Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

Quantifying the spatial variation in the potential productivity and yield gap of winter wheat in China

Despite the improvement in cultivar characters and management practices, large gaps between the attainable and potential yields still exist in winter wheat of China. Quantifying the crop potential yield is essential for estimating the food production capacity and improving agricultural policies to ensure food security. Gradually descending models and geographic infor- mation system （GIS） technology were employed to characterize the spatial variability of potential yields and yield gaps in winter wheat across the main production region of China. The results showed that during 2000-2010, the average potential yield limited by thermal resource （YGT） was 23.2 Mg ha-1, with larger value in the northern area relative to the southern area. The potential yield limited by the water supply （YGw） generally decreased from north to south, with an average value of 1.9 Mg ha-1 across the entire study region. The highest YGw in the north sub-region （NS） implied that the irrigation and drainage conditions in this sub-region must be improved. The averaged yield loss of winter wheat from nutrient deficiency （YGH） varied between 2.1 and 3.1 Mg ha-1 in the study area, which was greater than the yield loss caused by water limitation. The potential decrease in yield from photo-thermal-water-nutrient-limited production to actual yield （YGo） was over 6.0 Mg ha-1, ranging from 4.9 to 8.3 Mg ha^-1 across the entire study region, and it was more obvious in the southern area than in the northern area. These findings suggest that across the main winter wheat production region, the highest yield gap was induced by thermal resources, followed by other factors, such as the level of farming technology, social policy and economic feasibility. Furthermore, there are opportunities to narrow the yield gaps by making full use of climatic resources and developing a reasonable production plan for winter wheat crops. Thus, meeting the challenges of food security and sustainability in the coming decades is possible but will require considerable changes in water and nutrient management and socio-economic policies.

Variation trends of meteorological variables and their impacts on potential evaporation in Hailar region

Evaporation, which is an important factor in the water balance at the basin scale, is a critical variable in the determination of local available water resources. Since the potential evaporation is mainly influenced by meteorological variables, it is necessary to investigate the extent to which different meteorological variables affect the potential evaporation. The aim of this study was to explore the variation trends of different meteorological variables, and their impacts on the potential evaporation. This study selected the Hailar Meteorological Station of the Hailar region, which is situated in a cold, semi-arid, and sub-humid region, as a case study site. Based on observed daily meteorological data from 1951 to 2009, the potential evaporation was calculated with the Penman formula, and the variations of meteorological variables were investigated with the nonparametric Mann-Kendall test. The correlation between the potential evaporation and each meteorological variable at annual and seasonal scales was also analyzed. The results show that the annual and seasonal potential evaporation and air temperature present increasing trends, whereas the wind speed, sunshine duration, and relative humidity present decreasing trends. Among the meteorological variables, the air temperature and relative humidity are the key factors that affect potential evaporation at different time scales, and the impacts of other meteorological variables on the potential evaporation are not significant and vary with time scales.

Dynamic Variation Characteristics of Phosphorus in Paddy Field Runoff in Saline Land and Its Potential Environmental Effect

[Objective] The aim was to study the dynamic variation characteristics of phosphorus in paddy field runoff in saline land and its potential environmental effect. [Method] Taking Qianguo irrigation district in soda-saline land in Songnen Plain as study object, the dynamic variation law of phosphorus in paddy field runoff under different irrigation conditions and its potential environmental effect were discussed. [Result] Surface water in paddy field was alkaline, and scattered soil had poor fertilizer conservation capacity. Phosphorus accumulated in soil surface, which could increase the risk of phosphorus loss. Phosphorus loss in paddy field mainly occurred in irrigation period and runoff period caused by rainstorm. The concentration of total phosphorus (TP), particulate phosphorus (PP), total dissolved phosphorus (TDP) and dissolved reactive phosphorus (DRP) in paddy field runoff decreased with time, especially PP. Phosphorus concentration exceeded critical value and resulted to eutrophication, which threatened the water quality security of Chagan Lake. Phosphorus concentration in water recession canal increased with time, and eutrophication with different degrees appeared under high temperature. TP concentration in surface water of paddy field was highly negatively correlated with that in water recession canal, and the correlation coefficients R2(α=0.05)in three paddy fields were 0.850 9, 0.896 4 and 0.915 3, respectively. The pollution load of phosphorus in paddy field with the best irrigation condition was higher, and its pollution risk was the highest. Thus, such fields should be monitored and controlled mainly as the critical source area of phosphorus loss. [Conclusion] The study could provide theoretical foundations for developing saline land rationally, establishing optimal management measure of phosphorus in saline land and controlling phosphorus loss from farmland to protect local water resources.

