Search Results (3)

This paper presents a novel approach to synthesizing phased antenna arrays (PAAs) by combining Taylor-series expansion with neural networks (NNs), enhancing the PAA synthesis process for modern communication and radar systems. Synthesizing PAAs is crucial for these systems, offering versatile beamforming capabilities. Traditional methods often rely on complex analytical formulations or numerical optimizations, leading to suboptimal solutions or high computational costs. The proposed method uses Taylor-series expansion to derive analytical expressions for PAA radiation patterns and beamforming characteristics, simplifying the optimization process. Additionally, neural networks are employed to model the intricate relationships between PAA parameters and desired performance metrics, providing adaptive learning and real-time adjustments. A validation of the proposed method is performed on a dual-band 5G antenna, which exhibits marked resonances at 28.14 GHz and 37.88 GHz, with reflection coefficients of $S_{11}$ = −19 dB and $S_{11}$ = −19.33 dB, respectively. The integration of Taylor expansion with NNs offers improved efficiency, reduced computational complexity, and the ability to explore a broader design space. Simulation results and case studies demonstrate the effectiveness and applicability of the approach in practical scenarios. This work represents a significant advancement in PAA synthesis, showcasing the synergistic integration of mathematical modeling and artificial intelligence for optimized antenna design in modern communication and radar systems. Full article

The Dual Credit Policy is an important policy to promote the development of new energy vehicles unique to China. There is a lack of research that intuitively reflects the impact of the Dual Credit Policy on industrial development through an industry-based factual comparison of this policy. Based on the Taylor expansion and Cross-Entropy description, this article obtains the development regression function by the quantitative analysis of five indicators—the number of new energy vehicle-related patents, sales volume, production volume, the number of newly registered enterprises, infrastructure construction (the number of charging piles) before and after the implementation of the policy, and describes them quantitatively using the Taylor expansion to obtain the CPTI index. The CPCEI index is obtained by calculating the Cross-Entropy of the distribution of each indicator before and after policy implementation. The above two indices were compared for the growth trend and growth quantity, respectively. Finally, the following conclusions were obtained: 1. the Dual Credit Policy is more significantly promoted at the market level than the impact on the technical level; 2. although there is also incentive in infrastructure construction, it cannot fully react to the market demand; 3. the number of start-up’s operating in the new energy field increases, but the overall growth trend gradually slows down and fails to significantly change the existing structure of the market. This study suggests that the government should launch a special incentive policy for charging piles, and new energy manufacturers should expand their production capacity to meet the market demand. Full article

In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series approximation. It is shown that a spline based series approximation to an integral yields, in general, a higher accuracy for a set order of approximation than a dual Taylor series, a Taylor series and an antiderivative series. A spline based series for an integral has many applications and indicative examples are detailed. These include a series for the exponential function, which coincides with a Padé series, new series for the logarithm function as well as new series for integral defined functions such as the Fresnel Sine integral function. It is shown that these series are more accurate and have larger regions of convergence than corresponding Taylor series. The spline based series for an integral can be used to define algorithms for highly accurate approximations for the logarithm function, the exponential function, rational numbers to a fractional power and the inverse sine, inverse cosine and inverse tangent functions. These algorithms are used to establish highly accurate approximations for $\mathsf{\pi }$ and Catalan’s constant. The use of sub-intervals allows the region of convergence for an integral approximation to be extended. Full article