References of "Kiss, Gergely 50009166"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 30 1 2     Visual characterization of associative quasitrivial nondecreasing functions on finite chainsKiss, Gergely in Fuzzy Sets and Systems (in press)Detailed reference viewed: 34 (7 UL) Characterization of field homomorphisms through Pexiderized functional equationsGselmann, Eszter; Kiss, Gergely ; Vincze, Csabain Journal of Difference Equations and Applications (in press)Detailed reference viewed: 51 (6 UL) Characterizations of quasitrivial symmetric nondecreasing associative operationsDevillet, Jimmy ; Kiss, Gergely ; Marichal, Jean-Luc in Semigroup Forum (2019), 98(1), 154-171We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with ... [more ▼]We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this class. Finally we investigate the special situation where the chain is finite. [less ▲]Detailed reference viewed: 147 (51 UL) On biselective operationsDevillet, Jimmy ; Kiss, Gergely Scientific Conference (2018, June 07)See attached fileDetailed reference viewed: 44 (5 UL) The discrete Pompeiu problem on the planeKiss, Gergely ; Laczkovich, Miklós; Vincze, Csabain Monatshefte für Mathematik (2018)We say that a finite subset $E$ of the Euclidean plane $\R^2$ has the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\R^2\to \C$ is such that the sum of the values of ... [more ▼]We say that a finite subset $E$ of the Euclidean plane $\R^2$ has the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\R^2\to \C$ is such that the sum of the values of $f$ on any congruent (similar) copy of $E$ is zero, then $f$ is identically zero. We show that every parallelogram and every quadrangle with rational coordinates has the discrete Pompeiu property with respect to isometries. We also present a family of quadrangles depending on a continuous parameter having the same property. We investigate the weighted version of the discrete Pompeiu property as well, and show that every finite linear set with commensurable distances has the weighted discrete Pompeiu property with respect to isometries, and every finite set has the weighted discrete Pompeiu property with respect to similarities. [less ▲]Detailed reference viewed: 73 (5 UL) Functional equation that characterize higher order derivationsKiss, Gergely Scientific Conference (2018, June)Detailed reference viewed: 41 (3 UL) A characterization of n-associative, monotone, idempotent functions on an interval that have neutral elementsKiss, Gergely ; Somlai, Gaborin Semigroup Forum (2018)We investigate monotone idempotent n-ary semigroups and provide a generalization of the Czogala–Drewniak Theorem, which describes the idempotent monotone associative functions having a neutral element. We ... [more ▼]We investigate monotone idempotent n-ary semigroups and provide a generalization of the Czogala–Drewniak Theorem, which describes the idempotent monotone associative functions having a neutral element. We also present a complete characterization of idempotent monotone n-associative functions on an interval that have neutral elements. [less ▲]Detailed reference viewed: 105 (39 UL) Derivations and differential operators on rings and fieldsKiss, Gergely Scientific Conference (2018, June)Detailed reference viewed: 25 (0 UL) A generalization of the concept of distance based on the simplex inequalityKiss, Gergely ; Marichal, Jean-Luc ; Teheux, Bruno in Beitraege zur Algebra und Geometrie = Contributions to Algebra and Geometry (2018), 59(2), 247266We introduce and discuss the concept of \emph{$n$-distance}, a generalization to $n$ elements of the classical notion of distance obtained by replacing the triangle inequality with the so-called simplex ... [more ▼]We introduce and discuss the concept of \emph{$n$-distance}, a generalization to $n$ elements of the classical notion of distance obtained by replacing the triangle inequality with the so-called simplex inequality $d(x_1, \ldots, x_n)~\leq~K\, \sum_{i=1}^n d(x_1, \ldots, x_n)_i^z{\,}, \qquad x_1, \ldots, x_n, z \in X,$ where $K=1$. Here $d(x_1,\ldots,x_n)_i^z$ is obtained from the function $d(x_1,\ldots,x_n)$ by setting its $i$th variable to $z$. We provide several examples of $n$-distances, and for each of them we investigate the infimum of the set of real numbers $K\in\left]0,1\right]$ for which the inequality above holds. We also introduce a generalization of the concept of $n$-distance obtained by replacing in the simplex inequality the sum function with an arbitrary symmetric function. [less ▲]Detailed reference viewed: 159 (28 UL) On functional equations characterizing derivations: methods and examplesGselmann, Eszter; Kiss, Gergely ; Vincze, Csabain Results in Mathematics (2018)Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions ... [more ▼]Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and automorphisms are additive functions satisfying some further functional equations as well. It is an important question that how these morphisms can be characterized among additive mappings in general. The paper contains some multivariate characterizations of higher order derivations. The univariate characterizations are given as consequences by the diagonalization of the multivariate formulas. This method allows us to refine the process of computing the solutions of univariate functional equations of the form ∑k=1nxpkfk(xqk)=0, where pk and qk (k=1,…,n) are given nonnegative integers and the unknown functions f1,…,fn:R→R are supposed to be additive on the ring R. It is illustrated by some explicit examples too. As another application of the multivariate setting we use spectral analysis and spectral synthesis in the space of the additive solutions to prove that it is spanned by differential operators. The results are uniformly based on the investigation of the multivariate version of the functional equations. [less ▲]Detailed reference viewed: 68 (3 UL) Pointwise regularity of parameterized affine zipper fractal curves fractal curvesBárány, Balázs; Kiss, Gergely ; Kolossváry, Istvánin Nonlinearity (2018), 31(5), We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of ... [more ▼]We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of the pointwise Hölder exponent for a subinterval of the