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On the large time asymptotics of Schrödinger type equations with general data 一般数据下Schrödinger型方程的大时间渐近性

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-14 DOI: 10.1016/j.aim.2025.110774

Avy Soffer , Xiaoxu Wu

For the Schrödinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global solutions are asymptotically given by the sum of a free wave and a weakly localized part. The proof is based on constructing in an adapted way the Free Channel Wave Operator, and further tools from the recent works [21], [22], [35]. This work generalizes the results of the first part of [21], [22] to arbitrary dimension, and non-radial data.

对于具有一般相互作用项的Schrödinger方程，它可以是线性的，也可以是非线性的，时间相关的，并包含电荷转移势，我们证明了它的整体解是由自由波和弱局域部分的和渐近给出的。该证明是基于以一种适应的方式构造自由通道波算子，以及来自最近工作[21]，[22]，[35]的进一步工具。本工作将[21]、[22]第一部分的结果推广到任意维度和非径向数据。

引用次数: 0

Correction: "Distinguishing Phylogenetic Level-2 Networks with Quartets and Inter-Taxon Quartet Distances". 更正：“用四重奏和分类群间四重奏距离区分系统发育二级网络”。

IF 2.2 4区数学 Q2 BIOLOGY

Bulletin of Mathematical Biology

Pub Date : 2026-01-14 DOI: 10.1007/s11538-025-01564-5

Niels Holtgrefe, Elizabeth S Allman, Hector Baños, Leo van Iersel, Vincent Moulton, John A Rhodes, Kristina Wicke

引用次数: 0

Low-regularity global solution of the inhomogeneous nonlinear Schrödinger equations in modulation spaces 调制空间中非齐次非线性Schrödinger方程的低正则全局解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-14 DOI: 10.1016/j.jde.2026.114106

Divyang G. Bhimani , Diksha Dhingra , Vijay Kumar Sohani

The study of low regularity Cauchy data for nonlinear dispersive PDEs has been successfully achieved using modulation spaces in recent years. In this paper, we study the inhomogeneous nonlinear Schrödinger equation (INLS)

i u_{t} + Δ u \pm | x |^{- b} | u |^{α} u = 0 (b, α > 0)

on the whole space

R^{n}

having initial data in modulation spaces. In the subcritical regime

(0 < α < \frac{4 - 2 b}{n})

, we establish local well-posedness in

L^{2} + M^{α + 2, \frac{α + 2}{α + 1}} (\supset L^{2} + H^{s} for s > \frac{n α}{2 (α + 2)})

. By adapting Bourgain's high-low decomposition method, we establish global well-posedness in

M^{p, \frac{p}{p - 1}}

with

2 < p

and p sufficiently close to 2. This is the first global well-posedness result for INLS in modulation spaces, which contains certain Sobolev

H^{s}

(0 < s < 1)

and

L_{s}^{p} -

Sobolev spaces.

近年来，利用调制空间成功地研究了非线性色散偏微分方程的低正则性柯西数据。本文研究了调制空间中具有初始数据的整个空间Rn上的非齐次非线性Schrödinger方程（INLS）iut+Δu±|x| - b|u|αu=0（b,α>0）。在亚临界区（0<α<；4−20亿），我们建立了L2+Mα+2，α+2α+1（、L2+Hsfors>nα2(α+2)）的局部适定性。通过采用Bourgain的高低分解方法，我们建立了Mp，pp−1中2<；p和p充分接近2的全局适定性。这是包含一定Sobolev Hs （0<s<1）和Lsp−Sobolev空间的调制空间中INLS的第一个全局适定性结果。

引用次数: 0

Voting profiles admitting all candidates as knockout winners 投票资料显示所有候选人都是淘汰赛赢家

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-14 DOI: 10.1016/j.dam.2025.12.068

Bernard De Baets , Emilio De Santis

A set of

2^{n}

candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next round until the

n

th round (the final one) in which the final winner is declared. The candidates are arranged on a board in a given order, which is maintained among the remaining candidates at all rounds. A study of the size of the commission is carried out in order to obtain the desired result of any candidate being a possible winner. For

2^{n}

candidates with

n \geq 3

, we identify a voting profile with

4 n - 3

voters such that any candidate could win simply by choosing a proper initial order of the candidates. Moreover, in the setting of a random number of voters, we obtain the same results, with high probability, when the expected number of voters is large.

