scholarly journals On a new type of fractional difference operators on h-step isolated time scales

2021 ◽  
Vol 1 (1) ◽  
pp. 46-74
Author(s):  
Fahd Jarad ◽  
Thabet Abdeljawad ◽  
Abdon Atangana ◽  
Pshtiwan Othman Mohammed
Keyword(s):  
Time Scales ◽  
Power Law ◽  
Time Scale ◽  
Difference Operators ◽  
Step Size ◽  
Fractional Difference ◽  
Forward Difference ◽  
New Type

In this article, a new type of fractional sums and differences called the discrete weighted fractionaloperators are presented. The weighted backward and forward difference operators are defined on anisolated time scale with arbitrary step size and they obey the power law.

scholarly journals Characterizing the i-band variability of YSOs over six orders of magnitude in time-scale

2019 ◽  
Vol 491 (4) ◽  
pp. 5035-5055 ◽  
Author(s):  
Darryl J Sergison ◽  
Tim Naylor ◽  
S P Littlefair ◽  
Cameron P M Bell ◽  
C D H Williams
Keyword(s):  
Time Scales ◽  
Power Law ◽  
Time Scale ◽  
Fourier Transforms ◽  
Simulated Data ◽  
Class Ii ◽  
Structure Functions ◽  
Young Stellar Objects ◽  
Class Iii ◽  
Stellar Objects

ABSTRACT We present an i-band photometric study of over 800 young stellar objects in the OB association Cep OB3b, which samples time-scales from one minute to 10 yr. Using structure functions we show that on all time-scales (τ) there is a monotonic decrease in variability from Class I to Class II through the transition disc (TD) systems to Class III, i.e. the more evolved systems are less variable. The Class Is show an approximately power-law increase (τ0.8) in variability from time-scales of a few minutes to 10 yr. The Class II, TDs, and Class III systems show a qualitatively different behaviour with most showing a power-law increase in variability up to a time-scale corresponding to the rotational period of the star, with little additional variability beyond that time-scale. However, about a third of the Class IIs shows lower overall variability, but their variability is still increasing at 10 yr. This behaviour can be explained if all Class IIs have two primary components to their variability. The first is an underlying roughly power-law variability spectrum, which evidence from the infrared suggests is driven by accretion rate changes. The second component is approximately sinusoidal and results from the rotation of the star. We suggest that the systems with dominant longer time-scale variability have a smaller rotational modulation either because they are seen at low inclinations or have more complex magnetic field geometries. We derive a new way of calculating structure functions for large simulated data sets (the ‘fast structure function’), based on fast Fourier transforms.

scholarly journals On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1303
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Kadir Hamasalh
Keyword(s):  
Time Scale ◽  
Initial Value Problems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Discrete Fractional Calculus ◽  
Initial Value ◽  
Forward Difference ◽  
The Mean ◽  
Monotonicity Analysis ◽  
Monotonicity Results

Monotonicity analysis of delta fractional sums and differences of order υ∈(0,1] on the time scale hZ are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that y(z) is υ-increasing on Ma+υh,h, where the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and then, we can show that y(z) is υ-increasing on Ma+υh,h, where the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) for each z∈Ma+h,h. Conversely, if y(a+υh) is greater or equal to zero and y(z) is increasing on Ma+υh,h, we show that the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and consequently, we can show that the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) on Ma,h. Furthermore, we consider some related results for strictly increasing, decreasing, and strictly decreasing cases. Finally, the fractional forward difference initial value problems and their solutions are investigated to test the mean value theorem on the time scale hZ utilizing the monotonicity results.

scholarly journals GNSS-to-GNSS time offsets: study on the broadcast of a common reference time

GPS Solutions ◽  
2021 ◽  
Vol 25 (2) ◽  
Author(s):  
Ilaria Sesia ◽  
Giovanna Signorile ◽  
Tung Thanh Thai ◽  
Pascale Defraigne ◽  
Patrizia Tavella
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Reference Time ◽  
Single Time ◽  
Common Reference ◽  
Prediction Quality ◽  
Common Time ◽  
Time Offset ◽  
The Impact ◽  
Low Uncertainty

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.

Sensor-Based Estimation of Dim Light Melatonin Onset Using Features of Two Time Scales

2021 ◽  
Vol 2 (3) ◽  
pp. 1-15
Author(s):  
Cheng Wan ◽  
Andrew W. Mchill ◽  
Elizabeth B. Klerman ◽  
Akane Sano
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Light Exposure ◽  
Biological Activities ◽  
Second Step ◽  
Sampled Data ◽  
Dim Light Melatonin Onset ◽  
Dim Light ◽  
Using Data ◽  
Mean Square Errors

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.

scholarly journals Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

scholarly journals Locally and Remotely Forced Subtropical AMOC Variability: A Matter of Time Scales

2020 ◽  
Vol 33 (12) ◽  
pp. 5155-5172
Author(s):  
Quentin Jamet ◽  
William K. Dewar ◽  
Nicolas Wienders ◽  
Bruno Deremble ◽  
Sally Close ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
North Atlantic ◽  
Time Scale ◽  
Low Frequency ◽  
Meridional Overturning Circulation ◽  
Open Boundary ◽  
Overturning Circulation ◽  
Decadal Scale ◽  
Meridional Overturning

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).

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

2020 ◽  
Vol 26 (2) ◽  
pp. 173-183
Author(s):  
Kuldip Raj ◽  
Kavita Saini ◽  
Anu Choudhary
Keyword(s):  
Difference Operator ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Normed Spaces ◽  
Fractional Difference ◽  
New Approach ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Bounded Sequences

AbstractRecently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

scholarly journals A EEG-based emotion recognition model with rhythm and time characteristics

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Jianzhuo Yan ◽  
Shangbin Chen ◽  
Sinuo Deng
Keyword(s):  
Emotion Recognition ◽  
Time Scales ◽  
Time Scale ◽  
Short Term Memory ◽  
Recognition Model ◽  
Memory Network ◽  
Long Short Term Memory ◽  
Valence And Arousal ◽  
Memory Characteristics

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.

scholarly journals Fast Comparison of High-Precision Time Scales Using GNSS Receivers

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Vojtech Vigner ◽  
Jaroslav Roztocil
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
High Performance ◽  
Data Format ◽  
Common View ◽  
Log Files ◽  
Gnss Receivers ◽  
Precision Time ◽  
The Common ◽  
The Difference

Comparison of high-performance time scales generated by atomic clocks in laboratories of time and frequency metrology is usually performed by means of the Common View method. Laboratories are equipped with specialized GNSS receivers which measure the difference between a local time scale and a time scale of the selected satellite. Every receiver generates log files in CGGTTS data format to record measured differences. In order to calculate time differences recorded by two receivers, it is necessary to obtain these logs from both receivers and process them. This paper deals with automation and speeding up of these processes.

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