Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

Characterizing large-scale weak interlayer shear zones using conditional random field theory

The shear behavior of large-scale weak intercalation shear zones(WISZs)often governs the stability of foundations,rock slopes,and underground structures.However,due to their wide distribution,undulating morphology,complex fabrics,and varying degrees of contact states,characterizing the shear behavior of natural and complex large-scale WISZs precisely is challenging.This study proposes an analytical method to address this issue,based on geological fieldwork and relevant experimental results.The analytical method utilizes the random field theory and Kriging interpolation technique to simplify the spatial uncertainties of the structural and fabric features for WISZs into the spatial correlation and variability of their mechanical parameters.The Kriging conditional random field of the friction angle of WISZs is embedded in the discrete element software 3DEC,enabling activation analysis of WISZ C2 in the underground caverns of the Baihetan hydropower station.The results indicate that the activation scope of WISZ C2 induced by the excavation of underground caverns is approximately 0.5e1 times the main powerhouse span,showing local activation.Furthermore,the overall safety factor of WISZ C2 follows a normal distribution with an average value of 3.697.

ON A FAMILY OF CHEBYSHEV-HALLEY TYPE METHODS IN BANACH SPACE UNDER WEAKER SMALE CONDITION

In this paper, we discuss local convergence of a family of Chebychev Halley type methods with a parameter θ∈[0,1] in Banach space using Smale type δ criterion under 2 th γ condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.

Weak optimal inverse problems of interval linear programming based on KKT conditions

In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.

Prediction Research of Deformation Modulus of Weak Rock Zone under In-situ Conditions

Weak rock zone (soft interlayer, fault zone and soft rock) is the highlight of large-scale geological engineering research. It is an important boundary for analysis of rock mass stability. Weak rock zone has been formed in a long geological period, and in this period, various rocks have undergone long-term consolidation of geostatic stress and tectonic stress; therefore, under in-situ conditions, their density and modulus of deformation are relatively high. Due to its fragmentary nature, once being exposed to the earth's surface, the structure of weak rock zone will soon be loosened, its density will be reduced, and its modulus of deformation will also be reduced significantly. Generally, weak rock zone can be found in large construction projects, especially in the dam foundation rocks of hydropower stations. These rocks cannot be eliminated completely by excavation. Furthermore, all tests nowadays are carried out after the exposure of weak rock zone, modulus of deformation under in-situ conditions cannot be revealed. In this paper, a test method explored by the authors has been introduced. This method is a whole multilayered medium deformation method. It is unnecessary to eliminate the relatively complete rocks covering on weak rock zone. A theoretical formula to obtain the modulus of deformation in various mediums has also been introduced. On-site comparative trials and indoor deformation modulus tests under equivalent density conditions have been carried out. We adopted several methods for the prediction researches of the deformation modulus of weak rock zone under in-situ conditions, and revealed a fact that under in-situ conditions, the deformation modulus of weak rock zone are several times higher than the test results obtained after the exposure. In a perspective of geological engineering, the research findings have fundamentally changed peoples' concepts on the deformation modulus of weak rock zone, provided important theories and methods for precise definition of deformation modulus of deep weak rock zone under cap rock conditions, as well as for reasonable engineering applications.

LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

Effective Boundary Conditions for the Heat Equation with Interior Inclusion

Of concern is the scenario of a heat equation on a domain that contains a thin layer,on which the thermal conductivity is drastically different from that in the bulk.The multi-scales in the spatial variable and the thermal conductivity lead to computational difficulties,so we may think of the thin layer as a thickless surface,on which we impose"effective boundary conditions"(EBCs).These boundary conditions not only ease the computational burden,but also reveal the effect of the inclusion.In this paper,by considering the asymptotic behavior of the heat equation with interior inclusion subject to Dirichlet boundary condition,as the thickness of the thin layer shrinks,we derive,on a closed curve inside a two-dimensional domain,EBCs which include a Poisson equation on the curve,and a non-local one.It turns out that the EBCs depend on the magnitude of the thermal conductivity in the thin layer,compared to the reciprocal of its thickness.

High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.

One Parameter Family of N-Qudit Werner-Popescu States: Bipartite Separability Using Conditional Quantum Relative Tsallis Entropy

The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.

采动力学与岩层控制关键理论及工程应用

研究岩体采动力学响应和岩层控制技术对促进煤炭安全高效开采、保障能源稳定供给具有重要意义,是实现煤炭资源科学开采的理论基础。矿山岩体灾害(围岩变形、冲击地压等)频发,其形成-演化-发生全过程与采动力演化分布、岩层运动、开采扰动和能量演化密切相关。基于实用矿山压力控制理论,提出并阐述了采场岩层控制进展与控制准则,建立了定量分析的力学模型和设计方法,发展了针对性的岩体灾害控制技术,并创新研制了配套试验研究装备。采动力学与岩层控制理论将岩层控制分为采场岩层控制和巷道围岩控制;提出控制或利用采动岩层运动改变致灾条件,给出“给定变形”和“限定变形”准则;调控“3S”因素准则(围岩应力环境、围岩结构属性、围岩支护结构)改变围岩自稳能力。以岩体灾害控制为目标,提出了以“应力主控”为核心的释能主控技术;建立了岩体灾害控制大小原理和弱面判据(安全系数K、冲击危险性系数U);研发了采场矿压机械模拟试验系统、采动力试验系统和蠕变及动力扰动冲击加载试验系统,实现了实验室尺度还原采动力作用下岩体变形-破裂-运动过程,为研究采动力作用下岩体力学响应提供了试验装备;分别从采场岩层控制、地质软岩巷道控制、工程软岩巷道控制及冲击地压控制4个方向进行了工程案例研究,相关研究成果在工程应用中得到了验证。

