Search results for " Function"
showing 10 items of 9395 documents
Group topologies coarser than the Isbell topology
2011
Abstract The Isbell, compact-open and point-open topologies on the set C ( X , R ) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α ( X ) of compact families of open subsets of a topological space X . Those α ( X ) for which addition is jointly continuous at the zero function in C α ( X , R ) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α ( X ) for which C α ( X , R ) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, t…
Variations of selective separability II: Discrete sets and the influence of convergence and maximality
2012
A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …
Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra
2003
We give an upper estimate for the Łojasiewicz exponent $\ell(J,I)$ of an ideal $J\subseteq A(K^{n})$ with respect to another ideal I in the ring $A(K^{n})$ of germs analytic functions $f$ : $(K^{n},\mathrm{O})\rightarrow K$ , where $K=C$ or $R$ , using Newton polyhedrons. In particular, we give a method to estimate the Łojasiewicz exponent $\alpha_{0}(f)$ of a germ $f\in A(K^{n})$ that can be applied when $f$ is Newton degenerate with respect to its Newton polyhedron.
Evidence of oblate-prolate shape coexistence in the strongly-deformed nucleus 119Cs
2021
International audience; Prolate-oblate shape coexistence close to the ground state in the strongly-deformed proton-rich A≈120 nuclei is reported for the first time. One of the four reported bands in 119Cs, built on a 11/2− state at 670 keV, consists of nearly degenerate signature partners, and has properties which unequivocally indicate the strongly-coupled πh11/2[505]11/2− configuration associated with oblate shape. Together with the decoupled πh11/2[541]3/2− band built on the 11/2− prolate state at 110 keV, for which a half-life of T1/2=55(5)μs has been measured, the new bands bring evidence of shape coexistence at low spin in the proton-rich strongly deformed A≈120 nuclei, a phenomenon p…
Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
2021
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_i(u_t)d\mathbf X^i_t$ where $(L_t)_{t\in[0,T]}$ is a time-dependent family of unbounded operators acting on some scale of Banach spaces, while $\mathbf X\equiv(X,\mathbb X)$ is a two-step (non-necessarily geometric) rough path of H\"older regularity $\gamma >1/3.$ Besides dealing with non-autonomous evolution equations, our results also allow for unbounded operations in the noise term (up to some critical loss of regularity depending on that of the rough path $\mathbf X$). As a technical tool, we introduce a versi…
Structural changes induced by daily music listening in the recovering brain after middle cerebral artery stroke: a voxel-based morphometry study
2014
[Abstract.] Music is a highly complex and versatile stimulus for the brain that engages many temporal, frontal, parietal, cerebellar, and subcortical areas involved in auditory, cognitive, emotional, and motor processing. Regular musical activities have been shown to effectively enhance the structure and function of many brain areas, making music a potential tool also in neuro- logical rehabilitation. In our previous randomized controlled study, we found that listening to music on a daily basis can improve cognitive recovery and improve mood after an acute mid- dle cerebral artery stroke. Extending this study, a voxel-based morphometry (VBM) analysis utilizing cost function masking was perf…
On the stability of some controlled Markov chains and its applications to stochastic approximation with Markovian dynamic
2015
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading to the proof of the desired stability property. Of particular interest is the fact that the approach applies even in situations where the two components of the process present a time-scale separation, w…
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…
A Multilayered Plate Theory with Transverse Shear and Normal Warping Functions
2016
A multilayered plate theory which takes into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear behaviour, the fifth is related to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho-Parmerter and (a modified version of) Beakou-Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal s…
STABILITY OF A STOCHASTICALLY PERTURBED MODEL OF INTRACELLULAR SINGLE-STRANDED RNA VIRUS REPLICATION
2019
Compared to the replication of double-stranded RNA and DNA viruses, the replication of single-stranded viruses requires the production of a number of intermediate strands that serve as templates for the synthesis of genomic-sense strands. Two theoretical extreme mechanisms for replication for such single-stranded viruses have been proposed; one extreme being represented by the so-called linear stamping machine and the opposite extreme by the exponential growth. Of course, real systems are more complex and examples have been described in which a combination of such extreme mechanisms can also occur: a fraction of the produced progeny resulting from a stamping-machine type of replication that…