Search results for "vector [form factor]"
showing 10 items of 770 documents
THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE
2006
AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l…
Quasi-conformal mapping theorem and bifurcations
1998
LetH be a germ of holomorphic diffeomorphism at 0 ∈ ℂ. Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze 2πi )=H○S(z) (1). IfH λ is an unfolding of diffeomorphisms depending on λ ∈ (ℂ,0), withH 0=Id, one introduces its ideal $$\mathcal{I}_H$$ . It is the ideal generated by the germs of coefficients (a i (λ), 0) at 0 ∈ ℂ k , whereH λ(z)−z=Σa i (λ)z i . Then one can find a parameter solutionS λ (z) of (1) which has at each pointz 0 belonging to the domain of definition ofS 0, an expansion in seriesS λ(z)=z+Σb i (λ)(z−z 0) i with $$(b_i ,0) \in \mathcal{I}_H$$ , for alli. This result may be applied to the…
Stochastic differential equations with coefficients in Sobolev spaces
2010
We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth; for the drift coefficient $A_0$, we consider two cases: (i) $A_0$ is continuous whose distributional divergence $\delta(A_0)$ w.r.t. the Gaussian measure $\gamma_d$ exists, (ii) $A_0$ has the Sobolev regularity $W_\text{loc}^{1,p'}$ for some $p'>1$. Assume $\int_{\R^d} \exp\big[\lambda_0\bigl(|\delta(A_0)| + \sum_{j=1}^m (|\delta(A_j)|^2 +|\nabla A_j|^2)\bigr)\big] \d\gamma_d0$, in the case (i), if the pathwise uniqueness of solutions holds, then the push-f…
VECTOR MEASURES WITH VARIATION IN A BANACH FUNCTION SPACE
2003
Let E be a Banach function space and X be an arbitrary Banach space. Denote by E(X) the Kothe-Bochner function space defined as the set of measurable functions f : Ω → X such that the nonnegative functions ‖f‖X : Ω → [0,∞) are in the lattice E. The notion of E-variation of a measure —which allows to recover the pvariation (for E = Lp), Φ-variation (for E = LΦ) and the general notion introduced by Gresky and Uhl— is introduced. The space of measures of bounded E-variation VE(X) is then studied. It is shown, among other things and with some restriction of absolute continuity of the norms, that (E(X))∗ = VE′ (X ∗), that VE(X) can be identified with space of cone absolutely summing operators fr…
Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property
2010
Abstract Let X be a Banach space. For describing the space P ( C [ 0 , 1 ] , X ) of absolutely summing operators from C [ 0 , 1 ] to X in terms of the space X itself, we construct a tree space l 1 tree ( X ) on X. It consists of special trees in X which we call two-trunk trees. We prove that P ( C [ 0 , 1 ] , X ) is isometrically isomorphic to l 1 tree ( X ) . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X ∗ -valued sequence spaces.
A Probabilistic Approach to the Count-To-Infinity Problem in Distance-Vector Routing Algorithms
2013
Count-to-infinity problem is characteristic for routing algorithms based on the distributed implementation of the classical Bellman-Ford algorithm. In this paper a probabilistic solution to this problem is proposed. It is argued that by the use of a Bloom Filter added to the routing message the routing loops will with high probability not form. An experimental analysis of this solution for use in Wireless Sensor Networks in practice is also included.
Distributed Learning Automata-based S-learning scheme for classification
2019
This paper proposes a novel classifier based on the theory of Learning Automata (LA), reckoned to as PolyLA. The essence of our scheme is to search for a separator in the feature space by imposing an LA-based random walk in a grid system. To each node in the grid, we attach an LA whose actions are the choices of the edges forming a separator. The walk is self-enclosing, and a new random walk is started whenever the walker returns to the starting node forming a closed classification path yielding a many-edged polygon. In our approach, the different LA attached to the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygons, we perform …
A Novel Energy Model for MANETs based on Graphs with Activation Windows
2005
Energy usage optimization is still an important issue and a critical design factor for mobile ad hoc networks (MANETs). Only recently a few proposals appeared that consider energy-aware optimizations for routing protocols. In this paper we describe an analytical model for MANETs which is based on graphs with activation windows. The activation windows allow to model the on-off status of the network devices. Moreover, we propose an algorithm with pseudo-polynomial complexity, called STP algorithm (STPA), that based on the current position and state of the nodes determines the shortest time path between the source node and the destination node.
A Branch-and-Cut method for the Capacitated Location-Routing Problem
2011
International audience; Recent researches in the design of logistic networks have shown that the overall distribution cost may be excessive if routing decisions are ignored when locating depots. The Location-Routing Problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5–10 potential depots and 20–88 …
TBRA: A scalable routing algorithm in highly mobile large scale pure ad hoc wireless mesh networks
2009
In highly mobile pure ad-hoc wireless mesh networks, fast rerouting within low routing discovery delay is a mandatory requirement for routing algorithm to support interactive applications such as VoIP. Also, the communication overhead should be thwarted when networks grow to a large scale. We propose a Tree-Based Routing Algorithm - TBRA to facilitate such two goals. On one hand, TBRA has very low routing discovery delay due to its proactive property. On the other hand, TBRA performs more efficiently than other proactive protocols with respect to low communication overhead, which thanks to its short routing packet length, less numbers and smaller routing table size. Our modeling analysis an…