Closed Range Composition Operators on Hilbert Function Spaces

We show that a Carleson measure satisfies the reverse Carleson condition if and only if its Berezin symbol is bounded below on the unit disk D. We provide new necessary and sufficient conditions for the composition operator to have closed range on the Bergman space. The pull-back measure of area measure on D plays an important role. We also give a new proof in the case of the Hardy space and conjecture a condition in the case of the Dirichlet space

Closed Range Composition Operators on Hilbert Function Spaces

We show that a Carleson measure satisfies the reverse Carleson condition if and only if its Berezin symbol is bounded below on the unit disk D. We provide new necessary and sufficient conditions for the composition operator to have closed range on the Bergman space. The pull-back measure of area measure on D plays an important role. We also give a new proof in the case of the Hardy space and conjecture a condition in the case of the Dirichlet space

Free Vibrational Behavior of Bi-Directional Functionally Graded Composite Panel with and Without Porosities Using 3D Finite Element Approximations

Abstract: In the present study, the frequency characteristics of bi-directional functionally graded panels in rectangular planform with and without porosities are examined using 3D finite element approximations. In this work, the graded panel is consisted of metal and ceramic material, in which material properties vary smoothly in two directions. The material properties of this highly heterogeneous material are obtained using the Voigt model via extended power-law distribution of volume fractions. The present model is developed using a customized computer code and discretized using three dimensional solid 20-noded quadrilateral elements. The mesh refinement is carried out to conduct the convergence test and the validation test by comparing the obtained results with the previous reported results. At a later stage, a comprehensive parametric study is conducted through numerical illustrations which reveal that the geometrical and material parameters of bi-directional functionally graded panel affect its frequency characteristics, significantly

Free Vibrational Behavior of Bi-Directional Functionally Graded Composite Panel with and Without Porosities Using 3D Finite Element Approximations

Abstract: In the present study, the frequency characteristics of bi-directional functionally graded panels in rectangular planform with and without porosities are examined using 3D finite element approximations. In this work, the graded panel is consisted of metal and ceramic material, in which material properties vary smoothly in two directions. The material properties of this highly heterogeneous material are obtained using the Voigt model via extended power-law distribution of volume fractions. The present model is developed using a customized computer code and discretized using three dimensional solid 20-noded quadrilateral elements. The mesh refinement is carried out to conduct the convergence test and the validation test by comparing the obtained results with the previous reported results. At a later stage, a comprehensive parametric study is conducted through numerical illustrations which reveal that the geometrical and material parameters of bi-directional functionally graded panel affect its frequency characteristics, significantly

Measurement of turbulence and pitch of the airstream in the 5' × 7' tunnel of Indian Institute of Science

This article does not have an abstract

Low-Grade Serous Carcinoma – The Clinical Challenge

Low-grade serous carcinoma is one of the five major histological types of ovarian carcinoma associated with a specific biology. We reviewed three cases from our institution to demonstrate the variable clinical course and provide a brief review on this disease entity

Closed-Range Composition Operators on A2 and the Bloch Space

For any analytic self-map φ of {z : |z| \u3c 1} we give four separate conditions, each of which is necessary and sufficient for the composition operator Cφ to be closed-range on the Bloch space B . Among these conditions are some that appear in the literature, where we provide new proofs. We further show that if Cφ is closed-range on the Bergman space A2 , then it is closed-range on B , but that the converse of this fails with a vengeance. Our analysis involves an extension of the Julia-Carathéodory Theorem

Closed-Range Composition Operators on A2 and the Bloch Space

For any analytic self-map φ of {z : |z| \u3c 1} we give four separate conditions, each of which is necessary and sufficient for the composition operator Cφ to be closed-range on the Bloch space B . Among these conditions are some that appear in the literature, where we provide new proofs. We further show that if Cφ is closed-range on the Bergman space A2 , then it is closed-range on B , but that the converse of this fails with a vengeance. Our analysis involves an extension of the Julia-Carathéodory Theorem