Memory effect in time fractional Schrödinger equation

A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.

课堂,是有格局的——评李洁老师Unit 5 Helping our parents(Story time)一课

聆听了李洁老师的课,让我相信:课堂,也是有格局的。一、仁爱的情怀,营造自由的心理氛围课堂心理气氛是课堂教学的软环境,是师生关系、生生关系的悄然反映,要营造这样的心理氛围,需要教师有海纳百川的胸襟,宁静致远的涵养,更需要教师有仁爱的情怀。你看,李洁老师选的Monkey,Monkey,What are you doing?这首歌,内容和课文完全贴合。

Time-sensitivity of the Kaiser effect of acoustic emission in limestone and its application to measurements of in-situ stress

Measuring in-situ stress by using the Kaiser effect in rocks has such advantages as timeefficiency, low cost and little limitation, but the precision of the method is dependent on rock properties and delay time of the measurement. In this paper, experiments on the Kaiser effect in limestones were performed, and it was found that the limestones had good ability to retain a memory of their recent stress history and high time-sensitivity. The longer the experiment was delayed from the extraction of the stone, the larger the Felicity ratio was. As the Felicity ratio approached l, significant Kaiser effect was observed. In-situ stress should be determined by the limestone measurements when the delay time was 40-120 days. Finally, the in-situ stress in a limestone formation could be successfully measured in practice.

Memory effect on the pressure-temperature condition and induction time of gas hydrate nucleation

The focus of this study is to investigate the influence of memory effect and the relation of its existence with the dissociation temperature,using gas hydrate formation and dissociation experiments.This is beneficial because memory effect is considered as an effective approach to promote the thermodynamic and dynamic conditions of gas hydrate nucleation.Seven experimental systems （twenty tests in total） were performed in a 1 L pressure cell.Three types of hydrate morphology,namely massive,whiskery and jelly crystals were present in the experiments.The pressures and temperatures at the time when visual hydrate crystals appeared were measured.Furthermore,the influence of memory effect was quantified in terms of pressure-temperature-time （p-T-t） relations.The results revealed that memory effect could promote the thermodynamic conditions and shorten the induction time when the dissociation temperature was not higher than 25℃.In this study,the nucleation superpressure and induction time decrease gradually with time of tests,when the earlier and the later tests are compared.It is assumed that the residual structure of hydrate dissociation,as the source of the memory effect,provides a site for mass transfer between host and guest molecules.Therefore,a driving force is created between the residual structures and its surrounding bulk phase to promote the hydrate nucleation.However,when the dissociation temperature was higher than 25 ℃,the memory effect vanished.These findings provide references for the application of memory effect in hydrate-based technology.

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.

Mathematical Model for Tempering Time Effect on Quenched Steel Based on Hollomon Parameter

Through the differentiating and integrating process, a mathematical model for tempering time effect on quenched steel was derived based on the attribute of state function and the general equation of Hollomon parameter, which correlates the tempering hardness with the tempering time at different tempering temperature. Using the established model, the linear relationship between the tempering hardness and the tempering time in logarithm was proved theoretically, and the tempering hardness for various tempering time was reduced to the measurement and calculation of a hardness experiment tempered for 1 h at different tempering temperatures. Moreover, the hardness of steel 42CrMo and T8Mn tempered for various times at 200-600℃ was calculated using this method. The predicted results are in good agreement with those of the available experiments.

Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.

Study on Water and Soil Conservation Effects of Grassland Based on Live Vegetation Volume at Various Time Scales

Based on the observation data of rainfall,vegetation,runoff and sediment yield in the experimental plots located in Hetian Town,Changting County of Fujian Province during 2007-2010,the changing characteristics and interrelation of live vegetation volume of grass,rainfall parameters,and water(soil)conservation effect RE(SE)were analyzed at four time scales of rainfall event,month,season,and year.The results showed that with the increase of time scales,the rainfall and vegetation indicators increased or decreased more or less,and the variation range of RE was small,while SEslowly decreased.The mean REchanged by 10%-20% at different time scales,and the observed water conservation effect of the grassland was the best at season scale while the worst at year scale.The soil conservation effect of the grassland was the best at month scale and the worst at season scale.The water conservation effect of the grass was mainly controlled by rainfall factors,including rainfall duration and precipitation at rainfall event scale,and the maximum intensity of precipitation within 30 min at longer time scales.However,the soil conservation effect of the grass was mainly controlled by vegetation factors,including the contribution of the litter on soil surface at rainfall event scale,the interaction of rainfall and vegetation at month and season scales,and the live vegetation volume of the grass at year scale.Consequently,at different time scales,the factors influencing water and soil conservation changed and interacted,and the observed water and soil conservation effects were also different,indicating that the influence of time scales deserves attention in both research and management practices.

Introducing an effective coherence function to generate non-uniform ground motion on topographic site using time-domain boundary element method

In this study,a comprehensive parametric analysis was performed on non-uniform excitation of V-shaped topography using the boundary element method in time domain.For this purpose,wave scattering analysis was carried out on a topography subjected to the SV-wave for different predominant frequencies and shape ratios.Based on the numerical results,new coherence and time delay functions are proposed to generate non-uniform ground motion for topographic irregularities.The efficiency and accuracy of the proposed functions for real engineering problems are indicated by comparison with observations reported in previous literature.

