数学最新文献

{"title":"Finding irregular subgraphs via local adjustments","authors":"Jie Ma ,&nbsp;Shengjie Xie","doi":"10.1016/j.jctb.2025.04.008","DOIUrl":"10.1016/j.jctb.2025.04.008","url":null,"abstract":"<div><div>For a graph <em>H</em>, let <span><math><mi>m</mi><mo>(</mo><mi>H</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> denote the number of vertices of degree <em>k</em> in <em>H</em>. A conjecture of Alon and Wei states that for any <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, every <em>n</em>-vertex <em>d</em>-regular graph contains a spanning subgraph <em>H</em> satisfying <span><math><mo>|</mo><mi>m</mi><mo>(</mo><mi>H</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>−</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>|</mo><mo>≤</mo><mn>2</mn></math></span> for every <span><math><mn>0</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>d</mi></math></span>. This holds easily when <span><math><mi>d</mi><mo>≤</mo><mn>2</mn></math></span>. An asymptotic version of this conjecture was initially established by Frieze, Gould, Karoński and Pfender, subsequently improved by Alon and Wei, and most recently enhanced by Fox, Luo and Pham, approaching its complete range. All of these approaches relied on probabilistic methods.</div><div>In this paper, we provide a novel framework to study this conjecture, based on localized deterministic techniques which we call local adjustments. We prove two main results. Firstly, we show that every <em>n</em>-vertex <em>d</em>-regular graph contains a spanning subgraph <em>H</em> satisfying <span><math><mo>|</mo><mi>m</mi><mo>(</mo><mi>H</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>−</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>|</mo><mo>≤</mo><mn>2</mn><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> for all <span><math><mn>0</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>d</mi></math></span>, which provides the first bound independent of the value of <em>n</em>. Secondly, we confirm the case <span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span> of the Alon-Wei Conjecture in a strong form. Both results can be generalized to multigraphs and yield efficient algorithms for finding the desired subgraphs <em>H</em>. Furthermore, we explore a generalization of the Alon-Wei Conjecture for multigraphs and its connection to the Faudree-Lehel Conjecture concerning irregularity strength.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"174 ","pages":"Pages 71-98"},"PeriodicalIF":1.2,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895437","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":"Modified Adomian decomposition mechanism for hybrid nanofluid flow through rocket engine nozzle based CoFe2O4 and Ag nanoparticles","authors":"P.K. Pattnaik ,&nbsp;M.D. Shamshuddin ,&nbsp;Subhajit Panda ,&nbsp;S.R. Mishra ,&nbsp;Mohamed R. Eid","doi":"10.1016/j.chaos.2025.116521","DOIUrl":"10.1016/j.chaos.2025.116521","url":null,"abstract":"<div><div>The principal aim of the contemporary investigation is to examine the influences of a hybridized nanofluid using Cobalt ferrite and silver gold nanoparticles in a nozzle of rocket engine. Moreover, the contribution of the dissipative heat alongside the impact of thermal radiation energises the heat transport phenomenon. It has diverse industrialized implementations involving aeronautical engineering and the modeling of polymerized melts. In the context of mathematical modeling, using the correspondence alteration method (similarity transformation), the leading equations were renewed into a system of nonlinear ODEs. This issue is handled semi-analytically by utilizing the Modified Adomian Decomposition Method (MADM) in the MATLAB program to study the influence of relevant physical factors. The temperature and velocity profile graphs for important quantities are shown, as well as the logical and physical reasoning behind them. Verification is also performed to confirm the executed experiments. The results show Reynolds number clearly affects the flow speed of the nanofluid, as the speed declines immediate the side layer or the surface of the missile containing the nanofluid. A large heat flow, which upsurges the temperature and expands the boundary layer, is caused by an increment in the radiation parameter and Eckert number. The viscosity of nanoparticles increases, and the effect is more extensive if both nanoparticles volume fraction increases. The effect of cobalt ferrite nanoparticles is more noticeable than the consequence of silver nanomolecules on the relative heat capacity of the nanofluid. The surface friction of the hybridized nanofluid flow declines with the potential parameters studied. Rising the Eckert number reduces the heat transfer ranks of the nano-fuel.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116521"},"PeriodicalIF":5.3,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899111","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":"Corrigendum to “Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras” [J. Pure Appl. Algebra 227(4) (2023) 107281]","authors":"Zhekun He ,&nbsp;Jun Hu ,&nbsp;Huang Lin","doi":"10.1016/j.jpaa.2025.107981","DOIUrl":"10.1016/j.jpaa.2025.107981","url":null,"abstract":"","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107981"},"PeriodicalIF":0.