Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Exploration of Methods for Preparation of Cattle Eyeball Paraffin Sections

[Objective] This study aimed to establish a new method for preparing paraffin sections of cattle eyebal s. [Method] The conventional method was used to prepare paraffin sections for cattle eyebal s in the control and a new method termed＆quot;opening a window on cornea and refixation＆quot; was used to prepare paraffin sections for cattle eyebal s in the treatment group. [Result] After the prepared specimens in the treatment group were fixed, it could be macroscopical y observed that retina and choroid were closely connected, with detachment occurring at a smal portion be-tween the two. According to the paraffin sections, it was microscopical y observed that the continuity of trabecular meshwork was intact, as wel as the continuity be-tween different layers of eyebal wal , without detachment between them, no retinal detachment, no shrinkage of each layer of tissue cells. [Conclusion] This study pro-vides a foundation for the basic research and pathological study of eyebal s.

AModel for the Optimization of the Shale Gas HorizontalWell Section Based on the Combination of Different Weighting Methods in the Frame of the Game Theory

Existing“evaluation indicators”are selected and combined to build a model to support the optimization of shale gas horizontal wells.Towards this end,different“weighting methods”,including AHP and the so-called entropy method,are combined in the frame of the game theory.Using a relevant test case for the implementation of the model,it is shown that the horizontal section of the considered well is in the middle sweet spot area with good physical properties and fracturing ability.In comparison with the FSI(flow scanner Image)gas production profile,the new model seems to display better abilities for the optimization of horizontal wells.

Study on Modification of the Misgav Ladach Method for Cesarean Section

cases of pregnant women scheduled for delivery by cesarean section were randomly assigned to 59 cases in modification group with modified Misgav Ladach technique, 57 cases in Misgav Ladach group with Misgav Ladach technique and 56 cases in Pfannenstiel group with Pfannenstiel technique from May to Dec. 1999. The modified points included: transversely incising the fascia 2 to 3 cm, then dividing it bluntly; without opening and dissociating the visceral peritoneum; two layers suturing of low transverse uterine incision; closing the skin by continuous suturing. Results showed the average delivery time in the modification group was (3.6±2.6) min and (5.7±2.9) min in the Misgav Ladach group ( P <0.05). Median operating time was (28.3±5.4) min in modification group compared with (27.5±6.5) min in the Misgav Ladach group ( P >0.05). Average blood loss was (128±35) ml in modification group compared with (212±147) ml in the Pfannenstiel group ( P <0.05). It was concluded that the modified Misgav Ladach technique not only preserved all advantages of Misgav Ladach method, but also had additional advantages, such as faster in delivering the fetus, less damage, easier mastering for obstetricians.

Application of Golden Section Method to Channel Transect Design

During the desing of channel transect,the paper brings forward golden section method,which is 0.618 methods.In order to reduce the calculation volume of the natural depth of water h 0 and bottomˉwidth b which apply trial calculation method and graphic method,and improve the calculate precision,the mathematical model has been built up,the writer combines example to explain the train of thought,the result shows that the calculation precision is high,the correctness is tested and verified by the result which is calculated by hand.It can be referred to the hydroelectric works.

Research on Design Method of the Full Form Ship with Minimum Thrust Deduction Factor

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique（SUMT） interior point method of Nonlinear Programming（NLP） was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

The Research of Urban Rail Transit Sectional Passenger Flow Prediction Method

This paper studies the short-term prediction methods of sectional passenger flow, and selects BP neural network combined with the characteristics of sectional passenger flow itself. With a case study, we design three different schemes. We use Matlab to realize the prediction of the sectional passenger flow of the Beijing subway Line 2 and make comparative analysis. The empirical research shows that combining data characteristics of sectional passenger flow with the BP neural network have good prediction accuracy.

