Uniqueness theorems for algebraic functions

1992 ◽  
pp. 199-204
Author(s):  
A. Goldberg ◽  
V. Pyana
Keyword(s):  
Uniqueness Theorems ◽  
Algebraic Functions

scholarly journals Thermodynamic compatibility conditions of a new class of hysteretic materials

2021 ◽  
Author(s):  
Salvatore Sessa
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Iterative Procedure ◽  
Displacement Amplitude ◽  
Compatibility Conditions ◽  
Algebraic Functions ◽  
New Class ◽  
Thermodynamic Compatibility ◽  
Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

Normal approximations for distributions arising in the stochastic approach to chemical reaction kinetics

1981 ◽  
Vol 18 (01) ◽  
pp. 263-267 ◽  
Author(s):  
F. D. J. Dunstan ◽  
J. F. Reynolds
Keyword(s):  
Reaction Kinetics ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Stochastic Approach ◽  
Algebraic Functions ◽  
Chemical Reaction Kinetics ◽  
Normal Approximations ◽  
Formal Solutions

Earlier stochastic analyses of chemical reactions have provided formal solutions which are unsuitable for most purposes in that they are expressed in terms of complex algebraic functions. Normal approximations are derived here for solutions to a variety of reactions. Using these, it is possible to investigate the level at which the classical deterministic solutions become inadequate. This is important in fields such as radioimmunoassay.

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