Under the “dual carbon” goals, enhancing the energy supply for communication base stations is crucial for energy conservation and emission reduction. An individual base station with wind/photovoltaic (PV)/storage system exhibits limited scalability, resulting in poor economy and reliability. To address this, a collaborative power supply scheme for communication base station group is proposed. This paper establishes a capacity optimization configuration model for such integrated system and introduces a hybrid solution methodology combining random scenario analysis, Nondominated Sorting Genetic Algorithm II (NSGA-II), and Generalized Power Mean (GPM). Typical scenarios are solved using NSGA-II to generate a candidate solution set, which is then refined under operational constraints. The GPM method is applied to determine the final configuration by accounting for attribute correlations. A case study on a Chinese base station group, considering uncertainties in renewable generation, demonstrates the feasibility and effectiveness of the proposed approach.

Let R be a local Artin ring with residue field k of positive characteristic. We prove that every finite flat group scheme over R whose special fiber belongs to a certain explicit class of non-commutative k -group schemes is killed by its order. This is achieved via a classification result which relies on the study of the infinitesimal deformation theory for such non-commutative k -group schemes. The main result answers positively in a new case a question of Grothendieck in SGA 3 on whether all finite flat group schemes are killed by their order, and improves the currently best known result due to Schoof.

Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theory that can yields results in positive characteristic, and for group schemes that are not of finite type. The relation between loop and so-called toral torsors, is one of the central questions in the area. The present paper addresses this question in full generality.

The British Cabinet Mission Plan of 1946 represents the pivotal failure of late colonial constitutionalism in India. Designed as a final, comprehensive blueprint for an undivided federal India, the Plan's complex and ambiguous three-tiered structure-comprising a weak Union, compulsory provincial Groupings, and autonomous Provinces-was intended to reconcile the centralising aspirations of the Indian National Congress with the secessionist demands of the All-India Muslim League. Far from achieving reconciliation, the Mission exposed the profound, structural incompatibility between competing nationalist visions and the debilitating fatigue of the imperial state. The Plan's procedural vagueness, particularly concerning the mandatory nature of the grouping scheme, allowed both major parties to adopt strategically rigid interpretations, leading to an irreparable breakdown of political trust. This constitutional rupture transitioned the debate from an abstract legal arrangement to a communal and territorial emergency, effectively validating the logic of separation as the only administratively viable solution for the retreating colonial power. The Plan's failure thus operated as the decisive constitutional prelude, transforming ideological conflict into the violent, geographically defined tragedy of Partition.

Abstract In this note I give a conceptual proof of the fact that the mod 2 dual Steenrod algebra corepresents the group scheme of strict automorphisms of the formal additive group over $${\mathbb {F}}_2$$ F 2 . Contrary to existing proofs, it does not use the $$E_\infty $$ E ∞ -structure of $$H{\mathbb {F}}_2$$ H F 2 (Steenrod operations), nor does it proceed by producing a generators-and-relations presentation by some explicit calculation. Instead it relies on universal properties of bordism spectra, thus giving a stronger conceptual foundation for what is arguably the first instance of the well-studied deep connection between the algebraic geometry of formal groups and the stable homotopy category.

Abstract We compute the connected components of arbitrary parahoric level affine Deligne–Lusztig varieties and local Shimura varieties, thus resolving a folklore conjecture raised in (He in Some results on affine Deligne–Lusztig varieties. YouTube video, 2018; Zhou in Duke Math. J. 169(15):2937–3031, 2020) in full generality (even for non-quasisplit groups). We achieve this by relating them to the connected components of infinite level moduli spaces of $p$ p -adic shtukas, where we use v-sheaf-theoretic techniques such as the specialization map of kimberlites . Along the way, we give a $p$ p -adic Hodge-theoretic characterization of HN-irreducibility. As applications, we obtain many results on the geometry of integral models of Shimura varieties of Hodge type at arbitrary stabilizer-parahoric levels. In particular, we deduce new CM lifting results on integral models of Shimura varieties for quasisplit groups at parahoric levels that arise as stabilizer Bruhat–Tits group schemes.

