VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES

For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.

Generation of endurance time excitation functions using spectral representation method

In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.

Source time functions of the Gonghe，China earthquake retrieved from long－period digital waveform data using empirical Green＇s function technique

An earthquake of Ms= 6, 9 occurred at the Gonghe, Qinghai Province, China on April 26, 1990. Three larger aftershocks took place at the same region, Ms= 5. 0 on May 7, 1990, Ms= 6. 0 on Jan. 3, 1994 and Ms= 5. 7on Feb. 16, 1994. The long-period recordings of the main shock from China Digital Seismograph Network (CDSN) are deconvolved for the source time functions by the correspondent0 recordings of the three aftershocks asempirical Green's functions (EGFs). No matter which aftershock is taken as EGF, the relative source time functions (RSTFs) Obtained are nearly identical. The RSTFs suggest the Ms= 6. 9 event consists of at least two subevents with approximately equal size whose occurrence times are about 30 s apart, the first one has a duration of 12 s and a rise time of about 5 s, and the second one has a duration of 17 s and a rise time of about & s. COmParing the RSTFs obtained from P- and SH-phases respectively, we notice that those from SH-phases are a slightly more complex than those from p-phases, implying other finer subevents exist during the process of the main shock. It is interesting that the results from the EGF deconvolution of long-Period way form data are in good agreement with the results from the moment tensor inversion and from the EGF deconvolution of broadband waveform data. Additionally, the two larger aftershocks are deconvolved for their RSTFs. The deconvolution results show that the processes of the Ms= 6. 0 event on Jan. 3, 1994 and the Ms= 5. 7 event on Feb. 16,1994 are quite simple, both RSTFs are single impulses.The RSTFs of the Ms= 6. 9 main shock obtained from different stations are noticed to be azimuthally dependent, whose shapes are a slightly different with different stations. However, the RSTFs of the two smaller aftershocks are not azimuthally dependent. The integrations of RSTFs over the processes are quite close to each other, i. e., the scalar seismic moments estimated from different stations are in good agreement. Finally the scalar seismic moments of the three aftershocks are compared. The relative scalar seismic moment Of the three aftershocks deduced from the relative scalar seismic moments of the Ms=6. 9 main shock are very close to those inverted directly from the EGF deconvolution. The relative scalar seismic moment of the Ms =6. 9 main shock calculated using the three aftershocks as EGF are 22 (the Ms= 6. 0 aftershock being EGF), 26 (the Ms= 5. 7 aftershock being EGF) and 66 (the Ms= 5. 5 aftershock being EGF), respectively. Deducingfrom those results, the relative scalar sesimic moments of the Ms= 6. 0 to the Ms= 5. 7 events, the Ms= 6. 0 tothe Ms= 5. 5 events and the Ms= 5. 7 to the Ms= 5. 5 events are 1. 18, 3. 00 and 2. 54, respectively. The correspondent relative scalar seismic moments calculated directly from the waveform recordings are 1. 15, 3. 43, and 3. 05.

Time function of surface subsidence based on Harris model in mined-out area

The surface subsidence is a common environmental hazard in mined-out area. Based on careful analysis of the regularity of surface subsidence in mined-out area, we proposed a new time function based on Harris curve model in consideration of the shortage of current surface subsidence time functions. By analyzing the characteristics of the new time function, we found that it could meet the dynamic process, the velocity change process and the acceleration change process during surface subsidence. Then its rationality had been verified through project cases. The results show that the proposed time function model can give a good reflection of the regularity of surface subsidence in mined-out area and can accurately predict surface subsidence. And the prediction data of the model are a little greater than measured data on condition of proper measured data quantity, which is safety in the engineering. This model provides a new method for the analysis of surface subsidence in mined-out area and reference for future prediction, and it is valuable to engineering application.

