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The purpose of this paper is to develop a novel method for establishing the mathematical link between the restored Hogarth curve and the golden ratio, and to advance the potential application of the Hogarth curves in standardization of the garment pattern design by using this method.

The Hogarth curve was fully restored by using the plant design system (PDS) software package and divided the restored curve into two fragments based on the intersection point between the curve and the straight line joining the curve endpoints. The ratios between two fragments of curves and straight lines were calculated and compared with the golden ratio, respectively, which was set as a normalized value. The potential application of the restored Hogarth curves in the normalization of the garment pattern design was therefore studied by using the standard mannequins.

The ratio in the most beautiful curve, i.e., the fourth Hogarth curve, was found to be infinitely approaching to the golden ratio. Furthermore, the incorporation of the Hogarth curves into the garment pattern design demonstrated that the fourth Hogarth curve was the most aesthetic line.

This work offered a novel method for bridging the gaps between arts and maths, i.e., the mathematical relation between the Hogarth curves and the golden ratio. Such a method will provide the protocol to promote the potential applications of the Hogarth curves in the garment pattern design and the human body decoration.

Curves with various profiles have been demonstrated to be more attractive and decorative than the straight lines by William Hogarth. Among all kinds of curves, Hogarth proposed seven serpentine lines as the most beautiful curves, i.e., Hogarth curves. Those seven Hogarth curves are subsequently applied in a wide range of fields, e.g., sculpture, painting, architecture and fashion design, indicating their significance to the development of the formal beauty. Recently, the beauty of Hogarth curves has been suspected to be induced by their special-designed curvature, which could have the potential relationship with the Golden Ratio. The purpose of this paper is to explore the relationship between the Hogarth curves and golden ratio by comparing the curvature of curves with the Fibonacci sequence.

Each of the Hogarth curves was fully restored and divided into two parts according to the turning point of the curvature; the ratios of span, curvature and angles between these two parts were compared with the Fibonacci sequence.

The experimental results disclosed that the ratio of the fourth Hogarth curve, which was considered as the most beautiful line by Hogarth, was infinitely approaching the golden ratio. Based on the relationship between the fourth Hogarth curve and the golden ratio, the ratios of each curve were employed to define and normalize these curves, providing a quantitative way to redraw the Hogarth curves.

This research work unlocked the information of the relationship between the Hogarth curves and golden ratio, and proposed an effective and convenient mathematic way to quantify the Hogarth curves. The experimental findings disclosed the underlying mechanisms of the beauty of the forth Hogarth curves. Such a fundamental study will promote the establishment of the normalized methods for evaluating the beauty of arts and provide novel ideas for researchers and industrial technologists to use the Hogarth curves.

Beautiful and simple curves are most commonly employed in apparel design since they can not only simplify the manufacture process, but also significantly beautify the breast profile of customers. However, it is regularly difficult to choose the most suitable curve when producing the strip costume; this is due to the fact that the curve is a kind of aesthetics without any laws. The quantification and standardization to curves are necessary for fashion design. The purpose of this paper is to investigate the relationship between the stripe of costumes and the breast profiles of wearers.

Seven curves drawn derived from the Hogarth theory (Hogarth curves) were firstly diagrammatized by the central line technology using CorelDraw, and the format of bitmaps and quadratic functions of these selected curves were obtained respectively. Simulating formulas were subsequently used to interpret these curves. The standard of curves for apparel design was finally established after being evaluated by comparison between the different types of female breasts and the curves on the costumes.

The established models indicated that the fourth Hogarth curves was the most attractive one that combining the static state and the dynamic beauty, which could also help females to highlight the beautiful breast shapes.

This work provided the fundamentally understanding of the application of Hogarth curves in fashion design and the improvement on the effectiveness of the garment industry.

The purpose of this paper is to establish a combined model for selecting key indexes of complex equipment, and then improve the cost forecasting precision of the model. The problem how to choose the key elements of complex products has always been concerned on many fields, such as cost assessment, investment decision making, etc.

Using Grey System Theory to establish a cost estimation model of complicated equipment is more reasonable under the few data and poor information. Therefore, this paper constructs cost index’s system of complex equipment, and then quantitative and qualitative analysis methods are utilized to calculate the grey entropy between the characteristic parameter and the behavior parameters. Further, establish the grey relational clustering matrix of the behavior sequences by using the grey relative incidence analysis. Finally, the authors select key indicators according to the grey degree.

The experiment demonstrates that the cost key parameters of complex equipment can be successfully screened out by the proposed approach, and the cost estimation accuracy of complicated products is improved.

The method proposed in this paper could be utilized to solve some practical problems, particularly the selection of cost critical parameters for complex products with few samples and poor information. Taking the cost key indexes of civil aircraft as an example, the results verified the validity of the GICM model.

In this paper, the authors develop the method of GICM model. Taking the data of civil aircraft as an example, the authors screen the key indicators of complex products successfully, and improve the prediction accuracy of the GM (1, N) model by using the selected parameters, which provides a reference for some firms.

With the global economic slowdown in 2023, most universities in the central and western regions of China may face the problem of shortage of government financial funding, which is directly related to the development of science and technology of the universities. With the support of the local government, most of the ordinary universities have shifted attention to the transfer and transformation of intellectual property based on school-enterprise cooperation, hoping to seek more commercialization income as an extra source of income. Therefore, this paper aimed to study the current situation of university intellectual property, i.e. the reserve and distribution of transferable patents, discipline distribution of patents, and regional cooperation of university patents.

A patent database of 10 key universities in Henan Province of China from 2012 to 2021 was established. The evaluation indicator model by the Entropy method was conducted to reveal the interaction mechanism between quantity indicators, quality indicators, and value indicators. Based on the data analysis, the development direction of the discipline construction and school-enterprise cooperation for local universities was clear.

The findings indicated that the number of patent applications from ten key universities in Henan Province has been increasing rapidly over the years. The trend for authorized invention patents has remained relatively stable. Compared with the patent applications and authorizations, the growth of transferable patents was notably slow. The significance of strategic layout of dominant disciplines and related high-value patents was not appreciated enough by Chinese government and universities. There was a large difference of dominant disciplines between 10 key universities, and the patent level of each university was directly proportional to the number of dominant disciplines. The university patent level heavily relied on the researchers' contributions and the distribution mechanism of scientific research resources within the university. Guangdong Province and the Yangtze River Delta of China, being economically developed regions, exhibited the most active engagement in patent technology cooperation. Conversely, the central and western regions displayed relatively lower participation in high-value patent research and development.

This study can provide a unique perspective to understand and solve the financial bottleneck problem of ordinary universities in the central and western regions of China. The discipline construction and school-enterprise cooperation are just one of the existing schemes, but it still cannot solve the financial problems faced by local universities in China towards the government.

The findings of this study can serve as a foundation for further investigation into policies aimed at improving the financial problems of ordinary universities in the central and western regions of China.

As an important attempt, the study tried to focus the financial problem of universities in the central and western regions of China based on the evaluation of the current situation of university intellectual property. This research findings are of great value in finding optimal layout between university patents, disciplines and school-enterprise cooperation.