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This paper aims at studying the basic properties and chaotic synchronization of complex Lorenz system:

Numerically we show that this system is a chaotic system and exhibits chaotic attractors. The necessary conditions for system (⋆) to generate chaos are obtained. Analytical and numerical calculations are presented to achieve synchronization. Active control technique is used to synchronize chaotic attractors of equations (⋆).

In a recent paper [Chaos, Solitons Fractals21, 915 (2004)], both real and complex Van der Pol oscillators were introduced and shown to exhibit chaotic limit cycles. In the present work these oscillators are synchronized by applying an active control technique. Based on Lyapunov function, the control input vectors are chosen and activated to achieve synchronization. The feasibility and effectiveness of the proposed technique are verified through numerical simulations.

This paper introduces and analyzes new hyperchaotic complex Lorenz systems. These systems are 6-dimensional systems of real first order autonomous differential equations and their dynamics are very complicated and rich. In this study we extend the idea of adding state feedback control and introduce the complex periodic forces to generate hyperchaotic behaviors. The fractional Lyapunov dimension of the hyperchaotic attractors of these systems is calculated. Bifurcation analysis is used to demonstrate chaotic and hyperchaotic behaviors of our new systems. Dynamical systems where the main variables are complex appear in many important fields of physics and communications.

The ubiquitous presence of complexity in nature makes it necessary to seek new mathematical tools which can probe physical systems beyond linear or perturbative approximations. The random matrix theory is one such tool in which the statistical behavior of a system is modeled by an ensemble of its replicas. This paper is an attempt to review the basic aspects of the theory in a simplified language, aimed at students from diverse areas of physics.

This study synthesizes the anionic–nonionic surfactants by reacting tripropylene glycol, maleic anhydride, polyoxyethylenated stearyl ether and fumaric acid. The properties of a series of anionic–nonionic surfactants that feature hydrophilic groups with different lengths of chains are measured. The critical micelle concentration (CMC) value for these surfactants decreases as the length of the polyoxyethylene chain increases. This shows that long polyoxyethylene chains promote pre-micelle formation in the aqueous phase and adsorption at the interface surrounding the aqueous phase. The dispersion of a particle suspension of ${\mathrm{\text{TiO}}}_2$ is also determined using dynamic light scattering (DLS) and scanning electron microscopy (SEM). The results show that when anionic–nonionic surfactants are added into a ${\mathrm{\text{TiO}}}_2$ suspension, it prevents the precipitation of solid particles of ${\mathrm{\text{TiO}}}_2$ and allows greater de-aggregation of the nanoparticles. DLS data show that when the concentration of the anionic–nonionic surfactants is increased, the distribution range narrows and it becomes more uniform. The larger specific surface area of the surfactant results in greater dispersion of the suspension. The SEM results show that when anionic–nonionic surfactants feature hydrophilic groups with a shorter chain, a ${\mathrm{\text{TiO}}}_2$ suspension is more effectively dispersed.

This study investigated dye–surfactant interactions between a series of modified Gemini surfactants and commercial direct dyes in aqueous solution and their corresponding effects on cotton fabric dyeing. A surface tension meter was also used to measure surface activities of compounds containing electrolyte under conditions similar to those in dyeing processes. The surface tension measurements showed lower than normal surface tension in surfactant solutions containing electrolyte. From the UV-Vis spectra, the isosbestic point indicated that dye–surfactant complexes had formed and existed as hydrophilic interaction between direct dyes and modified Gemini surfactants. When dyeing cotton fabric with red dye and orange dye, the presence of these surfactants decreased dye uptake rate but increased for blue dye because the dye–surfactant interaction had formed a hydrophilic complex.

The empirical inductive algorithms that utilize the covering paradigm (such as the AQx and CNx families of inductive systems) comprise various heuristics and statistical tools so that the core of the covering paradigm remains often quite hidden. The goal of this paper is thus to disclose theoretical underlying principles of covering learning algorithms. By exploiting the set theory, the paper exhibits how the correctness and generality required for decision rules induced by a covering algorithm may be satisfied. The principle differences between a genuine theoretical approach and actual empirical machine learning algorithms are also discussed.

