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14 pages, 6425 KB  
Article
Improving Entity Understanding for Vision-Language Pre-Training via Active Learning
by Qunbo Wang, Sen Zhang, Boxuan Shao, Xize Guo, Jiayong An, Chao Fan, Yuanjun Jing, Junxian Li and Wenjun Wu
Big Data Cogn. Comput. 2026, 10(6), 198; https://doi.org/10.3390/bdcc10060198 (registering DOI) - 22 Jun 2026
Abstract
Although many researchers use pre-trained models to better solve downstream tasks, further exploration of more effective pre-training methods remains necessary, especially for multi-modal pre-training where high-quality training data is more difficult to obtain. This work aims to improve the knowledge-learning performance in multi-modal [...] Read more.
Although many researchers use pre-trained models to better solve downstream tasks, further exploration of more effective pre-training methods remains necessary, especially for multi-modal pre-training where high-quality training data is more difficult to obtain. This work aims to improve the knowledge-learning performance in multi-modal pre-training. Some researchers focus on injecting entity knowledge into language pre-trained models based on masked entity model (MEM) training, which masks entities randomly and lets the model recover. These methods cannot guarantee good performance due to the lack of consideration of which entities are more valuable for learning. Moreover, in multi-modal training data, some entities may be unrelated to visual content. In this work, for the vision-language pre-trained model, we propose a Masked Entity Model pre-training method based on Active learning (ActiveMEM). It is designed to actively mask important and informative entities—those that are both informative and uncertain—for the model to recover, thereby encouraging it to extract more valuable knowledge from the data. The proposed method is evaluated using three pre-training datasets and four downstream datasets, and the experimental results demonstrate the effectiveness of our method. Full article
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11 pages, 277 KB  
Article
On the Supremum of Singleton Ratios in Submodular Functions
by Laszlo Csirmaz
Mathematics 2026, 14(12), 2223; https://doi.org/10.3390/math14122223 (registering DOI) - 21 Jun 2026
Abstract
Let N be a finite set of cardinality n, and let aN. A submodular function f on N with f(a)=1 is defined to be a-reduced if, for any decomposition [...] Read more.
Let N be a finite set of cardinality n, and let aN. A submodular function f on N with f(a)=1 is defined to be a-reduced if, for any decomposition f=g+h into submodular functions, where h does not depend on a, it follows that h is identically zero. The maximal possible value of f on the remaining singletons defines a quantity λ that characterizes the degree to which one variable can constrain the value of another; geometrically, it also limits the possible elongation of the associated submodular base polytope. The parameter has concrete relevance: it caps the share-size lower bounds provable for secret-sharing schemes via the basic Shannon inequalities, and it controls the geometry of the base polytopes on which greedy submodular-optimization algorithms operate. We construct an example demonstrating that λ can be as large as Ω(n/logn). Furthermore, we establish a doubly exponential upper bound on λ. The problem of narrowing the gap between these bounds remains open. Full article
(This article belongs to the Section E: Applied Mathematics)
26 pages, 416 KB  
Article
Asymmetric Quantum Codes from τ-Paired Matrix-Product Codes
by Sami H. Saif and Shayea Aldossari
Mathematics 2026, 14(12), 2226; https://doi.org/10.3390/math14122226 (registering DOI) - 21 Jun 2026
Abstract
Asymmetric quantum codes are useful for quantum channels in which phase and bit errors occur with different probabilities, since the two distances, dz and dx, can be controlled separately. We develop a permutation-paired matrix-product construction for such codes over [...] Read more.
