完全乘方数极值问题

本义探讨若干相关的完全乘方数极值问题，多次应用到孙子定理及其推广，并提出进一步的问题。

奇妙的乘方数

153是一个在乘方运算下具有奇妙性质的三位数,把它的每一数位上数字都作3次方,并且将乘方的结果相加,得到: 13+53+33=1+125+27=153 可见三位数153等于它自己各位数字的3次方的和。

(n-1)套n的乘方数的砝码组合具有不等性

本文通过分析1套2的乘方数、2套3的乘方数的砝码组合具有不等性,推导出(n-1)套n的乘方数的砝码组合具有不等性,并利用此结论简要证明“(n-1)套n的乘方数的砝码,可以称出从1至全部砝码的任何值.”

与Fermat大定理有关联的代数等式

从直角三角形三边的关系式c2=a2+b2与公式:1=a2+b2=(a2+b2)2=(a2-b2)2+(2ab)2再由熟知的52=32+42展开讨论,发现并证明了引理1、引理2、引理3中的特性,这是本文的成果之一.把这些特性与Fermat大定理联系起来,虽还未证明Fermat大定理,但得出了定理1、定理2中与Fermat大定理有关联的代数等式,这是本文的成果之二.

Quality prediction and control of tube hollow

The quality prediction of tube hollow model based on the variance staged multiway partial least square (MPLS) method was proposed.The key aspects of staged decomposition of the productive data,calculation of the variance value,modeling,and on-lined prediction in the variance-staged MPLS method were introduced.Based on the model,iterative optimal control method was used for quality control of tube hollow.The experimental results show that the obvious benefits of this method are low maintenance cost,good real time function,high reliability precision,and practical application to on-line prediction and optimization on the quality of tube hollow.

The Least Square Solutions to the Quaternion Matrix Equation AX=B

A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.

Unknown parameter’s variance-covariance propagation and calculation in generalized nonlinear least squares problem

The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.

PARAMETERIZATION OF TRIANGULAR MESHES

A new algorithm called the weighted least square discrete parameterization (WLSDP) is presented for the parameterization of triangular meshes over a convex planar region. This algorithm is the linear combination of the discrete Conformal mapping(DCM) and the discrete Authalic mapping(DAM). It provides the good properties of both DCM and DAM, such as robustness and low distortion. By adjusting the scaling factor q embedded in the WLSDP, satisfactory parameterizations in different special applications can be achieved.

The Influence of Spiritual Values on Work Motivation, Management Control, and Quality of Financial Information on IFIs in Indonesia

This study aims to investigate the influence of spiritual values on work motivation, management control, and the quality of financial information on Islamic financial institutions （IFIs） in Indonesia. Spiritual values are measured using four reflexive indicators, namely, Shiddiq, Fathanah, Amanah, and Tabligh. Work motivation is formed by four formative indicators, namely, compensation, recognition, work experience, and openness. Management control variable is formed by four formative indicators, namely, planning, implementing, evaluating, and monitoring, and finally, the quality of financial information is manifested in four reflexive variables, namely, relevant, comparable, understandable, and consistent. Data are collected through questionnaires with 125 respondents as samples from three types of IFIs, such as Islamic banking, Islamic pawnshop, and Islamic insurance in Indonesia. Methods of data analysis include the use of partial least squares （PLS） to analyze the influence of spiritual values on work motivation, management control, and quality of financial information. The results of this study showed that the manifestation of spiritual values in IFIs is able to influence the quality of financial information through the media as motivation and management control, but directly spiritual values are not able to influence the quality of financial information. While work motivation and management control significantly influence the quality of financial information.

Advances in space-borne SAR interferometry and its application to ground deformation monitoring

The development of Differential Synthetic Aperture Radar Interferometry （D-InSAR）, in terms of its evolution from classic to advanced forms, such as Least-Squares approach, Permanent Scatterer Interferometry, Small Baseline Subset, and Coherent Pixel Technique, is reviewed, describing concisely the main principles of each method and highlighting the difference and relationship between them. Applications of InSAR technology in China were then introduced, together with the obstacles to overcome and feasible strategies, such as integrating MERIS/MODIS data to compensate for the atmospheric effect and GPS, and multi-platform SAR data to make InSAR technique practical and operational under various conditions. The latest devel- opments were then analyzed along with high-quality SAR data, available thanks to the newly launched high-tech satellites, TerraSAR-X, and Cosmo Sky-med, and conclusions were drawn about the main limitations of the technique.

Parameter Estimation with Constraints Based on Variational Method

The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.

