Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.
Designing and optimizing complex scientific code for new computing architectures is a challenging task. To address this issue in the E3SM land model (ELM) development, we developed a software tool called SPEL, which facilitates code generation, verification, and performance tuning using compiler directives within a Function Unit Test framework. In this paper, we present a SPEL extension that leverages the version control system (e.g., Git) to autonomous code generation and demonstrate its application to continuous code integration and development of the ELM software system. The study can benefit the scientific software development community.
Peter SchwartzDali WangFengming YuanPeter Thornton
In the digital age, the global character of the Internet has significantly improved our daily lives by providing access to large amounts of knowledge and allowing for seamless connections. However, this enormously interconnected world is not without its risks. Malicious URLs are a powerful menace, masquerading as legitimate links while holding the intent to hack computer systems or steal sensitive personal information. As the sophistication and frequency of cyberattacks increase, identifying bad URLs has emerged as a critical aspect of cybersecurity. This study presents a new approach that enables the average end-user to check URL safety using Microsoft Excel. Using the powerful VirusTotal API for URL inspections, this study creates an Excel add-in that integrates Python and Excel to deliver a seamless, user-friendly interface. Furthermore, the study improves Excel’s capabilities by allowing users to encrypt and decrypt text communications directly in the spreadsheet. Users may easily encrypt their conversations by simply typing a key and the required text into predefined cells, enhancing their personal cybersecurity with a layer of cryptographic secrecy. This strategy democratizes access to advanced cybersecurity solutions, making attentive digital integrity a feature rather than a daunting burden.
The deep integration of digital technology and the real economy is a vital engine for boosting high-quality growth of the real economy.As a result,it is necessary to investigate the effects of this integration on the real economy.This paper develops a two-sector model that incorporates the production sector and the technology research and development sector,taking into account both the factor attribute and the technical attribute of digital technology.Digital capital,general capital,skilled labor,and unskilled labor are considered as intermediate inputs in the model.Furthermore,this paper examines the effects of two integration modes,i.e.,factor-based integration and technology-based integration,on the development of the real economy and the biased technical change from a theoretical perspective.Empirical tests are conducted to support the analysis.The findings indicate that both factor-based integration and technology-based integration contribute positively to the development of the real economy,although technology-based integration exhibits diminishing marginal effects.Heterogeneity analysis reveals that factor-based integration plays a more significant role in promoting the development of the real economy in regions with geographical advantages,low levels of human resources,high marketization levels,or low market segmentation.On the other hand,technology-based integration assumes a greater role in facilitating the development of the real economy in regions with geographical disadvantages,low costs on human resources,low marketization levels,or high market segmentation.Further analysis demonstrates that the integration of digital technology and the real economy leads to digital capital-biased technical change and skilled labor-biased technical change.Therefore,it is imperative for the public sector to encourage the expansion of both factor-based integration and technology-based integration in the real economy.Additionally,it is also important to develop a reasonable industry layout plan and enhance the skill le
With the release of China Education Modernization 2035,education modernization has become a national strategic goal.In this context,Chongqing Energy Vocational College is actively exploring the“four integration and four innovation”specialized and creative integration talent cultivation mode,aiming at cultivating high-quality talents with innovative spirit and practical skills.This paper analyzes the status quo and challenges of talent cultivation in higher vocational education,puts forward the main practices of innovation-driven,creation and research,cross-border integration,and innovative practice,and has achieved remarkable results.Additionally,it summarizes the experience revelation and provides a reference for other higher vocational colleges and universities.