ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS,WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS,AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO-DIFFERENTIAL EQUATIO

The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.

Waiting times and stopping probabilities for patterns in Markov chains

Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ) and the stopping probabilities P(τ = τA)with A ∈ C, where τA is the waiting time until the pattern A appears as a run.

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME

The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.

Enhancing the resolution of sparse rock property measurements using machine learning and random field theory

The travel time of rock compressional waves is an essential parameter used for estimating important rock properties,such as porosity,permeability,and lithology.Current methods,like wireline logging tests,provide broad measurements but lack finer resolution.Laboratory-based rock core measurements offer higher resolution but are resource-intensive.Conventionally,wireline logging and rock core measurements have been used independently.This study introduces a novel approach that integrates both data sources.The method leverages the detailed features from limited core data to enhance the resolution of wireline logging data.By combining machine learning with random field theory,the method allows for probabilistic predictions in regions with sparse data sampling.In this framework,12 parameters from wireline tests are used to predict trends in rock core data.The residuals are modeled using random field theory.The outcomes are high-resolution predictions that combine both the predicted trend and the probabilistic realizations of the residual.By utilizing unconditional and conditional random field theories,this method enables unconditional and conditional simulations of the underlying high-resolution rock compressional wave travel time profile and provides uncertainty estimates.This integrated approach optimizes the use of existing core and logging data.Its applicability is confirmed in an oil project in West China.

Finite Time Domain Dynamics of Dirac Fields

In the present paper we consider the case of a Dirac field in a finite time domain and coupled to an external field. We decompose the field and its Hamiltonian in terms of creation and annihilation operators and path integrate it via Grassmannian variables techniques. In that way we obtain its finite time domain Green function. We use it in the perturbative study of the interaction of Dirac particles with classical electromagnetic waves.

Optimal Stopping Time to Buy an Asset When Growth Rate Is a Two-State Markov Chain

In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is modeled as a geometric Brownian motion with drift being a two-state Markov chain. Based on observations of asset prices, investors want to detect the change points of price trends as accurately as possible, so that they can make the decision to buy. Using filtering techniques and stochastic analysis, we will develop the optimal boundary at which investors implement their decisions when the posterior probability process reaches a certain threshold.

Seasonal Characteristics of Forecasting Uncertainties in Surface PM_(2.5)Concentration Associated with Forecast Lead Time over the Beijing-Tianjin-Hebei Region

Forecasting uncertainties among meteorological fields have long been recognized as the main limitation on the accuracy and predictability of air quality forecasts.However,the particular impact of meteorological forecasting uncertainties on air quality forecasts specific to different seasons is still not well known.In this study,a series of forecasts with different forecast lead times for January,April,July,and October of 2018 are conducted over the Beijing-Tianjin-Hebei(BTH)region and the impacts of meteorological forecasting uncertainties on surface PM_(2.5)concentration forecasts with each lead time are investigated.With increased lead time,the forecasted PM_(2.5)concentrations significantly change and demonstrate obvious seasonal variations.In general,the forecasting uncertainties in monthly mean surface PM_(2.5)concentrations in the BTH region due to lead time are the largest(80%)in spring,followed by autumn(~50%),summer(~40%),and winter(20%).In winter,the forecasting uncertainties in total surface PM_(2.5)mass due to lead time are mainly due to the uncertainties in PBL heights and hence the PBL mixing of anthropogenic primary particles.In spring,the forecasting uncertainties are mainly from the impacts of lead time on lower-tropospheric northwesterly winds,thereby further enhancing the condensation production of anthropogenic secondary particles by the long-range transport of natural dust.In summer,the forecasting uncertainties result mainly from the decrease in dry and wet deposition rates,which are associated with the reduction of near-surface wind speed and precipitation rate.In autumn,the forecasting uncertainties arise mainly from the change in the transport of remote natural dust and anthropogenic particles,which is associated with changes in the large-scale circulation.

