TY - JOUR AU - Erdélyi, Márton Kristóf AU - Tóth, Árpád AU - Zábrádi, Gergely TI - Matrix Kloosterman sums modulo prime powers JF - MATHEMATISCHE ZEITSCHRIFT J2 - MATH Z VL - 306 PY - 2024 IS - 4 PG - 21 SN - 0025-5874 DO - 10.1007/s00209-024-03467-y UR - https://m2.mtmt.hu/api/publication/34741100 ID - 34741100 N1 - Funding Agency and Grant Number: MTA-RI Lendulet "Momentum" Analytic Number Theory and Representation Theory Research Group; NKFIH Research Grants [FK-127906, K-135885, K 119528]; Renyi Institute Lendulet Automorphic Research Group; MTA-RI Lenduelet "Momentum" Analytic Number Theory and Representation Theory Research Group Funding text: Erdelyi was supported by the MTA-RI Lendulet "Momentum" Analytic Number Theory and Representation Theory Research Group, and by NKFIH Research Grants FK-127906 and K-135885. Toth was supported by by the Renyi Institute Lendulet Automorphic Research Group, by the NKFIH Research Grants K 119528 and K-135885. Zabradi was supported by the Renyi Institute Lenduelet Automorphic Research Group, by the MTA-RI Lenduelet "Momentum" Analytic Number Theory and Representation Theory Research Group, and by the NKFIH Research Grants FK-127906 and K-135885. We thank the referee for a careful reading and helpful comments. We are also grateful to the authors of the paper [5] who provided valuable suggestions for improvements in the presentation of the paper. We also thank them for many stimulating conversations during a Heilbronn research workshop on Effective equidistribution in homogeneous dynamics, that they organized at the University of Bristol. AB - We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on the case of prime moduli. These exponential sums arise in the theory of the horocyclic flow on GL_n G L n . LA - English DB - MTMT ER - TY - JOUR AU - Kiss, Gergely AU - Matolcsi, Dávid AU - Matolcsi, Máté AU - Somlai, Gábor TI - Tiling and weak tiling in (Zp)d JF - Sampling Theory, Signal Processing, and Data Analysis J2 - Sampl. Theory Signal Process. Data Anal. VL - 22 PY - 2024 IS - 1 SN - 2730-5716 DO - 10.1007/s43670-023-00073-7 UR - https://m2.mtmt.hu/api/publication/34429446 ID - 34429446 N1 - Alfréd Rényi Institute of Mathematics, HUN-REN, Reáltanoda u. 13-15, Budapest, 1053, Hungary Eötvös Loránd University, Pázmány Péter sétány 1/C, Budapest, 1111, Hungary Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics (BME), Müegyetem rkp. 3, Budapest, 1111, Hungary Export Date: 14 December 2023 Correspondence Address: Matolcsi, M.; Department of Analysis, Müegyetem rkp. 3, Hungary; email: matomate@renyi.hu AB - We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p -groups (\mathbb {Z}_p)^d ( Z p ) d , we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d=1, 2 d = 1 , 2 , and prove some partial results for d=3 d = 3 . LA - English DB - MTMT ER - 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 - Fehér, László AU - Nagy, János TI - Additive Combinatorics Using Equivariant Cohomology JF - ISRAEL JOURNAL OF MATHEMATICS J2 - ISR J MATH VL - accepted PY - 2024 SP - & SN - 0021-2172 UR - https://m2.mtmt.hu/api/publication/33676139 ID - 33676139 AB - We introduce a geometric method to study additive combinatorial problems. Using equivariant cohomology we reprove the Dias da Silva-Hamidoune theorem. We improve a result of Sun on the linear extension of the Erdős-Heilbronn conjecture. We generalize a theorem of G. Kós (the Grashopper problem) which in some sense is a simultaneous generalization of the Erdős-Heilbronn conjecture. We also prove a signed version of the Erdős-Heilbronn conjecture and the Grashopper problem. Most identities used are based on calculating the projective degree of an algebraic variety in two different ways. LA - English DB - MTMT ER - TY - GEN AU - Kátay, Tamás AU - Tóth, László Márton AU - Vidnyánszky, Zoltán TI - The CSP Dichotomy, the Axiom of Choice, and Cyclic Polymorphisms PY - 2023 UR - https://m2.mtmt.hu/api/publication/34202958 ID - 34202958 AB - We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- presents itself as the strength of the corresponding De Bruijin-Erdős-type compactness theorem over ZF. More precisely, if D is a structure, let KD stand for the following statement: for every structure X if every finite substructure of X admits a solution to D, then so does X. We prove that if D admits no cyclic polymorphism, and