Let K be an infinite field. If $\alpha $ and $\beta $ are algebraic and separable elements over K, then by the primitive element theorem, it is well known that $\alpha +u\beta $ is a primitive element for $K(\alpha , \beta )$ for all but finitely many elements $u\in K$. If we let

$$ \begin{align*}\xi_K(\alpha, \beta) = \{u\in K : K(\alpha, \beta) \ne K(\alpha+u\beta)\}\end{align*} $$

be the exceptional set, then by the primitive element theorem, $|\xi _K(\alpha , \beta )| < \infty $. Dubickas [‘An effective version of the primitive element theorem’, Indian J. Pure Appl. Math. 53(3) (2022), 720–726] estimated the size of this set when $K = \mathbb {Q}$. We take K to be a finite extension over $\mathbb {Q}$ or $\mathbb {Q}_p$, the field of p-adic numbers for some prime p, and estimate the size of the exceptional set.

We show that Kim-forking satisfies existence in all NSOP1 theories.

This study presents a conceptual replication of Jacob et al.’s (2018) comparison of L2 early-stage processing of derived vs. inflected words. Previous studies on this issue focused predominantly on L2 learners from morphologically complex, alphabetic L1s, and generally showed L2 decompositional processing of derived but not inflected words. This replication study examined whether the previous claim for a qualitative difference in L2 early-stage processing of derived and inflected words could generalize to L2 English learners from a morphologically isolating, logographic L1, i.e., Chinese learners of L2 English. Results from a masked priming lexical decision task showed qualitatively the same magnitude of priming in the derivational, inflectional, and form control conditions for Chinese learners of English, suggesting reliance on surface form information in the early-stage processing of both derived and inflected words. Results of the current study add to the literature on L2 early-stage processing of derived vs. inflected words.

Iron deficiency anemia is a major health problem worldwide. Iron is an essential micronutrient in the human body; its demand increases with fetal growth and gestation. Although it has been reported that glucose metabolism is also affected by iron deficiency, only few studies have investigated the influence of iron deficiency during gestation and in offspring. In this study, glucose metabolism in newborns was investigated in terms of maternal iron deficiency prior to pregnancy in a rat model. Briefly, rats were divided into control (CL) and iron deficiency (ID) groups. The levels of serum glucose and insulin and the protein expression of liver GLUT2 in neonates born to dams in the ID group increased. In contrast, the mRNA and protein expression levels of GLUT2 and GLUT4 in the skeletal muscle tended to decrease. In addition, the expression of p-Akt (Thr308), which is involved in GLUT4 membrane translocation, decreased, suggesting that GLUT4 translocation to the plasma membrane may not have been sufficiently promoted. These results suggest that maternal iron deficiency may influence glucose metabolism in neonates and potentially increase the risk of developing metabolic abnormalities and lifestyle-related diseases later in life.

Few village-born social movements have influenced international relations as much as the campaign against Myitsone Dam in Burma (Myanmar). This village-born resistance led in 2011 to the suspension of a major Burmese and Chinese infrastructure project. This suspension became a symbol of democratization in Burma and a much-discussed setback of Chinese development-investment abroad. However, research literature on the Myitsone Dam has tended to conflate the local rural resistance with the broader ethnic Kachin and Burmese anti-dam movements. In contrast, this study focuses specifically on the local villages directly affected by the project, exploring their diverse stories and responses to the mega-project. Combining diverse published sources with ethnographic fieldwork and interviews done since 2010, it tells a story of repression, resistance, social divisions, and complex relations with outsiders. This is a two-part article series. This article here – Part 1 – examines what occurred before the mega-project’s suspension. It tells the Myitsone Dam’s rural story from its earliest days until the mega-project’s fall: from 2002 to 2011. This story begins with the unexpected arrival of Japanese visitors and traces the village struggles up to the project’s dramatic downfall.

