We study the structure of potent elements in matrix rings with same diagonals and polynomial rings, motivated by Jacobson's theorem of commutativity. A ring shall be said to be PC if every potent element is central. We investigate the structure of PC rings in relation to the commutativity of rings. It is proved that if $R$ is a PC ring of prime characteristic then the polynomial ring over $R$ is also a PC ring. Every periodic PC ring is shown to be commutative.
{"title":"Structure of Rings Whose Potent Elements are Central","authors":"Tai Keun Kwak, Yang Lee, Yeonsook Seo","doi":"10.11650/tjm/231103","DOIUrl":"https://doi.org/10.11650/tjm/231103","url":null,"abstract":"We study the structure of potent elements in matrix rings with same diagonals and polynomial rings, motivated by Jacobson's theorem of commutativity. A ring shall be said to be PC if every potent element is central. We investigate the structure of PC rings in relation to the commutativity of rings. It is proved that if $R$ is a PC ring of prime characteristic then the polynomial ring over $R$ is also a PC ring. Every periodic PC ring is shown to be commutative.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135668202","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":"On the Maximal Number of Maximum Dissociation Sets in Forests with Fixed Order and Dissociation Number","authors":"Wanting Sun, Shuchao Li","doi":"10.11650/tjm/230204","DOIUrl":"https://doi.org/10.11650/tjm/230204","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47799614","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":"Ventcel-type Transmission Conditions for the Scattering of a Time-harmonic Wave Problem with Accuracy up to Order $3$","authors":"K. E. Boutarene, Sami Galleze","doi":"10.11650/tjm/230201","DOIUrl":"https://doi.org/10.11650/tjm/230201","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46532944","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 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":" ","pages":""},"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":" ","pages":""},"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}
This study investigated the spatial resolution and image quality of the continuous bed motion (CBM) method in a sensitive silicon photomultiplier (SiPM)-based positron emission tomography (PET)/computed tomography (CT) system compared with the traditional step-and-shoot (SS) method. Methods: Siemens Biograph Vision was used in this study. Data acquisition using the SS method was performed for 3 min per bed. In the CBM method, the bed speed ranged from 0.5 to 3.3 mm/s. The acquisition time equivalent to the SS method was 1.1 mm/s for 2-bed ranges and 0.8 mm/s for seven-bed ranges. The spatial resolution was investigated using 18F point sources and evaluated using the full width at half maximum. Image quality was investigated using a National Electrical Manufacturers Association International Electrotechnical Commission body phantom with six spheres 10-, 13-, 17-, 22-, 28-, and 37-mm inner diameters. The radioactivity concentration ratio of the 18F solution in all spheres and the background was approximately 4:1. The detectability of each sphere was visually evaluated on a five-step score. Image quality was physically evaluated using the noise equivalent count rate (NECphantom), contrast percentage of the 10-mm hot sphere (QH,10mm), background variability percentage (N10mm), and contrast-noise ratio (QH,10mm/N10mm). Results: The spatial resolution was not affected by the difference of acquisition methods and bed speeds. The detectability of the 10-mm sphere with a bed speed of 2.2 mm/s or faster was significantly inferior to that of the SS 2-bed method. In evaluating image quality, no significant difference in the contrast percentage was observed among the acquisition methods and speeds in the CBM method. However, the increasing bed speed in the CBM method increased the N10mm and decreased the NECphantom. When comparing the SS 2-bed method with the CBM method at 0.8 mm/s, no significant differences in all parameters were observed. Conclusion: In a SiPM-based PET/CT scanner, the CBM method provides equivalent spatial resolution and image quality in whole body PET images with same acquisition time using the SS method.
