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.

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

General Patterns of Spatial Distribution of the Integral Characteristics of Benthic Macrofauna of the Northwestern Pacific and Biological Structure of Ocean

Horizontal (geographic) and vertical (geonemic) spatial distribution of the integral properties of a large multispecies assemblage (1306 species of fish and invertebrate with body size ≥ 1 cm) from northwest Pacific sea bottom is investigated. There are total number and biomass, average animal size (mean individual weight), species diversity (Shannon’s index) and its components: species richness and evenness (Pielou’s index), i.e. generalized parameters describing benthic macrofauna as a whole. Correlations of these parameters with distance from shore and depth have been found as well as very weak latitudinal zonality display in the region. Even such well-known generalization as Humboldt-Wallace’s law and Bergman’s rule has no noticeable manifestations here. Earlier similar, but not identical, regularities were discovered in the northwest Pacific pelagic water layer. Collation of what there is in the two different sea zones results in new supplements to Zenkevich-Bogorov’s concept of biological structure of the ocean.

On the Equiconvergence of the Fourier Series and Integral of Distributions

We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.

An Integratable Distributed Bragg Reflector Laser by Low-Energy Ion Implantation Induced Quantum Well Intermixing

An integratable distributed Bragg reflector laser is fabricated by low energy ion implantation induced quantum well intermixing.A 4 6nm quasi continuous wavelength tuning range is achieved by controlling phase current and grating current simultaneously,and side mode suppression ratio maintains over 30dB throughout the tuning range except a few mode jump points.

概率积分integral from n=(-∞) to (+∞)(1/(2π)～(1/2)·e^(x^2/2))dx=1的多种证明

利用变量代换、微分中值定理、概率性质等方法 。

THE EVOLUTION OF SETTLEMENT LOCATION AND DISTRIBUTION IN URBAN-RURAL INTEGRATION

ＴＨＥＥＶＯＬＵＴＩＯＮＯＦＳＥＴＴＬＥＭＥＮＴＬＯＣＡＴＩＯＮＡＮＤＤＩＳＴＲＩＢＵＴＩＯＮＩＮＵＲＢＡＮＲＵＲＡＬＩＮＴＥＧＲＡＴＩＯＮＬｉａｏＲｏｎｇｈｕａ（廖荣华）ＣｈｅｎＸｉａｎｇｍａｎ（陈湘满）ＤｅｐａｒｔｍｅｎｔｏｆＧｅｏｇｒａｐｈｙ...

Distributed optimization of electricity-Gas-Heat integrated energy system with multi-agent deep reinforcement learning

The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high cost of communication and complex modeling.Meanwhile,the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency,which is difficult to apply online.For the coordinated optimization problem of the electricity-gas-heat IES in this study,we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient.Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization,dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy.Compared with centralized optimization,the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication.The proposed method considers the dual uncertainty of renewable energy and load in the training.Compared with the traditional iterative solution method,it can better cope with uncertainty and realize real-time decision making of the system,which is conducive to the online application.Finally,we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.

Benefit allocation model of distributed photovoltaic power generation vehicle shed and energy storage charging pile based on integrated weighting-Shapley method

In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley integrated-empowerment benefit-distribution method.First,through literature survey and expert interview to identify the risk factors at various stages of the project,a dynamic risk-factor indicator system is developed.Second,to obtain a more meaningful risk-calculation result,the subjective and objective weights are combined,the weights of the risk factors at each stage are determined by the expert scoring method and entropy weight method,and the interest distribution model based on multi-dimensional risk factors is established.Finally,an example is used to verify the rationality of the method for the benefit distribution of the charging-pile project.The results of the example indicate that the limitations of the Shapley method can be reasonably avoided,and the applicability of the model for the benefit distribution of the charging-pile project is verified.

PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION

A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito＇ s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.

Four distributed feedback laser array integrated with multimode-interference and semiconductor optical amplifier

Monolithic integration of four 1.55-μm-range InGaAsP/InP distributed feedback （DFB） lasers using varied ridge width with a 4 x 1-multimode-interference （MMI） optical combiner and a semiconductor optical amplifier （SOA） is demon- strated. The average output power and the threshold current are 1.8 mW and 35 mA, respectively, when the injection current of the SOA is 100 mA, with a side mode suppression ratio （SMSR） exceeding 40 dB. The four channels have a 1-nm average channel spacing and can operate separately or simultaneously.

Torque Distribution Strategy for Integrated Starter/ Generator Hybrid Bus Implemented by Fuzzy Algorithm

A torque distribution strategy was designed by using fuzzy logic to realize the optimal control. The vehicle load zones were dynamically divided into several zones by several torque lines to indicate the drivers demand and the high or low efficient operating areas of the diesel engine. The fuzzy logic controller with trapezoid membership function and Mamdani rule reference mechanism was utilized. There are over 100 rules used in this fuzzy-based torque distribution strategy which are sorted into four rule-bases. The fuel economy and acceleration tests were designed to test and validate the integrated starter/generator (ISG) bus perfor-mance using fuzzy-based torque distribution strategy. The fuel economy is improved 7.7% compared with the rule-based strategy. Finally the road test results reveal that there is about 15% improvement of fuel economy. And the 0-50 km/h acceleration time is 9.5% shorter than the original bus.

