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A loop whose inner mappings are automorphisms is an automorphic loop (or A-loop). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain central extensions based on trilinear forms, we construct several classes of commutative A-loops of order a power of 2. We initiate… (More)

- Premysl Jedlicka
- Bratislavske lekarske listy
- 2002

In many regions of the brain, the activity-dependent changes in synaptic strength depend on the frequency and timing of presynaptic stimulation and postsynaptic activity (synaptic plasticity), as well as the history of activity at those synapses (metaplasticity). The Bienenstock, Cooper and Munro (BCM) theory made several assumptions about how synapses… (More)

A loop is automorphic if its inner mappings are automorphisms. Using socalled associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. Starting with suitable elements of an anisotropic plane in the vector space of 2 × 2 matrices over the field of prime order p, we construct a family of… (More)

- Ales Drápal, Premysl Jedlicka
- Eur. J. Comb.
- 2010

We start by describing all the varieties of loops Q that can be defined by autotopisms αx, x ∈ Q, where αx is a composition of two triples, each of which becomes an autotopism when the element x belongs to one of the nuclei. In this way we obtain a unifying approach to Bol, Moufang, extra, Buchsteiner and conjugacy closed loops. We reprove some classical… (More)

- Premysl Jedlicka, Sylvester M. Greer, +6 authors David N. Cooper
- Human Genetics
- 1990

Two novel restriction fragment length polymorphisms (RFLPs) around the DXS115 (767) locus, detectable with the restriction enzymes MspI, are described. Since DXS115 is closely linked to the factor VIII gene (F8C), the MspI RFLP was employed in haemophilia A carrier detection. The utility of these RFLPs lies in the increased applicability and accuracy of… (More)

- Premysl Jedlicka, David Stanovský, Petr Vojtechovský
- Discrete Mathematics
- 2017

We enumerate three classes of non-medial quasigroups of order 243 = 35 up to isomorphism. There are 17 004 non-medial trimedial quasigroups of order 243 (extending the work of Kepka, Bénéteau and Lacaze), 92 non-medial distributive quasigroups of order 243 (extending the work of Kepka and Němec), and 6 non-medial distributive Mendelsohn quasigroups of order… (More)

A loop whose inner mappings are automorphisms is an automorphic loop (or A-loop). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain central extensions based on trilinear forms, we construct several classes of commutative A-loops of order a power of 2. We initiate… (More)

We enumerate three classes of non-medial quasigroups of order 243 = 3 up to isomorphism. There are 17004 non-medial trimedial quasigroups of order 243 (extending the work of Kepka, Bénéteau and Lacaze), 92 non-medial distributive quasigroups of order 243 (extending the work of Kepka and Němec), and 6 non-medial distributive Mendelsohn quasigroups of order… (More)

We consider Murphy’s polynomial selection algorithm for the general number field sieve. One of the steps in this algorithm consists of finding a minimum of an integral. However, the size of the polynomial coefficients causes the classical steepest descent algorithm to be ineffective. This article brings an idea how to improve the steepest descent algorithm… (More)

An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and (xy)−1 = x−1y−1 holds. Let Q be a finite commutative A-loop and p a prime. The loop Q has order a power of p if and only if every element of Q has order a power of p. The loop Q decomposes as a direct product of a… (More)