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Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

This paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.

In order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.

The proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.

Based on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

In this chapter, the authors consider the role of time for research in occupational stress and well-being. First, temporal issues in studying occupational health longitudinally, focusing in particular on the role of time lags and their implications for observed results (e.g., effect detectability), analyses (e.g., handling unequal durations between measurement occasions), and interpretation (e.g., result generalizability, theoretical revision) were discussed. Then, time-based assumptions when modeling lagged effects in occupational health research, providing a focused review of how research has handled (or ignored) these assumptions in the past, and the relative benefits and drawbacks of these approaches were discussed. Finally, recommendations for readers, an accessible tutorial (including example data and code), and discussion of a new structural equation modeling technique, continuous time structural equation modeling, that can “handle” time in longitudinal studies of occupational health were provided.

For the developing countries involving in the Belt and Road Initiative (BRI) with China as the main source of foreign development investment (FDI) and development as the top priority, it appears to attract more and more attention on how to make the best use of China’s outward foreign development investment. However, the contradictory evidence in the previous studies of FDI spillover effect and the remarkable time-lag feature of spillovers motivate us to analyze the mechanism of FDI spillover effect. The paper aims to discuss this issue.

The mechanism of FDI spillovers and the unavoidable lag effect in this process are empirically analyzed. Based on the panel data from the Belt and Road developing countries (BRDCs) and China’s direct investments (CDIs) from 2003 to 2017, the authors establish a panel vector autoregressive model, employing impulse response function and variance decomposition analysis, together with Granger causality test.

Results suggest a dynamic interactive causality mechanism. First, CDI promotes the economic growth of BRDCs through technical efficiency, human capital and institutional transition with combined lags of five, nine and eight years. Second, improvements in the technical efficiency and institutional quality promote economic growth by facilitating the human capital with integrated delays of six and eight years. Third, China’s investment directly affects the economic growth of BRDCs, with a time lag of six years. The average time lag is about eight years.

Based on the analysis on the mechanism and time lag of FDI spillovers, the authors have shown that many previous articles using one-year lagged FDI to examine the spillover effect have systematic biases, which contributes to the research on the FDI spillover mechanism. It provides new views for host countries on how to make more effective use of FDI, especially for BRDCs using CDIs.

In this paper, an analysis is presented of the research funding towards nanotechnology at the National Nanotechnology Initiative (NNI) and its relationship to the research output in Nanoscope, an application area of nanotechnology.

The paper analyzes the data collected from 1997 till 2006 and derives a definitive time lag between the allocation of research funds and issued patents and published journals. This assessment is achieved by identifying growth trends in patents, funds and publications and doing a curve‐fit analysis using the Fisher‐Pry model. Linear regression analysis is used to show the correlation between the funding and research outputs. Alongside, non‐linear programming objective function optimization technique is used to derive the time lag in years for each of the research outputs from the year of funds granted.

This paper demonstrated that there is a strong correlation between research funding and different research outputs. The time lag between funding and patents issued is evident from the patent trend analysis and Bibliometric analysis. In the case of Nanoscope, the patent time lag was found to be approximately five to six years, for journal article it was approximately two to three years and conference presentations happened right after the funding. The research outputs showed similar trends and were found to be interdependent as evident from our mathematical analysis.

While this study has shown that lag times exist within the chosen example of Nanoscope, and furthermore can be calculated to a precise degree, further data points in terms of additional emerging technologies would support the hypothesis in a more general term. A future study can look at developing technology roadmaps of the future based on the funding happening today.

The work takes bibliometric analysis to a further intelligence and establishes key linkages between these indicators.

This paper reports research on the impact of mass communication and the passage of time on consumer satisfaction and loyalty in a high‐involvement service setting. The study was based on a survey of two groups of individuals. A short‐time lag group consisted of individuals who were surveyed immediately after receiving a service and one year later. A long‐time lag group consisted of individuals who were surveyed immediately after they received a service and two years later. Satisfaction and loyalty decreased from the initial time of the service encounter for both the short‐time and long‐time groups. While satisfaction and loyalty declined over time for both groups, the results revealed no difference in the change in satisfaction between the two groups. In addition, exposure to mass communication did not influence the change in satisfaction and intention to return over time.

The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration.

The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration.

The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source.

A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction.

To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

The purpose of this paper is to present a new quantum‐inspired evolutionary hybrid intelligent (QIEHI) approach, in order to overcome the random walk dilemma for stock market prediction.

