Sr–Nd isotopes and geochemistry of the infrastructural rocks in the Meatiq and Hafafit core complexes, Eastern Desert, Egypt: Evidence for involvement of pre-Neoproterozoic crust in the growth of Arabian–Nubian Shield

Abstract Meatiq and Hafafit core complexes are large swells in the Eastern Desert of Egypt, comprising two major tectono‐stratigraphic units or tiers. The lower (infrastructure) unit is composed of variably cataclased gneissose granites and high‐grade gneisses and schists. It is structurally overlain by Pan–African ophiolitic mélange nappes (the higher unit). The two units are separated by a low‐angle sole thrust, along which mylonites are developed. Major and trace element data indicate formation of the gneissose granites in both volcanic arc and within‐plate settings. Nevertheless, all analyzed gneissose granites and other infrastructural rocks, exhibit low initial ratios (Sr_i) (<0.7027), positive ε_Nd(t) (+4.9 to +10.3) and Neoproterozoic Nd model age (T_DM) (592–831 Ma for the gneissose granite samples). Although these values are compatible with other parts of the Arabian– Nubian Shield considered to be juvenile, the ε_Nd(t) values and several incompatible element ratios of the gneissose granites are too low to be derived from a mantle source without contribution from an older continental crust. Our geological, Sr–Nd isotopic and chemical data combined with the published zircon ages indicate the existence of a pre‐Neoproterozoic continent in the Eastern Desert that started to break up at ca 800 Ma. Rifting and subsequent events caused the formation of oceanic crust and emplacement within‐plate alkali basalts in the hinterland domains of the old continent. The emplacement of basaltic magma might have triggered melting of lower crust in the old continent and resulted in emplacement of the within‐plate granite masses between 700 Ma and 626 Ma. The granite masses and other rocks in the old continent have been subjected to deformation during the over‐thrusting of Pan–African nappes, probably because of the oblique convergence between East and West Gondwanaland. Rb–Sr isotopes of the gneissose granites in both Meatiq and Hafafit core complexes defines an isochron age of 619 ± 25 Ma with Sr_i of 0.7009 ± 0.0017 and mean squares of weighted deviates = 2.0. We interpret this age as the date of thrusting of the Pan–African nappes in the Eastern Desert. Continued oblique convergence between East and West Gondwanaland could have resulted in the formation northwest–southeast‐trending Meatiq and Hafafit anticlinoriums.     

Improving the Quality of Municipal Solid Waste Compost by Using Expanded Perlite and Natural Zeolite

The scope of this study was to investigate the effects of natural zeolite and expanded perlite on the quality of municipal solid waste compost. Various ratios of the materials were added as supplements to the organic fraction of municipal solid waste. These applications were periodically compared with an untreated control process. The results obtained from experimental studies clearly showed that municipal solid waste collected from the metropolitan city center of Samsun, Turkey could not be composted without any additions due to the very high moisture content, which reached up to 75–80%. In the untreated control process, thermophilic temperatures were not supported during the composting. In this system, ammonia and other odors became a problem because of the high pH levels, and the electrical conductivity was too high for aged compost. However, the addition of natural zeolite and expanded perlite had a positive affect on the quality of the final compost. Natural zeolite trapped ammonium and reduced nitrogen losses from the compost. Expanded perlite held excess moisture and supported improved aeration. The results also indicated that the use of natural zeolite together with expanded perlite in municipal solid waste composting processes produced mature and stable compost.     

Distances of Galaxies from the Apparent Size Distribution of Dark Clouds. II NGC 224, NGC 2841 and NGC 7331

The distances of three Sb galaxies NGC 224, NGC 2841 and NGC 7331 have been determined using the apparent size distribution of dark interstellar clouds in each of them. The distances of NGC 224, NGC 2841, NGC 7331 were found to be 727.7 ± 63 kpc, 8.07 ± 0.16 Mpc and 7.22 ± 0.15 Mpc, respectively.     

The construction of a seventh-order Jupiter-Saturn analytical theory

We extend the construction of the Jupiter-Saturn theory to include all the terms up to the seventh order in the masses. The Hori-Lie transformation technique is employed. The Jacobian coordinates are adopted and the theory is expressed in terms of the canonical non-singular variables of H. Poincaré.     

Is there period-activity correlation in RS CVn-type binary systems?

The rotation period-activity luminosity and the rotation period-surface activity flux correlations for the components of RS CVn-type binaries are discussed. It is argued that such correlations, although they are required by dynamo generated magnetic fields, do not represent the dominant parameter in determining the level of activity. Evidences are given that these correlations may essentially be induced by the period-radius dependence for the components of RS CVn-type binaries, and in addition, this result may well be valid for all the late-type stars (single or binary components).     

The construction of a third order secular

In this part we find out the 24 equations of secular perturbation equations for the subsystem J-S-U-N. The solution of these equations by the Lagrange-Laplace procedure and the Eigen value Eigen vector is analysed. Also we refer to Hurwitz theorem to test stability.     

The construction of a general third-order planetary theory

We review in this part the outline of a third-order general planetary theory established through Von Zeipel's method and in terms of Poincaré's canonical variables We consider our system to consist of the Sun as the primary body, one disturbed planet, and one disturbing planet.     

Determination of secular terms in general planetary theory

A method to calculate secular terms of the two parts of the planetary disturbing function— when it is expressed in terms of the true anomalies or the eccentric anomalies instead of the mean anomalies - is described. Also an alternative method is outlined.     

Fourier analysis of the light curves of eclipsing variables,XV

A new general expression for the theoretical momentsA _2m of the light curves of eclipsing systems has been presented in the form of infinite series expansion. In this expansion, the terms have been given as the product of two different polynomials which satisfy certain three-term recursion formulae, and the coefficients diminish rapidly with increasing number of terms. Thus, the numerical values of the theoretical momentsA _2m can be generated recursively up to four significant figures for any given set of eclipse elements. This can be utilized to solve the eclipse elements in two ways: (i) with an indirect method (for the procedures see Paper XIV, Kopal and Demircan, 1978), (ii) with a direct method as minimization to the observational momentsA _2m (area fitting). The procedures given in Paper XIV for obtaining the elements of any eclipsing system consisting of spherical stars have been automated by making use of the new expression for the momentsA _2m of the light curves. The theoretical functionsf ₀,f ₂,f ₄,f ₆,g ₂ andg ₄ which are the functions ofa andc ₀, have been used to solve the eclipse elements from the observed photometric data. The closed-form expressions for the functionsf ₂,f ₄ andf ₆ have also been derived (Section 3) in terms of Kopal'sI-integrals.The automated methods for obtaining the eclipse elements from one minimum alone have been tested on the light curves of YZ (21) Cassiopeiae under the spherical model assumptions. The results of these applications will be given in Section 5 which follows a brief introduction to the procedure we followed.     

Expansion of the planetary mutual distance raised to any negative power by the method of symbolic differential operators

We present a literal approach to evaluate ^–s necessary for the construction of high order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high order and high degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of ^–s . We utilize Laplace coefficients and its derivatives to carry out the development, without dealing with Newcomb operators or Hansen's coefficients.