An inversion algorithm for recovering a coefficient of Sturm-Liouville operator (Analysis of inverse problems through partial differential equations and related topics)

In this paper, an efficient algorithm for recovering a density of Sturm-Liouville operator from given two spectra is investigated. Based on Lidskii's theorem and Mercer's theorem, we build a sequence of trace formulae which bridge explicitly the density and eigenvalues in terms of nonlinear Fredholm integral equations. Due to intrinsic difficulties on ill-posedness of an inverse spectral problem, a truncated Fourier series regularization method is utilized for reconstructing the unknown density. Moreover, shifted Legendre polynomials are carried to balance the different order of trace formulae. Numerical results are presented to illustrated the effectiveness and stability of the proposed reconstruction algorithm

Developing a Knowledge-based System for Complex Geometrical Product Specification (GPS) Data Manipulation.

Geometrical product specification and verification (GPS) matrix system is a universal tool for expressing geometrical requirements on product design drawings. It benefits product designers through providing detailed description of functional requirements for geometrical products, and through referring to corresponding manufacturing and verification processes. In order to overcome current implementation problems highlighted in this paper, a GPS knowledge base and a corresponding innovative inference mechanism have been researched, which led to the development of an integrated GPS knowledge-based system to facilitate rapid and flexible manufacturing requirements. This paper starts with a brief introduction of GPS, GPS application problems and the project background. It then moves on to demonstrate a unified knowledge acquisition and representation mechanism based on the category theory (CT) with five selected examples of this project. The paper concludes with a discussion on the future works for this projec

The effect of supercritical CO2 on failure mechanisms of hot dry rock

Hot dry rock is a clean, renewable resource of geothermal energy with good stability and a high utilization rate. Supercritical CO2 has shown promising results for improving the permeability and heat exchange of hot dry rock. In order to demonstrate the effect of supercritical CO2 on the failure mechanism of granite, the acoustic emission of granite during its failure process were studied in addition to X-ray diffraction, scanning electron microscopy, and optical electron microscopy investigations. The experimental results showed that for granite without supercritical CO2 treatment, as it approached failure, there were many acoustic emission events with a waiting time less than 0.0001 s, and that the power law exponent of the acoustic emission energy distribution decreased. The failure mechanisms were a combination of fracture and friction, with fracturing dominant. After immersion in supercritical CO2 , new cracks and pores appeared in the granite due to the dissolution of minerals, but friction was also a factor evidenced in particle crumbing. Generally, the acoustic emission statistical distributions of granite before and after supercritical CO2 soaking conformed to the seismic statistical distribution law. This study is conducive to increasing the understanding of artificial earthquakes induced by the development of hot dry rock.Cited as: Li, H., Jiang, X., Xu, Z., Bowden, S. The effect of supercritical CO2 on failure mechanisms of hot dry rock. Advances in Geo-Energy Research, 2022, 6(4): 324-333. https://doi.org/10.46690/ager.2022.04.0

A complete tree-level dictionary between simplified BSM models and SMEFT (d ≤\leq 7) operators

Finding all possible UV resonances of effective operators is an important task in the bottom-up approach of effective field theory. We present all the tree-level UV resonances for the dimension-5, -6 and -7 operators in the Standard Model effective field theory (SMEFT), and then obtain the correspondence between the UV resonances and the effective operators from the relations among their Wilson coefficients, through the functional matching and operator reduction procedure. This provides a cross-dimension UV/IR dictionary for the SMEFT at tree-level, and the methods used here, especially the on-shell construction of general UV Lagrangian and the systematic reduction of operators, are extendable for UV resonances of $d \geq 8$ operators in SMEFT and other EFTs.Comment: 55 pages, 1 figure, 12 table

Effect of source tampering in the security of quantum cryptography

The security of source has become an increasingly important issue in quantum cryptography. Based on the framework of measurement-device-independent quantum-key-distribution (MDI-QKD), the source becomes the only region exploitable by a potential eavesdropper (Eve). Phase randomization is a cornerstone assumption in most discrete-variable (DV-) quantum communication protocols (e.g., QKD, quantum coin tossing, weak coherent state blind quantum computing, and so on), and the violation of such an assumption is thus fatal to the security of those protocols. In this paper, we show a simple quantum hacking strategy, with commercial and homemade pulsed lasers, by Eve that allows her to actively tamper with the source and violate such an assumption, without leaving a trace afterwards. Furthermore, our attack may also be valid for continuous-variable (CV-) QKD, which is another main class of QKD protocol, since, excepting the phase random assumption, other parameters (e.g., intensity) could also be changed, which directly determine the security of CV-QKD.Comment: 9 pages, 6 figure