thus it is NP-complete by the CSP Dichotomy Theorem, then KD is equivalent to the Boolean Prime Ideal Theorem (BPI) over ZF. Conversely, we also show that if D admits a cyclic polymorphism, and thus it is in P, then KD is strictly weaker than BPI. LA - English DB - MTMT ER - TY - JOUR AU - Juhász, István AU - Soukup, Lajos AU - Szentmiklóssy, Zoltán TI - On a problem of Angelo Bella JF - TOPOLOGY AND ITS APPLICATIONS J2 - TOPOL APPL VL - 340 PY - 2023 SN - 0166-8641 DO - 10.1016/j.topol.2023.108714 UR - https://m2.mtmt.hu/api/publication/34188449 ID - 34188449 N1 - Alfréd Rényi Institute of Mathematics, Hungary Eötvös University of Budapest, Hungary Export Date: 14 February 2024 CODEN: TIAPD Correspondence Address: Juhász, I.; Alfréd Rényi Institute of MathematicsHungary; email: juhasz@renyi.hu Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, 129211 Funding text 1: The research on and preparation of this paper was supported by NKFIH grant no. K 129211 . LA - English DB - MTMT ER - TY - JOUR AU - Balka, Richárd AU - Elekes, Márton AU - Kiss, Viktor AU - Nagy, Donát AU - Poór, Márk TI - Compact sets with large projections and nowhere dense sumset JF - NONLINEARITY J2 - NONLINEARITY VL - 36 PY - 2023 IS - 10 SP - 5190 EP - 5215 PG - 26 SN - 0951-7715 DO - 10.1088/1361-6544/acebae UR - https://m2.mtmt.hu/api/publication/34126755 ID - 34126755 AB - We answer a question of Banakh, Jabłońska and Jabłoński by showing that for d ⩾ 2 there exists a compact set K ⊆ R d such that the projection of K onto each hyperplane is of non-empty interior, but K + K is nowhere dense. The proof relies on a random construction. A natural approach in the proofs is to construct such a K in the unit cube with full projections, that is, such that the projections of K agree with that of the unit cube. We investigate the generalization of these problems for projections onto various dimensional subspaces as well as for ℓ -fold sumsets. We obtain numerous positive and negative results, but also leave open many interesting cases. We also show that in most cases if we have a specific example of such a compact set then actually the generic (in the sense of Baire category) compact set in a suitably chosen space is also an example. Finally, utilizing a computer-aided construction, we show that the compact set in the plane with full projections and nowhere dense sumset can be self-similar. LA - English DB - MTMT ER - TY - ART AU - Bali, János AU - Fehér, László AU - Peternák, Zsigmond TI - Szimpliciális komplexus. a valós projektív tér háromszögelése TS - a valós projektív tér háromszögelése PY - 2023 UR - https://m2.mtmt.hu/api/publication/34046344 ID - 34046344 AB - műalkotásunk nem a bambuszpálcikákból összedrótozott, a mennyezetről függő tárgy. Nem a falra függesztett szénrajz. Nem a videók. Nem is ezek együttese: mindezek csak lenyomatai, tárgyi emlékei dialógusok sorozatának, ami főleg két matematikus, Fehér László és Bali János között zajlanak régóta, de kinyíltak a Hermina művészcsoport belső dialógusa felé, végül pedig közvetlenül, egy telefonhívással bevonták a videóművész Peternák Zsigmondot is. Folytatódtak a tárgy elkészülte után is, és remélhetőleg folytatódni fognak a kiállítással bármilyen módon kapcsolatba kerülőkben is. A tárgy és a rajzok, a műcím szavai szimbolikusak. De senki ne keressen bennük bármiféle kódolt szimbolikus üzenetet: egyszerűen hordozzák kiterjedt szimbolikus hátországukat, interferálnak a matematikai, pszichológiai, köznapi tapasztalatok, tér-élmények, absztrakciók és testi valóságok örömei. DB - MTMT ER - TY - JOUR AU - Laczkovich, Miklós AU - Vasenov, Ivan TI - TILING OF REGULAR POLYGONS WITH SIMILAR RIGHT TRIANGLES JF - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS J2 - ROCKY MT J MATH VL - 53 PY - 2023 IS - 1 SP - 153 EP - 155 PG - 3 SN - 0035-7596 DO - 10.1216/rmj.2023.53.153 UR - https://m2.mtmt.hu/api/publication/34040957 ID - 34040957 N1 - Export Date: 17 January 2024 Funding details: Hungarian Scientific Research Fund, OTKA, K124749 Funding text 1: Laczkovich was supported by the Hungarian National Foundation for Scientific Research, grant K124749. 2020 AMS Mathematics subject classification: 52C20. Keywords and phrases: tilings with right triangles, regular polygons. Received by the editors on September 3, 2021. 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 -