Effect of interplanetary magnetic field B_(x)on the polar electrojets as observed by CHAMP and Swarm satellites

Based on 16 years of magnetic field observations from CHAMP and Swarm satellites,this study investigates the influence of the Interplanetary Magnetic Field(IMF)Bx component on the location and peak current density of the polar electrojets(PEJs).We find that the IMF Bx displays obvious local time,seasonal,and hemispherical effects on the PEJs,as follows:(1)Compared to other local times,its influence is weakest at dawn and dusk.(2)In the midnight sectors of both hemispheres,the IMF Bx tends to amplify the westward PEJ when it is<0 in the Northern Hemisphere and when it is>0 in the Southern Hemisphere;this effect is relatively stronger in the local winter hemisphere.(3)At noontime,the IMF Bx intensifies the eastward current when it is<0 in the Northern Hemisphere;in the Southern Hemisphere when it is>0,it reduces the westward current;this effect is notably more prominent in the local summer hemisphere.(4)Moreover,the noontime eastward current shifts towards higher latitudes,while the midnight westward current migrates towards lower latitudes when IMF Bx is<0 in the Northern Hemisphere and when it is>0 in the Southern Hemisphere.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

The Optimal Stopping Time for Selling an Asset When It Is Uncertain Whether the Price Process Is Increasing or Decreasing When the Horizon Is Infinite

Assume that we want to shell an asset with unknown drift but known that the drift is a two value random variable, and the initial distribution can be estimated. As time goes by, this distribution is updated and base on the probability of the drift takes the small one gives us the stopping rule. Research results show that the optimal strategy to sell the asset is if the initial probability that the drift receives a small value greater than a certain threshold then liquidates the asset immediately, otherwise the asset holder will wait until the probability of the drift receives a small value passing a certain threshold, it is the optimal time to liquidate the asset.

Optimal Stopping Time for Holding an Asset

In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.

Existence and Uniqueness for Backward Stochastic Differential Equation to Stopping Time

In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping time with finite values and for the general stopping time we prove the result taking limit.We suggest a new approach to generalize the results for the case of constant time horizon to the case of stopping time horizon.

The Unified Field

This is a Unified Field description based on the holographic Time Dilation Cosmology, TDC, model, which is an eternal continuum evolving forward in the forward direction of time, at the speed of light, c, at an invariant 1 s/s rate of time. This is the Fundamental Direction of Evolution, FDE. There is also an evolution down time dilation gradients, the Gravitational Direction of Evolution, GDE. These evolutions are gravity, which is the evolutionary force in time. Gravitational velocities are compensation for the difference in the rate of time, dRt, in a dilation field, and the dRtis equal to the compensatory velocity’s percentage of c, and is a measure of the force in time inducing the velocity. In applied force induced velocities, the dRt is a measure of the resistance in time to the induced velocity, which might be called “anti-gravity” or “negative gravity”. The two effects keep the continuum uniformly evolving forward at c. It is demonstrated that gravity is already a part of the electromagnetic field equations in way of the dRt element contained in the TDC velocity formula. Einstein’s energy formula is defined as a velocity formula and a modified version is used for charged elementary particle solutions. A time dilation-based derivation of the Lorentz force ties gravity directly to the electromagnetic field proving the unified field of gravity and the EMF. It is noted how we could possibly create gravity drives. This is followed by a discussion of black holes, proving supermassive objects, like massive black hole singularities, are impossible, and that black holes are massless Magnetospheric Eternally Collapsing Objects (MECOs) that are vortices in spacetime. .

The Relevant Analysis on the Stop Time in Winter and Times of Plateau and the Index in Early Days for Garrisonned Plateau Constructors

Objective: Study the influence of the stop time in winter, times of plateau on the index in early days for plateau constructors meet;Method:Is it participate in plateau construction of 2002-2004 to choose,enter into the plateau again of 2003-2005 practise clothes finish to mate 326 materials “physical examination in front of the worker",which is passed in Nanshankou Hospital in early days, divided into 3 groups according to the difference of year for the physical examination, examine by leaning towards relevant analytical methods;Result: （1） In the situation of day controlling about the stop time in winter, times of garrison in plateau and blood and oxygen saturation lever （SaO2）, the systolic pressure （sBP） is presented and shouldered relevantly winter to control. Present positive correlation with the value of hemoglobin （Hb）;（2） It is stopped that in case of controlling and is garrisoned in the number of times of plateau in winter day and blood and oxygen saturation lever （SaO2） to present positive correlation. Present and shoulder with the hemoglobin （Hb） relevantly.Conclusion: In order to ensure the health of plateau constructors to the maximum extent, should try one’s best to reduce the number of times of returning to the plateau in possible cases. At the same time each one constructs for year and returns to the time that the hinterland concentrates rest should be on above 90 days.

