fractals, 23, 33-41.
http://dx.doi.org/10.1016/j.chaos.2004.03.031
[325] Nagasawa, M. (1997) Chaos, Solitons & Fractals, 8, 1773-1792.
http://dx.doi.org/10.1016/S0960-0779(97)00036-2
[326] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 7-12.
http://dx.doi.org/10.1016/j.chaos.2007.06.023
[327] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 37, 1289-1291.
http://dx.doi.org/10.1016/j.chaos.2008.02.002
[328] El Naschie, M.S. (2009) Chaos, Solitons & Fractals, 41, 1340-1343.
http://dx.doi.org/10.1016/j.chaos.2008.05.015
[329] Iovane, G. and Salerno, S. (2005) WSEAS Transactions on Mathematics, 4, 184.
[330] Liu, S.D., Liu, S.K., Fu, Z.T., Ren, K. and Guo, Y. (2003) Chaos, Solitons & Fractals, 15, 627-630.
http://dx.doi.org/10.1016/S0960-0779(02)00138-8
[331] Yang, C.D. (2008) Chaos, Solitons & Fractals, 38, 316-331.
http://dx.doi.org/10.1016/j.chaos.2008.01.019
[332] El Naschie, M.S., Olsen, S., He, J.H., Nada, S., Marek-Crnjac, L. and Helal, A. (2012) International Journal of Modern Nonlinear Theory and Application, 1, Article ID: 23087.
[333] Marek-Crnjac, L. (2006) Chaos, Solitons & Fractals, 27, 575-579.
http://dx.doi.org/10.1016/j.chaos.2005.04.099
[334] Pavlos, G.P., Iliopoulos, A.C., Karakatsanis, L.P., Tsoutsouras, V.G. and Pavlos, E.G. (2011) Complexity Theory and Physical Unification: From Microscopic to Macroscopic Level. Chaos Theory: Modeling, Simulation and Applications. World Scientific Publishing, 297-308.
http://dx.doi.org/10.1142/9789814350341_0035
[335] El Naschie, M.S. (1993) Chaos, Solitons & Fractals, 3, 481-488.
http://dx.doi.org/10.1016/0960-0779(93)90032-V
[336] Gottlieb, I. and Agop, M. (2007) Chaos, Solitons & Fractals, 34, 1025-1029.
http://dx.doi.org/10.1016/j.chaos.2006.03.108
[337] El Naschie, M.S. (2013) Electromagnetic and Gravitational Origin of Dark Energy in Kaluza-Klein D= 5 Spacetime. PIERS Proceeding, Stockholm, Sweden, 91-97.
[338] Sigalotti, L.D.G. and Rendón, O. (2007) Chaos, Solitons & Fractals, 32, 1611-1614.
http://dx.doi.org/10.1016/j.chaos.2006.08.034
[339] Ord, G.N. (1996) Journal of Physics A: Mathematical and General, 29, L123.
http://dx.doi.org/10.1088/0305-4470/29/5/007
[340] Saniga, M. (2005) Chaos, Solitons & Fractals, 23, 645-650.
http://dx.doi.org/10.1016/j.chaos.2004.05.018
[341] El Naschie, M.S. (2016) American Journal of Computational Mathematics, 6, 185.
http://dx.doi.org/10.4236/ajcm.2016.63020
[342] El Naschie, M.S. (1996) Chaos, Solitons & Fractals, 7, 1501-1506.
http://dx.doi.org/10.1016/0960-0779(96)80001-B
[343] Rossler, O.E. and Kuypers, H. (2005) Chaos, Solitons & Fractals, 25, 897-899.
http://dx.doi.org/10.1016/j.chaos.2004.11.097
[344] El Naschie, M.S. (2016) Advances in Pure Mathematics, 6, 446.
http://dx.doi.org/10.4236/apm.2016.66032
[345] El Naschie, M.S. (2013) Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 35-38.
[346] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 38, 609-611.
http://dx.doi.org/10.1016/j.chaos.2008.04.015
[347] He, J.H., Zhong, T., Xu, L., Marek-Crnjac, L., Nada, S.I. and Helal, M.A. (2011) Nonlinear Science Letters B, 1, 15-24.
