arXiv subjects

Jiang Yang

Publications and source records attributed to Jiang Yang.

At least 19 recordsLinked to original sources

arXiv2026

Three Problems on Separable Quotients of Precompact Abelian Groups

We address three problems on separable quotients of topological groups posed by Leiderman, Morris, and Tkachenko in \cite{LMT} published on Israel Journal of Mathematics. First, we construct in ZFC a connected Baire Pontryagin-reflexive dense subgroup of $\T^{\cc}$ whose countable subgroups are $h$-embedded and whose uncountable subgroups are dense. Its underlying abstract group is the circle group, and all its compact subsets are finite. Second, we construct a zero-dimensional Baire Pontryagin-reflexive example with the same subgroup properties whose underlying group is free abelian of rank $\cc$. Both examples have no nontrivial separable Hausdorff quotient. Third, for the group constructed in their Theorem~3.5, we determine every closed subgroup of every finite power up to an integral change of coordinates and prove that every countable subgroup of every Hausdorff quotient of a finite power is $h$-embedded and closed. The same conclusions hold for our free Baire reflexive example. These results answer Problem~1.25 negatively, Problem~3.12 affirmatively and realize all three regularity properties in Problem~3.14 simultaneously in \cite{LMT}.

math.GN↗

arXiv2026

Singular Submodules of Abelian Groups over Their Endomorphism Rings

Let $A$ be an abelian group and $E=\Endo_{\Z}(A)$. We give a module-theoretic description of the singular $E$-submodules asked for in Fuchs' Problem~1.2. For a unital ring $R$ and a left $R$-module $M$, put $W=I_R({}_RR)\oplus I_R(M)$ and $J=\Jaco(\Endo_R(W))$, and let $u$ be the image of $1_R$. The classical essential-kernel criterion yields \[ Z_R(M)=M\cap Ju. \] For $R=E$ and $M=A$, all singular submodules are therefore the $E$-submodules of $A\cap Ju$. Writing $T=t(A)$ and $B=A/T$, we prove a torsion-transfer formula, identify the torsion part as $\bigoplus_p pT_p$, and describe simultaneous prime lifting by a canonical obstruction. The resulting extension gives an $\Extt/\Homm$ parametrization of all singular submodules. We obtain explicit formulas for torsion groups and for $\Z(p^\infty)\oplus B$ with $B$ torsion-free; in the latter case the fully invariant subgroup lattice of $B$ occurs as an interval. The general description retains the induced endomorphism action and extension data, rather than giving a classification by classical group invariants.

math.GN↗

arXiv2026

Soft Posterior Speaker Injection for Multi-Talker Speech Recognition

Multi-talker automatic speech recognition (MT-ASR) remains challenging in the presence of overlapping speech. Hard segmentation introduces irreversible errors, whereas serialized output training (SOT) avoids explicit segmentation but does not condition a pretrained encoder on speaker activity. We propose Soft Posterior Speaker Injection (SPSI). A Soft Posterior Head predicts per-frame speaker posteriors $\hat{\mathbf{P}}$ and injects them into Whisper through Multi-layer Feature-wise Linear Modulation (MFLM) and Speaker Memory Prompts (SMP). The benefit of SPSI is largest where overlap is heaviest and under domain transfer. On controlled two-speaker LibriSpeech overlap, SPSI reduces concatenated minimum-permutation word error rate (cpWER) from $61.5\%$ to $60.0\%$ in the high-overlap bin, and from $51.9\%$ to $51.0\%$ on the full set, relative to SOT. By contrast, Speaker CE, SD-CTC, SA-DiCoW, and Pipeline (oracle/est.\ VAD) do not outperform SOT. Freeze-posterior overlap-heavy adaptation reduces held-out LibriCSS cpWER from $42.3\%$ to $36.8\%$ on sessions $8$--$9$, a $5.5$-point gain over SOT. The source code is available at https://github.com/HackerHyper/SPSI.

cs.SD↗

arXiv2026

The answer about Itzkowitz's Problems on FSIN groups

A topological group is functionally balanced if every bounded real-valued left uniformly continuous function is right uniformly continuous. We prove that every Hausdorff functionally balanced group has coinciding left and right uniformities, giving an affirmative answer to the Itzkowitz problem. Consequently, the classes of SIN, SFSIN and FSIN groups coincide.

math.GN↗

arXiv2026

A linear mass-lumped finite element method for the Landau-Lifshitz-Gilbert equation: unconditional energy dissipation and length preservation