Asymmetric quantum codes are useful for quantum channels in which phase and bit errors occur with different probabilities, since the two distances, dz and dx, can be controlled separately. We develop a permutation-paired matrix-product construction for such codes over Fq. The main task is to build classical code pairs C,DFq2kn satisfying the Hermitian inclusion DHC, while keeping explicit dimension and distance bounds. Let AFq2k×k be a non-singular-by-columns (NSC) matrix with AA=DPτ, where D is an invertible diagonal and Pτ corresponds to an involution τ. For C=[C1,,Ck]A and D=[D1,,Dk]A, we prove DH=[Dτ(1)H,,Dτ(k)H]A. Thus, the global inclusion DHC is equivalent to the shorter paired inclusions Dτ(i)HCi. This yields asymmetric quantum codes with parameters [[kn,i=1k(ri+si)kn,dz/dx]]q, where the bounds for dz and dx follow from NSC matrix-product distance estimates. For nested maximum distance separable (MDS) constituents, the paired conditions reduce to ri+sτ(i)n, giving explicit infinite families. Concrete τ-OD matrices and numerical examples show that nontrivial permutations can increase the quantum dimension while preserving prescribed lower bounds for dz and dx. Full article
35 pages, 2116 KB  
Review
Extracellular Vesicle-Derived MicroRNAs as Early Diagnostic Biomarkers of Diabetic Nephropathy and Cardiovascular Diseases in Type 2 Diabetes
by Yessenbekova Arailym, Arman Abaildayev and Belkozhayev Ayaz
Int. J. Mol. Sci. 2026, 27(12), 5581; https://doi.org/10.3390/ijms27125581 (registering DOI) - 20 Jun 2026
Abstract
Type 2 diabetes mellitus (T2DM) is a major driver of chronic kidney disease and cardiovascular morbidity worldwide. Extracellular vesicles (EVs), particularly exosomes, carry microRNAs (miRNAs) that reflect the pathophysiological state of their parent cells and represent promising non-invasive biomarkers. This review comprehensively examines [...] Read more.
Type 2 diabetes mellitus (T2DM) is a major driver of chronic kidney disease and cardiovascular morbidity worldwide. Extracellular vesicles (EVs), particularly exosomes, carry microRNAs (miRNAs) that reflect the pathophysiological state of their parent cells and represent promising non-invasive biomarkers. This review comprehensively examines the diagnostic and mechanistic roles of EV-derived miRNAs in diabetic nephropathy (DN) and cardiovascular diseases (CVDs) associated with T2DM. A PRISMA-guided literature search of PubMed, Scopus, Web of Science, and Embase identified 847 articles published between January 2020 and June 2026, of which 152 studies met the inclusion criteria. Several urinary exosomal miRNAs demonstrated significant diagnostic performance for DN, including miR-4534 (AUC = 0.786), miR-136-5p (sensitivity 72.2%, specificity 78.4%), and miR-142-3p. A meta-analysis of circulating miRNAs in diabetic kidney disease reported a pooled AUC of 0.79. In the cardiovascular setting, exosomal miR-155-5p (AUC = 0.901), miR-15a-3p (AUC = 0.874), and a four-miRNA panel (miR-433-3p/let-7b/miR-30-5p/miR-122-5p; AUC = 0.833) demonstrated strong diagnostic performance for ischemic heart disease and carotid atherosclerosis in T2DM. Mechanistically, key EV-associated miRNAs, including miR-21, miR-192, and the anti-fibrotic miR-29 family, participate in fibrosis, inflammation, oxidative stress, endothelial dysfunction, and cardiac remodeling pathways. EV-derived miRNAs therefore represent highly promising non-invasive biomarkers for the early diagnosis and monitoring of diabetic renal and cardiovascular complications. However, clinical translation requires standardized EV isolation and miRNA detection protocols, together with validation in large multicenter prospective cohorts. This review highlights the considerable diagnostic and translational potential of EV-derived miRNAs for precision medicine and liquid biopsy applications in T2DM complications. Full article
(This article belongs to the Section Molecular Pathology, Diagnostics, and Therapeutics)
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21 pages, 333 KB  
Article
Quillen–Suslin Theorem for Connected Cochain DG Algebras
by Xuefeng Mao and Biyan Zhu
Mathematics 2026, 14(12), 2215; https://doi.org/10.3390/math14122215 (registering DOI) - 20 Jun 2026
Abstract
Let A be a connected cochain differential graded algebra and P a finitely generated differential graded A-module. We show that P is semi-free if it is semi-projective and it is categorically free if it is categorically projective. It can be considered as [...] Read more.
Let A be a connected cochain differential graded algebra and P a finitely generated differential graded A-module. We show that P is semi-free if it is semi-projective and it is categorically free if it is categorically projective. It can be considered as a generalization of the well-known Quillen–Suslin Theorem in differential graded context. As an application, we show that the ghost length and the cone length of a compact differential graded module coincide. Full article
41 pages, 497 KB  
Article
Informational Holonomy Curvature and Its Discrete-to-Continuous Convergence
by David Gutierrez Ule
Int. J. Topol. 2026, 3(2), 13; https://doi.org/10.3390/ijt3020013 - 18 Jun 2026
Viewed by 77
Abstract
We introduce a notion of curvature based on informational holonomy. Let (M,g) be a smooth Riemannian manifold and let π:PM be a bundle of state spaces equipped fibrewise with a smooth divergence Dx [...] Read more.
