THE UPWIND OPERATOR SPLITTING FINITE DIFFERENCE METHOD FOR COMPRESSIBLE TWO-PHASE DISPLACEMENT PROBLEM AND ANALYSIS

For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.

A Class of Preconditioners Based on Positive-Definite Operator Splitting Iteration Methods for Variable-Coefficient Space-Fractional Diffusion Equations

After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized matrix.Moreover,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive constant.Meanwhile,the iteration methods introduce a new preconditioner for Krylov subspace methods.Numerical experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.

Operator Splitting Method for Coupled Problems:Transport and Maxwell Equations

In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.

OPERATOR-SPLITTING GALERKIN METHOD FOR ONE KIND OF OIN REACTION MODEL FOR THE POLLUTION IN GROUNDWATER

The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.

The Operator Splitting Method for Black-Scholes Equation

The Operator Splitting method is applied to differential equations occurring as mathematical models in financial models. This paper provides various operator splitting methods to obtain an effective and accurate solution to the Black-Scholes equation with appropriate boundary conditions for a European option pricing problem. Finally brief comparisons of option prices are given by different models.

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H;: Ux = x} and F（T） = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.

THREE HIGH-ORDER SPLITTING SCHEMES FOR 3D TRANSPORT EQUATION

Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.

Design Energy Efficient Water Utilization Systems Allowing Operation Split

这篇文章处理允许操作的有效的水利用系统切开了的精力的设计。象操作灵活性和基本投资那样的实际特征使潜水艇操作的数字成为了这个问题的一个重要参数。由独立对待直接、间接的传热，象操作一样的目标淡水和能量消耗切开了条件首先被获得。随后，一个混合整数非线性的编程(MINLP ) 模型为水网络和热空气冷却换热器网络(母鸡) 的设计被建立。建议系统的途径被限制到单个沾染物。从文学的例子被用来说明途径的适用性。

Schemes for Splitting Quantum Information with Four-Particle Genuine Entangled States

我们为由把四粒子的真纠缠的状态用作量隧道切开 single-qubit 和 two-qubit 状态建议二个计划。在发送者执行钟基础以后(或三深裂的 GHZ- 基础) 她的粒子上的大小，和合作者在他们的粒子上操作单个粒子的大小，州的接收装置能重建由使用适当单一的操作的发送者的原来的状态。在为切开 two-qubit 状态的计划，特别地，接收装置需要介绍一个辅助粒子并且执行一 C 不操作。

Hierarchical and probabilistic quantum information splitting of an arbitrary two-qubit state via two cluster states

Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements,and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement（POVM） instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.

Fourth-Order Splitting Methods for Time-Dependant Differential Equations

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.

Simplified Four-Qubit Cluster State for Splitting Arbitrary Single-Qubit Information

简化 four-qubit 簇状态(即，(| 0000 +| 0011 +| 1100 -| 1111 )/2 ) 为切开一个任意的 single-qubit 量信息(QI ) 被探索。在为切开 tri 的 QI 发送者和接收装置之中的四 qubits 的各种各样的可行分布或切开双性人被发现。当其它简明地被提及时，为分发代表，相应切开计划和他们的 LOCC (本地操作和古典通讯) 充分地被介绍。

Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation

Deep neural network is a powerful tool for many tasks.Understanding why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past years.In the literature of mathematical analysis of deep neural networks,a lot of works is dedicated to establishing representation theories.How to make connections between deep neural networks and mathematical algorithms is still under development.In this paper,we give an algorithmic explanation for deep neural networks,especially in their connections with operator splitting.We show that with certain splitting strategies,operator-splitting methods have the same structure as networks.Utilizing this connection and the Potts model for image segmentation,two networks inspired by operator-splitting methods are proposed.The two networks are essentially two operator-splitting algorithms solving the Potts model.Numerical experiments are presented to demonstrate the effectiveness of the proposed networks.

河北省建筑运行碳排放分析及影响因素研究

为了研究建筑运行阶段的碳排放问题,首先,在碳排放因子法的基础上,根据能源平衡表拆分法建立建筑运行碳排放计算模型,通过2005—2020年河北省建筑运行碳排放数据分析其碳排放变化特征。其次,运用STIRPAT模型对建筑运行碳排放影响因素进行了实证分析。结果表明,研究期间河北省建筑运行阶段碳排放增长了1.24倍,间接碳排放在运行阶段碳排放中占据主导地位,而居民生活在建筑运行碳排放行业结构中占比最大,常住人口数量是河北省建筑运行碳排放的最主要驱动因素。

Propagation and Pinning of Travelling Wave for Nagumo Type Equation

In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population growth with Allee effect. An analytical solution is derived for the traveling wave and the work is extended to a discrete formulation with a piecewise linear reaction function. We propose an operator splitting numerical scheme to solve the equation and demonstrate that the wave either propagates or gets pinned based on how the spatial mesh is chosen.

