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{ }}\cos E){\kern 1pt} dE. \end{array}$$(25) Completing the functions of the momenta given above (23) , it is convenient to introduce two more state functions w = U 1 / L , z = U 3 / L .$$\begin{array}{} \displaystyle w=U_1/L,\qquad z=U_3/L. \end{array}$$(26) The previous results may be summarized in the following theorem: Theorem 3. By composing the three symplectic transformations ( q 1 , q 2 , q 3 , q 4 Q 1 , Q 2 , Q 3 , Q 4 ) Projective Euler → ( ρ , ϕ , θ , ψ P , Φ , Θ , Ψ ) ↓ ↓ P A ( ℓ , u 1 , g , u 3 L , U 1 , G , U 3 ) Delaunay ← ( ρ , u 1 , u 2 , u 3 P joint probability density in phase space associated with continuous-time random walk. Physica A. 391, no. 15, 3858–3864. 10.1016/j.physa.2012.03.013 Kwok Sau Fa. Wang K.G. 2012 Integro-differential equation for joint probability density in phase space associated with continuous-time random walk Physica A. 391 15 3858 3864 10.1016/j.physa.2012.03.013 [10] Santos, L.T., Dorini, F.A., Cunha, M.C.C. (2010). The probability density function to the random linear transport equation. Appl. Math. Comput. 216, no. 5, 1524–1530. 10.1016/j.amc.2010.03.001 Santos L.T. Dorini F solution regarding some key parameters (as the pumping power of the skimmer). Finally, some conclusions are made in Section 4 2 Materials and Methods 2.1 Eulerian Mathematical Model Mathematical modelling of the transport and diffusion of an oil spill in the sea is of high interest to remediate the environmental impact (e.g., [ 24 , 25 , 26 ]). We have developed an Eulerian model for the case where the density of the pollutant is smaller than that of one of the sea water (so that it remains at the surface) and assuming that the layer-thickness of the pollutant h , is G. P. Labys W. C. Mitchell D. W. 1992 Evidence of chaos in commodity futures prices Journal of Futures Markets 12 291 305 10.1002/fut.3990120305 [28] A. Wei and R. M. Leuthold. (1998), Long Agricultural Futures Prices: ARCH, Long Memory or Chaos Processes? OFOR Paper 98-03. University of Illinois at Urbana-Champaign, Urbana. Wei A. Leuthold R. M. 1998 Long Agricultural Futures Prices: ARCH, Long Memory or Chaos Processes? OFOR Paper 98-03 University of Illinois at Urbana-Champaign Urbana [29] E. Panas and V. Ninni. (2000), Are oil markets chaotic? A non : 2.02.2017]. [23] http://www.eutelsat.com/en/home.html [access: 2.02.2017]. [24] Messier D., 2011, „Will a new space power rise along the Atlantic?”, The Space Review, 15.08.2011., http://www.thespacereview.com/article/2143/1 [access: 10.03.2017]. [25] https://www.kyivpost.com/article/content/ukraine-politics/first-launch-of-ukrainian-brazilianrocket-schedul-114278.html [access: 10.03.2017]. [26] http://ilot.edu.pl/wspolpraca/partnerzy-zagraniczni/uniwersytet-w-brasilii/ [access: 4.07.2017]. [27] Gocłowska-Bolek J., 2017, „Ameryka Łacińska w poszukiwaniu of fluid dynamics [ 8 , 24 ] or the Koterweg de Vries equations (KdV) which model waves on shallow water surfaces [ 17 , 25 ]. In the present paper we are going to focus our attention in Koterweg de Vries equations. The KdV equation u t + λ u u x + μ u x x x = 0$$ $$u_t+\lambda u u_x + \mu u_{xxx}=0$$ $$(1) was arised to model shallow water waves with weak nonlinearities and it is probably the most studied nonlinear evolution equation due to its wide applicability. The KdV equation ( 1 ) was generalized to a standard fifth order 1 Introduction This paper is mainly devoted to studying the regularity properties of global attractors for multivalued semiflows generated by strong solutions of reaction-diffusion equations. The existence and properties of global attractors for dynamical systems generated by reaction-diffusion equations have been studied by many authors over the last thirty years. For equations generating a single-valued semigroup such results are well known since the 80s (see e.g. [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 24 ], [ 34 ]). Moreover, deep results concerning the structure of },$$ and the corresponding upper-weight manufacturing compliance is defined by: P uw ( Ω ) = ∫ 0 H j ( c Ω h a )   d h . $$P_{\text{uw}}(\Omega) = \int_0^H{j(c^a_{\Omega_h})\:dh}.$$ (25) As we shall see in Section 5 , this formulation is well-suited when it comes to penalizing more specifically the upper region of each intermediate shape Ω h . As far as the shape derivative of P uw (Ω) is concerned, the exact same proof as that of Theorem 2 can be worked out, taking advantage of the definition ( 23 ) of g h , and the conclusions of this Theorem extend verbatim to

}{2}(f_w+F)F''-MF'=0,\quad '=\frac{d}{d\eta} $$(15) and the boundary conditions in Eq. (9) become F ( 0 ) = 0 , F ′ ( 0 ) = 1 , F ′ ( ∞ ) = 0.$$ $$F(0)=0,\quad F'(0)=1,\quad F'(\infty)=0.$$ $$(16) We introduce two variables ξ and G in the form G ( ξ ) = α F ( η ) a n d ξ = α η ,$$ G(\xi)=\alpha F(\eta) \quad and \quad \xi=\alpha\eta,  (17) where α > 0 is an amplification factor. In view of Eq. (17) , the system in Eqs. ( 15 - 16 ) is transformed to the form α 2 G ‴ + 1 2

2014-2019” Lotnictwo nr 3/2014 Magazyn miłośników lotnictwa wojskowego, cywilnego i kosmonautyki Wydawca Magnum X Sp. zo.o, Warszawa. [25] Müller H. Stolár M., 2006, “Siły Powietrzne Chorwacji” Przetłumaczył: Andrzej Kiński Lotnictwo nr 6/2006 Magazyn miłośników lotnictwa wojskowego, cywilnego i kosmonautyki Wydawca Magnum X Sp. zo.o, Warszawa. [26] “MiG-21 tylko dla doświadczonych pilotów, 2012, Przegląd Sił Powietrznych nr 03 (60) Kwartalnik, – przedruk 14 S. Hobson: Canada builds a future with equipment and experience gained in Afghanistan. “Jane’s International