Pub Date : 2026-01-15DOI: 10.1016/j.amc.2026.129954
Kaiyu Wang , Dan Ye
This paper investigates the problem of sensor attack detection and identification in cyber-physical systems, leveraging the advantage of zonotopes in dealing with stochastic properties. Unlike previous research that relies on system dynamics knowledge to infer safety boundaries and monitoring schemes, the proposed approach is geared toward addressing the challenges posed by unknown system dynamics, attack strategies, and attack locations. Firstly, we analyze the feasibility of using zonotopes for attack detection and deduce the necessary information quantity and observation window length requirement for effective detection. Subsequently, a zonotopes-based algorithm is proposed for computing the over-approximated reachable set and measurement set from noisy data. Then, an attack detection and identification strategy based on the predicted measurement set is developed. To reduce the computational complexity of the presented detection method, a column truncation algorithm is proposed. The effectiveness of the proposed method is validated through numerical simulations.
{"title":"Sensor attack detection and identification for cyber-physical systems: A data-driven approach","authors":"Kaiyu Wang , Dan Ye","doi":"10.1016/j.amc.2026.129954","DOIUrl":"10.1016/j.amc.2026.129954","url":null,"abstract":"<div><div>This paper investigates the problem of sensor attack detection and identification in cyber-physical systems, leveraging the advantage of zonotopes in dealing with stochastic properties. Unlike previous research that relies on system dynamics knowledge to infer safety boundaries and monitoring schemes, the proposed approach is geared toward addressing the challenges posed by unknown system dynamics, attack strategies, and attack locations. Firstly, we analyze the feasibility of using zonotopes for attack detection and deduce the necessary information quantity and observation window length requirement for effective detection. Subsequently, a zonotopes-based algorithm is proposed for computing the over-approximated reachable set and measurement set from noisy data. Then, an attack detection and identification strategy based on the predicted measurement set is developed. To reduce the computational complexity of the presented detection method, a column truncation algorithm is proposed. The effectiveness of the proposed method is validated through numerical simulations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"520 ","pages":"Article 129954"},"PeriodicalIF":3.4,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980863","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmva.2026.105605
Yuliang Bai, Niansheng Tang
Feature screening method is an important tool for screening active features in ultrahigh dimensional data analysis. Existing feature screening methods mainly focus on the fully observed data or missing responses at random. But in many applied fields such as biomedicine, social science and epidemiological studies, responses might be subject to nonignorable missingness due to various reasons such as dropout. To this end, this paper proposes a new adjusted Spearman rank correlation to screen active features by incorporating the Spearman rank correlation and its conditional expectation in the presence of nonignorable missing responses. To circumvent the notorious identification problem, we introduce instrumental variables into the propensity score (PS) function, which is specified by a more general semiparametric regression model. A nonparametric imputation method is developed to estimate the adjusted Spearman rank correlation. The proposed method has several desirable merits. First, it is model-free. Second, it is robust to outliers, heavy tailed data and the misspecification of the PS function. Third, under some weaker regularity conditions than existing missing data literature, it has sure screening property and ranking consistency, and can well control the false discovery rate regardless of known or consistently estimated parameters in the PS function. Simulation studies and two real examples are used to investigate the performance of the proposed methodologies.