We introduce a notion of curvature based on informational holonomy. Let (M,g) be a smooth Riemannian manifold and let π:PM be a bundle of state spaces equipped fibrewise with a smooth divergence Dx inducing an information metric gPx. Assuming a connection on P compatible with this fibrewise information geometry, we measure the deviation of holonomy around small geodesic triangles by transporting a reference state μx and comparing it to its image via the induced informational distance dx=2Dx. Normalizing the resulting distance defect by the geometric area yields a continuous informational holonomy (sectional) curvatureKholcont(x,Π). We prove that this limit exists for all (x,Π) and equals the norm of a vector Wx(Π;μx)TμxPx depending linearly on the curvature of the connection along Π. In geometric models induced from the Levi–Civita connection via an isometric representation, Kholcont becomes a scalar invariant of Rg|Π and, on spaces of constant sectional curvature, reduces to a constant multiple of |secg|. On the discrete side, we consider quasi-uniform sampling graphs whose edges carry channels approximating parallel transport. Discrete triangle holonomies define a curvature estimator, and under explicit sampling, area-approximation, and channel-consistency assumptions, we establish a discrete-to-continuum convergence theorem with a quantitative error bound controlled by the sampling scale. Full article
17 pages, 1173 KB  
Article
Charge–Capacitance Channel Decomposition Reveals Fabrication-Tolerant Design Windows for Disk Triboelectric Nanogenerators
by Shenchen Liu, Yangshi Shao, Xuhong Feng, Zehui Lin, Xiaoming Jing and Everett X. Wang
Materials 2026, 19(12), 2607; https://doi.org/10.3390/ma19122607 - 17 Jun 2026
Viewed by 205
Abstract
Disk triboelectric nanogenerator (TENG) design pursues high structural figure of merit (FOMS), yet nominal peak designs often sit in regions with steep geometric gradients; under a controlled ±10% symmetric perturbation proxy, worst-case FOMS retention near the peak [...] Read more.
Disk triboelectric nanogenerator (TENG) design pursues high structural figure of merit (FOMS), yet nominal peak designs often sit in regions with steep geometric gradients; under a controlled ±10% symmetric perturbation proxy, worst-case FOMS retention near the peak frontier falls to 2.7%. We decompose FOMS into a charge-transfer channel (Qsc,MACRS) and a capacitance channel (Csum1), and train a multi-output surrogate with a physics consistency constraint on 1944 COMSOL simulations to jointly predict Qsc,MACRS, Csum1, and FOMS across electrode-pair number, dielectric-thickness-to-radius ratio (h/R), air-gap-to-radius ratio (d/R), and dielectric constant. Evaluating 7776 design points reveals that 58.6% of the explored space is charge-dominant, 36.1% mixed, and 5.3% capacitance-dominant; raising dielectric constant shifts the mechanism toward capacitance-limited behavior, while a larger air gap reinforces charge-limited behavior. Mixed-regime windows tolerate the same perturbation proxy far better than peak-FOMS candidates, supplying candidate design windows for pre-fabrication screening within the validated simulation domain. The surrogate reaches pooled out-of-distribution FOMSRlog102=0.914 on 43 unseen structural and dielectric combinations. Delivered through an open-source Streamlit interface, the channel decomposition, mechanism mapping, and tolerance screening let designers identify the limiting mechanism and select candidate designs that are expected to tolerate geometric variation within the validated simulation domain, prior to fabrication. Full article
(This article belongs to the Special Issue Materials, Design, and Performance of Nanogenerators)
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19 pages, 339 KB  
Article
Quantitative Weighted Bound for Spectral Multiplier of Laplace Transform Type
by Mengli Zhu, Xiangxing Tao and Guoen Hu
Mathematics 2026, 14(12), 2143; https://doi.org/10.3390/math14122143 - 15 Jun 2026
Viewed by 82
Abstract
Let L be a non-negative and self-adjoint operator that is bounded on L2(Rn). Under the generalized Muckenhoupt weights Apρ,θ, we establish more refined quantitative weighted estimates for the Laplace-transform-type spectral multiplier [...] Read more.
