## What is/are Time Scales?

Time Scales - Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales.^{[1]}The time scales of the wake response to different pitch rates are quantified.

^{[2]}5) air quality over contemporary (1992 to 2014) time scales.

^{[3]}The Granger causality from investor attention to these cryptocurrency returns is asymmetric and varies across cryptocurrencies and time scales.

^{[4]}At seasonal (monthly) time scales, statistically significant decreasing trends in Epan were witnessed in pre-monsoon season (in the months of March, April and May) over all the seven sites of the Godavari basin.

^{[5]}Invading breast cancer cells transform the mechanics of their surroundings across a panorama of time scales.

^{[6]}The energy conversion steps depicted feature an integration of function from electronic to cell levels, spanning nearly 12 orders of magnitude in time scales.

^{[7]}We relate these dynamical processes to the predicted fluorescence depolarization, extract the time scales corresponding to them, and thus interpret the observed sub-ps fluorescence depolarization.

^{[8]}An increased damping coefficient increases fluctuations and time scales controlling condensate’s short-time evolution, a feature that can impact hadron formation at the QCD transition.

^{[9]}The multifeature learning network can automatically extract and fuse global and local features from different network depths and time scales of the raw vibration signal.

^{[10]}We uncover a hierarchy of time scales that characterize the relaxation dynamics of this system, spanning the picoseconds of ionic motion to the tens or hundreds of nanoseconds associated with fluctuations of the liquid-crystal interface in their presence.

^{[11]}We derive two types of growth laws per autocatalytic cycle, one relating growth rate to the relative fraction of the catalyst and its catalysis rate and the other relating growth rate to all the time scales in the cycle.

^{[12]}Therefore, transient studies on time scales from femtoseconds to microseconds can greatly help to elucidate the most relevant steps after photoexcitation.

^{[13]}To do so, we break these systems down into their elementary steps, which are almost invariably either unimolecular or bimolecular reactions that frequently occur on sub-second, often sub-millisecond, time scales.

^{[14]}These results paint a new picture of OAE1a in which volcanism, biological crisis, and oceanic deoxygenation are separated in time and linked through Earth system responses that operate on time scales of tens of thousands of years.

^{[15]}In this paper, the Hyers-Ulam-Rassias stability of high-dimensional quaternion fuzzy dynamic equations with impulses is first considered on time scales.

^{[16]}, eddy-resolving), especially over time scales longer than one season.

^{[17]}In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time.

^{[18]}They can then be probed experimentally over a remarkably large range of time scales and length scales, including imaging of the individual moments.

^{[19]}Furthermore, the two different types of reorientational motions are distinguished from each other by their own characteristic scattering patterns and time scales.

^{[20]}Firstly, on the basis of the nonshifted Pfaff-Birkhoff principle on time scales, Birkhoff’s equations for nonshifted variables are deduced; then, Noether’s quasi-symmetry for the nonshifted Birkhoffian system is proved and time-scale conserved quantity is presented.

^{[21]}It unifies the fields of fluid and solid mechanics by extending the fields of application of these equations to all space and time scales.

^{[22]}In this paper, we consider a multi-species Lotka-Volterra type competitive system with delays and feedback controls on time scales.

^{[23]}Gravitational waves, electromagnetic waves, neutrinos and cosmic rays cover a wide range of wavelengths and time scales.

^{[24]}In addition, time scales for structural relaxation and cooling processes are extracted from a global kinetic analysis of the transient spectra.

^{[25]}In this paper, we introduce the notion of exponentially convex functions on time scales and then we establish Hermite-Hadamard type inequalities for this class of functions.

^{[26]}Over many size and time scales, behaviors such as locomotion or feeding require mechanical movements.

^{[27]}This fortuitous similarity of time scales ensures that stellate spikes get relegated to the least excitable phase of theta and the network encodes the external drive but ignores recurrent excitation.

^{[28]}Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}ε and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}ε is the ratio of the time scales of the phase variables and synaptic weights, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ defines the sharpness of the plasticity boundary function.

^{[29]}In this chapter we study a class of second-order integro-dynamic equations on time scales.

^{[30]}While the Earth’s core field varies on time scales of months to years, electric currents in the ionosphere and magnetosphere change within seconds to days, e.

^{[31]}During the study period, nearly half of the years experienced a meteorological drought at all-time scales.

^{[32]}Results show that air pollution predictability in association with the optimal observational network is limited in the time scales about 6 days.

^{[33]}This suggests that X-ray scattering is a viable probe for measuring electronic processes at time scales faster than nuclear motion.

