scholarly journals Conditions for Linear Dependence of Two Operators

2010 ◽  
pp. 411-434 ◽  
Author(s):  
Bojan Kuzma ◽  
Gorazd Lešnjak ◽  
Chi-Kwong Li ◽  
Tatjana Petek ◽  
Leiba Rodman
Keyword(s):  
Linear Dependence

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.

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.

scholarly journals Evaluation of the Effective Material Use from the View of EU Environmental Policy Goals

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4759
Author(s):  
Marcela Taušová ◽  
Katarína Čulková ◽  
Peter Tauš ◽  
Lucia Domaracká ◽  
Andrea Seňová
Keyword(s):  
Cluster Analysis ◽  
Linear Dependence ◽  
Energy Savings ◽  
Tax Burden ◽  
Eu Countries ◽  
Eu Member States ◽  
Average Value ◽  
Negative Results ◽  
Policy Goals ◽  
Environmental Goals

Humanity is dependent on natural resources. Use and productivity of these resources plays an important role in energy savings and circular economy. The goal of this contribution is to evaluate productivity of resources in the frame of EU countries. Single analysis deals with data from the publicly available portal database and collected data were processed in the statistical software JMP. The trend of development and analysis of variability and linear dependence helped to create cluster analysis and comparison of the EU countries. The results from the view of average value of the indicator registered the growth, and from the view of variability the statistically important differences were verified for EU member states. Some pairs of indicators recorded positive, while some pairs recorded negative linear dependence. Cluster analysis shows two groups of countries—the first one with positive results, having the lowest tax burden in the case of energy taxes and environment, and the second one with negative results, having the highest tax burden of environmental and energy policy. The results are useful for a proper setting of energy and environmental goals that can increase the effectiveness of resource productivity in the countries studied.

Collision Induced Microwave Absorption in N2, CH4, and N2–Ar, N2–CH4 Mixtures at 1.1 and 2.3 cm−1

1974 ◽  
Vol 52 (9) ◽  
pp. 821-829 ◽  
Author(s):  
I. R. Dagg ◽  
G. E. Reesor ◽  
J. L. Urbaniak
Keyword(s):  
Microwave Absorption ◽  
Quadrupole Moment ◽  
Linear Dependence ◽  
Relaxation Times ◽  
High Sensitivity ◽  
Higher Order ◽  
Induced Absorption ◽  
High Q ◽  
Order Dependence

Collision induced microwave absorption is reported in pure N2, N2–Ar, N2–CH4, mixtures, and in pure CH4 in the 35 and 70 GHz regions (1.1 and 2.3 cm−1) at a temperature of 22 °C. The measurements are accomplished using overmoded high Q cavities capable of pressurization of up to 5000 p.s.i.g. The apparatus and method are described. With the high sensitivity attained, the results in pure N2 from 30 → 250 amagat reveal terms in the square and cube of the density from which the relaxation times are calculated. The linear dependence on frequency of the collision induced absorption up to 2.3 cm−1 is established. Higher order dependence on the density is observed in the N2–Ar and N2–CH4 mixtures. Various estimates of the quadrupole moment of N2 are given, making use of earlier results in other frequency regions.

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