Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy a... more Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of Cn. Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study composition operators in poly discs and characterize those operators which are bounded or compact in Hardy and weighted Bergman spaces. In addition to Carleson measure theorems resembling those of [5], [6], we give necessary and sufficient conditions satisfied by the maps inducing bounded or compact composition operators. We conclude by considering the role of angular derivatives on the compactness question explicitly.
Abstract. We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0... more Abstract. We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α< 1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.
International Journal of Mathematics and Mathematical Sciences, 1999
We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces0<α<1.... more We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces0<α<1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.
The human microbiota composition is associated with a number of diseases including obesity, infla... more The human microbiota composition is associated with a number of diseases including obesity, inflammatory bowel disease, and bacterial vaginosis. Thus, microbiome research has the potential to reshape clinical and therapeutic approaches. However, raw microbiome count data require careful pre-processing steps that take into account both the sparsity of counts and the large number of taxa that are being measured. Filtering is defined as removing taxa that are present in a small number of samples and have small counts in the samples where they are observed. Despite progress in the number and quality of filtering approaches, there is no consensus on filtering standards and quality assessment. This can adversely affect downstream analyses and reproducibility of results across platforms and software. We introduce PERFect, a novel permutation filtering approach designed to address two unsolved problems in microbiome data processing: (i) define and quantify loss due to filtering by implement...
The computation of the norm of composition operators on Hardy spaces is very hard, even for choic... more The computation of the norm of composition operators on Hardy spaces is very hard, even for choice of fairly simple symbol maps. In this pa- per, we shall give an approach comparing the norm of these operators with the spectral radius, the action of the operators and their adjoints on the re- producing kernel functions. Our goal is to characterize,
Proceedings of the 2005 Ieee International Conference on Robotics and Automation, 2005
ABSTRACT This paper develops new, analytical methods to find a large class of Orthogonal Gough-St... more ABSTRACT This paper develops new, analytical methods to find a large class of Orthogonal Gough-Stewart Platforms (OGSPs) having desired manipulabilities at a single point. In contrast, prior methods have been computationally intensive, relying on numerical search techniques. The new techniques are directly applicable to clean sheet design of micro-manipulators, vibration isolators, and Cartesian stiffness matrices. In addition, straightforward methods for retro-fitting existing OGSPs are illustrated. The approach relies on symmetrically repeating a strut at least three times.
Proceedings of the 2005 Ieee International Conference on Robotics and Automation, Apr 18, 2005
ABSTRACT Parallel mechanisms frequently possess an unstable type of singularity that has no count... more ABSTRACT Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the past has been tackled by exhaustive numerical searches of the mechanism workspace using an accurate analytical model of the mechanism kinematics. This paper considers the singularity determination problem from a geometric perspective for n-legged spatial parallel mechanisms. By using the constraints on the passive joint velocities, a necessary condition for unstable singularity is derived that identifies the reason for such singularities.
Proceedings 2006 Ieee International Conference on Robotics and Automation 2006 Icra 2006, May 15, 2006
ABSTRACT For any manipulator, fault tolerance is a desirable property. This paper shows that for ... more ABSTRACT For any manipulator, fault tolerance is a desirable property. This paper shows that for any serial or parallel manipulator functioning about a single point in its workspace, the mean square of the relative manipulabilities over all possible failures, with a given number of links failing at a time, is always constant irrespective of the geometry of the manipulator. In this paper optimal fault tolerant manipulability is defined for parallel manipulators. This concept is applied to orthogonal Gough-Stewart platforms (OGSPs) to identify a class of symmetric OGSPs having optimal fault tolerant manipulability. As an example, an 8-strut OGSP having this property is described
ABSTRACT The well-known theorems of Stieltjes, Hamburger and Hausdorff establish conditions on in... more ABSTRACT The well-known theorems of Stieltjes, Hamburger and Hausdorff establish conditions on infinite sequences of real numbers to be moment sequences. Further, works by Carath\&#39;{e}odory, Schur and Nevanlinna connect moment problems to problems in function theory and functions belonging to various spaces. In many problems associated with realization of a signal or an image, data may be corrupt or missing. Reconstruction of a function from moment sequences with missing terms is an interesting problem leading to advances in image and/or signal reconstruction. It is easy to show that a subsequence of a moment sequence may not be a moment sequence. Conditions are obtained to show how rigid the space of sub-moment sequences is and necessary and sufficient conditions for a sequence to be a sub-moment sequence are established. A deep connection between the sub-moment measures and the moment measures is derived and the determinacy of the moment and sub-moment problems are related. This problem is further related to completion of positive Hankel matrices.
We give two characterizations of cones over ellipsoids in real normed vector spaces. Let $C$ be a... more We give two characterizations of cones over ellipsoids in real normed vector spaces. Let $C$ be a closed convex cone with nonempty interior such that $C$ has a bounded section of codimension $1$. We show that $C$ is a cone over an ellipsoid if and only if every bounded section of $C$ has a center of symmetry. We also show that $C$ is a cone over an ellipsoid if and only if the affine span of $\partial C \cap \partial(a - C)$ has codimension $1$ for every point $a$ in the interior of $C$. These results generalize the finite-dimensional cases proved in (Jerónimo-Castro and McAllister, 2013).
International Conference on Robotics and Automation, 2004
Optimal geometric design is of key importance to the performance of a manipulator. First, this pa... more Optimal geometric design is of key importance to the performance of a manipulator. First, this paper extends the work in Y. Yi, et al., (2004) to generate a class of isotropic Gough-Stewart platforms (GSPs) with an odd number of struts. Then, it develops methods for finding a highly fault tolerant GSP from that class. Two optimization criteria are considered, isotropy
Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy a... more Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of Cn. Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study composition operators in poly discs and characterize those operators which are bounded or compact in Hardy and weighted Bergman spaces. In addition to Carleson measure theorems resembling those of [5], [6], we give necessary and sufficient conditions satisfied by the maps inducing bounded or compact composition operators. We conclude by considering the role of angular derivatives on the compactness question explicitly.