Polynomial Root Finding on Frequency Estimation with Sub-Nyquist Temporal Sampling

This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies and joint aliasing frequencies-time delay phases in multi-signal situation is presentcd. Since the sum of time delay phases determined from the least squares estimation shows the characteristics of the corre- sponding parameters pairs, then the pairmatching method is conducted by combining it with estimated parameters mentioned above. Although the proposed method is computationally simpler than the conventional schemes, simulation results show that it can approach optimum estimation performance.

Research on the Model of Linear Data Fitting Method

By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expression between the volume and quantity in scientific experiments and engineering practice, this article analyzed data error by commonly linear data fitting method, and proposed improved process of the least distance squ^re method based on least squares method. Finally, the paper discussed the advantages and disadvantages through the example analysis of two kinds of linear data fitting method, and given reasonable control conditions for its application.

奇妙的数字金字塔

埃及古金字塔吸引着众多科学家去探索其中的奥秘．至今，有的谜底还没有被破解．同样，在自然数领域内，也蕴藏着一种奇妙的金字塔——数学金字塔，它的魅力不亚于埃及古金字塔．我国古代数学家杨辉就发现了两数和的乘方的展开式中各项系数的变化规律．

Uncertainty analysis of hydrological processes based on ARMA-GARCH model

Uncertainty analysis and risk analysis are two important areas of modern water resource management,in which accurate variance estimation is required.The traditional runoff model is established under the assumption that the variance is a constant or it changes with the seasons.However,hydrological processes in the real world are often heteroscedastic,which can be tested by McLeod-Li test and Engle Lagrange multiplier test.In such cases,the GARCH model of hydrological processes is established in this article.First,the seasonal factors in the sequence are removed.Second,the traditional ARMA model is established.Then,the GARCH model is used to correct the residual.At last,the daily runoff data in 1949-2001 of Yichang Hydrological Station is taken to be an example.The result shows that compared to the traditional ARMA model,the GARCH model has the ability to predict more accurate confidence intervals under the same confidence level.

A numerical study of passenger side airbag deployment based on arbitrary Lagrangian-eulerian method

The passenger side airbags(PAB)are usually larger than the driver airbags.Therefore,the inflator of PAB is more powerful with high mass rate.In this paper,an Arbitrary Lagrangian-Eulerian(ALE)method based computational method is developed to simulate the deployment of a PAB.The tank test is used to test the property of the inflator.Through comparison of numerical and experimental results,the ALE method is validated.Based on a failed airbag test,a smaller sub-airbag is placed inside PAB to disperse the gas flow to directions which are less damaging.By applying dynamic relaxation,the initial mesh corresponding to the experimental terms is obtained.The results indicate that the interior pressure and impact force coincide with the test data,and the method in this paper is capable of capturing airbag deploying process of the PAB module accurately.

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2). It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

3-Lie Algebras Realized by Cubic Matrices

Associative multiplications of cubic matrices are provided.The N3-dimensional3-Lie algebras are realized by cubic matrices,and structures of the 3-Lie algebras are studied.

Study on Adjoint-Based Optimization Method For Multi-Stage Turbomachinery

Adjoint-based optimization method is a hotspot in turbomachinery.First,this paper presents principles of adjoint method from Lagrange multiplier viewpoint.Second,combining a continuous route with thin layer RANS equations,we formulate adjoint equations and anti-physical boundary conditions.Due to the multi-stage environment in turbomachinery,an adjoint interrow mixing method is introduced.Numerical techniques of solving flow equations and adjoint equations are almost the same,and once they are converged respectively,the gradients of an objective function to design variables can be calculated using complex method efficiently.Third,integrating a shape perturbation parameterization and a simple steepest descent method,a frame of adjoint-based aerodynamic shape optimization for multi-stage turbomachinery is constructed.At last,an inverse design of an annular cascade is employed to validate the above approach,and adjoint field of an Aachen 1.5 stage turbine demonstrates the conservation and areflexia of the adjoint interrow mixing method.Then a direct redesign of a 1+1 counter-rotating turbine aiming to increase efficiency and apply constraints to mass flow rate and pressure ratio is taken.

Flow Stress Model of Stainless Steel 0Cr13Ni5Mo at Elevated Temperature

For a more accurate forming calculation and numerical simulation of hydraulic turbine blade, ex- perimental studies on the flow stress of stainless steel 0Crl3Ni5Mo were carried out upon Gleeble-1500 thermal simulator under different deformation conditions. The results then were analyzed and the effects of all influencing factors were summarized consequently. New mathematic models were conceived. Utilizing the software Matlab, regression coefficients were calculated by the least square method. The model has an eminent capability of curve-fitting performance with impact structure whose correlation coefficient is up to 0.908 0 and the cosine coefficient is 0.995 8. All mathematic models and process parameters can be used in engineering calculations or computer simulations.