Silicon passivated emitter and rear contact(PERC) solar cells with V-groove texture were fabricated using maskless alkaline solution etching with in-house developed additive. Compared with the traditional pyramid text...Silicon passivated emitter and rear contact(PERC) solar cells with V-groove texture were fabricated using maskless alkaline solution etching with in-house developed additive. Compared with the traditional pyramid texture, the V-groove texture possesses superior effective minority carrier lifetime, enhanced p–n junction quality and better applied filling factor(FF). In addition, a V-groove texture can greatly reduce the shading area and edge damage of front Ag electrodes when the V-groove direction is parallel to the gridline electrodes. Due to these factors, the V-groove solar cells have a higher efficiency(21.78%) than pyramid solar cells(21.62%). Interestingly, external quantum efficiency(EQE) and reflectance of the V-groove solar cells exhibit a slight decrease when the incident light angle(θ) is increased from 0° to 75°, which confirms the excellent quasi omnidirectionality of the V-groove solar cells. The proposed V-groove solar cell design shows a 2.84% relative enhancement of energy output over traditional pyramid solar cells.展开更多
Continuum robots with high flexibility and compliance have the capability to operate in confined and cluttered environments. To enhance the load capacity while maintaining robot dexterity, we propose a novel non-const...Continuum robots with high flexibility and compliance have the capability to operate in confined and cluttered environments. To enhance the load capacity while maintaining robot dexterity, we propose a novel non-constant subsegment stiffness structure for tendon-driven quasi continuum robots(TDQCRs) comprising rigid-flexible coupling subsegments.Aiming at real-time control applications, we present a novel static-to-kinematic modeling approach to gain a comprehensive understanding of the TDQCR model. The analytical subsegment-based kinematics for the multisection manipulator is derived based on screw theory and product of exponentials formula, and the static model considering gravity loading,actuation loading, and robot constitutive laws is established. Additionally, the effect of tension attenuation caused by routing channel friction is considered in the robot statics, resulting in improved model accuracy. The root-mean-square error between the outputs of the static model and the experimental system is less than 1.63% of the arm length(0.5 m). By employing the proposed static model, a mapping of bending angles between the configuration space and the subsegment space is established. Furthermore, motion control experiments are conducted on our TDQCR system, and the results demonstrate the effectiveness of the static-to-kinematic model.展开更多
Damage caused due to low-velocity impacts in composites leads to substantial deterioration in their residual strength and eventually provokes structural failure.This work presents an experimental investigation on the ...Damage caused due to low-velocity impacts in composites leads to substantial deterioration in their residual strength and eventually provokes structural failure.This work presents an experimental investigation on the effects of different patch and parent laminate stacking sequences on the enhancement of impact strength of Carbon Fiber Reinforced Polymers(CFRP)composites by utilising the adhesively bonded external patch repair technique.Damage evolution study is also performed with the aid of Acoustic Emission(AE).Two different quasi-isotropic configurations were selected for the parent laminate,viz.,[45°/45°/0°/0°]s and[45°/0°/45°/0°]s.Quasi Static Indentation(QSI)test was performed on both the pristine laminates,and damage areas were detected by using the C-scan inspection technique.Damaged laminates were repaired by using a single-sided patch of two different configurations,viz.,[45°/45°/45°/45°]and[45°/0°/0°/45°],and employing a circular plug to fill the damaged hole.Four different combinations of repaired laminates with two configurations of each parent and patch laminate were produced,which were further subjected to the QSI test.The results reveal the effectiveness of the repair method,as all the repaired laminates show higher impact resistance compared to the respective pristine laminates.Patches of[45°/0°/0°/45°]configuration when repaired by taking[45°/45°/0°/0°]s and[45°/0°/45°/0°]s as parents exhibited 68%and 73%higher peak loads,respectively,than the respective pristine laminates.Furthermore,parent and patch of configuration[45°/0°/45°/0°]s and[45°/0°/0°/45°],respectively,attain the highest peak load,whereas[45°/45°/0°/0°]s and[45°/45°/45°/45°]combinations possess the most gradual decrease in the load.展开更多
Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grai...Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grain boundaries produce a pinning atmosphere that exerts a drag pressure on the boundary motion,which strongly affects the grain growth behavior during annealing.In the current work,the characteristics of grain growth in an annealed Mg-1 wt.%Mn-1 wt.%Nd magnesium alloy were investigated by advanced experimental and modeling techniques.Systematic quasi in-situ orientation mappings with a scanning electron microscope were performed to track the evolution of local and global microstructural characteristics as a function of annealing time.Solute segregation at targeted grain boundaries was measured using three-dimensional atom probe tomography.Level-set computer simulations were carried with different setups of driving forces to explore their contribution to the microstructure development with and without solute drag.The results showed that the favorable growth advantage for some grains leading to a transient stage of abnormal grain growth is controlled by several drivers with varying importance at different stages of annealing.For longer annealing times,residual dislocation density gradients between large and smaller grains are no longer important,which leads to microstructure stability due to predominant solute drag.Local fluctuations in residual dislocation energy and solute concentration near grain boundaries cause different boundary segments to migrate at different rates,which affects the average growth rate of large grains and their evolved shape.展开更多
Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dyn...Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.展开更多
The California bearing ratio (CBR) test is the most widely spread method of determining the bearing strength of the pavement material and is fundamental to pavement design practice in most countries. This test is expe...The California bearing ratio (CBR) test is the most widely spread method of determining the bearing strength of the pavement material and is fundamental to pavement design practice in most countries. This test is expensive, laborious and time consuming, and to overcome this, Quasi static cone penetrometer machine was fabricated and used to measure the consistency limits (liquid limit-LL, Plastic limit-PL and Plasticity index-PI), which were used to develop an empirical equation to determine CBR. Soil samples were collected and unsoaked CBR, PL, LL and PI were determined according to BS 1377 part 9 and BS 1377-2;1990. Quasi static penetration forces at 20 mm depth of penetration were also determined at consistency limits. It was found that the force of 1020 gf and 60 gf was achieved at a depth of 20 mm at PI and LL respectively. The correlation and regression analysis between consistency limits, and the experimental CBR obtained showed coefficient of determination, R<sup>2</sup> = 0.907 between CBR and all the parameters using multiple linear regression analysis (MLRA). The regression equation developed was used together with the relationship developed between the Quasi static Penetration force at consistency limits and the tested consistency limits to come up with the General Empirical Equation. Verification of the formula showed that the correlation can be used accurately to determine the un soaked CBR.展开更多
准比例谐振(quasi-proportion resonant,Quasi-PR)控制器可克服传统比例谐振(proportion resonant,PR)控制器带宽窄、抗频率偏移能力差的缺点,基于此提出了基于三单相Quasi-PR控制的中点箝位式(neutral point clamped,NPC)三电平光伏并...准比例谐振(quasi-proportion resonant,Quasi-PR)控制器可克服传统比例谐振(proportion resonant,PR)控制器带宽窄、抗频率偏移能力差的缺点,基于此提出了基于三单相Quasi-PR控制的中点箝位式(neutral point clamped,NPC)三电平光伏并网逆变器控制策略。Quasi-PR控制器继承了传统PR控制器的优点,避免了矢量控制策略中复杂的坐标变换、解耦控制和前馈补偿等,简化了控制算法。同时当电网频率发生偏移时,Quasi-PR控制器仍能实现对交流电流的无静差跟踪。此外,为减少电网不平衡时产生的较大谐波电流含量,设计了基于Quasi-PR控制的分次谐波补偿器。仿真结果表明了所提控制策略的有效性。展开更多
针对Quasi-UDG模型下无线传感器网络随机部署的拓扑特征,提出了一种非测距基于权重的定位算法EWLS(Enhanced Weighted Least Square).首先,设计出一种节点跳数和距离关系估计的方法,然后依据跳数值与距离关系的概率表达式,给出EWLS定位...针对Quasi-UDG模型下无线传感器网络随机部署的拓扑特征,提出了一种非测距基于权重的定位算法EWLS(Enhanced Weighted Least Square).首先,设计出一种节点跳数和距离关系估计的方法,然后依据跳数值与距离关系的概率表达式,给出EWLS定位算法中节点测量距离信息的权重.仿真实验表明,在不同的锚节点密度、Quasi-UDG模型因子和平均邻居节点数的参数下,EWLS算法定位误差较小,同最小均方误差相比,有效地提高了节点定位的精度.展开更多
This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas...This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas complex superhypernetworks in order to make a relation between labeled objects in the form of details andgeneralities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzesthem in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole tothe whole group of objects at the same time.We have investigated the properties of fuzzy (quasi) superhypergraphsbased on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valuedfuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based onthe permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi)superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introducedin this study and it is applied in designing the real problem in the real world. Finally, the problem of businesssuperhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.展开更多
Soft clay may cause quasi preconsolidation effect under the constant hydrostatic pressure after some time. The result of drained triaxial test represents the effective stress yield surface, which can be described by ...Soft clay may cause quasi preconsolidation effect under the constant hydrostatic pressure after some time. The result of drained triaxial test represents the effective stress yield surface, which can be described by simple binary linear fabric model. Therefore the pore pressure and deformation of clay can be decided. It also can be used to resolve the real boundary problems with finite element method.展开更多
Earthquakes triggered by dynamic disturbances have been confirmed by numerous observations and experiments.In the past several decades,earthquake triggering has attracted increasing attention of scholars in relation t...Earthquakes triggered by dynamic disturbances have been confirmed by numerous observations and experiments.In the past several decades,earthquake triggering has attracted increasing attention of scholars in relation to exploring the mechanism of earthquake triggering,earthquake prediction,and the desire to use the mechanism of earthquake triggering to reduce,prevent,or trigger earthquakes.Natural earthquakes and large‐scale explosions are the most common sources of dynamic disturbances that trigger earthquakes.In the past several decades,some models have been developed,including static,dynamic,quasi‐static,and other models.Some reviews have been published,but explosiontriggered seismicity was not included.In recent years,some new results on earthquake triggering have emerged.Therefore,this paper presents a new review to reflect the new results and include the content of explosion‐triggered earthquakes for the reference of scholars in this area.Instead of a complete review of the relevant literature,this paper primarily focuses on the main aspects of dynamic earthquake triggering on a tectonic scale and makes some suggestions on issues that need to be resolved in this area in the future.展开更多
In this paper, the authors generalize the definition of χ 2 distribution and introduce a quasi χ 2 distribution, and then prove several properties of it, find the necessary and sufficient conditions of i...In this paper, the authors generalize the definition of χ 2 distribution and introduce a quasi χ 2 distribution, and then prove several properties of it, find the necessary and sufficient conditions of independence about multivariate normal distributions, matrix normal distributions and two parts of the Wishart distribution.展开更多
基金Project supported by the Key-Area Research and Development Program of Guangdong Province,China (Grant No.2021B0101260001)Guangdong Basic and Applied Basic Research Foundation (Grant No.2019A1515110411)the National Natural Science Foundation of China (Grant No.61904201)。
文摘Silicon passivated emitter and rear contact(PERC) solar cells with V-groove texture were fabricated using maskless alkaline solution etching with in-house developed additive. Compared with the traditional pyramid texture, the V-groove texture possesses superior effective minority carrier lifetime, enhanced p–n junction quality and better applied filling factor(FF). In addition, a V-groove texture can greatly reduce the shading area and edge damage of front Ag electrodes when the V-groove direction is parallel to the gridline electrodes. Due to these factors, the V-groove solar cells have a higher efficiency(21.78%) than pyramid solar cells(21.62%). Interestingly, external quantum efficiency(EQE) and reflectance of the V-groove solar cells exhibit a slight decrease when the incident light angle(θ) is increased from 0° to 75°, which confirms the excellent quasi omnidirectionality of the V-groove solar cells. The proposed V-groove solar cell design shows a 2.84% relative enhancement of energy output over traditional pyramid solar cells.
