arXiv subjects

Zhenghua Xu

Publications and source records attributed to Zhenghua Xu.

At least 19 recordsLinked to original sources

arXiv2026

Fast Frequency Services from HVDC-Connected Offshore Wind Power Plants: A Review in the European Context

The rapid expansion of offshore wind energy is central to the European Union's climate-neutrality targets, with High Voltage Direct Current-connected offshore wind power plants (HVDC-OWPPs) becoming increasingly important for integrating gigawatt-scale renewable generation over long distances. Simultaneously, the phase-out of conventional synchronous generators, together with the gradual withdrawal of renewable-energy subsidies, are creating growing demand for ancillary service provision from HVDC-OWPPs as alternatives. This paper presents a comprehensive review of fast frequency services from HVDC-OWPPs in the European context, focusing on inertia support, fast frequency reserve (FFR), and frequency containment reserve (FCR). The review covers both mandatory grid-code requirements and commercial service products, including the latest developments from ENTSO-E, ACER, NESO, TenneT, and Energinet. Furthermore, the paper discusses the key technical gaps and challenges in the practical implementation of fast frequency services from HVDC-OWPPs, highlighting the limited fast response capacity, complexity of stacking optimization, asymmetric provision of inertia, and overall coordination of an HVDC-OWPP system.

eess.SY↗

arXiv2026

Monogenic functions over real alternative *-algebras: fundamental results and applications

The concept of monogenic functions over real alternative $\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. This paper explores the fundamental properties of these monogenic functions, focusing on the Cauchy-Pompeiu integral formula and Taylor series expansion in hypercomplex subspaces, among which the non-commutativity and especially non-associativity of multiplications demand full considerations. The theory presented herein provides a robust framework for understanding monogenic functions in the context of real alternative $\ast$-algebras, shedding light on the interplay between algebraic structures and hypercomplex analysis.

math.CV↗

arXiv2026

Monogenic functions over real alternative *-algebras: the several hypercomplex variables case

The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\ast$-algebras, which naturally extends the theory of several complex variables to a very general setting. In this new setting, we develop some fundamental properties, such as Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.

math.CV↗

arXiv2026

Generalized partial-slice monogenic functions: the octonionic case

In a recent paper [Trans. Amer. Math. Soc. 378 (2025), 851-883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The present paper shall extend the study of generalized partial-slice monogenic functions from the associative case of Clifford algebras to non-associative alternative algebras, such as octonions. The new class of functions encompasses the regular functions [Rend. Sem. Mat. Univ. Padova 50 (1973), 251-267] and slice regular functions [Rocky Mountain J. Math. 40 (2010), no. 1, 225-241] over octonions, indeed both appear in the theory as special cases. In the non-associative setting of octonions, we shall develop some fundamental properties such as identity theorem, Representation Formula, Cauchy (and Cauchy-Pompeiu) integral formula, maximum modulus principle, Fueter polynomials, Taylor series expansion. As a complement, the paper also introduces and discusses the notion of generalized partial-slice (and regular) functions. Although the study is limited to the case of octonions, it is clear from the statements and the arguments in the proofs that the results hold more in general in real alternative algebras equipped with a notion of conjugation.

math.CV↗

arXiv2026

Octonionic Riesz-Dunford functional calculus

The Riesz-Dunford functional calculus over the algebra of octonions, denoted by $\mathbb{O}$, has long been an open problem due to the nonassociativity of octonions. Two core obstacles hinder its development: first, the generalization of the resolvent operator series identity produces unexpected associator terms that invalidate standard expansions; second, the nonassociativity spoils the analyticity of the resolvent operator, a key property for defining a functional calculus via Cauchy integrals. In this paper, we initiate the study of the Riesz-Dunford functional calculus for bounded power-associative para-linear operators in Banach octonionic bimodules. To address the above issues, we introduce several pivotal concepts: power-associative operators (to eliminate the unwanted associator terms and recover valid resolvent series expansions), the notions of regular inverse of $R_s-T$ for $s\in Ø$ (which serve as the octonionic versions of the resolvent operator), $\mathbb{C}_J$-extendable power-associative operators, and $\mathbb{C}_J$-liftable power-associative operators (to characterize the slice regularity of the resolvent operators). Based on these notions, we define two types of octonionic spectra: the pull-back spectrum $σ^*(T)$ and the push-forward spectrum $σ_*(T)$. These give rise to the left and right slice regular functional calculi of bounded power-associative para-linear operators, respectively. This theory unifies the Riesz-Dunford functional calculus over division algebras ($ \mathbb{C}, \mathbb{H}, \mathbb{O}$) and fills the six-decade-long gap in octonionic (nonassociative) functional analysis.

