scholarly journals Decay rate of iterated integrals of branched rough paths

2018 ◽  
Vol 35 (4) ◽  
pp. 945-969 ◽  
Author(s):  
Horatio Boedihardjo
Keyword(s):  
Decay Rate ◽  
Rough Paths ◽  
Iterated Integrals

scholarly journals VARIETIES OF SIGNATURE TENSORS

2019 ◽  
Vol 7 ◽  
Author(s):  
CARLOS AMÉNDOLA ◽  
PETER FRIZ ◽  
BERND STURMFELS
Keyword(s):  
Brownian Motion ◽  
Algebraic Geometry ◽  
Lie Groups ◽  
Stochastic Analysis ◽  
Piecewise Linear ◽  
Nilpotent Lie Groups ◽  
Rough Paths ◽  
Iterated Integrals ◽  
Parametric Curve

The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is examined here through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic paths and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures.

Bacterial die-away rates in red sea waters

1995 ◽  
Vol 32 (2) ◽  
pp. 45-52 ◽  
Author(s):  
H. Z. Sarikaya ◽  
A. M. Saatçi
Keyword(s):  
Solar Radiation ◽  
Decay Rate ◽  
Sea Water ◽  
Membrane Filter ◽  
Linear Regression Analysis ◽  
Total Coliform ◽  
Coliform Bacteria ◽  
Decay Rate Constant ◽  
Solar Intensity ◽  
Log Normal

Total coliform bacteria have been chosen as the indicator organism. Coliform die-away experiments have been carried out in unpolluted sea water samples collected at about 100 m off the coastline and under controlled environmental conditions. The samples were transformed into one litre clean glass beakers which were kept at constant temperature and were exposed to the solar radiation. The membrane filter technique was used for the coliform analysis. The temperature ranged from 20 to 40° C and the dilution ratios ranged from 1/50 to 1/200. Coliform decay rate in the light has been expressed as the summation of the coliform decay rate in the dark and the decay rate due to solar radiation. The solar radiation required for 90 percent coliform removal has been found to range from 17 cal/cm2 to 40 cal/cm2 within the temperature range of 25 to 30° C. Applying the linear regression analysis two different equations have been given for the high (I>10 cal/cm2.hour) and low solar intensity ranges in order to determine the coliform decay rate constant as a function of the solar intensity. T-90 values in the light have been found to follow log-normal distribution with a median T-90 value of 32 minutes. The corresponding T-90 values in the dark were found to be 70-80 times longer. Coliform decay rate in the dark has been correlated with the temperature.

scholarly journals Energy Gap Dependence of the Nonradiative Decay Rate Constant of 1-Anilino-8-naphthalene Sulfonate in Reverse Micelles.

1999 ◽  
Vol 15 (5) ◽  
pp. 413-419 ◽  
Author(s):  
Noboru KITAMURA ◽  
Norio SAKATA ◽  
Haeng-Boo KIM ◽  
Satoshi HABUCHI
Keyword(s):  
Decay Rate ◽  
Rate Constant ◽  
Reverse Micelles ◽  
Energy Gap ◽  
Decay Rate Constant ◽  
Nonradiative Decay ◽  
Nonradiative Decay Rate

scholarly journals Massive Dirac quasinormal modes in Schwarzschild–de Sitter black holes: Anomalous decay rate and fine structure

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Almendra Aragón ◽  
Ramón Bécar ◽  
P. A. González ◽  
Yerko Vásquez
Keyword(s):  
Black Holes ◽  
Fine Structure ◽  
Decay Rate ◽  
Quasinormal Modes ◽  
De Sitter

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

scholarly journals Invisible neutrino decay: first vs second oscillation maximum

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Kaustav Chakraborty ◽  
Debajyoti Dutta ◽  
Srubabati Goswami ◽  
Dipyaman Pramanik
Keyword(s):  
Decay Rate ◽  
Survival Probability ◽  
Mixing Angle ◽  
Decay Lifetime ◽  
Long Baseline ◽  
Physics Potential ◽  
Normal Mass ◽  
Compare And Contrast ◽  
Neutrino Decay ◽  
Oscillation Maximum