一组2n名候选人被提交给委员会。在每一轮比赛中，该委员会的每个成员都以两两比较的方式投票，一半的候选人被淘汰出局，剩下的人进入下一轮比赛，直到第n轮（最后一轮）宣布最终获胜者。候选人按照给定的顺序排列在棋盘上，在所有回合中都保留在剩余的候选人中。对委员会的规模进行研究，以获得任何候选人可能获胜的预期结果。对于n≥3的2n个候选人，我们确定了一个有4n−3个选民的投票配置文件，这样任何候选人都可以通过选择合适的候选人初始顺序来获胜。此外，在选民人数随机的情况下，当期望选民人数较大时，我们得到的结果是相同的，而且概率很大。

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引用次数: 0

A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary 具有navier -滑移边界的无穷长管道中Leray问题的一个改进唯一性结果

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-14 DOI: 10.1016/j.jde.2026.114108

Zijin Li , Ning Liu , Taoran Zhou

We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe

D = Σ \times R

. We show that if the flux Φ of the solution is no larger than a critical value that is independent with the friction ratio of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio

α \in] 0, \infty]

, and it is surprising since the prescribed uniqueness breaks down immediately when

α = 0

, even if

Φ = 0

Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux

Φ_{0} \geq \frac{π}{16}

provided that Σ is a unit disk.

考虑无限管D=Σ×R中具有Navier-slip边界条件的广义Leray问题。我们证明，如果解的通量Φ不大于与纳维-滑移边界条件的摩擦比无关的临界值，则问题的解必须是具有给定通量的平行泊泽维尔流。与已知的相关三维结果相比，这似乎是第一个临界通量大小随摩擦比α∈]0，∞而均匀的结论，令人惊讶的是，当α=0时，即使Φ=0，规定的唯一性也会立即失效。我们的证明主要依赖于在纳维滑动边界条件下对泊泽维尔流的精细梯度估计。另外，在Σ为单位圆盘的条件下，证明了临界通量Φ0≥π16。

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引用次数: 0

Availability of Charged tRNAs Drives Maximal Protein Synthesis at Intermediate Levels of Codon Usage Bias. 在密码子使用偏倚的中间水平上，带电trna的可用性驱动最大蛋白合成。

IF 2.2 4区数学 Q2 BIOLOGY

Bulletin of Mathematical Biology

Pub Date : 2026-01-14 DOI: 10.1007/s11538-025-01587-y

Alexis M Hill, Kelly To, Claus O Wilke

Synonymous codon usage can influence protein expression, since codons with high numbers of corresponding tRNAs are naturally translated more rapidly than codons with fewer corresponding tRNAs. Although translation efficiency ultimately depends on the concentration of aminoacylated (charged) tRNAs, many theoretical models of translation have ignored tRNA dynamics and treated charged tRNAs as fixed resources. This simplification potentially limits these models from making accurate predictions in situations where charged tRNAs become limiting. Here, we derive a mathematical model of translation with explicit tRNA dynamics and tRNA re-charging, based on a stochastic simulation of this system that was previously applied to investigate codon usage in the context of gene overexpression. We use the mathematical model to systematically explore the relationship between codon usage and the protein expression rate, and find that in the regime where tRNA charging is a limiting reaction, it is always optimal to match codon frequencies to the tRNA pool. Conversely, when tRNA charging is not limiting, using 100% of the preferred codon is optimal for protein production. We also use the tRNA dynamics model to augment a whole-cell simulation of bacteriophage T7. Using this model, we demonstrate that the high expression rate of the T7 major capsid gene causes rare charged tRNAs to become entirely depleted, which explains the sensitivity of the major capsid gene to codon deoptimization.

同义密码子的使用可以影响蛋白质的表达，因为具有大量相应trna的密码子自然比具有较少相应trna的密码子翻译得更快。虽然翻译效率最终取决于氨基酰化（带电）tRNA的浓度，但许多翻译理论模型忽略了tRNA动力学，将带电tRNA视为固定资源。这种简化可能会限制这些模型在带电trna受限的情况下做出准确的预测。在此，我们基于该系统的随机模拟，推导了具有显式tRNA动力学和tRNA再充电的翻译数学模型，该系统先前用于研究基因过表达背景下密码子的使用。我们利用数学模型系统地探索了密码子使用与蛋白质表达率之间的关系，发现在tRNA充电是限制性反应的情况下，密码子频率与tRNA池匹配总是最优的。相反，当tRNA充电不受限制时，使用100%的首选密码子是蛋白质生产的最佳选择。我们还使用tRNA动力学模型来增强噬菌体T7的全细胞模拟。利用该模型，我们证明了T7主衣壳基因的高表达率导致罕见的带电trna完全耗尽，这解释了主衣壳基因对密码子反优化的敏感性。