math.FA↗

arXiv2026

Octonionic isometric isomorphisms and partial isometry

Very recently, two new notions of para-linear mappings and weak associative orthonormal bases were introduced in octonionic functional analysis, which have been proved to be powerful in formulating the basic theory, such as the Riesz representation theorem and the Parseval theorem. In this article, we continue exploring more properties of these two concepts and initiate the study of octonionic para-linear isometric operators. Surprisingly, it is proven that the condition of the para-linear operator on a Hilbert octonionic bimodule being an isometric isomorphism is equivalent to it mapping any associative orthonormal basis to a weak associative orthonormal basis, which implies also that an octonionic matrix is an isometry if and only if the system of its row vectors is a weak associative orthonormal basis. Furthermore, we introduce the concept of para-linear partial isometric operators and establish the aforementioned analogue in this new setting. Based on these facts, we can provide naturally a new viewpoint of James questions by modifying the definition of octonionic Stiefel space.

math.FA↗

arXiv2026

On the Fueter-Sce theorem and Cauchy-Kovalevskaya extensions over alternative $\ast$-algebras

Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this paper, we further develop the theory of generalized partial-slice monogenic functions defined on hypercomplex subspaces and with values in a real alternative $\ast$-algebra and we concentrate on the Fueter-Sce theorem, three types of Cauchy-Kovalevskaya extensions, and their various internal relationships. The paper proposes more bridges between the theories of monogenicity, harmonicity, and generalized partial-slice monogenicity.

math.CV↗

arXiv2025

AMLP: Adjustable Masking Lesion Patches for Self-Supervised Medical Image Segmentation

Self-supervised masked image modeling (MIM) methods have shown promising performances on analyzing natural images. However, directly applying such methods to medical image segmentation tasks still cannot achieve satisfactory results. The challenges arise from the facts that (i) medical images are inherently more complex compared to natural images, and the subjects in medical images often exhibit more distinct contour features; (ii) moreover, the conventional high and fixed masking ratio in MIM is likely to mask the background, limiting the scope of learnable information. To address these problems, we propose a new self-supervised medical image segmentation framework, called Adjustable Masking Lesion Patches (AMLP), which employs Masked Patch Selection~(MPS) strategy to identify patches with high probabilities of containing lesions to help model achieve precise lesion reconstruction. To improve the categorization of patches in MPS, we further introduce Relative Reconstruction Loss (RRL) to better learn hard-to-reconstruct lesion patches. Then, Category Consistency Loss (CCL) is proposed to refine patch categorization based on reconstruction difficulty, enhancing difference between lesions and backgrounds. Moreover, an Adjustable Masking Ratio (AMR) strategy is proposed to gradually increase the masking ratio over training to expand~the scope of learnable mutual information. Extensive~experiments on two medical segmentation datasets demonstrate the superior performances of the proposed AMLP w.r.t. the SOTA self-supervised methods; the results prove that AMLP effectively addresses the challenges of applying masked modeling to medical images and capturing accurate lesion details that are crucial for segmentation tasks.

cs.CV↗

arXiv2025

Modeling Uncertainty Trends for Timely Retrieval in Dynamic RAG

Dynamic retrieval-augmented generation (RAG) allows large language models (LLMs) to fetch external knowledge on demand, offering greater adaptability than static RAG. A central challenge in this setting lies in determining the optimal timing for retrieval. Existing methods often trigger retrieval based on low token-level confidence, which may lead to delayed intervention after errors have already propagated. We introduce Entropy-Trend Constraint (ETC), a training-free method that determines optimal retrieval timing by modeling the dynamics of token-level uncertainty. Specifically, ETC utilizes first- and second-order differences of the entropy sequence to detect emerging uncertainty trends, enabling earlier and more precise retrieval. Experiments on six QA benchmarks with three LLM backbones demonstrate that ETC consistently outperforms strong baselines while reducing retrieval frequency. ETC is particularly effective in domain-specific scenarios, exhibiting robust generalization capabilities. Ablation studies and qualitative analyses further confirm that trend-aware uncertainty modeling yields more effective retrieval timing. The method is plug-and-play, model-agnostic, and readily integrable into existing decoding pipelines. Implementation code is included in the supplementary materials.

cs.CL↗

arXiv2025

Language Drift in Multilingual Retrieval-Augmented Generation: Characterization and Decoding-Time Mitigation

Multilingual Retrieval-Augmented Generation (RAG) enables large language models (LLMs) to perform knowledge-intensive tasks in multilingual settings by leveraging retrieved documents as external evidence. However, when the retrieved evidence differs in language from the user query and in-context exemplars, the model often exhibits language drift by generating responses in an unintended language. This phenomenon is especially pronounced during reasoning-intensive decoding, such as Chain-of-Thought (CoT) generation, where intermediate steps introduce further language instability. In this paper, we systematically study output language drift in multilingual RAG across multiple datasets, languages, and LLM backbones. Our controlled experiments reveal that the drift results not from comprehension failure but from decoder-level collapse, where dominant token distributions and high-frequency English patterns dominate the intended generation language. We further observe that English serves as a semantic attractor under cross-lingual conditions, emerging as both the strongest interference source and the most frequent fallback language. To mitigate this, we propose Soft Constrained Decoding (SCD), a lightweight, training-free decoding strategy that gently steers generation toward the target language by penalizing non-target-language tokens. SCD is model-agnostic and can be applied to any generation algorithm without modifying the architecture or requiring additional data. Experiments across three multilingual datasets and multiple typologically diverse languages show that SCD consistently improves language alignment and task performance, providing an effective and generalizable solution in multilingual RAG.

