Attila Nagy

Bio: Attila Nagy is an academic researcher from Budapest University of Technology and Economics. The author has contributed to research in topics: Semigroup & Special classes of semigroups. The author has an hindex of 9, co-authored 76 publications receiving 298 citations.

Special Classes of Semigroups

Abstract: Preface. 1. Preliminaries. 2. Putcha semigroups. 3. Commutative semigroups. 4. Weakly commutative semigroups. 5. R-, L-, H-commutative semigroups. 6. Conditionally commutative semigroups. 7. RC-commutative semigroups. 8. Quasi commutative semigroups. 9. Medial semigroups. 10. Right commutative semigroups. 11. Externally commutative semigroups. 12. E-m semigroups, exponential semigroups. 13. WE-m semigroups. 14. Weakly exponential semigroups. 15. (m,n)-commutative semigroups. 16. n(2)-permutable semigroups. Bibliography. Index.

Weakly exponential semigroups

Abstract: In the previous chapter we dealt with semigroups in which, for a fixed integer m ≥ 2 and every elements a and b, there is a non-negative integer k such that (ab) m+k =a m b m =(ab) k a m b m . In this chapter we deal with semigroups which satisfy this condition for every integer m ≥ 2. These semigroups are called weakly exponential semigroups. It follows from results of the previous chapter that every weakly exponential semigroup is a semilattice of weakly exponential archimedean semigroups. A semigroup is a weakly exponential archimedean semigroup containing at least one idempotent element if and only if it is a retract extension of a rectangular abelian group by a nil semigroup. It is also proved that every weakly exponential archimedean semigroup without idempotent element has a non-trivial group homomorphic image. We prove that every weakly exponential semigroup is a band of weakly exponential t-archimedean semigroups. As a consequence of the previous chapter, a semigroup is a subdirectly irreducible weakly exponential semigroup with a globally idempotent core if and only if it is isomorphic to either G or G 0 or B, where G is a non-trivial subgroup of a quasicyclic p-group (p is a prime) and B is a non-trivial subdirectly irreducible band. At the end of the chapter, we determine the weakly exponential ∆-semigroups. We prove that a semigroup S is a weakly exponential ∆-semigroup if and only if one of the following satisfied. (1) S is isomorphic to either G or G 0, where G is a non-trivial subgroup of a quasicyclic p-group.

On an implementation of the Solovay-Kitaev algorithm

Abstract: In quantum computation we are given a finite set of gates and we have to perform a desired operation as a product of them. The corresponding computational problem is approximating an arbitrary unitary as a product in a topological generating set of $SU(d)$. The problem is known to be solvable in time $polylog(1/\epsilon)$ with product length $polylog(1/\epsilon)$, where the implicit constants depend on the given generators. The existing algorithms solve the problem but they need a very slow and space consuming preparatory stage. This stage runs in time exponential in $d^2$ and requires memory of size exponential in $d^2$. In this paper we present methods which make the implementation of the existing algorithms easier. We present heuristic methods which make a time-length trade-off in the preparatory step. We decrease the running time and the used memory to polynomial in $d$ but the length of the products approximating the desired operations will increase (by a factor which depends on $d$). We also present a simple method which can be used for decomposing a unitary into a product of group commutators for $2

Permutative Semigroups Whose Congruences Form a Chain

Abstract: Semigroups whose congruences form a chain are often termed Δ-semigroups. The commutative Δ-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative Δ-semigroups. It turns out that there are only six noncommutative examples, each of which has at most three elements.

A Complete Bibliography of Lecture Notes in Mathematics (1985{1989)

Abstract: (1 < p ≤ ∞) [LS87f]. (2) [HR88a]. (2m− 2) [KL88]. (A0, A1)θ1 [Xu87a]. (α, β) [Pie88a, Fin88a]. (d ≥ 1) [Wsc85a]. (λ) [DM85b]. (Z/2) [Car86b]. (nα) [Sch85h]. (φ)2 [BM89c]. (τ − λ)u = f [Wei87r]. (x, t) [Lum87, Lum89]. (X1 −X3, X2 −X3) [SW87]. 0 [Caz88, Kas86, Pro87]. 0 < p < 1 [Cle87]. 1 [Bak85a, DD85, Drm87, Eli88, FT88a, Gek86d, HN88, Kos86a, LT89, Pet89a, Pro87, Tan87, vdG89]. 1/4 [KS86e]. 1 ≤ q < 2 [Gue86]. 2 [BPPS87, Cam88, Cat85a, ES87b, Gan85e, Gol86a, HRL89g, Hei85, Hua86, Kan89, KB86, Li86, LT89, Mil87b, Mur85a, Qui85b, SP89, Shi85, Spe86, Wal85b, Wan86]. 2m− 2 [Kos88b]. 2m− 3 [Kos88b]. 2m− 4 [Kos88b]. 2× 2 [Vog88]. 3 [Aso89, BPPS87, BW85c, BG88b, Che86d, Fis86, Gab85, Gu87a, HLM85b, Kam89b, Kir89c, Lev85c, Mil85c, Néd86, Pet86, Ron86, Sch85b, ST88, Tur88b, Wan86, Wen85, tDP89, vdW86]. 4 [Bau88a, Don85a, FKV88, Kha88, Kir89l, SS86, Seg85b, Wal85b]. 5 [Ito89, Kir89e, SV85]. 5(4) [Cas86]. 5819539783680 [KSX87]. 6 [PH89, Žub88].

Trefftz-Based Methods for Time-Harmonic Acoustics

Abstract: Over the last decade, Computer Aided Engineering (CAE) tools have become essential in the assessment and optimization of the acoustic characteristics of products and processes. The possibility of evaluating these characteristics on virtual prototypes at almost any stage of the design process reduces the need for very expensive and time consuming physical prototype testing. However, despite their steady improvements and extensions, CAE techniques are still primarily used by analysis specialists. In order to turn them into easy-to-use, versatile tools that are also easily accessible for designers, several bottlenecks have to be resolved. The latter include, amongst others, the lack of efficient numerical techniques for solving system-level functional performance models in a wide frequency range. This paper reviews the CAE modelling techniques which can be used for the analysis of time-harmonic acoustic problems and focusses on techniques which have the Trefftz approach as baseline methodology. The basic properties of the different methods are highlighted and their strengths and limitations are discussed. Furthermore, an overview is given of the state-of-the-art of the extensions and the enhancements which have been recently investigated to enlarge the application range of the different techniques. Specific attention is paid to one very promising Trefftz-based technique, which is the so-called wave based method. This method has all the necessary attributes for putting a next step in the evolution towards truly virtual product design.