^{[34]}We investigate the stationary equilibrium of the model, and show that the setup is compatible with universal price diffusion at small times, and non-universal mean-reversion at time scales at which fluctuations in fundamentals decay.

^{[35]}Despite the advantages of optical tweezers, the time scales used in this technology were inconsistent with physiological scenarios, which led to the development of magnetic tweezers, where proteins are covalently linked with the glass surface, which in turn increases the observation window of a single biomolecule from minutes to weeks.

^{[36]}We found significant synchronous whole-community phenology at a wide range of time scales, consistent with shared environmental responses or positive interactions among species.

^{[37]}Finally, the resilience, vulnerability, and frequency of probability metrics indicated that the 12-month time scale of drought affected the basin more severely than other time scales.

^{[38]}The fast (pico- to nanoseconds) time scales and harsh environments of the HED experiments at the NIF impose tight constraints on the performance of these instruments, both in terms of temporal and spatial resolution, background rejection as well as their survivability.

^{[39]}In this work, we investigate the controllability results of a fractional integro-differential equation with non-instantaneous impulses on time scales.

^{[40]}Full fidelity simulations of this process are not feasible due to the vast range of length and time scales inherent to it.

^{[41]}This leads to a definition of network bursts, that does not depend on the practitioner's individual judgment as the usage of subjective thresholds and time scales.

^{[42]}They evolve on time scales ranging from strong wind events, seasons to multiple decades due to biogeomorphic interactions.

^{[43]}However, many phenomena of interest take place on time scales that are out of reach of standard molecular simulations.

^{[44]}However, relying on buoyancy as the sole driving force may lead to several potential difficulties, one of which is generation of (possibly) time-varying nonlinearities in the dynamical system, where a difference in the time scales of heat transfer and fluid flow causes the flow to change from a steady-state regime to either an oscillatory regime or a flow-reversal regime, both of which are undesirable.

^{[45]}Ultrafast microscopy takes advantage of photons and electrons to measure dynamics in matter on the fundamental space and time scales.

^{[46]}We discuss the effect that a fine-graining of the stress distribution provided by the flow solver has on the transport model prediction, and we examine the space and time scales at which the averaged values of the transport rate, obtained using the local stress distribution, converge to the transport rate predicted using the average stress.

^{[47]}We then evaluate complementarity across various space-time scales in the Colombian power sectors, considering hydro and wind projects.

^{[48]}Recently, theoretical and experimental findings have shown that the temporal response windows also gradually enlarge, so that early sensory neural circuits operate on short-time scales whereas higher association areas are capable of integrating information over a long period of time.

^{[49]}In this paper, we describe nonconservative field theories on time scales—a model that brings together, in a single theory, discrete and continuous cases.

^{[50]}

## precipitation evapotranspiration index

Besides, as the meteorological drought index, Standardized Precipitation Evapotranspiration Index (SPEI) time series were calculated for the region in question at different time scales (SPEI3, SPEI6, SPEI12, etc.^{[1]}Here we use Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) at three different time scales (24, 48, and 60 months) to identify long-term droughts in India for the observed record of 1951–2015.

^{[2]}In this study, Standardized Precipitation Index (SPI) using only precipitation data and Standardized Precipitation Evapotranspiration Index (SPEI) using precipitation and temperature data are considered at various time scales changing from 1 to 24 months for a more detailed drought characterization.

^{[3]}In this article, the standard precipitation evapotranspiration index (SPEI) on four time scales: SPEI-3, SPEI-6, SPEI-9, and SPEI-12 are used to measure and predict drought.

^{[4]}Standardized Precipitation Evapotranspiration Index (SPEI), Reconnaissance Drought Index (RDI) and Standardized Precipitation Index (SPI), the accuracy of these indices was evaluated at 1-, 3-, 6- and 12-month time scales.

^{[5]}The Standardized Precipitation-Evapotranspiration Index (SPEI) at multiple time scales (i.

^{[6]}The Standardized Precipitation Evapotranspiration Index at 12-month time scales (SPEI-12) displays moderate-to-severe dry conditions over all countries during the near-future period, then the wet condition is projected from mid-future to far-future periods.

^{[7]}In this study, the ability of one such multi-scalar index, the Standardized Precipitation Evapotranspiration Index (SPEI), computed at a range of time scales, was examined to see how well it could model historically observed warm season monthly and annual streamflow in 24 natural-flowing watersheds of western Canada.