The proposed QIEHI method is inspired by the Takens' theorem and performs a quantum‐inspired evolutionary search for the minimum necessary dimension (time lags) embedded in the problem for determining the characteristic phase space that generates the financial time series phenomenon. The approach presented in this paper consists of a quantum‐inspired intelligent model composed of an artificial neural network (ANN) with a modified quantum‐inspired evolutionary algorithm (MQIEA), which is able to evolve the complete ANN architecture and parameters (pruning process), the ANN training algorithm (used to further improve the ANN parameters supplied by the MQIEA), and the most suitable time lags, to better describe the time series phenomenon.

This paper finds that, initially, the proposed QIEHI method chooses the better prediction model, then it performs a behavioral statistical test to adjust time phase distortions that appear in financial time series. Also, an experimental analysis is conducted with the proposed approach using six real‐word stock market times series, and the obtained results are discussed and compared, according to a group of relevant performance metrics, to results found with multilayer perceptron networks and the previously introduced time‐delay added evolutionary forecasting method.

The paper usefully demonstrates how the proposed QIEHI method chooses the best prediction model for the times series representation and performs a behavioral statistical test to adjust time phase distortions that frequently appear in financial time series.

Computerising inventory control procedures is usually an attempt to gain better control over stock availability. The effectiveness of the procedures depends on the time delays imparted by such events as order processing and delivery. Through these time delays, much of a finished goods physical distribution system is linked together through the inventory control procedures. Changing the length of any one time element through changes in inventory stocking rules, order processing methods or selected transportation services impacts on the economics of the entire physical distribution system. Little is understood about the effects of time change in such complex systems. In this article, the actual computer inventory control procedures of a chemical company were computer simulated. Physical distribution system design decisions and their associated time delay effects were explored by interrogating the model. Surprising effects were discovered, some of them being counter‐intuitive to what simple theory would predict. Management guidelines were provided as to the system‐wide economic consequences of change in individual elements of a physical distribution system.

Based on the literature of IT strategic alignment and e-collaboration, the purpose of this paper is to specify how e-business strategic alignment (e-alignment) influences e-collaboration capabilities and improves firm performance, and whether the time-lag effect existed in this relationship.

The authors tested the research hypotheses using a field survey of 145 Chinese corporations. The research model was validated using SmartPLS 2.0 with both subjective and objective data collected from the survey and Oriana database.

The results support the notion of a positive and significant link between e-alignment and e-collaboration capabilities and between e-collaboration capabilities and firm performance. The authors also show that the effect of e-alignment on performance is fully mediated by e-collaboration capabilities and that e-collaboration with suppliers has a one-year time-lag effect on firm performance.

This research extends and integrates the literature on IT strategic alignment and e-collaboration, and explains why and how e-alignment generates firm performance.

This paper includes two implications for managers. First, when formulating e-business strategies, managers should focus on establishing e-collaboration capabilities with partners. Second, the downstream process is the direct sources of business value. Managers should take the establishment of e-selling process as a critical business strategy.

By focussed on intermediate factors and time-lag effects, this study provides significant implications for IT strategic alignment and e-collaboration literature.

Today, a firm’s major concern is to know the way in which an innovation is adopted in the marketplace. The purpose of this paper is to focus on the two-stage nature of diffusion process in which the time lag between people being informed and their act of making final purchase is considered.

The paper discusses an approach based on the time lag for modeling awareness and adoption process as two separate and yet connected processes. Varying forms of time lag (constant, deterministic or random) have been considered while modeling the required framework. Furthermore, an equivalence approach has been shown between the present framework and the two well-known and established approaches of infinite queuing theory and hazard rate function.

The results are verified on sales data of two different consumer durables and it show good prediction capability of proposed models in capturing the real-life scenario. Further, the equivalence approach helps us to quantify such scenarios which were difficult to be modeled with any one particular approach. Further, the possibility of capturing different market scenarios by studying various distribution functions has been identified.

The proposed methodology is based on a two-stage adoption process. The same can be extended to a multi-stage adoption process as in today’s competitive environment. “Motivation” is one such factor that is highly important which can be considered in some later studies. In future, the authors wish to study the multi-stage adoption process considering the different forms of time lag function.

The equivalence approach discussed in the paper can help to cater the possibility of capturing different market scenarios by studying various distribution functions.

The proposed approach helps to cater the time lag between awareness and adoption process and develop different mean value functions to account for the manner in which sales are happening under different circumstances. The proposed methodical approach can also help decision makers in managing their available resources in a prudent manner.