[348] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 35, 303-307.
http://dx.doi.org/10.1016/j.chaos.2007.07.025
[349] Agop, M. and Enache, V. (2007) Chaos, Solitons & Fractals, 32, 296-301.
http://dx.doi.org/10.1016/j.chaos.2006.04.068
[350] Ho, M.W. (2014) Golden Geometry of E-Infinity Fractal Spacetime. The Story of Phi, Part 5.
[351] Agop, M. and Craciun, P. (2006) Chaos, Solitons & Fractals, 30, 441-452.
http://dx.doi.org/10.1016/j.chaos.2005.12.048
[352] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 36, 1200-1204.
http://dx.doi.org/10.1016/j.chaos.2007.09.039
[353] Marek-Crnjac, L. (2012) Quantum Gravity in Cantorian Space-Time. INTECH Open Access Publisher. http://dx.doi.org/10.5772/37232
[354] El Naschie, M.S. (2003) Chaos, Solitons & Fractals, 17, 797-807.
http://dx.doi.org/10.1016/S0960-0779(02)00684-7
[355] El Naschie, M.S. (2014) Natural Science, 6, 1259.
http://dx.doi.org/10.4236/ns.2014.616115
[356] Agop, M. and Gottlieb, I. (2006) Journal of Mathematical Physics, 47, 53503-53503.
http://dx.doi.org/10.1063/1.2196747
[357] Giné, J. (2008) Chaos, Solitons & Fractals, 35, 1-6.
http://dx.doi.org/10.1016/j.chaos.2007.06.097
[358] Auffray, J.P. (2015) Journal of Modern Physics, 6, 1478.
http://dx.doi.org/10.4236/jmp.2015.611152
[359] Agop, M., Ioannou, P.D., Nica, P., Galusca, G. and Stefan, M. (2005) Chaos, Solitons & Fractals, 23, 1497-1509.
http://dx.doi.org/10.1016/S0960-0779(04)00439-4
[360] He, J.H. and Huang, Z. (2006) Chaos, Solitons & Fractals, 27, 1108-1114.
http://dx.doi.org/10.1016/j.chaos.2005.04.082
[361] Iovane, G. (2007) Chaos, Solitons & Fractals, 31, 1041-1053.
http://dx.doi.org/10.1016/j.chaos.2006.03.109
[362] Argyris, J., Ciubotariu, C. and Andreadis, I. (1998) Chaos, Solitons & Fractals, 9, 1651-1701. http://dx.doi.org/10.1016/S0960-0779(97)00193-8
[363] Agop, M., Ioannou, P.D., Luchian, D., Nica, P., Radu, C. and Condurache, D. (2004) Chaos, Solitons & Fractals, 21, 515-536.
http://dx.doi.org/10.1016/j.chaos.2003.12.053
[364] Rossler, O.E., Fröhlich, D., Kleiner, N., Pfaff, M. and Argyris, J. (2004) Chaos, Solitons & Fractals, 20, 205-208.
http://dx.doi.org/10.1016/S0960-0779(03)00358-8
[365] Agop, M., Ioannou, P.D., Coman, P., Ciobanu, B. and Nica, P. (2001) Chaos, Solitons & Fractals, 12, 1947-1982.
http://dx.doi.org/10.1016/S0960-0779(00)00161-2
[366] Mukhamedov, A.M. (2007) Chaos, Solitons & Fractals, 33, 717-724.
http://dx.doi.org/10.1016/j.chaos.2006.11.016
[367] Harabagiu, A., Niculescu, O., Colotin, M., Bibire, T.D., Gottlieb, I. and Agop, M. (2009) Romanian Reports in Physics, 61, 395-400.
