Search results for " function"
showing 10 items of 9395 documents
Nonlinear diffusion in transparent media: the resolvent equation
2017
Abstract We consider the partial differential equation u - f = div ( u m ∇ u | ∇ u | ) u-f=\operatornamewithlimits{div}\biggl{(}u^{m}\frac{\nabla u}{|\nabla u|}% \biggr{)} with f nonnegative and bounded and m ∈ ℝ {m\in\mathbb{R}} . We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ℋ N - 1 {{\mathcal{H}}^{N-1}} -Hausdorff measure. Results and proofs extend to more general nonlinearities.
Existence and comparison results for a singular semilinear elliptic equation with a lower order term
2014
This paper deals with the homogeneous Dirichlet problem for a singular semilinear elliptic equation with a first order term. When the datum is bounded we prove an existence result and we show that any solution can be compared with the solution to a suitable symmetrized problem.
Co-occurrence of discourse markers in English : from juxtaposition to composition
2019
Abstract In this paper, we report on a qualitative analysis of co-occurring discourse markers, that is, sequences of adjacent discourse markers that belong to the same unit but may express different functions. We examine several formal and functional features of these co-occurring strings on the basis of corpus examples extracted from conversational data in English. In particular, we focus on scope, meaning-in-context (or functions), syntactic category and position. Our analysis reveals several degrees of integration: differences in scope allow us to differentiate juxtaposition and combination of markers. In the case of combination, difference in meaning integration allows us to distinguish…
Fully representable and*-semisimple topological partial*-algebras
2012
We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome …
Information potential for some probability density functions
2021
Abstract This paper is related to the information theoretic learning methodology, whose goal is to quantify global scalar descriptors (e.g., entropy) of a given probability density function (PDF). In this context, the core concept is the information potential (IP) S [ s ] ( x ) : = ∫ R p s ( t , x ) d t , s > 0 of a PDF p(t, x) depending on a parameter x; it is naturally related to the Renyi and Tsallis entropies. We present several such PDF, viewed also as kernels of integral operators, for which a precise relation exists between S[2](x) and the variance Var[p(t, x)]. For these PDF we determine explicitly the IP and the Shannon entropy. As an application to Information Theoretic Learning w…
Planar maps whose second iterate has a unique fixed point
2007
Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) t…
The Spectrum of Analytic Mappings of Bounded Type
2000
Abstract A Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E ′ is weakly compact. For a complex Banach space E and a complex Banach algebra F , let H b ( E , F ) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow H b ( E , F ) with the usual Frechet topology. M ( H b ( E , F ), F ) denotes the set of all non-null continuous homomorphisms from H b ( E , F ) to F . A subset of G EF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets G EF and M ( H b ( E , F ), F ) do not coincide. We prove that if E is symmetrically regu…
On the additivity of block designs
2016
We show that symmetric block designs $${\mathcal {D}}=({\mathcal {P}},{\mathcal {B}})$$D=(P,B) can be embedded in a suitable commutative group $${\mathfrak {G}}_{\mathcal {D}}$$GD in such a way that the sum of the elements in each block is zero, whereas the only Steiner triple systems with this property are the point-line designs of $${\mathrm {PG}}(d,2)$$PG(d,2) and $${\mathrm {AG}}(d,3)$$AG(d,3). In both cases, the blocks can be characterized as the only k-subsets of $$\mathcal {P}$$P whose elements sum to zero. It follows that the group of automorphisms of any such design $$\mathcal {D}$$D is the group of automorphisms of $${\mathfrak {G}}_\mathcal {D}$$GD that leave $$\mathcal {P}$$P in…
On ergodic operator means in Banach spaces
2016
We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesaro means.
Connected components in the space of composition operators onH∞ functions of many variables
2003
LetE be a complex Banach space with open unit ballBe. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onBe with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideBe form a path connected component. WhenE is a Hilbert space or aCo(X)- space, the path connected components are shown to be the open balls of radius 2.