TY - JOUR AU - Lerf, Verona AU - Borics, Gábor AU - Tóth, István AU - Kisantal, Tibor AU - Lukács, Áron AU - Tóthmérész, Béla AU - Buczolich, Zoltán AU - Bárány, Balázs AU - Végvári, Zsolt AU - Török-Krasznai, Enikő TI - Measures of morphological complexity of microalgae and their linkage with organism size JF - HYDROBIOLOGIA J2 - HYDROBIOLOGIA VL - 851 PY - 2024 SP - 751 EP - 764 PG - 14 SN - 0018-8158 DO - 10.1007/s10750-023-05338-9 UR - https://m2.mtmt.hu/api/publication/34140740 ID - 34140740 N1 - Funding Agency and Grant Number: Hungarian Scientific Research Fund (NKFIH OTKA) [K-132150] Funding text: This work was supported by Hungarian Scientific Research Fund (NKFIH OTKA) project no.: K-132150. A. L. was supported by KKP-144068 during manuscript writing. AB - In phytoplankton ecology the shape of microalgae appears predominantly as a categorical variable. Using shape-realistic 3D models of 220 microalgae we proposed and calculated six shape metrics and tested how these relate to each other and to the size of the microalgae. We found that some of the metrics are more sensitive to elongation, while others are related to multicellularity. We found a linear relationship between shape measures and the greatest axial linear dimensions of the microalgae. Our findings suggest that there is an evolutionary trade-off between the shape and size of the microalgae. It is important to stress that we found that surface area to volume ratio of the microalgae are hyperbolic functions of the length and volume for each shape. In our study, we demonstrated that the proposed shape metrics serve as suitable quantitative traits, and help to understand better how simple shapes evolved to more complex outlines. LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Leobacher, Gunther AU - Steinicke, Alexander TI - Continuous functions with impermeable graphs JF - MATHEMATISCHE NACHRICHTEN J2 - MATH NACHR VL - 296 PY - 2023 IS - 10 SP - 4778 EP - 4805 PG - 28 SN - 0025-584X DO - 10.1002/mana.202200268 UR - https://m2.mtmt.hu/api/publication/34024227 ID - 34024227 LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán TI - Almost Everywhere Convergence Questions of Series of Translates of Non-Negative Functions JF - REAL ANALYSIS EXCHANGE J2 - REAL ANALYSIS EXCHANGE VL - 48 PY - 2023 IS - 1 SP - 49 EP - 76 PG - 28 SN - 0147-1937 DO - 10.14321/realanalexch.48.1.1663223339 UR - https://m2.mtmt.hu/api/publication/33755338 ID - 33755338 N1 - Export Date: 9 May 2023 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu Funding details: Horizon 2020 Framework Programme, H2020, 741420 Funding details: European Research Council, ERC Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, 124003 Funding text 1: 60F20Key words: almost everywhere convergence, asymptotically dense sets, Borel–Cantelli lemma, laws of large numbers, zero-one laws Received by the editors September 15, 2022 Communicated by: Paul D. Humke ∗The project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 741420). This author was also supported by the Hungarian National Research, Development and Innovation Office–NKFIH, Grant 124003 and at the time of part of the work on this paper was holding a visiting researcher position at the Rényi Institute. LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Seuret, Stéphane TI - Measures, annuli and dimensions JF - MATHEMATISCHE ZEITSCHRIFT J2 - MATH Z VL - 303 PY - 2023 IS - 4 SN - 0025-5874 DO - 10.1007/s00209-023-03230-9 UR - https://m2.mtmt.hu/api/publication/33682478 ID - 33682478 N1 - Export Date: 4 April 2023 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu Funding details: Horizon 2020 Framework Programme, H2020, 741420 Funding details: European Research Council, ERC Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, 124003, ANR-16-CE33-0020 Funding text 1: Zoltán Buczolich’s project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 741420). This author was supported by the Hungarian National Research, Development and Innovation Office—NKFIH, Grant 124003 and at the time of completion of this paper was holding a visiting researcher position at the Rényi Institute. Stéphane Seuret was supported by Grant ANR-16-CE33-0020 MULTIFRACS. AB - Given a Radon probability