{"title":"Model-free feature screening for ultrahigh dimensional data with responses missing not at random","authors":"Yuliang Bai, Niansheng Tang","doi":"10.1016/j.jmva.2026.105605","DOIUrl":"10.1016/j.jmva.2026.105605","url":null,"abstract":"<div><div>Feature screening method is an important tool for screening active features in ultrahigh dimensional data analysis. Existing feature screening methods mainly focus on the fully observed data or missing responses at random. But in many applied fields such as biomedicine, social science and epidemiological studies, responses might be subject to nonignorable missingness due to various reasons such as dropout. To this end, this paper proposes a new adjusted Spearman rank correlation to screen active features by incorporating the Spearman rank correlation and its conditional expectation in the presence of nonignorable missing responses. To circumvent the notorious identification problem, we introduce instrumental variables into the propensity score (PS) function, which is specified by a more general semiparametric regression model. A nonparametric imputation method is developed to estimate the adjusted Spearman rank correlation. The proposed method has several desirable merits. First, it is model-free. Second, it is robust to outliers, heavy tailed data and the misspecification of the PS function. Third, under some weaker regularity conditions than existing missing data literature, it has sure screening property and ranking consistency, and can well control the false discovery rate regardless of known or consistently estimated parameters in the PS function. Simulation studies and two real examples are used to investigate the performance of the proposed methodologies.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"213 ","pages":"Article 105605"},"PeriodicalIF":1.4,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977542","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}
Pub Date : 2026-01-15DOI: 10.1134/S1234567825040044
Stepan Orevkov
A rational function on a real algebraic curve (C) is called separating if it takes real values only at real points. Such a function defines a covering (mathbb R Ctomathbb{RP}^1). Let (c_1,dots,c_r) be the connected components of (mathbb R C). M. Kummer and K. Shaw defined the separating semigroup of (C) as the set of all sequences ((d_1(f),dots,d_r(f))) where (f) is a separating function, and (d_i(f)) is the degree of the restriction of (f) to (c_i).
In the present paper, we describe the separating semigroups of all genus 4 curves. For the proofs, we consider the canonical embedding of (C) into a quadric (X) in (mathbb P^3), and apply Abel’s theorem to 1-forms on (C) obtained as Poincaré residues of certain meromorphic 2-forms.
在实代数曲线(C)上的有理函数，如果只在实点取实值，则称为分离函数。这样的函数定义了一个覆盖(mathbb R Ctomathbb{RP}^1)。设(c_1,dots,c_r)为(mathbb R C)的连接组件。M. Kummer和K. Shaw将(C)的分离半群定义为所有序列的集合((d_1(f),dots,d_r(f)))，其中(f)为分离函数，(d_i(f))为(f)对(c_i)的限制程度。在本文中，我们描述了所有4属曲线的分离半群。对于证明，我们考虑(C)的正则嵌入到(mathbb P^3)上的二次曲面(X)中，并将Abel定理应用到(C)上的1-形中，得到若干亚纯2-形的poincar残。
{"title":"Separating Semigroup of Genus 4 Curves","authors":"Stepan Orevkov","doi":"10.1134/S1234567825040044","DOIUrl":"10.1134/S1234567825040044","url":null,"abstract":"<p> A rational function on a real algebraic curve <span>(C)</span> is called separating if it takes real values only at real points. Such a function defines a covering <span>(mathbb R Ctomathbb{RP}^1)</span>. Let <span>(c_1,dots,c_r)</span> be the connected components of <span>(mathbb R C)</span>. M. Kummer and K. Shaw defined the separating semigroup of <span>(C)</span> as the set of all sequences <span>((d_1(f),dots,d_r(f)))</span> where <span>(f)</span> is a separating function, and <span>(d_i(f))</span> is the degree of the restriction of <span>(f)</span> to <span>(c_i)</span>. </p><p> In the present paper, we describe the separating semigroups of all genus 4 curves. For the proofs, we consider the canonical embedding of <span>(C)</span> into a quadric <span>(X)</span> in <span>(mathbb P^3)</span>, and apply Abel’s theorem to 1-forms on <span>(C)</span> obtained as Poincaré residues of certain meromorphic 2-forms. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 4","pages":"421 - 429"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145963680","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}
Pub Date : 2026-01-15DOI: 10.1134/S1234567825040019
Anastasia Vikulova
We construct an example of a field and a smooth del Pezzo surface of degree (2) over this field without points such that its automorphism group is isomorphic to (mathrm{PSL}_2(mathbb{F}_7) times mathbb{Z}/2mathbb{Z}), which is the largest possible automorphism group for del Pezzo surfaces of degree (2) over an algebraically closed field of characteristic zero.