We develop a linear, unconditionally energy-dissipative, mass-lumped finite element method for the highly nonlinear Landau--Lifshitz--Gilbert (LLG) equation on quasi-uniform triangular meshes. The method is built on a projection strategy for enforcing the nonconvex pointwise constraint $|\mathbf{m}| = 1$, whose simultaneous preservation with unconditional energy stability remains challenging for standard finite element discretizations. The key innovation is a unified hybrid finite element-finite difference framework that underlies both the design and the analysis of the proposed method. In the scheme construction, we exploit the weak formulation and nodal structure of mass-lumped finite element method, while incorporating suitable interpolation operators and a node-wise length-preserving mechanism inspired by finite difference discretizations. This combination yields a linear scheme that preserves the node-wise unit-length constraint and satisfies a discrete energy dissipation law. The same hybrid framework also plays a central role in the error analysis, where the weak formulation and quasi-uniform mesh structure of finite elements are combined with interpolation-based and nodewise finite difference method to control the strongly nonlinear damping term and to establish an optimal-order error estimate. More importantly, the proposed method provides a unified framework that systematically integrates the geometric flexibility of finite element method with the pointwise constraint-preserving property of finite difference method, and thus offers a general strategy for designing and analyzing structure-preserving discretizations of constrained dissipative systems. Numerical experiments, including a classical blow-up simulation, confirm the predicted accuracy, energy dissipation, and robustness of the method.

math.NA↗

arXiv2026

Stability and error analysis of fully discrete original energy-dissipative and length-preserving scheme for the Landau-Lifshitz-Gilbert equation

The Landau-Lifshitz-Gilbert (LLG) equation, regarded as a gradient flow with manifold constraint, is the fundamental model describing magnetization dynamics in ferromagnetic materials. It is well known that the normalized tangent plane method is able to simultaneously achieve the non-convex manifold constraint and original energy dissipation. However, the associated computational cost of this numerical approach is exceedingly high. By contrast, the projection method is more straightforward to implement, while it often compromises the inherent energy dissipative property of the continuous model, and the error analysis turns out to be even more challenging. In this work, we first construct a linear and fully discrete finite difference numerical scheme, based on the projection method for the LLG equation, which is capable of simultaneously preserving the non-convex manifold constraint $|\mathbf{m}| = 1$ and an unconditional original energy dissipation. In the error analysis, the classical theoretical technique becomes ineffective, due to the presence of the nonlinear Laplacian term, which in turn poses a significant challenge. To overcome this subtle difficulty, we carefully rewrite the numerical method in an equivalent weak form, in which a point-wise length preserving feature of the numerical solution plays an essential role. As a result of these estimates in the reformulated weak form, an optimal convergence rate could be theoretically established. In our knowledge, this numerical method is the first linear algorithm that preserves the following combined theoretical properties: (i) point-wise length preservation, (ii) unconditional original energy dissipation, (iii) a theoretical justification of convergence analysis and optimal rate error estimate.

math.NA↗

arXiv2026

Countable uniformly discrete sets in functionally balanced groups

We prove that every countable left uniformly discrete subset of a Hausdorff functionally balanced topological group is right thin. As applications, we answer two questions of Bouziad and Troallic: every left precompact subset of a Hausdorff functionally balanced group is right precompact, and every Hausdorff $ω$-narrow functionally balanced group is a SIN group.

math.GN↗

arXiv2026

HERMES: a multi-agent framework for structured knowledge extraction from ultra-long documents in geoscience

Authoritative scientific knowledge in geoscience remains largely trapped in legacy monographs and historical literature, where unstructured text and complex layouts hinder computational access. We introduce HERMES, a scalable multi-agent framework that extracts structured data from ultra-long scientific documents. Using a coordinating large language model, HERMES integrates domain constraints, validation rules and evidence tracing within a unified document-level extraction process that incorporates parsed text, tables, figures and captions. Applied to the 55-volume Treatise on Invertebrate Paleontology, the system produced a structured database of 32,277 fossil taxonomic entities and 451,878 attributes, released online at https://treatise.geolex.org. Extraction performance remained stable across fossil groups (average F1 scores of approximately 0.90 for entities and 0.91 for attributes), improving per-volume efficiency approximately sixfold relative to the tested fully manual baseline. Evaluation in palaeomagnetism and geochemistry, conducted without additional model training, demonstrated transfer across distinct geoscience domains. This work provides a practical pathway to transform historical scientific literature into FAIR-oriented structured data, offering a sustainable infrastructure for data-intensive disciplines and large-scale knowledge integration.

cs.CL↗

arXiv2026

Residual profiles and bounded generation in pro-$p$ completions of amalgamated products