Abstract. We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0... more Abstract. We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α< 1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.
International Journal of Mathematics and Mathematical Sciences, 1999
We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces0<α<1.... more We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces0<α<1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.
The human microbiota composition is associated with a number of diseases including obesity, infla... more The human microbiota composition is associated with a number of diseases including obesity, inflammatory bowel disease, and bacterial vaginosis. Thus, microbiome research has the potential to reshape clinical and therapeutic approaches. However, raw microbiome count data require careful pre-processing steps that take into account both the sparsity of counts and the large number of taxa that are being measured. Filtering is defined as removing taxa that are present in a small number of samples and have small counts in the samples where they are observed. Despite progress in the number and quality of filtering approaches, there is no consensus on filtering standards and quality assessment. This can adversely affect downstream analyses and reproducibility of results across platforms and software. We introduce PERFect, a novel permutation filtering approach designed to address two unsolved problems in microbiome data processing: (i) define and quantify loss due to filtering by implement...
The computation of the norm of composition operators on Hardy spaces is very hard, even for choic... more The computation of the norm of composition operators on Hardy spaces is very hard, even for choice of fairly simple symbol maps. In this pa- per, we shall give an approach comparing the norm of these operators with the spectral radius, the action of the operators and their adjoints on the re- producing kernel functions. Our goal is to characterize,
Proceedings of the 2005 Ieee International Conference on Robotics and Automation, 2005
ABSTRACT This paper develops new, analytical methods to find a large class of Orthogonal Gough-St... more ABSTRACT This paper develops new, analytical methods to find a large class of Orthogonal Gough-Stewart Platforms (OGSPs) having desired manipulabilities at a single point. In contrast, prior methods have been computationally intensive, relying on numerical search techniques. The new techniques are directly applicable to clean sheet design of micro-manipulators, vibration isolators, and Cartesian stiffness matrices. In addition, straightforward methods for retro-fitting existing OGSPs are illustrated. The approach relies on symmetrically repeating a strut at least three times.
Proceedings of the 2005 Ieee International Conference on Robotics and Automation, Apr 18, 2005
ABSTRACT Parallel mechanisms frequently possess an unstable type of singularity that has no count... more ABSTRACT Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the past has been tackled by exhaustive numerical searches of the mechanism workspace using an accurate analytical model of the mechanism kinematics. This paper considers the singularity determination problem from a geometric perspective for n-legged spatial parallel mechanisms. By using the constraints on the passive joint velocities, a necessary condition for unstable singularity is derived that identifies the reason for such singularities.
Proceedings 2006 Ieee International Conference on Robotics and Automation 2006 Icra 2006, May 15, 2006
ABSTRACT For any manipulator, fault tolerance is a desirable property. This paper shows that for ... more ABSTRACT For any manipulator, fault tolerance is a desirable property. This paper shows that for any serial or parallel manipulator functioning about a single point in its workspace, the mean square of the relative manipulabilities over all possible failures, with a given number of links failing at a time, is always constant irrespective of the geometry of the manipulator. In this paper optimal fault tolerant manipulability is defined for parallel manipulators. This concept is applied to orthogonal Gough-Stewart platforms (OGSPs) to identify a class of symmetric OGSPs having optimal fault tolerant manipulability. As an example, an 8-strut OGSP having this property is described
ABSTRACT The well-known theorems of Stieltjes, Hamburger and Hausdorff establish conditions on in... more ABSTRACT The well-known theorems of Stieltjes, Hamburger and Hausdorff establish conditions on infinite sequences of real numbers to be moment sequences. Further, works by Carath\&#39;{e}odory, Schur and Nevanlinna connect moment problems to problems in function theory and functions belonging to various spaces. In many problems associated with realization of a signal or an image, data may be corrupt or missing. Reconstruction of a function from moment sequences with missing terms is an interesting problem leading to advances in image and/or signal reconstruction. It is easy to show that a subsequence of a moment sequence may not be a moment sequence. Conditions are obtained to show how rigid the space of sub-moment sequences is and necessary and sufficient conditions for a sequence to be a sub-moment sequence are established. A deep connection between the sub-moment measures and the moment measures is derived and the determinacy of the moment and sub-moment problems are related. This problem is further related to completion of positive Hankel matrices.
We give two characterizations of cones over ellipsoids in real normed vector spaces. Let $C$ be a... more We give two characterizations of cones over ellipsoids in real normed vector spaces. Let $C$ be a closed convex cone with nonempty interior such that $C$ has a bounded section of codimension $1$. We show that $C$ is a cone over an ellipsoid if and only if every bounded section of $C$ has a center of symmetry. We also show that $C$ is a cone over an ellipsoid if and only if the affine span of $\partial C \cap \partial(a - C)$ has codimension $1$ for every point $a$ in the interior of $C$. These results generalize the finite-dimensional cases proved in (Jerónimo-Castro and McAllister, 2013).
International Conference on Robotics and Automation, 2004
Optimal geometric design is of key importance to the performance of a manipulator. First, this pa... more Optimal geometric design is of key importance to the performance of a manipulator. First, this paper extends the work in Y. Yi, et al., (2004) to generate a class of isotropic Gough-Stewart platforms (GSPs) with an odd number of struts. Then, it develops methods for finding a highly fault tolerant GSP from that class. Two optimization criteria are considered, isotropy
Uploads
Papers by Farhad Jafari