Results 1  10
of
18
02099683/97/$6.00 (~)1997 JAnos Bolyai Mathematical Society
, 1996
"... For q an odd prime power, and 1 < n < q, the Desarguesian plane PG(2,q) does not contain an (nq q§ 1. In t roduct ion A (k,n)a rc in a projective plane is a set of k points, at most n on every line. If the order of the plane is q, then k < 1 + (q + 1) (n 1) = qn q + n with equality if ..."
Abstract
 Add to MetaCart
For q an odd prime power, and 1 < n < q, the Desarguesian plane PG(2,q) does not contain an (nq q§ 1. In t roduct ion A (k,n)a rc in a projective plane is a set of k points, at most n on every line. If the order of the plane is q, then k < 1 + (q + 1) (n 1) = qn q + n with equality if and only if every line intersects the arc in 0 or n points. Arcs realizing the upper bound are called maximal arcs. Equality in the bound implies that n lq or n=q+l. If 1 < n < q, then the maximal arc is called nontrivial. The only known examples of nontrivial maximal arcs in Desarguesian projective planes, are the hyperovals (n = 2), and, for n> 2 the Denniston arcs [2] and an infinite family constructed by Thas [5, 7]. These exist for all pairs (n,q) = (2a,2b), 0 < a < b. It is conjectured in [6] that for odd q maximal arcs do not exist. In that paper this was proved for (n,q) (3,3h). The special case (n,q) = (3,9) was settled earlier by Cossu [1]. In a recent paper on sets of type (re,n) [3] this conjecture is labeled "most wanted" research problem. In this note we shall show that the conjecture is true in generM. We shall consider point sets in the ai~ne plane AG(2,q) instead of PG(2,q). This is no restriction; there is always a line disjoint from a nontrivial maximal arc. The points of AG(2,q) can be identified with the elements of GF(q 2) in a suitable way, so that in fact all point sets can be considered as subsets of this field. Note
support received through János Bolyai Scholarship of the Hun garian Academy of Science.
"... Comparison of additive and reactive phosphorusbased flame retardants in epoxy resins ..."
Abstract
 Add to MetaCart
Comparison of additive and reactive phosphorusbased flame retardants in epoxy resins
\v coLLoQUlA MATHEMATICA SOCIETATIS JANOS BOLYAI 5. HILBERT SPACE OPERATORS. TIHANY (HUNGARY), 1970 Symbols of operators and quantization
"... Let L z ( M) be the Hilbert space of functions squareintegrable on a measure space M.It is convenient to define linear operators on L2(M)bymeansof func'ons of two variables. The best known way is by means of kernel: (Af)(r) : Jxc*,9)f t9)dg. Incase of suchacorrespondencebetweenoperators A and ..."
Abstract
 Add to MetaCart
Let L z ( M) be the Hilbert space of functions squareintegrable on a measure space M.It is convenient to define linear operators on L2(M)bymeansof func'ons of two variables. The best known way is by means of kernel: (Af)(r) : Jxc*,9)f t9)dg. Incase of suchacorrespondencebetweenoperators A and functions 9(x,9), we shall call the function g(r,U) the symbol of the corresponding operator A. The kernel K {x, g) is the particular case of symbol. In this paper we give a survey on different sorts of symbols, considering mainly the case when M is the real ndimensional euclidean space with the usual Lebesque measure. One of the sources of appearance of symbols is the expression of operators in algebras of operators through generators 0 u and Qn, where 0u and Q1 are the "operators of impulse and coordinate " well known from quantum mechanics:
COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 37. FINITE AND INFINITE SETS, EGER (HUNGARY), 1981. SIZE RAMSEY NUMBERS INVOLVING MATCHINGS
"... Let F, G and H be finite, simple and undirected graphs. The edges and number of edges of a graph F will be denoted by E(F) and I E(F) I respectively. A graph F (G, H) if every 2coloring (say red and blue) of E(F) produces either a "red " G or a "blue " H. The size Ramsey number ..."
Abstract
 Add to MetaCart
Let F, G and H be finite, simple and undirected graphs. The edges and number of edges of a graph F will be denoted by E(F) and I E(F) I respectively. A graph F (G, H) if every 2coloring (say red and blue) of E(F) produces either a "red " G or a "blue " H. The size Ramsey number r(G, H) = min f l E(F) 1: F> (G, H)}. For t> 1, the graph consisting of t independent edges will be denoted by tK2. In this paper, bounds and in some cases exact values will be calculated for r(tK2, G) for various classical graphs G, for example, when G is either a small order graph, a path, a cycle, a complete graph or a complete bipartite graph. Asymptotic results are obtained for some graphs in which exact values could not be calculated. 1
COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 4. COMBINATORIAL THEORY AND ITS APPLICATIONS, BALATONFURED (HUNGARY), 1969. On a lemma of HajndFolkman bY
"... proved the following Lemma: Let ISI = bf, A; c 9, IA;1 = n be subsets of 9 so that to every element x of 9 there is an A; not containing x. We define now a graph as follows: XE 9, y e 9 are joined if for some A; they are both contained in A;. The Lemma asserts that this graph contains a complete gr ..."
