Search results for " function"
showing 10 items of 9395 documents
Degree of monotonicity in aggregation process
2010
In this paper we introduce a fuzzy order relation notion in the description of aggregation process. Namely, we use the fuzzy order relation to define the degree of monotonicity, which is equal to 1 for a monotone function with respect to a crisp order relation. In that case, integration of fuzzy order relation allows us to generalize the notion of monotonicity and we try to investigate the benefits of using fuzzy relations instead of a crisp relation. Further we illustrate this definition by examples and study the properties of aggregation functions which have a certain degree of monotonicity.
Unconditionally convergent multipliers and Bessel sequences
2016
Abstract We prove that every unconditionally summable sequence in a Hilbert space can be factorized as the product of a square summable scalar sequence and a Bessel sequence. Some consequences on the representation of unconditionally convergent multipliers are obtained, thus providing positive answers to a conjecture by Balazs and Stoeva in some particular cases.
On a Conjecture on Bidimensional Words
2003
We prove that, given a double sequence w over the alphabet A (i.e. a mapping from Z2 to A), if there exists a pair (n0, m0) ∈ Z2 such that pw(n0, m0) < 1/100n0m0, then w has a periodicity vector, where pw is the complexity function in rectangles of w.
Sensitivity Versus Certificate Complexity of Boolean Functions
2016
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been notoriously hard to obtain even exponential bounds. Since block sensitivity is known to be polynomially related to certificate complexity, an equivalent of proving this conjecture would be showing that the certificate complexity is polynomially related to sensitivity. Previously, it has been shown that $$bsf \le Cf \le 2^{sf-1} sf - sf-1$$. In this work, we give a better upper bound of $$bsf \le Cf \le \max \left 2^{sf-1}\left sf-\frac{1}{3}\right , sf\right $…
Factorization of homomorphisms through H∞(D)
2003
AbstractWeakly compact homomorphisms between (URM) algebras with connected maximal ideal space are shown to factor through H∞(D) by means of composition operators and to be strongly nuclear. The spectrum of such homomorphisms is also described. Strongly nuclear composition operators between algebras of bounded analytic functions are characterized. The path connected components of the space of endomorphisms on H∞(D) in the uniform operator topology are determined.
Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces
1993
In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…
Approximate convex hull of affine iterated function system attractors
2012
International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…
Unary Languages Recognized by Two-Way One-Counter Automata
2014
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponents form some trivial unary regular language. In this paper, we present some non-trivial subsets of these languages. By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear–space Turing machines. We also show …
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.
Functional calculi for convolution operators on a discrete, periodic, solvable group
2009
Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and let T=∫SpL2TλdE(λ) be its spectral resolution. Let F be a Borel bounded function on [−a,a], SpL2T⊂[−a,a]. We say that F is a spectral Lp-multiplier for T, if F(T)=∫SpL2TF(λ)dE(λ) is a bounded operator on Lp(X,μ). The paper deals with l1-multipliers, where X=G is a discrete (countable) solvable group with ∀x∈G, x4=1, μ is the counting measure and TΦ:l2(G)∋ξ↦ξ∗Φ∈l2(G), where Φ=Φ∗ is a l1(G) function, suppΦ generates G. The main result of the paper states that there exists a Ψ on G such that all l1-multipliers for TΨ are real analytic at every interior point of Spl2(G)TΨ. We also exhibit self-adjoint Φ′s in l1(G) suc…