非局部Gray-Scott模型的二阶线性化差分格式

研究周期边界条件下的非局部Gray-Scott模型,提出一种高效数值格式。基于算子分裂思想将原问题拆分为线性非局部子问题和非线性子问题。对于线性非局部子问题,结合复化梯形公式和Crank-Nicolson公式,建立时空二阶差分格式;对于非线性子问题,结合Crank-Nicolson公式及Rubin-Graves线性化技术,建立线性求解格式。结果表明:非局部Gray-Scott模型的二阶线性化差分格式具有稳定性、收敛性及有效性。

基于局部高斯分布模型的图像配准方法

提出了一种基于统计和变分相结合的非刚体图像配准新模型。假设残差图像服从具有不同均值和方差的局部高斯分布,由此得到一个双重能量泛函,再结合变分的正则化方法,得到了一种配准新模型。该方法的新颖之处在于,保真项中引入了权重函数和一些控制参数。其中权重函数可以自动有效地区分残差图像中灰度对比度不同的区域,控制参数的引入提高了算法的鲁棒性。合成图像、二维肺部CT及三维大脑MRI图像的配准结果证明了这一方法的有效性和准确性。

某办公建筑多联机空调系统设计及运行分析

为了掌握办公建筑多联机空调系统的运行情况,本文以郑州市某办公建筑为研究对象,介绍了多联机空调系统的设计,基于智慧运行平台、调研、测试数据,分析了典型房间室内温度、相对湿度,分析了多联机空调系统整体能耗、月能耗、典型日能耗特征。结果表明,该办公建筑存在下班未及时关闭空调的情况;供暖季典型房间室内温度高于设计温度;多联机空调系统全年空调建筑面积能耗强度为35.64 kW·h/m^(2);能耗强度具有明显的季节性,供暖季室外温度变化较大,能耗强度变化较大,制冷季室外温度变化较小,能耗强度变化较小。本研究为推广多联机空调系统提供参考。

基于运行大数据的长江流域家用多联机系统部分负荷运行特性分析

长江流域家用空调的运行特性一直是学者们关注的焦点,然而前期的研究一般以分体式的挂机或柜机为研究对象,针对家用多联机的部分负荷特性的研究相对缺乏。基于长江流域家用多联机的运行大数据,分别从冬夏两季、全时段、不同时段、不同城市多方面对该地区3个典型城市的部分负荷运行特性进行了量化分析;然后分析了对多联机系统功率的影响因素,并基于多种影响因素与机组运行功率的耦合关系,开发了系统功率的预测模型,基于该模型对家用多联机系统的节能潜力进行了讨论。研究结果表明:对于家用多联机系统,其夏季部分负荷率在30%~60%之间的占比最大,达到48.4%,其冬季部分负荷率小于30%的占比最大,达到59.7%;家用多联机系统在不同季节、不同城市、不同时段下的部分负荷特性均存在差异;与此同时,系统负荷需求和系统部分负荷率对系统功率的影响最大,基于本研究开发的系统功率预测模型,当负荷需求较低时,将18、16、14 kW的机组容量分别调整至16、14、12 kW后,夏季制冷模式功率下降了7%~13%,冬季制热模式功率下降了3%~22%,因此,对于在一定环境工况下低负荷运行时间占比较大的用户,适当匹配稍小的机组容量(提升部分负荷率),将有助于系统节能。该研究结论可为家用多联机的性能开发、运行控制逻辑优化、设备选型提供数据支撑与参考。

AN INDEFINITE-PROXIMAL-BASED STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD

The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requirements.He et al.(SIAM J.Optim.24:1011-1040,2014)proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a suitable underdetermined relaxation factor.In this paper,we further extend the so-called strictly contractive Peaceman-Rachford splitting method by using two different relaxation factors.Besides,motivated by the recent advances on the ADMM type method with indefinite proximal terms,we employ the indefinite proximal term in the strictly contractive Peaceman-Rachford splitting method.We show that the proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is convergent and also prove the o(1/t)convergence rate in the nonergodic sense.The numerical tests on the l 1 regularized least square problem demonstrate the efficiency of the proposed method.