scholarly journals Multivariate Dynamic Sneak-Out Inequalities on Time Scales

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ammara Nosheen ◽  
Aneeqa Aslam ◽  
Khuram Ali Khan ◽  
Khalid Mahmood Awan ◽  
Hamid Reza Moradi

In this study, we extend some “sneak-out” inequalities on time scales for a function depending on more than one parameter. The results are proved by using the induction principle and time scale version of Minkowski inequalities. In seeking applications, these inequalities are discussed in classical, discrete, and quantum calculus.

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Iqrar Ansari ◽  
Khuram Ali Khan ◽  
Ammara Nosheen ◽  
Ðilda Pečarić ◽  
Josip Pečarić

AbstractIn this paper, we present some inequalities for Csiszár f-divergence between two probability measures on time scale. These results extend some known results in the literature and offer new results in h-discrete calculus and quantum calculus. We also present several inequalities for divergence measures.


2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Saeeda Fatima Tahir ◽  
Muhammad Mushtaq ◽  
Muhammad Muddassar

Inequalities become a hot topic for researcher due to its wide applications in means and sum, numerical integration, quantum calculus. Different generalizations and refinements are made by researchers. Here, in this article, we give another generalization of integral inequalities and harmonizing them on time scale T from R.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Iqrar Ansari ◽  
Khuram Ali Khan ◽  
Ammara Nosheen ◽  
Ðilda Pečarić ◽  
Josip Pečarić

AbstractThe main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted time scales Jensen’s inequality. These results offer new inequalities in h-discrete calculus and quantum calculus and extend some known results in the literature. The lower bounds of some divergence measures are also presented. Moreover, the obtained discrete results are given in the light of the Zipf–Mandelbrot law and the Zipf law.


2018 ◽  
Vol 60 (1) ◽  
pp. 123-144 ◽  
Author(s):  
A. A. El-Deeb ◽  
H. A. Elsennary ◽  
Eze R. Nwaeze

Abstract In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Monika Dryl ◽  
Delfim F. M. Torres

We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.


Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.


GPS Solutions ◽  
2021 ◽  
Vol 25 (2) ◽  
Author(s):  
Ilaria Sesia ◽  
Giovanna Signorile ◽  
Tung Thanh Thai ◽  
Pascale Defraigne ◽  
Patrizia Tavella

AbstractWe present two different approaches to broadcasting information to retrieve the GNSS-to-GNSS time offsets needed by users of multi-GNSS signals. Both approaches rely on the broadcast of a single time offset of each GNSS time versus one common time scale instead of broadcasting the time offsets between each of the constellation pairs. The first common time scale is the average of the GNSS time scales, and the second time scale is the prediction of UTC already broadcast by the different systems. We show that the average GNSS time scale allows the estimation of the GNSS-to-GNSS time offset at the user level with the very low uncertainty of a few nanoseconds when the receivers at both the provider and user levels are fully calibrated. The use of broadcast UTC prediction as a common time scale has a slightly larger uncertainty, which depends on the broadcast UTC prediction quality, which could be improved in the future. This study focuses on the evaluation of two different common time scales, not considering the impact of receiver calibration, at the user and provider levels, which can nevertheless have an important impact on GNSS-to-GNSS time offset estimation.


2021 ◽  
Vol 2 (3) ◽  
pp. 1-15
Author(s):  
Cheng Wan ◽  
Andrew W. Mchill ◽  
Elizabeth B. Klerman ◽  
Akane Sano

Circadian rhythms influence multiple essential biological activities, including sleep, performance, and mood. The dim light melatonin onset (DLMO) is the gold standard for measuring human circadian phase (i.e., timing). The collection of DLMO is expensive and time consuming since multiple saliva or blood samples are required overnight in special conditions, and the samples must then be assayed for melatonin. Recently, several computational approaches have been designed for estimating DLMO. These methods collect daily sampled data (e.g., sleep onset/offset times) or frequently sampled data (e.g., light exposure/skin temperature/physical activity collected every minute) to train learning models for estimating DLMO. One limitation of these studies is that they only leverage one time-scale data. We propose a two-step framework for estimating DLMO using data from both time scales. The first step summarizes data from before the current day, whereas the second step combines this summary with frequently sampled data of the current day. We evaluate three moving average models that input sleep timing data as the first step and use recurrent neural network models as the second step. The results using data from 207 undergraduates show that our two-step model with two time-scale features has statistically significantly lower root-mean-square errors than models that use either daily sampled data or frequently sampled data.


2020 ◽  
Vol 33 (12) ◽  
pp. 5155-5172
Author(s):  
Quentin Jamet ◽  
William K. Dewar ◽  
Nicolas Wienders ◽  
Bruno Deremble ◽  
Sally Close ◽  
...  

AbstractMechanisms driving the North Atlantic meridional overturning circulation (AMOC) variability at low frequency are of central interest for accurate climate predictions. Although the subpolar gyre region has been identified as a preferred place for generating climate time-scale signals, their southward propagation remains under consideration, complicating the interpretation of the observed time series provided by the Rapid Climate Change–Meridional Overturning Circulation and Heatflux Array–Western Boundary Time Series (RAPID–MOCHA–WBTS) program. In this study, we aim at disentangling the respective contribution of the local atmospheric forcing from signals of remote origin for the subtropical low-frequency AMOC variability. We analyze for this a set of four ensembles of a regional (20°S–55°N), eddy-resolving (1/12°) North Atlantic oceanic configuration, where surface forcing and open boundary conditions are alternatively permuted from fully varying (realistic) to yearly repeating signals. Their analysis reveals the predominance of local, atmospherically forced signal at interannual time scales (2–10 years), whereas signals imposed by the boundaries are responsible for the decadal (10–30 years) part of the spectrum. Due to this marked time-scale separation, we show that, although the intergyre region exhibits peculiarities, most of the subtropical AMOC variability can be understood as a linear superposition of these two signals. Finally, we find that the decadal-scale, boundary-forced AMOC variability has both northern and southern origins, although the former dominates over the latter, including at the site of the RAPID array (26.5°N).


2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Jianzhuo Yan ◽  
Shangbin Chen ◽  
Sinuo Deng

Abstract As an advanced function of the human brain, emotion has a significant influence on human studies, works, and other aspects of life. Artificial Intelligence has played an important role in recognizing human emotion correctly. EEG-based emotion recognition (ER), one application of Brain Computer Interface (BCI), is becoming more popular in recent years. However, due to the ambiguity of human emotions and the complexity of EEG signals, the EEG-ER system which can recognize emotions with high accuracy is not easy to achieve. Based on the time scale, this paper chooses the recurrent neural network as the breakthrough point of the screening model. According to the rhythmic characteristics and temporal memory characteristics of EEG, this research proposes a Rhythmic Time EEG Emotion Recognition Model (RT-ERM) based on the valence and arousal of Long–Short-Term Memory Network (LSTM). By applying this model, the classification results of different rhythms and time scales are different. The optimal rhythm and time scale of the RT-ERM model are obtained through the results of the classification accuracy of different rhythms and different time scales. Then, the classification of emotional EEG is carried out by the best time scales corresponding to different rhythms. Finally, by comparing with other existing emotional EEG classification methods, it is found that the rhythm and time scale of the model can contribute to the accuracy of RT-ERM.


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