Fast High Order Algorithm for Three-Dimensional Helmholtz Equation Involving Impedance Boundary Condition with Large Wave Numbers

Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.

Unconditional and Conditional QTL Mapping for Tiller Numbers at Various Stages with Single Segment Substitution Lines in Rice(Oryza sativa L.)

Tiller is one of the most important agronomic traits which influences quantity and quality of effective panicles and finally influences yield in rice. It is important to understand ＂static＂ and ＂dynamic＂ information of the QTLs for tillers in rice. This work was the first time to simultaneously map unconditional and conditional QTLs for tiller numbers at various stages by using single segment substitution lines in rice. Fourteen QTLs for tiller number, distributing on the corresponding substitution segments of chromosomes 1, 2, 3, 4, 6, 7 and 8 were detected. Both the number and the effect of the QTLs for tiller number were various at different stages, from 6 to 9 in the number and from 1.49 to 3.49 in the effect, respectively. Tiller number QTLs expressed in a time order, mainly detected at three stages of 0-7 d, 14-21 d and 35-42 d after transplanting with 6 positive, 9 random and 6 negative expressing QTLs, respectively. Each of the QTLs expressed one time at least during the whole duration of rice. The tiller number at a specific stage was determined by sum of QTL effects estimated by the unconditional method, while the increasing or decreasing number in a given time interval was controlled by the total of QTL effects estimated by the conditional method. These results demonstrated that it is highly effective and accurate for mapping of the QTLs by using single segment substitution lines and the conditional analysis methodology.

Effect of bolt inclination angle on shear behavior ofbolted joints under CNL and CNS conditions

Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting performance.In this study,a new artificial molding method based on 3D scanning and printing technology was first proposed to prepare bolted joints with an inclined bolt.Then,the effects of the bolt inclination angle and boundary conditions on the shear behavior and failure characteristic of bolted joints were addressed by conducting direct shear tests under both CNL and CNS conditions.Results indicated that rock bolt could significantly improve the shear behavior of rock joints,especially in the post-yield deformation region.With the increase of bolt inclination angle,both the maximum shear stress and the maximum friction coefficient increased first and then decreased,while the maximum normal displacement decreased monotonously.Compared with CNL conditions,the maximum shear stress was larger,whereas the maximum normal displacement and friction coefficient were smaller under the CNS conditions.Furthermore,more asperity damage was observed under the CNS conditions due to the increased normal stress on the shear plane.

Rice condition numbers of QR and Cholesky factorizations

A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .

Mining Applicable Elite Alleles of Growth Duration, Plant Height and Panicle Number per Plant by Conditional QTL Mapping in Japonica Rice

Unconditional and conditional QTL mapping were conducted for growth duration (GD), plant height (PH) and effective panicle number per plant (PN) using a recombinant inbred line (RIL) population derived from a cross between two japonica rice varieties Xiushui 79 and C Bao. The RIL population consisted of 254 lines was planted in two environments, Nanjing and Sihong, Jiangsu Province, China. Results showed that additive effects were major in all of QTLs for GD, PH and PN detected by the two methods, and the epistatic effects explained a small proportion of phenotypic variation. No interactions were detected between additive QTL and environment, and between epistatic QTL pairs and environment. After growth duration was adjusted to an identical level, RM80-160bp was detected as an applicable elite allele for PN, with an additive effect of 0.71. When effective panicle number per plant was adjusted to an identical level, RM448-240bp was detected as an applicable elite allele for GD, with an additive effect of 4.64. After plant height was adjusted to an identical level, RM80-160bp was detected as an applicable elite allele for PN, with an additive effect of 0.62, and RM448-240bp was detected as an applicable elite allele for GD, with an additive effect of 3.89. These applicable elite alleles could be used to improve target traits without influencing the other two traits.

Structured condition numbers and statistical condition estimation for the LDU factorization

In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.

Mining Elite Alleles of Growth Duration and Productive Panicle Number per Plant by Association Mapping with Conditional Phenotypic Value in Japonica Rice

To provide genetic information and materials for breeding hybrid japonica rice with wide adaptability and strong competitive advantage of yield, elite alleles and their carrier varieties of growth duration （GD） and productive panicle number per plant （PN） were detected. A natural population composed of 94 japonica varieties was phenotyped for the GD, PN and plant height （PH） in two environments. The conditional phenotypic data were transferred by the linear model method in software QGAStation 1.0, and association mapping based on the unconditional and conditional phenotype values of GD and PN was analyzed by using general linear model in software TASSEL. A total of 34 simple sequence repeat （SSR） marker loci associated with GD and PN were detected in the two environments. Among them, 15 were associated with GD, and 19 were associated with PN. Four elite alleles of RM8095-120bp, RM7102-176bp, RM72-170bp and RM72-178bp were associated with GD, and their carrier varieties were Hongmangshajing, Nipponbare, Hongmangshajing and Nannongjing 62401, respectively. These elite alleles from the carrier varieties can shorten GD by 2.03-9.93 d when they were introduced into improved materials. RM72-182bp associated with PN was an elite allele, and its carrier variety was Xiaoqingzhong. It can increase PN by three when introduced into improved materials. Moreover, these elite alleles can be used to improve target traits without influencing another two traits.

An Improved Semi-Orthogonal User Selection Algorithm Based on Condition Number for Multiuser MIMO Systems

In Multiple-Input Multiple-Out （MIMO） systems, the user selection algorithm plays an important role in the realization of multiplexing gain. In this paper, an improved Semi-orthogonal User Selection algorithm based on condition number is proposed. Besides, a new MIMO pre- coding scheme is designed. The proposed SUS- CN （SUS with condition number） algorithm outperforms the SUS algorithm for the selection of users with better matrix inversion property, thus a higher information rate for selected user pair is achieved. The designed MIMO precoding matrix brings benefits of the power equality at transmitted terminals, the limited dynamic range of the power over time, and a better power efficiency. The simulation results give the key insights into the im- pact of the different condition number value and users on the sum-rate capacity.