我们构造了一个域和该域上阶为(2)的光滑del Pezzo曲面的例子，使其自同构群与(mathrm{PSL}_2(mathbb{F}_7) times mathbb{Z}/2mathbb{Z})同构，这是特征为零的代数闭域上阶为(2)的del Pezzo曲面的最大可能自同构群。
{"title":"The Largest Automorphism Group of a Del Pezzo Surface of Degree (2) without Points","authors":"Anastasia Vikulova","doi":"10.1134/S1234567825040019","DOIUrl":"10.1134/S1234567825040019","url":null,"abstract":"<p> We construct an example of a field and a smooth del Pezzo surface of degree <span>(2)</span> over this field without points such that its automorphism group is isomorphic to <span>(mathrm{PSL}_2(mathbb{F}_7) times mathbb{Z}/2mathbb{Z})</span>, which is the largest possible automorphism group for del Pezzo surfaces of degree <span>(2)</span> over an algebraically closed field of characteristic zero. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 4","pages":"391 - 397"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145963737","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}
Pub Date : 2026-01-15DOI: 10.1016/j.spl.2026.110655
Pritam Sarkar , Soumi Thakur Chakraborty , Ayan Pal
We investigate the conditions of infinite divisibility of the Exponentiated Pareto (EP) distribution supported on the entire positive half-line , along with its discrete analogue defined on the set of non-negative integers. The EP distribution is defined via the cumulative distribution function (CDF) , where and , is the CDF of Pareto Type II (Lomax) distribution with tail parameter The discrete counterpart is defined as the integer part of a random variable following the EP distribution. The main results assert that both the continuous and discrete versions of the EP distribution are infinitely divisible if A brief discussion of the Lévy process corresponding to the infinitely divisible case for is provided along with a real world data illustration.
研究了整条正半线上（0,∞）支持的幂Pareto （EP）分布的无限可除性条件，以及它在非负整数集上定义的离散模拟。EP分布通过累积分布函数（CDF） [F(x)]α来定义，其中α>；0， F(x)=1−(1+x)−λ,x>；0为尾部参数为λ>；0的Pareto Type II （Lomax）分布的CDF。离散对应项定义为随机变量X遵循EP分布的整数部分。主要结果表明，如果α∈(0,1)，EP分布的连续和离散版本都是无限可分的。简要讨论了与α∈(0,1)无限可除情况相对应的lsamvy过程，并给出了一个真实世界的数据说明。
{"title":"When is an Exponentiated Pareto distribution infinitely divisible?","authors":"Pritam Sarkar , Soumi Thakur Chakraborty , Ayan Pal","doi":"10.1016/j.spl.2026.110655","DOIUrl":"10.1016/j.spl.2026.110655","url":null,"abstract":"<div><div>We investigate the conditions of infinite divisibility of the Exponentiated Pareto (EP) distribution supported on the entire positive half-line <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span>, along with its discrete analogue defined on the set of non-negative integers. The EP distribution is defined via the cumulative distribution function (CDF) <span><math><msup><mrow><mrow><mo>[</mo><mi>F</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>]</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup></math></span> , where <span><math><mrow><mi>α</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mo>−</mo><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup><mo>,</mo><mi>x</mi><mo>></mo><mn>0</mn></mrow></math></span>, is the CDF of Pareto Type II (Lomax) distribution with tail parameter <span><math><mrow><mi>λ</mi><mo>></mo><mn>0</mn><mo>.</mo></mrow></math></span> The discrete counterpart is defined as the integer part of a random variable <span><math><mi>X</mi></math></span> following the EP distribution. The main results assert that both the continuous and discrete versions of the EP distribution are infinitely divisible if <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>.</mo></mrow></math></span> A brief discussion of the Lévy process corresponding to the infinitely divisible case for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> is provided along with a real world data illustration.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110655"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979445","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}
Pub Date : 2026-01-15DOI: 10.1016/j.chaos.2026.117928
Miguel Moreno , Alexandre R. Nieto , Miguel A.F. Sanjuán
