Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

Periodic boundary value problem for the first order functional differential equations with impulses

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.

The determination of the relative permittivity of periodic stratified media based on the iterative time-reversal method

In this paper, we present a new method to determine the relative permittivity of periodic stratified media using the iterative time-reversal method. Based on transmission line theory, the focal peak value of iterative time-reversal electro- magnetic waves, which contain information about the periodic stratified medium, is computed in pulse-echo mode. Using the relationship between the focal peak value and the relative permittivity of the periodic stratified medium, the relative permittivity can be obtained by measuring the focal peak value. Numerical simulations are conducted, and the results demonstrate the feasibility of the proposed approach to the measurement of the relative permittivity of a periodic stratified medium.

Partial or Truncated Sharing Values of Meromorphic Functions with Their Shifts

We mainly study the periodicity theorems of meromorphic functions having truncated or partial sharing values with their shifts, where meromorphic functions are of hyper order less than 1 and N（r, f） aT（r; f） for some positive number a.

The Existence and Uniqueness of the Solution for Perio dical Boundary Value Problems of 2k th Order Differential Equations with Resonance

In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.

Spatial Distribution of High-temperature Risk with a Return Period of Different Years in the Yangtze River Delta Urban Agglomeration

Against the background of global warming,research on the spatial distribution of high-temperature risk is of great significance to effectively prevent the adverse effects of high temperatures.By using air temperature data from 1951 to 2018 measured by meteorological stations located in the Yangtze River Delta urban agglomeration,the daily maximum air temperature distribution is interpolated at a resolution of 1 km based on the local thin disk smooth spline function;the high-temperature threshold for return periods of 5,10,20 and 30 yr are then calculated by using the generalized extreme value method.The yearly average high-temperature intensity and high-temperature days are finally calculated as high-temperature danger factors.Socioeconomic statistical data and remotely sensed image data in 2018 are used as the background data to calculate the spatial distribution of high-temperature vulnerability factors and prevention capacity factors,which are then used to compute the high-temperature risk index during different recurrence periods in the Yangtze River Delta urban agglomerations.The results show that the spatial distribution features of high-temperature risk in different return periods are similar.The high-temperature risk index gradually increases from northeast to southwest and from east coast to inland,which has obvious latitude variation characteristics and a relationship with the comprehensive influence of the underlying surface and urban scale.In terms of time variation,the high-temperature risk index and its spatial distribution difference gradually decreases with increasing return period.In different cities,the high-temperature risk in the central area of the city is generally higher than that in the surrounding suburban areas.Jinhua,Hangzhou of Zhejiang Province and Xuancheng of Anhui Province are the top three cities with high-temperature risk in the study area.

The coupling of dynamics and permeability in the hydrocarbon accumulation period controls the oil-bearing potential of low permeability reservoirs:a case study of the low permeability turbidite reservoirs in the middle part of the third member of Shahejie

