An expansion formula for fractional derivatives of variable order

In this work we extend our previous results and derive an expansion formula for fractional derivatives of variable order. The formula is used to determine fractional derivatives of variable order of two elementary functions. Also we propose a constitutive equation describing a solidifying material and determine the corresponding stress relaxation function.     

Wave equation for generalized Zener model containing complex order fractional derivatives

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.     

Seasonal variations of cytosolic antioxidant enzyme activities in the liver and white muscle of thinlip gray mullet (Liza ramada Risso) from the Adriatic Sea

The activity of cytosolic antioxidative defence enzymes in the liver and white muscle of thinlip gray mullet (Liza ramada Risso) were compared in winter and spring in the Adriatic Sea. Activity of antioxidative enzymes is functionally organized due to metabolic demands: analyses of variance and correlation analysis revealed tissue- and seasonal- specific organization of antioxidative enzymes. In winter GST activity increased in both tissues compared with spring. At the same time decreased GSH-Px and GR activities were observed and this effect was more pronounced in liver then in white muscle. From correlation analyses it is concluded that the antioxidative components correlate, but the composition of the antioxidative defence system is different in respect to season and tissue. This means that the antioxidative defence system reorganizes its structure due to oxidative demands and to protect the tissues against reactive oxygen species and to establish homeostasis. Discriminant analyses separated groups according to the complete organization of individual components of the system very well and identified individual components (CAT, GST and GR) which contribute most to the differences. Statistical differences were observed between enzyme activities in tissues (liver and muscle) in both winter and spring, and between seasons (winter and spring) for liver tissue only. Since environmental parameters, such as temperature and oxygen concentration in the sea differ with season, we conclude that in this species the tissues examined expressed their antioxidative defence systems in different ways in respect of external/environmental conditions. We propose that tissue- and seasonal- specific levels of antioxidant enzyme activities should be considered in the interpretation of data from future biomonitoring field studies, especially in relation to low temperature.     

The effect of an external magnetic field on the resonant neutralization of negative ions near a solid state surface

The influence of an external magnetic field on the resonant neutralization of negative ions near a solid state surface is considered. It is shown that the magnetic field reduces the neutralization probability considerably.     

New analytic approach to the theory of charge exchange in atom-multiply charged ion collisions

A new method is discussed for the solution of many-level charge-exchange problems. The results provide the distribution of the final electronic states over the angular quantum numbers in analytical form. The obtained Z oscillations (Z is the ion charge) of the cross sections are found to be in good agreement with recent experimental data.     

Three points method for searching the best least absolute deviations plane

In this paper a new method for estimation of optimal parameters of a best least absolute deviations plane is proposed, which is based on the fact that there always exists a best least absolute deviations plane passing through at least three different data points. The proposed method leads to a solution in finitely many steps. Moreover, a modification of the aforementioned method is proposed that is especially adjusted to the case of a large number of data and the need to estimate parameters in real time. Both methods are illustrated by numerical examples on the basis of simulated data and by one practical example from the field of robotics.     

Collision processes of Hydride species in Hydrogen plasmas: III. The Silane family

Cross sections are provided for most important collision processes of the Silicon‐Hydrides from the “Silanefamily”: SiH_y (y = 1 ? 4) molecules and their ions SiH⁺_y, with (plasma) electrons and protons. The processes include: electron impact ionization and dissociation of SiH_y, dissociative excitation, ionization and recombination of SiH⁺_y ions with electrons, and charge ‐ and atom ‐ exchange in proton collisions with SiH_y. All important channels of dissociative processes are considered. Information is also provided on the energetics (reactants/products energy loss / gain) of each individual reaction channel. Total and partial cross sections are presented in compact analytic forms. The critical assessment of data, derivation of new data and presentation of results follow closely the concepts of the recently published related databases for Carbon‐Hydrides, namely for the Methane family [1, 2], and for the Ethane‐ and the Propane families [3], respectively. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal structure of rosmanol-9-ethylether

The title compound: 2H-10,4a-(epoxy-methano)-phenantren-12-one-1,3,4,9,10,10a-hexahydro-5,6-dihydroxy-9-etoxy-1,1-dirnethyl-7-(1-methylethyl), was isolated fromSalvia officinalis L. andHyssopus officinalis L. C₂₂H₃₀O₅, orthorhombic, P2₁2₁2₁, (No. 19)a=8.309(1),b=11.320(2),c=22.060(3) Å,V=2075.0(9) ų,Z=4,D _x=1.199 g·cm^–3, (CuK)=1.54184 Å,=6.43 cm^–1, F(000)=808,T=296(1) K. The structure was solved by direct methods and refined toR=0.047 for 1824 observed reflections collected on a CAD-4 diffractometer. In the course of structure refinement conformational disorder of the isopropyl moiety and the terminal methyl group pertaining to the ethoxy ligand was established. They result altogether in four different conformers.Alternatively it can be termed 9-ethoxyrosmanol.