Projective Line Research Articles

Q-opers,QQ-systems, and Bethe Ansatz II: Generalized minors

AbstractIn this paper, we describe a certain kind ofq-connections on a projective line, namelyZ-twisted(G,q){(G,q)}-opers with regular singularities using the language of generalized minors. In part one we explored the correspondence between theseq-connections and𝑄𝑄\mathit{QQ}-systems/Bethe Ansatz equations. Here we associate to aZ-twisted(G,q){(G,q)}-oper a class of meromorphic sections of aG-bundle, satisfying certain difference equations, which we refer to as(G,q){(G,q)}-Wronskians. Among other things, we show that the𝑄𝑄\mathit{QQ}-systems and their extensions emerge as the relations between generalized minors, thereby putting the Bethe Ansatz equations in the framework of cluster mutations known in the theory of double Bruhat cells.

An a priori bound for rational functions on the Berkovich projective line

We establish a local a priori bound on the dynamics of a rational function f of degree >1 on the Berkovich projective line over an algebraically closed field of arbitrary characteristic that is complete with respect to a non-trivial and non-archimedean absolute value, and deduce an equidistribution result for moving targets towards the equilibrium (or canonical) measure μ f of f, under the no potentially good reduction condition. This partly answers a question posed by Favre and Rivera-Letelier. We also obtain an equidistribution on the averaged value distribution of the derivatives of the iterated polynomials.

Producing Knowledge in Struggle

This essay discusses the cultural work and practice behind this special issue, and the processes and specific institutionalities that had to be navigated in order to bring this project forward. We address the relative absence of spaces for discussion and consideration of Afro-Indigenous histories, cultures, intersections, and provide a preview of the contributors to this Part II of the Dividing Lines project.

Risk analysis and countermeasures of TBM tunnelling over the operational tunnel

To study the risk and control countermeasures of the TBM tunnel construction adjacent to the operational railway tunnel, based on the TBM tunnel project of Chongqing Rail Transit Line 5, this paper first evaluates the quality health degree of the operational tunnel lining (OTL) structure according to the on-site structural inspection. Then, the displacement, internal force, and proximity influence scope influenced by the metro TBM tunnel construction are studied using numerical simulation. Finally, the corresponding control countermeasures are proposed. The results show that: (1) The adjacent construction of the upper TBM tunnel will lead to the uplift deformation trend of the lower operational tunnel, and the uplift deformation of the vault is greater than that of the ballast bed. The influence scope is roughly a parallelogram, with the long axis parallel to the operational tunnel and the short axis parallel to the new TBM subway tunnel. (2) TBM tunnelling over the operational tunnel will cause the transformation of the mechanical mode of the OTL structure from the small eccentric compression mode to the large eccentric compression mode. The OTL structure between the left and right lines of TBM is unfavorable. (3) The longitudinal curve of the bending moment and axial force of the OTL fluctuates greatly within the influence range. The bending moment and axial force are reduced in operational tunnel construction joints. Based on field evaluation and numerical analysis, this paper puts forward some risk control countermeasures, such as TBM tunnelling parameters control, pea-gravel backfilling, backfill grouting, and bottom grouting, which can effectively solve the risk of the operational tunnel structure in the adjacent construction. This study has important reference value for risk control and safety assessment of tunnel in complex adjacent tunnel construction.

Frobenius-Perron theory for projective schemes

The Frobenius-Perron theory of an endofunctor of a k \Bbbk -linear category (recently introduced in Chen et al. [Algebra Number Theory 13 (2019), pp. 2005–2055]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories of commutative and noncommutative projective schemes. In particular, we calculate the Frobenius-Perron dimension for domestic and tubular weighted projective lines, define Frobenius-Perron generalizations of Calabi-Yau and Kodaira dimensions, and provide examples. We apply this theory to the derived categories associated to certain Artin-Schelter regular and finite-dimensional algebras.

Homogeneous non-split superstrings of odd dimension 4

Let $\mathbf L_k$ be the holomorphic line bundle of degree $k \in \mathbb Z$ on the projective line. Here, the tuples $(k_1 k_2 k_3 k_4)$ for which there does not exists homogeneous non-split supermanifolds $CP^{1|4}_{k_1 k_2 k_3 k_4}$ associated with the vector bundle $\mathbf L_{−k_1} \oplus \mathbf L _{−k_2} \oplus \mathbf L_{−k_3} \oplus \mathbf L_{−k_4}$ are classified. \\For many types of the remaining tuples, there are listed cocycles that determine homogeneous non-split supermanifolds. \\Proofs follow the lines indicated in the paper Bunegina V.A., Onishchik A.L., Homogeneous supermanifolds associated with the complex projective line.neous supermanifolds associated with the complex projective line. J. Math. Sci. V. 82 (1996)3503­--3527.

Generalized Tevelev degrees of [formula omitted

Let (C,p1,…,pn) be a general curve. We consider the problem of enumerating covers of the projective line by C subject to incidence conditions at the marked points. These counts have been obtained by the first named author with Pandharipande and Schmitt via intersection theory on Hurwitz spaces and by the second named author with Farkas via limit linear series. In this paper, we build on these two approaches to generalize these counts to the situation where the covers are constrained to have arbitrary ramification profiles: that is, additional ramification conditions are imposed at the marked points, and some collections of marked points are constrained to have equal image.

Prediction of rock mass class ahead of TBM excavation face by ML and DL algorithms with Bayesian TPE optimization and SHAP feature analysis

In this paper, field construction data from the Singapore Metro Line project were used to study the mapping relationship and establish the prediction model between TBM operation data and the ground condition ahead of the excavation face. The study presents a multi-classifier competition mechanism to construct ten separate classifiers, including logistic regression, support vector machine, random forest, extremely randomized trees, adaptive boosting machine, extreme gradient boosting (Xgboost), light gradient boosting (LightGBM), categorical boosting, long short-term memory and convolutional neural network. The acquired data were used to select 28 key TBM operating parameters by a correlation-based feature selection method, and the selected parameters in the stabilization phase after removing the outliers were calculated as the input to the classifier, and a relatively balanced training set was obtained by the synthetic minority oversampling technique. The hyperparameters of each classifier were optimized using tree Parzen estimator Bayesian optimization. The prediction results show that LightGBM presents the best results among ten different machine and deep learning algorithms with an accuracy of 96.22%, precision of 96.94%, recall of 97.33% and F1-score of 97.33%. In addition, the effect of the input parameters of the LightGBM model on the prediction accuracy of the model was analyzed using Shapley additive explanations, and the effect of sample imbalance on the prediction performance was discussed.

Research on Construction Technology of Deep Foundation Pit of High Voltage Transmission Line in Plateau Area

With the further expansion of China power grid, it is the current and future trend of power system development to set up high-voltage or even ultra-high-voltage transmission lines. Because the construction environment of high-voltage transmission lines is very complex and changeable, how to ensure the construction quality and progress of transmission lines according to the construction drawings provided by the design unit is the key to the construction of transmission lines. The quality level of deep foundation pit excavation is a representative factor that profoundly affects the construction quality level of high-voltage transmission line projects in plateau areas. Only by managing the construction quality of all sub-projects in the power system can the stability of power operation be effectively guaranteed. This paper expounds the key points of deep foundation pit excavation construction technology, in order to analyze the deep foundation construction technology of high-voltage transmission lines in plateau area, and provide theoretical support for the deep foundation pit construction of high-voltage transmission lines in plateau area.

Simple fibrations in -surfaces

Abstract We introduce the notion of a simple fibration in $(1,2)$ -surfaces – that is, a hypersurface inside a certain weighted projective space bundle over a curve such that the general fibre is a minimal surface of general type with $p_g=2$ and $K^2=1$ . We prove that almost all Gorenstein simple fibrations over the projective line with at worst canonical singularities are canonical threefolds ‘on the Noether line’ with $K^3=\frac 43 p_g-\frac {10}3$ , and we classify them. Among them, we find all the canonical threefolds on the Noether line that have previously appeared in the literature. The Gorenstein simple fibrations over ${\mathbb {P}}^1$ are Cartier divisors in a toric $4$ -fold. This allows to us to show, among other things, that the previously known canonical threefolds on the Noether line form an open subset of the moduli space of canonical threefolds, that the general element of this component is a Mori Dream Space and that there is a second component when the geometric genus is congruent to $6$ modulo $8$ ; the threefolds in this component are new.