In this paper autonomous and nonautonomous modified hyperchaotic complex Lü systems are proposed. Our systems have been generated by using state feedback and complex periodic forcing. The basic properties of these systems are studied. Parameters range for hyperchaotic attractors to exist are calculated. These systems have very rich dynamics in a wide range of parameters. The analytical results are tested numerically and excellent agreement is found. A circuit diagram is designed for one of these hyperchaotic complex systems and simulated using Matlab/Simulink to verify the hyperchaotic behavior.

In this work, we introduce and investigate the modified projective lag synchronization (MPLS) of two nonidentical hyperchaotic complex nonlinear systems. The idea of an active control technique based on complex Lyapunov function with lag in time is used for an approach to investigate MPLS of hyperchaotic attractors of these systems. For illustration, this approach is applied to hyperchaotic complex Chen and Lü systems. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve MPLS.

In this paper, we prove that if a surface diagram of a surface-knot has at most two triple points and the lower decker set is connected, then the surface-knot group is isomorphic to the infinite cyclic group.

Analysis of the cutting forces during machining operations is an important issue. The rough end mill with the serrated profile is broadly used for reduction of cutting forces during milling operation. Since cutting force changes in random behavior during end milling, in this paper we employ fractal theory to analyze the complex structure of cutting force signal. For this purpose, we investigated the influence of variations of cutting depth on variations of fractal structure of cutting forces in wet and dry machining conditions. The results of our analysis showed the variations of fractal structure of cutting forces between different cutting depths, in wet and dry conditions. The employed methodology in this research is not limited to rough end milling and can potentially be applied to other types of machining operations, where the variations of cutting forces is an important issue.

It is known that geometry of cutting tool affects the cutting forces in machining operations. In addition, the value of cutting forces changes during machining operations and creates a chaotic time series (signal). In this paper, we analyze the variations of the complex structure of cutting force signal in rough end milling operation using fractal theory. In fact, we analyze the variations of cutting force signal due to variations of tool geometry (square end mill versus serrated end mill). In case of each type of end mill, we did the machining operation in wet and dry conditions. Based on the results, the fractal structure of cutting force signal changes based on the type of milling tool. We also did the complexity analysis using approximate entropy to check the variations of the complexity of cutting force signal, where the similar behavior of variations between different conditions was obtained. The method of analysis that was used in this research can be applied to other machining operations to study the influence of different machining parameters on variations of fractal structure of cutting force.

Investigating human eye movement is one of the major research topics in vision science. It is known that human eye movement is related to external stimuli. In this way, the analysis of human eye movement due to different types of external stimuli is very important in vision science. Beside all reported analysis, no one has discovered any relation between the complex structure of moving visual stimuli and the complex structure of human eye movement. This study reveals the relationship between the complexity of human eye movement signal and the applied visual stimuli. For this purpose, we employ fractal theory. We demonstrated that the fractal dynamics of human eye movement in both horizontal and vertical directions shifts toward the fractal dynamics of moving visual target as stimulus. The capability observed in this research opens new doors to scientists to study the relation between the human eye movement and the applied stimuli.

Analysis of workpiece surface quality is one of the major issues in manufacturing engineering. Turning operation is a famous machining operation that is widely used in machining of materials. In this research, we investigate the surface finish of machined workpiece from turning operation. For this purpose, we employ fractal theory to study the complex structure of machined workpiece’s surface in different conditions. The applied parameters include the variations of cutting depth, feed rate and spindle speed in wet and dry machining conditions. Based on the obtained results, we found the correlation between the increment of fractal dimension of machined surface and the increment of cutting depth, feed rate and spindle speed in wet machining condition. The obtained results will be discussed in relation with the complexity of machined surface. The employed method of analysis in this research can be widely applied to the analysis of the effect of different machining parameters and conditions on the surface quality of machined workpiece in case of different machining operations.