Time lag characteristics of sap flow in seed-maize and their implications for modeling transpiration in an arid region of Northwest China

Plant capacity for water storage leads to time lags between basal stem sap flow and transpiration in various woody plants. Internal water storage depends on the sizes of woody plants. However, the changes and its influencing factors in time lags of basal stem flow during the development of herbaceous plants including crops remain unclear. A field experiment was conducted in an arid region of Northwest China to examine the time lag characteristics of sap flow in seed-maize and to calibrate the transpiration modeling. Cross-correlation analysis was used to estimate the time lags between stem sap flow and meteorological driving factors including solar radiation（R_s） and vapor pressure deficit of the air（VPD_（air））. Results indicate that the changes in seed-maize stem sap flow consistently lagged behind the changes in R_s and preceded the changes in VPD_（air） both on hourly and daily scales, suggesting that light-mediated stomatal closures drove sap flow responses. The time lag in the maize＇s sap flow differed significantly during different growth stages and the difference was potentially due to developmental changes in capacitance tissue and/or xylem during ontogenesis. The time lags between stem sap flow and R_s in both female plants and male plants corresponded to plant use of stored water and were independent of total plant water use. Time lags of sap flow were always longer in male plants than in female plants. Theoretically, dry soil may decrease the speed by which sap flow adjusts ahead of shifts in VPD_（air） in comparison with wet soil and also increase the speed by which sap flow adjusts to R_s. However, sap flow lags that were associated with R_s before irrigation and after irrigation in female plants did not shift. Time series analysis method provided better results for simulating seed-maize sap flow with advantages of allowing for fewer variables to be included. This approach would be helpful in improving the accuracy of estimation for canopy transpiration and conductance using meteorological measurements.

Source time functions of the 1999, Jiji (Chi-Chi) earthquake from GDSN long period waveform data using aftershocks as empirical Green's functions

A large earthquake (Mw=7.6) occurred in Jiji (Chi-Chi), Taiwan, China on September 20, 1999, and was followed by many moderate-size shocks in the following days. Two of the largest aftershocks with the magnitudes of Mw=6.1 and Mw=6.2, respectively, were used as empirical Green's functions (EGFs) to obtain the source time functions (STFs) of the main shock from long-period waveform data of the Global Digital Seismograph Network (GDSN) including IRIS, GEOSCOPE and CDSN. For the Mw=6.1 aftershock of September 22, there were 97 pairs of phases clear enough from 78 recordings of 26 stations; for the Mw=6.2 aftershock of September 25, there were 81 pairs of phases clear enough from 72 recordings of 24 stations. For each station, 2 types of STFs were retrieved, which are called P-STF and S-STF due to being from P and S phases, respectively. Totally, 178 STF individuals were obtained for source-process analysis of the main shock. It was noticed that, in general, STFs from most of the stations had similarities except that those in special azimuths looked different or odd due to the mechanism difference between the main shock and the aftershocks; and in detail, the shapes of the STFs varied with azimuth. Both of them reflected the stability and reliability of the retrieved STFs. The comprehensive analysis of those STFs suggested that this event consisted of two sub-events, the total duration time was about 26 s, and on the average, the second event was about 7 s later than the first one, and the moment-rate amplitude of the first event was about 15% larger than that of the second one.

The Application of Multiquadric Function Fitting to Borehole Strain Time Series Data Processing

Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain a valuable fitting result,from which the physical connotation of the original data and its possible applications were analyzed.Meanwhile,a brief comparison was made between the results of multiquadric function fitting and polynomial fitting.

Region-time-length algorithm and its application to the study of intermediate-short term earthquake precursor in North China

The Region-Time-Length Algorithm (RTL algorithm) is introduced and improved in the paper. Compared with the original definition, the influence of rupture length on RTL function is emphasized and the weights of epicentral distance function, time function, and rupture length function are ensured to be equal. The retrospective examinations of RTL algorithm in North China have indicated that the anomalies obtained by the improved RTL algorithm show the short or intermediate-short term precursory features in most cases. There are two types of RTL anomalous patterns before the main shock. For the I-type, the variation pattern of the VRTL, numerical values of the VRTL(x, y, z, t) function, is complete and most of them have shown the changing pattern of rising from 0 turning dropping or dropping from 0 turning rising. For the II-type, the variation pattern of VRTL is not complete, which increases or decreases quickly from 0 and there is no evident turning, the main shock generally occurs in the short period around the peak VRTL. The rising of VRTL indicates an increase of seismic activity relative to the background level, which means the enhancement of seismic activity, while the dropping of VRTL indicates the decrease of seismic activity relative to the background level, which represents the seismic quiescence to a certain extent. According to statistical examination results of RTL algorithm in North China, the methods to distinguish the intermediate and short-term anomalies and to estimate the occurrence time of the coming main shock are given in the paper. For both I and II-type RTL anomalies, the R-value, i.e., the forecasting score, is about 0.6 and 0.3 for the 3 months forecasting period and about 0.7 and 0.4 for the 6 months forecasting period. The preliminary discussion is also made for the influences of characteristic time-span t0, characteristic distance r0, and threshold magnitude M0 on computation of VRTL, as well as some other significant problems in application.

Finite time stability and stabilization of hybrid dynamic systems

Finite time stability and stabilization are studied for hy-brid dynamic systems. By combining multiple Lyapunov function and finite time Lyapunov function, a sufficient condition of finite time stability is given for the system. Compared with the previ-ous works, our results have less conservativeness. Furthermore, based on the state partition of continuous and resetting parts of system, a hybrid feedback controller is constructed, which stabi-lizes the closed-loop systems in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the pro-posed method.

Source parameters determination for earthquakes in Kushiro,Japan considering source time function

This paper applies a new formulation to do moment tensor inversion for earthquakes in the Kushiro area of Japan. Comparing with conventional moment tensor inversion method, the new one takes the effect of source time function into consideration. For the inversion, best solution is obtained by minimizing the difference between the observed seismograms and the synthetic ones. And the best-fitting focal depth is determined from the variance reduction. The results indicate that half duration of source time function is proportional to the magnitude of earthquakes. Large earthquakes have long half duration, whereas that of moderate-small earthquakes is comparatively shorter. The focal mechanisms of all three earthquakes are of thrust fault type, which is mainly ascribed to the collision of the North American plate with the Eurasia plate in the late Cretaceous or Paleogene.

A new escape time algorithm of constructing Julia set

Escape time algorithm is an effective theoretical algorithm of constructing fractal graphics. The key of this algorithm lies in the construction of escape time function. A new escape time function is presented based on the research of escape time algorithm. An accelerated escape time algorithm is carried out in this paper. The experiments have demonstrated that the new algorithm is not only as precise as the old, but also faster when it is used to construct Julia set.

Lumped Time Distribution Function of Dynamic Equilibrium System and Its Application in Calculating Molecular Weight Distribution of Polymer

The lumped time distribution functions were proposed, which can be used for describing the dynamicsystems with two or more than two states of the end of growing polymer chain during chain addition polymerization.Numerical analysis of the lumped time distribution functions was carried out. The method for calculating molecularweight distribution of polymer in the stable free radical polymerization and more general cases was developed basedon the lumped time distribution functions.

Envelope Functions of Time Histories in Seismic Safety Evaluation and Scenario Earthquakes

It has been a period of time since the concept of scenario earthquake was proposed, but this concept has rarely been used in seismic safety evaluation in China since then. Meanwhile, because of the uncertainties of magnitudes-distances pairs, there is large arbitrariness while determining the envelope function of time histories in seismic hazard analysis. In this paper, we describe a method to control the envelope functions of the time histories by introducing the most-likely combinations of magnitude and distance of the scenario earthquakes based on a probabilistic method, revise the software of the ellipse model for seismic hazard analysis, and give a computation example.

Modeling Breast Cancer Incidence Rates: A Comparison between the Components of Functional Time Series (FTS) Model Applied on Karachi (Pakistan) and US Data

Several studies showed that the breast cancer incidence rates are higher in high-income (developed) countries, due to the link of breast cancer with several risk factors and the presence of systematic screening policies. Some of the authors suggest that lower breast cancer incidence rates in low-income (developing) countries probably reflect international variation in hormonal factors and accessibility to early detection facilities. Recent studies showed that the breast cancer increased rapidly among women in Pakistan (a developing country) and it became the first malignancy among females of Pakistan. Although, the incidence rates may contain important evidence for understanding and control of the disease;however in Pakistan, the breast cancer incidence data have never been available in the last five decades since independence;rather, only hospital-based data are available. In this study, we intend to apply Functional Time Series (FTS) models to the breast cancer incidence rates of United State (developed country), and to see the difference between various components (age and time) of Functional Time Series (FTS) models applied independently on the breast cancer incidence rates of Karachi (Pakistan) and US. Past studies have already suggested that the incidence of US breast cancer cases was expected to increase in the coming decades. A progressive increase in the number of new cases is already predetermined by the high birth rate that occurred during the middle part of the century, and it will lead to nearly a doubling in the number of cases in about 4 decades. We also obtain 15 years predictions of breast cancer incidence rates in United States and compare them with the forecasts of incidence curves for Karachi. Development of methods for cancer incidence trend forecasting can provide a sound and accurate foundation for planning a comprehensive national strategy for optimal partitioning of research resources between the need for development of new treatments and the need for new research directed toward primary preventive measures.