Visual Odometry With Point and Line Features Based on Underground Tunnel Environment

Compared with the interior environment, there exists a lot of noise and dust in an underground tunnel, and the light is unstable, which is difficult to track by the direct method. Moreover, errors in line segment projection and line feature drift under the influence of light can lead to significant deviations in the odometry. Consequently, to improve the accuracy and robustness of visual odometry, a point-line feature stereo visual odometry system is proposed in this paper. The system combines ORB features and LSD line features; using the angle relationship of line projection, we propose a new method for calculating the reprojection error of line features, reconstruct the reprojection model based on line features, and construct a new reprojection error model based on point-line features, which adds an angle constraint to the reprojection of line features and solves the instability caused by line projection error. It is shown in our experiments on the KITTI, New College dataset, that the translation error of our system is reduced by about 40% on average compared to PLVO, with a reduction in relative positioning error. Experiments in the hallway and underground tunnel environments have shown that the maximum positioning error of our system has been reduced by 75% in hallways and by 56.7% in an underground tunnel. Therefore, our algorithm effectively improves the localization accuracy and is more advantageous in low-texture environments.

Education, training and mobility, knowledge management: towards a common effort to ensure a future workforce in Europe and abroad

Continuous and future-oriented education and training as well as knowledge management for young talents are required for the safe and reliable operation of nuclear reactors and nuclear facilities in Europe. A dedicated line of collaborative projects addresses the specific needs, such as lack of personnel (project ENEN+: “attract, retain and develop new nuclear talents beyond academic curricula”). State-of-the-art approaches and in-depth knowledge are provided when it comes to reactor physics (project GRE@T-PIONEeR: “graduate education alliance for teaching the physics and safety of nuclear reactors”) or nuclear radiochemistry (project A-CINCH: “augmented cooperation in education and training in nuclear and radiochemistry”). A highly skilled nuclear engineer must undergo experimental work to better observe theoretical principles at work. Following the ENEEP (European nuclear experimental educational platform) initiative, a network of research reactors and special laboratories is made available for performing such activities. Another issue found is that the results of Euratom-funded research activities are spread across multiple platforms and websites making it difficult to find relevant information within a reasonable timeframe. Such a situation requires the application of knowledge management actions. The PIKNUS project aims to define a concept of a knowledge management method and tool to improve the sharing and availability of Euratom research results. All projects successfully demonstrate that European collaboration could address certain needs to attract, develop and retain young talents in future-oriented nuclear fields.

P – T – Х диаграмма состояния системы Co – Mg

Up to now Co – Mg alloys have not been studied in detail. The information available in the literature refers to the study of changes in the Co – Mg system in the composition-temperature coordinates. However, this does not take into account the significant difference in vapor pressure values of Mg and Co in the alloy, which significantly reduces the accuracy of the results obtained. It is proposed to analyze the Co – Mg system in the coordinates composition-temperature-pressure. The following results have been obtained and presented in the article: a detailed description of the Mg – Co system diagram in the pressure-temperature coordinates, the projections of the three-phase equilibrium lines, some isobaric and isothermal sections of the p – T – X state diagram of Mg – Co system, Mg – Co state diagram in coordinates temperature – partial pressure Mg. The results obtained in this work can be successfully used in the development of ternary and more alloys containing cobalt and magnesium.

