Variational Iteration Method for Solving Time Fractional Burgers Equation Using Maple

The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.

Monitoring models for base flow effect and daily variation of dam seepage elements considering time lag effect

Affected by external environmental factors and evolution of dam performance, dam seepage behavior shows nonlinear time-varying characteristics. In this study, to predict and evaluate the long-term development trend and short-term fluctuation of the dam seepage behavior, two monitoring models were developed, one for the base flow effect and one for daily variation of dam seepage elements. In the first model, to avoid the influence of the time lag effect on the evaluation of seepage variation with the time effect component of seepage elements, the base values of the seepage element and the reservoir water level were extracted using the wavelet multi-resolution analysis method, and the time effect component was separated by the established base flow effect monitoring model. For the development of the daily variation monitoring model for dam seepage elements, all the previous factors, of which the measured time series prior to the dam seepage element monitoring time may have certain influence on the monitored results, were considered. Those factors that were positively correlated with the analyzed seepage element were initially considered to be the support vector machine(SVM) model input factors, and then the SVM kernel function-based sensitivity analysis was performed to optimize the input factor set and establish the optimized daily variation SVM model. The efficiency and rationality of the two models were verified by case studies of the water level of two piezometric tubes buried under the slope of a concrete gravity dam.Sensitivity analysis of the optimized SVM model shows that the influences of the daily variation of the upstream reservoir water level and rainfall on the daily variation of piezometric tube water level are processes subject to normal distribution.

Study on the Influence of Airgun Excitation Conditions on Airgun Signals and Travel Time Variation Measurements

Because of the different excitation conditions of the airgun source,there will be subtle differences in airgun signals.Travel time variation of airgun signals often mix into source information which can’t fully reflect the evolution of the medium.This article uses the airgun signals from the Binchuan Transmitting Seismic Station to analyze the airgun signal′s characteristics of phase and correlation.We conducted a comparative analysis of the effects of the pair difference method and the deconvolution method on eliminating the influence of the excitation conditions in travel time variation.The results show that:(1)The pressure pulse and its subsequent wave of airgun source wavelet are less affected by excitation conditions that we can use it to obtain high-precision excitation moments.(2)Deconvolution can improve the correlation of the airgun signal.(3)The pair difference method can’t eliminate the influence of excitation conditions in travel time variation.Deconvolution can reduce excitation condition interference and the influence of the excitation condition in the travel time variation after deconvolution of the vertical signal is significantly reduced.

Accession-specific flowering time variation in response to nitrate fluctuation in Arabidopsis thaliana

Flowering time,a key transition point from vegetative to reproductive growth,is regulated by an intrinsic complex of endogenous and exogenous signals including nutrient status.For hundreds of years,nitrogen has been well known to modulate flowering time,but the molecular genetic basis on how plants adapt to ever-changing nitrogen availability remains not fully explored.Here we explore how Arabidopsis natural variation in flowering time responds to nitrate fluctuation.Upon nitrate availability change,we detect accession-and photoperiod-specific flowering responses,which also feature a accession-specific dependency on growth traits.The flowering time variation correlates well with the expression of floral integrators,SOC1 and FT,in an accession-specific manner.We find that gene expression variation of key hub genes in the photoperiod-circadian-clock(GI),aging(SPLs)and autonomous(FLC)pathways associates with the expression change of these integrators,hence flowering time variation.Our results thus shed light on the molecular genetic mechanisms on regulation of accession-and photoperiod-specific flowering time variation in response to nitrate availability.

Variational Inference Based Kernel Dynamic Bayesian Networks for Construction of Prediction Intervals for Industrial Time Series With Incomplete Input

Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.