Grey Repairable System Analysis

In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering community. Accordingly, we propose a small-sample based approach to estimate repair improvement effects by partitioning system stopping times into intrinsic functioning times and repair improvement times. An industrial data set is used for illustrative purposes in a stepwise manner.

Tempo-spatial rupture process of the 1997Mani, Xizang(Tibet), China earthquake of Ms=7.9

An earthquake of Ms=7.4 occurred in Mani, Xizang (Tibet), China on November 8, 1997. The moment tensor ofthis earthquake was inverted using the long period body wave form data from China Digital Seismograph Network(CDSN). The apparent source time functions (AS TFs) were retrieved from P and S waves, respectively, using thedeconvolution technique in frequency domain, and the tempo-spatial rupture process on the fault plane was imagedby inverting the azimuth dependent AS TFs from different stations. The result of the moment tensor inversionindicates that the P and T axes of earthquake-generating stress field were nearly horizontal, with the P axis in theNNE direction (29), the T axis in the SEE direction (122) and that the NEE-SWW striking nodal plane andNNW-SSE striking nodal plane are mainly left-lateral and right-lateral strike-slip, respectively; that this earthquakehad a scalar seismic moment of 3.4xl02o N. .m, and a moment magnitude of Mw=7.6. Taking the aftershock distribution into account, we proposed that the earthquake rupture occurred in the fault plane with the strike of 250,the dip of 88 and the rake of 19. On the basis of the result of the moment tensor inversion, the theoretical seismograms were synthesized, and then the AS T Fs were retrieved by deconvoving the synthetic seismograms fromthe observed seismograms. The A S T Fs retrieved from the P and S waves of different stations identically suggestedthat this earthquake was of a simple time history, whose ASTF can be approximated with a sine function with thehalf period of about 10 s. Inverting the azimuth dependent A S T Fs from P and S waveforms led to the imageshowing the tempo-spatial distribution of the rupture on the fault plane. From the 'remembering' snap-shots, therupture initiated at the western end of the fault, and then propagated eastward and downward, indicating an overallunilateral rupture. However, the slip distribution is non-uniform, being made up of three sub-areas, one in thewestern end, about 10 km deep ('western area'), another about 55 kin away from the western end and about 35 Iondeep ('eastern area'), the third about 30 km away from the western end and around 40 km deep ('central area').The total rupture area was around 70 km long and 60 km wide. From the 'forgetting' snap-shots, the rupturingappeared quite complex, with the slip occurring in different position at different time, and the earthquake being ofthe characteristics of 'healing pulse'. Another point we have to stress is that the locations in which the ruptureinitiated and terminated were not where the main rupture took place. Eventually, the static slip distribution wascalculated, and the largest slip values of the three sub-areas were 956 cm, 743 cm and 1 060 cm, for the western.eastern and central areas, respectively. From the slip distribution, the rupture mainly distributed in the fault about70 km eastern to the epicenter; from the aftershock distribution. however, the aftershocks were very sparse in thewest to the epicenter while densely clustered in the east to the epicenter It indicated that the Maul Ms=7.9 earthquake was resulted from the nearly eastward extension of the NEE-SWW to nearly E-W striking fault in thenorthwestern Tibetan plateau.

Functional Causality between Oil Prices and GDP Based on Big Data

This paper examines the causal relationship between oil prices and the Gross Domestic Product(GDP)in the Kingdom of Saudi Arabia.The study is carried out by a data set collected quarterly,by Saudi Arabian Monetary Authority,over a period from 1974 to 2016.We seek how a change in real crude oil price affects the GDP of KSA.Based on a new technique,we treat this data in its continuous path.Precisely,we analyze the causality between these two variables,i.e.,oil prices and GDP,by using their yearly curves observed in the four quarters of each year.We discuss the causality in the sense of Granger,which requires the stationarity of the data.Thus,in the first Step,we test the stationarity by using the Monte Carlo test of a functional time series stationarity.Our main goal is treated in the second step,where we use the functional causality idea to model the co-variability between these variables.We show that the two series are not integrated;there is one causality between these two variables.All the statistical analyzes were performed using R software.

