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Odd Coloring of Planar Graphs without Short Cycles 无短圈平面图的奇着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-15 DOI: 10.1007/s10255-026-0121-2
Ping Chen, Xin Zhang
{"title":"Odd Coloring of Planar Graphs without Short Cycles","authors":"Ping Chen,&nbsp;Xin Zhang","doi":"10.1007/s10255-026-0121-2","DOIUrl":"10.1007/s10255-026-0121-2","url":null,"abstract":"<div><p>An odd coloring of a graph is a proper coloring with the additional constraint that each non-isolated vertex has at least one color that appears an odd number of times in its open neighborhood. Determining if a graph is odd <i>k</i>-colorable is NP-complete for <i>k</i> ≥ 3. It is known that planar graphs are odd 8-colorable and triangle-free planar graphs are odd 7-colorable. In this paper we prove that planar graphs without 4-cycles and 5-cycles, or 4-cycles and 6-cycles, are odd 7-colorable.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 3","pages":"985 - 995"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458982","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}
引用次数: 0
Existence of Standing Wave Solutions for Perturbed Quasilinear Schrödinger Systems with Critical Growth 临界增长的摄动拟线性Schrödinger系统驻波解的存在性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-15 DOI: 10.1007/s10255-026-0090-5
Shu-lin Zhang
{"title":"Existence of Standing Wave Solutions for Perturbed Quasilinear Schrödinger Systems with Critical Growth","authors":"Shu-lin Zhang","doi":"10.1007/s10255-026-0090-5","DOIUrl":"10.1007/s10255-026-0090-5","url":null,"abstract":"<div><p>In this paper, we study the existence of standing wave solutions for the following perturbed quasilinear Schrödinger systems in ℝ<sup><i>N</i></sup></p><div><div><span>$$left{begin{aligned}-varepsilon^2 Delta u + V(x)u-varepsilon^2 Delta [(1+u^2)^{frac12}]frac{u}{2(1+u^2)^{frac12}}&amp;=K(x)|u|^{2^*-2}u+F_u(x,u,v),-varepsilon^2 Delta v + V(x)v-varepsilon^2 Delta [(1+v^2)^{frac12}]frac{v}{2(1+v^2)^{frac12}}&amp;=K(x)|v|^{2^*-2}v+F_v(x,u,v).end{aligned}right.$$</span></div></div><p>Under some suitable conditions, by using the variational approach, we establish the existence of standing wave solutions for the above system for sufficiently small <i>ε</i>, for any <i>m</i> ∈ ℕ, the system admits at least <i>m</i> pairs of solutions for sufficiently small <i>ε</i>. Moreover, these solutions converge to (<i>u</i><sub><i>ε</i></sub>, <i>v</i><sub><i>ε</i></sub>) → (0, 0) in a suitable Sobolev space as <i>ε</i> → 0. Our results improve and supplement some existing relevant results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 3","pages":"996 - 1012"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458900","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}
引用次数: 0
Strichartz Type Estimates of the Airy Equation Airy方程的Strichartz型估计
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-07 DOI: 10.1007/s10255-026-0094-1
Jie Chen, Fan Gu, Bo-ling Guo
{"title":"Strichartz Type Estimates of the Airy Equation","authors":"Jie Chen,&nbsp;Fan Gu,&nbsp;Bo-ling Guo","doi":"10.1007/s10255-026-0094-1","DOIUrl":"10.1007/s10255-026-0094-1","url":null,"abstract":"<div><p>In this article, we show the necessary and sufficient conditions for the inequality <span>(Vert u Vert_{{{L}_{t}^{q}}{{L}_{x}^{r}}} underset{sim}{&lt;} Vert u Vert_{{{X}^{s,b}}})</span>, where </p><div><div><span>$$Vert u Vert_{{{X}^{s,b}}} := {Vert{hat u}(tau, ; xi) langle xi rangle^{s} langle tau - xi^{3}rangle^{b}Vert}_{{L}_{tau, xi}^{2}}.$$</span></div></div><p>Here, we provide a complete classification of the indices relationships for which this inequality holds true. Such estimates will be very useful in solving the well-posedness for low regularity well-posedness of the Korteweg-de Vries equations and stochastic Korteweg-de Vries equations.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1365 - 1371"},"PeriodicalIF":0.9,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027600","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}
引用次数: 0
Bipartite Turán Problem on Complete Bipartite Graphs 完全二部图的Turán问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-07 DOI: 10.1007/s10255-026-0114-1
Lan-xin Wang, Xia Zhang