Research on the Application of Time Structure Variation Analysis to the Jiashi-Bachu Earthquake Swarm Sequence

In 1997 - 2003, 27 earthquakes with M≥ 5.0 occurred in the Jiashi-Bachu area of Xinjiang. It was a rare strong earthquake swarm activity. The earthquake swarm has three time segments of activity with different magnitudes in the years 1997, 1998 and 2003. In different time segments, the seismic activity showed strengthenin-qguiet changes in various degrees before earthquakes with M ≥ 5.0. In order to delimitate effectively the precursory meaning of the clustering （strengthening） quiet change in sequence and to seek the time criterion for impending prediction, the nonlinear characteristics of seismic activity have been used to analyze the time structure characteristics of the earthquake swarm sequence, and further to forecast the development tendency of earthquake sequences in the future. Using the sequence catalogue recorded by the Kashi Station, and taking the earthquakes with Ms≥ 5.0 in the sequence as the starting point and the next earthquake with Ms = 5.0 as the end, statistical analysis has been performed on the time structure relations of the earthquake sequence in different stages. The main results are as follows： （1） Before the major earthquakes with M ≥ 5.0 in the swarm sequence, the time variation coefficient （δ-value） has abnormal demonstrations to different degrees. （2） Within 10 days after δ= 1, occurrence of earthquakes with M ≥ 5.0 in the swarm is very possible. （3） The time variation coefficient has three types of change. （4） The change process before earthquakes with M5.0 is similar to that before earthquakes with M6.0, with little difference in the threshold value. In the earthquake swarm sequence, it is difficult to delimitate accurately the attribute of the current sequences （foreshock or aftershock sequence） and to judge the magnitude of the follow-up earthquake by δ-value. We can only make the judgment that earthquakes with M5.0 are likely to occur in the sequence. （5） The critical clustering characteristics of the sequence are hierarchical. Only corresponding to a certain magnitude can the sequence have the variation state of critical clustering. （6） The coefficient of the time variation has a clear meaning in physics. After the clustering-quiet state of earthquake activity has appeared, it can describe clearly the randomness of the seismogenic system. Furthermore, it can efficiently clarify whether or not the clustering quiescence variation is of some prognostic meaning. In the case that the earthquake frequency attenuation is essentially normal （h 〉 1 ） and there is no remarkable clustering-quiescence state, it is still possible to discover the abnormal change of the sequence from the time variation coefficient. On the contrary, in the later period of swarm activity, after the appearance of many seismic quiescence phenomena, this coefficient did not appear abnormally, even when h 〈 1, suggesting that the δ-value diagnosis is more universal.

Interdecadal Variations of Phase Delays Between Two Nino Indices at Different Time Scales

Phase delays between two Nino indices-sea surface temperatures in Nino regions 1+2 and 3.4 (1950-2001)-at different time scales are detected by wavelet analysis. Analysis results show that there are two types of period bifurcations in the Nino indices and that period bifurcation points exist only in the region where the wavelet power is small. Interdecadal variation features of phase delays between the two indices vary with different time scales. In the periods of 40-72 months, the phase delay changes its sign in 1977: Nino 1+2 indices are 2-4 months earlier than Nino 3.4 indices before 1977, but 3-6 months later afterwards. In the periods of 20-40 months, however, the phase delay changes its sign in another way: Nino 1+2 indices are 1-4 months earlier before 1980 and during 1986-90, but 1-4 months later during 1980-83 and 1993-2001.

Trans-Thoracic Echocardiographic Aortic Blood Flow Peak Velocity Variation, Distance Minute, Aortic Velocity Time Integral and Postoperative Outcome in Pediatric Surgical Patients—An Observational Pilot Study Protocol

Background: A Randomized Controlled Trial (RCT) has been elaborated where goal directed fluid and hemodynamic therapy (GDFHT) will be realized with trans-thoracic echocardiographic aortic blood flow peak velocity variation (ΔVpeak) and distance minute (DM) to guide fluid therapy and hemodynamics in high risk pediatric surgical patients. This RCT will clarify the impact of GDFHT with ΔVpeak and DM on postoperative outcome in terms of morbidity, length of stay in the intensive care unit (LOSICU), length of mechanical ventilation (LMV) and length of hospital stay (LOS) in children. To determine values of ΔVpeak, DM and VTI predictive of these postoperative outcomes, an observational pilot study will be realized. This pilot study is described here. The primary objective of this study is to determine values of ΔVpeak, DM and ITV predictive of postoperative outcome in children in terms of morbidity. The secondary objectives are to determine values of ΔVpeak, DM and ITV predictive of LOSICU, LMV, LOS, intraoperative, postoperative fluid administration and vasoactive-inotropic therapy. Methods: 500 - 1000 children aged less than 18 years will be included prospectively. Statistic analysis will be realized with XLSTAT 2019.4.2 software or plus. Results and Conclusions: This trial protocol will determine values of ΔVpeak, DM and ITV with echocardiography predictive of postoperative outcome in children.

