Influence of confined water on the limit support pressure of tunnel face in weakly water-rich strata

In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.

LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT

In this article, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d, random environments.

Upper-bound limit analysis based on the natural element method

The natural element method （NEM） is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.

Limit Analysis for the Mechanical Structure of the ITER Neutron Shielding Block

The ITER neutron shielding blocks are located between the inner shell and the outer shell of the vacuum vessel （VV） with the main function of providing neutron shielding. Conskicring the combined loads of the shielding blocks during the plasma operation of the ITER, limit analysis for one typical ferromagnetic （FM） shielding block has been performed and the structural design has bccn evaluated based on the American Society of Mechanical Engineers （ASME） criterion and European standards. Results show that the collapse load of this shielding block is three times the specified load, which is much higher than the design requirement of 1.25. The structure of this neutron shielding block has a sufficient safety margin.

A Recursive Algorithm for Offspring's Genotype Frequency of Selfing Population on Multiple Alleles with Limited Loci

This paper studies the offspring＇s genotype frequency of the selfing population on multiple alleles with limited loci.A recursive algorithm is given for it.It is discovered that the genotype frequency of homozygous gene of limited loci increases by generations.Relative increment reduces by generations and the genotype frequency tends to a definite value finally.The genotype frequency of limited loci with hybrid gene tends to 0 finally.But it is possibility that the genotype frequency increases in previous generations then reduces later.It is found that the number of the hybrid gene are more,the speeds tending to 0 are quicker.

Climatic envelope of evergreen sclerophyllous oaks and their present distribution in the eastern Himalaya and Hengduan Mountains

Evergreen sclerophyllous oaks （the E.S. oaks, Quercus section Heterobalanus） are the dominant species of the local ecosystem in the eastern Himalaya and the Hengduan Mountains, southwest China. In this study, we document the climatic envelope of the seven E.S. oak species and examine the relationships between climate and their distribution. This was done using a principal components analysis （PCA） and multiple regression analysis （MRA） of nine climatic indices. The main climatic envelope of the E.S. oaks were： mean temperature of the warmest month （MTW）= 12.0-19.5℃, warmth index （WI） = 33.2-88.9℃ month, annual biotemperature （BT）=-6.9- -0.3 ℃, coldness index （CI）=-30.4- -10.1 ℃ month, mean temperature of the coldest month （MTC）=-3.7-3.0℃ and annual precipitation （AP）=701-897 mm at the lower limits; and MTW=8.3-16.1℃, WI=15.7-59.1℃ month, BT=3.6-8.9℃, CI=-55.4-19.3℃ month, MTC=8.3-16.1 ℃ and AP=610-811 mm at the upper limits. The climatic range of the E.S. oaks is wide and includes two climatic zones, the cool-temperature zone and the subpolar zone. The PCA and MRA results suggest that the thermal climate plays a major role and precipitation plays a secondary role in controlling the large-scale distribution of the E.S. oaks, except Quercus monimotricha. In thermal regimes, BT and/or MTW are most important for both lower and upper limits of the E.S. oaks. Furthermore, our results indicate that the upper distribution limits of the E.S. oaks are less determined by low temperatures and their duration （CI） than by other factors.

Effects of the phase variation and high-order momentum transfer components of NN amplitude on p-~4He elastic scattering

Elastic scattering differential cross sections for a p- ~4He system are calculated within the framework of optical limit approximation of the Glauber multiple scattering model. Three different ranges for proton energy(E_(lab)), 19〈E_(lab)〈50 Me V, 100≤E_(lab)≤1730 Me V, and 45 ≤E_(lab)≤393 Ge V are considered. It is shown that the Pauli blocking fails to describe the data up to the proton energy, E_(lab)〈100 Me V. For higher proton energies, a qualitative agreement is obtained. The observed elastic scattering differential cross section is nicely reproduced in the whole range of scattering angles in the center of mass system up to Θ_(c.m.)〈200° for 19〈E_(lab) ≤100 Me V when the effect of both the nucleon–nucleon(NN) phase variation parameter γNN and higher-order momentum transfer components(λ_n; n = 1 and 2) of(NN) elastic scattering amplitude is included. In the range of 200 E_(lab) 1730 Me V, introducing λ_n plays a significant role in describing the data up to the momentum transfer, q^2≤1:2(Ge V/c)~2.Moreover, it is found that considering only the effect of phase variation parameter, cNN, improved the agreement in the region of minima for elastic scattering differential cross section for 45≤E_(lab)≤393 Ge V. The values of cNNand kn as a function of incident proton energies are presented.

Iterative and adjusting method for computing stream function and velocity potential in limited domains and convergence analysis

The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.

On the Smarandache LCM Sequence

For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n^k),and give some interesting relevant results.

Multiple solutions and fermion mass effect in QED_3

Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics （QCD） is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models which can be applied to Fermi acting-energy between quark and gluon. This paper applies quantum electrodynamics in 2 ＋ 1 dimensions （QED3） to the Fermi condensation problems. First, the Dyson-Schwinger equation which the fermions satisfy is constructed, and then the Fermi energy gap is solved. Theoretical calculations show that within the chirality limit, there exist three solutions for the energy gap; beyond the chirality limit, there are two solutions; all these solutions correspond to different fermion condensates. It can be concluded that the fermion condensates within the chirality limit can be used to analyze the existence of antiferromagnetic, pseudogap, and superconducting phases, and two fermion condensates are discovered beyond the chirality limit.