This paper completely classifies when the pro-$p$ completion of an amalgamated product has bounded generation, assuming its starting vertex groups are already boundedly generated. We first prove that the pro-$p$ completion of any abstract amalgam always naturally forms a proper pro-$p$ amalgam. Within this framework, we show that bounded generation is extremely rare. Specifically, the completed group is boundedly generated if and only if one of the vertex groups completely collapses into the edge group (meaning it has an index of 1), or in the highly specific case where $p=2$ and both vertex groups have an index of exactly 2 over the edge intersection.Additionally, we develop a new set of criteria to determine when the original vertex and edge groups map into the completion without collapsing. Finally, we provide a cautionary counterexample: for any given prime $p$, we construct an amalgam whose pro-$p$ completion is boundedly generated, but its full profinite completion is not. This demonstrates that possessing bounded generation at a single prime does not guarantee that the full profinite group will share this property.

math.GR↗

arXiv2026

The Hartman--Mycielski construction in topological MV-algebras

Recently, topological MV-algebras have been investigated by several mathematicians. In this paper, we mainly show that for every Hausdorff topological MV-algebra $A$, there exists a natural topological isomorphism $i_A:A\rightarrow A^\bullet$ of $A$ onto a closed subalgebra of the pathwise connected, locally pathwise connected topological MV-algebra $A^\bullet$. Furthermore, we show that there is an extension to a bounded continuous function on the MV-algebra $A^\bullet$ for each continuous real-valued bounded function on a topological MV-algebra $A$. Finally, we prove that if $φ:A_1\rightarrow A_2$ is a continuous homomorphism of topological MV-algebras, then $φ$ admits a natural extension to a continuous homomorphism $φ^\bullet:A_1^\bullet\rightarrow A_2^\bullet$; in addition, if $φ$ is open and onto, then so is $φ^\bullet$.

math.GN↗

arXiv2026

Pseudocompact Topological $MV$-Algebras

Recently, topological MV-algebras have been investigated by several mathematicians. In this paper, we find that every topological $MV$-algebra is a Mal'tsev space introduced by Mal'tsev in 1954. Hence, applying the theorem of Reznichenko and Uspenskij on pseudocompact Mal'tsev spaces, we show that the product of arbitrary family of pseudocompact topological $MV$-algebras are pseudocompact. We also prove that every $σ$-compact topological $MV$-algebra is ccc. Secondly, we obtain that the Stone-Čech compactification of a pseudocompact topological $MV$-algebra carries a natural compact topological $MV$-algebra structure extending the original one. Finally, we prove that: let $I$ be a closed ideal in a pseudocompact topological $MV$-algebra $A$ and $ι_1:A\hookrightarrow\bet A$ is the naturally injective; then $\cl_{βA}ι_1(I)$ is a closed ideal of $βA$ and $ βA/\cl_{βA}ι_1(I)\cong β(A/I)$.

math.GN↗

arXiv2026

Filter-induced linear topologies on residuated lattices: Hausdorffness, profiniteness, and finiteness conditions

We study linear topologies on residuated lattices generated by systems of filters, with emphasis on the uniform structures and separation properties that they determine. A down-directed family of filters gives a natural compatible uniformity, and the associated topology makes the residuated lattice into a topological algebra. We characterize Hausdorffness by the triviality of the intersection of the underlying filter system. For compact topological residuated lattices, we prove the equivalence between topological profiniteness, residual finiteness, and representation as a closed subdirect product of finite discrete residuated lattices. We also analyze the descending chain condition ($DCC$) on filters. Under $DCC$, every filter system has a least element; hence every zero-dimensional linear topology is induced by a single filter, and the canonical map from filters to zero-dimensional linear topologies is bijective. This gives a corrected form of earlier representation arguments and identifies precisely where $DCC$ is required. Finally, working throughout in $\mathrm{ZFC}$, we give a sufficient criterion for the existence of non-discrete Hausdorff linear topologies, illustrated by the Gödel algebra.

math.GN↗

arXiv2026

A Reversibility Characterization of Locally Finite Groups by Cellular Automata

For cellular automata over finite alphabets, bijectivity already implies reversibility. Over infinite alphabets this implication may fail, and the remaining obstruction in the periodic case was recorded by Ceccherini-Silberstein and Coornaert as Open Problem 2 in \emph{Cellular Automata and Groups}. We prove an exact group-theoretic characterization. A group $G$ is locally finite if and only if, over every alphabet, every bijective cellular automaton $A^G\to A^G$ is reversible. Equivalently, if $G$ is not locally finite, then for every infinite alphabet $A$ there exists a bijective cellular automaton $A^G\to A^G$ whose inverse is not a cellular automaton. The counterexample is already obtained on a countable alphabet. Its local rule has a rank track, a direction track and a binary data track; the forward map is triangular along finite directed chains of arbitrary length, so its inverse is defined pointwise but has no uniform finite memory. As a consequence, Open Problem 2 has an affirmative answer, and the periodicity hypothesis is unnecessary for the negative direction.

