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On *L*^{r}
-regularity of global attractors generated by strong solutions of reaction-diffusion equations

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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

###### Vibrations attenuation of a system excited by unbalance and the ground movement by an impact element

collisions is old, but the development of advanced computational facilities and software tools at the end of the 20th century brought new possibilities for its investigation. The topic is massively studied by many authors focusing on the impact systems (see e.g. [ 1 – 7 ]), the pendulums [ 8 ], the gear transmissions systems [ 9 ], the systems with clearances and non smooth stiffness ( [ 10 , 11 ]) and electromechanical systems ( [ 12 ]). In this paper, a system formed by a rotor and its casing flexibly coupled with a baseplate and of an impact body, which is separated

###### Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results

. $$ $P_{\text{uw}}(\Omega) = \int_0^H{j(c^a_{\Omega_h})\:dh}.$$ (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 this new case. Also, using a similar analysis to that of Section 4.3 (and working out similar calculations

###### Study the combustion processes of space debris in the Earth’s atmosphere by meteoric TV camera

recommendations for the design of optimal meteor camera are formulated. The most efficient in the ratio of “price/performance” are a standard video camera with CCD or CMOS image sensor size 1/2 inch (the sizes of a pixel 8.6 × 8.3 micron or more) and lens relative aperture of 1 : 1.2 ( Fig. 1 ). Fig. 1 The extreme sensitivity of the Watec CCD (stars) with afrequency 25 frame/sec and lenses with different characteristics. The camera Watec WAT-902H2 - one of the most sensitive black-and-white video cameras with a 1/2 inch CCD receiver, equal to. One of the features of

###### Calculation of line of site periods between two artificial satellites under the action air drag

) 54.081 258.4665 301.12 186.4076 M (degree) 125.1605 101.4671 170.9719 173.7019 p ( kg=km 3 ) 3.63E-05 4.6E-05 0.000354 0.000369 p o ( kg=km 3 ) 0.000145 0.000145 0.000697 0.000697 h 0 (Km) ( kg=km 3 ) 600 600 500 500 H (Km) 71.835 71.835 63.822 63.822 Epoch Year & Julian Date 18180. 59770749 18180. 82019665 18182.935593 18182.93790454 time of data (min) 2018 06 29 2018 06 29 2018 07 01 2018 07 01 13:31:30 19:41:03.004 21:57:32.134 22:30:32.994 B * 2.5E-05

###### Period Variation Study and Light Curve Analysis of the Eclipsing Binary GSC 02013-00288

.26 R= 560 nm -0.01 0.03 0.30 0.26 I= 800 nm -0.01 0.03 0.28 0.25 Some of interesting in all light curves of IK Boo is the existence of a hump like distortion waves between phase 0.75 and 0.90 ( Figure 3 ). This phenomenon displays when the primary goes free from the secondary and it has been recorded for the RS CVn binary systems as flare-like episodes (Zeilik, et al., [ 29 ]). 5 Period variation study The first light elements was obtained by Blättler and Diethelm [ 3 ] by performing a linear regression to 10 times of minima

###### Affine Transformation Based Ontology Sparse Vector Learning Algorithm

ofimage patches, Computers in Biology and Medicine 73 56 70 10.1016/j.compbiomed.2016.03.022 [18] M. K. Khormuji and M. Bazrafkan, (2016), A novel sparse coding algorithm for classification of tumors based on gene expression data , Medical & Biological Engineering & Computing, 54, No 6, 869-876. 10.1007/s11517-015-1382-8 Khormuji M. K. Bazrafkan M. 2016 A novel sparse coding algorithm for classification of tumors based on gene expression data, Medical & Biological Engineering & Computing 54 6 869 876 10.1007/s11517-015-1382-8 [19] G. Ciaramella and A. Borzí

###### Attractors for a nonautonomous reaction-diffusion equation with delay

}+ \int_{\Omega} b(t,u^m_t)\frac{\partial u^m}{\partial t} + \int_{\Omega} g\frac{\partial u^m}{\partial t}\,. \end{array}$$ (2.4) On the other hand, we have d d t F ( u ) = d F d u ∂ u ∂ t , = f ( u ) ∂ u ∂ t . $$\begin{array}{} \displaystyle \frac{d}{d t} F(u) = \frac{dF}{d u} \,\frac{\partial u}{\partial t}\,,\\ \displaystyle \qquad\qquad= f(u) \, \frac{\partial u}{\partial t} \,. \end{array}$$ (2.5) So d d t ∫ Ω F ( u ) = ∫ Ω f ( u ) ∂ u ∂ t . $$\begin{array}{} \displaystyle \frac{d}{d t}\int_{\Omega} F(u) = \int_{\Omega} f(u)\frac{\partial u

###### Nonlinear waves in a simple model of high-grade glioma

. (46) and their corresponding homoclinic orbits. Fig. 2 Bright solitary waves for β = 0.3, ϕ 0 = 0.5 and c = 2.5. (a) Profiles from Eq. (45) (solid curve) and the explicit solution given by Eq. (46) (dashed curve). (b) Homoclinic orbits from Eq. (45) (solid curve) and Eq. (46) (dashed curve). 4.2 Minimum speed of positive solutions We now wish to determine the minimum speed c 0 above which the solutions of Eq. (45) are positive for all ξ , since biologically feasible solutions for the tumor density must be positive for all ξ

###### On the classical and nonclassical symmetries of a generalized Gardner equation

c μ 3 h ‴ + b μ h 2 h ′ + a μ h h ′ + d μ h ′ − λ h ′ + e h + f = 0. $$\begin{array}{} \displaystyle \begin{equation}\label{edor}c \mu^3h'''+b \mu h^{2 } h'+a \mu h h' + d \mu h'-{ \lambda} h'+e h+f=0.\end{equation} \end{array}$$ (25) We assume that equation ( 25 ) has a solution in the following form h ( z ) = a 0 + a 1 Y + ⋯ + a N Y N , $$\begin{array}{} \displaystyle \begin{equation}\label{hs} \begin{array}{rcl} h(z)&=&\displaystyle a_0+a_1Y+\cdots +a_N Y^N,\end{array} \end{equation} \end{array}$$ (26) where a n ( n = 0,1,..., N ) are constant