Search results for "Secondary"
showing 10 items of 1765 documents
New spaces of matrices with operator entries
2019
In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a finite number of diagonals. We will use the Schur product with Toeplitz matrices generated by summability kernels to describe such a class and show that in the case of Toeplitz matrices it can be identified with the space of continuous functions with values in $\mathcal B(H)$. We shall also introduce matriceal versions with operator entries of classical spaces of holomorphic functions such as $H^\infty(\mathbb{D})$ and $A(\mathbb{D})$ when dealing with upper t…
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…
On a representation theorem for finitely exchangeable random vectors
2016
A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$. We give an alternative and shorter proof of the representation result (Jaynes \cite{Jay86} and Kerns and Sz\'ekely \cite{KS06}) stating that the law of $X$ is a mixture of product probability measures with respect to a signed mixing measure. The result is "finitistic" in nature meaning that it is a matter of linear algebra for finite $S$. The passing from finite $S$ to an arbitrary one may pose some measure-theoretic difficulties which are avoided by our p…
On almost nilpotent varieties of subexponential growth
2015
Abstract Let N 2 be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity x ( y z ) ≡ 0 . We introduce two new varieties, denoted by V sym and V alt , contained in the variety N 2 and we prove that V sym and V alt are the only two varieties almost nilpotent of subexponential growth.
Almost disjoint families of countable sets and separable complementation properties
2012
We study the separable complementation property (SCP) and its natural variations in Banach spaces of continuous functions over compacta $K_{\mathcal A}$ induced by almost disjoint families ${\mathcal A}$ of countable subsets of uncountable sets. For these spaces, we prove among others that $C(K_{\mathcal A})$ has the controlled variant of the separable complementation property if and only if $C(K_{\mathcal A})$ is Lindel\"of in the weak topology if and only if $K_{\mathcal A}$ is monolithic. We give an example of ${\mathcal A}$ for which $C(K_{\mathcal A})$ has the SCP, while $K_{\mathcal A}$ is not monolithic and an example of a space $C(K_{\mathcal A})$ with controlled and continuous SCP …
Weighted norm inequalities in a bounded domain by the sparse domination method
2019
AbstractWe prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains. As an application we show that certain nonnegative supersolutions of the p-Laplace equation and distance weights are p-admissible in a bounded domain, in the sense that they support versions of the p-Poincaré inequality.
Editor's Choice – Follow-up of Patients After Revascularisation for Peripheral Arterial Diseases: A Consensus Document From the European Society of C…
2019
International audience; Peripheral arterial diseases comprise different clinical presentations, from cerebrovascular disease down to lower extremity artery disease, from subclinical to disabling symptoms and events. According to clinical presentation, the patient's general condition, anatomical location and extension of lesions, revascularisation may be needed in addition to best medical treatment. The 2017 European Society of Cardiology guidelines in collaboration with the European Society for Vascular Surgery have addressed the indications for revascularisation. While most cases are amenable to either endovascular or surgical revascularisation, maintaining long-term patency is often chall…
Effects of Canopy Gap Disturbance on Forest Birds in Boreal Forests
2013
We studied the effects of small-scale disturbance on breeding, forest passerine birds in an old-growth and managed boreal forests in northern Finland. Small-scale disturbance (< 2 ha) in an old-growth and managed forests originated from wind falls and small clear cuts. Continuous forest without gaps was used as a control for both management types (old-growth and managed forests). Passerines' response to disturbance was examined by estimating species richness and abundance of different ecological groups. Species richness and the total abundance of birds did not differ between gap and non-gap plots, neither did the abundance of most ecological groups. Management type or study year were the mo…
Double adjunctions and free monads
2011
We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in "Monads in Double Categories", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove …
Number of drugs used in secondary cardiovascular prevention and late survival in the population of Valencia Community, Spain.
2019
Abstract Background Drug treatment for secondary prevention of cardiovascular disease is recommended by guidelines, but it is not always followed in real life. This study wanted to assess the size of this gap and its impact on mortality in subjects after a cardiovascular event (MACE). Methods Patients with any of MACE in the period from January 1st 2011 to December 31st 2013, and more than one year of follow-up were selected from population of the Valencian Community. Drugs for secondary prevention were antiplatelets, renin-angiotensin system blockers and statins. Assessment of treatment was performed one year after the initial event. Mortality risk was assessed using Cox by the number of d…