In this article, we investigate the maximal bilinear Riesz means $S^{alpha }_{*}$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{alpha }_{*}$ is bounded from $L^{p_{1}}times L^{p_{2}}$ into $% L^{p}$ for $2leq p_{1}, p_{2}leq infty $ and $1/p=1/p_{1}+1/p_{2}$ when $% alpha $ is large than a suitable smoothness index $alpha (p_{1},p_{2})$. For obtaining a lower index $alpha (p_{1},p_{2})$, we define two important auxiliary operators and investigate their $L^{p}$ estimates,which play a key role in our proof.
{"title":"Maximal Estimates for the Bilinear Riesz Means on Heisenberg Groups","authors":"Min Wang, Hua Zhu","doi":"10.11650/tjm/230802","DOIUrl":"https://doi.org/10.11650/tjm/230802","url":null,"abstract":"In this article, we investigate the maximal bilinear Riesz means $S^{alpha }_{*}$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{alpha }_{*}$ is bounded from $L^{p_{1}}times L^{p_{2}}$ into $% L^{p}$ for $2leq p_{1}, p_{2}leq infty $ and $1/p=1/p_{1}+1/p_{2}$ when $% alpha $ is large than a suitable smoothness index $alpha (p_{1},p_{2})$. For obtaining a lower index $alpha (p_{1},p_{2})$, we define two important auxiliary operators and investigate their $L^{p}$ estimates,which play a key role in our proof.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49441114","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}
Let $R$ be the Ehrhart ring of the stable set polytope of a cycle graph which is not Gorenstein. We describe the non-Gorenstein locus of $mathrm{Spec} R$. Further, we show that $R$ is almost Gorenstein. Moreover, we show that the conjecture of Hibi and Tsuchiya is true.
{"title":"Non-Gorenstein Locus and Almost Gorenstein Property of the Ehrhart Ring of the Stable Set Polytope of a Cycle Graph","authors":"Mitsuhiro Miyazaki","doi":"10.11650/tjm/221104","DOIUrl":"https://doi.org/10.11650/tjm/221104","url":null,"abstract":"Let $R$ be the Ehrhart ring of the stable set polytope of a cycle graph which is not Gorenstein. We describe the non-Gorenstein locus of $mathrm{Spec} R$. Further, we show that $R$ is almost Gorenstein. Moreover, we show that the conjecture of Hibi and Tsuchiya is true.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42122675","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":"Domination, Independent Domination and $k$-independence in Trees","authors":"Gang Zhang, Baoyindureng Wu","doi":"10.11650/tjm/211005","DOIUrl":"https://doi.org/10.11650/tjm/211005","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44011637","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}
A spacelike surface in Minkowski space $mathbb{R}_1^3$ is called a $K^alpha$-translator of the flow by the powers of Gauss curvature if satisfies $K^alpha= langle N,vec{v}rangle$, $alpha neq 0$, where $K$ is the Gauss curvature, $N$ is the unit normal vector field and $vec{v}$ is a direction of $mathbb{R}_1^3$. In this paper, we classify all rotational $K^alpha$-translators. This classification will depend on the causal character of the rotation axis. Although the theory of the $K^alpha$-flow holds for spacelike surfaces, the equation describing $K^alpha$-translators is still valid for timelike surfaces. So we also investigate the timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation.
{"title":"Rotational $K^{alpha}$-translators in Minkowski Space","authors":"M. Aydın, Rafael L'opez","doi":"10.11650/tjm/230602","DOIUrl":"https://doi.org/10.11650/tjm/230602","url":null,"abstract":"A spacelike surface in Minkowski space $mathbb{R}_1^3$ is called a $K^alpha$-translator of the flow by the powers of Gauss curvature if satisfies $K^alpha= langle N,vec{v}rangle$, $alpha neq 0$, where $K$ is the Gauss curvature, $N$ is the unit normal vector field and $vec{v}$ is a direction of $mathbb{R}_1^3$. In this paper, we classify all rotational $K^alpha$-translators. This classification will depend on the causal character of the rotation axis. Although the theory of the $K^alpha$-flow holds for spacelike surfaces, the equation describing $K^alpha$-translators is still valid for timelike surfaces. So we also investigate the timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42001507","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}
In this paper, we study the concept of approximate directional efficiency for set-valued constrained and unconstrained optimization problems. In our work, we concerned with finding conditions under which the Clarke penalization technique can be applied, and we derive some optimality conditions via variational analysis tools such as limiting normal cones and its corresponding normal coderivative.
