Search results for "Crete"
showing 10 items of 2495 documents
Defining relations of minimal degree of the trace algebra of 3×3 matrices
2008
Abstract The trace algebra C n d over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n , d ⩾ 2 . Minimal sets of generators of C n d are known for n = 2 and n = 3 for any d as well as for n = 4 and n = 5 and d = 2 . The defining relations between the generators are found for n = 2 and any d and for n = 3 , d = 2 only. Starting with the generating set of C 3 d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C 3 d is equal to 7 for any d ⩾ 3 . We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8. The proofs are based …
Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics
2007
The original publication is available at www.springerlink.com ; ISBN 978-3-540-75519-7 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, \ie surfaces of algebraic degree~2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is {\em complete} in the sense that it can handle all kinds of…
Refined Finiteness and Degree Properties in Graphs
2020
Summary In this article the finiteness of graphs is refined and the minimal and maximal degree of graphs are formalized in the Mizar system [3], based on the formalization of graphs in [4].
Topological direct sum decompositions of banach spaces
1990
LetY andZ be two closed subspaces of a Banach spaceX such thatY≠lcub;0rcub; andY+Z=X. Then, ifZ is weakly countably determined, there exists a continuous projectionT inX such that ∥T∥=1,T(X)⊃Y, T −1(0)⊂Z and densT(X)=densY. It follows that every Banach spaceX is the topological direct sum of two subspacesX 1 andX 2 such thatX 1 is reflexive and densX 2**=densX**/X.
Grover’s Algorithm with Errors
2013
Grover’s algorithm is a quantum search algorithm solving the unstructured search problem of size n in \(O(\sqrt{n})\) queries, while any classical algorithm needs O(n) queries [3].
Derived categories of irreducible projective curves of arithmetic genus one
2006
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all $t$ -structures of this category is given. We describe the moduli space of stability conditions, obtain a complete classification of all spherical objects in this category and show that the group of exact auto-equivalences acts transitively on them. Harder–Narasimhan filtrations in the sense of Bridgeland are used as our main technical tool.
Deterministic generalized automata
1995
A generalized automaton (GA) is a finite automaton where the single transitions are defined on words rather than on single letters. Generalized automata were considered by K. Hashiguchi who proved that the problem of calculating the size of a minimal GA is decidable.
The Complexity of Probabilistic versus Quantum Finite Automata
2002
We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1 - ? for all ? > 0 with O(log2 n) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2?(n/log n) states.
Non-constructive Methods for Finite Probabilistic Automata
2007
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
NON-CONSTRUCTIVE METHODS FOR FINITE PROBABILISTIC AUTOMATA
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. However, the proof is non-constructive. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures not proved but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.