Abstract This work concerns representations of a finite flat group scheme G defined over a noetherian commutative ring R . The focus is on lattices, namely, finitely generated G -modules that are projective as R -modules, and on the full subcategory of all G -modules projective over R generated by the lattices. The stable category of such G -modules is a rigidly-compactly generated, tensor triangulated category. The main result is that this stable category is stratified and costratified by the natural action of the cohomology ring of G . Applications include formulas for computing the support and cosupport of tensor products and the module of homomorphisms, and a classification of the thick ideals in the stable category of lattices.

BackgroundGender identity (GI) is the unified and persistent self-perception on the male-female spectrum, and its acquisition is a multifactorial process. GI is generally consolidated around ages 3–4 years. The gender identity questionnaire for children (GIQC) aims to assess GI in both clinical and non-clinical populations. The aim of the research is to evaluate GI in relation to social and biological factors.MethodsSingle-center, prospective birth-cohort study enrolling those born at term, appropriate for gestational age. The GIQC was administered to the parents at age 3. The scoring was performed through the original coding scheme and the new coding scheme for the non-clinical group based on three scales: female typical behavior (FTB), male typical behavior (MTB), and cross-gender (CG). Anthropometrics, anogenital distances, and urinary hormone assessment were performed at birth, 3, 6 and 36 months.Results86 children (males 53) participated. FTB, MTB, and CG scores differed significantly according to sex: boys (3.28 ± 0.59) scored higher than girls (2.45 ± 0.44) on MTB, while girls (3.41 ± 0.75) scored higher than boys (1.92 ± 0.61) on FTB. Girls (4.14 ± 0.64) scored higher than boys (3.66 ± 0.88) on the CG scale. Within the whole sample, the FTB scale showed a moderate negative correlation with MTB (r: −0.464, P < 0.01) and a positive one with CG (r: 0.377, P < 0.001) in the female population. Correlations exist between MTB and ano-scrotal distance (AGD-AS) in males, and between MTB and ano-clitoral distance (AGD-AC) in females.ConclusionOur findings confirm that by age 3, most children express differentiated sex-typed behavior according to the sex assigned at birth. In addition, androgenization appears to play a role in GI development in males.

The tame fundamental group scheme for an algebraic variety is the maximal linearly reductive quotient of Nori’s fundamental group scheme. In this paper, we study the tame fundamental group schemes of smooth curves defined over algebraically closed fields of positive characteristic and develop the theory of cospecialization maps for them. As a result, we see that the tame fundamental group schemes heavily depend on the curves. We also see that numerical invariants of curves can be reconstructed from the tame fundamental group schemes.

Abstract We give a construction of integral local Shimura varieties which are formal schemes that generalise the well-known integral models of the Drinfeld p-adic upper half spaces. The construction applies to all classical groups, at least for odd p. These formal schemes also generalise the formal schemes defined by Rapoport-Zink via moduli of p-divisible groups, and are characterised purely in group-theoretic terms. More precisely, for a local p-adic Shimura datum $(G, b, \mu)$ and a quasi-parahoric group scheme ${\mathcal {G}} $ for G, Scholze has defined a functor on perfectoid spaces which parametrises p-adic shtukas. He conjectured that this functor is representable by a normal formal scheme which is locally formally of finite type and flat over $O_{\breve E}$ . Scholze-Weinstein proved this conjecture when $(G, b, \mu)$ is of (P)EL type by using Rapoport-Zink formal schemes. We prove this conjecture for any $(G, \mu)$ of abelian type when $p\neq 2$ , and when $p=2$ and G is of type A or C. We also relate the generic fibre of this formal scheme to the local Shimura variety, a rigid-analytic space attached by Scholze to $(G, b, \mu , {\mathcal {G}})$ .