Potential Power of the Pyramidal Structure III: Discovery of Pyramid Effects with and without Seasonal Variation

Since October 2007, we have been conducting rigorous scientific research on the unexplained “power” of a pyramidal structure (PS). From our research results so far, we could classify the pyramid effects by the PS into the following two types. (i) The pyramid effects in which the PS converted the test subject’s unexplained energy to affect biosensors when the test subject entered the PS and meditated. (ii) The pyramid effects in which the potential power of the PS affected biosensors if the test subject had not been inside the PS for at least 20 days and the test subject’s unexplained energy was excluded. In this paper, we report new results regarding (ii). As a result of dividing a year according to the four seasons of winter, spring, summer, and autumn and analyzing the pyramid effect of each period, the following points were found. 1) There was a pyramid effect without seasonal variation. The pyramid effect on the lower and upper layers was different throughout the year for the biosensors placed at the PS apex in two layers, regardless of the season. 2) There was a pyramid effect with seasonal variation. The value of the psi index, which indicates the magnitude of the pyramid effect, changed as the seasons changed, while different pyramid effects were maintained on the lower and upper layers. Regarding the change in the pyramid effect depending on the season, the psi index in summer was larger than that in winter in both the lower and upper layers. From these results, we found that there are two types of potential power at the PS apex: seasonal potential power and non-seasonal potential power.

QUASI-VARIATIONAL PRINCIPLE FOR THE VORTEX-POTENTIAL FUNCTION OF ROTATIONAL FLOW IN THREE-DIMENSION PIPE

The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.

A VARIATIONAL METHOD FOR COMPUTING POTENTIAL COEFFICIENTS USING DIFFERENT TYPES OF GRAVIMETRIC DATA

In this paper,a variational method is presented for solving theclassical gravimetric,satellite gravimetric and satellite altimetric mixed typeboudary value problem to obtain the potential coefficients.According to thisprinciple,classical gravimetric data（height measured by geometric levelling orheight triangulation）,satellite gravimetric data（height measured by satellitegeodesy technique）and satellite altimetric data can be used jointly to calculate thepotential coefficients.

A novel SVPWM strategy considering neutral-point potential balancing for three-level NPC inverter

This paper proposes a novel SVPWM （space vector pulse width modulation） strategy for the three-level neutral-point-clamped voltage source inverter, based on the particular disposition of all the redundant voltage vectors. The new modulation approach shows superior performance for harmonic voltage and balancing control of neutral-point potential compared to the popular eight-stage centered SVPWM. It realizes suppression of inverter neutral-point potential variation by accurately modifying redundant factor of small vectors pairs, only requiring information of DC-link capacitor voltages and three-phase load currents. This is convenient to apply and is compatible of digital computer realization. Feasibility of the proposed control approach is verified by simulation and experimental results.

A neutral-point potential balance control strategy for three-level inverter based on VSVPWM

The topology of diode neutral-point-clamped(NPC)three-level inverter is prone to neutral-point potential offset.When the sum of three-phase current is zero,the virtual space vector pulse width modulation(VSVPWM)scheme does not cause the neutral-point voltage offset,but it lacks the ability to balance the deviation.For this reason,a neutral-point potential control strategy combining virtual space vector modulation and loop width control is proposed.The neutral-point potential is balanced by introducing the distribution factor for the regions with redundant vectors.For other regions,the potential is controlled by selecting a suitable switching sequence.Meanwhile,the effect on the virtual vector modulation is reduced within the loop width by setting an appropriate loop width,thereby improving the balance effect.The simulation results show that the proposed method has a strong ability to control the offset and has excellent potential balance performance under the conditions of balanced load,unbalanced load and asymmetric capacitance parameters.

GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS

From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.

Spatiotemporal variations of maximum seasonal freeze depth in 1950s–2007 over the Heihe River Basin, Northwest China

Investigation on spatiotemporal variations of maximum seasonal freeze depth （MSFD） over the Heihe River Basin is of great importance for systematic understanding of regional climate and environmental change, ecological-hydrological processes, water resources assessment, construction and resource development. Based on soil and air temperatures at the meteorological stations of the China Meteorological Administration （CMA） over the Heihe River Basin, MSFDs time series are structured into a composite time series over the 1960-2007 period. Evaluating the averaged MSFD time series for 1960 2007 reveals a statistically significant trend of 4.0 cm/decade or a net change of-19.2 cm for the 48-year period over the basin. The MSFD had significantly negative correlation with mean annual air temperature （MAAT）, winter air temperature, mean annual ground surface temperature （MAGST）, degree days of thawing for the air （DDTa） as well as for the surface （DDTs）, and degree days of freezing for the surface （DDFs）. While there was significantly positive correlation between DDF,. and MSFD time series, MSFD was deeper and changed greatly in the Heihe River source area. It was shallower in the east-central basin and gradually deepened in other sections of the basin. The MSFD distribution pattern in 2003-2005 is consistent with that of averaged degree days of freezing for air （DDFa） in 1960-2007. However, the maximum of MSFD may not be accurate, because there is no long term observation data in the deep seasonally frozen ground regions near the lower boundary of permafrost. With increasing elevation, averaged DDFa increased at a rate of 51.6 ℃-day/100m, therefore, the MSFG and the date reaching MSFG became deeper and later, respectively.

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRDINGER-POISSON EQUATIONS WITH SIGN-CHANGING POTENTIAL

In this article, we study the following nonhomogeneous Schrodinger-Poissone quations{-△u＋λV（x）u＋K（x）Фu=f（x,u）＋g（x）,x∈R^3,-△Ф=k（x）u^2, x∈R^3}where λ 〉 0 is a parameter. Under some suitable assumptions on 11, K, f and g, the existence of multiple solutions is proved by using the Ekeland＇s variational principle and the Mountain Pass Theorem in critical point theory. In particular, the potential V is allowed to be signchanging.

Development of Measuring System of Plant Electrical Potential and Its Application

Based on the characters of plant potentials, it introduced the construction and technology in developing the measuring system of plant electrical potentials, the input impedance of the amplifier must be enough high(= 1010～ 1012Ω) in order to measuring the plant weak signals and ensuring high common mode rejection ratio (CMRR). And wavelet transform was applied in denoising based on cross-validation (CV)threshold value. the experiment showed that this system could effectively detect the change of plant potentials,four-week old cucumber was stimulated by heat wounding, the variation potential (VP) and action potential(AP) would be evoked, the AP's varying amplitude can reach 40mV; the AP changed very fast, its duration time is about 0.01～0.02s and its amplitude often change from 15μV～5mV.

Characterization of event-related potentials in obsessive compulsive disorder patients: Comparison with depression and generalized anxiety disorder patients

