We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs 〈L1,L2〉 of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to L1 and L2, respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary a...

Aims. This paper describes a systematic search for high-order multiplicity among wide visual Pre-Main Sequence (PMS) binaries. Methods. We conducted an Adaptive Optics survey of a sample of 58 PMS wide binaries from various star-forming regions, which include 52 T Tauri systems with mostly Kand M-type primaries, with the NIR instrument NACO at the VLT. Results. Of these 52 systems, 7 are found ...

A set of positive integers with the property that product any two them is successor a perfect square called Diophantine D ( − 1 ) $D(-1)$ -set. Such objects are usually studied via system generalized Pell equations naturally attached to under scrutiny. In this paper, an innovative technique introduced in study -quadruples. The main novelty uncovering quadratic equation relating various paramete...

In this paper, we propose a new approach for fast processing of SPARQL queries on large RDF datasets containing RDF quadruples (or quads). Our approach called RIQ employs a decrease-and-conquer strategy: Rather than indexing the entire RDF dataset, RIQ identifies groups of similar RDF graphs and indexes each group separately. During query processing, RIQ uses a novel filtering index to first id...

A D(−1)-quadruple is a set of positive integers {a, b, c, d}, with a < b < c < d, such that the product of any two elements from this set is of the form 1+n2 for some integer n. Dujella and Fuchs showed that any such D(−1)-quadruple satisfies a = 1. The D(−1) conjecture states that there is no D(−1)-quadruple. If b = 1+ r2, c = 1+ s2 and d = 1+ t2, then it is known that r, s, t, b, c and d are ...

For nonnegative integers q, n, d , let Aq(n, d) denote themaximum cardinality of a code of length n over an alphabet [q]with q letters and with minimum distance at least d . We consider the following upper bound on Aq(n, d). For any k, let Ck be the collection of codes of cardinality at most k. Then Aq(n, d) is at most the maximum value of ∑ v∈[q]n x({v}), where x is a function C4→R+ such that ...

Schur proved that for any finite partition of the naturals, some cell contains two numbers and their sum. We use Ramsey’s theorem to prove a noncommutative Schur theorem for permutation quadruples {x, y, xy, yx}. By Schur’s theorem [2], for any r ∈ N, there exists n ∈ N such that for any r-coloring of {1, 2, . . . , n}, one has a monochromatic “Schur triple.” That is, a 3-element set of the for...

Let n be an integer. A set of positive integers {al9 -..,am} is said to have the property of Diophantus of order n, symbolically D(n) if, for all i,j-\...ym, i^j, the following holds: apj +n = b?, where btj is an integer. The set {a1,...,am} is called aDiophantine m-tuple. In this paper we construct several Diophantine quadruples whose elements are represented using generalized Fibonacci number...