数学最新文献

{"title":"Incompleteness of the Ewald–Shephard space of asymmetry classes","authors":"Dong Qiu,&nbsp;Yixia Wu,&nbsp;Xingyu Zhang","doi":"10.1112/mtk.70134","DOIUrl":"https://doi.org/10.1112/mtk.70134","url":null,"abstract":"<p>This paper answers a long-standing open problem concerning the completeness of the metric space of asymmetry classes introduced by Ewald and Shephard (1966). We prove that this metric space is <i>incomplete</i> for <span></span><math></math>. Our approach reveals that the Ewald–Shephard metric <span></span><math></math> is equivalent to a quotient metric on a certain function space of odd continuous functions modulo linear functions, and that the Lipschitz regularity of odd parts of support functions constitutes an essential obstruction to completeness. We explicitly construct a Cauchy sequence of asymmetry classes whose limit cannot be represented by any compact convex body, thereby rigorously establishing the incompleteness of the space.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gibbons–Tsarev Type Systems and Eventual Identities","authors":"Alessandro Arsie,&nbsp;Paolo Lorenzoni,&nbsp;Sara Perletti,&nbsp;Karoline van Gemst","doi":"10.1111/sapm.70321","DOIUrl":"https://doi.org/10.1111/sapm.70321","url":null,"abstract":"<p>We show that non-diagonalizable reductions of the dKP equation associated with regular non-semisimple <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifolds cannot exist. The proof is based on the derivation and study of a generalized Gibbons–Tsarev system (gGT system) in the non-semisimple/non-diagonalizable setting. Remarkably, a class of solutions of the gGT system is defined by eventual identities of the underlying regular <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifold structure. Furthermore, we use these vector fields to construct integrable reductions of Pavlov's hydrodynamic chain. In this case, the corresponding solutions are defined for any choice of Jordan block structure of the operator of multiplication by an eventual identity.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conformable Logistic Dynamic Equations on Timescales","authors":"Mahammad Khuddush,&nbsp;Svetlin G. Georgiev","doi":"10.1111/sapm.70322","DOIUrl":"https://doi.org/10.1111/sapm.70322","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we study an autonomous conformable logistic dynamic equation in proportional conformable calculus on timescales. A reciprocal transformation reduces the nonlinear problem to a mixed first-order conformable equation and yields an exact representation, including the constant-coefficient solution with effective carrying capacity &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$K_{alpha }=k(1-kappa _1/r)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Under the positivity condition &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {D}_{alpha }(t)=kappa _0+mu (t)(r-kappa _1)&gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, positive solutions are global and forward invariant. According to the relation between &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$kappa _1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, solutions converge to a positive equilibrium, exhibit algebraic extinction in the critical case, or decay exponentially. For the standard proportional choice, the critical order is &lt;span&gt;&lt;/span&gt;&lt;ma","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Paley–Wiener-Type Theorems for the Quaternion Dunkl Transform","authors":"Shanshan Li,&nbsp;Minggang Fei","doi":"10.1007/s00006-026-01466-2","DOIUrl":"10.1007/s00006-026-01466-2","url":null,"abstract":"<div><p>The aim of this paper is to establish several versions of Paley–Wiener-type theorems for the two-sided quaternion Dunkl transform (QDT) in <span>(mathbb {R}^2)</span>. This transform combines the non-commutative structure of quaternions with the reflection symmetry and weighted analysis inherent in Dunkl theory.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Heegaard Floer slice genus and clasp number bounds","authors":"András Juhász,Ian Zemke","doi":"10.4171/qt/268","DOIUrl":"https://doi.org/10.4171/qt/268","url":null,"abstract":"We define several concordance invariants using knot Floer homology, which give improvements over known slice genus and clasp number bounds from Heegaard Floer homology. We also prove that the involutive correction terms of Hendricks and Manolescu give both a slice genus and a clasp number bound.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact Response to Perturbations and Dynamical Indicators in a Tumor-Growth Model","authors":"T. M. C. Priyanka,&nbsp;A. Gowrisankar,&nbsp;Lamberto Rondoni","doi":"10.1111/sapm.70323","DOIUrl":"https://doi.org/10.1111/sapm.70323","url":null,"abstract":"<div>\u0000 \u0000 <p>We formulate a three-dimensional tumor–immune model obtained by adding to an established tumor–host–effector system two phenomenological perturbation terms, whose signs are motivated by the reported tumor-promoting and effector-suppressing influence of regulatory B cells; their coefficients are dynamical control parameters and are not calibrated to biological rates. The perturbed and unperturbed dynamics are compared using phase portraits, Lyapunov exponents, parameter sensitivity, and multifractal indicators. Because trajectory-wise prediction is intrinsically limited in chaotic regimes and initial cell populations are only partially known, we also extend exact response theory, originally developed in nonequilibrium molecular dynamics, to the relevant non-compact positive set of populations values. Admissible initial densities are introduced to control boundary terms and ensure the validity of the exact response identity for finite-time ensemble averages. The resulting