**Last Call for ICCA11 Mini-symposium****: Quaternion ****&** **C****lifford Fourier transforms ****& ****wavelets ****3**** (QCFTW****3****)**

**■ ****Abstract**** Submission:** Please submit the** QCFTW3** *abstract* you will present (at most 1 page) online by *04** June 201**7: *

http://www.icca11.ugent.be/index.php?page=registrationabstracts

*Dear Colleagues*,

On behalf of the Scientific Committee of ICCA11, it is a great pleasure for us to invite you to the historic city of **Ghent (Belgium)** to present some of your latest results.

We are organizing a 3^{rd} session on Quaternion and Clifford Fourier transforms and wavelets (QCFTW3) **at ****Ghent**** University****, Ghent**, 7-11 Aug. 2017 as part of

*1**1**th** International Conference on Clifford Algebras and their Applications** 201*

*7*

*(ICCA1*

*1*

*)***■ ****Description.** Quaternion and Clifford Fourier and Wavelet Transforms as refinement and generalization of the 1D complex Fourier and wavelet theory play an increasing role in different areas of mathematics, physics, computer science, engineering, and beyond. We want to discuss the state of the art in mathematics and application of these hypercomplex Fourier and wavelet transforms and give ideas for new developments.

**■ ****Idea.** We aim to bring together experts working in theoretical research and applied sciences active in fields related to quaternion and Clifford Fourier and wavelet transforms and extensions to other Clifford integral transforms (not restricted to the topics below). We intend to cover the discussion of these transforms and the presentation of new methods that develop and apply them.

**■ ****History.** Previous sessions have been organized at the conferences ICCA9 in Weimar (2011) and ICCA10 in Tartu (2014). They brought together contributions on this topic and related Clifford integral transforms. Proceedings appeared as a book with Springer: *Quaternion and Clifford Fourier Transforms and Wavelets*, TIM 27, **Hitzer**, E., **Sangwine**, S. J. (Eds.), 2013, and a special issue of AACA (due 2016).

**■ ****Topics.** We invite scientists and engineers working with discrete and continuous quaternion and Clifford Fourier and wavelet transforms in the following fields:

*pure and applied Clifford analysis, geometric calculus, hypercomplex analysis, harmonic analysis, or quaternion analysis**solution of partial differential equations, boundary and initial value problems**approximation theory, sampling, and numerical simulations**wavelets with application in physics, visualization, signal analysis, (color) image processing, feature extraction, medical imaging, applications in numerical analysis**practical applications in engineering sciences in general, in particular in electric**al engineering, robotics, classical mechanics, navigation, guidance and control systems, geographic information systems, seismology, and data registration*

**■ ICCA11 Best Presentation Award: **If you are under 29 years old, then we encourage you to apply by 04 June 2017 for the new ICCA11 Best Presentation Award:

https://www.icca11.ugent.be/index.php?page=presentationaward

**■ ****Proceedings.** Proceedings of ICCA11, including our mini-symposium, will appear as a special issue of the journal Adv. of Appl. Cliff. Algs., Springer-Birkhäuser. Manuscripts (max. 15 pages) will be subject to the usual refereeing process, and are due Sunday, 03 December 2017.

**■ ****Registration.** When you register online for ICCA11, please indicate that your contribution is for this mini-symposium (QCFTW3).

*Please feel free to contact us! With kind regards,*

*Hendrik De Bie* (Ghent, Belgium)

Hendrik.DeBie_AT_UGent.be

*Todd Ell *(Burnsville, USA)

todd.a.ell_AT_gmail.com

*Eckhard Hitzer *(Tokyo, Japan)

hitzer_AT_icu.ac.jp

*Steve Sangwine* (Essex, UK)

sjs_AT_essex.ac.uk

*Source:* https://www.icca11.ugent.be/docs/minisymposia_QCFTW3_v4.pdf, https://www.icca11.ugent.be/index.php?page=presentationaward

also here we mention some as say prof dr mircea orasanu and prof horia orasanu as followings

MECHANICAL HOLONOMIC AND NON HOLONOMIC SYSTEMS

Author Horia Orasanu

ABSTRACT

The way in which such a system manifests itself cannot be exclusively predicted only by the behavior of individual elements. Its manifestation is also induced by the manner in which the elements relate in order to influence global behavior. The most significant properties of complex systems are emergence, self-organization, adaptability, etc. [1–4].

Examples of complex systems can be found in human societies, brains, the Internet, ecosystems, biological evolution, stock markets, economies and many others [1, 2]. Particularly, polymers are examples of such complex systems. Their forms include a multitude of organizations starting from simple, linear chains of identical structural units and ending with very complex chains consisting of sequences of amino acids that form the building blocks of living fields. One of the most intriguing polymers in nature is DNA, which creates cells by means of a simple, but very elegant language. It is responsible for the remarkable way in which individual cells organize into complex systems, such as organs, which, in turn, form even more complex systems, such as organisms. The study of complex systems can offer a glimpse into the realistic dynamics of polymers and solve certain difficult problems (protein folding) [1–4].