Key technologies for the novel distributed numerical control integrated system

A novel distributed numerical control (DNC) integrated system based on plug-in software technology is proposed. It connects new or old numerical control (NC) machine tools which have inhomogeneous numerical control systems with CAD/CAM system by CANbus network. A DNC computer is able to control 15 sets of NC machine tools reliably at the same time. The novel DNC system increases the efficiency of machine tools and improve the production management level by realizing non-paper production, agile manufacturing, networked manufacturing and so on in the near future. Key technologies to construct the novel DNC integrated system include the integration of inhomogeneous numerical control systems, NC program restart, and algorithm for communication competition. Such system has demonstrated successful applications in some corporations that have acquired good economic benefits and social effects.

Thermal integrity profiling of cast-in-situ piles in sand using fiber-optic distributed temperature sensing

Defects in cast-in-situ piles have an adverse impact on load transfer at the pile‒soil interface and pile bearing capacity. In recent years, thermal integrity profiling (TIP) has been developed to measure temperature profiles of cast-in-situ piles, enabling the detection of structural defects or anomalies at the early stage of construction. However, using this integrity testing method to evaluate potential defects in cast-in-situ piles requires a comprehensive understanding of the mechanism of hydration heat transfer from piles to surrounding soils. In this study, small-scale model tests were conducted in laboratory to investigate the performance of TIP in detecting pile integrity. Fiber-optic distributed temperature sensing (DTS) technology was used to monitor detailed temperature variations along model piles in sand. Additionally, sensors were installed in sand to measure water content and matric suction. An interpretation method against available DTS-based thermal profiles was proposed to reveal the potential defective regions. It shows that the temperature difference between normal and defective piles is more obvious in wet sand. In addition, there is a critical zone of water migration in sand due to the water absorption behavior of cement and temperature transfer-induced water migration in the early-age concrete setting. These findings could provide important insight into the improvement of the TIP testing method for field applications.

Spacial Distribution Characteristics, Activity and Degradation Capability of the Biofilm in Integrated Vertical-flow Constructed Wetland

The spacial distribution characteristics, activity and degradation capability of the biofilm in integrated vertical-flow constructed wetland were investigated. Results showed that the biofilm widely distributed in the substrate of integrated vertical-flow constructed wetland and mainly in the 0-10 cm top layer where the activity ofdehydrogenase of the biofilm was also higher than that of other layers. The water quality could also affect the activity of the biofilm, for the TF（1,3,5-Triphenylformazan） amount reduced by the biofim incubated in water of the higher eutrophication was larger, too. The PCP （pentachlorophenol） removal rate by the substrate with biofilm was 1.5 times that without biofilm. In total, the biofilm of the down-flow chamber appeared larger biomass, higher dehydrogenase activity and stronger degradation capability of organic contamination than that in up-flow chamber and it was the major place for removal of the organic matters in waste water.

Integrated approach for understanding spatio-temporal changes in forest resource distribution in the central Himalaya

Intense anthropogenic exploitation has altered distribution of forest resources. This change was analyzed using visual interpretation of satellite data of 1979, 1999 and 2009. Field and interactive social surveys were conducted to identify spatial trends in forest degradation and data were mapped on forest cover and land use maps. Perceptions of villagers were compiled in a pictorial representation to understand changes in forest resource distribution in central Himalaya from 1970 to 2010. For- ested areas were subject to degradation and isolation due to loss of con- necting forest stands. Species like Lantana camara and Eupatorium adenophorum invaded forest landscapes. Intensity of human pressure differed by forest type and elevation. An integrated approach is needed to monitor forest resource distribution and disturbance.

Fire Distribution of Integrated Missile-gun Air Defense System Based on Earlier Damage Criterion

The fire distribution can be divided into weapon assignment and firing time scheduling. The criterion of weapon allocation is that a target with greater threat has higher priority. And the criterion of firing time scheduling is that a target can be damaged with the expected probability before a specific time. A fire distribution scheme and a program for the integrated missile-gun air defense system based on a criterion of earlier damage were presented. An example was taken to illustrate its effectiveness.

Path integral Monte Carlo study of(H_2)_n@C_(70)(n = 1, 2, 3)

The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.

Integrated and Unintegrated Parton Distributions

We compare the twist-2 and twist-4 parton distributions both in integrated and unintegrated parton distributions. We find that when x decreases the difference between the twist-2 and twist-4 patton distributions become obvious except for the valence quark distributions. We hope the future experiments may distinguish whether the twist-4 correction is needed or not and select a reasonable unintegrated parton distribution model

Phase Space Path Integral Representation for Wigner Function

Quantum interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperatures and under extreme conditions. In this work we have generalized the path integral representation for Wigner function to strongly coupled three-dimensional quantum system of particles with Boltzmann and Fermi statistics. In suggested approach the explicit expression for Wigner function was obtained in harmonic approximation and Monte Carlo method allowing numerical calculation of Wigner function, distribution functions and average quantum values has been developed. As alternative more accurate single-momentum approach and related Monte Carlo method have been developed to calculation of the distribution functions of degenerate system of interacting fermions. It allows partially overcoming the well-known sign problem for degenerate Fermi systems.