formulation quantifies both instantaneous and cumulative changes in tumor, host, and effector-cell observables under finite parameter perturbations, without requiring a small-perturbation approximation. Numerical tests verify the response identity against direct Monte Carlo propagation and assess sampling and time-discretization errors. For the parameter ranges studied, the perturbations can move the model between periodic and chaotic regimes, while ensemble averages remain considerably smoother than individual trajectories, and are capable of significant predictions. Long-time averaged responses are consistent across three admissible initial ensembles, although instantaneous dispersion can remain substantial. The analysis therefore separates attractor geometry from finite-time statistical response and provides a mathematically controlled framework for uncertainty-aware comparison of tumor-growth models, especially relevant in the potentially most interesting transients. The biological interpretation remains qualitative: The perturbation coefficients are not clinically calibrated rates, and any correspondence with regulatory B-cell biology requires independent experimental validation.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"J-Einstein critical metrics for quadratic curvature functionals","authors":"Xiaomin Chen,&nbsp;Halyson Baltazar","doi":"10.1007/s10455-026-10064-1","DOIUrl":"10.1007/s10455-026-10064-1","url":null,"abstract":"<div><p>Lin-Yuan introduced the concept of the <i>J</i>-Einstein metric, which is a generalization of Bach-flat metric on 4-dimensional manifolds. In this article, we study the <i>J</i>-Einstein metrics as the critical point of quadratic curvature functionals involving the Ricci curvature and scalar curvature. We get some interesting results, which can be viewed as the improvement of Sheng-Wang’s conclusions on Bach-flat critical metrics (Bach-flat critical metrics for quadratic curvature functionals, <i>Ann. Glob. Anal. Geom.</i> 2018).</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Real Heegaard Floer Homology","authors":"Gary Guth,Ciprian Manolescu","doi":"10.1007/s00039-026-00754-0","DOIUrl":"https://doi.org/10.1007/s00039-026-00754-0","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"68 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A longitudinal Bayesian framework for estimating causal dose-response relationships.","authors":"Yu Luo, Kuan Liu, Ramandeep Singh, Daniel J Graham","doi":"10.1515/ijb-2026-0010","DOIUrl":"https://doi.org/10.1515/ijb-2026-0010","url":null,"abstract":"<p><p>Existing causal methods for time-varying exposure and time-varying confounding focus on estimating the average causal effect of a time-varying binary treatment on an end-of-study outcome, offering limited tools for characterizing marginal causal dose-response relationships under continuous exposures. We propose a scalable, nonparametric Bayesian framework for estimating marginal longitudinal causal dose-response functions with repeated outcome measurements. Our approach targets the average potential outcome at any fixed dose level and accommodates time-varying confounding through the generalized propensity score. The proposed approach embeds a Dirichlet process specification within a generalized estimating equations structure, capturing temporal correlation while making minimal assumptions about the functional form of the continuous exposure. We apply the proposed methods to monthly metro ridership and COVID-19 case data from major international cities, identifying causal relationships and the dose-response patterns between higher ridership and increased case counts.</p>","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149167406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust Estimation and Inference for Time-Varying Unconditional Volatility","authors":"Adam Lee,&nbsp;Rickard Sandberg,&nbsp;Genaro Sucarrat","doi":"10.1111/jtsa.70034","DOIUrl":"https://doi.org/10.1111/jtsa.70034","url":null,"abstract":"<p>We derive a general and robust estimator of a large class of parametric specifications of time-varying unconditional volatility of financial returns, both univariate and multivariate, and establish the Consistency and Asymptotic Normality (CAN) of the estimator. A number of well-known and widely used parametric specifications, for many of which asymptotic results have not been specifically established, are contained in the class. The estimator is robust in the sense that the exact specification of the conditional volatility dynamics need not be known or estimated, and in the sense that the stochastic component need not be strictly stationary. The latter is especially important in light of recent findings, which document that financial returns are frequently characterised by a non-stationary zero-process. Our estimator is also robust to the well-known “curse of dimensionality” in multivariate models due to its equation-by-equation nature. While our estimator does not require the exact specification of the conditional volatility dynamics to be known or estimated, our results imply that the scaled GARCH(1,1) specification is well-defined under both correct and incorrect specifications. So we provide methods for its estimation in a second step. Also, due to the assumptions we rely upon, our results extend directly to the Multiplicative Error Model (MEM) interpretation of volatility models. This means our results can also be applied to other non-negative processes like volume, duration, realised volatility, dividends, unemployment, and so on. Three numerical applications illustrate the versatility of our results.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 6","pages":"1139-1152"},"PeriodicalIF":1.2,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}