Search results for "Linear"
showing 10 items of 7165 documents
Berinde mappings in orbitally complete metric spaces
2011
Abstract We give a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. Some examples are given to illustrate our obtained result.
A fractal set from the binary reflected Gray code
2005
The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of $N$ the set is examined from the point of view of time series analysis
Scalable Ellipsoidal Classification for Bipartite Quantum States
2008
The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as s…
On the solutions to 1-Laplacian equation with L1 data
2009
AbstractIn the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the problems(0.1){−div(|∇up|p−2∇up)=finΩ,up=0on∂Ω, where p>1, Ω is a bounded open set of RN (N⩾2) with Lipschitz boundary and f belongs to L1(Ω). We prove that these renormalized solutions pointwise converge, up to “subsequences,” to a function u. With a suitable definition of solution we also prove that u is a solution to a “limit problem.” Moreover we analyze the situation occurring when more regular data f are considered.
Pietsch's factorization theorem for dominated polynomials
2007
Abstract We prove that, like in the linear case, there is a canonical prototype of a p -dominated homogeneous polynomial through which every p -dominated polynomial between Banach spaces factors.
Nonlinear embeddings: Applications to analysis, fractals and polynomial root finding
2016
We introduce $\mathcal{B}_{\kappa}$-embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by $\kappa$, a finite or denumerable set of objects at $\kappa=0$ (e.g. numbers, functions, vectors, coefficients of a generating function...) to their ordinary sum at $\kappa \to \infty$. We show that $\mathcal{B}_{\kappa}$-embeddings can be used to design nonlinear irreversible processes through this connection. A number of examples of increasing complexity are worked out to illustrate the possibilities uncovered by this concept. These include not only smooth functions but also fractals on the real line and on the complex plane. As an application, we use $\mat…
Polynomial identities on superalgebras: Classifying linear growth
2006
Abstract We classify, up to PI-equivalence, the superalgebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. As a consequence we determine the linear functions describing the graded codimensions of a superalgebra.
On the size of transducers for bidirectional decoding of prefix codes
2012
In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [ IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X . We find some bounds of such a number of states in relation wi…
Quantum Finite Multitape Automata
1999
Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automata. This …
Probabilistic Reversible Automata and Quantum Automata
2002
To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.