The relationships between permeability and dynamics in hydrocarbon accumulation determine oil- bearing potential （the potential oil charge） of low perme- ability reservoirs. The evolution of porosity and permeability of low permeability turbidite reservoirs of the middle part of the third member of the Shahejie Formation in the Dongying Sag has been investigated by detailed core descriptions, thin section analyses, fluid inclusion analyses, carbon and oxygen isotope analyses, mercury injection, porosity and permeability testing, and basin modeling. The cutoff values for the permeability of the reservoirs in the accumulation period were calculated after detailing the accumulation dynamics and reservoir pore structures, then the distribution pattern of the oil-bearing potential of reservoirs controlled by the matching relationship between dynamics and permeability during the accumulation period were summarized. On the basis of the observed diagenetic features and with regard to the paragenetic sequences, the reservoirs can be subdivided into four types of diagenetic facies. The reservoirs experienced two periods of hydro- carbon accumulation. In the early accumulation period, the reservoirs except for diagenetic facies A had middle to high permeability ranging from 10 × 10-3 gm2 to 4207 × 10-3 lain2. In the later accumulation period, the reservoirs except for diagenetic facies C had low permeability ranging from 0.015 × 10-3 gm2 to 62× 10-3 -3m2. In the early accumulation period, the fluid pressure increased by the hydrocarbon generation was 1.4-11.3 MPa with an average value of 5.1 MPa, and a surplus pressure of 1.8-12.6 MPa with an average value of 6.3 MPa. In the later accumulation period, the fluid pressure increased by the hydrocarbon generation process was 0.7-12.7 MPa with an average value of 5.36 MPa and a surplus pressure of 1.3-16.2 MPa with an average value of 6.5 MPa. Even though different types of reservoirs exist, all can form hydrocarbon accumulations in the early accumulation per- iod. Such types of reservoirs can form hydrocarbon accumulation with high accumulation dynamics; however, reservoirs with diagenetic facies A and diagenetic facies B do not develop accumulation conditions with low accumu- lation dynamics in the late accumulation period for very low permeability. At more than 3000 m burial depth, a larger proportion of turbidite reservoirs are oil charged due to the proximity to the source rock, Also at these depths, lenticular sand bodies can accumulate hydrocarbons. At shallower depths, only the reservoirs with oil-source fault development can accumulate hydrocarbons. For flat surfaces, hydrocarbons have always been accumulated in the reservoirs around the oil-source faults and areas near the center of subsags with high accumulation dynamics.

Chinese Thoughts on domain on the value of standard during the period of social transition

values occupy an important position in the lives of the people, almost all the joy, happiness, sadness, unfortunately are related with the values. It pervades all aspects of social life, reflects the contradictions and conflicts of the various aspects. While Chinese society is undergoing a transformation of the special period, Social value orientation of instability makes further thought and exploration,in order to get a judgement conform to social development and human interests of social value standard.

SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.

Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral

We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.

EXISTENCE OF SOLUTIONS FOR PERIODIC BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.

PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

Research on goal-setting method of rock drivage based on the balance among period, cost and quality

On the basis of the analysis on the disadvantages of the original goal-setting about rock drivage, this paper defined the ＂life cycle quality＂. With project management theory and the Cobb-Douglas function, ＂quality-cost and quality-price curve model＂ and the ＂total cost-period prediction model＂ were built. Then the goal-setting method of the balance among quality, cost and period of rock drivage was constructed by finding ＂life cycle cost＂ through ＂life cycle quality＂ using ＂quality-cost and quality-price curve model＂ and ensuring period through ＂life cycle cost＂ using ＂total cost-period prediction model＂ （hereinafter referred to as the ＂three goals balance method＂）. ＂Value contribution＂ which is the value of the contribution to a mine because of rock drivage, was found in the process of constructing the ＂quality-cost and quality-price curve model＂. An industrial test was done in coal mine A with the research results, staff footage efficiency improved by 24.24%, the period shortened by 14.3%, the ＂life cycle cost＂ dropped by 2.09%, the ＂life cycle quality price＂ improved by 3.29%, and value contribution increased by 25.3%. The result shows that the new goal method setting on the basis of coal mine profit maximization can ensure construc- tion period. At the same time, it can realize cost and quality objectives and the optimization and balance of relationship among them; rewarding excavation teams by ＂value contribution＂ can combine organizational goal with personal goal, it significantly raise the employee＇s work efficiency.

Determining the time and space domains forestimating b value in seismic zoning

To take the seismic zone that includes the great shock with M S8.5 as the statistical unit of estimating b value can often lead to more large variance, because the seismogenic zone of the great shock with M S8.5 are larger than that delineated in general seismic zone. Two-level statistical units are considered in this paper. The seismic province is the first level unit that is suitable for group of earthquakes including the great shock of M S8.5. A seismic province can be divided into several seismic zones. They can be taken as the second level unit for group of quakes in which the super magnitude of the greatest shock do not exceed 8. Because of the nonstationarity in time of seismic activity, the unbalancedness of data and differential of seismic temporal series feature in different areas need to be considered when we select the time period for estimating b value. According to local conditions, the time period is selected at one′s discretion in order to reflect seismicity level of this statistical unit in future 100 years.

