To further investigate the forming mechanism and springback characteristics of strips under multi-square punch forming (MSPF) considering partial-unloading effects, a series of concave form ing tests of strips are con...To further investigate the forming mechanism and springback characteristics of strips under multi-square punch forming (MSPF) considering partial-unloading effects, a series of concave form ing tests of strips are conducted on the MSPF machine. This paper aims to reveal the physical mecha nism of the elastic-plastic deformation in the MSPF process considering the effect of the forming ap proaches, and derive appropriate mathematical interpretations. The theoretical model is firstly estab lished to analyse the concave forming mechanism and springback characteristics of the strip, and its accuracy is then validated by experimental data. The forming history and load evolutions are depicted to explore the required forming capacity through the proposed analytical method. Besides, the paramet ric studies are carried out to discuss their effects on the springback of the strip. The results suggest that the deformation paths of the strip are influenced by the forming approach, and the springback of the strip in convex forming is larger than that in concave forming.展开更多
We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th...We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.展开更多
Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,su...Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.展开更多
Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differen...Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.展开更多
Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and applicatio...Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and application of Xh?K0. Fundamental factors for numerical simplification are provided respectively for bi-variable indeterminate forms, tri-variable indeterminate forms and the universal extending multiplier.展开更多
Supplementary annotations on special forms 1to 4, discussion on the general characteristics of K(t) and K(t, t), and analyses on two noticeable limits are presented in this part. It is demonstrated that strong and wea...Supplementary annotations on special forms 1to 4, discussion on the general characteristics of K(t) and K(t, t), and analyses on two noticeable limits are presented in this part. It is demonstrated that strong and weak parabolic transforms can be employed to change the standard form of a multi-variable indeterminate form into xmK type, hence to derive the standard formulae of the limit and the differential.展开更多
This paper focuses on the advantages of formative assessment and explores a better application of it in English class to facilitate art students’learning and further improve their oral English performance.
Address forms is one of markers of politeness and is an indispensable part of communication. An appropriate address form promotes interpersonal communication smoothly. An address form is polite in one culture, but mig...Address forms is one of markers of politeness and is an indispensable part of communication. An appropriate address form promotes interpersonal communication smoothly. An address form is polite in one culture, but might be inappropriate in another culture. The paper contrasts address forms in English and Chinese culture and explores the reasons for their different choice of address terms.展开更多
To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati...To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.展开更多
Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classic...Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.展开更多
The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation b...The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.展开更多
文摘To further investigate the forming mechanism and springback characteristics of strips under multi-square punch forming (MSPF) considering partial-unloading effects, a series of concave form ing tests of strips are conducted on the MSPF machine. This paper aims to reveal the physical mecha nism of the elastic-plastic deformation in the MSPF process considering the effect of the forming ap proaches, and derive appropriate mathematical interpretations. The theoretical model is firstly estab lished to analyse the concave forming mechanism and springback characteristics of the strip, and its accuracy is then validated by experimental data. The forming history and load evolutions are depicted to explore the required forming capacity through the proposed analytical method. Besides, the paramet ric studies are carried out to discuss their effects on the springback of the strip. The results suggest that the deformation paths of the strip are influenced by the forming approach, and the springback of the strip in convex forming is larger than that in concave forming.
基金supported by National Natural Science Foundation of China(12061080,12161087 and 12261093)the Science and Technology Project of the Education Department of Jiangxi Province(GJJ211601)supported by National Natural Science Foundation of China(11871305).
文摘We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
文摘Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.
文摘Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.
文摘Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and application of Xh?K0. Fundamental factors for numerical simplification are provided respectively for bi-variable indeterminate forms, tri-variable indeterminate forms and the universal extending multiplier.
文摘Supplementary annotations on special forms 1to 4, discussion on the general characteristics of K(t) and K(t, t), and analyses on two noticeable limits are presented in this part. It is demonstrated that strong and weak parabolic transforms can be employed to change the standard form of a multi-variable indeterminate form into xmK type, hence to derive the standard formulae of the limit and the differential.
文摘This paper focuses on the advantages of formative assessment and explores a better application of it in English class to facilitate art students’learning and further improve their oral English performance.
文摘Address forms is one of markers of politeness and is an indispensable part of communication. An appropriate address form promotes interpersonal communication smoothly. An address form is polite in one culture, but might be inappropriate in another culture. The paper contrasts address forms in English and Chinese culture and explores the reasons for their different choice of address terms.
文摘To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.
文摘Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.
文摘The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.
