A millimeter wave H-plane duplexer with E-plane filters has been designed. The channel filters are connected via a T-junction which is compensated by a cylindrical post and analyzed by integral Contour method.Moreover, the junction discontinuity effects have been taken into account. The combination of filters and compensated T-junction allows for low-cost manufacturing. The E-plane filters are analyzed separately, by the mode matching method. The scattering parameters of the combination of filters and T-junction are obtained. The diameter and position of the compensating post and the length of the T-junction arms are optimized in order to achieve the desired performance. This procedure saves computational time and memory. The duplexer has been built for 38GHz and the theory was verified by measurements.

Regarding the airfoil optimization design of multi-rotor unmanned aerial vehicles, this paper proposes an integral airfoil design method based on upper airfoil Contour optimization. Firstly, by designing concave descent input curves with 0-1 distribution, the upper arc of different optimized airfoils is obtained using the Tangent circles method. Secondly, an integral airfoil generation method is developed after establishing the middle arc. As the upper and lower arcs of different shapes are randomly combined, various airfoil profiles are obtained by random assortment. Finally, the effectiveness and accuracy of the designed airfoil are validated through Python programming. The airfoil is generated by the XFOIL program, and the optimal airfoil is output with a lift-to-drag ratio as the target. Meanwhile, an accurate Fluent analysis model is established, and a comparison verification is conducted on the data with the attack angle falling within [-8.02, 12.04] and lift-to-drag ratio falling within [-50, 100]. After Fluent modeling of the designed airfoil, the Euclidean distance between the calculated angle-lift-drag ratio data curve and the data curve tested by the wind tunnel is 0.0331, while the Euclidean distance between the simulated data in the literature and the wind tunnel data is 0.0408. It indicates that our precise model achieves 18.9% higher accuracy than the literature model. Testing and verification results indicate that our designed airfoil based on upper arc optimization and its corresponding airfoil library can meet the design requirements for the aerodynamic performance of airfoils in practical applications. It provides a valuable reference for the development of airfoil design, optimization, and generation methods.

In this paper, we consider a fourth order mixed partial differential equation with some initial and boundary conditions which is unsolvable by classical methods such as Fourier, Fourier-Bircove and Laplace Transformation methods. For this problem we will apply the Contour integral and asymptotic methods. The convergence of the appeared integrals, existence and uniqueness of solution, satisfying the solution and holding the given initial  and boundary conditions are stablished by complex analysis theory and related Contour integrals. Finally, the form of analytic  and approximate solutions are given due to different cases of eigenvalues distributions in the  complex plane.

This paper suggests a simple analytical method for Volterra-Fredholm integral equations, the solution process is similar to that by variational-based analytical method, e. g., Ritz method, however, the method requires no establishment of the variational principle for the discussed problem, making the method much attractive for practical applications. The examples show the method is straightforward and effective, and the method can also be extended to other nonlinear problems.

Abstract: Capacity, also known as a non-additive measure, is an extension of the Lebesgue measure. In recent years, bi-capacity was presented as a generalization of capacity with several bipolar fuzzy integrals related to bi-capacity, one of them being the bipolar Shilkret integral. In this paper, we propose a new approach to calculating the bipolar Shilkret integral to be suitable for bipolar scales. Then, we give some main properties of this integral related to bi-capacity.