{"title":"Bipartite Turán Problem on Complete Bipartite Graphs","authors":"Lan-xin Wang,&nbsp;Xia Zhang","doi":"10.1007/s10255-026-0114-1","DOIUrl":"10.1007/s10255-026-0114-1","url":null,"abstract":"<div><p>The bipartite Turán number of a bipartite graph <i>H</i>, denoted by ex(<i>m, n; H</i>), is the maximum number of edges in subgraphs of <i>K</i><sub><i>m,n</i></sub> containing no copies of <i>H</i>. In this paper, we determine the bipartite Turán number of the complete bipartite graphs ex(<i>m; n; K</i><sub><i>s,t</i></sub>) = <i>mn</i> − (⌊(<i>n</i> − <i>t</i>)/<i>s</i>⌋(<i>m</i> − <i>s</i>) + <i>m</i> + <i>n</i> − <i>s</i> − <i>t</i> + 1) when <i>n</i> ≥ <i>s</i> + <i>t</i> and <i>t</i> ≥ <i>s</i>, if one of the following is satisfied: <i>n</i> = <i>s</i> + <i>t</i>; <i>m</i> ≤ <i>s</i> + (<i>t</i> − 1)/(⌊(<i>n</i> − <i>t</i>)/<i>s</i>⌋ + 1); <i>s</i>∣(<i>n</i> − <i>t</i>) and <i>m</i> ≤ <i>sn</i>/(<i>n</i> − <i>t</i>); being <i>m</i> ≥ 2<i>s</i> if <i>m</i> = <i>sn</i>/(<i>n</i> − <i>t</i>).</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1280 - 1290"},"PeriodicalIF":0.9,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149028966","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}
引用次数: 0
Energy Detection for Cognitive Radio with Distributional Uncertainty and Signal Variety under Nonlinear Expectation Theory 非线性期望理论下具有分布不确定性和信号变化的认知无线电能量检测
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-07 DOI: 10.1007/s10255-026-0104-3
Jia-liang Fu, Wen-xuan Lang
{"title":"Energy Detection for Cognitive Radio with Distributional Uncertainty and Signal Variety under Nonlinear Expectation Theory","authors":"Jia-liang Fu,&nbsp;Wen-xuan Lang","doi":"10.1007/s10255-026-0104-3","DOIUrl":"10.1007/s10255-026-0104-3","url":null,"abstract":"<div><p>Classical energy detection (ED) methods for cognitive radio (CR) have addressed noise uncertainty as deviations in noise power and signal uncertainty as variability in signal characteristics, which use probabilistic methods and assume fixed probability distributions for both. In practical scenarios, due to the uncertainty in probability models and the significant variation of primary signals encountered by receivers across different radio technologies, wireless environments exhibit not only distributional uncertainty but also substantial signal variety. In this paper, we develop a generalized formulation of energy detection based on nonlinear expectation theory, where both the signal and noise distributions are uncertain. We utilize the <i>G</i>-normal distribution to characterize channel noise. Moreover, to capture practical signal variety, the absolute values of transmitted signal random variables are assumed to lie within a bounded range <span>([{underline sigma}_{X}, , {overline sigma}_{X}])</span>. The worst-case detection performance is then characterized by a double supremum over all admissible distributions and all possible signal realizations. We derive estimates for the minimum and maximum detection error probabilities, and demonstrate the validity of the results through numerical simulations. The proposed model generalizes the classical theoretical analysis of energy detection and offers a potential theoretical foundation for robust detection and information-theoretic analysis under distributional uncertainty.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1312 - 1325"},"PeriodicalIF":0.9,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027603","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}
引用次数: 0
Potential Measures for Spectrally Negative Lévy Processes on the Last Exit Time 在最后退出时间处理频谱负的lsamvy过程的可能措施
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-06-05 DOI: 10.1007/s10255-026-0101-6
Ying-qiu Li, Yu-shao Wei, He-song Wang
{"title":"Potential Measures for Spectrally Negative Lévy Processes on the Last Exit Time","authors":"Ying-qiu Li,&nbsp;Yu-shao Wei,&nbsp;He-song Wang","doi":"10.1007/s10255-026-0101-6","DOIUrl":"10.1007/s10255-026-0101-6","url":null,"abstract":"<div><p>In this paper, we consider potential measures of spectrally negative Lévy processes for the last exit time killed on exiting interval, some exit identities are needed for our main results. Our results are expressed in terms of scale functions.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 3","pages":"969 - 984"},"PeriodicalIF":0.9,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458872","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}
引用次数: 0
Large Deviations for the LS Estimator in Nonlinear Regression Model under Sub-linear Expectations 亚线性期望下非线性回归模型LS估计量的大偏差
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-026-0015-3
Yi Wu, Xue-jun Wang, Li-xin Zhang
{"title":"Large Deviations for the LS Estimator in Nonlinear Regression Model under Sub-linear Expectations","authors":"Yi Wu,&nbsp;Xue-jun Wang,&nbsp;Li-xin Zhang","doi":"10.1007/s10255-026-0015-3","DOIUrl":"10.1007/s10255-026-0015-3","url":null,"abstract":"<div><p>In this paper, we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations. The large deviation results for the estimator are established under some general conditions. As applications, the results on weak consistency and strong consistency are obtained under the meaning of capacity. A simulation study is also presented to verify the validity of the theoretical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"474 - 488"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579592","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}
