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.

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.

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.

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.

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.

The optimum source－time function for generating finite－difference synthetic seismograms

A source-time function plays an important role in generating finite-difference synthetic seismograms.In this regard,we consider the amplitude spectra of five different time functions.This investigation shows that when the high-frequency signals of the time function carry more power than the main signal,the tailing phenomena would be associated with the main signal which is not desirable in producing finite-difference synthetic seismograms.It is illustrated that the time function denoted by is the optimal source-time function among those examined in this paper for generating finite-difference synthetic seismograms.This matter is also verified by making finite-difference synthetic seismograms over an elastic earth model consisting of a layer over a half space.

Functional Confirmation Using a Medical X-Ray System of a Semiconductor Survey Meter

In recent years, semiconductor survey meters have been developed and are in increasing demand worldwide. This study determined if it is possible to use the X-ray system installed in each medical facility to calculate the time constant of a semiconductor survey meter and confirm the meter’s function. An additional filter was attached to the medical X-ray system to satisfy the standards of N-60 to N-120, more copper plates were added as needed, and the first and second half-value layers were calculated to enable comparisons of the facility’s X-ray system quality with the N-60 to N-120 quality values. Next, we used a medical X-ray system to measure the leakage dose and calculate the time constant of the survey meter. The functionality of the meter was then checked and compared with the energy characteristics of the meter. The experimental results showed that it was possible to use a medical X-ray system to reproduce the N-60 to N-120 radiation quality values and to calculate the time constant from the measured results, assuming actual leakage dosimetry for that radiation quality. We also found that the calibration factor was equivalent to that of the energy characteristics of the survey meter.

Fast Evaluation of Time-Domain Green Function for Finite Water Depth

For computation of large amplitude motions of ships fastened to a dock, a fast evaluation scheme is implemented for computation of the time-domain Green function for finite water depth. Based on accurate evaluation of the Green function directly, a fast approximation method for the Green function is developed by use of Chebyshev polynomials. Examinations are carried out of the accuracy of the Green function and its derivatives from the scheme. It is shown that when an appropriate number of polynomial terms are used, very accurate approximation can be obtained.

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.

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.

Adaptive Time Frequency Distribution Based on Linear Chirp Modulated Gaussian Functions

We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.

Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C（s）. Three cases including linear delay, cubic delay and global delay in the system are considered respectively. The simulation results indicate that the linear delay enhances the fluctuation of the system （reduces the stability of the system） while the cubic delay and global delay weaken it （enforce the stability of the system）, and the effect of cubic delay is more pronounced than the linear delay and global delay.

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.

Female Sexual Dysfunction and Timed Intercourse: A Prospective Study of 105 Infertile Women

Introduction: Timed intercourse (TI) based on ovulation monitoring is an effective and common choice for treatment of infertility. However, TI related female sexual dysfunction remains to be elucidated. Method and Material: This was a prospective study and 105 infertile women were included using the Female Sexual Function Index (FSFI) to assess their sexual function in general sexual life (GSL) and TI cycle. Results: The mean age of the patients was 29.4 ± 3.4 years and the duration of infertility was 1.8 ± 0.5 years. The mean score of FSFI was 25.2 in GSL cycle and 24.5 in TI cycle (p = 0.008). Scores of 5 out of 6 domains of FSFI during GSL cycle were significantly higher than the counterparts during TI cycle. Female sexual function was related to stress, which mostly came from patients themselves and parents. The stronger the stress was, the more domains of FSFI were affected. Conclusion: Infertility is an important factor affecting female sexual function, especially TI condition reduced FSFI score in several domains, and this may be related to infertile stress.

Approximation Theorems for Exponentially Bounded <i>a</i>-Times Integrated Cosine Function

In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.

A time-dependent density functional theory investigation of plasmon resonances of linear Au atomic chains

We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time- dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction （blueshifts）. In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on.

Preliminary Clinical Study of Real-time Three-dimensional Echo-cardiographic Volume-time Curve in Evaluating Left Ventricular Diastolic Function

The volume-time curve change in patients with normal left ventricular （LV） diastolic function and diastolic dysfunction was evaluated by real-time three-dimensional echocardiography （RT3DE）. LV diastolic dysfunction was defined by E＇〈A＇ in pulse-wave tissue Doppler for inter-ventricular septal （IVS） of mitral annulus. In 24 patients with LV diastolic dysfunction, including 12 patients with delayed relaxation （delayed relaxation group） and 12 patients with pseudo-normal function （pseudo-normal group） and 24 normal volunteers （control group）, data of full-volume image were acquired by real-time three-dimensional echocardiography and subjected to volume-time curve analysis. EDV （end-diastolic volume）, ESV （end-systolic volume）, LVEF （left ventricular ejection fraction）, PER （peak ejection rate）, PFR （peak filling rate） from RT3DE were examined in the three groups. Compared to the control group, PFR （diastolic filling index of RT3DE） was significantly reduced in the delayed relaxation group and pseudo-normal group （P〈0.05）. There were no significant differences in EDV, ESV, LVEE PER （P〉0.05）. It is concluded that PFR, as a diastolic filling index of RT3DE, can reflect the early diastolic function and serve as a new non-invasive, quick and accurate tool for clinical assessment of LV diastolic function.

Changes in brain activation patterns according to cross-training effect in serial reaction time task An functional MRI study

Cross-training is a phenomenon related to motor learning, where motor performance of the untrained limb shows improvement in strength and skill execution following unilateral training of the homologous contralateral limb. We used functional MRI to investigate whether motor performance of the untrained limb could be improved using a serial reaction time task according to motor sequential learning of the trained limb, and whether these skill acquisitions led to changes in brain activation patterns. We recruited 20 right-handed healthy subjects, who were randomly allocated into training and control groups. The training group was trained in performance of a serial reaction time task using their non-dominant left hand, 40 minutes per day, for 10 days, over a period of 2 weeks. The control group did not receive training. Measurements of response time and percentile of response accuracy were performed twice during pre- and post-training, while brain functional MRI was scanned during performance of the serial reaction time task using the untrained right hand. In the training group, prominent changes in response time and percentile of response accuracy were observed in both the untrained right hand and the trained left hand between pre- and post-training. The control group showed no significant changes in the untrained hand between pre- and post-training. In the training group, the activated volume of the cortical areas related to motor function （i.e., primary motor cortex, premotor area, posterior parietal cortex） showed a gradual decrease, and enhanced cerebellar activation of the vermis and the newly activated ipsilateral dentate nucleus were observed during performance of the serial reaction time task using the untrained right hand, accompanied by the cross-motor learning effect. However, no significant changes were observed in the control group. Our findings indicate that motor skills learned over the 2-week training using the trained limb were transferred to the opposite homologous limb, and motor skill acquisition of the untrained limb led to changes in brain activation patterns in the cerebral cortex and cerebellum.