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895031","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":"Studying the divisibility of power LCM matrices by power GCD matrices on gcd-closed sets","authors":"Jianrong Zhao ,&nbsp;Chenxu Wang ,&nbsp;Yu Fu","doi":"10.1016/j.jcta.2025.106063","DOIUrl":"10.1016/j.jcta.2025.106063","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; be a gcd-closed set (i.e. &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;). In 2002, Hong proposed the divisibility problem of characterizing all gcd-closed sets &lt;em&gt;S&lt;/em&gt; with &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; such that the GCD matrix (&lt;em&gt;S&lt;/em&gt;) divides the LCM matrix &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; in the ring &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. For &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; and &lt;/mtext&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⇒&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. In 2009, Feng, Hong and Zhao answered this problem in the context where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. In 2022, Zhao, Chen and Hong obtained a necessary and sufficient condition on the gcd-closed set &lt;em&gt;S&lt;/em&gt; with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Meanwhile, they raised a conjecture on the necessary and sufficient condition such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; holds for the remaining case &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. In this paper, we confirm the Zhao-Chen-Hong conjecture from a novel perspective, consequently solve Hong's open problem completely.&lt;/d","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"215 ","pages":"Article 106063"},"PeriodicalIF":0.9,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895609","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":"Nonlinear excitation and bi-directional propagation of heavy-nucleus-acoustic waves in multi-component unmagnetized quantum plasmas","authors":"Debprasad Pradhan,&nbsp;Debjit Dutta","doi":"10.1016/j.chaos.2025.116462","DOIUrl":"10.1016/j.chaos.2025.116462","url":null,"abstract":"<div><div>The nonlinear dynamics and finitely small amplitude wave excitation of heavy-nucleus-acoustic waves (HNAWs) in extremely dense unmagnetized degenerate quantum plasma comprising inertial non-relativistically degenerate heavy-nuclei, non-inertial non-relativistically degenerate light-nuclei and ultra-relativistically degenerate electrons and positrons are theoretically investigated through the lens of the generalized Boussinesq equation. By employing Hirota’s method and Hereman’s technique, diverse <span><math><mi>N</mi></math></span>-soliton solutions are unveiled and revealing intriguing potential structures. Compressive profiles are observed in both subsonic and supersonic regimes, while rarefactive profiles are exclusively present only in the supersonic regime. Beyond traditional solitary waves, the present study identifies multi-solitons (one-, two-, three-) and Kuznetsov-Ma breathers (single, double) phenomena, showcasing their interactions with solitons and other breathers via higher-order solutions. Furthermore, it emphasizes the phase shift for two-soliton and three-soliton, the influence of plasma parameters on HNAWs and the key significance of wave number. This exploration highlights the rich nonlinear wave phenomena inherent in relativistic astrophysical plasmas, offering a fresh perspective on their complex dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116462"},"PeriodicalIF":5.3,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899112","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":"Convergence analysis of three semidiscrete numerical schemes for nonlocal geometric flows including perimeter terms","authors":"Wei Jiang, Chunmei Su, Ganghui Zhang","doi":"10.1093/imanum/draf015","DOIUrl":"https://doi.org/10.1093/imanum/draf015","url":null,"abstract":"We present and analyze three distinct semidiscrete schemes for solving nonlocal geometric flows incorporating perimeter terms. These schemes are based on the finite difference method, the finite element method and the finite element method with a specific tangential motion. We offer rigorous proofs of quadratic convergence under $H^{1}$-norm for the first scheme and linear convergence under $H^{1}$-norm for the latter two schemes. All error estimates rely on the observation that the error of the nonlocal term can be controlled by the error of the local term. Furthermore, we explore the relationship between the convergence under $L^infty $-norm and manifold distance. Extensive numerical experiments are conducted to verify the convergence analysis, and demonstrate the accuracy of our schemes under various norms for different types of nonlocal flows.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"52 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143893397","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":"Weak colourings of Kirkman triple systems","authors":"Andrea C. Burgess, Nicholas J. Cavenagh, Peter Danziger, David A. Pike","doi":"10.1007/s10623-025-01635-7","DOIUrl":"https://doi.org/10.1007/s10623-025-01635-7","url":null,"abstract":"<p>A <span>(delta )</span>-colouring of the point set of a block design is said to be <i>weak</i> if no block is monochromatic. The <i>chromatic number</i> <span>(chi (S))</span> of a block design <i>S</i> is the smallest integer <span>(delta )</span> such that <i>S</i> has a weak <span>(delta )</span>-colouring. It has previously been shown that any Steiner triple system has chromatic number at least 3 and that for each <span>(vequiv 1)</span> or <span>(3pmod {6})</span> there exists a Steiner triple system on <i>v</i> points that has chromatic number 3. Moreover, for each integer <span>(delta geqslant 3)</span> there exist infinitely many Steiner triple systems with chromatic number <span>(delta )</span>. We consider colourings of the subclass of Steiner triple systems which are resolvable. A <i>Kirkman triple system</i> consists of a resolvable Steiner triple system together with a partition of its blocks into parallel classes. We show that for each <span>(vequiv 3pmod {6})</span> there exists a Kirkman triple system on <i>v</i> points with chromatic number 3. We also show that for each integer <span>(delta geqslant 3)</span>, there exist infinitely many Kirkman triple systems with chromatic number <span>(delta )</span>. We close with several open problems.