地铁车站弱电设备间设备发热量确定方法

介绍了一种地铁车站弱电设备间设备发热量确定新方法,该方法利用弱电设备发热量实测数据与模型预测数据相互验证,可以有效提高弱电设备发热量确定结果的准确性。研究了室内气温、地铁是否运营、设备额定功率和车站类型等因素对设备发热量的影响。研究结果表明:基于间接测量和预测模型的地铁车站弱电设备间设备发热量确定方法可以提高和保障设备发热量计算结果的准确性;室内气温会显著影响设备外表面和围护结构内表面温度及围护结构内表面热流密度,但对设备外表面热流密度的影响较小;地铁是否运营对弱电设备间设备发热量有较大影响,地铁运营期间设备发热量大于非运营期间;设备额定功率对弱电设备间设备发热量峰值有较大影响,车站类型和建筑面积对设备发热量峰值的影响很小。

有限元强度折减法分析软基边坡稳定性

有限元强度折减法在均质土坡和岩石边坡中已有较多的研究和应用,但应用到强度较低的软基边坡,其模型网格划分和边界条件,与均质边坡有所不同。经对比研究得出软基边坡模型的网格节点密度达到每米2点较为适宜,模型边界应以修正后的坡高H来界定。结合具体工程案例,利用有限元强度折减法复核其稳定,并与极限平衡法进行了对比,结果表明前述网格划分和模型边界设置较为适宜,且有限元强度折减法可以较好的反映边坡应力应变分布。

基于定位收缩法的局部阴影条件下光伏最大功率点跟踪

光伏最大功率点跟踪是提高光伏发电效率的重要手段。在局部阴影条件下,光伏阵列的特性曲线呈现多峰形状,常规的传统算法容易陷入局部最优。如何在局部阴影条件下找到全局最大功率点(global maximum power point,GMPP)至关重要。提出了一种定位收缩法(locate and shrink algorithm,LSA),采用收缩边界的思想使得边界逐渐收缩到GMPP。LSA第一阶段提出了一种峰的定位方法,通过自适应采样结合I-V特性曲线能够定位主要峰的占空比范围。定位法能够与其他单峰算法结合,具有较强的扩展性。第二阶段提出了一种基于三点准则的收缩法,能够在单峰范围内通过收缩边界快速找到峰值点,并且具有很强的环境适应性。将LSA与多个算法进行仿真和硬件实验对比,结果表明LSA在跟踪速度、跟踪精度和稳态振荡方面有着明显优势。

基于t检验和逐步网络搜索的有向基因调控网络推断算法

为了克服基于条件互信息的路径一致算法(PCA-CMI)无法识别调控方向的缺陷,并进一步提高网络推断准确率,提出了一种基于t检验和逐步网络搜索的有向网络推断算法(DNI-T-SRS)。首先,对不同实验条件下的表达数据进行t检验以辨别基因调控的上下游关系,指导路径一致(Path Consensus)算法中条件基因的选取,根据CMI2(Conditional Mutual Inclusive Information)剔除网络中的冗余边,得到了基于t检验的有向调控关系推断算法CMI2NI-T(CMI2-based Network Inference guided by t-Test);然后,建立有向调控关系对应的米氏微分方程模型对数据进行拟合,根据贝叶斯信息准则进行逐步网络搜索以修正网络推断结果。利用CMI2NI-T推断DREAM6挑战中的两个测试网络,所得到的曲线下面积(AUC)分别为0.7679和0.9796,相较于PCA-CMI分别提高了16.23%和11.62%;通过进一步的数据拟合后DNI-T-SRS的推断准确率分别达到了86.67%和100.00%,相较于PCA-CMI分别提高了18.19%和10.52%。实验结果表明,所提DNI-T-SRS算法能够有效剔除间接调控关系并保留直接调控连接,得到精确的基因调控网络推断结果。

高效的一次性弱间隙序列模式挖掘算法

间隙约束序列模式挖掘作为序列模式挖掘的一个重要分支,可以发现模式在序列中的重复出现。然而,当前研究主要针对单项序列进行挖掘,并且序列中每一项都被认为具有相同意义。为解决该问题,提出一次性弱间隙序列模式挖掘(OWP)算法,该算法由准备阶段、支持度计算和候选模式生成3个步骤组成。在准备阶段,建立倒排索引,并对不频繁的项进行剪枝;在支持度计算方面,利用倒排索引结构记录出现位置,避免对原始数据集的重复扫描;在候选模式生成方面,采用模式连接策略,减少冗余候选模式的生成。在项集序列和单项序列共6个真实数据集上的实验结果表明,OWP算法相比OWP-p、Ows-OWP和OWP-e算法在运行时间上分别提升了2.653、1.348、3.592倍,在内存消耗上分别减少了3.51%、0.07%、5%,说明OWP算法可以更高效地挖掘出用户感兴趣的模式。此外,OWP算法在以D1数据集为基础的6倍大小的数据集上的运行时间比D1数据集增长了3.763倍,内存消耗增长了2.310倍,运行时间和内存消耗的增加倍数均小于数据集大小的增加倍数,说明OWP算法具有良好的可扩展性。