The Effect of Time and Temperature Variables on Some Routine Coagulation Tests among Subjects of African Descent in Sokoto, North Western Nigeria

This study evaluated the effects of time and temperature variables on routine Pro-thrombin Time test and Activated Partial Thromboplastin Time (APTT) test among subjects of African descent in Sokoto, North Western Nigeria. Samples of 99 subjects made up of 49 male and 50 female subjects with mean age 38.3 ± 22.3 years. Coagulation tests were performed immediately specified times after phlebotomy up to 24 hours (0, 1, 2, 3, 4 and 24 hours at room temperature of 40 degrees C. Our data demonstrate that prothrombin time and APTT results are stable for up to 2 hours, remaining constant regardless of storage conditions. Post hoc tests using Bonferroni correction revealed that there were increases in PT time from 0 hour to 4 hours (17.82 ± 0.61 seconds vs 18.30 ± 0.59 seconds, respectively), from 0 hour to 24 hours (17.82 ± 0.61 seconds vs 18.48 ± 0.59 seconds, respectively), from 2 hours to 4 hours (17.89 ± 0.58 seconds vs 18.30 ± 0.59 seconds), from 2 hours to 24 hours (17.89 ± 0.58 seconds vs 18.48 ± 0.58 seconds), which were all statistically significant (p = 0.002 and p < 0.000, p < 0.000, p < 0.000, respectively). However, the increase in PT time from 0 hour to 2 hours (17.82 ± 0.61 seconds vs 17.89 ± 0.59 seconds, respectively) and from 4 hours to 24 hours (18.30 ± 0.59 vs 18.48 ± 0.59 seconds, respectively) were not statistically significant (p = 1, p = 0.428). A repeated measure ANOVA determined that mean PTTK time differed statistically significantly between time points F (3, 291) = 119.22, p < 0.001. Post hoc tests using Bonferroni correction revealed that there were increase in PTTK time from 0 hour to 2 hours (37.86 ± 1.04 seconds vs 39.94 ± 1.07 seconds, respectively), from 0 hour to 4 hours (37.86 ± 1.04 seconds vs 42.34 ± 1.11 seconds, respectively), from 0 hours to 24 hours (37.86 ± 1.04 seconds vs 44.93 ± 1.20 seconds), from 2 hours to 4 hours (39.94 ± 1.07 seconds vs 42.34 ± 1.11 seconds), from 2 hours to 24 hours (39.94 ± 1.07 seconds vs 44.93 ± 1.20 seconds) and from 4 hours to 24 hours (42.43 ± 1.11 vs 44.93 ± 1.20 seconds), which were all statistically significant at p < 0.001). Therefore, we conclude that there are no statistically significant differences in the PT and APTT between 0 and 2 hours. A longer timing (after 2 hours) from phlebotomy collection of blood from respondents elicited a statistically significant increase in the PT and APTT result. There were no statistically significant differences in the PT and APTT result determined 4 hours and 24 hours after phlebotomy. Longer timing from collection of blood from respondents elicited a statistically significant increment/increase in the clotting time using PTTK. Our data demonstrate that PT and APTT results are stable for 2 hours remaining constant regardless of storage conditions.

Time and Dose-related Effects of the Pyrethroid Fluvalinate on Haemolymph Carbohydrates and Gut Lipids of Honeybees,Following in vivo Injection of very Low Doses

The injection to emerging adult workerbees with fluvalinate doses ranging from 1 femtomol to 1 nanomol per individual resulted in a reduction of haemolymph carbohydrate concentrations, particularly at the lowest dose 1 hour after injections. At the same time, a large increase was observed for triacylglycerols and to a much lesser extent for steroids and phospholipids with 0.1 picomol per bee. By contrast, fatty acids, steroids and triacylglycerols exhibited a depress at the higher dose. Most responses were thus biphasic, showing that much attention should be paid to the effects of very low doses of pesticide.

RESIDENCE TIME DISTRIBUTION IN AN OPEN REACTOR:EFFECT OF BACKGROUND REACTANT ON TRACER DISPERSION

A new approach is presented for deriving the residence time distribution(RTD)in open-type reactors with exclusion of residence in the fore section.Inasmuch as failure to predict the con-version of chemical reactions has been evidenced in many occasions,numerical solution of tracerdispersion in the presence of background concentration gradient of reactant is given to demonstratethe strong effect of background reactant on the true RTD a reactant molecule experiences.Withinthe error of computation,the conversion of a first-order chemical reaction under steady state is shownto be equal in both closed and open reactors,despite difference in relevant

A Study of Retention Time Gradient Effect of Gradientally Loaded Columns

In this work, the 'retention time gradient effect' of gradient GC columns is intensively studied to establish some equations and formulas for structure calculation of chromatographic columns. In addition, the relevant computer programs are designed.

