On the Linear Dependence of a Finite Set of Additive Functions

2011 ◽  
Vol 62 (1-2) ◽  
pp. 67-71
Author(s):  
Imre Kocsis
Keyword(s):  
Linear Dependence ◽  
Additive Functions ◽  
Finite Set ◽  
Set Of Additive Functions

Non-linear dependence of the dielectric properties of chick embryo myoblast membranes exposed to a sinusoidal 50 Hz magnetic field

1991 ◽  
Vol 60 (6) ◽  
pp. 877-890 ◽  
Author(s):  
Martino Grandolfo ◽  
Maria Santini ◽  
Paolo Vecchia ◽  
Adalberto Bonincontro ◽  
Cesare Cametti ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Dielectric Properties ◽  
Chick Embryo ◽  
Linear Dependence ◽  
Non Linear

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

Oxidation of (1-hydroxybenzyl)ferrocene and its derivatives substituted in phenyl ring with bis(triphenylsilyl) chromate

1982 ◽  
Vol 47 (12) ◽  
pp. 3375-3380 ◽  
Author(s):  
Jaroslav Holeček ◽  
Karel Handlíř ◽  
Milan Nádvorník ◽  
Milan Vlček
Keyword(s):  
Linear Dependence ◽  
Rate Constants ◽  
Oxidation Rate ◽  
Phenyl Ring ◽  
Equilibrium Constants ◽  
Aprotic Solvents ◽  
Protonation Equilibrium ◽  
Oxidation Of Alcohols ◽  
Hammett Σ Constants ◽  
Sulphuric Acid Medium

Kinetics have been studied of oxidation of (1-hydroxybenzyl)ferrocenes substituted in phenyl ring with bis(triphenylsilyl) chromate in benzene solutions as well as protonation of these alcohols in sulphuric acid medium. Logarithms of the oxidation rate constants (kobs, 20-40 °C) and those of the protonation equilibrium constants (KR+, 25 °C) show linear dependence on the Hammett σ constants, the ρ constant values being -0.86 to -0.40 and -2.50, respectively. These negative values suggest that the both processes are influenced by the same effects and confirm the mechanism proposed earlier for oxidation of alcohols with ferrocenyl substituent by action of bis(triphenylsilyl) chromate in aprotic solvents.

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

2021 ◽  
Author(s):  
Patrick Mehlitz ◽  
Leonid I. Minchenko
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Bilevel Optimization ◽  
Regularity Property ◽  
Constant Rank Constraint Qualification ◽  
Existence Criterion ◽  
Set Valued Mappings

AbstractThe presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

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