On Monotone Method for Second Order Periodic Boundary Value Problems and Periodic Solutions of Functional Difference Equations

In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β

带有Caratheodory函数的积分微分方程的周期边值问题

本文研究一类带有Caratheodory函数的二阶积分微分方程的周期边值问题，应用比较结果和单调迭代法证得最大解和最小解的存在性．

Projected Changes in Temperature and Precipitation Extremes over China as Measured by 50-yr Return Values and Periods Based on a CMIP5 Ensemble

Future changes in the 50-yr return level for temperature and precipitation extremes over China's Mainland are investigated based on a CMIP5 multi-model ensemble for RCP2.6, RCP4.5 and RCP8.5 scenarios. The following indices are analyzed： TXx and TNn （the annual maximum and minimum of daily annual maximum consecutive 5-day precipitation） and CDD maximum and minimum surface temperature）, RX5day （the （maximum annual number of consecutive dry days）. After first validating the model performance, future changes in the 50-yr return values and return periods for these indices are investigated along with the inter-model spread. Multi-model median changes show an increase in the 50-yr return values of TXx and a decrease for TNn, more specifically, by the end of the 21st century under RCP8.5, the present day 50-yr return period of warm events is reduced to 1.2 yr, while extreme cold events over the country are projected to essentially disappear. A general increase in RX5day 50-yr return values is found in the future. By the end of the 21st century under RCP8.5, events of the present RX5day 50-yr return period are projected to reduce to 〈 10 yr over most of China. Changes in CDD-50 show a dipole pattern over China, with a decrease in the values and longer return periods in the north, and vice versa in the south. Our study also highlights the need for further improvements in the representation of extreme events in climate models to assess the future risks and engineering design related to large-scale infrastructure in China.

EXACT SOLUTION FOR ORTHOTROPIC MATERIALS WEAKENED BY DOUBLY PERIODIC CRACKS OF UNEQUAL SIZE UNDER ANTIPLANE SHEAR

Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.

Periodic Boundary Value Problem for Functional Differential Equations with Impulses

Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.

Resources of Colored-leaf Trees and Their Phenological Ornamental Characteristics in Lhasa City

By using biological five points,expert consultation and fuzzy comprehensive evaluation,the species,phenological ornamental characteristics,and landscape application of colored-leaf trees in Lhasa City were surveyed systematically. The results show that there are 42 species of colored-leaf trees in Lhasa City,belonging to 31 genera and 18 families,of which there are 5,19,and 18 species of spring,autumn,and common colored-leaf trees,accounting for 11.90%,45.24% and 42.86% of total number of the investigated tree species respectively. It is clearly seen that there are too few species of spring colored-leaf trees in the city. There are 19 and 17 species of trees possessing red and yellow leaves,while the leaves of other 6 species of colored-leaf trees are shown in other colors,and the number of their species accounts for 45.24%,40.48% and 14.28% of total number of the investigated tree species respectively. The best ornamental periods of spring,autumn and common colored-leaf trees in Lhasa City average 38.4,41.8 and 251.8 d respectively. Prunus cerasifera Ehrhar f. atropurpurea Rehd.,Ulmus pumila L.,Populus × beijingensis W. Y. Hsu,and Salix alba are applied most frequently in Lhasa City,and their relative frequency is 18.67%,10.29%,9.91% and 8.95% respectively. According to the comprehensive assessment value of their ornamental characteristics,the ornamental characteristics of 15 species of colored-leaf trees in Lhasa City are good or very good,and there is a positive correlation between the comprehensive assessment value and relative frequency. Based on the investigation,the current application situation and problems of colored-leaf trees in Lhasa City were analyzed,and solutions to the problems were proposed.