[368] Ord, G.N. (1999) Chaos, Solitons & Fractals, 10, 499-512.
http://dx.doi.org/10.1016/S0960-0779(98)00255-0
[369] Castro, C. and Granik, A. (2000) Chaos, Solitons & Fractals, 11, 2167-2178.
http://dx.doi.org/10.1016/S0960-0779(00)00027-8
[370] Castro, C. (2002) Chaos, Solitons & Fractals, 13, 203-207.
http://dx.doi.org/10.1016/S0960-0779(00)00268-X
[371] Ahmed, N. (2004) Chaos, Solitons & Fractals, 21, 773-781.
http://dx.doi.org/10.1016/j.chaos.2004.01.013
[372] Sidharth, B.G. (2001) Chaos, Solitons & Fractals, 12, 2357-2361.
http://dx.doi.org/10.1016/S0960-0779(00)00182-X
[373] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 36, 819-822.
http://dx.doi.org/10.1016/j.chaos.2007.09.020
[374] El Naschie, M.S. (2008) Chaos, Solitons & Fractals, 36, 819-822.
http://dx.doi.org/10.1016/j.chaos.2007.09.020
[375] El Naschie, M.S. (2008) Freudental Magic Square and Its Dimensional Implication for and High Energy Physics. Chaos, Solitons & Fractals, 36, 546-549.
http://dx.doi.org/10.1016/j.chaos.2007.09.017
[376] Fred, Y.Y. (2009) Chaos, Solitons & Fractals, 41, 2301-2305.
http://dx.doi.org/10.1016/j.chaos.2008.09.004
[377] El-Okaby, A.A. (2008) Chaos, Solitons & Fractals, 38, 1305-1317.
http://dx.doi.org/10.1016/j.chaos.2008.02.034
[378] Sidharth, B. and Altaisky, M.V. (Eds.) (2012) Frontiers of Fundamental Physics 4. Springer Science & Business Media.
[379] Buzea, C.G., Agop, M., Galusca, G., Vizureanu, P. and Ionita, I. (2007) Chaos, Solitons & Fractals, 34, 1060-1074.
http://dx.doi.org/10.1016/j.chaos.2006.03.122
[380] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 23, 683-688.
http://dx.doi.org/10.1016/j.chaos.2004.06.032
[381] El Naschie, M.S. (2005) A Note on Various Supersymmetric Extensions of the Standard Model of High-Energy Particles and E-Infinity Theory. Chaos, Solitons & Fractals, 23, 683-688. http://dx.doi.org/10.1016/j.chaos.2004.06.032
[382] Ahmed, E. and Hegazi, A.S. (2000) Chaos, Solitons & Fractals, 11, 1759-1761.
http://dx.doi.org/10.1016/S0960-0779(99)00082-X
[383] Tomaschitz, R. (1997) Fractals, 5, 215-220.
http://dx.doi.org/10.1142/S0218348X97000206
[384] Castro, C. (2000) Foundations of Physics, 30, 1301-1316.
http://dx.doi.org/10.1023/A:1003640606529
[385] Christianto, V. (2003) Apeiron, 10, 231.
[386] Colotin, M., Niculescu, O., Bibire, T.D., Gottlieb, I., Nica, P. and Agop, M. (2009) Romanian Reports in Physics, 61, 387-394.
[387] Dariescu, C., Dariescu, M.A. and Murariu, G. (2007) Chaos, Solitons & Fractals, 34, 1030-1036.
http://dx.doi.org/10.1016/j.chaos.2006.04.070
[388] Agop, M., Jarcau, M. and Stroe, A. (2005) Chaos, Solitons & Fractals, 25, 781-790.
http://dx.doi.org/10.1016/j.chaos.2004.12.036
[389] Lorenzi, M.G., Francaviglia, M. and Iovane, G. (2008) APLIMAT-Journal of Applied Mathematics, 1, 109-119.
[390] He, J.H., Liu, Y., Mo, L.F., Wan, Y.Q. and Xu, L. (2008) Electrospun Nanofibres and Their Applications. iSmithers, Shawbury, Shrewsbury, Shropshire, UK.