spectrum. We give an equivalent characterization for the existence of regular pointwise Hölder exponent for Lebesgue almost every point. In this case, we extend the multifractal analysis to the full spectrum. In particular, we apply our results for de Rham’s curve. [less ▲]Detailed reference viewed: 36 (2 UL) Derivations and differential operators on rings and fieldsKiss, Gergely in Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica (2018)Let R be an integral domain of characteristic zero. We prove that a function D : R → R is a derivation of order n if and only if D belongs to the closure of the set of differential operators of degree n ... [more ▼]Let R be an integral domain of characteristic zero. We prove that a function D : R → R is a derivation of order n if and only if D belongs to the closure of the set of differential operators of degree n in the product topology of R^R, where the image space is endowed with the discrete topology. In other words, f is a derivation of order n if and only if, for every finite set F ⊂ R, there is a differential operator D of degree n such that f = D on F. We also prove that if d1, . . . , dn are nonzero derivations on R, then d1 ◦ . . . ◦ dn is a derivation of exact order n. [less ▲]Detailed reference viewed: 41 (2 UL) The discrete Pompeiu problem on the planeKiss, Gergely Presentation (2017, November 27)The discrete Pompeiu problem is stemmed from an integral-geometric question on the plane. The problem is whether we can reconstruct a function if we know the average values of the function on every ... [more ▼]The discrete Pompeiu problem is stemmed from an integral-geometric question on the plane. The problem is whether we can reconstruct a function if we know the average values of the function on every congruent copy of a given pattern. After introducing the theory of spectral analysis on discrete Abelian groups, I show some results for the discrete version of the problem. One of the arguments is connected to a coloring problem of the plane. One of them is a geometric construction and some others based on some geometric and combinatoric properties of the plane. I also mention some unsolved questions of the topic. My talk is based on a joint work with M. Laczkovich and Cs. Vincze. [less ▲]Detailed reference viewed: 88 (4 UL) Associative idempotent nondecreasing functions are reducibleKiss, Gergely ; Somlai, Gaborin Semigroup Forum (2017)An n-variable associative function is called reducible if it can be written as a composition of a binary associative function. In this paper we summarize the known results when the function is defined on ... [more ▼]An n-variable associative function is called reducible if it can be written as a composition of a binary associative function. In this paper we summarize the known results when the function is defined on a chain and nondecreasing. The main result of this paper shows that associative idempotent and nondecreasing functions are uniquely reducible. [less ▲]Detailed reference viewed: 62 (9 UL) Recent results on conservative and symmetric n-ary semigroupsKiss, Gergely ; Devillet, Jimmy ; Marichal, Jean-Luc Scientific Conference (2017, June 16)See attached fileDetailed reference viewed: 75 (17 UL) Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroupsKiss, Gergely ; Somlai, Gaborin Torra, Vicenç; Mesiar, Radko; De Baets, Bernard (Eds.) Aggregation Functions in Theory and in Practice (2017)We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that ... [more ▼]We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that if F_n is idempotent, n-associative function which is monotone in each of its variables, defined on an interval I and has a neutral element, then F_n is combination of the minimum and maximum operation. Moreover we can characterize the n-ary semigroups (I,F_n) where F_n has the previous properties. [less ▲]Detailed reference viewed: 32 (3 UL) On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equationsKiss, Gergely ; Vincze, Csabain Aequationes Mathematicae (2017)As a continuation of our previous work [2] the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation ... [more ▼]As a continuation of our previous work [2] the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The idea is based on the fundamental work of [5]. Using spectral analysis in some related varieties we can prove the existence of special solutions (automorphisms) of the functional equation but spectral synthesis allows us to describe the entire space of solutions on a large class of finitely generated fields. It is spanned by the so-called exponential monomials which can be given in terms of automorphisms of CC and differential operators. We apply the general theory to some inhomogeneous problems motivated by quadrature rules of approximate integration [8], see also [7, 9]. [less ▲]Detailed reference viewed: 59 (3 UL) On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equationsKiss, Gergely ; Vincze, Csabain Aequationes Mathematicae (2017)The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations using spectral analysis in a translation invariant closed linear subspace of additive ... [more ▼]The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The application of spectral analysis in some related varieties is a new and important trend in the theory of functional equations; especially they have successful applications in the case of homogeneous linear functional equations. The foundations of the theory can be found in Kiss and Varga (Aequat Math 88(1):151–162, 2014) and Kiss and Laczkovich (Aequat Math 89(2):301–328, 2015). We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to Koclȩga-Kulpa and Szostok (Ann Math Sylesianae 22:27–40, 2008), see also Koclȩga-Kulpa and Szostok (Georgian Math J 16:725–736, 2009; Acta Math Hung 130(4):340–348, 2011). They are motivated by quadrature rules of approximate integration. [less ▲]Detailed reference viewed: 62 (1 UL) Discrete Pompeiu problem on the plainKiss, Gergely Presentation (2016, December)Detailed reference viewed: 31 (3 UL) A characterisation of associative idempotent nondecreasing functions with neutral elementsKiss, Gergely ; Laczkovich, Miklós; Marichal, Jean-Luc et alScientific Conference (2016, June)Detailed reference viewed: 75 (14 UL) 1 2