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.

RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.

ON THE APPROXIMATE COMPUTATION OF EXTREME EIGENVALUES AND THE CONDITION NUMBER OF NONSINGULAR MATRICES

From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a 'by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on AT A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.

COMPONENTWISE CONDITION NUMBERS FOR GENERALIZED MATRIX INVERSION AND LINEAR LEAST SQUARES

We present componentwise condition numbers for the problems of MoorePenrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given.

Generation of Complex Matrices Belonging to Matrix Groups with Controlled Condition Number

The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical problems and complex control problems. In this work, the authors try to generate matrices such that： （1） the condition number of these types of matrices is controlled and （2） The algorithm used to generate these matrices preserves their structure.

Application of uncertain type of AHP to condition assessment of cable-stayed bridges

In order to guarantee the safety service and life-span of long-span cable-stayed bridges, the uncertain type of analytic hierarchy process （AHP） method is adopted to access the bridge condition. The correlative theory and applied objects of uncertain type of AHP are introduced, and then the optimal transitive matrix method is chosen to calculate the interval number judgment matrix, which makes the weights of indices more reliable and accurate. Finally, with Harbin Songhua River Cable-Stayed Bridge as an example, an index system and an assessment model are proposed for the condition assessment of this bridge, and by using uncertain type of AHP, the weights of assessment indices are fixed and the final assessment results of the bridge are calculated, which proves the feasibility and practicability of this method. The application of this assessment method can provide the scientific basis for maintenance and management of long-span cable-stayed bridges.

Geometric Condition of 3UPS-S Parallel Mechanism in Singular Configuration

The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.

滇池西岸山地区域SCS-CN模型优化

[目的]模拟计算滇池西岸山洪产流量,为该区面山截洪设施的修建,减少山洪灾害和保护滇池水环境提供科学决策的依据。[方法]基于SCS-CN产流模型,选取昆明滇池西岸山地区域2019,2020年的33场实测降雨径流数据,通过坡度结合前期影响雨量对CN值进行分级优化设定。采用穷举法对λ进行优化取值。再以2021年的19场实测降雨径流数据验证优化SCS-CN模型的模拟精度及其参数适用性。[结果]①采用坡度及前期影响雨量分级优化得到的CN值仅适用于降雨量<30 mm的中小型降雨;对于降雨量≥30 mm的强降雨,需根据场次降雨前5 d的降雨总量采用线性内插法对标准SCS-CN模型中AMC等级进行修改,再确定对应的坡度CN修正值。②适合滇池西岸山地区域中小型降雨和强降雨的最佳初损系数λ值分别为0.15,0.2。③经验证,中小型降雨和强降雨下的NSE值分别为0.8522,0.7978,模型合格率分别为93.33%和75%。[结论]优化的SCS-CN模型用于滇池西岸山地区域<30 mm的中小型降雨和≥30 mm的强降雨情况下的产流计算是可行的,可为该区地表径流预测及SCS-CN模型的进一步优化提供科学依据和理论参考。

Solving ill-conditioning observation equations via truncated SVD

To mitigate the ill effects and obtain more accurate and stable solution of the observation equations, the so-called truncated singular-value decomposition (TSVD) method is introduced by modifying the small (nonzero) singular values of the coefficients matrix. The proposed method directly disposed the ill-conditioning observation equations, which differs considerably from the traditional normal equation method. An application explains that TSVD can mitigate the ill conditioning.

Novel method based on ant colony opti mization for solving ill-conditioned linear systems of equations

A novel method based on ant colony optimization （ACO）, algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.

Testing a bell-shaped function for estimation of fully expanded leaf area in modern maize under potential production conditions

Accurate leaf area simulation is critical for the performance of crop growth models. Area of fully expanded individual leaves of maize hybrids released before 1995 (defined as old hybrids) has been simulated using a bell-shaped function (BSF) and the relationship between its parameters and total leaf number (TLNO). However, modern high-yielding maize hybrids show different canopy architectures. The function parameters calibrated for old hybrids will not accurately represent modern hybrids. In this study, we evaluated these functions using a dataset including old and modern hybrids that have been widely planted in China in recent years. Maximum individual leaf area (Y_0) and corresponding leaf position (X_0) were not predicted well by TLNO (R^2= 0.56 and R^2= 0.70) for modern hybrids. Using recalibrated shape parameters a and b with values of Y_0 and X_0 for modern hybrids, the BSF accurately predicted individual leaf area (R^2= 0.95–0.99) and total leaf area of modern hybrids (R^2= 0.98). The results show that the BSF is still a robust way to predict the fully expanded leaf area of maize when parameters a and b are modified and Y_0 and X_0 are fitted. Breeding programs have led to increases in TLNO of maize but have not altered Y_0 and X_0, reducing the correlation between Y_0, X_0, and TLNO. For modern hybrids, the values of Y_0 and X_0 are hybrid-specific. Modern hybrids tend to have less-negative values of parameter a and more-positive values of parameter b in the leaf profile. Growth conditions, such as plant density and environmental conditions, also affect the fully expanded leaf area but were not considered in the original published equations. Thus, further research is needed to accurately estimate values of Y_0 and X_0 of individual modern hybrids to improve simulation of maize leaf area in crop growth models.

On Conditional Probabilities of Factoring Quadratics

Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.