[391] Yildiz, A., De, U.C. and Cetinkaya, A. (2013) Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 83, 239-245.
http://dx.doi.org/10.1007/s40010-013-0071-y
[392] Sidharth, B.G. (2002) Chaos, Solitons & Fractals, 14, 1325-1330.
http://dx.doi.org/10.1016/S0960-0779(02)00085-1
[393] Ord, G.N. and Gualtieri, J.A. (1998) Biosystems, 46, 21-28.
http://dx.doi.org/10.1016/S0303-2647(97)00077-4
[394] Zhong, T. and He, J.H. (2013) Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 46-49.
[395] Dariescu, C. and Dariescu, M.A. (2007) Chaos, Solitons & Fractals, 32, 8-14.
http://dx.doi.org/10.1016/j.chaos.2006.05.042
[396] Sidharth, B.G. (2002) Chaos, Solitons & Fractals, 14, 525-527.
http://dx.doi.org/10.1016/S0960-0779(01)00197-7
[397] Agop, M., Oprea, I., Sandu, C., Vlad, R., Buzea, C.G. and Matsuzawa, H. (2000) Some Properties of the World Crystal in Fractal Spacetime Theory. Australian Journal of Physics, 53, 231-240.
[398] Castro, C. and Granik, A. (2000) On M Theory, Quantum Paradoxes and the New Relativity. arXiv preprint physics/0002019.
[399] El Naschie, M.S. (2005) Chaos, Solitons & Fractals, 25, 911-913.
http://dx.doi.org/10.1016/j.chaos.2004.12.002
[400] Meissner, W. (1996) Chaos, Solitons & Fractals, 7, 697-709.
http://dx.doi.org/10.1016/0960-0779(94)00220-7
[401] Buzea, C.G., Rusu, I., Bulancea, V., Badarau, G., Paun, V.P. and Agop, M. (2010) Physics Letters A, 374, 2757-2765.
http://dx.doi.org/10.1016/j.physleta.2010.04.044
[402] Cristescu, C.P., Mereu, B., Stan, C. and Agop, M. (2009) Chaos, Solitons & Fractals, 40, 975-980.
http://dx.doi.org/10.1016/j.chaos.2007.08.054
[403] Penrose, R. (2004) The Road to Reality. A Complete Guide to the Laws of the Universe. Jonathan Cape, London.
[404] Green, B. (2004) The Fabric of the Cosmos. Penguin Books, London.
[405] Hawkings, S and Ellis, G. (1973) The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511524646
[406] ‘tHooft, G. (1997) In Search of the Ultimate Building Blocks. Cambridge University Press, Cambridge.
[407] Davies, P. (Editor) (1989) The New Physics. Cambridge University Press, Cambridge.
[408] Halpern, P. (2004) The Great Beyond. John Wiley, New Jersey.
[409] Zeilinger, A. (2003) Einstein’s Schleier. C. H. Beck Verlog, Munchen.
[410] Crowell, L.B. (2005) Quantum Fluctuations of Spacetime. World Scientific, Singapore.
http://dx.doi.org/10.1142/5952
[411] Smolin, L. (2000) Three Roads to Quantum Gravity. Weidenfeld and Nicolson, London.
[412] ‘tHooft, G. (1994) Under the Spell of the Gauge Principle. World Scientific, Singapore.
[413] Kaku, M. (2000) Strings, Conformal Fields and M-Theory. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-0503-6
[414] Connes, A. (1994) Non-Commutative Geometry. Academic Press, San Diego.
[415] Becker, K., Becker, M. and Schwarz, J. (2007) String Theory and M-Theory. Cambridge University Press, Cambridge.
[416] Green, M., Schwarz, J. and Witten, E. (1987) Superstring Theory. Vol. I and II. Cambridge University Press, Cambridge.
[417] El Naschie, M.S. (2016) Journal of Modern Physics, 7, 1953-1962.
http://dx.doi.org/10.4236/jmp.2016.714173
[418] Weinberg, S. (1995) The Quantum Theory of Fields. Vol. I. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9781139644167
[419] Oriti, D. (Editor) (2009) Approaches to Quantum Gravity. Cambridge University Press, Cambridge.

  
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