PLASTIC LIMIT LOAD ANALYSIS OF DEFECTIVE PIPELINES

The integrity assessment of defective pipelines represents a practically important task of structural analysis and design in various technological areas,such as oil and gas indus- try,power plant engineering and chemical factories.An iterative algorithm is presented for the kinematic limit analysis of 3-D rigid-perfectly plastic bodies.A numerical path scheme for radial loading is adopted to deal with complex multi-loading systems.The numerical procedure has been applied to carry out the plastic collapse analysis of pipelines with part-through slot under internal pressure,bending moment and axial force.The effects of various shapes and sizes of part-through slots on the collapse loads of pipelines are systematically investigated and evaluated.Some typical failure modes corresponding to different configurations of slots and loading forms are studied.

DUAL RANDOM MODEL OF INCREASING LIFE INSURANCE FOR MULTIPLE-LIFE STATUS

In this paper the dual random model of increasing life insurance for multiple-life status is discussed.The mth moment of the present value of benefits are calculated and the respective expressions of the moments under joint life status or last- survivor status are presented.Fur-thermore,the limiting distribution of average cost of a portfolio of increasing life insurance for multiple-life status is studied.

New ex vivo demyelination/remyelination models to defeat multiple sclerosis and neuromyelitis optica

Multiple sclerosis (MS) and neuromyelitis optica (NMO) are inflammatory diseases of the central nervous system (CNS) resulting in CNS inflammation, infiltration of peripheral immune cells, loss of myelin and oligodendrocytes, interruption of axonal communication, and neurologic deficits. Following oligodendrocyte injury, newly generated myelinating oligodendrocytes derived from oligodendrocyte progenitors (OPCs) may produce new myelin sheaths around denuded axons (remyelination) restoring neuronal function (Verden and Macklin, 2016). While remyelination is apparent in MS lesions, the process is often inefficient;in NMO, remyelination is even more limited.

LIMIT OF ITERATES FOR BERNSTEIN POLYNOMIALS DEFINED ON A TRIANGLE

Let f ∈ C[0,1] , and Bn(f,x) be the n-th Bernstein polynomial associated with function f. In 1967, the limit of iterates for Bn(f,x) was given by Kelisky and Rivlin. After this, Many mathematicians studied and generalized this result. But anyway, all these discussions are only for univariate case. In this paper, the main contribution is that the limit of iterates for Bernstein polynomial defined on a triangle is given completely.

Multiple Schubert's Updating Matrix and Its Compact Representation

Schubert's method for solving systems of sparse equations has achieved a great deal of computational success. In this paper, Schubert's method was extended to multiple version, and the compact representation of multple Schubert's updating matrix was derived. The compact representation could be used to efficiently implement limited memory methods for large problems.

SINR-BASED ANTENNA COMBINING FOR MULTIUSER MIMO-OFDM WITH LIMITED FEEDBACK

A multiuser Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) broadcast channel is considered where both transmitter and receivers are equipped with multiple antennas. The Channel State Information (CSI) is quantized and provided through limited feedback links. In the first part of this work, the Maximum Expected SINR Combining (MESC) strategy for feedback decrease is investigated. Then a combination of MESC with subcarrier assigning is presented to further reduce the feedback load. The basic idea is the subcarriers are partitioned into resource blocks. For each block, only one quantized channel vector is feedback. The simulation results show MESC can obtain the performance gain over the relevant combiner strategies in MIMO-OFDM system. Moreover the effectiveness on the reduction of feedback overhead by the use of partitioning blocks in the studied system is evaluated.

Sequential Approach with Matrix Framework for Various Types of Economic Thermal Power Dispatch Problems

This paper presents a sequential approach with matrix framework for solving various kinds of economic dispatch problems. The objective of the economic dispatch problems of electrical power generation is to schedule the committed generating units output so as to meet the required load demand while satisfying the system equality and inequality constraints. This is a maiden approach developed to obtain the optimal dispatches of generating units for all possible load demands of power system in a single execution. The feasibility of the proposed method is demonstrated by solving economic load dispatch problem, combined economic and emission dispatch problem, multiarea economic dispatch problem and economic dispatch problem with multiple fuel options. The proposed methodology is tested with different scale of power systems. The generating unit operational constraints are also considered. The simulation results obtained by proposed methodology for various economic dispatch problems are compared with previous literatures in terms of solution quality. Numerical simulation results indicate an improvement in total cost saving and hence the superiority of the proposed method is also revealed for economic dispatch problems.

Factors Influencing the Iterative Accuracy of Ground Water Level in Forecasting the Water Burst of Deep Drawdown Mines

The purpose of this paper is to discuss the influential factors of iteration accuracy when we use iteration to determine the numerical model for predicting water yield of deep drawdown mines and calculating the groundwater level. The relationship among the calculation error of groundwater level, the pumping rate, the limit of iteration convergence error, the calculation time, and the aquifer parameters were discussed by using an ideal model. Finally, the water yield of Dianzi iron mine was predicted using the testified numerical model. It is indicated that the calculation error of groundwater level is related to the limit of iteration convergence error, the calculation time and the aquifer parameters, but not to the pumping rate and the variation of groundwater level.

一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式

应用权函数的方法,Euler-Maclaurin求和公式,Abel部分求和公式及实分析技巧,求出了一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式.作为应用,考虑了特殊参数下不等式中最佳常数因子联系多参数的等价条件及一些特殊不等式.

THE MULTIPLICITY OF ZERO AND LIMIT CYCLES FOR ABEL EQUATIONS

In this paper we will investigate the multiplicity of zero solution for a class of Abel equation, and obtain better estimation on multiplicity than that given by Alwash and Lloyd for the equation of a certain form, and solve a conjecture posed by Ye Yanqian for the equation of another form. As a by-product, the considered equation may have at least four small amplitude limit cycles. The method of this paper is useful for computing the focal value of a critical point of focus type for polynomial system that can be transformed into Abel equation or Abel form.