Tool wear is an important issue that happens in all machining operations when the tool exerts forces on the workpiece. Therefore, engineers should choose the optimum values for machining parameters and conditions to reduce the amount of tool wear and increase its life. Machine vibration is one of the factors that highly affects tool wear. Since both tool wear and machine vibration signal have complex structures, in this research we employ fractal theory to find out their relation. In this paper, we analyze the relation between tool wear and machine vibration signal in different experiments where the depth of cut, feed rate and spindle speed change. The obtained results showed that tool wear and machine vibration signal are related to each other in case of variations of depth of cut and feed rate in different experiments, where both fractal structures get more complex by the increment of these machining parameters. The obtained method of analysis in this research can be potentially applied to other machining operations in order to link the machine vibration to the structure of tool wear.

Surface finish is one of the most important issues that is discussed in machining of materials. In fact, reaching the required surface finish is the key scale in analysis of the quality of machined workpiece. Chip formation is an important factor that highly affects the surface finish of machined workpiece. In this research, we analyze the relationship between surface finish and chip formation by fractal analysis of their surfaces. Since both patterns have complex structures, we calculate their fractal dimension in case of different experiments in which machining parameters change. The result of analysis indicates that the variations of fractal dimension of machined surface show a reverse pattern compared to the fractal dimension of chip surface in case of variations of depth of cut and feed rate. However, in case of variations of spindle speed, the variations of fractal dimension of machined surface show a similar pattern with the fractal dimension of chip surface. Therefore, it can be said that the complexity of machined surface is linked to the complexity of chip surface. The method of analysis used in this research can be further applied to other manufacturing operations.

Tool wear is one of the unwanted phenomena in machining operations where tool has direct contact with the workpiece. Tool wear is an important issue in milling operation that is caused due to different parameters such as machine vibration. Tool wear shows complex structure, and machine vibration is a chaotic signal that also is complex. In this research, we analyze the correlation between tool wear and machine vibration using fractal theory. We run the experiments in which machining parameters, namely depth of cut, feed rate and spindle speed change, and accordingly analyze the variations of fractal dimension of tool wear versus the fractal dimension of machine vibration signal. Based on the obtained results, variations of complexity of tool wear are reversely correlated with the variations of complexity of vibration signal. Fractal analysis could potentially be applied to other machining operations in order to investigate the relation between tool wear and machine vibration.

More than 25% of unintentional gunshot injuries and more than 15% of intentional gunshot injuries involve extremities.

In these patients, early acute multidisciplinary treatment is essential and critical to achieve a satisfactory mobility and composite wounds repair.

We hereby report a logistic delayed successful treatment of a complex arm gunshot wound with a free fibula flap. The significance of this case report is related to the necessity of emphasising the organised and multidisciplinary approach required to cure these patients in the proper way from a surgical and medical point of view.

In order to improve the technological innovation effect of compound high-tech industry, this paper studies its dynamic resource allocation technology with the support of 5G communication technology, and analyzes the application of 5G communication technology in technological innovation of compound high-tech industry. In the uplink and downlink of wireless energy-carrying communication system, this paper studies the joint optimization of subcarrier allocation and power allocation of uplink and downlink to maximize the uplink and downlink weighted sum rate of the system. Moreover, this paper adopts the joint optimization algorithm of power and sub-carrier based on Lagrangian dual method and ellipsoid method to obtain the maximum information transmission rate of uplink and downlink. In addition, this paper constructs an intelligent innovation management system. The research results show that the dynamic resource allocation method based on 5G communication proposed in this paper has a very good effect in the application of technological innovation in complex high-tech industries.

Human eye movement is a key concept in the field of vision science. It has already been established that human eye movement responds to external stimuli. Hence, investigating the reaction of the human eye movement to various types of external stimuli is important in this field. There have been many researches on human eye movement that were previously done, but this is the first study to show a relation between the complex structure of human eye movement and the complex structure of static visual stimulus. Fractal theory was implemented and we showed that the fractal dynamics of the human eye movement is related to the fractal structure of visual target as stimulus. The outcome of this research provides new platforms to scientists to further investigate on the relation between eye movement and other applied stimuli.