Correspondingly, theoretical models that describe the dynamics of complex systems are sophisticated [1–4]. However, the situation can be standardized taking into account that the complexity of interaction processes imposes various temporal resolution scales, while pattern evolution implies different freedom degrees [5].

In order to develop new theoretical models, we must admit that complex systems displaying chaotic behavior acquire self-similarity (space-time structures seem to appear) in association with strong fluctuations at all possible space-time scales [1–4]. Then, in the case of temporal scales that are large with respect to the inverse of the highest Lyapunov exponent, the deterministic trajectories are replaced by a collection of potential trajectories, while the concept of definite positions by that of probability density. One of the most interesting examples is the collision process in complex systems, a case in which the dynamics of the particles can be described by non-differentiable curves.

Since non-differentiability appears as the universal property of complex systems, it is necessary to construct a non-differentiable physics. Thus, the complexity of the interaction processes is replaced by non-differentiability; accordingly, it is no longer necessary to use the whole classical “arsenal” of quantities from standard physics (differentiable physics).

This topic was developed within scale relativity theory (SRT) [6,7] and non-standard scale relativity theory (NSSRT) [8–22]. In this case, we assume that the movements of complex system entities take place on continuous, but non-differentiable, curves (fractal curves), so that all physical phenomena involved in the dynamics depend not only on space-time coordinates, but also on space-time scale resolution. From such a perspective, physical quantities describing the dynamics of complex systems may be considered fractal functions [6,7]. Moreover, the entities of the complex system may be reduced to and identified with their own trajectories, so that the complex system will behave as a special fluid lacking interaction (via their geodesics in a non-differentiable (fractal) space). We have called such fluid a “fractal fluid” [8–22].

In the present paper, we shall introduce new concepts, like non-differentiable entropy, informational non-differentiable entropy, informational non-differentiable energy, etc., in the NSSRT approach (the scale relativity theory with an arbitrary constant fractal dimension).

1 INTRODUCTION

Complex systems are large interdisciplinary research topics that have been studied by means of a mixed basic theory that mainly derives from physics and computer simulation. Such systems are made of many interacting elementary units that are called “agents”.

Based on a fractal potential, which is the “source” of the non-differentiability of trajectories of the complex system entities, we establish the relationships among non-differentiable entropy. The correlation fractal potential-non-differentiable entropy implies uncertainty relations in the hydrodynamic representation, while the correlation of informational non-differentiable entropy/informational non-differentiable energy implies specific uncertainty relations through a maximization principle of the informational non-differentiable entropy and for a constant value of the informational non-differentiable energy. The constant value of the informational non-differentiable energy made explicit for the harmonic oscillator induces a quantification condition. We note that there exists a large class of complex systems that take smooth trajectories. However, the analysis of the dynamics of these classes is reducible to the above-mentioned statements by neglecting their fractality.

2. Hallmarks of Non-Differentiability

Let us assume that the motion of complex system entities takes place on fractal curves (continuous, but non-differentiable). A manifold that is compatible with such movement defines a fractal space. The fractal nature of space generates the breaking of differential time reflection invariance. In such a context, the usual definitions of the derivative of a given function with respect to time [6,7],

dFdt=limΔt→0+F(t+Δt)−F(t)Δt=limΔt→0−F(t)−F(t−Δt)Δt

(1)

are equivalent in the differentiable case. The passage from one to the other is performed via Δt → − Δt transformation (time reflection invariance at the infinitesimal level). In the non-differentiable case, (dQ+dt) and (dQ−dt) are defined as explicit functions of t and dt,

dQdt+limΔt→0+Q(t,t+Δt)−Q(t,Δt)Δt

and:

dQdt=limΔt→0−Q(t,Δt)−Q(t,t−Δt)Δt

(2)

The sign (+) corresponds to the forward process, while (−) corresponds to the backward process. Then, in space coordinates dX, we can write [6,7]:

dX±=dx±+dξ±=v±dt+dξ±

(3)

with v± the forward and backward mean speeds,

v+=dx+dt=limΔt→0+⟨X(t+Δt)−X(t)Δt⟩v−=dx−dt=limΔt→0−⟨X(t)+X(t−Δt)Δt⟩

(4)

and dξ± a measure of non-differentiability (a fluctuation induced by the fractal properties of trajectory) having the average:

⟨dξ±⟩=0,

(5)

References

1. Liljebäck P, Stavdahl Ø, Beitnes A (2006) SnakeFighter – development of a water hydraulic fire fighting snake robot. In: Proc. IEEE international conference on control, automation, robotics, and vision ICARCV, Singapore.

2. Wang Z, Appleton E (2003) The concept and research of a pipe crawling rescue robot. Adv Robot 17.4: 339–358.

3. Fjerdingen SA, Liljebäck P, Transeth AA (2009) A snake-like robot for internal inspection of complex pipe structures (PIKo). In: Proc. IEEE/RSJ international conference on intelligent robots and systems, St. Louis, MO, USA.