measure \mu μ supported in {\mathbb {R}}^d R d , we are interested in those points x around which the measure is concentrated infinitely many times on thin annuli centered at x . Depending on the lower and upper dimension of \mu μ , the metric used in the space and the thinness of the annuli, we obtain results and examples when such points are of \mu μ -measure 0 or of \mu μ -measure 1. The measure concentration we study is related to “bad points” for the Poincaré recurrence theorem and to the first return times to shrinking balls under iteration generated by a weakly Markov dynamical system. The study of thin annuli and spherical averages is also important in many dimension-related problems, including Kakeya-type problems and Falconer’s distance set conjecture. LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Hanson, Bruce AU - Maga, Balázs AU - Vértesy, Gáspár TI - Strong one-sided density without uniform density JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG VL - 86 PY - 2023 SP - 13 EP - 23 PG - 11 SN - 0031-5303 DO - 10.1007/s10998-022-00455-9 UR - https://m2.mtmt.hu/api/publication/32750764 ID - 32750764 N1 - Department of Analysis, ELTE Eötvös Loránd University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN 55057, United States Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, 1053, Hungary Export Date: 8 September 2022 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Maga, Balázs AU - Vértesy, Gáspár TI - Generic Hölder level sets and fractal conductivity JF - CHAOS SOLITONS & FRACTALS J2 - CHAOS SOLITON FRACT VL - 164 PY - 2022 SN - 0960-0779 DO - 10.1016/j.chaos.2022.112696 UR - https://m2.mtmt.hu/api/publication/33124160 ID - 33124160 N1 - Department of Analysis, ELTE Eötvös Loránd, University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda street 13-15, Budapest, 1053, Hungary Export Date: 4 October 2022 CODEN: CSFOE Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Maga, Balázs AU - Vértesy, Gáspár TI - Generic Hölder level sets on fractals JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 516 PY - 2022 IS - 2 SN - 0022-247X DO - 10.1016/j.jmaa.2022.126543 UR - https://m2.mtmt.hu/api/publication/33072066 ID - 33072066 AB - Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the topological Hausdorff dimension of fractals was defined. In this paper we start to study level sets of generic 1-Hölder-α functions defined on fractals. This is related to some sort of “thickness”, “conductivity” properties of fractals. The main concept of our paper is D⁎(α,F) which is the essential supremum of the Hausdorff dimensions of the level sets of a generic 1-Hölder-α function defined on the fractal F. We prove some basic properties of D⁎(α,F), we calculate its value for an example of a “thick fractal sponge”, we show that for connected self similar sets D⁎(α,F) it equals the Hausdorff dimension of almost every level in the range of a generic 1-Hölder-α function. © 2022 The Author(s) LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Järvenpää, Esa AU - Järvenpää, Maarit AU - Keleti, Tamás AU - Pöyhtäri, Tuomas TI - Fractal percolation is unrectifiable JF - ADVANCES IN MATHEMATICS J2 - ADV MATH VL - 390 PY - 2021 PG - 61 SN - 0001-8708 DO - 10.1016/j.aim.2021.107906 UR - https://m2.mtmt.hu/api/publication/32216495 ID - 32216495 LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Hanson, Bruce AU - Maga, Balázs AU - Vértesy, Gáspár TI - Big and little Lipschitz one sets JF - EUROPEAN JOURNAL OF MATHEMATICS J2 - EUR J MATH VL - 7 PY - 2021 IS - 2 SP - 464 EP - 488 PG - 25 SN - 2199-675X DO - 10.1007/s40879-021-00458-9 UR - https://m2.mtmt.hu/api/publication/31981091 ID - 31981091 N1 - Department of Analysis, ELTE Eötvös Loránd, University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN 55057, United States Cited By :1 Export Date: 8 September 2022 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Eisner, Tanja TI - Divergence of weighted square averages in L1 JF - ADVANCES IN MATHEMATICS J2 - ADV MATH VL - 384 PY - 2021 PG - 19 SN - 0001-8708 DO - 10.1016/j.aim.2021.107727 UR - https://m2.mtmt.hu/api/publication/31965623 ID - 31965623 N1 - Export Date: 20 January 2023 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER -