On Symmetrizable Systems of Second Kind

2000 ◽  
Vol 67 (4) ◽  
pp. 797-802 ◽  
Author(s):  
S. Adhikari
Keyword(s):  
Structural Dynamics ◽  
Original Work ◽  
Similarity Transformation ◽  
Equivalence Transformation ◽  
Linear Transformations ◽  
Equivalence Transformations ◽  
Linear Dynamical Systems ◽  
New Approach ◽  
Multiple Parameter ◽  
Symmetric Systems

We discuss under what conditions multiple-parameter asymmetric linear dynamical systems can be transformed into equivalent symmetric systems by nonsingular linear transformations. So far, in structural dynamics literature this problem has been addressed in the context of the original work by Taussky. Taussky’s approach of symmetrization was based on similarity transformation. In this paper an approach is proposed to transform asymmetric systems into symmetric systems by equivalence transformation. We call Taussky’s approach of symmetrization by similarity transformation “first kind” and proposed approach by equivalence transformation “second kind.” Since equivalence transformations are most general nonsingular linear transformations, conditions of symmetrizability obtained here are more “liberal” than the first kind and numerical calculations also become more straightforward. Several examples are provided to illustrate the new approach. [S0021-8936(00)00504-3]

scholarly journals A Method of Symmetrization of Asymmetric Dynamical Systems

2005 ◽  
Vol 12 (4) ◽  
pp. 309-315 ◽  
Author(s):  
C.Q. Liu
Keyword(s):  
Dynamical Systems ◽  
Numerical Calculations ◽  
Equivalence Transformation ◽  
Symmetric Matrices ◽  
New Approach ◽  
Symmetric Systems

This paper presents an approach to transform asymmetric systems into symmetric systems by equivalence transformation and discusses what forms of restrictions should be imposed on the system matrices so that they can be simultaneously transformed into symmetric matrices. Conditions of symmetrizability obtained here are more “liberal” and numerical calculations of this transformation are more straightforward. Several examples are provided to illustrate the new approach.

Tacitean history: Francis Bacon’s History of the Reign of King Henry VII

2018 ◽  
pp. 17-42 ◽  
Keyword(s):  
Economic History ◽  
Original Work ◽  
New Approach ◽  
History Of ◽  
Henry Vii ◽  
The Relationship ◽  
Classical History

This chapter is concerned with the approach to commerce and finances employed in Francis Bacon's History of the Reign of King Henry VII (1622). Bacon's account, it is shown, was shaped by his reading of legal records, classical history (particularly Tacitus) and the writing of Machiavelli and his various critics. Through drawing on these sources, Bacon developed a detailed commentary on Henry's achievements as a manager of England's commercial interests and, more generally, a neo-Machiavellian analysis of the relationship between government and trade. The result was a highly original work, which offered a new approach to England's economic history.

A New Approach to the Theory of Canonical Decomposition of Linear Dynamical Systems

1973 ◽  
Vol 11 (1) ◽  
pp. 148-158 ◽  
Author(s):  
P. D’Alessandro ◽  
A. Isidori ◽  
A. Ruberti
Keyword(s):  
Dynamical Systems ◽  
Canonical Decomposition ◽  
Linear Dynamical Systems ◽  
New Approach

Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions

1959 ◽  
Vol 11 ◽  
pp. 383-396 ◽  
Author(s):  
Marvin Marcus ◽  
Roger Purves
Keyword(s):  
Symmetric Function ◽  
Symmetric Functions ◽  
Similarity Transformation ◽  
Elementary Symmetric Function ◽  
Linear Transformations ◽  
Elementary Symmetric Functions ◽  
Image Position

In this paper we examine the structure of certain linear transformations T on the algebra of w-square matrices Mn into itself. In particular if A ∈ Mn let Er(A) be the rth elementary symmetric function of the eigenvalues of A. Our main result states that if 4 ≤ r ≤ n — 1 and Er(T(A)) = Er(A) for A ∈ Mn then T is essentially (modulo taking the transpose and multiplying by a constant) a similarity transformation:No such result as this is true for r = 1,2 and we shall exhibit certain classes of counterexamples. These counterexamples fail to work for r = 3 and the structure of those T such that E3(T(A)) = E3(A) for all ∈ Mn is unknown to us.

scholarly journals Vectorial product concentration obtained with a permeable immobilized enzyme membrane. A new approach to the analysis of biological transport systems

1986 ◽  
Vol 235 (3) ◽  
pp. 693-698 ◽  
Author(s):  
B Maïsterrena ◽  
L J Blum ◽  
G Bardeletti ◽  
P R Coulet
Keyword(s):  
Theoretical Analysis ◽  
Enzyme Level ◽  
Product Distribution ◽  
Porous Membrane ◽  
Transport Systems ◽  
Collagen Membrane ◽  
Biological Transport ◽  
New Approach ◽  
The Mathematical Model ◽  
Symmetric Systems

The theoretical analysis of the distribution on both sides of a flat porous membrane of the product generated by an enzyme covalently bound only on to one side of the membrane separating two compartments of widely different volumes is presented. Contrary to what occurs with heterogeneous symmetric systems, the diffusional limitations at the enzyme level play a prominent role, not only on the apparent enzyme activity, but also on product flux-splitting. The mathematical model developed shows that it is possible to concentrate the reaction product in the compartment opposite to that where the reaction occurs. The influence of the parameters and of the physical characteristics of an asymmetrical system on product distribution is analysed. This theoretical analysis is in excellent agreement with experimental data obtained with glucose oxidase immobilized on a porous collagen membrane.

scholarly journals Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Asmat Ara
Keyword(s):  
Approximate Solution ◽  
Nonlinear Oscillator ◽  
High Accuracy ◽  
Force Term ◽  
Hamiltonian Approach ◽  
New Approach ◽  
Suggested Technique ◽  
Multiple Parameter ◽  
Approximate Frequency ◽  
Relationship Of

We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.

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