The Banach—Rudin—Carleson Interpolation Theorems and the Norms of Embedding Operators for Some Classes of Analytical Functions

1972 ◽  
pp. 1-28
Author(s):  
S. A. Vinogradov
Keyword(s):  
Analytical Functions

Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

2021 ◽  
pp. 095440622110127
Author(s):  
Mohammad Reza Salehi Kolahi ◽  
Hossein Rahmani ◽  
Hossein Moeinkhah
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Fe Simulation ◽  
Shear Deformation Theory ◽  
Mechanical Analysis ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
First Order ◽  
Analytical Functions ◽  
Plane Elasticity Theory

In this paper, the first order shear deformation theory is used to derive an analytical formulation for shrink-fitted thick-walled functionally graded cylinders. It is assumed that the cylinders have constant Poisson’s ratio and the elastic modulus varies radially along the thickness with a power function. Furthermore, a finite element simulation is carried out using COMSOL Multiphysics, which has the advantage of defining material properties as analytical functions. The results from first order shear deformation theory are compared with the findings of both plane elasticity theory and FE simulation. The results of this study could be used to design and manufacture for elastic shrink-fitted FG cylinders.

History Matching and Predicting GOR Behavior With Analytical Functions

1986 ◽  
Vol 1 (03) ◽  
pp. 300-312 ◽  
Author(s):  
D.M. Chang ◽  
H.H. Haldorsen ◽  
P.A. Kirwan
Keyword(s):  
History Matching ◽  
Analytical Functions

Back Analysis Methods in Geotechnical Engineering

2014 ◽  
Vol 1020 ◽  
pp. 423-428 ◽  
Author(s):  
Eva Hrubesova ◽  
Marek Mohyla
Keyword(s):  
Rock Mass ◽  
Geotechnical Engineering ◽  
Back Analysis ◽  
Rheological Parameters ◽  
Analysis Method ◽  
Direct Optimization ◽  
Initial Stress State ◽  
Analytical Functions ◽  
Is Evaluation

The paper deals with the back analysis method in geotechnical engineering, that goal is evaluation the more objective and reliable parameters of the rock mass on the basis of in-situ measurements. Stress, deformational, strength and rheological parameters of the rock mass are usually determined by some inaccuracies and errors arising from the complexity and variability of the rock mass. This higher or lower degree of imprecision is reflected in the reliability of the mathematical modelling results. The paper presents the utilization of direct optimization back analysis method, based on the theory of analytical functions of complex variable and Kolosov-Muschelischvili relations, to the evaluation of initial stress state inside the rock massif.

Turbocharger Map Reduction for Control-Oriented Modeling

2011 ◽  
Author(s):  
Karla Stricker ◽  
Lyle Kocher ◽  
Ed Koeberlein ◽  
D. G. Van Alstine ◽  
Greg Shaver
Keyword(s):  
Control Systems ◽  
Exchange Process ◽  
Variable Geometry ◽  
Shaft Speed ◽  
Analytical Functions ◽  
Nozzle Position ◽  
Mass Flows ◽  
Estimation And Control ◽  
Gas Exchange Process ◽  
And Control

The gas exchange process in a modern diesel engine is generally modeled using manufacturer-provided performance maps that describe mass flows through, and efficiencies of, the turbine and compressor. These maps are typically implemented as look-up tables requiring multiple interpolations based on pressure ratios across the turbine and compressor, as well as the turbocharger shaft speed. In the case of variable-geometry turbochargers, the nozzle position is also an input to these maps. This method of interpolating or extrapolating data is undesirable when modeling for estimation and control, and though there have been several previous efforts to reduce dependence on turbomachinery maps, many of these approaches are complex and not easily implemented in engine control systems. As such, the aim of this paper is to reduce turbocharger maps to analytical functions for models amenable to estimation and control.

Divergence Speed Prediction for Practical Slung Load Shapes

2015 ◽  
Author(s):  
Brandon Liberi ◽  
Chau Ton ◽  
Narayanan Komerath
Keyword(s):  
Control System ◽  
Robust Control ◽  
Wind Tunnel ◽  
Flight Control ◽  
Flight Control System ◽  
Wind Tunnel Experiments ◽  
Flight Testing ◽  
Flight Vehicles ◽  
Analytical Functions ◽  
Speed Prediction

Given the innumerable combinations of flight vehicles, loads and flight conditions, alternatives are sought to flight testing, to certify the safe flight speed with slung loads. With well-resolved airload maps now feasible for arbitrary shapes as analytical functions, dynamic simulation predicts divergence speeds, regardless of the symmetry of the object. Likely modes of amplification are found using wind tunnel experiments with free-swinging objects. A robust control formulation enables safe flight close to divergence speed where the flight control system can prevent disturbance amplification.

Distortion theorems in the class Kn(D)

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Eduard G. Kir’yatskii
Keyword(s):  
Analytical Functions ◽  
Distortion Theorems

AbstractThis article presents the analysis of properties of functions belonging to the class KThe subclass K̃The author touches classical and at the same time urgent questions, arising at the study of analytical functions, belonging to some class.

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