Digital Interactive Design and Robot-Assisted Preparation Experiment of Tooth Veneer Preparation: An in Vitro Proof-of-Concept

In the fixed prosthesis process dental prosthesis treatment, the dentist needs to conceive the morphology of the tooth preparation and make numerous micro-adjustments by manual operation. This study aims to establish a digital design system for accurate designing of veneer preparation and study the trajectory planning of the robot-assisted preparation. According to the standard operation requirements, the projection line segmentation method based on point drawing is proposed for interactive selection to ensure the margin smoothness of the preparation area. The preparation depth is parameterized, and the foldback point correction method based on secondary segmentation is used for repairing the offset preparation area to ensure surface smoothness. The fenestration preparation model was obtained in the digital interactive design software. The model is divided into two feature areas which are interpolated by the B-spline curve and NURBS surface, respectively. The isoparametric curve method is used to plan the preparation trajectory. The experimental and theoretical values of the target feature points from the X, Y and Z coordinate directions were also calculated and analyzed. The experiment is carried out by the physical prototype of the tooth preparation robot. The maximum error of the feature points on the preparation are 0.180 mm, 0.104 mm and 0.142 mm in X, Y and Z directions, respectively. The confidence interval of the system error is stable within 0.30 mm. The error of the feature points verifies the feasibility of the digital interactive design system and the correctness of the trajectory planning of tooth veneer preparation. The system could have the potential to assist dentists in the precise design of the veneer preparation, improve the processing efficiency and ensure the effect of tooth veneer prosthesis.

Телефонизация как начальный шаг Департамента уделов по развитию имений Массандра и Ай-Даниль

The article, based on archival materials, refers to one of the episodes of the initial period of the existence of Massandra and Ai-Danil as the possessions of the Department of Provinces. The author notes that the mentioned estates, acquired in 1889 from the heirs of His Serene Highness Prince S.M.Vorontsov, were considered as an opportunity to develop and increase the wine-making and wine-trading activities of the Department. The article notes that one of the measures in this direction was the telephone line installation to provide communication both within the estates between the administration, the vineyards, the wine cellar and the winemaker's apartment, and between Massandra and the wine warehouse in Yalta. The author notes that the initiative to install telephones came from officials of the local province administration, who secured the consent of the chief of the Yalta Post and Telegraph Office to carry out all the necessary work and take on a new communication line. The chief of the Department of Provinces, for his part, supported this idea, in principle coordinating its implementation with the Main Directorate of Posts and Telegraphs. However, upon receipt of a detailed project and an estimate of its cost, the Department of Provinces was at a loss, since the calculated amount was one and a half times higher than that indicated in the preliminary justification. This required additional verification of the correctness and validity of the calculations on the spot. In the end, the telephone line project was nevertheless completed by the autumn of 1891 for an amount that was only slightly higher than the originally announced figures.

Modelling shared logistics resources in loosely coupled software architectures

This research is part of the City Line project, a collaborative initiative within Belgium aiming to promote collaboration between various logistics operators, from cargo bikes to trucks, while ensuring low emissions for last-mile deliveries in cities. The objective is to integrate all relevant information regarding shared assets into a digital collaborative logistics platform managed by a third-party logistics provider acting as a central decision-maker coordinating transportation activities. First, we describe how the digital platform receives the services offered by the logistics operators and the delivery requests. Then, we propose an incremental method to assign the transport demand to the best route according to environmental and economic factors.

ТРАНСФОРМАЦІЇ МІСЬКОГО ПРОСТОРУ ЛЬВОВА В КОНТЕКСТІ ФОРМУВАННЯ ЗЕЛЕНИХ ЗВ’ЯЗКІВ НА МІКРОРАЙОНІ РЯСНЕ

Understanding the many interrelationships between humans and natural environment is increasingly important in light of significant socio-ecological challenges such as large-scale biodiversity loss and global climate change. How people conceptualize, evaluate, and embody human-nature interactions is largely the result of diverse disciplinary, theoretical, sociocultural, and political contexts. Over the past five years, the city of Lviv has become a platform for implementing the modern practices in the field of spatial planning and urban development. The introduction of separate public transport lanes, convenient and inclusive public spaces and comfortable green zones steadily increases the city's ranking position. At the same time, not all districts and neighbourhoods of the city have developed plans and projects that could locally improve the standard of living and comfort of city residents. The article presents the development of the Green Line project for one of the most remote micro-districts in the city of Lviv – Riasne. Taking into account global trends and international practices, it is concluded that green connections, which can connect several important areas within the neighbourhood and provide fast and comfortable routes for pedestrians and cyclists, will be a significant addition to the neighborhood's architectural landscape. The implementation of the Green Line project will help address several issues, including the division of the micro-district into Riasne-1 and Riasne-2, a lack of recreational areas, green public spaces, and underdeveloped pedestrian and bicycle accessibility. An analysis of the historical context, socio-economic development, and current transformations has allowed the development of a project that can be used in the future to create new green areas and connections in this research neighbourhood. An essential aspect of this article is the dissemination of practices for transforming urban spaces and green areas in remote areas and micro-districts of the city, which require fundamental changes in spatial planning and the creation of new spaces for the leisure and recreation of local residents.

