Search results for "Orff"
showing 10 items of 199 documents
Bifurcations of cuspidal loops
1997
A cuspidal loop for a planar vector field X consists of a homoclinic orbit through a singular point p, at which X has a nilpotent cusp. This is the simplest non-elementary singular cycle (or graphic) in the sense that its singularities are not elementary (i.e. hyperbolic or semihyperbolic). Cuspidal loops appear persistently in three-parameter families of planar vector fields. The bifurcation diagrams of unfoldings of cuspidal loops are studied here under mild genericity hypotheses: the singular point p is of Bogdanov - Takens type and the derivative of the first return map along the orbit is different from 1. An analytic and geometric method based on the blowing up for unfoldings is propos…
Convolutional Neural Network With Shape Prior Applied to Cardiac MRI Segmentation.
2019
In this paper, we present a novel convolutional neural network architecture to segment images from a series of short-axis cardiac magnetic resonance slices (CMRI). The proposed model is an extension of the U-net that embeds a cardiac shape prior and involves a loss function tailored to the cardiac anatomy. Since the shape prior is computed offline only once, the execution of our model is not limited by its calculation. Our system takes as input raw magnetic resonance images, requires no manual preprocessing or image cropping and is trained to segment the endocardium and epicardium of the left ventricle, the endocardium of the right ventricle, as well as the center of the left ventricle. Wit…
Common Fixed points for multivalued generalized contractions on partial metric spaces
2013
We establish some common fixed point results for multivalued mappings satisfying generalized contractive conditions on a complete partial metric space. The presented theorems extend some known results to partial metric spaces. We motivate our results by some given examples and an application for finding the solution of a functional equation arising in dynamic programming.
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.
Resonance between Cantor sets
2007
Let $C_a$ be the central Cantor set obtained by removing a central interval of length $1-2a$ from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if $\log b/\log a$ is irrational, then \[ \dim(C_a+C_b) = \min(\dim(C_a) + \dim(C_b),1), \] where $\dim$ is Hausdorff dimension. More generally, given two self-similar sets $K,K'$ in $\RR$ and a scaling parameter $s>0$, if the dimension of the arithmetic sum $K+sK'$ is strictly smaller than $\dim(K)+\dim(K') \le 1$ (``geometric resonance''), then there exists $r<1$ such that all contraction ratios of the similitudes defining $K$ and $K'$ are powers of $r$ (``algebraic resonance…
Regular Minimality and Thurstonian-type modeling
2009
Abstract A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision ru…
On the cardinality of almost discretely Lindelof spaces
2016
A space is said to be almost discretely Lindelof if every discrete subset can be covered by a Lindelof subspace. Juhasz et al. (Weakly linearly Lindelof monotonically normal spaces are Lindelof, preprint, arXiv:1610.04506 ) asked whether every almost discretely Lindelof first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under $$2^{<{\mathfrak {c}}}={\mathfrak {c}}$$ (which is a consequence of Martin’s Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhasz et al. (First-countable and almost discretely Lindelof $$T_3$$ spaces have cardinality at most continuum, preprint, arXiv:1612.06651 ). We conclude with a few rel…
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
On a pair of fuzzy $\varphi$-contractive mappings
2010
We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.
A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces
2013
Abstract In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming.