The invertibility of combinations of two orthogonal projectors aP ＋ bQ - cPQ - dQP is researched by using the CSdecomposition of matrices and properties of orthogonal projectors. The Moore-enrose inverse of the combi...The invertibility of combinations of two orthogonal projectors aP ＋ bQ - cPQ - dQP is researched by using the CSdecomposition of matrices and properties of orthogonal projectors. The Moore-enrose inverse of the combinations is presented under some special conditions.展开更多
In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group invers...In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group inverses of them are derived. The work of this paper extends some previous results.展开更多
Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are...Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.展开更多
Based on the constructivism, using the College English（new edition） CD-ROMs for classroom teaching as main media, this paper explores the feasibility of the classroom teaching mode of appropriate combination of trad...Based on the constructivism, using the College English（new edition） CD-ROMs for classroom teaching as main media, this paper explores the feasibility of the classroom teaching mode of appropriate combination of traditional methods with the multimedia overhead projector. The new teaching mode proves to be successful in that it has greatly improved the students＇ ability to use English in an all-round way and has obvious advantages over the only traditional method.展开更多
In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory. We have already established that one-parameter projection operators can be constructed from the uni...In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory. We have already established that one-parameter projection operators can be constructed from the unit circle . As discussed in the previous article these operators form a Lie group known as the Projection Group. In the first section, we will show that the concepts from my first article are consistent with existing theory [1] [2]. In the second section, it will be demonstrated that not only such operators are mutually congruent but also we can define a group action on ?by using the rotation group [3] [4]. It will be proved that the group acts on elements of ?in a non-faithful but ∞-transitive way consistent with both group operations. Finally, in the last section we define the group operation ?in terms of matrix operations using the operator and the Hadamard Product;this construction is consistent with the group operation defined in the first article.展开更多
In the present study,the influence of dynamic process parameters such as water pressure,traverse speed and abrasive mass flow rate on depth of penetration and surface topography in high strength AZ91 magnesium alloy w...In the present study,the influence of dynamic process parameters such as water pressure,traverse speed and abrasive mass flow rate on depth of penetration and surface topography in high strength AZ91 magnesium alloy were investigated using Abrasive Water Jet(AWJ)cutting technology.Process parameters were varied at 3 levels and influences of each parameter on penetration ability were identified using analysis of variance(ANOVA).Contribution of water pressure and traverse speed on jet penetration found higher compared to abrasive mass flow rate.Profile projector was used to measure depth of penetration.Microstructural features and topography of cut surfaces were examined using Scanning Electron Microscopy(SEM).Micro cutting and ploughing were observed on the top and bottom portion of the cut which were similar to that of modes of deformation in other ductile materials like aluminium and steel.Surface roughness of cut surfaces was measured using Taylor Hobson surface roughness tester.Surface roughness found higher at higher traverse speeds and lower at lower traverse speeds.This study also highlights the suitability of AWJ cutting technology for cutting magnesium and its alloys.展开更多
This paper concerns the optimization problem for multilayered ultrasonic transducer with active porous piezoelectric layer. The dependences of the effective moduli for porous piezoelectric material on porosity have be...This paper concerns the optimization problem for multilayered ultrasonic transducer with active porous piezoelectric layer. The dependences of the effective moduli for porous piezoelectric material on porosity have been previously obtained and allowed to decrease the number of design variables. The multiobjective optimization problem based on the Pareto-frontier calculation has been solved using the live-link of finite-element (FE) package Comsol Multiphysics with MATLAB.展开更多
A novel direction of arrival （DOA） estimation method is proposed when uncorrelated, correlated, and coherent sources coexist under color noise field. The uncorrelated and correlated sources are firstly estimated usi...A novel direction of arrival （DOA） estimation method is proposed when uncorrelated, correlated, and coherent sources coexist under color noise field. The uncorrelated and correlated sources are firstly estimated using the conventional spatial spectrum estimation method, then the noise and uncorrelated sources in Toeplitz structure are eliminated using differencing, finally by exploiting the property of oblique projection, the contributions of correlated sources are then eliminated from the covariance matrix and only the coherent sources remain. So the coherent sources can be estimated by the technique of modified spatial smoothing. The number of sources resolved by this approach can exceed the number of array elements without repeatedly estimating correlated sources. Simulation results demonstrate the effectiveness and efficiency of our proposed method.展开更多
With the coming of information age and the development of computer science, digitalization of whole garment is becoming more and more important. The surface of whole garment is sequent and glossy so that it is lack of...With the coming of information age and the development of computer science, digitalization of whole garment is becoming more and more important. The surface of whole garment is sequent and glossy so that it is lack of the texture characteristic which is the key of digital 3D modeling. According to this reason, the structure illumination is steered into a method of this paper. The paper proposes the method by which 3D model of whole garment is created from 2D image sequences directly but not by the common techniques using general CAD model. In the paper the structure illumination is generated by the slide projector and the modeling of whole garment is based on the strict theory of the digital photogrammetry, computer vision and image processing pattern recognition. Because whole garment is lack of the applicable texture for matching, the characteristic texture generated by the structure illumination is added onto the surface of whole garment. After the characteristic texture is extracted from images and is matched well, 3D coordinates of the characteristic texture can be calculated out by the space forward intersection. Then the whole garment model is acquired by connecting all neighhour space points in the TIN and rendering the real texture of whole garment automatically. The 3D modeling method is untouched so that it is nondestructive which is just suitable for the messaline and the clothing. The method of whole garment 3D modeling proposed in the paper is flexible, effective and practical, which is confirmed by the results of the reconstructing experiments.展开更多
基金Supported by the Hubei Normal University Research Grant (2008D54)
文摘The invertibility of combinations of two orthogonal projectors aP ＋ bQ - cPQ - dQP is researched by using the CSdecomposition of matrices and properties of orthogonal projectors. The Moore-enrose inverse of the combinations is presented under some special conditions.
基金Supported by the National Natural Science Foundation of China(11271105)the Key Research Project of Educational Department of Hubei Province(D20122202)Youth Research Project of Educational Department of Hubei Province(B20122203)
文摘In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group inverses of them are derived. The work of this paper extends some previous results.
文摘Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.
文摘Based on the constructivism, using the College English（new edition） CD-ROMs for classroom teaching as main media, this paper explores the feasibility of the classroom teaching mode of appropriate combination of traditional methods with the multimedia overhead projector. The new teaching mode proves to be successful in that it has greatly improved the students＇ ability to use English in an all-round way and has obvious advantages over the only traditional method.
文摘In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory. We have already established that one-parameter projection operators can be constructed from the unit circle . As discussed in the previous article these operators form a Lie group known as the Projection Group. In the first section, we will show that the concepts from my first article are consistent with existing theory [1] [2]. In the second section, it will be demonstrated that not only such operators are mutually congruent but also we can define a group action on ?by using the rotation group [3] [4]. It will be proved that the group acts on elements of ?in a non-faithful but ∞-transitive way consistent with both group operations. Finally, in the last section we define the group operation ?in terms of matrix operations using the operator and the Hadamard Product;this construction is consistent with the group operation defined in the first article.
基金The authors would like to express their sincere thanks and appreciation to Center of Excellence(CoE)in advanced materials research and TEQIP,BMS College of Engineering,Ben-galuru,Karnataka,India,for providing financial assistance in conducting this research work.
文摘In the present study,the influence of dynamic process parameters such as water pressure,traverse speed and abrasive mass flow rate on depth of penetration and surface topography in high strength AZ91 magnesium alloy were investigated using Abrasive Water Jet(AWJ)cutting technology.Process parameters were varied at 3 levels and influences of each parameter on penetration ability were identified using analysis of variance(ANOVA).Contribution of water pressure and traverse speed on jet penetration found higher compared to abrasive mass flow rate.Profile projector was used to measure depth of penetration.Microstructural features and topography of cut surfaces were examined using Scanning Electron Microscopy(SEM).Micro cutting and ploughing were observed on the top and bottom portion of the cut which were similar to that of modes of deformation in other ductile materials like aluminium and steel.Surface roughness of cut surfaces was measured using Taylor Hobson surface roughness tester.Surface roughness found higher at higher traverse speeds and lower at lower traverse speeds.This study also highlights the suitability of AWJ cutting technology for cutting magnesium and its alloys.
文摘This paper concerns the optimization problem for multilayered ultrasonic transducer with active porous piezoelectric layer. The dependences of the effective moduli for porous piezoelectric material on porosity have been previously obtained and allowed to decrease the number of design variables. The multiobjective optimization problem based on the Pareto-frontier calculation has been solved using the live-link of finite-element (FE) package Comsol Multiphysics with MATLAB.
基金supported by the National Natural Science Foundation of China(60601016).
文摘A novel direction of arrival （DOA） estimation method is proposed when uncorrelated, correlated, and coherent sources coexist under color noise field. The uncorrelated and correlated sources are firstly estimated using the conventional spatial spectrum estimation method, then the noise and uncorrelated sources in Toeplitz structure are eliminated using differencing, finally by exploiting the property of oblique projection, the contributions of correlated sources are then eliminated from the covariance matrix and only the coherent sources remain. So the coherent sources can be estimated by the technique of modified spatial smoothing. The number of sources resolved by this approach can exceed the number of array elements without repeatedly estimating correlated sources. Simulation results demonstrate the effectiveness and efficiency of our proposed method.
文摘With the coming of information age and the development of computer science, digitalization of whole garment is becoming more and more important. The surface of whole garment is sequent and glossy so that it is lack of the texture characteristic which is the key of digital 3D modeling. According to this reason, the structure illumination is steered into a method of this paper. The paper proposes the method by which 3D model of whole garment is created from 2D image sequences directly but not by the common techniques using general CAD model. In the paper the structure illumination is generated by the slide projector and the modeling of whole garment is based on the strict theory of the digital photogrammetry, computer vision and image processing pattern recognition. Because whole garment is lack of the applicable texture for matching, the characteristic texture generated by the structure illumination is added onto the surface of whole garment. After the characteristic texture is extracted from images and is matched well, 3D coordinates of the characteristic texture can be calculated out by the space forward intersection. Then the whole garment model is acquired by connecting all neighhour space points in the TIN and rendering the real texture of whole garment automatically. The 3D modeling method is untouched so that it is nondestructive which is just suitable for the messaline and the clothing. The method of whole garment 3D modeling proposed in the paper is flexible, effective and practical, which is confirmed by the results of the reconstructing experiments.