Let L be a non-negative and self-adjoint operator that is bounded on L2(Rn). Under the generalized Muckenhoupt weights Apρ,θ, we establish more refined quantitative weighted estimates for the Laplace-transform-type spectral multiplier M(L): the weighted bound is improved from [w]Apρ,θmax{1,1/(p1)} to [w]Apρ,θ1/p([w]Aρ,θ1/p+[w1p]Aρ,θ1/p), and the weak-type endpoint estimate at p=1 is provided. For the composition M(L1)M(L2), we obtain the strong-type and weak-type weighted estimates, revealing the dependence on [w]Apρ,θ, [w]Aρ,θ and [w1p]Aρ,θ. These results refine the weight constant dependency and extend composition theory to spectral multipliers. Full article
26 pages, 3982 KB  
Article
SW-SpeedDLM: Sliding Window Speculative Decoding for Diffusion Language Models Under Long Context Constraints
by Dai Teng, Minjae Rhee, Yuxuan Qin, Bingjie Zi and Wenhe Liu
Mathematics 2026, 14(12), 2137; https://doi.org/10.3390/math14122137 - 15 Jun 2026
Viewed by 189
Abstract
Masked diffusion language models (MDLMs) apply full bidirectional attention at every denoising step, which incurs O(Tn2) cost in the number of steps T and the sequence length n. For an 8B parameter model at n = 8192 [...] Read more.
Masked diffusion language models (MDLMs) apply full bidirectional attention at every denoising step, which incurs O(Tn2) cost in the number of steps T and the sequence length n. For an 8B parameter model at n = 8192 with T = 128, the KV cache alone exceeds 40 GB and rules out long document generation on a single GPU. We introduce SW-SpeedDLM, an inference wrapper for pretrained MDLMs that generates sequences of up to 16,384 tokens on one A100 with 40 GB. The framework comprises three components, each targeting a distinct bottleneck. Segmented SlidingWindow Denoising (SSWD) restricts each denoising loop to a window of W tokens and reduces the per-step cost to O(W2n/S). Cross-Segment KV Compression (CSKV) encodes each completed window into C summary tokens that later windows attend to at O(C) cost. Window Level Speculative Acceptance (WLSA) lets a small draft model propose k denoising steps that the target model verifies in a single forward pass, yielding up to 2.4× per window speedup. We prove that WLSA preserves the exact marginal distribution of the target model. On MDLM-860M and LLADA-8B across PG-19, LongBench, and WritingPrompts, SW-SpeedDLM achieves 3.7× higher throughput at n = 8192 than full attention generation at n = 2048 (its maximum feasible length) and lowers peak memory by 2.5× relative to full attention at n = 4096, the longest length full attention can support before exhausting GPU memory, while also increasing PG-19 bits per character by only 0.18. Full article
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22 pages, 867 KB  
Article
RankBridge: Privacy-Preserving Rank-Based Explanation Clustering for Heterogeneous Federated Phishing Detection
by Panhapiseth Lim, Priyanka Kumar, Richard Zanni and Timothy Lambdin
Computation 2026, 14(6), 137; https://doi.org/10.3390/computation14060137 - 15 Jun 2026
Viewed by 196
Abstract
Federated learning lets organizations train a shared model without pooling private data. The standard method, Federated Averaging, requires all participants to use the same input features, a condition that fails in cross-sector phishing detection, where banks analyze URL structure and hospitals analyze email [...] Read more.
Federated learning lets organizations train a shared model without pooling private data. The standard method, Federated Averaging, requires all participants to use the same input features, a condition that fails in cross-sector phishing detection, where banks analyze URL structure and hospitals analyze email content. We present RankBridge, a system that groups participants by comparing ranked lists of SHapley Additive exPlanations (SHAP) feature importance rather than model weights or gradients. Each participant trains a local LightGBM model, extracts the top-K features by SHAP importance, and sends a 60-byte ranked list of feature indices to a central server. The server applies rank correlation and Ward’s hierarchical clustering to identify similarly threatened organizations. RankBridge operates in two modes: ModelShare, where models are also shared within each discovered group for prediction ensembling, and RankOnly, where the server returns only a group label and each participant keeps their model private. Across 32 participants in five organization types, RankBridge (ModelShare) achieves F1 =0.853 (AUC =0.926) on synthetic data and F1 =0.772 (AUC =0.812) on real phishing data, and it is the only method to outperform isolated local training on both. On real heterogeneous data the standard baselines adapted to LightGBM, including Federated Averaging, retain a moderate thresholded F1 (≈0.73) but their ranking quality collapses to near-random (AUC 0.59, PR-AUC 0.66), whereas RankBridge sustains AUC =0.812 and PR-AUC =0.819. RankBridge recovers the correct organizational groupings with Normalized Mutual Information (NMI) =0.973. The rank-based grouping channel itself transmits 60 bytes per participant per round, roughly 10,000× less than a full model upload. Full article
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38 pages, 13992 KB  
Article
A Q-Learning-Enhanced Cuckoo Catfish Optimizer (CCO-RL): A Comparative Study of Nine Metaheuristics Applied to CEC2017, CEC2022 and Engineering Design Problems
by Arar Al Tawil, Amnah Alshahrani, Bilal Ibrahim Alqudah and Hana Fathi
Biomimetics 2026, 11(6), 422; https://doi.org/10.3390/biomimetics11060422 - 14 Jun 2026
Viewed by 171
Abstract
The Cuckoo Catfish Optimizer (CCO) is a recent swarm method with four built-in movement strategies. Its weakness is not the moves themselves but the way it chooses among them: a fixed chain of random-versus-threshold (rand>C) tests that ignores how [...] Read more.
