Volume 50

Denote Mm×n(k) to be the set of all m × n matrices over k, and PMm×n(k) to be its affine space. Let Dm,n,r ⊂ PMm×n(k) be the subvariety consisting of the projective classes of all m × n matrices with rank less than or equal to r. We study the minimal integer k > 0 such that for any linear subspace L of dimension k in PMm×n(k), Dm,n,r ∩ L ̸= ∅. We get some partial results about this problem. Specially, when m = n = r + 1, we solve this problem for k = R, C and Q.

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This study investigates the origin of tidal forces within the Earth-Moon system, formulating the corresponding dynamic equations and solving them using Python for computational modeling. This allows for the prediction of tidal intensity at specific locations and times. The methodologies and Python algorithms developed quantify the impact of Earth‘s tidal forces on the Moon, analyzing the deformation and thermal effects caused by tidal force variations across different distances. This framework also elucidates the mechanisms behind Io‘s volcanic activity. The computational approach, characterized by accuracy and precision, enhances the interpretability of the results through data visualization. This study lays a foundational basis for extending the analysis to other celestial bodies under diverse conditions, contributing to the broader field of celestial mechanics.

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This research is motivated by Atiyah, Hitchin, and Singer’s paper Self-duality in Four-Dimensional Riemannian Geometry , which introduced a relationship between self-dual Yang-Mills fields on smooth manifolds and holomorphic vector bundles on their twistor spaces. Here, self-duality is a specific structure in 4-dimensional manifolds and Yang-Mills fields are gauge fields that satisfy Yang-Mills equations in 4-dimensions and are corresponded to the holomorphic bundles on twistor spaces. In this paper, we extend the relationship from vector bundles to a generalization of the Yang-Mills fields. To achieve this purpose, we apply Atiyah, Hitchin, and Singer’s theorem to cohesive modules, which was originally introduced by Block in in studying coherent sheaves over complex manifolds and the relations between homomorphic torus and its dual non-commutative torus. We introduce the notion of cohesive self-dual Yang-Mills modules and show that the twistor correspondence actually induces the equivalence between the dg category of cohesive self-dual Yang Mills modules P_(A_SD ) and the dg category of holomorphic cohesive modules P_(A_Hol ) on the twistor spaces.

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Multipartite quantum-information transmission has been a key task for practice purposes and applications in the past decades. In this paper, we present a novel protocol for the multiqubit super dense coding, by using the Greenberger-Horne-Zeilinger (GHZ) states. Our protocol involves measurements doable in the current technique of labs, and thus is possibly realizable and may be extendable to more complicated cases for many systems. In quantum physics, the way the object is measured will affect the code, and the information won’t work like puzzles as the condition in general physics which means that, when the divided message is put together, the complete information will be obtained. It requires more complex work to get useful information, like the cooperation of code accepters. To compare with the way in general physics, it is more safe in quantum physics.

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In this study, we classified single-cell routine Pap smear images by applying deep learning algorithms such as AlexNet, VggNet, GoogleNet and MobileNet and compared their classification effects. The results show that the loss of all four models on both the training and test sets shows a trend of gradually decreasing and stabilising. Specifically, the loss of AlexNet gradually decreases from 0.637 to 0.212, VggNet from 0.777 to 0.278, GoogleNet from 1.77 to 0.31, and MobileNet from 0.809 to 0.267. At the same time, MobileNet exhibits the highest maximum and average accuracies which reached 93.9% and 88.3%, respectively, followed by GoogleNet model with 92.9% and 88.0%, AlexNet with 92% and 88.0%, and VggNet with 90.1% and 86.7%. The results show that MobileNet exhibits superior classification results in this task, which provides strong support for its potential application in the classification of single-cell routine Pap smear images. These findings are of great significance for further exploring the application of deep learning in the field of medical imaging and provide a useful reference for future related research.

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With information entropy gradually taking the lead in modern information theory development, it begins to hold greater influence over multiple research areas as well as technology innovation. This paper aims to clarify people’s confusion with the development of entropy theory and provide a brief overview of the origin of entropy theory, including the original Shannon’s proposal, variants such as relative entropy and conditional entropy, and entropy concepts proposed by other scientists, such as Rényi Tsallis entropy. The paper also includes the current application of entropy, studies hotspots, and predicts future entropy development trends. This research paper is able to add more coherence and consistency to information entropy’s development, helping more people to better understand the concept of entropy and its derivation. At the same time, with hotspots of entropy fields of study, this paper hopes to attract more people to devote themselves to studying entropy-related fields, and boost technological development.

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The evolution of white LEDs, both organic and inorganic, has marked a transformative era in lighting technology known as solid-state lighting. This revolution is driven by electroluminescence, where electron-hole pairs recombine to emit light. While OLEDs have achieved high internal quantum efficiency, limited out-coupling efficiency remains a challenge. Improving light out-coupling efficiency is crucial for enhancing LED performance. This paper employs the Transfer Matrix Method to analyze the optical properties of OLEDs and aims to enhance light coupling, efficiency, and overall impact of LED and OLED technologies.

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This research looks into the association between fishing and microplastic contamination across countries, with a particular focus on how the growth of microplastic levels can impact fishery production. Through the use of a mixed-effect model we were able to look through data from 100 nations during the period 1990-2021, where fishery yield data was extracted from The World Bank and microplastic concentration data was obtained from the National Centers for Environmental Information; population data served as a control variable in our analysis. We found that there is indeed a significant negative correlation between levels of microplastics and fishing yield: an increase by 1 piece of microplastic per cubic meter leads to decrease in fishing yield by anything between 65 and 100 metric tonnes (95% confidence interval). This relationship held true for about 93% of all coastal countries studied. To accommodate for differences amongst nations, we introduced random intercepts and slopes in our mixed-effect model which helped capture variations specific to each country while still identifying an overarching pattern. The research we are doing is on the connection between fish catches and microplastic pollution which takes place in the different countries of the world, where we focus more on how high microplastic levels influence fishery production. Having made use of a mixed-effect model, we have been able to look at data that represents 100 nations within the period of time between 1990 and 2021; The World Bank provided us with fishery yield data while microplastic concentration data came from the National Centers for Environmental Information. In addition to these variables, population data was used as a control variable. The summary of our analysis points towards a significant inverse relationship noted between microplastic levels and fishing yield: an increase by one piece of plastic results in a decline by somewhere between 65 to 100 metric tonnes (95% confidence interval). This generalization held true for about 93% coastal countries considered under this study. To capture specific variations among nations but also identify an overall trend line while dealing with inter-country variability, random intercepts and slope components were included as part of our mixed-effect model methodology.

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