Reduced conformal geometrodynamics

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040023 ◽  
Author(s):  
Andrej B. Arbuzov ◽  
Alexander E. Pavlov
Keyword(s):  
Gravitational Field ◽  
Dynamical Systems ◽  
Coordinate System ◽  
Tangent Space ◽  
Equations Of Motion ◽  
Mean Value ◽  
Hamiltonian Reduction ◽  
Square Root ◽  
The Mean ◽  
Static Background

The global time in geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The reduced Hamiltonian equations of motion of gravitational field in semi-geodesic coordinate system are written.

scholarly journals Genetic Differences and Environmental Variations in Calyx-end Fruit Cracking among Japanese Persimmon Cultivars and Selections

HortScience ◽  
2002 ◽  
Vol 37 (1) ◽  
pp. 164-167 ◽  
Author(s):  
Masahiko Yamada ◽  
Akihiko Sato ◽  
Yasuo Ukai
Keyword(s):  
Variance Components ◽  
Mean Value ◽  
Diospyros Kaki ◽  
Square Root ◽  
Environmental Variance ◽  
Japanese Persimmon ◽  
Single Tree ◽  
Fruit Cracking ◽  
Environmental Variations ◽  
The Mean

Environmental variance components were estimated for calyx-end fruit cracking in pollination-constant and nonastringent cultivars and selections of Japanese persimmon (Diospyros kaki Thunb.). The cracking value of a tree in a cultivar or selection (genotype) (X) was evaluated as the number of fruit that cracked divided by the total number (25) of fruit evaluated from each tree. Because the mean value of X was correlated with the variance of X, analyses of variance were performed using its square root value. The variance associated with genotyp× year interaction was the largest of environmental variance components. The variances associated among years and among trees within genotypes were very small. The mean percentage of cracked fruit in evaluation for 10 years was 3% for `Fuyu', 11% for `Matsumotowase-Fuyu', and 12% for `Izu'. On the basis of the environmental variance components obtained, it is proposed that all offspring genotypes exhibiting a phenotypic cracking incidence of less than 20% and 11% should be selected in single-year and three-year evaluations, respectively, when those genotypes are evaluated using 25 fruits from a single tree, in order to successfully select all genotypes with an genotypic incidence of less than 3%.

The Response of a SDOF System Driven by a Periodic Random Force

2017 ◽  
Vol 1144 ◽  
pp. 153-158
Author(s):  
Vladimír Sana ◽  
Ondrej Rokos ◽  
Jiří Maca
Keyword(s):  
Monte Carlo ◽  
Phase Shift ◽  
Equations Of Motion ◽  
Random Force ◽  
Mean Value ◽  
Newmark Method ◽  
Sdof System ◽  
Average Acceleration ◽  
The Mean ◽  
Duhamel’S Integral

This work deals with the response of a linear undamped SDOF system exposed to a force with random amplitude, phase shift, or their combination. The first two moments, the mean value and the variance, of the response will be determined analytically through the Duhamel's integral, and compared to the numerical Monte Carlo simulations. Integration of associated equations of motion will be performed by the Newmark method of average acceleration.

The investigations of pulsar integral radio luminosities

1996 ◽  
Vol 160 ◽  
pp. 59-60
Author(s):  
Igor’ F. Malov ◽  
Oleg I. Malov ◽  
Valerij M. Malofeev
Keyword(s):  
Mean Value ◽  
Main Mechanism ◽  
Square Root ◽  
Mean Square ◽  
Pulsar Period ◽  
Light Cylinder ◽  
Curvature Radiation ◽  
The Mean ◽  
The Difference ◽  
Integral Radio

We have calculated accurate integral radio luminositiesLfor 232 pulsars (Malov et al., 1994) using new average spectra of these objects. Histogram ofL-distribution is characterized by the mean value < logL>= 28.45 and by the mean-square-root deviationS= 1.0. We have analysed also data for short-periodic pulsars (P < 0.1 s) and long-periodic ones (P > 1 s) separately.The main goal of such separation was to test the hypothesis on two types of pulsars (Malov, 1987): i) for the first group of objects radiation is emitted from the neighbourhood of the light cylinder (r=rLC=cP/2π, P is the pulsar period), ii) for the second one emission is generated at distancesr≪rLC. In the second case the main mechanism of radiation is curvature radiation. For the first group of pulsars the radiation is connected with the cyclotron mechanism. The difference between two basic mechanisms and the locations of the emission generation regions must cause some differences in the observable features for these two classes of pulsars.

scholarly journals Time–Energy and Time–Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 679 ◽  
Author(s):  
Gian Paolo Beretta
Keyword(s):  
Master Equation ◽  
Uncertainty Relation ◽  
Hamiltonian Dynamics ◽  
Mean Value ◽  
Uncertainty Relations ◽  
Square Root ◽  
Quantum Thermodynamics ◽  
Uncertainty Distribution ◽  
Unitary Evolution ◽  
The Mean

In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam–Tamm–Messiah time–energy uncertainty relation τ F Δ H ≥ ℏ / 2 provides a general lower bound to the characteristic time τ F = Δ F / | d ⟨ F ⟩ / d t | with which the mean value of a generic quantum observable F can change with respect to the width Δ F of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty Δ H (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty Δ S (square root of entropy fluctuations). For example, we obtain the time–energy-and–time–entropy uncertainty relation ( 2 τ F Δ H / ℏ ) 2 + ( τ F Δ S / k B τ ) 2 ≥ 1 where τ is a characteristic dissipation time functional that for each given state defines the strength of the nonunitary, steepest-entropy-ascent part of the assumed master equation. For purely dissipative dynamics this reduces to the time–entropy uncertainty relation τ F Δ S ≥ k B τ , meaning that the nonequilibrium dissipative states with longer lifetime are those with smaller entropy uncertainty Δ S .