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"26 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143893852","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":"Ground state solution for a generalized Choquard Schr $$ddot{text {o}}$$ dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces","authors":"Shilpa Gupta, Gaurav Dwivedi","doi":"10.1007/s13540-025-00411-7","DOIUrl":"https://doi.org/10.1007/s13540-025-00411-7","url":null,"abstract":"<p>This paper aims to establish the existence of a weak solution for the following problem: </p><span>$$begin{aligned} (-Delta )^{s}_{mathcal {H}}u(x) +V(x)h(x,x,|u|)u(x)=left( int _{{mathbb R}^{N}}dfrac{K(y)F(u(y))}{|x-y|^lambda },textrm{d}yright) K(x)f(u(x)), end{aligned}$$</span><p>in <span>({mathbb R}^{N})</span> where <span>(Nge 1)</span>, <span>(sin (0,1), lambda in (0,N), mathcal {H}(x,y,t)=int _{0}^{|t|} h(x,y,r)r dr,)</span> <span>( h:{mathbb R}^{N}times {mathbb R}^{N}times [0,infty )rightarrow [0,infty ))</span> is a generalized <i>N</i>-function and <span>((-Delta )^{s}_{mathcal {H}})</span> is a generalized fractional Laplace operator. The functions <span>(V,K:{mathbb R}^{N}rightarrow (0,infty ))</span>, non-linear function <span>(f:{mathbb R}rightarrow {mathbb R})</span> are continuous and <span>( F(t)=int _{0}^{t}f(r)dr.)</span> First, we introduce the homogeneous fractional Musielak–Sobolev space and investigate their properties. After that, we pose the given problem in that space. To establish our existence results, we use variational technique based on the mountain pass theorem. We also prove the existence of a ground state solution by the method of Nehari manifold.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"4 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894041","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":"Macroscopic quantum coherence and quantum complete synchronization in molecular optomechanical system","authors":"Jia-Xin Peng ,&nbsp;Chengsong Zhao ,&nbsp;P. Djorwe ,&nbsp;Kongkui Berinyuy Emale ,&nbsp;Zhong-Wei Yu ,&nbsp;Muhammad Asjad","doi":"10.1016/j.chaos.2025.116473","DOIUrl":"10.1016/j.chaos.2025.116473","url":null,"abstract":"<div><div>Large-scale coherence networks are key platforms for implementing multichannel quantum information processing and quantum computation. Here, we show how to prepare macroscopic quantum coherence between the cavity field (molecular collective mode) and the molecular collective mode (molecular collective mode) in a molecular optomechanical system composed of <span><math><mi>N</mi></math></span> organic molecules. The results indicate that increasing the number of molecules can significantly improve the cavity–molecule and the molecule–molecule quantum coherences. In addition, we find that the equal weight distribution of the two molecular collective modes can establish the strongest molecule–molecule quantum coherence. Particularly, the two types of quantum coherence prepared exhibit strong robustness to bath temperature and molecular damping channel. Further, we discuss the quantum complete synchronization of the two molecular collective modes, and then explore the potential relationship between quantum synchronization and quantum coherence. Finally, a strategy is provided to detect the quantum coherence and quantum synchronization.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116473"},"PeriodicalIF":5.3,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895457","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":"Lattice codes for CRYSTALS-Kyber","authors":"Shuiyin Liu, Amin Sakzad","doi":"10.1007/s10623-025-01640-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01640-w","url":null,"abstract":"<p>This paper describes a constant-time lattice encoder for the National Institute of Standards and Technology (NIST) recommended post-quantum encryption algorithm: Kyber. The first main contribution of this paper is to refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This result shows that the Kyber encoding problem is essentially a sphere packing in a hypercube. The original Kyber encoder uses the integer lattice for sphere packing purposes, which is far from optimal. Our second main contribution is to construct optimal lattice codes to ensure denser packing and a lower decryption failure rate (DFR). Given the same ciphertext size as the original Kyber, the proposed lattice encoder enjoys a larger decoding radius, and is able to encode much more information bits. This way we achieve a decrease of the communication cost by up to <span>(32.6%)</span>, and a reduction of the DFR by a factor of up to <span>(2^{85})</span>. Given the same plaintext size as the original Kyber, e.g., 256 bits, we propose a bit-interleaved coded modulation (BICM) approach, which combines a BCH code and the proposed lattice encoder. The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling further compression of the ciphertext. Compared with the original Kyber encoder, the communication cost is reduced by <span>(24.49%)</span>, while the DFR is decreased by a factor of <span>(2^{39})</span>. The proposed encoding scheme is a constant-time algorithm, thus resistant against the timing side-channel attacks.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"114 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143893779","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}