scholarly journals Time decay for porosity problems

2021 ◽  
Author(s):  
Jacobo Baldonedo ◽  
José R. Fernández ◽  
Ramón Quintanilla
Keyword(s):  
Time Decay

scholarly journals Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Nakao Hayashi ◽  
Chunhua Li ◽  
Pavel I. Naumkin
Keyword(s):  
Lower Bound ◽  
Positive Root ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Time Decay ◽  
Large Initial Data ◽  
Initial Value ◽  
Optical Fields ◽  
Gauge Invariant ◽  
Dissipative Condition

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearityλup-1uof orderpn<p≤1+2/nfor arbitrarily large initial data, where the lower boundpnis a positive root ofn+2p2-6p-n=0forn≥2andp1=1+2forn=1.Our purpose is to extend the previous results for higher space dimensions concerningL2-time decay and to improve the lower bound ofpunder the same dissipative condition onλ∈C:Im⁡ λ<0andIm⁡ λ>p-1/2pRe λas in the previous works.

scholarly journals Intra-cluster correlations from the CLustered OUtcome Dataset bank to inform the design of longitudinal cluster trials

2021 ◽  
pp. 174077452110208
Author(s):  
Elizabeth Korevaar ◽  
Jessica Kasza ◽  
Monica Taljaard ◽  
Karla Hemming ◽  
Terry Haines ◽  
...  
Keyword(s):  
Sample Size ◽  
Discrete Time ◽  
Correlation Coefficients ◽  
Time Decay ◽  
Randomised Trials ◽  
Cluster Randomised Trials ◽  
Cluster Randomised ◽  
Sample Size Calculations ◽  
Correlation Structures ◽  
Cluster Correlation

Background: Sample size calculations for longitudinal cluster randomised trials, such as crossover and stepped-wedge trials, require estimates of the assumed correlation structure. This includes both within-period intra-cluster correlations, which importantly differ from conventional intra-cluster correlations by their dependence on period, and also cluster autocorrelation coefficients to model correlation decay. There are limited resources to inform these estimates. In this article, we provide a repository of correlation estimates from a bank of real-world clustered datasets. These are provided under several assumed correlation structures, namely exchangeable, block-exchangeable and discrete-time decay correlation structures. Methods: Longitudinal studies with clustered outcomes were collected to form the CLustered OUtcome Dataset bank. Forty-four available continuous outcomes from 29 datasets were obtained and analysed using each correlation structure. Patterns of within-period intra-cluster correlation coefficient and cluster autocorrelation coefficients were explored by study characteristics. Results: The median within-period intra-cluster correlation coefficient for the discrete-time decay model was 0.05 (interquartile range: 0.02–0.09) with a median cluster autocorrelation of 0.73 (interquartile range: 0.19–0.91). The within-period intra-cluster correlation coefficients were similar for the exchangeable, block-exchangeable and discrete-time decay correlation structures. Within-period intra-cluster correlation coefficients and cluster autocorrelations were found to vary with the number of participants per cluster-period, the period-length, type of cluster (primary care, secondary care, community or school) and country income status (high-income country or low- and middle-income country). The within-period intra-cluster correlation coefficients tended to decrease with increasing period-length and slightly decrease with increasing cluster-period sizes, while the cluster autocorrelations tended to move closer to 1 with increasing cluster-period size. Using the CLustered OUtcome Dataset bank, an RShiny app has been developed for determining plausible values of correlation coefficients for use in sample size calculations. Discussion: This study provides a repository of intra-cluster correlations and cluster autocorrelations for longitudinal cluster trials. This can help inform sample size calculations for future longitudinal cluster randomised trials.

Literary work education model based on intelligent machine learning and reader scoring criteria factors

2021 ◽  
pp. 1-10
Author(s):  
Lei Han ◽  
Wei Li ◽  
Ming Zang
Keyword(s):  
Machine Learning ◽  
Prediction Method ◽  
Literary Work ◽  
Time Decay ◽  
Recommendation Algorithm ◽  
Intelligent Machine ◽  
Literary Education ◽  
Education Model ◽  
Work Education ◽  
Rating Criteria

In order to improve the effect of literary works education, this paper combines intelligent machine learning and reader scoring criteria factors to construct an intelligent education model, and proposes a collaborative filtering recommendation algorithm based on item proportion factors and time decay. When calculating the user similarity, this paper adds the scale factor of the intersection of common scoring items to all the scoring items, and considers the non-intersection part of the user scoring items. Secondly, when predicting the project score, this paper adds a time decay function, combines the forgetting curve law to modify the score prediction method, and combines the actual needs to construct the basic framework of the education model. In addition, this paper designs experiments to verify the performance of the literary work education model constructed in this paper. The research results show that the literary work education model constructed in this paper based on intelligent machine learning and reader rating criteria factors has a certain role in promoting the effect of literary education.

scholarly journals Global small data solutions for semilinear waves with two dissipative terms

2021 ◽  
Author(s):  
Wenhui Chen ◽  
Marcello D’Abbicco ◽  
Giovanni Girardi
Keyword(s):  
Wave Equations ◽  
Space Dimension ◽  
Full Range ◽  
Small Data ◽  
Decay Estimates ◽  
Time Decay ◽  
Nonexistence Result ◽  
Derivative Type ◽  
Long Time ◽  
Dissipative Terms

AbstractIn this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity $$|u|^p$$ | u | p or nonlinearity of derivative type $$|u_t|^p$$ | u t | p , in any space dimension $$n\geqslant 1$$ n ⩾ 1 , for supercritical powers $$p>{\bar{p}}$$ p > p ¯ . The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive $$L^r-L^q$$ L r - L q long time decay estimates for the solution in the full range $$1\leqslant r\leqslant q\leqslant \infty $$ 1 ⩽ r ⩽ q ⩽ ∞ . The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers $$p<{\bar{p}}$$ p < p ¯ .

Measurements of the Collisionally Quenched Lifetime of CO in Hydrocarbon Flames

1994 ◽  
Vol 48 (9) ◽  
pp. 1118-1124 ◽  
Author(s):  
Sara Agrup ◽  
Marcus Aldén
Keyword(s):  
Laser Induced Fluorescence ◽  
Polyaromatic Hydrocarbon ◽  
Time Decay ◽  
Collisional Quenching ◽  
Time Resolved ◽  
Hydrocarbon Flames ◽  
Effective Lifetime ◽  
Ethylene Flame ◽  
Oxygen Flame ◽  
Different Parts

Time-resolved laser-induced fluorescence (LIF) from CO molecules in hydrocarbon flames was studied. Collisional quenching constants were evaluated on the basis of the exponential decays. Effective lifetime in a methane/oxygen flame was observed to vary between 250 and 400 ps depending on the position within the flame, and from 400 to 600 ps in the non-sooty parts of an ethylene/air flame. Fluorescence, constituting simultaneous spatially and temporally resolved decays, was also registered from various sections along a laser beam that probed different parts of the flame. Spectral recordings revealed not only the expected CO peaks but also, in the ethylene flame, laser-induced emission from C2 Swan bands and from polyaromatic hydrocarbon (PAH) emission that affected the fluorescence time decay in the sooty part of the flame.

Time decay of the remanent magnetization in TDAE-C60

1994 ◽  
Vol 50 (17) ◽  
pp. 13051-13053 ◽  
Author(s):  
R. Blinc ◽  
P. Cevc ◽  
D. Arčon ◽  
D. Mihailovič ◽  
P. Venturini
Keyword(s):  
Remanent Magnetization ◽  
Time Decay
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