The distribution of the natural radioisotopes 238U, 226Ra, 232Th, and 40K in addition to their radiological parameters in granitic rock samples from five different localities (Gebel El-Missikat, Gebel El-Gidamy, Gebel Ria El-Garra, Gebel El-Aradiya, and Gebel Kab Amira) in the central area of the Eastern Desert, Egypt, was measured using high purity germanium (HPGe) detector-based γ-spectrometry. The average activity concentrations of 238U, 226Ra, 232Th, and 40K in all five studied areas are higher than the corresponding global average values. The highest average activity concentrations of 238U and 226Ra were observed in Gebel El-Missikat, whereas the highest average value of 232Th activity concentration was found at Gebel El-Gidamy, and the highest concentration of 40K was obtained at Gebel El-Aradiya. The radiological hazard parameters radium equivalent (Raeq), external hazard index (Hex), internal hazard index (Hin), absorbed dose rate (ADR), annual effective dose rate (AEDR) outdoors, annual gonadal dose equivalent (AGDE), and excess lifetime cancer risks (ELCR) were calculated to assess the radiation hazards associated with the rock samples. The average values of these parameters are higher than the recommended reference levels. The obtained data provide a valuable future database for estimating the impact of radioactive contamination in the studied area and in the places where the rocks are used.

The distribution of the natural radioisotopes 238U, 226Ra, 232Th, and 40K in addition to their radiological parameters in granitic rock samples from five different localities (Gebel El-Missikat, Gebel El-Gidamy, Gebel Ria El-Garra, Gebel El-Aradiya, and Gebel Kab Amira) in the central area of the Eastern Desert, Egypt, was measured using high purity germanium (HPGe) detector-based γ-spectrometry. The average activity concentrations of 238U, 226Ra, 232Th, and 40K in all five studied areas are higher than the corresponding global average values. The highest average activity concentrations of 238U and 226Ra were observed in Gebel El-Missikat, whereas the highest average value of 232Th activity concentration was found at Gebel El-Gidamy, and the highest concentration of 40K was obtained at Gebel El-Aradiya. The radiological hazard parameters radium equivalent (Raeq), external hazard index (Hex), internal hazard index (Hin), absorbed dose rate (ADR), annual effective dose rate (AEDR) outdoors, annual gonadal dose equivalent (AGDE), and excess lifetime cancer risks (ELCR) were calculated to assess the radiation hazards associated with the rock samples. The average values of these parameters are higher than the recommended reference levels. The obtained data provide a valuable future database for estimating the impact of radioactive contamination in the studied area and in the places where the rocks are used.

The aim of this paper is to investigate the control of chaotic Burke-Shaw
system using Pyragas method. This system is derived from Lorenz system which
has several applications in physics and engineering (e.g. secure
communications). The linear stability and the existence of Hopf bifurcation
of this system are investigated. Based on the characteristic equation, a
theorem is stated and proved. This theorem is used to calculate the interval
values of the time delay $ au $ at which this system is stable (unstable).
By establishing appropriate time delay $ au $ and feedback strength $K$
ranges, one of the unstable equilibria of this system can be controlled to
be stable. We, also, introduced the fractional version of this system which is not
studied in the literature as far as we know. The advantage of the fractional
order system is that, the system has extra parameter which enriches its
dynamics. Increasing the number of parameters may be used to increase the
security of the transmitted information. We apply the Pyragas method to
control the chaotic behavior of fractional Burke-Shaw system. As we did for
the integer order, we determine the values of $ au $ and $K$ which
guarantee that the fractional version is stable. Finally, to support the
analytical results, some numerical simulations are carried out which
indicate that chaotic solution is turned to be stable if $ au $ passes
through certain intervals. The bifurcation diagrams are calculated.

The aim of this paper is to investigate the control of chaotic Burke-Shaw
system using Pyragas method. This system is derived from Lorenz system which
has several applications in physics and engineering (e.g. secure
communications). The linear stability and the existence of Hopf bifurcation
of this system are investigated. Based on the characteristic equation, a
theorem is stated and proved. This theorem is used to calculate the interval
values of the time delay $ au $ at which this system is stable (unstable).
By establishing appropriate time delay $ au $ and feedback strength $K$
ranges, one of the unstable equilibria of this system can be controlled to
be stable. We, also, introduced the fractional version of this system which is not
studied in the literature as far as we know. The advantage of the fractional
order system is that, the system has extra parameter which enriches its
dynamics. Increasing the number of parameters may be used to increase the
security of the transmitted information. We apply the Pyragas method to
control the chaotic behavior of fractional Burke-Shaw system. As we did for
the integer order, we determine the values of $ au $ and $K$ which
guarantee that the fractional version is stable. Finally, to support the
analytical results, some numerical simulations are carried out which
indicate that chaotic solution is turned to be stable if $ au $ passes
through certain intervals. The bifurcation diagrams are calculated.