The Cuckoo Catfish Optimizer (CCO) is a recent swarm method with four built-in movement strategies. Its weakness is not the moves themselves but the way it chooses among them: a fixed chain of random-versus-threshold (rand>C) tests that ignores how each agent is actually doing and keeps no memory of which move has been paying off. On harder, higher-dimensional problems, this rigidity drains diversity and the search stalls. We propose CCO-RL, which hands the choice of move to a small tabular Q-learning controller. For every agent at every iteration, the controller reads a 48-state summary of the agent’s crowding, its recent stagnation and how far the run has progressed, then picks one of the four moves. A bounded reward and a decaying ε-greedy rule let it learn a policy online with no extra function evaluations. We test CCO-RL against the original CCO and eight popular metaheuristics on CEC2017 (D=30,50) and CEC2022 (D=20): 70 instances, 30 runs each. CCO-RL earns the best overall Friedman rank (1.69) and significantly beats every external competitor according to the Nemenyi test. It also finds the best mean design in three engineering problems. Full article
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18 pages, 2768 KB  
Article
Extracellular Vesicle-like Associated microRNAs in Monofloral Honeys: Molecular Characterization and Functional Pathways
by Diana Marisol Abrego-Guandique, Silvia Nuzzo, Olubukunmi Amos Ilori, Ilaria Leone, Mario Zanfardino, Enrico Gallo, Paola Tucci, Filippo Luciani, Maria Cristina Caroleo, Roberto Cannataro and Erika Cione
Int. J. Mol. Sci. 2026, 27(12), 5297; https://doi.org/10.3390/ijms27125297 - 11 Jun 2026
Viewed by 231
Abstract
Recent studies have identified microRNAs (miRNAs) in honey, opening a new and promising area of nutrition research. In this view, pasteurized and unpasteurized samples of Eucalyptus, Orange Blossom, Chestnut, and Sulla honeys were analyzed using manual and semi-automated RNA extraction methods. Semi-automated extraction [...] Read more.
Recent studies have identified microRNAs (miRNAs) in honey, opening a new and promising area of nutrition research. In this view, pasteurized and unpasteurized samples of Eucalyptus, Orange Blossom, Chestnut, and Sulla honeys were analyzed using manual and semi-automated RNA extraction methods. Semi-automated extraction yielded significantly higher RNA amounts than manual methods, while pasteurization selectively affected miRNA presence, depending on the type of honey. The panel of conserved miRNAs monitored was let-7a-5p, miR-1-3p, miR-7-5p, miR-10a-5p, miR-33a-5p, miR-34a-5p, miR-92a-3p, miR-125b-5p and miR-133a-3p, across honey varieties and in their extracellular vesicles with structures approximately 200 nm in diameter that retain four miRNAs in all honey types, miR-1-3p, miR-34a-5p, miR-92a-3p, and miR-133a-3p. Bioinformatic analyses of validated miRNA targets revealed enrichment in pathways related to cytoskeletal organization, transcriptional regulation, protein stability, and immune system processes, with Reactome categories clustering around signal transduction, protein metabolism, and immune interactions. Cell–type–specific enrichment suggested that gastric isthmus progenitor cells, stromal cells, and immune subsets could be potential targets, implying roles in epithelial renewal, immune modulation, and wound healing. Overall, these findings enhance our understanding of honey as a source of conserved miRNAs in extracellular vesicles, highlighting its potential as a natural carrier that protects miRNAs from degradation. This study offers new insights into the health-promoting properties of honey, warranting further preclinical studies. Full article
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9 pages, 827 KB  
Article
Let’s Be Realistic with Rurality: Timely Surgical Management of Open Fractures in Rural and Remote Patients
by Travis Jennings, Katie Wang, William G. Blakeney and Nicholas Calvert
J. Clin. Med. 2026, 15(12), 4516; https://doi.org/10.3390/jcm15124516 - 11 Jun 2026
Viewed by 111
Abstract
Background: Rurality in Western Australia presents challenges in the management of open fractures for the state’s trauma centre. Open fractures are associated with high morbidity, and the BOA Standards for Trauma and Orthopaedics (BOAst) guidelines recommend timelines for surgical management to minimise complications. [...] Read more.