基金Project supported by the National Natural Science Foundation of China (Grant No.61973167)the Jiangsu Funding Program for Excellent Postdoctoral Talent。
文摘Continuum robots with high flexibility and compliance have the capability to operate in confined and cluttered environments. To enhance the load capacity while maintaining robot dexterity, we propose a novel non-constant subsegment stiffness structure for tendon-driven quasi continuum robots(TDQCRs) comprising rigid-flexible coupling subsegments.Aiming at real-time control applications, we present a novel static-to-kinematic modeling approach to gain a comprehensive understanding of the TDQCR model. The analytical subsegment-based kinematics for the multisection manipulator is derived based on screw theory and product of exponentials formula, and the static model considering gravity loading,actuation loading, and robot constitutive laws is established. Additionally, the effect of tension attenuation caused by routing channel friction is considered in the robot statics, resulting in improved model accuracy. The root-mean-square error between the outputs of the static model and the experimental system is less than 1.63% of the arm length(0.5 m). By employing the proposed static model, a mapping of bending angles between the configuration space and the subsegment space is established. Furthermore, motion control experiments are conducted on our TDQCR system, and the results demonstrate the effectiveness of the static-to-kinematic model.
基金the financial support by the Council of Scientific&Industrial Research(CSIR)-Research Scheme,India(22/0809/2019-EMR-II)。
文摘Damage caused due to low-velocity impacts in composites leads to substantial deterioration in their residual strength and eventually provokes structural failure.This work presents an experimental investigation on the effects of different patch and parent laminate stacking sequences on the enhancement of impact strength of Carbon Fiber Reinforced Polymers(CFRP)composites by utilising the adhesively bonded external patch repair technique.Damage evolution study is also performed with the aid of Acoustic Emission(AE).Two different quasi-isotropic configurations were selected for the parent laminate,viz.,[45°/45°/0°/0°]s and[45°/0°/45°/0°]s.Quasi Static Indentation(QSI)test was performed on both the pristine laminates,and damage areas were detected by using the C-scan inspection technique.Damaged laminates were repaired by using a single-sided patch of two different configurations,viz.,[45°/45°/45°/45°]and[45°/0°/0°/45°],and employing a circular plug to fill the damaged hole.Four different combinations of repaired laminates with two configurations of each parent and patch laminate were produced,which were further subjected to the QSI test.The results reveal the effectiveness of the repair method,as all the repaired laminates show higher impact resistance compared to the respective pristine laminates.Patches of[45°/0°/0°/45°]configuration when repaired by taking[45°/45°/0°/0°]s and[45°/0°/45°/0°]s as parents exhibited 68%and 73%higher peak loads,respectively,than the respective pristine laminates.Furthermore,parent and patch of configuration[45°/0°/45°/0°]s and[45°/0°/0°/45°],respectively,attain the highest peak load,whereas[45°/45°/0°/0°]s and[45°/45°/45°/45°]combinations possess the most gradual decrease in the load.
基金support of the Deutsche Forschungsgemeinschaft(DFG),Grant no.AL 1343/7–1,AL 1343/8–1,Yi 103/3–1。
文摘Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grain boundaries produce a pinning atmosphere that exerts a drag pressure on the boundary motion,which strongly affects the grain growth behavior during annealing.In the current work,the characteristics of grain growth in an annealed Mg-1 wt.%Mn-1 wt.%Nd magnesium alloy were investigated by advanced experimental and modeling techniques.Systematic quasi in-situ orientation mappings with a scanning electron microscope were performed to track the evolution of local and global microstructural characteristics as a function of annealing time.Solute segregation at targeted grain boundaries was measured using three-dimensional atom probe tomography.Level-set computer simulations were carried with different setups of driving forces to explore their contribution to the microstructure development with and without solute drag.The results showed that the favorable growth advantage for some grains leading to a transient stage of abnormal grain growth is controlled by several drivers with varying importance at different stages of annealing.For longer annealing times,residual dislocation density gradients between large and smaller grains are no longer important,which leads to microstructure stability due to predominant solute drag.Local fluctuations in residual dislocation energy and solute concentration near grain boundaries cause different boundary segments to migrate at different rates,which affects the average growth rate of large grains and their evolved shape.
文摘Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.