The present paper is dedicated to the popular life of the Armenian-Americans, their demeanor, their way of living and speaking in that important period, rich in significant events. This work is the first attempt to present the oral tradition of the Armenians living in the USA, which, regrettably, has never been written down, nor subjected to a scientific study before. Whereas, as a reflector of popular life, it includes answers to a great number of questions. The comparative analysis of the popular materials and the sex-age groups of the Armenian-Americans narrators, studied by the method of quantitative analysis, shows the correlation of the numerical scheme of the sex-age groups of the 206 Armenian-American narrators and of the 1,165 units of materials they have com municated us. We have elucidated the quantitative and qualitative changes of the traditional folklore, as well as the level of Armenian-preservation of the 5 genera tions in the course of a 100 years. During our five research trips to the USA (in 1979, 1990, 2001, 2004, 2008), we have, though intermittently, writing down, audio- and video-recording word for word, fragment for fragment, assembled the unique primary source relics of the Armenian popular oral tradition of the Armenian-Americans. That is the reason, why a particular importance was attached to those diverse historico-cognitive popular and cultural national values communicated by the representatives of the various generations of the Armenian community in the USA with the purpose of saving them from total loss and bequeathing them to the coming generations.

A Dynamic Evolution Value Assessment Scheme for Maritime Target Groups Based on Attention Mechanism and Hybrid Quantification Methods

Abstract While the splinter property is a local property for Noetherian schemes in characteristic zero, Bhatt observed that it imposes strong conditions on the global geometry of proper schemes in positive characteristic. We show that if a proper scheme over a field of positive characteristic is a splinter, then its Nori fundamental group scheme is trivial and its Kodaira dimension is negative. In another direction, Bhatt also showed that any splinter in positive characteristic is a derived splinter. We ask whether the splinter property is a derived invariant for projective varieties in positive characteristic and give a positive answer for normal Gorenstein projective varieties with big anticanonical divisor. We also show that global F -regularity is a derived invariant for normal Gorenstein projective varieties in positive characteristic.

Automorphism group schemes of special simple Jordan pairs of types I and IV

Context Large predatory sharks such as the white shark (WS) and shortfin mako (SMK) have been historically depleted to Critically Endangered levels in the Mediterranean Sea. Despite their low abundance, the Tunisian Plateau seemingly plays a crucial ecological role as a potential nursery and feeding ground, supporting the early life stages of these species. Aims Here we investigated the trophic ecology of WS and SMK, which co-exist in the Tunisian Plateau, focusing on juveniles and young-of-the-year (YOY). Methods We conducted stable isotope analysis of carbon (δ13C) and nitrogen (δ15N) from muscle samples to assess the trophic niche breadth and overlap between the two species. We estimated the possible prey contribution with Bayesian mixing models under two prey-grouping schemes, namely, functional prey categories (cephalopods, small pelagics, large pelagics, demersal fishes, dolphins) and habitat-based categories (coastal-pelagic, oceanic-pelagic, coastal-demersal, bathyal-demersal). Key results White sharks had significantly higher δ15N values than did shortfin makos, but no differences in age classes or sexes were detected, and no inter- or intraspecific variation in δ13C values were observed. Corrected standard ellipse areas were similar, with only ~12% core-area overlap between species, providing evidence for niche partitioning. The mixing model results were consistent across prey grouping schemes; WS seemingly display a generalist diet both in functional preys and foraging habitat, whereas SMK rely more on small pelagic fishes largely derived from coastal-pelagic habitats. Conclusions Trophic segregation between WS and SMK supports their co-existence on the Tunisian Plateau. Such differential resource use is likely to minimize interspecific competition and promote stable sympatry in this productive area. Implications Our results constitute the first isotopic and mixing-model-based dietary assessment of early life stage WS and SMK in the central Mediterranean. Their sightings may reflect both a higher population abundance in the region and intense fishing pressure. Given their trophic roles and the potential ecological consequences of their decline, incorporating trophic information with complementary methods (e.g. telemetry) could be useful to track feeding-ground utilization. Such integrated approach could inform timing and placement of mitigation measures (e.g. gear modifications) tailored to each species’ trophic habits, helping sustain their survival in the Mediterranean Sea.

