On Bounded Matrices with Non-Negative Elements

1958 ◽  
Vol 10 ◽  
pp. 587-591 ◽  
Author(s):  
C. R. Putnam
Keyword(s):  
Simple Point ◽  
Finite Matrix ◽  
Bounded Matrices ◽  
Nonnegative Eigenvalue

It is known (Perron (10); Frobenius (5, 6)) that if A = (a ik ) is a finite matrix with elements aik ⩾ 0, then A has a real, nonnegative eigenvalue μ, satisfying μ =max|λ| where λ is in the spectrum of A, with a corresponding eigenvector x = (x 1, … , xn) for which x i≥ 0. Moreover if a ik > 0, then μ is a simple point of the spectrum with an eigenvector x (unique, except for constant multiples) with components xi ≥0. Much has been written on this and related issues; cf., for example, the recent papers (4, 12) wherein are given several references.

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

scholarly journals An efficient optimizer for simple point process models

2013 ◽  
Author(s):  
Ahmed Gamal-Eldin ◽  
Guillaume Charpiat ◽  
Xavier Descombes ◽  
Josiane Zerubia
Keyword(s):  
Point Process ◽  
Process Models ◽  
Simple Point ◽  
Point Process Models

A simple point vortex model for two‐dimensional decaying turbulence

1992 ◽  
Vol 4 (5) ◽  
pp. 1036-1039 ◽  
Author(s):  
R. Benzi ◽  
M. Colella ◽  
M. Briscolini ◽  
P. Santangelo
Keyword(s):  
Point Vortex ◽  
Two Dimensional ◽  
Simple Point ◽  
Vortex Model ◽  
Decaying Turbulence ◽  
Point Vortex Model

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

Elastothermodynamic Damping of Fiber-Reinforced Metal-Matrix Composites

1995 ◽  
Vol 62 (2) ◽  
pp. 441-449 ◽  
Author(s):  
K. B. Milligan ◽  
V. K. Kinra
Keyword(s):  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Axial Strain ◽  
Second Law Of Thermodynamics ◽  
Infinite Matrix ◽  
Matrix Composites ◽  
Fiber Reinforced ◽  
Continuous Fiber ◽  
Finite Matrix ◽  
Starting Point

Recently, taking the second law of thermodynamics as a starting point, a theoretical framework for an exact calculation of the elastothermodynamic damping in metal-matrix composites has been presented by the authors (Kinra and Milligan, 1994; Milligan and Kinra, 1993). Using this work as a foundation, we solve two canonical boundary value problems concerning elastothermodynamic damping in continuous-fiber-reinforced metal-matrix composites: (1) a fiber in an infinite matrix, and (2) using the general methodology given by Bishop and Kinra (1993), a fiber in a finite matrix. In both cases the solutions were obtained for the following loading conditions: (1) uniform radial stress and (2) uniform axial strain.

scholarly journals Experimental Validation of the Mean Pitch Theory

2021 ◽  
Vol 2090 (1) ◽  
pp. 012042
Author(s):  
T Meda ◽  
A Rogala
Keyword(s):  
Control Systems ◽  
Experimental Validation ◽  
Significant Loss ◽  
Simple Point ◽  
Fire Control ◽  
Mass Model ◽  
Body Model ◽  
Rigid Body Model ◽  
The Mean ◽  
In Fire

Abstract There are several types of exterior ballistic models used to calculate projectile’s flight trajectories. The most complex 6 degree of freedom rigid body model has many disadvantages to using it to create firing tables or rapid calculations in fire control systems. Some of ballistic phenomena can be simplified by empirical equations without significant loss of accuracy. This approach allowed to create standard NATO ballistic model for spin stabilized projectiles named Modified Point of Mass Model (PM Model). For fin (aerodynamically) stabilized projectiles like mortar projectiles simple Point of Mass Model is commonly used. The PM Model excludes many flight phenomena in calculations. In this paper authors show the mean pitch theory as an approximation of the natural fin stabilised projectile pitch during flight. The theory allows for simple improvement of accuracy of the trajectories calculation. In order to validate the theory data obtained from shooting of supersonic mortar projectiles were used. The comparison of accuracy between simple PM Model and PM Model including mean pitch theory were shown. Results were also compared with the angle of response theory.

scholarly journals Modules with Chain Conditions for Finite Matrix Subgroups

1997 ◽  
Vol 190 (1) ◽  
pp. 68-87 ◽  
Author(s):  
Wolfgang Zimmermann
Keyword(s):  
Chain Conditions ◽  
Finite Matrix

Comparison of under-actuated and fully-actuated serial robotic arms: a case study

2021 ◽  
pp. 1-13
Author(s):  
Matteo Bottin ◽  
Giulio Rosati
Keyword(s):  
Degrees Of Freedom ◽  
Simple Point ◽  
Controllable System ◽  
Robotic Arms ◽  
Passive Joint ◽  
Final Configuration ◽  
Vibration Behavior ◽  
Rotational Joint ◽  
Point To Point

Abstract Under-actuated robots are very interesting in terms of cost and weight since they can result in a state-controllable system with a number of actuators lower than the number of joints. In this paper, a comparison between an under-actuated planar 3 degrees of freedom (DOF) robot and a comparable fully-actuated 2 degrees of freedom robot is presented, mainly focusing on the performances in terms of trajectories, actuator torques, and vibrations. The under-actuated system is composed of 2 active rotational joints followed by a passive rotational joint equipped with a torsional spring. The fully-actuated robot is inertial equivalent to the under-actuated manipulator: the last link is equal to the sum of the last two links of the under-actuated system. Due to the conditions on the inertia distribution and spring placement, in a simple point-to-point movement the last passive joint starts and ends in a zero-value configuration, so the 3 DOF robot is equivalent, in terms of initial and final configuration, to the 2 DOF fully-actuated robot, thus they can be compared. Results show how while the fully actuated robot is better in terms of reliable trajectory and actuator torques, the under-actuated robot wins in flexibility and vibration behavior.

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