Background: Rurality in Western Australia presents challenges in the management of open fractures for the state’s trauma centre. Open fractures are associated with high morbidity, and the BOA Standards for Trauma and Orthopaedics (BOAst) guidelines recommend timelines for surgical management to minimise complications. This study aimed to describe the timelines to surgical management for rural patients with severe open fractures and to identify system-level factors contributing to delays. Methods: A retrospective single-centre study was conducted on all rural patients with open fractures requiring fixation and soft-tissue coverage between January 2020 and December 2023. Data was collected from the trauma registry and electronic medical records, including injury characteristics, transfer details, timing of surgical management, and complications. Results: Fifteen rural patients met the inclusion criteria. The median time to initial debridement from first healthcare presentation was 27.6 h. The mean transfer time to the trauma centre was 14.5 h, and the median time to definitive fixation and soft tissue coverage was 159.7 h. Identified modifiable factors to minimise delays on arrival to the trauma hospital include prioritisation of rural patients at the time of arrival, accessibility to an orthoplastics theatre, and minimising the total number of debridements prior to definitive reconstruction. Conclusions: Substantial delays in the surgical management of rural patients with open fractures were observed, largely related to interhospital transfer and system-level factors at the tertiary centre. These delays limit the feasibility of compliance with the BOAst guidelines and highlight the need for context-specific strategies to improve the timely care of this high-risk population. Full article
(This article belongs to the Section Orthopedics)
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17 pages, 306 KB  
Article
Idempotent Symmetry and Monogenic Functions in a Commutative Bicomplex-Type Algebra
by Ji Eun Kim
Symmetry 2026, 18(6), 998; https://doi.org/10.3390/sym18060998 - 10 Jun 2026
Viewed by 175
Abstract
Let A={p+Jq:p,qC,J2=1} be the commutative bicomplex-type algebra in which J commutes with the scalar imaginary unit. A Cauchy–Riemann-type operator D¯ is studied on [...] Read more.
Let A={p+Jq:p,qC,J2=1} be the commutative bicomplex-type algebra in which J commutes with the scalar imaginary unit. A Cauchy–Riemann-type operator D¯ is studied on domains in C2. In the active coordinates ξ=z1iz2 and η=z1+iz2, the equation D¯f=0 is diagonal in the idempotent basis: the e+-component is holomorphic in ξ with η as the parameter, while the e-component is holomorphic in η with ξ as the parameter. The expression e+F(ξ)+eG(η) is the parameter-independent subcase. From this decomposition, one obtains a slice characterization, a criterion for separatedness, a comparison with ordinary holomorphic functions of two complex variables, active-variable Cauchy formulas and estimates, local series with parameter-dependent coefficients, reflection symmetry, and Hardy and Bergman kernel lifts on the separated Hilbert spaces. Full article
(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)
21 pages, 402 KB  
Article
Frobenius Pullback Map on Moduli of Principal G-Bundles
by Xiaoyu Su and Yumin Zhong
Mathematics 2026, 14(12), 2076; https://doi.org/10.3390/math14122076 - 10 Jun 2026
Viewed by 126
Abstract
Let G be a connected reductive group over K with charK=p>0. In this paper, we prove via deformation-theoretic techniques that the Frobenius pullback of a general stable G-bundle on a curve X remains stable in the [...] Read more.
Let G be a connected reductive group over K with charK=p>0. In this paper, we prove via deformation-theoretic techniques that the Frobenius pullback of a general stable G-bundle on a curve X remains stable in the moduli stack of G-bundles with fixed topological type. We then present some applications of the main theorem. Full article
(This article belongs to the Special Issue Advanced Researches in Algebraic Geometry)
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