Measurement of ^(232)Th(n,2n)^(231)Th reaction cross-sections at neutron energies of 14.1 MeV and 14.8 MeV using neutron activation method

In this study, the activation cross-sections were measured for ^(232)Th(n,2n)^(231)Th reactions at neutron energies of 14.1 and 14.8 MeV, which were produced by a neutron generator through a T(d,n)~4He reaction. Induced gamma-ray activities were measured using a low background gamma ray spectrometer equipped with a high resolution HPGe detector. In the cross-section calculations, corrections were made regarding the effects of gamma-ray attenuation, dead-time, fluctuation of the neutron flux, and low energy neutrons. The measured cross-sections were compared with the literature data, evaluation data(ENDF-B/VII.1, JENDL-4.0 and CENDL-3.1), and the results of the model calculation(TALYS1.6).

Efficient Calculation of the Radar Cross Section at the Interior Resonance by the Inverse Power Method

It is well known that the incorrect results will be given using either the electric or magnetic field integral equation to calculate the radar cross section (RCS) of a closed body at the interior resonance. In this paper, an effective iterative technique is used to correct the calculated surface current density from the electric field integral equation. The radar cross section is computed for an infinite conducting circular cylinder at the interior resonance, and the obtained results are in good agreement with the analytical results. The backscattering cross section of an infinite triangular cylinder in the vicinity of a resonant frequency is also calculated. It is shown that the presence method is efficient and accurate.

Solving multi-object radar cross section based on wide-angle parabolic equation method

Based on a Pade approximation, a wide-angle parabolic equation method is introduced for computing the multiobject radar cross section （RCS） for the first time. The method is a paraxial version of the scalar wave equation, which solves the field by marching them along the paraxial direction. Numerical results show that a single wide-angle parabofic equation run can compute multi-object RCS efficiently for angles up to 45 ° . The method provides anew and efficient numerical method for computation electromagnetics.

Two New Identification Methods for Encephalitozoon cuniculi on Tissue Section

[ Objective] The paper aimed to search new identification methods of Encephalitozoon cuniculi on tissue sections. [ Method] Using improved Gram staining method and methyl green pyronin staining method, the pathological sections of sick rabbits were stained and identified. [ Result] The pathological changes in brain tissue could be clearly observed on sections, but parasites were not examined in pathological brain tissues stained by common staining method. When the pathological section was stained by improved Gram staining method, the pathological changes in brain tissue were not ouly stained very clearly, but blue parasites were also found in brain tissues. The parasites in epithelioid cells were stained into purple ones by methyl green pyronin staining method. [ Conclusion] The im- proved Gram staining method and methyl green pyronin staining method performed good staining effects of E. cuniculi in pathological sections, which were conducive to rapid diagnosis of encephalitozoonosis in rabbit.

Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes

Tunnels are now an integral part of the infrastructure in major cities around the world. For many reasons, these tunnels have horseshoe-shaped cross-sections with round top and flat bottom. This paper presents some improvements to the use of the Hyperstatic Reaction Method-HRM for analysing tunnels with horseshoe-shaped cross-sections when these tunnels operate under the influence of earthquakes, particularly in cases when the tunnel lining is a continuous lining. The analysis used parameters of a tunnel from the Hanoi metro system, as well as parameters of the strongest earthquake that may occur in the central Hanoi area in the improved HRM and 2 D numerical methods using the ABAQUS software. On the basis of the results obtained, the paper gives conclusions about the HRM methodology when it is used to calculate tunnels that have horseshoe cross-sections operating under the influence of earthquakes.

Scaled radar cross section measurement method for lossy targets via dynamically matching reflection coefficients in THz band

In the terahertz band,the dispersive characteristic of dielectric material is one of the major problems in the scaled radar cross section(RCS)measurement,which is inconsistent with the electrodynamics similitude deducted according to the Maxwell’s equations.Based on the high-frequency estimation method of physical optics(PO),a scaled RCS measurement method for lossy objects is proposed through dynamically matching the reflection coefficients according to the distribution of the object facets.Simulations of the model of SLICY are conducted,and the inversed RCS of the lossy prototype is obtained using the proposed method.Comparing the inversed RCS with the calculated results,the validity of the proposed method is demonstrated.The proposed method provides an effective solution to the scaled RCS measurement for lossy objects in the THz band.

