Search results for "Crete"
showing 10 items of 2495 documents
Saturated formations and products of connected subgroups
2011
Abstract For a non-empty class of groups C , two subgroups A and B of a group G are said to be C -connected if 〈 a , b 〉 ∈ C for all a ∈ A and b ∈ B . Given two sets π and ρ of primes, S π S ρ denotes the class of all finite soluble groups that are extensions of a normal π-subgroup by a ρ-group. It is shown that in a finite group G = A B , with A and B soluble subgroups, then A and B are S π S ρ -connected if and only if O ρ ( B ) centralizes A O π ( G ) / O π ( G ) , O ρ ( A ) centralizes B O π ( G ) / O π ( G ) and G ∈ S π ∪ ρ . Moreover, if in this situation A and B are in S π S ρ , then G is in S π S ρ . This result is then extended to a large family of saturated formations F , the so-c…
On the Quadratic Type of Some Simple Self-Dual Modules over Fields of Characteristic Two
1997
Let G be a finite group and let K be an algebraically closed field of Ž characteristic 2. Let V be a non-trivial simple self-dual KG-module we . say that V is self-dual if it is isomorphic to its dual V * . It is a theorem of w x Fong 4, Lemma 1 that in this case there is a non-degenerate G-invariant alternating bilinear form, F, say, defined on V = V. We say that V is a KG-module of quadratic type if F is the polarization of a non-degenerate w x G-invariant quadratic form defined on V. In a previous paper 6 , the present authors described some methods to decide if such a module V is of w x quadratic type. One of the main results of 6 is the following. Suppose that Ž . G is a group with a s…
BOUNDING THE NUMBER OF IRREDUCIBLE CHARACTER DEGREES OF A FINITE GROUP IN TERMS OF THE LARGEST DEGREE
2013
We conjecture that the number of irreducible character degrees of a finite group is bounded in terms of the number of prime factors (counting multiplicities) of the largest character degree. We prove that this conjecture holds when the largest character degree is prime and when the character degree graph is disconnected.
Ambainis-Freivalds’ Algorithm for Measure-Once Automata
2001
An algorithm given by Ambainis and Freivalds [1] constructs a quantum finite automaton (QFA) with O(log p) states recognizing the language Lp = {ai| i is divisible by p} with probability 1 - Ɛ , for any Ɛ > 0 and arbitrary prime p. In [4] we gave examples showing that the algorithm is applicable also to quantum automata of very limited size. However, the Ambainis-Freivalds algoritm is tailored to constructing a measure-many QFA (defined by Kondacs andWatrous [2]), which cannot be implemented on existing quantum computers. In this paper we modify the algorithm to construct a measure-once QFA of Moore and Crutchfield [3] and give examples of parameters for this automaton. We show for the lang…
Improved Constructions of Quantum Automata
2008
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use $\frac{4}{\epsilon} \log 2p + O(1)$ states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction of [2]. Similarly to [2], our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some preliminary results in this direction.
Coding Partitions: Regularity, Maximality and Global Ambiguity
2007
The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences. We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an ap…
Remarks on the semivariation of vector measures with respect to Banach spaces.
2007
Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.
Multilevel Bandwidth and Radio Labelings of Graphs
2008
This paper introduces a generalization of the graph bandwidth parameter: for a graph G and an integer k ≤ diam(G), the k-level bandwidth Bk(G)of G is defined by Bk(G) = minγ max{|γ(x)-γ(y)|-d(x, y)+1 : x, y ∈ V (G), d(x, y) ≤ k}, the minimum being taken among all proper numberings γ of the vertices of G. We present general bounds on Bk(G) along with more specific results for k = 2 and the exact value for k = diam(G). We also exhibit relations between the k-level bandwidth and radio k-labelings of graphs from which we derive a upper bound for the radio number of an arbitrary graph.
Span programs for functions with constant-sized 1-certificates
2012
Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the element distinctness, the triangle and other problems. The usual way to solve them is by quantum walk on the Johnson graph. We propose a solution for the same problems using span programs. The span program is a computational model equivalent to the quantum query algorithm in its strength, and yet very different in its outfit. We prove the power of our approach by designing a quantum algorithm for the triangle problem with query complexity O(n35/27) that is better than O(n13/10) of the best p…
Hausdorff dimension from the minimal spanning tree
1993
A technique to estimate the Hausdorff dimension of strange attractors, based on the minimal spanning tree of the point distribution is extensively tested in this work. This method takes into account in some sense the infimum requirement appearing in the definition of the Hausdorff dimension. It provides accurate estimates even for a low number of data points and it is especially suited to high-dimensional systems.