以人为本,共建“生长”课堂——译林新版五下Unit 5 Helping our parents(Story time)一课的教学设计

【设计理念】译林新版《英语》五下Unit 5 Helping our parents这一单元围绕孩子帮助父母做家务这一话题,呈现了现在进行时的用法。作为第一课时的教学内容,Story time板块以Mike的视角呈现了布朗一家人周六一天的生活场景。课文内容贴近学生的生活,容易引起学生的共鸣,且将现在进行时融合在故事情境中更利于学生掌握。《义务教育英语课程标准(2011年版)》指出,英语课程承担着提高学生综合人文素养的任务,英语教学要体现工具性与人文性的双重属性。

Effects of time lag and stress loading rate on permeability in low permeability reservoirs

In order to study the effect of time lag and stress loading rates on rock deformation,the conventional stepped stress loading mode was changed into a continuous mode to investigate the effect of effective pressure on permeability and porosity.The time lag effect of rock deformation illustrating the relationship between changes in permeability and steady time was studied.Permeability reduction ratios were measured under different stress loading rates which were achieved by different pump rate settings.The results show that permeability and porosity gradually decrease with increases in effective pressure.Permeability at high effective pressure attains stability quickly.Steady times at low effective pressure are very long.Reduction in permeability at lower stress loading rates is small,while,in contrast,it is large at high stress loading rates.

Research for time-temperature equivalence effect of rock(Ⅰ):Theory research

In order to know about the rheological properties of rock in a long range of the time scale,method of increasing temperature was brought forward to accelerate the rheological process of rock,which could extend the time scale of experimental test data.Firstly,based on the generalized linear viscoelastic constitutive equation with temperature variable,the creep behavior of rock was divided into three types according to the different strain dependences of the time,that is,Hookean deformation,Newtonian flow,and retarded elasticity.Then the general equivalence relationship between time parameter and temperature parameter was derived for each type of strain.Finally,the relation between time parameter and temperature parameter in the whole creep was considered and the general theory of time-temperature equivalence effect(TTEE) of rock was established.This research reveals: ①The temperature effect on the instantaneous strain could be modified through vertical shift.②The key point of the TTEE of Newtonian flow depends on whether in the study of linear viscoelastic behavior of rock change of temperature is completely equivalent to a shift of the logarithmic time scale or not.③By plotting the results of a creep experiment performed at different temperatures and comparing the curves obtained,one can decide whether the rock considered have TTEE.④The TTEE of the whole creep should satisfy that the horizontal shift function of Newtonian flow and retarded elasticity is consentaneous.

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.

Research for time-temperature equivalence effect of rock(Ⅱ):Experimental research

With the creep test data of granite taken from Three Gorges,the existence of time-temperature equivalence effect(TTEE) of granite is investigated.Based on the creep test data at different temperatures,which are 20 ℃,60 ℃,80 ℃,100 ℃,200 ℃,300 ℃,four-component viscoelastic Burgers model is presented to characterize the creep curves.The parameters of elasticity modulus and viscosity coefficient in the constitutive model at different temperatures and their functional dependences on temperature are obtained.Then,according to the basic theory of TTEE presented in research(I),the TTEE of granite is investigated through modifying the compliance curves with vertical shift function and checking the coincidence of the modified curves with horizontal shift functions.It is concluded that:① Burgers model could appropriately characterize the creep property of granite in a short time scale.② Both elastic modulus and viscosity coefficient in the Burgers model decay exponentially with temperature.③ The coincidence of the curves at different temperatures after vertical shift modification and horizontal shift is fine,which indicates the existence of TTEE of granite.④The master curves which reflect the long time scale test data at temperatures 20 ℃,100 ℃,200 ℃ are obtained.

Time-effect relationship of acupuncture on histopathology, ultrastructure, and neuroethology in the acute phase of cerebral hemorrhage

Many clinical studies have addressed the treatment of acute cerebral hemorrhage using acupuncture. However, few studies have examined the relationship between time of acupuncture and curative effect on cerebral hemorrhage. By observing the effect of acupuncture on changes in histopathology, ultrastructure, and neuroethology in a cerebral hemorrhage model of rats, we have directly examined the time-effect relationship of acupuncture. The rat model of cerebral hemorrhage was produced by slowly injecting autologous blood to the right caudate nucleus. The experimental groups were: 3-, 9-, 24-, and 48-hour model groups; and 3-, 9-, 24-, and 48-hour acupuncture groups. The sham-operation group was used for comparison. Acupuncture was performed at the Neiguan(PC6) and Renzhong(DU26) acupoints, twice a day, 6 hours apart, for 5 consecutive days. Brain tissue changes were observed by light microscopy and transmission electron microscopy. Neuroethology was assessed using Bederson and Longa scores. Our results show that compared with the sham-operation and model groups, Bederson and Longa scores were lower in each acupuncture group, with visibly improved histopathology and brain tissue ultrastructure. Further, the results were better in the 3-and 9-hour acupuncture groups than the 24-and 48-hour acupuncture groups. Our findings show that acupuncture treatment can relieve pathological and ultrastructural deterioration and neurological impairment caused by the acute phase of cerebral hemorrhage, and may protect brain tissue during this period. In addition, earlier acupuncture intervention following cerebral hemorrhage(by 3 or 9 hours) is associated with a better treatment outcome.