math.GR↗

arXiv2026

Closed Image Characterizations of Locally Finite Groups via Cellular Automata

We prove that a group $G$ is locally finite if and only if, for some (equivalently, every) infinite set $A$, every cellular automaton $A^G\to A^G$ has closed image in the prodiscrete topology. Equivalently, this holds if and only if every linear cellular automaton $V^G\to V^G$ has closed image for some pair $(K,V)$ with $V$ infinite-dimensional over the field $K$ (equivalently, for every such pair). This gives affirmative answers to Open Problems 6 and 7 of Ceccherini-Silberstein and Coornaert. More precisely, if $G$ is not locally finite, then for every infinite set $A$ there is a finite-memory cellular automaton $A^G\to A^G$ with non-closed image, and for every field $K$ and every infinite-dimensional $K$-vector space $V$ there is such a linear cellular automaton $V^G\to V^G$. The common obstruction is constructed on a countable direct-sum alphabet from an infinite ray in a locally finite Cayley graph. A direct-summand argument gives arbitrary vector-space alphabets, while an alphabet-retract principle gives arbitrary infinite set alphabets.

math.GN↗

arXiv2026

Quotient homomorphisms of Topological MV-Algebras and Applications

For a topological group, the quotient map modulo a subgroup is open and the quotient map modulo a compact subgroup is perfect. In this paper we prove and develop the corresponding compact-ideal theory for topological $MV$-algebras. We show that if $I$ is an ideal of a topological $MV$-algebra $A$, then the natural quotient homomorphism $q:A\longrightarrow A/I$, where $A/I$ is endowed with the quotient topology, is a continuous open quotient map and $A/I$ is again a topological $MV$-algebra. If, in addition, $I$ is compact, then $q$ is perfect. As applications, we study three-space phenomena in topological $MV$-algebras. Under compact-kernel hypotheses we prove three-space theorems for compactness, local compactness, $σ$-compactness, Lindelöfness and paracompactness under the separation hypotheses stated below. We also prove a first-countability three-space theorem for locally convex topological $MV$-algebras.

math.GN↗

arXiv2026

Ultrafilter Equivalence and Asymptotic Types of Five Classical t-Norms

We study five classical $t$-norms on the unit interval from the viewpoint of ultrafilter concentration. For a fixed ultrafilter $\mathcal U$ on $[0,1]$, we introduce an equivalence relation identifying two operations whenever they coincide on $A\times A$ for some $A\in\mathcal U$. We show that their asymptotic behavior is governed by two concentration regimes. In the near-$1$ regime, the five operations determine four distinct ultrafilter-equivalence classes. In the low-value regime, the Łukasiewicz, nilpotent minimum, and drastic $t$-norms collapse to the zero operation. We encode these reductions in a discrete quotient category and record simple ultrametric models for the two regimes. We further interpret the classification inside classical ultrapowers: the near-$1$ and near-$0$ regimes become exact algebraic phenomena on infinitesimal monads, and saturation yields a compactness principle for countable systems of asymptotic identities. Finally, we indicate how the same viewpoint interacts with residual fuzzy implications generated by $t$-norms.

math.GN↗

arXiv2026

Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities

In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to Multilayer Perceptron. Many different function representations have already been tried, but we show that Sinc interpolation proposes a viable alternative, since it is known in numerical analysis to effectively represent both smooth functions and functions with singularities. This is important not only for function approximation but also for solving the partial differential equations with physics-informed neural networks. Through a series of experiments, we show that SincKANs provide better results in almost all of the examples we have considered.

cs.LG↗

arXiv2026

A second-order product-type implicit-explicit Runge-Kutta method preserving unit length and energy dissipation structures for gradient flows of vector fields

Gradient flows of unit vector fields arise in a wide range of physical models such as harmonic map heat flows, nematic liquid crystals, and magnetization dynamics. Designing numerical schemes that simultaneously preserve the unit length constraint and dissipate energy is essential for reliable simulations of such systems. Although projection methods can effectively enforce the unit length constraint, ensuring energy dissipation under projection, especially in high-order schemes, remains challenging. Unlike traditional implicit-explicit Runge-Kutta (IMEX-RK) methods, in this work we propose a general methodology for constructing product-type IMEX-RK schemes that offers greater adaptability to various models with the goal of designing structure-preserving numerical schemes. For gradient flows of unit vector fields with Dirichlet energy, we design a linear and second-order numerical scheme that simultaneously preserves energy dissipation and the unit length constraint by using product-type IMEX-RK methods and projection techniques. Numerical experiments verify the accuracy, stability, and structure-preserving properties of the scheme. According to our best knowledge, this is the first second-order linear scheme that can preserve both the unit length and the original Dirichlet energy for harmonic map heat flows.

math.NA↗