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引用次数: 0

Fixed-time control strategy for high-speed unmanned system under switching topology 切换拓扑下高速无人系统的定时控制策略

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-14 DOI: 10.1016/j.chaos.2026.117902

Xuyang Wang , Xin Ning , Zheng Wang , Zhansheng Chen

This paper proposes a fixed-time stability-based control strategy for high-speed unmanned systems (HSUSs) considering practical switching topology scenarios. First, a fixed-time disturbance observer (FixTDO) with initial condition-independent convergence time is designed to handle the system disturbances. Subsequently, an auxiliary system is constructed to address communication switching topology constraints. Furthermore, a fixed-time controller is synthesized to enhance transient performance and system robustness, with a first-order filter incorporated to eliminate differentiation-induced computational divergence. Finally, comparative simulation studies validate the effectiveness and operational feasibility of the proposed algorithm.

本文提出了一种基于固定时间稳定性的高速无人系统（HSUSs）控制策略，考虑了实际切换拓扑场景。首先，设计了收敛时间与初始条件无关的定时扰动观测器（FixTDO）来处理系统扰动。随后，构建了一个辅助系统来解决通信交换拓扑约束问题。此外，合成了一个固定时间控制器以增强系统的瞬态性能和鲁棒性，并加入了一个一阶滤波器以消除微分引起的计算发散。最后，通过对比仿真研究验证了所提算法的有效性和运行可行性。

引用次数: 0

The Role of Host Immunity and the Environment in Seasonal Disease Dynamics. 宿主免疫和环境在季节性疾病动态中的作用。

IF 2.2 4区数学 Q2 BIOLOGY

Bulletin of Mathematical Biology

Pub Date : 2026-01-14 DOI: 10.1007/s11538-025-01582-3

Gabriel K Kosmacher, Dillon Max, Zoi Rapti, Carla E Cáceres, Tara E Stewart Merrill

In both human and wildlife disease systems, temporal shifts in host immunity may shape the timing and severity of epidemics. Yet, immune responses, as well as seasonal patterns in their expression, are difficult to measure. Rather, field studies collect phenomenological data on infection outcomes. Pairing epidemic data of multiple outbreaks with models that directly parameterize immune metrics can be a powerful approach for exploring the role of time-varying immunity on disease. Field data can be used to determine how well a parameterized model can reproduce trends and differences observed among outbreaks.Previous work in the Daphnia dentifera-Metschnikowia bicuspidata focal host-fungal pathogen disease system has not taken full advantage of coupling patterns in nature with mechanisms predicted by theory. Here, we study a mathematical model accounting for host immunity in the form of resistance to and recovery from M. bicuspidata infections and temporal variation in key aspects of the system's epidemiology and ecology. Specifically, host population birth, predation and transmission rates, the fraction of recovering hosts, as well as the fungal spore yield were allowed to vary within the epidemic season. Modifying the system's carrying capacity produces good correspondence between observed and model-estimated densities. Adjusting the transmission rate, spore yield, and the fraction of recovering hosts, captures the timing of disease outbreaks, as well as other qualitative features of outbreaks, such as the disparity between the prevalence of early- and late-stage infections. Our findings suggest that host immunological parameters are an important within-host constraint on disease dynamics.

在人类和野生动物疾病系统中，宿主免疫的时间变化可能会影响流行病的时间和严重程度。然而，免疫反应及其表达的季节性模式很难测量。相反，实地研究收集有关感染结果的现象学数据。将多次暴发的流行病数据与直接参数化免疫指标的模型配对，可以成为探索时变免疫对疾病作用的有力方法。现场数据可用于确定参数化模型在多大程度上再现疫情之间观察到的趋势和差异。以往关于牙水蚤-双尖斑蚤局灶寄主-真菌病原体疾病系统的研究工作没有充分利用自然界的耦合模式和理论预测的机制。在这里，我们研究了一个数学模型，该模型以宿主免疫的形式，以抵抗和恢复双尖毛绦虫感染的形式，以及系统流行病学和生态学关键方面的时间变化。具体而言，宿主种群的出生、捕食率和传播率、恢复宿主的比例以及真菌孢子产量在流行季节内都是变化的。修改系统的承载能力可以在观测密度和模型估计密度之间产生良好的对应关系。调整传播率、孢子产量和恢复宿主的比例，可以捕捉到疾病爆发的时间，以及爆发的其他定性特征，例如早期和晚期感染流行率之间的差异。我们的研究结果表明，宿主免疫参数是宿主内疾病动力学的重要约束。

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引用次数: 0

Density of 2-critical signed graphs 2临界符号图的密度

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-14 DOI: 10.1016/j.disc.2026.114998

Reza Naserasr , Weiqiang Yu

A balanced k-coloring of a signed graph

(G, σ)

which has no negative loop is to partition its vertices into k sets each of which induces a balanced subgraph, that is a subgraph with no negative cycle. The notion, through basic graph operation, captures the classic proper coloring of graphs as special case.