cs.CL↗

arXiv2025

Holistic Grid-Forming Control for HVDC-Connected Offshore Wind Power Plants to Provide Frequency Response

HVDC-connected offshore wind power plants (OWPPs) are expected to provide inertial response and frequency containment reserve (FCR) to help address the frequency control challenges caused by the growing penetration of power electronics in power systems. Initially dominated by communication-based and grid-following (GFL) control, recent efforts have shifted towards incorporating communication-free and grid-forming (GFM) control into HVDC-OWPP systems to enhance their frequency response capability. This paper proposes a holistic GFM control based on dual-port GFM control to improve the coordination across the entire AC-DC-AC dynamics. A frequency response model of a typical HVDC-OWPP system is developed for GFM control design. Then, dual-port GFM control and virtual synchronous generator control are implemented respectively on the HVDC system and OWPP of the typical system, where the asynchronism of onshore and offshore frequencies is revealed. Next, holistic GFM control is proposed to improve the synchronization and DC voltage regulation. Finally, simulations on the delivery of FCR and inertial response are carried out to verify the feasibility and effectiveness of the proposed control.

eess.SY↗

arXiv2025

MPL: Multiple Programming Languages with Large Language Models for Information Extraction

Recent research in information extraction (IE) focuses on utilizing code-style inputs to enhance structured output generation. The intuition behind this is that the programming languages (PLs) inherently exhibit greater structural organization than natural languages (NLs). This structural advantage makes PLs particularly suited for IE tasks. Nevertheless, existing research primarily focuses on Python for code-style simulation, overlooking the potential of other widely-used PLs (e.g., C++ and Java) during the supervised fine-tuning (SFT) phase. In this research, we propose \textbf{M}ultiple \textbf{P}rogramming \textbf{L}anguages with large language models for information extraction (abbreviated as \textbf{MPL}), a novel framework that explores the potential of incorporating different PLs in the SFT phase. Additionally, we introduce \texttt{function-prompt} with virtual running to simulate code-style inputs more effectively and efficiently. Experimental results on a wide range of datasets demonstrate the effectiveness of MPL. Furthermore, we conduct extensive experiments to provide a comprehensive analysis. We have released our code for future research.

cs.CL↗

arXiv2025

Teodorescu transform for slice monogenic functions and applications

In the past few years, the theory of slice monogenic functions has been developed rapidly mainly motivated by the applications to an elegant functional calculus for non-commuting operators. In this article, we introduce the Teodorescu transform in the theory of slice monogenic functions, which turns out to be the right inverse of a slice Cauchy-Riemann operator. The boundednesses of the Teodorescu transform and its derivatives are investigated as well. A Hodge decomposition of the $\mathcal{L}^p$ space and a generalized Bergman projection are introduced at the end as applications.

math.CV↗

arXiv2024

Generalized partial-slice monogenic functions

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of Möbius transformations preserving the partial symmetry of the involved domains.

math.CV↗

arXiv2024

Power-bounded quaternionic operators

Recently, the conception of slice regular functions was allowed to introduce a new quaternionic functional calculus, among which the theory of semigroups of linear operators was developed into the quaternionic setting, even in a more general case of real alternative $*$-algebras. In this paper, we initiate to study the discrete case and introduce the notion of power-bounded quaternionic operators. In particular, by the spherical Yosida approximation, we establish a discrete Hille-Yosida-Phillips theorem to give an equivalent characterization of quaternionic linear operators being power-bounded. A sufficient condition of the power-boundedness for quaternionic linear operators is also given. In addition, a non-commutative version of the Katznelson-Tzafriri theorem (J. Funct. Anal. 68: 313-328, 1986) for power-bounded quaternionic operators is formulated in terms of the $S$-spectrum.

math.SP↗

arXiv2024

Almansi-type decomposition and Fueter-Sce theorem for generalized partial-slice regular functions

Very recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced to unify the theory of monogenic functions and of slice monogenic functions over Clifford algebras. Inspired by the work of A. Perotti, in this paper we provide two analogous versions of the Almansi decomposition in this new setting. Additionally, two enhancements of the Fueter-Sce theorem have been obtained for generalized partial-slice regular functions.

math.CV↗

arXiv2024

Segal-Bargmann transform for generalized partial-slice monogenic functions

The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to develop the Segal-Bargmann transform and give a Schrödinger representation in the setting of generalized partial-slice monogenic functions. To this end, the generalized partial-slice Cauchy-Kovalevskaya extension plays a crucial role.

math.CV↗

arXiv2024

Invariance of iterated global differential operator for slice monogenic functions

In this article, we present the symmetry group of a global slice Dirac operator and its iterated ones. Further, the explicit forms of intertwining operators of the iterated global slice Dirac operator are given. At the end, we introduce a variant of the global slice Dirac operator, which allows functions considered to be defined on the whole Euclidean space. The invariance property and the intertwining operators of this variant of the global slice Dirac operator are also presented.

math.CV↗