Pipeline inspection robots play a crucial role in maintaining the integrity of pipeline systems across various industries. In this paper, a novel pipeline inspection robot is designed based on a four degrees-of-freedom (DOF) generalized parallel mechanism (GPM). First, a four DOF mechanism is introduced using numerical and graph synthesis. The design employs numerical and graph synthesis methods to achieve an ideal symmetric configuration, enhancing the robot’s adaptability and mobility. The coupling mid-platform, inspired by parallelogram mechanisms, enables synchronized contraction motion, allowing the robot to adjust to different pipe diameters. Then, the constraints of the pipeline inspection robot in the elbow are analyzed based on task requirements. Through kinematic and performance analyses using screw theory, the mechanism’s feasibility in practical applications is confirmed. Theoretical analysis, simulations, and experiments demonstrate the robot’s ability to achieve active steering in T-branches and elbows. Experimental validation in straight and bent pipes shows that the robot meets the expected speed targets and can successfully navigate complex pipeline environments. This research highlights the potential of GPMs in advancing the capabilities of pipeline inspection robots for real-world applications.

We derive the exact asymptotics of $\mathbb{P} {\{\sup\nolimits_{\boldsymbol{t}\in {\mathcal{A}}}X(\boldsymbol{t})>u \}} \textrm{ as}\ u\to\infty,$ for a centered Gaussian field $X({\boldsymbol{t}}),\ {\boldsymbol{t}}\in \mathcal{A}\subset\mathbb{R}^n$, $n>1$ with continuous sample paths almost surely, for which $\arg \max_{\boldsymbol{t}\in {\mathcal{A}}} {\mathrm{Var}}(X(\boldsymbol{t}))$ is a Jordan set with a finite and positive Lebesgue measure of dimension $k\le n$ and its dependence structure is not necessarily locally stationary. Our findings are applied to derive the asymptotics of tail probabilities related to performance tables and chi processes, particularly when the covariance structure is not locally stationary.

This work proposes an optimization approach for the time-consuming parts of Light Detection and Ranging (LiDAR) data processing and IMU-LiDAR data fusion in the LiDAR-inertial odometry (LIO) method. Two key novelties enable faster and more accurate navigation in complex, noisy environments. Firstly, to improve map update and point cloud registration efficiency, we employ a sparse voxel maps with a new update function to construct a local map around the mobile robot and utilize an improved Generalized Iterative Closest Point algorithm based on sparse voxels to achieve LiDAR point clouds association, thereby boosting both map updating and computational speed. Secondly, to enhance real-time accuracy, this paper analyzes the residuals and covariances of both IMU and LiDAR data in a tightly coupled manner, and achieves system state estimation by fusing sensor information through Gauss-Newton method, effectively mitigating localization deviations by appropriately weighting the LiDAR covariances. The performance of our method is evaluated against advanced LIO algorithms using eight open datasets and five self-collected campus datasets. Results show a 24.7–60.1% reduction in average processing time per point cloud frame, along with improved robustness and higher precision motion trajectory estimation in most cluttered and complex indoor and outdoor environments.

This article argues that contemporary Indian law is animated by two intertwined imaginings of law: as a rational, rule-bound process and as a power that makes decisions as a normless act of prerogative. Through ethnographic fieldwork in Delhi’s terrorism courts, the paper examines petitions written by individuals accused under anti-terror laws, revealing how these texts invoke the dual legal imaginaries. Petitions—ranging from formal legal documents to handwritten pleas—are analysed through the idea of epistolarity, to pay attention to both the form and content of these petitions. The article argues that these letters are affective and rhetorical performances that simultaneously invoke imaginings of the law as both rule and prerogative. In doing so, the subjectivity of the petitioners oscillates between rights-bearing citizens and humble supplicants praying for the law’s intervention.

This small project was initiated to create a broader understanding of the working properties of sarsen and its challenges. This notoriously durable coarse-grained sandstone is most familiarly associated with the Phase 3 monument at Stonehenge, Wiltshire, although its exploitation persisted into the twentieth century. Discussion has focused on the probable methods employed in prehistory to work the stone: splitting, flaking and pecking. These techniques have rarely been applied in practice, but have been considered broadly in this project. The preliminary results, obtained from a single block of saccharoidal sarsen, have reawakened understanding and appreciation of the potential provided by shock waves to split and shape this intractable silicate successfully and repeatedly using direct percussion, techniques that were familiar to Neolithic communities to work flint. The flaking properties of the stone are considered together with attributes of hammer mode in comparison with data from prehistoric stone assemblages at Stonehenge. The discussion questions to what extent flaking could be controlled repeatedly to form a major part of monolith production. Results derived from the laborious nature of pecking supplement previous attempts to recreate dressed surfaces at Stonehenge. Efficiency was not improved by applying heat to the surface of the stone; indeed, it confirmed that uncontrolled, excessive heat shatters the structure of sarsen, rendering it unworkable.