Having observed the importance of balanced 2-coloring, in this work we study structural conditions which permit a signed graph to admit a 2-coloring. More precisely, slightly modifying the notion of color-critical, we say a signed graph is k-critical if it admits no balanced k-coloring but every proper subgraph of it admits such a coloring.

We show that if

(G, σ)

is a 2-critical signed graph whose underlying graph is not

K_{5}

or an odd cycle, then

| E (G) | \geq \frac{21 | V (G) | - 2 d + 1}{10}

where d is the maximum number of vertex disjoint digons in

(G, σ)

. As a corollary we conclude that, except for the signed graph

(K_{5}, -)

, any signed simple graph with maximum average degree at most 4.2 admits a balanced 2-coloring.

无负环的有符号图（G,σ）的平衡k-着色是将其顶点划分为k个集，每个集引出一个平衡子图，即无负环的子图。这个概念通过基本的图运算，将经典的图的适当着色作为特例。在观察到平衡2-着色的重要性之后，本文研究了允许一个符号图允许2-着色的结构条件。更准确地说，稍微修改一下色临界的概念，我们说一个有符号图是k临界的，如果它不允许平衡的k染色，但它的每个固有子图都允许这样的染色。证明了如果（G,σ）是一个底图不是K5或奇环的2临界符号图，则|E(G)|≥21|V(G)|−2d+110，其中d为（G,σ）中顶点不相交双子的最大个数。作为推论，我们得出，除了有符号图（K5,−）外，任何最大平均度不超过4.2的有符号简单图都是平衡的2-着色。

{"title":"Density of 2-critical signed graphs","authors":"Reza Naserasr , Weiqiang Yu","doi":"10.1016/j.disc.2026.114998","DOIUrl":"10.1016/j.disc.2026.114998","url":null,"abstract":"<div><div>A balanced <em>k</em>-coloring of a signed graph <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span> which has no negative loop is to partition its vertices into <em>k</em> sets each of which induces a balanced subgraph, that is a subgraph with no negative cycle. The notion, through basic graph operation, captures the classic proper coloring of graphs as special case.</div><div>Having observed the importance of balanced 2-coloring, in this work we study structural conditions which permit a signed graph to admit a 2-coloring. More precisely, slightly modifying the notion of color-critical, we say a signed graph is <em>k</em>-critical if it admits no balanced <em>k</em>-coloring but every proper subgraph of it admits such a coloring.</div><div>We show that if <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span> is a 2-critical signed graph whose underlying graph is not <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> or an odd cycle, then<span><span><span><math><mo>|</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>≥</mo><mfrac><mrow><mn>21</mn><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>−</mo><mn>2</mn><mi>d</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>10</mn></mrow></mfrac></math></span></span></span> where <em>d</em> is the maximum number of vertex disjoint digons in <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span>. As a corollary we conclude that, except for the signed graph <span><math><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>,</mo><mo>−</mo><mo>)</mo></math></span>, any signed simple graph with maximum average degree at most 4.2 admits a balanced 2-coloring.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 6","pages":"Article 114998"},"PeriodicalIF":0.7,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980076","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}

引用次数: 0

Z2-torus actions on positively curved manifolds 正弯曲流形上的z2环面作用

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.difgeo.2026.102332

Farida Ghazawneh

Kennard, Khalili Samani, and Searle showed that for a

Z_{2}

-torus,

Z_{2}^{r}

, acting on a closed, positively curved Riemannian n-manifold,

M^{n}

, with a non-empty fixed point set for n large enough and r approximately half the dimension of M, then

M^{n}

is homotopy equivalent to

S^{n}

R P^{n}

C P^{\frac{n}{2}}

, or a lens space. In this paper, we lower r to approximately

2 n / 5

and show that we still obtain the same result.

Kennard， Khalili Samani和Searle证明了对于一个z2环面Z2r，作用于一个封闭的，正弯曲的黎曼n流形Mn，当n足够大且r约为M的一半维数时，具有一个非空不动点集，则Mn等价于Sn， RPn， CPn2或透镜空间。在本文中，我们将r降低到大约2n/5，并表明我们仍然得到相同的结果。

引用次数: 0

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