Effects of Short Time Variation in the River Discharge on the Salt Wedge Intrusion in the Yura Estuary, a Micro Tidal Estuary, Japan

A numerical model was developed to investigate salinity distribution in the Yura Estuary, a micro tidal estuary in Japan. The model results show that the salinity distribution as represented by salt wedge intrusion agreed well with field observations. In addition to the seasonal variation, the salt wedge responds over short time scales according to the flood events. The retreat of the salt wedge is dependent on the scale of the river discharge;the salt wedge moved back and disappeared from the estuary when over250 m3·s-1 of fresh water was discharged from the estuary and it takes ~11 days for salt wedge to recover from the fresh water discharge event. The Yura Estuary has on average three floods during summer, this coincides with when phytoplankton is most productive in the river and indicates that the short temporal variations in the river discharge has important effects not only on the hydrodynamics, but also on the ecosystem in the estuary.

Finite Time Ruin Probability with Variable Interest Rate and Extended Regular Variation

Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.

Bayesian Estimation of Population Size via Capture-Recapture Model with Time Variation and Behavioral Response

We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without further restrictions. The novelty of this article is to expand the current research practice by developing a hierarchical Bayesian approach with the assumption that the odds of recapture bears a constant relationship to the odds of initial capture. A real-data example of deer mice population is given to illustrate the proposed method. Three simulation studies are developed to inspect the performance of the proposed Bayesian estimates. Compared with the maximum likelihood estimates discussed in Chao et al. (2000), the hierarchical Bayesian estimate provides reasonably better population estimation with less mean square error;moreover, it is sturdy to underline relationship between the initial and re-capture probabilities. The sensitivity study shows that the proposed Bayesian approach is robust to the choice of hyper-parameters. The third simulation study reveals that both relative bias and relative RMSE approach zero as population size increases. A R-package is developed and used in both data example and simulation.

Variation of Calcium Oxalate (CaOx) Crystals in Porang Corms (Amorphophallus muelleri Blume) at Different Harvest Time

Harvest time is assumed to potentially influence shape and size variation of calcium oxalate (CaOx) crystals;therefore it needs to be observed microscopically. This research used porang corms from the second growing period which were planted to produce the vegetative phase of third growing period. These corms were obtained based on the harvest time had determined. The harvest time was determined, i.e. 1) at two weeks before the plants shed (R0 - 1);2) when the plants shed (R0) and 3) at two weeks after the plants shed (R0 + 1). Slides for microscopic observation were obtained from slices on the edge and center of porang corms. Organ slices were cleared using modified clearing method. Parameters observed were the shape and the size of CaOx crystal. The variations of styloid, prism, druse and raphide crystals found in porang corms at the three harvest time were 1, 2, 3 and 37 variations respectively. The variation of CaOx crystals tended to be same in porang corms at three harvest times. The variation of these crystals tended to be static. It is also known that raphide crystal has the greatest variation amount. On the contrary, styloid crystal has the fewest variation amounts. This abundance of a number of raphide crystal variations is possibly due to its role as a defense mechanism in porang corms.

foF2 Seasonal Asymmetry Time Variation at Korhogo Station from 1992 to 2002

foF2 seasonal asymmetry is investigated at Korhogo station from 1992 to 2002. We show that equinoctial asymmetry is less pronounced and somwhere is absent trough out solar cycle phase. In general, the absence of equinoctial asymmetry may be due to the fact that in equinox and for each solar cycle phase, the asymmetry is due to Russell-McPherron mechanism. The solstice anomaly or annual anomaly is always observed throughout solar cycle phase. The minimum value of ΔfoF2 is inferior than −60% seen during all solar cycle phase at 0700 LT. This annual asymmetry may be due to interplanetary corpuscular radiation.