A New Perspective on Time and Gravity

This paper presents a hypothesis regarding the existence of time fused in spacetime, assuming that time possesses the properties of both a particle and a field. This duality is referred to as the field-particle of time (FPT). The analysis shows that when the FPT moves through matter, it causes time dilation. The FPT is also a significant element that appears in relativistic kinetic energy (KE = (γ - 1) · mc2). Accelerating matter to near the speed of light requires relativistic energy approaching infinity, which corresponds to the relativistic kinetic energy. Meanwhile, the potential energy (PE = mc2) from the rest mass remains constant. Then, the mass-energy equation can be rearranged in terms of PE and KE, as shown in E = (1 + (γ - 1)) · mc2. The relativistic energy of the FPT also directly affects the gravitational attraction of matter. It transfers energy to each other through spacetime. The analysis demonstrates that the gravitational force is inversely proportional to the distance squared, following Newton’s law of gravity, and it varies with the relative velocity of matter. The relationship equation between relative time and the gravitational constant indicates that a higher intensity of the gravitational field leads to a slower reference time for matter, in accordance with the general theory of relativity. A thought experiment presents a comparison of two atomic clocks placed in different locations. The first one is placed in a room temperature, around 25°C, on the surface of the Earth, and the second one is placed in high-density areas. The analysis, considering the presence of the FPT, shows that the reference time slows down in high-density areas. Therefore, the second clock must be noticeably slower than the first one, indicating the existence of the FPT passing through both atomic clocks at different speeds.

基于载流子抽取模型的Trench Gate/Field-stop IGBT驱动器有源箝位功能分析

针对Trench gate/Field-stop IGBT结构特有的关断过程中集电极电流下降率不可控问题,引入了载流子抽取模型来模拟器件关断过程中的集电极电流下降阶段器件内部载流子的动态行为特性,并以此为基础分析了驱动器为适应Trench gate/Field-Stop IGBT结构这种关断特性而引入的有源箝位功能的作用机理,验证了载流子抽取模型在器件级与电路级交互作用分析中的实用性,为后续实现器件与电路的最佳匹配奠定了基础。

Decay rates and time lags of heat conduction in building construction under field conditions

The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.

Zero-Sum Continuous-Time Markov Games with One-Side Stopping

The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.

Nitrogen and phosphorus changes and optimal drainage time of flooded paddy field based on environmental factors

While many controlled irrigation and drainage techniques have been adopted in China, the environmental effects of these techniques require further investigation. This study was conducted to examine the changes of nitrogen and phosphorus of a flooded paddy water system after fertilizer application and at each growth stage so as to obtain the optimal drainage time at each growth stage. Four treatments with different water level management methods at each growth stage were conducted under the condition of ten-day continuous flooding. Results show that the ammonia nitrogen （ NH4-N ） concentration reached the peak value once the fertilizer was applied, and then decreased to a relatively low level seven to ten days later, and that the nitrate nitrogen （NO^-N） concentration gradually rose to its peak value, which appeared later in subsurface water than in surface water. Continuous flooding could effectively reduce the concentrations of NH^-N , NO3-N, and total phosphorus （TP） in surface water. However, the paddy water disturbance, in the process of soil surface adsorption and nitrification, caused NH]-N to be released and increased the concentrations of NH4-N and NO^-N in surface water. A multi-objective controlled drainage model based on environmental factors was established in order to obtain the optimal drainage time at each growth stage and better guide the drainage practices of farmers. The optimal times for surface drainage are the fourth, sixth, fifth, and sixth days after flooding at the tillering, jointing-booting, heading-flowering, and milking stages, respectively.