Pub Date : 2023-08-18DOI: 10.1007/s10998-023-00542-5
Barbara Łupińska
{"title":"Existence and nonexistence results for fractional mixed boundary value problems via a Lyapunov-type inequality","authors":"Barbara Łupińska","doi":"10.1007/s10998-023-00542-5","DOIUrl":"https://doi.org/10.1007/s10998-023-00542-5","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42138081","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}
Pub Date : 2023-08-17DOI: 10.1007/s10998-023-00541-6
A. Rinot, Roy Shalev, S. Todorcevic
{"title":"A new small Dowker space","authors":"A. Rinot, Roy Shalev, S. Todorcevic","doi":"10.1007/s10998-023-00541-6","DOIUrl":"https://doi.org/10.1007/s10998-023-00541-6","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47649383","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}
Pub Date : 2023-08-12DOI: 10.1007/s10998-023-00543-4
R. Baker
{"title":"The exceptional set for integers of the form $$[p_1^c]+[p_2^c]$$","authors":"R. Baker","doi":"10.1007/s10998-023-00543-4","DOIUrl":"https://doi.org/10.1007/s10998-023-00543-4","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45246674","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}
Pub Date : 2023-08-10DOI: 10.1007/s10998-023-00534-5
Haihong Fan, W. Zhai
{"title":"On the consecutive k-free values for certain classes of polynomials","authors":"Haihong Fan, W. Zhai","doi":"10.1007/s10998-023-00534-5","DOIUrl":"https://doi.org/10.1007/s10998-023-00534-5","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45014308","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}
Pub Date : 2023-06-05DOI: 10.1007/s10998-023-00529-2
M. Z. Garaev
In 1997 we proved that if n is of the form $$begin{aligned} 4k, quad 8k-1quad {textrm{or}} quad 2^{2m+1}(2k-1)+3, end{aligned}$$ where $$k,min {mathbb {N}} $$ , then there are no positive rational numbers x, y, z satisfying $$begin{aligned} xyz = 1, quad x+y+z = n. end{aligned}$$ Recently, N. X. Tho proved the following statement: let $$ain mathbb N$$ be odd and let either $$nequiv 0pmod 4$$ or $$nequiv 7pmod 8$$ . Then the system of equations $$begin{aligned} xyz = a, quad x+y+z = an. end{aligned}$$ has no solutions in positive rational numbers x, y, z. A representative example of our result is the following statement: assume that $$a,nin {mathbb {N}}$$ are such that at least one of the following conditions holds: Then the system of equations $$begin{aligned} xyz = a, quad x+y+z = an. end{aligned}$$ has no solutions in positive rational numbers x, y, z.
1997年，我们证明了如果n的形式为$$begin{aligned} 4k, quad 8k-1quad {textrm{or}} quad 2^{2m+1}(2k-1)+3, end{aligned}$$，其中$$k,min {mathbb {N}} $$，则不存在正有理数x, y, z满足$$begin{aligned} xyz = 1, quad x+y+z = n. end{aligned}$$。最近，n . x . Tho证明了以下命题:设$$ain mathbb N$$为奇数，且取$$nequiv 0pmod 4$$或$$nequiv 7pmod 8$$。那么方程组$$begin{aligned} xyz = a, quad x+y+z = an. end{aligned}$$在正有理数x, y, z中没有解。我们的结果的一个代表性的例子是下面的陈述:假设$$a,nin {mathbb {N}}$$是这样的，至少满足下列条件之一:那么方程组$$begin{aligned} xyz = a, quad x+y+z = an. end{aligned}$$在正有理数x, y, z中没有解。
{"title":"On integer values of sum and product of three positive rational numbers","authors":"M. Z. Garaev","doi":"10.1007/s10998-023-00529-2","DOIUrl":"https://doi.org/10.1007/s10998-023-00529-2","url":null,"abstract":"In 1997 we proved that if n is of the form $$begin{aligned} 4k, quad 8k-1quad {textrm{or}} quad 2^{2m+1}(2k-1)+3, end{aligned}$$ where $$k,min {mathbb {N}} $$ , then there are no positive rational numbers x, y, z satisfying $$begin{aligned} xyz = 1, quad x+y+z = n. end{aligned}$$ Recently, N. X. Tho proved the following statement: let $$ain mathbb N$$ be odd and let either $$nequiv 0pmod 4$$ or $$nequiv 7pmod 8$$ . Then the system of equations $$begin{aligned} xyz = a, quad x+y+z = an. end{aligned}$$ has no solutions in positive rational numbers x, y, z. A representative example of our result is the following statement: assume that $$a,nin {mathbb {N}}$$ are such that at least one of the following conditions holds: Then the system of equations $$begin{aligned} xyz = a, quad x+y+z = an. end{aligned}$$ has no solutions in positive rational numbers x, y, z.","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135658763","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}
Pub Date : 2023-06-05DOI: 10.1007/s10998-023-00527-4
David E. Hong, Dan Ismailescu, Alex Kwak, Grace Y. Park
Approximation of convex disks by inscribed and circumscribed polygons is a classical geometric problem whose study is motivated by various applications in robotics and computer aided design. We consider the following optimization problem: given integers $$3le nle m-1$$ , find the value or an estimate of $$begin{aligned} r(n,m)=max _{Pin {mathcal {P}}_m},, min _{Qin {mathcal {P}}_n,,Q supseteq P} frac{|Q|}{|P|} end{aligned}$$ where P varies in the set $${mathcal {P}}_m$$ of all convex m-gons, and, for a fixed m-gon P, the minimum is taken over all n-gons Q containing P; here $$|cdot |$$ denotes area. It is easy to prove that $$r(3,4)=2$$ , and from a result of Gronchi and Longinetti it follows that $$r(n-1, n)= 1+frac{1}{n}tan left( pi /{n}right) tan left( {2pi }/{n}right) $$ for all $$nge 6$$ . In this paper we show that every unit area convex pentagon is contained in a convex quadrilateral of area no greater than $$3/sqrt{5}$$ thus determining the value of r(4, 5). In all cases, the equality is reached only for affine regular polygons.