Study on noise in simultaneous geomagnetic difference data caused by the effect of S_q local-time variation

A new concept is suggested on tectonomagnetic research about the noise in simultaneous geomagnetic difference data caused by the effect of Sq local-time variation, together with the method of theoretical calculation. The level of the noise and its contribution to the total noises of the differences data are analyzed. The result indicates that the noise increases linearly with the increase of the distance between the two stations in the range of 40° longitude-difference, and its increasing rate is about 0.4 nT/（°）at latitude 40°N. The example calculated at a pair of sites with longitude-difference 0.357°, shows that the noise is about one fifth of the total noises of the difference data on geomagnetic quiet-day.

LEGENDRE SERIES SOLUTIONS FOR TIME-VARIATION DYNAMICS

In this topic, a new. approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and Legendre integral operator matrix. The theoretical basis for effective solution of time-variation dynamics is therefore established, which is beneficial to further research of time-variation science.

Variational iteration method for solving time-fractional diffusion equations in porous the medium

The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.

Electromagnetic response function for the semi-annual variations estimated by the single-station method using the night-time values of the geomagnetic fields

The geomagnetic night-time values were used to estimate the electromagnetic response function Q1 for half-year period. If the spatial structure of the source field can be described by the approximation, one can estimate the Q1 value using the single-station Z/H method. This technique enables us to carry out regional deep gcomagnetic sounding by the method. The data used for analyses are geomagnetic night-time values for about, typically, 26 years from 5 good-quality stations and for several years from 34 stations distributed over the globe. The results indicate that the night-time values yield more reliable response estimates for half-year period compared to the usual estimates obtained from daily means. It implies that the approximation for the night-time fields holds good for the half-year period, but the daily means are not suitable for estimating the response function of the semi-annual variations by using the single-station method. Source field analyses for daily means data and night-time means data have also been carried out in this paper.

The sea-air oscillator model of decadal variations in subtropical cells and equatorial Pacific SST

In this paper a time delay equation for sea-air oscillator model is studied. The aim is to create an approximate solving method of nonlinear equation for sea-air oscillator model. Employing the method of variational iteration, it obtains the approximate solution of corresponding equation. This method is an approximate analytic method, which can be often used for analysing other behaviour of the sea surface temperature anomaly of the atmosphere-ocean oscillator model.

Morphological variation of star dune and implications for dune management: a case study at the Crescent Moon Spring scenic spot of Dunhuang, China

Aerial photographs and 3-D laser scans of a 90-m high star dune at the Crescent Moon Spring scenic spot in Dunhuang,China,are used to investigate the changes in dune morphology on timescales from months to decades.The result revealed that relative-equilibrium airflow strength in three wind directions of northeast,west and south was an important condition for the stability of star dunes with limited migration.Transverse and longitudinal airflows exerted a crucial impact on variation processes of star dune morphology.Controlled by transverse airflows,the easterly winds,the east side was dominated by wind erosion;and strong deposition occurred on the south-south-east arm with a maximum deposition rate of 0.44 m/a in the 46-a monitoring period,causing the east side becoming steep and high.Controlled by longitudinal airflows,the westerly winds,the west-north-west side was mainly eroded and the north arm migrated from west to east with a rate of 0.30 m/a,causing the dune slope becoming gentle and elongate.The local air circulation(southerly winds)exerted a significant impact on the development process of the star dune.Due to the influence of human activities,the south side present surface processes from a concave profile to a convex profile in 46 a,which is a potential threat to the Crescent Moon Spring.The results indicate that rehabilitating the airflow field at most is a crucial strategy to the protection of Crescent Moon Spring from burial.Opening up the passage of easterly,westerly and southerly winds through intermediately cutting the protection forest,demolishing the enclosed wall and changing the pavilion into a porous pattern have been suggested to protect the Crescent Moon Spring from burial.

EVOLUTION FILTRATION PROBLEMS WITH SEAWATER INTRUSION: TWO-PHASE FLOW DUAL MIXED VARIATIONAL ANALYSIS

Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.