The effect of back-bombardment (BB) electrons is consideredone of the main obstaclesfor extensive use of thermionic RF guns (T-RF). The 10 hexaboride materials named (Ca, Sr, Ba, La, Ce, Pr, Nd, Sm, Eu, and Gd) B6 are investigated in this paper to survey the effect of the cathode material on reducing BB electrons and compare them with LaB6 (which is widely used as a thermionic cathode). A numerical model was used to conduct this paper. Besides the numerical calculations, an experiment has been performed to determine the work functions of CeB6 andLaB6.Theresultsfromthenumericalcalculations revealed that (Ba, Ca, and Nd) B6 are less affected by BB electrons: 42%, 50%, and 59%, respectively, compared with LaB6, for low beam current applications. In contrast, for high beam current duties, (Nd, Ce, and Sm) B6 have minimum influence by BB electrons compared with other hexaborides. The study concluded that BB electrons are strongly affected by the properties of the cathode material, especially thermionic emission and material density. Moreover, the study suggests that it is worthwhile to prepare BaB6, CaB 6, NdB 6, and SmB 6 as cathode materials, then to subject them to a real experimental test using T-RF gun to compare their performance and BB effect against LaB6

Depending on double compound synchronization and compound combination synchronization, a new kind of synchronization
is introduced which is the double compound combination synchronization (DCCS) of eight n-dimensional
chaotic systems. This kind may be considered as a generalization of many types of synchronization. In the communication,
based on many of drive and response systems, the transmitted and received signals will be more secure. Using the
Lyapunov stability theory and nonlinear feedback control, analytical formulas of control functions are obtained to insure
our results. The corresponding analytical expression and numerical treatment are used to show the validity and feasibility
of our proposed synchronization scheme. The eight memristor-based Chua oscillators are considered as an example. Other
examples can be similarly investigated. The proposed synchronization technique is supported using the MATLAB simulation
outcomes. We obtain the same results of numerical treatment of our synchronization using simulation observations of
our example.

Depending on double compound synchronization and compound combination synchronization, a new kind of synchronization
is introduced which is the double compound combination synchronization (DCCS) of eight n-dimensional
chaotic systems. This kind may be considered as a generalization of many types of synchronization. In the communication,
based on many of drive and response systems, the transmitted and received signals will be more secure. Using the
Lyapunov stability theory and nonlinear feedback control, analytical formulas of control functions are obtained to insure
our results. The corresponding analytical expression and numerical treatment are used to show the validity and feasibility
of our proposed synchronization scheme. The eight memristor-based Chua oscillators are considered as an example. Other
examples can be similarly investigated. The proposed synchronization technique is supported using the MATLAB simulation
outcomes. We obtain the same results of numerical treatment of our synchronization using simulation observations of
our example.

Depending on double compound synchronization and compound combination synchronization, a new kind of synchronization
is introduced which is the double compound combination synchronization (DCCS) of eight n-dimensional
chaotic systems. This kind may be considered as a generalization of many types of synchronization. In the communication,
based on many of drive and response systems, the transmitted and received signals will be more secure. Using the
Lyapunov stability theory and nonlinear feedback control, analytical formulas of control functions are obtained to insure
our results. The corresponding analytical expression and numerical treatment are used to show the validity and feasibility
of our proposed synchronization scheme. The eight memristor-based Chua oscillators are considered as an example. Other
examples can be similarly investigated. The proposed synchronization technique is supported using the MATLAB simulation
outcomes. We obtain the same results of numerical treatment of our synchronization using simulation observations of
our example.

This paper deals with a kind of synchronization of dynamical systems with complex variables which is
called generalized complex modified hybrid function projective synchronization (GCMHFPS) of time delay
complex chaotic (hyperchaotic) systems. In other words, that the time delay complex systems can
be synchronized up to a complex function transformation matrix. Moreover, the elements of the transformation
matrix are complex functions of the states of drive system and time, where this matrix is not
square. The idea of an active control method based on complex Krasovskii–Lyapunov functional is used to
achieve GCMHFPS of time delay complex systems. Furthermore, based on the non-diagonal complex function
transformation matrix, the modules and phases errors between one state of the complex response
system and more than one of the states of the drive system are studied which have not been discussed
before as far as we know. The analytical expression regarding the stability of this technique is derived
and excellent agreement is found upon comparison with numerical calculations. In particular, we show
through studying the time evolution of error, modulus and phase that the proposed scheme is effective
for controlling time delay complex systems.

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Some fractional-order hyperchaotic complex systems are introduced in this paper. These
hyperchaotic systems appear in several fields of applied sciences, e.g., secure communication
and laser physics. The values of the fractional-order and the parameters at which
these systems have hyperchaotic attractors are calculated based on the sign of their Lyapunov
exponents. The fractional Lyapunov dimension is computed for these hyperchaotic
attractors. On the other hand, we introduced the new definition of what is called generalized
function projective combination synchronization (GFPCS). This new kind of synchronization
may be considered as a generalization of many kinds of synchronization in the literature.
To study this kind of synchronization we state a scheme based on the tracking control technique.
An example is considered for the scaling functions which is the nonlinear one. The
active control method cannot be used in this scheme since its error is large.

Some fractional-order hyperchaotic complex systems are introduced in this paper. These
hyperchaotic systems appear in several fields of applied sciences, e.g., secure communication
and laser physics. The values of the fractional-order and the parameters at which
these systems have hyperchaotic attractors are calculated based on the sign of their Lyapunov
exponents. The fractional Lyapunov dimension is computed for these hyperchaotic
attractors. On the other hand, we introduced the new definition of what is called generalized
function projective combination synchronization (GFPCS). This new kind of synchronization
may be considered as a generalization of many kinds of synchronization in the literature.
To study this kind of synchronization we state a scheme based on the tracking control technique.
An example is considered for the scaling functions which is the nonlinear one. The
active control method cannot be used in this scheme since its error is large.

Some fractional-order hyperchaotic complex systems are introduced in this paper. These
hyperchaotic systems appear in several fields of applied sciences, e.g., secure communication
and laser physics. The values of the fractional-order and the parameters at which
these systems have hyperchaotic attractors are calculated based on the sign of their Lyapunov
exponents. The fractional Lyapunov dimension is computed for these hyperchaotic
attractors. On the other hand, we introduced the new definition of what is called generalized
function projective combination synchronization (GFPCS). This new kind of synchronization
may be considered as a generalization of many kinds of synchronization in the literature.
To study this kind of synchronization we state a scheme based on the tracking control technique.
An example is considered for the scaling functions which is the nonlinear one. The
active control method cannot be used in this scheme since its error is large.

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.