The Rulkov model, which simulates the behavior of biological neurons, is modified by replacing one of its control parameters with a memristive, sigmoid-type function of finite memory. This modification causes the parameter to vary according to the system’s history throughout the simulation. Previous works usually modify the Rulkov model by introducing additional parameters altering its behavior. Here, by contrast, we retain the original equations and allow the control parameters to vary in time, thereby preserving the model’s fundamental properties. In this sense, the proposed model is locally equivalent in time to the original one. However, unlike the original model, which reproduces a single neuronal regime per simulation, the new memristive version exhibits both uniform and chaotic transitions among multiple neuronal activity regimes. Its dynamics are examined with respect to the rate at which the memristive function changes and the number of internal states it stores. Three distinct scenarios emerge around a bifurcation point. Before the bifurcation, the system undergoes uniform transitions toward a stable bursting regime. After the bifurcation, it shows uniform transitions toward a final spiking or silent regime. At the bifurcation point, highly complex transitions arise. As examples, we present trajectories in which the neuron chaotically switches between regimes without ever settling, and trajectories for which it requires around 140000 map iterations to reach a stationary regime.
{"title":"Complex transitions between spiking, bursting and silent regimes in a new memristive Rulkov neuronal model","authors":"Miguel Moreno , Alexandre R. Nieto , Miguel A.F. Sanjuán","doi":"10.1016/j.chaos.2026.117928","DOIUrl":"10.1016/j.chaos.2026.117928","url":null,"abstract":"<div><div>The Rulkov model, which simulates the behavior of biological neurons, is modified by replacing one of its control parameters with a memristive, sigmoid-type function of finite memory. This modification causes the parameter to vary according to the system’s history throughout the simulation. Previous works usually modify the Rulkov model by introducing additional parameters altering its behavior. Here, by contrast, we retain the original equations and allow the control parameters to vary in time, thereby preserving the model’s fundamental properties. In this sense, the proposed model is locally equivalent in time to the original one. However, unlike the original model, which reproduces a single neuronal regime per simulation, the new memristive version exhibits both uniform and chaotic transitions among multiple neuronal activity regimes. Its dynamics are examined with respect to the rate at which the memristive function changes and the number of internal states it stores. Three distinct scenarios emerge around a bifurcation point. Before the bifurcation, the system undergoes uniform transitions toward a stable bursting regime. After the bifurcation, it shows uniform transitions toward a final spiking or silent regime. At the bifurcation point, highly complex transitions arise. As examples, we present trajectories in which the neuron chaotically switches between regimes without ever settling, and trajectories for which it requires around 140000 map iterations to reach a stationary regime.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117928"},"PeriodicalIF":5.6,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976351","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}
Pub Date : 2026-01-15DOI: 10.1016/j.aam.2026.103041
Lili Mu , Volkmar Welker
For a polynomial with positive integer coefficients Bell and Skandera (2007) [2] ask if real-rootedness of implies that there is a simplicial complex with f-vector or equivalently a simplicial complex with f-polynomial . In this paper we discover properties implied by the real-rootedness of in terms of the binomial representation , . We use these to partially answer the question by Bell and Skandera. We also describe two further approaches to the question and use one to verify that some well studied real-rooted classical polynomials are f-polynomials.
Finally, we provide a series of results showing that the set of f-vectors of simplicial complexes is closed under constructions also preserving real-rootedness of their generating polynomials.