{"title":"Exact Penalization and Optimality Conditions for Approximate Directional Minima","authors":"Teodor Chelmuş","doi":"10.11650/TJM/211004","DOIUrl":"https://doi.org/10.11650/TJM/211004","url":null,"abstract":"In this paper, we study the concept of approximate directional efficiency for set-valued constrained and unconstrained optimization problems. In our work, we concerned with finding conditions under which the Clarke penalization technique can be applied, and we derive some optimality conditions via variational analysis tools such as limiting normal cones and its corresponding normal coderivative.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48754486","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":"Blow-up in Coupled Solutions for a $4$-dimensional Semilinear Elliptic Kuramoto–Sivashinsky System","authors":"Lilia Larbi, N. Trabelsi","doi":"10.11650/tjm/220601","DOIUrl":"https://doi.org/10.11650/tjm/220601","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44998661","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}
. The uniform stabilization of a semilinear wave equation with variable coef-ficients and nonlinear boundary conditions is considered. The uniform decay rate is established by the Riemannian geometry method.
。研究一类具有非线性边界条件的变系数半线性波动方程的一致镇定问题。用黎曼几何方法建立了均匀衰减率。
{"title":"Uniform Stabilization for a Semilinear Wave Equation with Variable Coefficients and Nonlinear Boundary Conditions","authors":"El-Hadi Kamel, A. Ainouz, A. Khemmoudj","doi":"10.11650/tjm/220302","DOIUrl":"https://doi.org/10.11650/tjm/220302","url":null,"abstract":". The uniform stabilization of a semilinear wave equation with variable coef-ficients and nonlinear boundary conditions is considered. The uniform decay rate is established by the Riemannian geometry method.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46351763","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":"Labeling Trees of Small Diameters with Consecutive Integers","authors":"Wei-Tian Li, Yi-Shun Wang","doi":"10.11650/tjm/221103","DOIUrl":"https://doi.org/10.11650/tjm/221103","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48052337","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}
. The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all n -vertex k -uniform hypertrees, we determine the k -uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all n -vertex k -uniform unicyclic hypergraphs, we obtain the k -uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the k -uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.
{"title":"Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs","authors":"Xiangxiang Liu, Ligong Wang","doi":"10.11650/tjm/220604","DOIUrl":"https://doi.org/10.11650/tjm/220604","url":null,"abstract":". The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all n -vertex k -uniform hypertrees, we determine the k -uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all n -vertex k -uniform unicyclic hypergraphs, we obtain the k -uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the k -uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43552524","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}
. In this paper, we investigate the L 2 boundedness of Fourier integral operator T φ,a with rough symbol a ∈ L ∞ S mρ and rough phase φ ∈ L ∞ Φ 2 which satisfies (cid:12)(cid:12) { x : |∇ ξ φ ( x, ξ ) − y | ≤ r } (cid:12)(cid:12) ≤ C ( r n − 1 + r n ) for any ξ, y ∈ R n and r > 0. We obtain that T φ,a is bounded on L 2 if m < ρ ( n − 1) / 2 − n/ 2 when 0 ≤ ρ ≤ 1 / 2 or m < − ( n + 1) / 4 when 1 / 2 ≤ ρ ≤ 1. When ρ = 0 or n = 1, the condition of m is sharp. Moreover, the maximal wave operator is a special class of T φ,a which is studied in this paper. Thus, our main theorem substantially extends and improves some known results about the maximal wave operator.
． 在这个L 2 boundedness》,这篇文章我们investigate傅立叶集成运营商Tφ和rough符号a∈a, L∞smρ和野蛮时期φ∈L∞Φ2萨蒂哪种fi冰(cid 12: 12) (cid) {x: |∇ξφ(x, yξ)−|≤r} (cid 12: 12) (cid)≤r C (n−1 + r∈r y n)为任何ξ,n和r > 0。我们得到那个φT,如果a是bounded on L 2 m <ρ(n−1)/ 2−n / 2当0≤ρ≤1 - 2或m <−(n + 1) / 4当1 / 2≤ρ≤1。当ρ= 0或n = 1, m是夏普之雾。而且,最大限度的浪潮是运营商a T特别届φ,哪种是studied in this paper)。因此，我们主要的物质扩展和一些最著名的结果关于最高浪潮运营商。
{"title":"Global $L^{2}$-boundedness of a New Class of Rough Fourier Integral Operators","authors":"Jiawei Dai, Qiang Huang","doi":"10.11650/tjm/220403","DOIUrl":"https://doi.org/10.11650/tjm/220403","url":null,"abstract":". In this paper, we investigate the L 2 boundedness of Fourier integral operator T φ,a with rough symbol a ∈ L ∞ S mρ and rough phase φ ∈ L ∞ Φ 2 which satisfies (cid:12)(cid:12) { x : |∇ ξ φ ( x, ξ ) − y | ≤ r } (cid:12)(cid:12) ≤ C ( r n − 1 + r n ) for any ξ, y ∈ R n and r > 0. We obtain that T φ,a is bounded on L 2 if m < ρ ( n − 1) / 2 − n/ 2 when 0 ≤ ρ ≤ 1 / 2 or m < − ( n + 1) / 4 when 1 / 2 ≤ ρ ≤ 1. When ρ = 0 or n = 1, the condition of m is sharp. Moreover, the maximal wave operator is a special class of T φ,a which is studied in this paper. Thus, our main theorem substantially extends and improves some known results about the maximal wave operator.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47526394","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}
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