文摘The California bearing ratio (CBR) test is the most widely spread method of determining the bearing strength of the pavement material and is fundamental to pavement design practice in most countries. This test is expensive, laborious and time consuming, and to overcome this, Quasi static cone penetrometer machine was fabricated and used to measure the consistency limits (liquid limit-LL, Plastic limit-PL and Plasticity index-PI), which were used to develop an empirical equation to determine CBR. Soil samples were collected and unsoaked CBR, PL, LL and PI were determined according to BS 1377 part 9 and BS 1377-2;1990. Quasi static penetration forces at 20 mm depth of penetration were also determined at consistency limits. It was found that the force of 1020 gf and 60 gf was achieved at a depth of 20 mm at PI and LL respectively. The correlation and regression analysis between consistency limits, and the experimental CBR obtained showed coefficient of determination, R<sup>2</sup> = 0.907 between CBR and all the parameters using multiple linear regression analysis (MLRA). The regression equation developed was used together with the relationship developed between the Quasi static Penetration force at consistency limits and the tested consistency limits to come up with the General Empirical Equation. Verification of the formula showed that the correlation can be used accurately to determine the un soaked CBR.
文摘准比例谐振(quasi-proportion resonant,Quasi-PR)控制器可克服传统比例谐振(proportion resonant,PR)控制器带宽窄、抗频率偏移能力差的缺点,基于此提出了基于三单相Quasi-PR控制的中点箝位式(neutral point clamped,NPC)三电平光伏并网逆变器控制策略。Quasi-PR控制器继承了传统PR控制器的优点,避免了矢量控制策略中复杂的坐标变换、解耦控制和前馈补偿等,简化了控制算法。同时当电网频率发生偏移时,Quasi-PR控制器仍能实现对交流电流的无静差跟踪。此外,为减少电网不平衡时产生的较大谐波电流含量,设计了基于Quasi-PR控制的分次谐波补偿器。仿真结果表明了所提控制策略的有效性。
文摘针对Quasi-UDG模型下无线传感器网络随机部署的拓扑特征,提出了一种非测距基于权重的定位算法EWLS(Enhanced Weighted Least Square).首先,设计出一种节点跳数和距离关系估计的方法,然后依据跳数值与距离关系的概率表达式,给出EWLS定位算法中节点测量距离信息的权重.仿真实验表明,在不同的锚节点密度、Quasi-UDG模型因子和平均邻居节点数的参数下,EWLS算法定位误差较小,同最小均方误差相比,有效地提高了节点定位的精度.
文摘This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas complex superhypernetworks in order to make a relation between labeled objects in the form of details andgeneralities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzesthem in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole tothe whole group of objects at the same time.We have investigated the properties of fuzzy (quasi) superhypergraphsbased on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valuedfuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based onthe permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi)superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introducedin this study and it is applied in designing the real problem in the real world. Finally, the problem of businesssuperhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.
文摘Soft clay may cause quasi preconsolidation effect under the constant hydrostatic pressure after some time. The result of drained triaxial test represents the effective stress yield surface, which can be described by simple binary linear fabric model. Therefore the pore pressure and deformation of clay can be decided. It also can be used to resolve the real boundary problems with finite element method.
基金supported by the National Natural Science Foundation of China(NSFC grants No.12172036,51774018)the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT,IRT_17R06)+2 种基金the Russian Foundation for Basic Research,Grant Number 20‐55‐53032Russian State Task number 1021052706247‐7‐1.5.4the Government of Perm Krai,research project No.С‐26/628.
文摘Earthquakes triggered by dynamic disturbances have been confirmed by numerous observations and experiments.In the past several decades,earthquake triggering has attracted increasing attention of scholars in relation to exploring the mechanism of earthquake triggering,earthquake prediction,and the desire to use the mechanism of earthquake triggering to reduce,prevent,or trigger earthquakes.Natural earthquakes and large‐scale explosions are the most common sources of dynamic disturbances that trigger earthquakes.In the past several decades,some models have been developed,including static,dynamic,quasi‐static,and other models.Some reviews have been published,but explosiontriggered seismicity was not included.In recent years,some new results on earthquake triggering have emerged.Therefore,this paper presents a new review to reflect the new results and include the content of explosion‐triggered earthquakes for the reference of scholars in this area.Instead of a complete review of the relevant literature,this paper primarily focuses on the main aspects of dynamic earthquake triggering on a tectonic scale and makes some suggestions on issues that need to be resolved in this area in the future.
文摘In this paper, the authors generalize the definition of χ 2 distribution and introduce a quasi χ 2 distribution, and then prove several properties of it, find the necessary and sufficient conditions of independence about multivariate normal distributions, matrix normal distributions and two parts of the Wishart distribution.