对于系数为正整数的多项式f(t)=1+f0t+⋯+fd−1td, Bell and Skandera(2007)[2]，问f(t)的实数性是否意味着存在一个具有f-向量（1,f0，…，fd−1）的简单复形，或者等价地具有f-多项式f(t)的简单复形。本文发现了f(t)在二项表示形式fi=(xi+1i+1)， i≥0下的实数根所蕴涵的性质。我们用这些来部分回答Bell和Skandera提出的问题。我们还描述了两种进一步的方法来解决这个问题，并使用一种方法来验证一些研究得很好的实根经典多项式是f多项式。最后，我们给出了一系列结果，证明了简单复形的f向量集在构造下是封闭的，并且保持了它们的生成多项式的实根性。
{"title":"On a question about real-rooted polynomials and f-polynomials of simplicial complexes","authors":"Lili Mu , Volkmar Welker","doi":"10.1016/j.aam.2026.103041","DOIUrl":"10.1016/j.aam.2026.103041","url":null,"abstract":"<div><div>For a polynomial <span><math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>t</mi><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msub><msup><mrow><mi>t</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with positive integer coefficients Bell and Skandera (2007) <span><span>[2]</span></span> ask if real-rootedness of <span><math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> implies that there is a simplicial complex with <em>f</em>-vector <span><math><mo>(</mo><mn>1</mn><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo></math></span> or equivalently a simplicial complex with <em>f</em>-polynomial <span><math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. In this paper we discover properties implied by the real-rootedness of <span><math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> in terms of the binomial representation <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mrow><mo>(</mo><mtable><mtr><mtd><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mtd></mtr></mtable><mo>)</mo></mrow></math></span>, <span><math><mi>i</mi><mo>≥</mo><mn>0</mn></math></span>. We use these to partially answer the question by Bell and Skandera. We also describe two further approaches to the question and use one to verify that some well studied real-rooted classical polynomials are <em>f</em>-polynomials.</div><div>Finally, we provide a series of results showing that the set of <em>f</em>-vectors of simplicial complexes is closed under constructions also preserving real-rootedness of their generating polynomials.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"175 ","pages":"Article 103041"},"PeriodicalIF":1.3,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981043","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}
Pub Date : 2026-01-15DOI: 10.1016/j.aam.2026.103044
Foster Tom
We prove that a graph with a cut vertex whose deletion produces at least five connected components must be missing a connected partition of some type. We prove that this also holds if there are four connected components that each have at least two vertices. In particular, the chromatic symmetric function of such a graph cannot be e-positive. This brings us very close to the conjecture by Dahlberg, She, and van Willigenburg of non-e-positivity for all trees with a vertex of degree at least four. We also prove that spiders with four legs cannot have an e-positive chromatic symmetric function.
{"title":"Graphs missing a connected partition","authors":"Foster Tom","doi":"10.1016/j.aam.2026.103044","DOIUrl":"10.1016/j.aam.2026.103044","url":null,"abstract":"<div><div>We prove that a graph with a cut vertex whose deletion produces at least five connected components must be missing a connected partition of some type. We prove that this also holds if there are four connected components that each have at least two vertices. In particular, the chromatic symmetric function of such a graph cannot be <em>e</em>-positive. This brings us very close to the conjecture by Dahlberg, She, and van Willigenburg of non-<em>e</em>-positivity for all trees with a vertex of degree at least four. We also prove that spiders with four legs cannot have an <em>e</em>-positive chromatic symmetric function.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"175 ","pages":"Article 103044"},"PeriodicalIF":1.3,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981044","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}
Pub Date : 2026-01-15DOI: 10.1007/s10440-026-00768-8
Mustafa Avci
In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.
{"title":"Monotone Operator Methods for a Class of Nonlocal Multi-Phase Variable Exponent Problems","authors":"Mustafa Avci","doi":"10.1007/s10440-026-00768-8","DOIUrl":"10.1007/s10440-026-00768-8","url":null,"abstract":"<div><p>In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"201 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145983379","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}
Pub Date : 2026-01-15DOI: 10.1134/S1234567825040068
Yuri Prokhorov
We investigate birational properties of hypersurfaces of degree (6) in the weighted projective space (mathbb{P}(1,1,2,2,3)). In particular, we prove that any such quasi-smooth hypersurface is not rational.
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