Integrated In Silico Analysis of Proteogenomic and Drug Targets for Pancreatic Cancer Survival.

Pancreatic cancer remains a major health concern, being among the deadliest forms of cancer with over 80% of the patients presenting with metastatic disease. According to the American Cancer Society, for all stages of pancreatic cancer combined, the 5-year survival rate is less than 10%. Genetic research on pancreatic cancer has generally been focused on familial pancreatic cancer, which is only 10% of all pancreatic cancer patients. This study focuses on finding genes that impact the survival of pancreatic cancer patients which can be used as biomarkers and potential targets to develop personalized treatment options. We used cBioPortal platform using NCI-initiated The Cancer Genome Atlas (TCGA) dataset to find genes that were altered differently in different ethnic groups which can serve as potential biomarkers and analyzed the genes' impact on patient survival. MD Anderson Cell Lines Project (MCLP) and genecards.org were also utilized to identify potential drug candidates that can target the proteins encoded by the genes. The results showed that there are unique genes that are associated with each race category which may influence the survival outcomes of patients, and their potential drug candidates were identified.

Research on the Protection and Utilisation Design Strategy of Hangzhou Traditional Villages on “Three Rivers and Two Banks” from the Perspective of Clusters

At the beginning of 2023, Hangzhou launched the "Poetry Road Culture - Three Rivers and Two Banks" Water Golden Tourism Line Project, aimed at revitalizing the countryside in the western part of Hangzhou and creating a model area of common wealth. This article integrates natural and cultural resources on "Three Rivers and Two Banks" in Hangzhou, using kernel density analysis, proximity analysis, and weighted spatial superposition analysis of ArcGIS 10.8 software to classify the traditional villages on "Three Rivers and Two Banks" in Hangzhou into high-resource characteristic villages, intermediate resource characteristic villages, and general resource characteristic villages based on the distribution of resource characteristics. Finally, the traditional villages are examined within a systematic geographical framework to explore the establishment of traditional village cluster protection and development modes and methods. Strategies such as historical excavation, cluster construction, culture and tourism integration are proposed to achieve the goal of coordinating the rational allocation of regional resources, facilitating facility sharing, enhancing the endogenous dynamics of traditional villages, and forming distinctive village brand and cultural groups. This research aims to provide valuable insights for the protection of traditional village clusters.

A REBIRTH OF THE EUROPEAN POLITICAL COMMUNITY?

The article addresses a new birth of the European Political Community (EPC) concept, which was proposed by the President of France in May 2022, and its implementation. The author traces evolution of the idea since the birth of the European Communities and F. Mitterand’s «European Confederation» and notes the modern interest for the possibilities of creating an organization with a greater political and geographical scope than the European Union. The article examines the proposals of E. Macron, and that of Ch. Michel, the President of the European Council, who took up the initiative, on the EPC participants, the new Community’s goals and objectives, its institutional architecture and the difference from the EU neighborhood policy. Particular attention is paid to the problem of possible duplication by the EPC of the other organizations’ functions – the Council of Europe, OSCE, NATO. The author dwells on the inaugural meeting of the EPC participants – the summit in Prague on October 6, 2022. It is noted that at the summit, some practical actions were taken in the direction of future «project lines» in the field of energy, mobility, protection of critical infrastructures and repelling cyber attacks, as well as bilateral meetings were held. However, the absence of a joint declaration as the main result of the meeting indicates the vulnerability of the new organization to the disagreements of its members.