Single and group sampling plans are conventional methods for assessing the quality of submitted lots of products. The group scheme is considered as more efficient than the single sampling plan with respect to cost and time to reach the final decision about the submitted lot. In this paper, a group sampling plan for the lot acceptance is developed for the time-truncated life test when the lifetime of a product follows the Weibull distribution. The test plans are constructed by minimizing and limiting a weighted-average of the producer and consumer risks. Integer nonlinear programing is used to determine the optimal number of groups and the acceptance number. Several tables and figures are constructed to analyze the behavior of the proposed test plans. A comparison of the suggested GASP and the traditional optimal two-point plan shows that the proposed optimal plans outperform the optimal two-point plan in terms of sample size. A real data analysis is presented for illustration of the results. The results derived for Weibull distribution are also valid for any other lifetime model.

For each integer n > 0 , we construct a smooth group scheme R n → S n of finite type, where S n is a scheme of finite type over Z , that parameterizes all connected reductive groups of rank at most n. We also construct an analogous family for quasi-split reductive groups. These results generalize earlier work over finite fields and provide a framework for studying invariants of reductive groups over arbitrary fields. In particular, they allow one to reduce questions about arbitrary reductive groups of bounded rank to questions about a single group scheme defined over a finite type scheme over Z .

BackgroundDiagnosis-related group (DRG) systems for healthcare reimbursement were recently introduced among hospitals in China, raising concerns about cost-shifting, where hospitals may increase charges for self-financing patients to offset reimbursement cuts by DRG. In 2018, both Nanchang and Ganzhou Cities in Jiangxi Province installed DRG information systems, but only Nanchang fully implemented the DRG system during the 2019–2020 pilot period.Materials and methodsDrawing from a healthcare administrative dataset of 14,310 patients' records, this study investigates the hospitalization costs associated with Intraocular Lens (IOL) implantation procedures in Jiangxi Province, China, from 2017 to 2020. By applying the quantile difference-in-differences (DID) and difference-in-difference-in-difference (DDD) methodologies, the research examines the impacts of DRG implementation on hospitalization costs, with a particular focus on self-financing patients.ResultsUpon the implementation of DRG in hospitals in Nanchang, the IOL cost ratio for patients in Nanchang was lower on average by 0.047 (p < 0.001), with the largest reduction observed at higher quantiles (e.g., Q75: −0.105, Q90: −0.091) (p < 0.001). The DDD model revealed a decrease of 0.226 in the IOL cost ratio for self-financing patients in DRG hospitals post-implementation. These results remained robust across various healthcare cost ratios.ConclusionThe study indicates that implementing the DRG system in Chinese hospitals effectively constrained healthcare costs without causing unintended cost-shifting among self-financing patients. The system's heightened impacts on higher quantiles indicate its efficacy in addressing high-cost outliers. These outcomes are likely attributed to the centralized medical procurement and healthcare information technology integrated into the Chinese healthcare system.

Abstract Let S be a fine and saturated (fs) log scheme, and let F be a group scheme over the underlying scheme of S which is étale locally representable by (1) a finite dimensional $\mathbb{Q}$ -vector space, or (2) a finite rank free abelian group, or (3) a finite abelian group. We give a full description of all the higher direct images of F from the Kummer log flat site to the classical flat site. In particular, we show that: in case (1) the higher direct images of F vanish; and in case (2) the first higher direct image of F vanishes and the nth ( $n\gt 1$ ) higher direct image of F is isomorphic to the $(n-1)$ -th higher direct image of $F\otimes_{{\mathbb Z}}{\mathbb Q}/{\mathbb Z}$ . In the end, we make some computations when the base is a standard henselian log trait or a Dedekind scheme endowed with the log structure associated to a finite set of closed points.

We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular, in the context of quantum chemistry, it is crucial to have energy estimates with error bounds, as captured by guarantees on the problem's sampling complexity. In particular, when limited to Pauli basis measurements, the smallest sampling complexity guarantee comes from a simple single-shot estimator via a straightforward argument based on Hoeffding's inequality. In this work, we construct an adaptive estimator using the state's actual variance. Technically, our estimation method is based on the empirical Bernstein stopping (EBS) algorithm and grouping schemes, and we provide a rigorous tail bound, which leverages the state's empirical variance. In a numerical benchmark of estimating ground-state energies of several Hamiltonians, we demonstrate that EBS consistently improves upon elementary readout guarantees up to 1 order of magnitude.