本研究调查了基于灵敏硅光电倍增管（SiPM）的正电子发射计算机断层扫描（PET）/计算机断层扫描（CT）系统中的连续床面运动（CBM）方法与传统的步进扫描（SS）方法相比的空间分辨率和图像质量。方法：本研究使用西门子 Biograph Vision。使用 SS 方法采集数据时，每个床位持续 3 分钟。在 CBM 方法中，床速范围为 0.5 至 3.3 mm/s。相当于 SS 方法的采集时间，2 床范围为 1.1 mm/s，7 床范围为 0.8 mm/s。使用 18F 点源对空间分辨率进行了研究，并使用半最大全宽进行了评估。使用美国国家电气制造商协会国际电工委员会的人体模型对图像质量进行了研究，该模型有六个球体，内径分别为 10 毫米、13 毫米、17 毫米、22 毫米、28 毫米和 37 毫米。所有球体中 18F 溶液的放射性浓度与背景浓度之比约为 4:1。每个球体的可探测性通过五步评分法进行目测评估。图像质量通过噪声等效计数率（NECphantom）、10 毫米热球的对比度百分比（QH,10mm）、背景变异百分比（N10mm）和对比度-噪声比（QH,10mm/N10mm）进行物理评估。结果显示空间分辨率不受采集方法和床速差异的影响。床速为 2.2 mm/s 或更快的 10 mm 球体的可探测性明显低于 SS 2 床方法。在评估图像质量时，CBM 方法的不同采集方法和速度在对比度百分比上没有明显差异。然而，CBM 方法中床速的增加提高了 N10mm，降低了 NECphantom。将 SS 双床法与 CBM 法以 0.8 mm/s 的速度进行比较时，在所有参数上均未见明显差异。结论在基于 SiPM 的 PET/CT 扫描仪中，CBM 方法与 SS 方法在相同的采集时间内提供了同等的全身 PET 图像空间分辨率和图像质量。
{"title":"Continuous bed motion in a silicon photomultiplier-based scanner provides equivalent spatial resolution and image quality in whole body PET images at similar acquisition times using the step-and-shoot method.","authors":"Kodai Kumamoto, Hideaki Sato, Yuji Tsutsui, Shinichi Awamoto, Yasuo Yamashita, Shingo Baba, Masayuki Sasaki","doi":"10.2967/jnmt.121.263240","DOIUrl":"10.2967/jnmt.121.263240","url":null,"abstract":"<p><p>This study investigated the spatial resolution and image quality of the continuous bed motion (CBM) method in a sensitive silicon photomultiplier (SiPM)-based positron emission tomography (PET)/computed tomography (CT) system compared with the traditional step-and-shoot (SS) method. <b>Methods:</b> Siemens Biograph Vision was used in this study. Data acquisition using the SS method was performed for 3 min per bed. In the CBM method, the bed speed ranged from 0.5 to 3.3 mm/s. The acquisition time equivalent to the SS method was 1.1 mm/s for 2-bed ranges and 0.8 mm/s for seven-bed ranges. The spatial resolution was investigated using <sup>18</sup>F point sources and evaluated using the full width at half maximum. Image quality was investigated using a National Electrical Manufacturers Association International Electrotechnical Commission body phantom with six spheres 10-, 13-, 17-, 22-, 28-, and 37-mm inner diameters. The radioactivity concentration ratio of the <sup>18</sup>F solution in all spheres and the background was approximately 4:1. The detectability of each sphere was visually evaluated on a five-step score. Image quality was physically evaluated using the noise equivalent count rate (NECphantom), contrast percentage of the 10-mm hot sphere (QH,10mm), background variability percentage (N10mm), and contrast-noise ratio (QH,10mm/N10mm). <b>Results:</b> The spatial resolution was not affected by the difference of acquisition methods and bed speeds. The detectability of the 10-mm sphere with a bed speed of 2.2 mm/s or faster was significantly inferior to that of the SS 2-bed method. In evaluating image quality, no significant difference in the contrast percentage was observed among the acquisition methods and speeds in the CBM method. However, the increasing bed speed in the CBM method increased the N10mm and decreased the NECphantom. When comparing the SS 2-bed method with the CBM method at 0.8 mm/s, no significant differences in all parameters were observed. <b>Conclusion:</b> In a SiPM-based PET/CT scanner, the CBM method provides equivalent spatial resolution and image quality in whole body PET images with same acquisition time using the SS method.</p>","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87021229","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":" ","pages":""},"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":"1 1","pages":""},"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":" ","pages":""},"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":"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":" ","pages":""},"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}
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