4. Dacic DB, Nesic D, Teel AR, Wang W. Path following for nonlinear systems with unstable zero dynamics: an averaging solution. IEEE Trans Automatic Control. 2011;56:880–886. doi: 10.1109/TAC.2011.2105130. [Cross Ref]

5. Hirose S. Biologically inspired robots: snake-like locomotors and manipulators. Oxford, England: Oxford University Press; 1993.

6. Matsuno F, Sato H (2005) Trajectory tracking control of snake robots based on dynamic model. In: Proc. IEEE international conference on robotics and automation, 3029–3034. 18-22 April 2005.

7. Date H, Hoshi Y, Sampei M (2000) Locomotion control of a snake-like robot based on dynamic manipulability. In: Proc. IEEE/RSJ international conference on intelligent robots and systems, Takamatsu, Japan.

8. Tanaka M, Matsuno F (2008) Control of 3-dimensional snake robots by using redundancy. In: Proc. IEEE international conference on robotics and automation, 1156–1161, Pasadena, CA.

9. Ma S, Ohmameuda Y, Inoue K, Li B (2003) Control of a 3-dimensional snake-like robot. In: Proc. IEEE international conference on robotics and automation, vol. 2, 2067–2072, Taipei, Taiwan.

10. Tanaka M, Matsuno F (2009) A study on sinus-lifting motion of a snake robot with switching constraints. In: Proc. IEEE international conference on robotics and automation, 2270–2275. 12-17 May 2009.

11. Prautsch P, Mita T, Iwasaki T (2000) Analysis and control of a gait of snake robot. Trans IEE J Ind Appl Soc 120-D: 372–381.

12. McIsaac K, Ostrowski J. Motion planning for anguilliform locomotion. IEEE Trans Robot Automation. 2003;19:637–652. doi: 10.1109/TRA.2003.814495. [Cross Ref]

13. Hicks G, Ito K. A method for determination of optimal gaits with application to a snake-like serial-link structure. IEEE Trans Automatic Control. 2005;50:1291–1306. doi: 10.1109/TAC.2005.854583. [Cross Ref]

14. Ma S, Ohmameuda Y, Inoue K (2004) Dynamic analysis of 3-dimensional snake robots. In: Proc. IEEE/RSJ international conference on intelligent robots and systems, 767–772. 28 Sept.-2 Oct. 2004.

15. Ma S. Analysis of creeping locomotion of a snake-like robot. Adv Robot. 2001;15(2):205–224. doi: 10.1163/15685530152116236. [Cross Ref]

16. Liljebäck P, Pettersen KY, Stavdahl Ø, Gravdahl JT (2013) Snake robots – modelling, mechatronics, and control. Advances in industrial control. Springer.

17. Liljebäck P, Haugstuen IU, Pettersen KY. Path following control of planar snake robots using a cascaded approach. IEEE Trans Control Syst Technol. 2012;20:111–126.

18. Rezapour E, Pettersen KY, Liljebäck P, Gravdahl JT (2013) Path following control of planar snake robots using virtual holonomic constraints. Paper presented at the IEEE international conference on robotics and biomimetics, Shenzhen, China. [PMC free article] [PubMed]

19. Liljebäck P, Pettersen KY, Stavdahl Ø, Gravdahl JT. Controllability and stability analysis of planar snake robot locomotion. IEEE Trans Automatic Control. 2013;56(6):1365–1380. doi: 10.1109/TAC.2010.2088830. [Cross Ref]

20. Westervelt ER, Grizzle JW, Chevallereau C, Choi JH, Morris B. Feedback control of dynamic bipedal robot locomotion. Boca Raton: CRC press; 2007.

21. Maggiore M, Consolini L. Virtual holonomic constraints for Euler-Lagrange systems. IEEE Trans on Automatic Control. 2013;58(4):1001–1008. doi: 10.1109/TAC.2012.2215538. [Cross Ref]

22. Consolini L, Maggiore M (2010) Control of a bicycle using virtual holonomic constraints. In: Proc. 49th IEEE conference on decision and control, Atlanta, Georgia, USA, December 15-17, 2010.

23. Shiriaev A, Perram JW, Canudas-de-Wit C. Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach. IEEE Trans Automatic Control. 2005;50(8):1164–1176. doi: 10.1109/TAC.2005.852568. [Cross Ref]

24. Freidovich L, Robertsson A, Shiriaev A, Johansson R. Periodic motions of the Pendubot via virtual holonomic constraints: theory and experiments. Automatica. 2008;44(3):785–791. doi: 10.1016/j.automatica.2007.07.011. [Cross Ref]

25. Spong MW, Hutchinson S, Vidyasagar M. Robot modeling and control. New York: John Wiley and Sons; 2006.

26. Bullo F, Lewis A (2005) Geometric control of mechanical systems. Springer.

27. Fossen TI. Marine control systems: guidance, navigation and control of ships, rigs and underwater vehicles. Marine Cybernetics: Trondheim, Norway; 2002.

here we consider some more aspects as say prof dr mircea orasanu and prof horia orasanu