In this paper we introduce the concept of generalized fuzzy soft mappings on families of generalized fuzzy soft sets and
study the properties of generalized fuzzy soft images ( inverse images) of generalized fuzzy soft sets. Furthermore, generalized fuzzy
soft continuous mappings, generalized fuzzy soft open (closed) mappings and generalized fuzzy soft homeomorphisms are introduced.

In this paper we introduce the concept of generalized fuzzy soft mappings on families of generalized fuzzy soft sets and
study the properties of generalized fuzzy soft images ( inverse images) of generalized fuzzy soft sets. Furthermore, generalized fuzzy
soft continuous mappings, generalized fuzzy soft open (closed) mappings and generalized fuzzy soft homeomorphisms are introduced.

The Campanian-Eocene succession exposed at Wadi Tarfa and north Wadi Qena area, north Eastern Desert, Egypt is differentiated from base to top into: the pre-Middle Campanian (Santonian?) Rakhiyat Formation (R), the Middle Campanian-Late Maastrichtian Sudr Formation (S), the redefined Late Danian-Early Thanetian Beida Formation (B), the Early Late Thanetian Tarawan Formation (T), the Latest Late Thanetian-Lower Ypresian Esna Formation (Es), the Late Lower Ypresian-Late Upper Ypresian Thebes Formation (Th) and the newly recorded Middle Lutetian El Mereir Formation (M). The ages given here for the rock units depend on a high resolution planktonic foraminiferal zonation.
Field observations, beside the microfacies and benthonic paleobathymetric investigations, helped also in reaching a third order resolution of these sequences into their lowstand, transgressive, regressive and highstand systems tracts.

The Campanian-Eocene succession exposed at Wadi Tarfa and north Wadi Qena area, north Eastern Desert, Egypt is differentiated from base to top into: the pre-Middle Campanian (Santonian?) Rakhiyat Formation (R), the Middle Campanian-Late Maastrichtian Sudr Formation (S), the redefined Late Danian-Early Thanetian Beida Formation (B), the Early Late Thanetian Tarawan Formation (T), the Latest Late Thanetian-Lower Ypresian Esna Formation (Es), the Late Lower Ypresian-Late Upper Ypresian Thebes Formation (Th) and the newly recorded Middle Lutetian El Mereir Formation (M). The ages given here for the rock units depend on a high resolution planktonic foraminiferal zonation.
Field observations, beside the microfacies and benthonic paleobathymetric investigations, helped also in reaching a third order resolution of these sequences into their lowstand, transgressive, regressive and highstand systems tracts.

The Campanian-Eocene succession exposed at Wadi Tarfa and north Wadi Qena area, north Eastern Desert, Egypt is differentiated from base to top into: the pre-Middle Campanian (Santonian?) Rakhiyat Formation (R), the Middle Campanian-Late Maastrichtian Sudr Formation (S), the redefined Late Danian-Early Thanetian Beida Formation (B), the Early Late Thanetian Tarawan Formation (T), the Latest Late Thanetian-Lower Ypresian Esna Formation (Es), the Late Lower Ypresian-Late Upper Ypresian Thebes Formation (Th) and the newly recorded Middle Lutetian El Mereir Formation (M). The ages given here for the rock units depend on a high resolution planktonic foraminiferal zonation.
Field observations, beside the microfacies and benthonic paleobathymetric investigations, helped also in reaching a third order resolution of these sequences into their lowstand, transgressive, regressive and highstand systems tracts.

The Campanian-Eocene succession exposed at Wadi Tarfa and north Wadi Qena area, north Eastern Desert, Egypt is differentiated from base to top into: the pre-Middle Campanian (Santonian?) Rakhiyat Formation (R), the Middle Campanian-Late Maastrichtian Sudr Formation (S), the redefined Late Danian-Early Thanetian Beida Formation (B), the Early Late Thanetian Tarawan Formation (T), the Latest Late Thanetian-Lower Ypresian Esna Formation (Es), the Late Lower Ypresian-Late Upper Ypresian Thebes Formation (Th) and the newly recorded Middle Lutetian El Mereir Formation (M). The ages given here for the rock units depend on a high resolution planktonic foraminiferal zonation.
Field observations, beside the microfacies and benthonic paleobathymetric investigations, helped also in reaching a third order resolution of these sequences into their lowstand, transgressive, regressive and highstand systems tracts.