^{[8]}Also, the standardized precipitation evapotranspiration index (SPEI) was applied to assess drought conditions in selected constant and progressively increasing reference time periods, including 1-month, 3-month, 6-month and 12-month time scales (27 reference time periods) starting in October.

^{[9]}This study investigated monthly meteorological observation data of 79 meteorological stations from 1955 to 2014 to calculate the standardized precipitation evapotranspiration index at different time scales.

^{[10]}

## 1 3 6

An assessment of drought conditions through the SPI and the SPEI on time scales of 1, 3, 6, and 12 months exposed the role of these systems on drought busting in the MLSHD.^{[1]}First, drought events were identified using standardized indices at the 1-3-6 month time scales.

^{[2]}The SPI and RDI on the time scales of 1, 3, 6 and 12 months were calculated using the Drought Indices Calculator (DrinC) software and characterized into the magnitude, duration, and severity of the drought.

^{[3]}In this context, monthly precipitation data for Lebanon during the period from 1926 through 2015 was analyzed using SPI at different time scales of 1, 3, 6, 9, and 12 months.

^{[4]}Standardized Precipitation Index (SPI) and Streamflow Drought Index (SDI) were computed at 1, 3, 6, 9 and 12-month time scales using in situ precipitation and streamflow data, respectively, for 35 years (1980–2014).

^{[5]}The meteorological droughts were identified based on the Standardized Precipitation Index (SPI), while the hydrological droughts were determined on the basis of the Standardized Runoff Index (SRI) in various time scales (1, 3, 6, 9 and 12 months) in the period of 1981–2016.

^{[6]}Both SPI and SPEI were found successfully to detect temporal variation in drought at different time scales (1, 3, 6, 9, and 12 months).

^{[7]}However, an assessment of the Standardized Precipitation Index (SPI) and the Standardized Precipitation–Evapotranspiration Index (SPEI) on time scales of 1, 3, 6, and 12 months revealed a positive impact of rainfall increase on the attenuation of short and long term accumulated drought conditions, particularly in the center and north regions.

^{[8]}The drought assessment was conducted using the Standardized Precipitation Index (SPI) at 1, 3, 6 and 12-month time scales.

^{[9]}

## empirical mode decomposition

Selecting the Yihe watershed in the rocky mountainous area of northern China as a case study, multivariate empirical mode decomposition (MEMD) was adopted to analyze the time scales of the monthly runoff and its influencing factors, i.^{[1]}Based on this, this paper proposes using the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to decompose the load and get multiple components of different time scales.

^{[2]}The abnormal signals in communication network are decomposed into multiple IMF components of different time scales by using the empirical mode decomposition method.

^{[3]}As an important algorithm for signal analysis, empirical mode decomposition can analyze the change trend of air quality well, smooth the complex and changeable air quality data, and get the change trend of air quality under different time scales.

^{[4]}An ensemble empirical mode decomposition (EEMD) method is adopted to separate salinity and temperature signals at different time scales; a focus is placed on interdecadal component in this study.

^{[5]}This paper measures the information transmission and relationships between Chinese stock market and the commodity futures market on different time scales novelly by combining the transfer entropy from information theory and the multi-scale analysis technique, the complete empirical mode decomposition based on adaptive noise (CEEMDAN).

^{[6]}First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is used to decompose the different water quality variables at different time scales step by step to generate a series of intrinsic mode function (IMF) components with the same characteristic scale.

^{[7]}

## sea surface temperature

Although internal TPDV arises to a large extent as a residual of independent El Niño–Southern Oscillation (ENSO) events, it can also result from oceanic processes occurring at decadal time scales involving the upper-ocean overturning circulation known as subtropical-tropical cells and in response to internal atmospheric variability in the extra-tropical Pacific and changes in sea surface temperature in other ocean basins.^{[1]}Comparisons with data from glider transects and remotely sensed sea surface temperature and altimetry data have been used to validate our approach from daily to seasonal and interannual time scales.

^{[2]}We investigated the possible effects of the winter sea surface temperature (SST) in the North Pacific Ocean on the MWD on interannual to interdecadal time scales.

^{[3]}However, sea surface temperature (SST) variability arising from Indian Ocean internal processes has not been well understood particularly on decadal and longer time scales, and the external influence from the tropical Pacific has not been quantified.

^{[4]}Our analysis found that two prominent source regions control the LSO variability at interannual time scales in the ASMA region, associated with the Pacific and Indian Ocean sea surface temperatures.

^{[5]}Through a time-dependent complex network framework applied to a thirty-year long dataset of sea surface temperatures over the Mediterranean Sea, we provide compelling evidence that ocean ecoregionalization based on connectivity can be achieved at spatial and time scales relevant to conservation management and planning.

^{[6]}In many settings, the degree of cyclization of isoGDGTs is correlated with temperature, forming the basis of the TEX86 paleothermometer that is widely used to reconstruct sea surface temperature (SST) across a range of time scales.

^{[7]}

## multi time scale

With the scheduling characteristics of multiple types of flexible loads in day-ahead and intra-day time scales considered comprehensively, a multi-time-scale optimization scheduling model of RIES is established, which takes into account the economy of system operation and the demand response.^{[1]}The multi-time scale coordinated optimization strategy with multiple time scales and multiple optimization objectives is used to coordinate and optimize the dispatch of distributed power sources and interruptible loads in the distribution network from three time scales: day-ahead, intra-day rolling, and real-time.

^{[2]}We also introduce a multi-time scale structure composed of two-time scales: a longer coarse-grained time scale for daily horizon with 15-minutes resolution and a shorter fine-grained time scale for 15-minutes horizon with 1-second resolution.

^{[3]}In response to this problem, this paper firstly establishes the basic structure of a regional multi-energy system based on energy hub (EH) and expresses the uncertainty of source load prediction under multiple time scales; secondly, according to the scheduling characteristics and equipment control characteristics of each energy network in RMES, consider Uncertainty, the RMES multi-time-scale scheduling method is proposed; then, according to this method, with the lowest scheduling cost as the optimization goal, the RMES multi-time-scale scheduling optimization model is constructed; finally, the simulation example proves that the optimization model can effectively reduce the RMES Cost of scheduling.

^{[4]}

## density functional theory

Here we combine time-resolved spectroscopic studies, on time scales ranging from femtoseconds to seconds, with density functional theory (DFT) calculations to elucidate and apply the acidochromism of a recently designed iminothioindoxyl (ITI) photoswitch.^{[1]}On one hand, the system sizes and simulation time scales required are prohibitive for first-principles methods like density functional theory (DFT).

^{[2]}Density functional theory calculations allow simulation of the observed changes in the pDOS and thus identification of the transient inter- and intramolecular vibrational modes at nanosecond time scales.

^{[3]}, for applications where characteristic time scales exceed the reach of methods including Kohn-Sham density functional theory, which are commonly used for reference data generation.

^{[4]}

## sea level rise

Ultimately, we find that cyclonic winds generate sea level rise along the western and eastern coasts of Hudson Bay at the synoptic and seasonal time scales, suggesting an amplification of the bay-wide cyclonic geostrophic circulation in fall (October–November), when cyclonic vorticity is enhanced, and Hudson Bay is ice-free.^{[1]}They can also respond to processes that take place at larger time scales, as plate tectonics, sea level rise or even climatological patterns with teleconnections all over the world, as the well know North Atlantic Oscillation (NAO) or El Niño-Southern Oscillation (ENSO).

^{[2]}Black zone cyanobacteria are highly SLR sensitive and over long time scales comparative imagery of black zones could present a proper indicator of average sea level rise.

^{[3]}However, the ability of nourishment to mitigate the effects of storms and sea level rise (SLR) and improve coastal resilience over decadal time scales is not well understood.

^{[4]}

## across multiple length

This mapping is extraordinarily complex because it involves thousands of molecular interactions that are dynamically coupled across multiple length and time scales.^{[1]}A large number of such methods have been developed, taking a range of approaches to bridging across multiple length and time scales.

^{[2]}By tracking events and cellular states across multiple length and time scales, circuits will transform how we decipher the causal link between molecular events and phenotypes to improve the selectivity and sensitivity of cell-based assays.

^{[3]}

## longer time scale

The multiresolution spectra show that time scales of variations of pollutant concentration and vertical velocity component increase from the canyon top to the pedestrian-level centre, indicating longer time-scale flow structures are dominant inside the street canyon.^{[1]}These ocean feedbacks on time scales longer than the CCKW life cycle help elucidate how locally driven processes can rectify onto longer time-scale processes in the coupled ocean--atmosphere system.

^{[2]}These ocean feedbacks on time scales longer than the CCKW 35 life cycle help elucidate how locally driven processes can rectify onto longer time-scale 36 processes in the coupled ocean–atmosphere system.

^{[3]}

## global climate change

Being able to accurately estimate inherent optical properties (IOPs) at long time scales is key to comprehending the aquatic biological and biogeochemical responses to long-term global climate change.^{[1]}These observations improve our understanding of carbon sinks in closed basins at various time scales, and provide a basis for the future mitigation policies to global climate change.

