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The main objective of this paper is to obtain the fractional integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for s-exponentially convex functions. Furthermore, a Hadamard inequality is obtained for fractional integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known fractional integrals and functions which are convex, exponentially convex, and s-convex.

This paper studies the guidance scheme for the terminal guidance problem subject to input constraints, attack angle constraints, and second-order dynamics of missile autopilot. Firstly, the guidance system model with the above multi-constraint model is given. Secondly, an anti-saturation back-stepping guidance law which makes use of the low-pass filter to avoid the differential of the virtual control signals is designed based on the terminal sliding mode method, auxiliary system, and adaptive technique. Finally, Lyapunov theory and numerical simulations are utilized to prove that the states of the system under the proposed guidance law are uniformly ultimately bounded.

In this paper, an image encryption algorithm based on the H-fractal and dynamic self-invertible matrix is proposed. The H-fractal diffusion encryption method is firstly used in this encryption algorithm. This method crosses the pixels at both ends of the H-fractal, and it can enrich the means of pixel diffusion. The encryption algorithm we propose uses the Lorenz hyperchaotic system to generate pseudorandom sequences for pixel location scrambling and self-invertible matrix construction to scramble and diffuse images. To link the cipher image with the original image, the initial values of the Lorenz hyperchaotic system are determined using the original image, and it can enhance the security of the encryption algorithm. The security analysis shows that this algorithm is easy to implement. It has a large key space and strong key sensitivity and can effectively resist plaintext attacks.

A theoretical model was developed for permeability-induced inductance variations under influences of H/E field applications in bulk composite of polycrystalline spinel ferrites and piezoelectric ceramics with coil wound around. Strain-mediated magnetization changes in ferrites facilitate the permeability variations and a significant tunability in inductance from converse magnetoelectric coupling mechanisms can be achieved as expected. Modeling the inductance variations, i.e. inductance responses with frequency, was performed in terms of thickness, frequency, Young's modulus, density as well as resonance dymanic at mechanical electromagnetic resonance frequency. From the magnetostrictive/piezoelectric constitutive equations in consideration of boundary conditions, we derive permeability expressions to allow for a quantitative description of inductance traces involved magnetic relaxation occurring around longitudinal acoustic mode in the presence of H/E field applications. The model was applied to a specific ferrite-piezoelectric tunable inductor of Ni 0.7 Zn 0.3 Ga 0.02 F e 1.98 O 4 /PZT/Ni 0.7 Zn 0.3 Ga 0.02 Fe 1.98 O 4 trilayer with coil. Then, we explicitly calculate the amplitude and tendency of inductance variations with frequency using the theory and evaluate the accordance with the corresponding experimental findings. The theory is of importance for studies on the underlying physics such field-induced permeability variations and resonance dynamics in ME tunable inductor devices. In particular, it helps to explain the recent measurements for which magnetic relaxation phenomenon occurring in typical inductance versus frequency characteristics.

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A high-Q magnetoelectric (ME) gyrator consisting of a trilayer laminate of nickel-iron-based constant elasticity alloy (Ni–Fe–Cr) and lead zirconate titanate with a coil wound around it has been developed and systematically characterized. Highly efficient magneto-mechanical-electric conversion can be achieved by means of the combination contributions of high quality factors from individuals, and much energy can be transferred through the gyration device. Under an electromechanical resonance frequency of 54.04 kHz, experimental results show that maximum efficiency reaches as high as 88.5% under an extremely low input density of 3.31 µW/cm3 with an optimum load resistance of 9.6 kΩ and a magnetic bias of 66 Oe. Such a highly efficient ME gyrator with a high Q factor can be beneficial or degrade the design goals that are likely to be achievable for practical applications in compact power transfer electronic devices.

As an effective method for image security protection, image encryption is widely used in data hiding and content protection. This paper proposes an image encryption algorithm based on an improved Hilbert curve with DNA coding. Firstly, the discrete wavelet transform (DWT) decomposes the plaintext image by three-level DWT to obtain the high-frequency and low-frequency components. Secondly, different modes of the Hilbert curve are selected to scramble the high-frequency and low-frequency components. Then, the high-frequency and low-frequency components are reconstructed separately using the inverse discrete wavelet transform (IDWT). Then, the bit matrix of the image pixels is scrambled, changing the pixel value while changing the pixel position and weakening the strong correlation between adjacent pixels to a more significant correlation. Finally, combining dynamic DNA coding and ciphertext feedback to diffuse the pixel values improves the encryption effect. The encryption algorithm performs the scrambling and diffusion in alternating transformations of space, frequency, and spatial domains, breaking the limitations of conventional scrambling. The experimental simulation results and security analysis show that the encryption algorithm can effectively resist statistical attacks and differential attacks with good security and robustness.