Spatial and temporal rupture process of the January 26, 2001, Gujarat, India, M_S=7.8 earthquake

The source parameters, such as moment tensor, focal mechanism, source time function (STF) and temporal-spatial rupture process, were obtained for the January 26, 2001, India, MS=7.8 earthquake by inverting waveform data of 27 GDSN stations with epicentral distances less than 90? Firstly, combining the moment tensor inversion, the spatial distribution of intensity, disaster and aftershocks and the orientation of the fault where the earthquake lies, the strike, dip and rake of the seismogenic fault were determined to be 92? 58?and 62? respectively. That is, this earthquake was a mainly thrust faulting with the strike of near west-east and the dipping direction to south. The seismic moment released was 3.51020 Nm, accordingly, the moment magnitude MW was calculated to be 7.6. And then, 27 P-STFs, 22 S-STFs and the averaged STFs of them were determined respectively using the technique of spectra division in frequency domain and the synthetic seismogram as Greens functions. The analysis of the STFs suggested that the earthquake was a continuous event with the duration time of 19 s, starting rapidly and ending slowly. Finally, the temporal-spatial distribution of the slip on the fault plane was imaged from the obtained P-STFs and S-STFs using an time domain inversion technique. The maximum slip amplitude on the fault plane was about 7 m. The maximum stress drop was 30 MPa, and the average one over the whole rupture area was 7 MPa. The rupture area was about 85 km long in the strike direction and about 60 km wide in the down-dip direction, which, equally, was 51 km deep in the depth direction. The rupture propagated 50 km eastwards and 35 km westwards. The main portion of the rupture area, which has the slip amplitude greater than 0.5 m, was of the shape of an ellipse, its major axis oriented in the slip direction of the fault, which indicated that the rupture propagation direction was in accordance with the fault slip direction. This phenomenon is popular for strike-slip faulting, but rather rare for thrust faulting. The eastern portion of the rupture area above the initiation point was larger than the western portion below the initiation point, which was indicative of the asymmetrical rupture. In other words, the rupturing was kind of unilateral from west to east and from down to up. From the snapshots of the slip-rate variation with time and space, the slip rate reached the largest at the 4th second, that was 0.2 m/s, and the rupture in this period occurred only around the initiation point. At the 6th second, the rupture around the initiation point nearly stopped, and started moving outwards. The velocity of the westward rupture was smaller than that of the eastward rupture. Such rupture behavior like a circle mostly stopped near the 15th second. After the 16th second, only some patches of rupture distributed in the outer region. From the snapshots of the slip variation with time and space, the rupture started at the initiation point and propagated outwards. The main rupture on the area with the slip amplitude greater than 5 m extended unilaterally from west to east and from down to up between the 6th and the 10th seconds, and the western segment extended a bit westwards and downwards between the 11th and the 13th seconds. The whole process lasted about 19 s. The rupture velocity over the whole rupture process was estimated to be 3.3 km/s.

Seismic source ruptures of several strong earth-quakes of 1989 in Sichuan region of China

Several strong earthquakes occurred in the regions of Batang and Xiaojin of Sichuan Province in 1989. This paper uses broadband waveform data from GDSN, by the forward trial-and-error modeling for multiple subevent, in terms of analysis on quasi-source time function or qSTF of station, to study source rupture characteristics of these strong earthquakes and to discuss tectonic background of earthquake occurrence regions preliminarily.

Temporal Characteristics of GaAs NEA and Alkali Metal Photocathodes

The temporal characteristics of GaAs NEA and alkali metal photocathodes are studied using Monte Carlo simulation method. The electron transit time and its distribution functions in the photocathodes are calculated. Based on the results, the time modulation transfer functions and temporal resolutions of the photocathodes are obtained. The results show that the response time and temporal resolution of alkali metal photocathode is in femitosecond order and those of GaAs NEA photocathode are in picosecond order.