Generalized response displacement methods for seismic analysis of underground structures with complex cross section

The response displacement method(RDM)is recommended for the seismic analysis of underground structures in the transverse direction for many codes,including bases for design of structures-seismic actions for designing geotechnical works(ISO 23469)and code for seismic design of urban rail transit structures(GB 50909-2014).However,there are some obvious limitations in the application of RDM.Springs and the shear stress of the soil could be approximately evaluated for the structures having a simple cross section,such as rectangular and circular structures.It is necessary to propose simplified seismic analysis methods for structures with complex cross sections.This paper refers to the idea of RDM and proposes three generalized response displacement methods(GRDM).In GRDM1,a part of the soil surrounding a structure is selected to generate a generalized underground structure with a rectangular cross section,and the same analysis model as RDM is applied to analyze the responses of the structure.In GRDM2,a hollow soil model without a generalized structure is used to compute the equivalent load caused by the relative displacement of the soil,and the soil-structure interaction model is applied to calculate the responses of the structure.In GRDM3,a continuous soil model is applied to compute the equivalent load caused by the relative displacement and shear stress of the soil,and the soil-structure interaction model is applied to analyze the responses of the structure,which is the same as the model used in GRDM2.The time-history analysis method(THAM)is used to evaluate the accuracy of the proposed simplified methods.Results show that the error of GRDM1 is about 20%,while the error is only 5%for GRDM2 and GRDM3.Among the three proposed methods,GRDM3 has obvious advantages regarding calculation efficiency and accuracy.Therefore,it is recommended to use GRDM3 for the seismic response analysis of underground structures that have conventional simple or complex cross sections.

An effective method to calculate the electron impact excitation cross sections of helium from ground state to a final channel in the whole energy region

The electron impact excitation(EIE) cross sections of an atom/ion in the whole energy region are needed in many research fields, such as astrophysics studies, inertial confinement fusion researches and so on. In the present work, an effective method to calculate the EIE cross sections of an atom/ion in the whole energy region is presented. We use the EIE cross sections of helium as an illustration example. The optical forbidden 1^(1)S–n^(1)S(n = 2–4) and optical allowed 1^(1)S–n^(1)P(n = 2–4) excitation cross sections are calculated in the whole energy region using the scheme that combines the partial wave R-matrix method and the first Born approximation. The calculated cross sections are in good agreement with the available experimental measurements. Based on these accurate cross sections of our calculation, we find that the ratios between the accurate cross sections and Born cross sections are nearly the same for different excitation final states in the same channel. According to this interesting property, a universal correction function is proposed and given to calculate the accurate EIE cross sections with the same computational efforts of the widely used Born cross sections,which should be very useful in the related application fields. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00142.

ON THE LIMIT CASE OF THE STEP-REDUCTION METHOD FOR CALCULATING NON-UNIFORM BEAM WITH VARIOUS SECTIONS

In this paper, the step reduction method is discussed, which was advanced by Prof. Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not in the pure mathematics sense but in the mechanics sense.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

RADAR CROSS-SECTION COMPUTATIONS OF ARBITRARILY COMPLICATED TARGETS BY APPLYING THE PANEL METHOD

The present paper deals with the method for the radar cross-section (RCS)computations of arbitrarily complicated targets based on the work by D. Klement et al.(1988).This method is convenient in use, fast in operation and precise in calculating RCS of a complicatedtarget. With this method, the RCS of classic scatterers, for example, a cone and a cylinder, arecomputed with the result of good agreement with experimental data. Furthermore, the RCS’of an aircraft model at various attitudes are calculated with the result of good agreement withexperimental data also.

A method of analysing experimental data of nuclear reaction cross sections

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