ON THE CALCULATION OF LYAPUNOV CHARACTERISTIC EXPONENTS FOR CONTINUOUS-TIME LTV DYNAMICAL SYSTEMS USING DYNAMIC EIGENVALUES

2012 ◽  
Vol 22 (01) ◽  
pp. 1250019
Author(s):  
MIGUEL ÁNGEL GUTIÉRREZ DE ANDA
Keyword(s):  
Dynamical Systems ◽  
Continuous Time ◽  
Linear Time ◽  
Analytic Solutions ◽  
Mean Value ◽  
Time Varying ◽  
Characteristic Exponents ◽  
Lyapunov Characteristic Exponents ◽  
The Mean ◽  
Time Linear

The concept of the dynamic eigenvalues may be used, in principle, to formulate in a general way analytic solutions of continuous-time linear time-varying dynamical (LTV) systems. It has also been suggested that the mean value of these quantities may be used to calculate Lyapunov characteristic exponents for the aforementioned systems. In this article, it will be demonstrated that this conjecture is not necessarily valid.

scholarly journals Restricted mean value theorems and the metric theory of restricted Weyl sums

2020 ◽  
Author(s):  
Changhao Chen ◽  
Igor E Shparlinski
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Square Root ◽  
Mean Values ◽  
Line Segments ◽  
Exceptional Sets ◽  
Natural Measure ◽  
Measure Spaces ◽  
The Mean ◽  
Almost All

Abstract We study the behaviour of Weyl sums on a subset ${\mathcal X}\subseteq [0,1)^d$ with a natural measure µ on ${\mathcal X}$. For certain measure spaces $({\mathcal X}, \mu),$ we obtain non-trivial bounds for the mean values of the Weyl sums, and for µ-almost all points of ${\mathcal X}$ the Weyl sums satisfy the square root cancellation law. Moreover, we characterize the size of the exceptional sets in terms of Hausdorff dimension. Finally, we derive variants of the Vinogradov mean value theorem averaging over measure spaces $({\mathcal X}, \mu)$. We obtain general results, which we refine for some special spaces ${\mathcal X}$ such as spheres, moment curves and line segments.

scholarly journals Predicting relationships between solar jet variables

2019 ◽  
Author(s):  
Leonard A Freeman
Keyword(s):  
Shock Wave ◽  
Initial Velocity ◽  
Linear Equations ◽  
Correlation Coefficients ◽  
Mean Value ◽  
Square Root ◽  
Simple Physical Interpretation ◽  
Scatter Plots ◽  
The Mean ◽  
The Relationship

Abstract Studies of spicules and similar solar jets reveal a strong correlation between some of the kinematic variables, particularly between the initial velocity V, and the subsequent deceleration, a. It has been proposed that there is a linear relationship between these two variables and that this offers proof for a shock wave mechanism acting on the spicules, although the linear equations found are all different. It is shown here that the relationship is better described by a non-linear form: V is proportional to the square root of a. This relationship between V and a also provides a simple physical interpretation for the results. The different linear equations are found to be simply tangents to this (a, V) curve. Another method used to investigate the (a, V) connection is to determine the correlation coefficients between the kinematic variables from their scatter plots. It is also shown how these correlations also can be predicted from the mean value of the acceleration and height and their standard deviations for the sample under consideration. The implications of these results and the possibility that spicule behaviour is partly due to magnetic fields are discussed.

scholarly journals Error reduction in promoted confidence factor of a rule using improved fuzzy rule promotion technique

2014 ◽  
Vol 14 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Lokesh Jain ◽  
Harish Kumar ◽  
Ravinder Kumar Singla ◽  
Pritpal Singh ◽  
Jagjeet Singh Lore
Keyword(s):  
Information Dissemination ◽  
Fuzzy Rule ◽  
Error Reduction ◽  
Mean Value ◽  
Square Root ◽  
Confidence Factor ◽  
True Value ◽  
Rule Set ◽  
The Mean ◽  
Dissemination System

Abstract A dynamic fuzzy rule promotion approach for the promotion of a confidence factor of a rule for every successful session in diagnosis of a disease in crops by using the specific rules, has already been proposed in literature. This technique has the limitation that an error in the initial estimation of weights reduces linearly after every session the rule is being used. In this paper an improved approach has been proposed using the square root of sum of squares of frequencies, which are spread around the mean true value to reduce the error around a mean value. A rule set for the diseases and their symptoms for the paddy plant has been provided to make comparison between the previous and the improved approach. It has been shown that the improved approach decreases the error in uncertainty of estimation of weight for rules after every successful session. It has also been proposed that the improved approach must be applied in agricultural information dissemination system.

PARTICLE PRODUCTION BY THE FORMATION OF A GLOBAL MONOPOLE

1991 ◽  
Vol 06 (20) ◽  
pp. 3613-3623 ◽  
Author(s):  
CARLOS O. LOUSTO
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Gravitational Field ◽  
Scalar Field ◽  
Particle Production ◽  
Mean Value ◽  
Global Symmetry ◽  
Global Monopole ◽  
Order Of Magnitude ◽  
The Mean

We study pair production by the changing gravitational field of a global monopole during its formation in the very early universe after the breaking of a global symmetry. We obtain a result of the same order of magnitude as in the case of gauge strings ρ~(Gη2)2/τ4, where η is the mean value of the scalar field and τ is the time at which the phase transition occurs. We also discuss how a global monopole inside a mini-black-hole affects its final stages of evolution. We find that neither the Hawking temperature nor the entropy-area relation is essentially modified by the presence of the monopole.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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