Abstract
 Add to MetaCart
proved the following Lemma: Let ISI = bf, A; c 9, IA;1 = n be subsets of 9 so that to every element x of 9 there is an A; not containing x. We define now a graph as follows: XE 9, y e 9 are joined if for some A; they are both contained in A;. The Lemma asserts that this graph contains a complete graph of n+ ( vertices. We are going to generalise and extend this Lemma in various directions and establish some connections with RAMSEY ’ s theorem. First we have to introduce some notations. The basic elements of an rgraph are its vertices and the rtuples formed from some of its vertices. Kr ( n) is the complete Pgraph of n vertices and all its (:) rtuples. For r2 we obtain the ordinary graphs. Let 9 be a set. A family of subsets A; c 9 defines an rgraph f+c’) ( 9; A,)...) as follows: The vertices are the elements of 9, an rtuple belongs to our graph if and only if it is a subset of one of our A’s. Such rgraphs were, as far as I know, first studied in [l] in a context that differs from this. We say that the family can be 311represented by i vertices if there are i elements Y,,.. 7 xi of 9, sothat
COLLOQUIA MATHEMATICA SOCIETATIS JÁNOS BOLYAI 34.TOPICS IN CLASSICAL NUMBER THEORY BUDAPEST (HUNGARY), 1981. SOME RESULTS IN COMBINATORIAL NUMBER THEORY
"... We should like to state here some new results in combinatorial number theory. 1. In [31 p.50 the following question was asked: "Let A={a1<a2<...} and B={b1<b2<...I be sequences of integers satisfying A(x)> Ex l/2, B(x)> Ex l/2 for some e>O. Is it true that (1) a í a.7 = b ..."
Abstract
 Add to MetaCart
We should like to state here some new results in combinatorial number theory. 1. In [31 p.50 the following question was asked: "Let A={a1<a2<...} and B={b1<b2<...I be sequences of integers satisfying A(x)> Ex l/2, B(x)> Ex l/2 for some e>O. Is it true that (1) a í a.7 = bk b t has infinitely many solutions? " (A(x) and B(x) are the number of elements of A and B up to x, resp.) R. Freud observed that the answer was negative: we write the numbers in binary scale, and select for A those ones which contain only even powers of two, and forB those which contain only odd powers of two. Then (1) is possible only in the trivial case, and m = lim inf min{A(x), B(x)} = 1 xLater P. Erdős and R. Freud investigated general properties of sequences A and B for which (1) has only trivial solutions. We state here some of these results: 1.1. m> 21/4 e is attainable. 1.2. The largest possible value of s = lim sup A(x)B(x)/x is 2. More precisely, if xlim sup x(n) _ then A(n)B(n) ? 2nx(n) is attainable n for infinitely many n by suitable A and s, but A(n)B(n)2n for any A and s. 1.3. s = lim inf A(x)B(x)/x is at most 14/9, xmore precisely (5/2)s + 2s 5 7. Also s + ( 3/2)s < 4, which shows that s=2 implies s<_1. It is not yet known whether s>l is possible at all.1.4. If m>o, then neither A(x)/J; nor B(x)/fx can tend to a limit. Several further theorems are proved on the behaviour of A(x)B(x)/x, A(x)/,lx and B(x)/fx. The results with detailed proofs will appear in Ell, and another forthcoming paper will deal with related problems 2. Now we consider permutations of integers. In the finite case let al,a2,...,an be a permutation of the integers 1,2,...,n, and in the infinite case let al,a2,...,ai,... be a permutation of all positive integers P.Erdős, R.Freud and N.Hegyvári investigated several estimations concerning the values of [a i ~ a i+l~ and (a i la i+l). 2.1. In the finite case
141The Crown and the Lollards Tolerance, Intolerance and State Policy The Crown and the Lollards in Later Medieval England
"... is a fellow of the Hungarian Academy of Arts and Sciences; he received the János Bolyai ..."
Abstract
 Add to MetaCart
is a fellow of the Hungarian Academy of Arts and Sciences; he received the János Bolyai
Introductory Course on Relation Algebras, FiniteDimensional Cylindric Algebras, and Their Interconnections
 Algebraic Logic
, 1990
"... These are notes for a short course on relation algebras, finitedimensional cylindric algebras, and their interconnections, delivered at the Conference on Algebraic Logic, Budapest, Hungary, August 814, 1988, sponsored by the the Janos Bolyai Mathematical Society. ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
These are notes for a short course on relation algebras, finitedimensional cylindric algebras, and their interconnections, delivered at the Conference on Algebraic Logic, Budapest, Hungary, August 814, 1988, sponsored by the the Janos Bolyai Mathematical Society.
Supported by Bolyai Janos Postdoctoral Scholarship of the Hungarian Academy of Sciences
, 2009
"... www.wjgnet.com ..."
The emergence of modern number theory in Hungary
"... The goal of this paper is to present an introduction to the emergence of modern number theory in Hungary by recounting the lives of some of its most influential mathematicians, and examining developments in the mathematical life of Hungary in the nineteenth century. Special attention is given to th ..."
Abstract
 Add to MetaCart
to the predecessors of Pal Erd}os and Pal Turan, including Janos Bolyai, Gyula K}onig, Gusztav Rados, and Mihaly Bauer, and to the mathematical publications and societies they were instrumental in founding.
Results 1  10
of
18