Abstract We study the physics potential of the long-baseline experiments T2HK, T2HKK and ESSνSB in the context of invisible neutrino decay. We consider normal mass ordering and assume the state ν3 as unstable, decaying into sterile states during the flight and obtain constraints on the neutrino decay lifetime (τ3). We find that T2HK, T2HKK and ESSνSB are sensitive to the decay-rate of ν3 for τ3/m3 ≤ 2.72 × 10−11s/eV, τ3/m3 ≤ 4.36 × 10−11s/eV and τ3/m3 ≤ 2.43 × 10−11s/eV respectively at 3σ C.L. We compare and contrast the sensitivities of the three experiments and specially investigate the role played by the mixing angle θ23. It is seen that for experiments with flux peak near the second oscillation maxima, the poorer sensitivity to θ23 results in weaker constraints on the decay lifetime. Although, T2HKK has one detector close to the second oscillation maxima, having another detector at the first oscillation maxima results in superior sensitivity to decay. In addition, we find a synergy between the two baselines of the T2HKK experiment which helps in giving a better sensitivity to decay for θ23 in the higher octant. We discuss the octant sensitivity in presence of decay and show that there is an enhancement in sensitivity which occurs due to the contribution from the survival probability Pμμ is more pronounced for the experiments at the second oscillation maxima. We also obtain the combined sensitivity of T2HK+ESSνSB and T2HKK+ESSνSB as τ3/m3 ≤ 4.36 × 10−11s/eV and τ3/m3 ≤ 5.53 × 10−11s/eV respectively at 3σ C.L.

scholarly journals Nondestructive Detection of the Gel State of Preserved Eggs Based on Dielectric Impedance

Foods ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 394
Author(s):  
Cheng-Han Li ◽  
Chun-Hung Hsieh ◽  
Cheng-Chu Hung ◽  
Ching-Wei Cheng
Keyword(s):  
Decay Rate ◽  
Mechanical Vibration ◽  
Scientific Basis ◽  
Nondestructive Method ◽  
Inspection System ◽  
Nyquist Diagram ◽  
Detection Technology ◽  
The Difference ◽  
The Individual

After completing the production of preserved eggs, traditionally, the degree of gelling is judged by allowing workers to tap the preserved eggs with their fingers and sense the resulting oscillations. The amount of oscillation is used for the quality classification. This traditional method produces varying results owing to the differences in the sensitivity of the individual workers, who are not objective. In this study, dielectric detection technology was used to classify the preserved eggs nondestructively. The impedance in the frequency range of 2–300 kHz was resolved into resistance and reactance, and was plotted on a Nyquist diagram. Next, the diagram curve was fitted in order to obtain the equivalent circuit, and the difference in the compositions of the equivalent circuits corresponding to gelled and non-gelled preserved eggs was analyzed. A preserved egg can be considered an RLC series circuit, and its decay rate is consistent with the decay rate given by mechanical vibration theory. The Nyquist diagrams for the resistance and reactance of preserved eggs clearly showed that the resistance and reactance of gelled and non-gelled eggs were quite different, and the classification of the eggs was performed using Bayesian network (BN). The results showed that a BN classifier with two variables, i.e., resistance and reactance, can be used to classify preserved eggs as gelled or non-gelled, with an accuracy of 81.0% and a kappa value of 0.62. Thus, a BN classifier based on resistance and reactance demonstrates the ability to classify the quality of preserved egg gel. This research provides a nondestructive method for the inspection of the quality of preserved egg gel, and provides a theoretical basis for the development of an automated preserved egg inspection system that can be used as the scientific basis for the determination of the quality of preserved eggs.

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