^{[2]}Our analysis highlights that a large portion of the natural environmental variability at short and long time scales is underexplored in experimental designs, which may provide a path to extend our understanding on the response of corals to global climate change.

^{[3]}

## relatively small classical

A quantitative description of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem.^{[1]}A quantitative description of the violation of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem.

^{[2]}A quantitative description of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem.

^{[3]}

## low frequency component

The first low-frequency component (LFC), computed using this method, is an index of OHT variability that maximizes the ratio of low-frequency variance (occurring at decadal and longer time scales) to total variance.^{[1]}This study isolates the mechanisms driving North Atlantic SST variability on decadal time scales using low-frequency component analysis, which identifies the spatial and temporal structure of low-frequency variability.

^{[2]}Moreover, the fluctuation characteristics of time series at different time scales were extracted, and the IMF components were reconstructed into short-term high-frequency components, medium-term important event low-frequency components and long-term trend components.

^{[3]}

## nuclear magnetic resonance

In this chapter, we present a brief overview of solution and solid-state nuclear magnetic resonance (NMR) spectroscopic methods for the characterization of composition and chemical microstructure of PET and also associated chain dynamics over multiple time scales.^{[1]}Solid state nuclear magnetic resonance (ssNMR), with its ability to probe local structure, to track ionic motion in different length/time scales, to study lithium/sodium dendrites, and to investigate interfacial issues, has unique advantages in characterizing such oxide-type solid state batteries.

^{[2]}Here, we report the conformational dynamics of DUBA on the microsecond-to-millisecond time scales characterized by nuclear magnetic resonance relaxation dispersion experiments.

^{[3]}

## ocean atmosphere system

The proxies provide new insight into the evolution of atmospheric CO2 concentrations at time scales from tens of millions to thousands of years, and the direct evidence to the significant ocean acidification during the mass extinction events, and the CO2 cycling in ocean-atmosphere system during the Last Deglaciation and post-industrial periods.^{[1]}The paper presents the review of the model study of the role of the Southern Ocean in the processes of interaction of the ocean-atmosphere system at short time scales impacting the El Nino–Southern Oscillation (ENSO).

^{[2]}

## genome size evolution

The plant order Brassicales provides an excellent system to further test if genome size evolution patterns are consistent across larger time scales, as there are numerous WGDs.^{[1]}Our study provides unprecedented insights into genome size evolution at microevolutionary time scales and thus paves the way for studying genome size evolution in contemporary populations rather than inferring patterns and processes a posteriori from species comparisons.

^{[2]}

## partial cross correlation

Using a detrended partial-cross-correlation analysis, our results show that net cross-correlations vary across time scales.^{[1]}Comparing the methods of time-delay multiscale multifractal detrended partial cross-correlation analysis method (time-delay MM-DPXA) and time-delay multiscale multifractal detrended cross-correlation analysis method (time-delay MM-DCCA), we find that cross-correlation and partial cross-correlation have different properties on different time scales and different time delays.

^{[2]}

## 3 6 9

The Standard Precipitation Index (SPI) was calculated for 3-, 6-, 9-, and 12-monthly time scales for ten southern African countries.^{[1]}

## financial risk contagion

Using a sample composed of nine international stock markets from January 4, 1999, to May 13, 2021, the empirical study reveals that: (1) EMD-Copula-CoVaR models can effectively measure the multiscale financial risk contagion, and the financial risk contagion is significant at all time scales; (2) The high-frequency component is the major contributor of financial risk contagion; meanwhile, the low-frequency component is the smallest among all time scale components; (3) The risk export of the US financial market to other markets, except the UK under the original and medium-frequency component, is higher than that it receives; and (4) Even though the magnitude of overall financial risk contagion is similar for the COVID-19 pandemic, Subprime Crises, 9/11 terrorist attack and other crises, the relative importance of different frequency components is heterogeneous.^{[1]}

## Different Time Scales

, means, extremes, variability on different time scales) for eelgrass bioindicators using lasso regression and commonality analysis.^{[1]}We analysed individual tree and stand characteristics and regeneration of all species to understand how different abiotic factors at different time scales affected stand species dynamics in relation to tree decline and mortality.

^{[2]}Recently, based on field observations, some nonlinear methods have successfully revealed the complex emergent properties (long-term persistence, multi-fractal, etc) in coupling correlation between O3 and its precursors at different time scales.

^{[3]}We study the direction of volatility spillover between Internet finance and banks by the Diebold-Yilmaz volatility spillover index mode