BACKGROUND： Study results of event-refated potential in obsessive compulsive disorder （OCD） remain controversial, potentially as a result of different instruments utilized and their differing technical characteristics. OBJECTIVE： To investigate the differences in several common event-related potentials, Le. contingent negative variations, P300, and mismatch negativity （MMN）, in OCD patients, depression patients, generalized anxiety disorder （GAD） patients, and healthy controls. DESIGN, TIME AND SETTING： A case-control study was performed in the Department of Electrophysiology, Shanghai Mental Health Center from May 2002 to December 2005. PARTICIPANTS： A total of 38 OCD patients, 20 depression patients, and 18 GAD patients, who were diagnosed according to the criteria of Chinese Classification of Mental Disorders （Version 3）, formulated by the Chinese Psychiatry Association, were selected from the Outpatient Department of Shanghai Mental Health Center. Patients with two or more the above diseases were excluded. In addition, 28 healthy people, gender and age matched, were selected as controls. METHODS： Contingent negative variations, P300, and MMN were recorded by a Nicolet Spirit Instrument. All electrodes were attached at Cz according to the Intemationa11020 system, with the mastoid leads as reference and Fpz as ground. MAIN OUTCOME MEASURES： Amplitude and latency of contingent negative variations, P300, and MMN. RESULTS： The contingent negative variations, P300, and MMN were different （P 〈 0.01）. OCD patients showed an increased MI amplitude compared with controls, depression, and GAD patients （P 〈 0.01）. Target P300 amplitudes were significantly lower in OCD, depression, and GAD patients compared with controls （P 〈 0.01）. Moreover, N2 latency and latency of MMN were prolonged in OCD and depression groups compared with controls （P 〈 0.05）. CONCLUSION： Event-related potentials were different in depression, GAD, and OCD patients and healthy controls. In particular, OCD patients exhibited unique characteristics.

Contingent negative variation of mood disorder patients

Studies on brain-evoked potential and contingent negative variation （CNV） in mood disorder remain controversial. To date, no CNV difference between unipolar and bipolar depression has been reported. Brain-evoked potentials were measured in the present study to analyze CNV in three subtypes of mood disorder （mania, unipolar depression, and bipolar depression）, and these results were compared with normal controls. In the mania group, CNV amplitude B was greater than in controls, and the depression group exhibited lower CNV amplitude B and smaller A-S＇2 area, and prolonged post-imperative negative variation latency. The CNV comparison between unipolar and bipolar depression found that the prolonged post-imperative negative variation latency was only in unipolar depression. These results suggest that prolonged post-imperative negative variation latency is a characteristic of unipolar depression, and CNV amplitude change is a state characteristic of mood disorder patients.

Variation of Plant Electrophysiology in Cucumber under Different Water Status

AP and VP were measured in cucumbers under water sufficiency and water stress. The results indicated that, the AP would be evoked by electrical impulse, for water-stressed cucumber, its amplitude could reached more than 40 mV which was obviously greater than that (about 10-20 mV) of plant under well-watered, and no VP came out. Along with the intensity of light increased, the VP appeared going-up trend, and accompanied by evidently spiking electrical signal, for plant under water stress, the VP increased more clearly, but the change of spiking amplitude of AP (about 3 mV) was rather smaller than that (8-10 mV) of plant under well-watered.

Field source characteristic of gravity variation in Hexi region before Menyuan Ms6.4 earthquake based on the Euler deconvolution

This study adopted the Euler deconvolution method to conduct an inversion and interpretation of the depth and spatial distribution pattern of field source that lead to gravity variation. For this purpose, mobile gravity data from four periods in the Hexi region between 2011 and 2015 were obtained from an observation network. With a newly established theoretical model, we acquired the optimum inversion parameters and conducted calculation and analysis with the actual data. The results indicate that one is the appropriate value of the structure index for the inversion of the mobile gravity data. The inversion results of the actual data showed a comparable spatial distribution of the field source and a consistent structural trend with observations from the Qilian-Haiyuan Fault zone between 2011 and 2015. The distribution was in a blocking state at the epicenter of the Menyuan earthquake in 2016. Our quantitative study of the field source provides new insights into the inversion and interpretation of signals of mobile gravity variation.

Topological Tail Pressure for Asymptotically Sub-additive Continuous Potentials

We define the topological tail pressure and the conditional pressure for asymptotically sub-additive continuous potentials on topological dynamical systems and obtain a variational principle for the topological tail pressure without any additional assumptions.

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.

Study on Application of Hypervirial Therem in the Variational Method

We discuss a methodology problem which is crucially important for solving the Sch?dinger equation in terms of the variational method. We present a complete analysis on the application of the hypervirial theorem for judging the quality of the trial wavefunction without invoking the precise solutions.