引用次数: 0
A Note on the Liouville Type Theorem for the Steady-state Magnetohydrodynamic Equations 关于稳态磁流体动力学方程的Liouville型定理的注记
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-026-0022-4
Hui-ying Fan, Meng Wang
{"title":"A Note on the Liouville Type Theorem for the Steady-state Magnetohydrodynamic Equations","authors":"Hui-ying Fan,&nbsp;Meng Wang","doi":"10.1007/s10255-026-0022-4","DOIUrl":"10.1007/s10255-026-0022-4","url":null,"abstract":"<div><p>In this paper, we are concentrated on demonstrating the Liouville type theorem for the stationary incompressible Magnetohydrodynamic equations in the whole space, the half-space, or a periodic slab, and presenting the solution must vanish under the condition that for some 0 ≤ <i>δ</i> ≤ 1 &lt; <i>L</i> and <span>(q = {{6({3 - delta})} over {6 - delta}},mathop {lim ,inf}limits_{R to infty} {1 over R}Vert{({{bf{u}},{bf{h}}})}Vert_{R &lt; vert x vert &lt; LR}^{3 - delta} = 0)</span>. We also deduce sufficient conditions by allowing shrinking ratio <i>L</i> = 1 + <i>R</i><sup>−<i>α</i></sup>. When in slab with zero boundary condition, stronger decay rate is needed. We do not assume the global bound of the velocity field u and the magnetic field h and investigate the Liouville type theorems by the conditions lim inf rather than lim.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"450 - 461"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-026-0022-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579596","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}
引用次数: 0
Patterns of Emergent Nonlinear Waves in an Initial Discontinuity Problem of the Bad Jaulent-Miodek Equation Bad Jaulent-Miodek方程初始不连续问题中涌现非线性波的模式
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-024-1142-3
Ya-qing Liu, Bo-ling Guo, Deng-shan Wang
{"title":"Patterns of Emergent Nonlinear Waves in an Initial Discontinuity Problem of the Bad Jaulent-Miodek Equation","authors":"Ya-qing Liu,&nbsp;Bo-ling Guo,&nbsp;Deng-shan Wang","doi":"10.1007/s10255-024-1142-3","DOIUrl":"10.1007/s10255-024-1142-3","url":null,"abstract":"<div><p>By means of the Whitham modulation theory, this paper studies the discontinuous initial value problem of the bad Jaulent-Miodek (JM) equation, which is compared with the good JM equation. The linear stability of the good and bad JM equations is analyzed to show the difference between the two equations. Also the physical significance of the JM equations is discussed by considering the reduction of the Euler’s equation. Then the zero-, one-, two-phase periodic solutions and the corresponding Whitham equations in the framework of the bad JM equation are derived by finite-gap integration approach. The degeneration of the one-phase periodic solution along with the genus-one Whitham equation are analyzed by taking the two sides limits of the modulus <i>m</i> of the Jacobi elliptic functions. The basic rarefaction wave patterns and dispersive shock wave patterns are proposed analytically and graphically, and then the complete classification of solutions and the all possible waveforms evolving from discontinuous initial values in the bad JM equation are established. In the results, various patterns of emergent nonlinear waves that appear to be new and are being detected for the first time</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"582 - 607"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579598","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}
引用次数: 0
On the Some Nonlinear Boundary Value Problems of Type Vibration in Sobolev Spaces with Variable Exponents 变指数Sobolev空间型振动的非线性边值问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-026-0089-y
Fouzia Bouzeghaya, Boubakeur Merouani
{"title":"On the Some Nonlinear Boundary Value Problems of Type Vibration in Sobolev Spaces with Variable Exponents","authors":"Fouzia Bouzeghaya,&nbsp;Boubakeur Merouani","doi":"10.1007/s10255-026-0089-y","DOIUrl":"10.1007/s10255-026-0089-y","url":null,"abstract":"<div><p>In this work, we investigate a class of nonlinear boundary value problems within the framework of Sobolev spaces with variable exponents. After establishing precise formulations of these problems, we reformulate them as nonlinear hyperbolic-type equations. For each of the six problems considered, we establish both existence and uniqueness results. Furthermore, we address the associated stationary problems and prove the existence of solutions by applying a suitable variant of Brouwer’s fixed-point theorem.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"353 - 370"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579595","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}
引用次数: 0
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