We treat a variation of graph domination which involves a partition (V 1, V 2,..., Vk ) of the vertex set of a graph G and domination of each partition class V i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.
{"title":"Distance Domination in Vertex Partitioned Graphs","authors":"A. Frendrup, Z. Tuza, P. Vestergaard","doi":"10.1556/314.2022.00006","DOIUrl":"https://doi.org/10.1556/314.2022.00006","url":null,"abstract":"We treat a variation of graph domination which involves a partition (V\u0000 1, V\u0000 2,..., Vk\u0000 ) of the vertex set of a graph G and domination of each partition class V\u0000 i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115965047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.
{"title":"Hamilton Triangle of a Triangle in the Isotropic Plane","authors":"Z. Kolar-Begović, V. Volenec","doi":"10.1556/314.2022.00001","DOIUrl":"https://doi.org/10.1556/314.2022.00001","url":null,"abstract":"In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126889998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.
证明了一类误差稳定的AR(1)过程的协方差参数的裁剪最小二乘估计的弱相合性。
{"title":"Trimmed Least Square Estimators for Stable Ar(1) Processes","authors":"A. Bazarova, I. Berkes, Lajos Horváth","doi":"10.1556/314.2022.00003","DOIUrl":"https://doi.org/10.1556/314.2022.00003","url":null,"abstract":"We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"285 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132876764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we establish some Ostrowski type inequalities for double integral mean of absolutely continuous functions. An application for special means is given as well.
本文建立了绝对连续函数的二重积分均值的Ostrowski型不等式。并提出了特殊手段的申请。
{"title":"Some Inequalities of Ostrowski Type for Double Integral Mean of Absolutely Continuous Functions","authors":"S. Dragomir","doi":"10.1556/314.2022.00005","DOIUrl":"https://doi.org/10.1556/314.2022.00005","url":null,"abstract":"In this paper we establish some Ostrowski type inequalities for double integral mean of absolutely continuous functions. An application for special means is given as well.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134032264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the 1980’s the author proved lower bounds for the mean value of the modulus of the error term of the prime number theorem and other important number theoretic functions whose oscillation is in connection with the zeros of the Riemann zeta function. In the present work a general theorem is shown in a simple way which gives a lower bound for the mentioned mean value as a function of a hypothetical pole of the Mellin transform of the function. The conditions are amply satisfied for the Riemann zeta function. In such a way the results recover the earlier ones (even in a slightly sharper form). The obtained estimates are often optimal apart from a constant factor, at least under reasonable conditions as the Riemann Hypothesis. This is the case, in particular, for the error term of the prime number theorem.
{"title":"On the Mean Value of Arithmetic Error Terms","authors":"J. Pintz","doi":"10.1556/314.2022.00007","DOIUrl":"https://doi.org/10.1556/314.2022.00007","url":null,"abstract":"In the 1980’s the author proved lower bounds for the mean value of the modulus of the error term of the prime number theorem and other important number theoretic functions whose oscillation is in connection with the zeros of the Riemann zeta function. In the present work a general theorem is shown in a simple way which gives a lower bound for the mentioned mean value as a function of a hypothetical pole of the Mellin transform of the function. The conditions are amply satisfied for the Riemann zeta function. In such a way the results recover the earlier ones (even in a slightly sharper form). The obtained estimates are often optimal apart from a constant factor, at least under reasonable conditions as the Riemann Hypothesis. This is the case, in particular, for the error term of the prime number theorem.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133515524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.
本文推广了Schatte[11]和Atlagh and Weber[2]的结果，给出了随机变量序列沿给定整数序列满足几乎确定中心极限定理的条件。
{"title":"On the Almost Sure Central Limit Theorem Along Subsequences","authors":"I. Berkes, E. Csáki","doi":"10.1556/314.2022.00002","DOIUrl":"https://doi.org/10.1556/314.2022.00002","url":null,"abstract":"Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121344866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.
{"title":"Inequalities for the First and Second Derivatives of Algebraic Polynomials on an Ellipse","authors":"Tatiana M. Nikiforova","doi":"10.1556/314.2021.00020","DOIUrl":"https://doi.org/10.1556/314.2021.00020","url":null,"abstract":"We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130330297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.
{"title":"A Theory of Congruences and Birkhoff’s Theorem for Matroids","authors":"S. Veldsman","doi":"10.1556/314.2021.00015","DOIUrl":"https://doi.org/10.1556/314.2021.00015","url":null,"abstract":"A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"13 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113944494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let (M, [g]) be a Weyl manifold and TM be its tangent bundle equipped with Riemannian g−natural metrics which are linear combinations of Sasaki, horizontal and vertical lifts of the base metric with constant coefficients. The aim of this paper is to construct a Weyl structure on TM and to show that TM cannot be Einstein-Weyl even if (M, g) is fiat.
{"title":"The Metrics G = agS + bgH + cgV on the Tangent Bundle of a Weyl Manifold","authors":"M. Altunbaş","doi":"10.1556/314.2021.00017","DOIUrl":"https://doi.org/10.1556/314.2021.00017","url":null,"abstract":"Let (M, [g]) be a Weyl manifold and TM be its tangent bundle equipped with Riemannian g−natural metrics which are linear combinations of Sasaki, horizontal and vertical lifts of the base metric with constant coefficients. The aim of this paper is to construct a Weyl structure on TM and to show that TM cannot be Einstein-Weyl even if (M, g) is fiat.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116108612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give all functions ƒ , E: ℕ → ℂ which satisfy the relation for every a, b, c ∈ ℕ, where h ≥ 0 is an integers and K is a complex number. If n cannot be written as a2 + b2 + c2 + h for suitable a, b, c ∈ ℕ, then ƒ (n) is not determined. This is more complicated if we assume that ƒ and E are multiplicative functions.
{"title":"Arithmetical Functions Commutable with Sums of Squares II","authors":"I. Kátai, B. Phong","doi":"10.1556/314.2021.00016","DOIUrl":"https://doi.org/10.1556/314.2021.00016","url":null,"abstract":"We give all functions ƒ , E: ℕ → ℂ which satisfy the relation\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 for every a, b, c ∈ ℕ, where h ≥ 0 is an integers and K is a complex number. If n cannot be written as a2 + b2 + c2 + h for suitable a, b, c ∈ ℕ, then ƒ (n) is not determined. This is more complicated if we assume that ƒ and E are multiplicative functions.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134026237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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