内切多边形逼近凸盘是一个经典的几何问题，其研究受到机器人和计算机辅助设计的各种应用的推动。我们考虑以下优化问题:给定整数$$3le nle m-1$$，求出所有凸m-gon集合$${mathcal {P}}_m$$中P变化的值或估计值$$begin{aligned} r(n,m)=max _{Pin {mathcal {P}}_m},, min _{Qin {mathcal {P}}_n,,Q supseteq P} frac{|Q|}{|P|} end{aligned}$$，并且对于一个固定的m-gon P，取所有包含P的n-gon Q的最小值;这里$$|cdot |$$表示面积。很容易证明$$r(3,4)=2$$，从Gronchi和Longinetti的结果可以得出$$r(n-1, n)= 1+frac{1}{n}tan left( pi /{n}right) tan left( {2pi }/{n}right) $$适用于所有$$nge 6$$。在本文中，我们证明了每个单位面积的凸五边形都包含在一个面积不大于$$3/sqrt{5}$$的凸四边形中，从而确定了r(4,5)的值。在所有情况下，只有仿射正多边形才能达到这个等式。
{"title":"On the smallest area $$(n-1)$$-gon containing a convex n-gon","authors":"David E. Hong, Dan Ismailescu, Alex Kwak, Grace Y. Park","doi":"10.1007/s10998-023-00527-4","DOIUrl":"https://doi.org/10.1007/s10998-023-00527-4","url":null,"abstract":"Approximation of convex disks by inscribed and circumscribed polygons is a classical geometric problem whose study is motivated by various applications in robotics and computer aided design. We consider the following optimization problem: given integers $$3le nle m-1$$ , find the value or an estimate of $$begin{aligned} r(n,m)=max _{Pin {mathcal {P}}_m},, min _{Qin {mathcal {P}}_n,,Q supseteq P} frac{|Q|}{|P|} end{aligned}$$ where P varies in the set $${mathcal {P}}_m$$ of all convex m-gons, and, for a fixed m-gon P, the minimum is taken over all n-gons Q containing P; here $$|cdot |$$ denotes area. It is easy to prove that $$r(3,4)=2$$ , and from a result of Gronchi and Longinetti it follows that $$r(n-1, n)= 1+frac{1}{n}tan left( pi /{n}right) tan left( {2pi }/{n}right) $$ for all $$nge 6$$ . In this paper we show that every unit area convex pentagon is contained in a convex quadrilateral of area no greater than $$3/sqrt{5}$$ thus determining the value of r(4, 5). In all cases, the equality is reached only for affine regular polygons.","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135658808","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}
Pub Date : 2023-06-02DOI: 10.1007/s10998-023-00528-3
Zhenyu Guo, Lu Zhao
{"title":"Existence of ground states for fractional Choquard–Kirchhoff equations with magnetic fields and critical exponents","authors":"Zhenyu Guo, Lu Zhao","doi":"10.1007/s10998-023-00528-3","DOIUrl":"https://doi.org/10.1007/s10998-023-00528-3","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46613791","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}
Pub Date : 2023-05-29DOI: 10.1007/s10998-023-00520-x
R. Kamocki, Cezary Obczyński
{"title":"On the single partial Caputo derivatives for functions of two variables","authors":"R. Kamocki, Cezary Obczyński","doi":"10.1007/s10998-023-00520-x","DOIUrl":"https://doi.org/10.1007/s10998-023-00520-x","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46229493","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}
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