We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu ...We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.展开更多
Concave vertex of an object is an important parameter for analyzing an object’s shape. A new algorithm for searching concave vertex is proposed in this paper. The new algorithm requires tracking the border firstly,an...Concave vertex of an object is an important parameter for analyzing an object’s shape. A new algorithm for searching concave vertex is proposed in this paper. The new algorithm requires tracking the border firstly,and then uses sampling border to obtain coordinates sequence of discrete boundary points. Each sampling point of the discrete border is determined to be either concave or convex according to the value of vector product. Two inflexions can be searched by the change of concavo-convex trend. The region between two inflexions is defined as concave area. The values of distance are calculated between all boundary points on the concave area and a straight line connected by two inflexions. The boundary point corresponding to the greatest distances is max concave vertex,or the object’s concave vertex. Experimental results have proved that the new algorithm can extract the max concave vertexes of an object accurately and reliably.展开更多
The transverse single-spin asymmetry forρ^(0) production in semi-inclusive deep inelastic scattering was recently reported by the COMPASS Collaboration.Using the Sivers function extracted from pion and kaon productio...The transverse single-spin asymmetry forρ^(0) production in semi-inclusive deep inelastic scattering was recently reported by the COMPASS Collaboration.Using the Sivers function extracted from pion and kaon productions,we perform a calculation of the Sivers asymmetry within the transverse momentum-dependent factorization.Our results are consistent with the COMPASS data,supporting the universality of the Sivers function in the semi-inclusive deep inelastic scattering process for different final-state hadrons within current experimental uncertainties.While different parametrizations of the Sivers function from global analyses allow describing the data equally well,we obtain very different predictions on the Sivers asymmetry ofρand K^(*)productions at electron-ion colliders,which therefore are expected to provide further constraints.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second,...A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second, a summation process of term by term integrated results and a formula of the bulging were introduced, and an analytical solution of stress effective factor was obtained. It is proved that the expression of power by the above linear integration is the same as that of traditional immediate integration. Also, the solution was simplified by series expansion and compared by slab forging test with the others. It turns out that the calculated result of total forging pressure is basically in agreement with measured value in the actual press test.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined...A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined by the ratio of coordinate increments.Furthermore,inner-product of the vector for plastic power was term integrated by term and summed.Thereafter,through a formula for determination of bulge an analytical solution of stress effective factor was obtained.Finally,through compression tests,the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine.It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%.However,when the reduction gets up to 25.34% and 33.12%,the corresponding errors between the calculated and measured results also get up to 6% and 13.5%,respectively.展开更多
Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the effici...Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.展开更多
For the task of visual-based automatic product image classification for e-commerce,this paper constructs a set of support vector machine(SVM) classifiers with different model representations.Each base SVM classifier i...For the task of visual-based automatic product image classification for e-commerce,this paper constructs a set of support vector machine(SVM) classifiers with different model representations.Each base SVM classifier is trained with either different types of features or different spatial levels.The probability outputs of these SVM classifiers are concatenated into feature vectors for training another SVM classifier with a Gaussian radial basis function(RBF) kernel.This scheme achieves state-of-the-art average accuracy of 86.9%for product image classification on the public product dataset PI 100.展开更多
The comprehension of Prof. Tai's symbolic vector method in vector analysis presented, some problems are found and some suggestions are provided to solve them. Some defenses for Gibbs' symbol have been made as ...The comprehension of Prof. Tai's symbolic vector method in vector analysis presented, some problems are found and some suggestions are provided to solve them. Some defenses for Gibbs' symbol have been made as well. Key words: symbolic vector(? ?; operator; vector product model展开更多
By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé i...By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.展开更多
Kamaugh maps are widely used in the logic synthesis. However, the number of the variable it can deal with is limited. In this paper, two kinds of function shrinking techniques are proposed, and a fast algorithm to con...Kamaugh maps are widely used in the logic synthesis. However, the number of the variable it can deal with is limited. In this paper, two kinds of function shrinking techniques are proposed, and a fast algorithm to configure a truth vector into a XOR function is realized. There is no variable number limitation for this algorithm.展开更多
Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier...Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.展开更多
Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to ...Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR4. One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures, if the rotations are compared in spaces of three and four dimensions.展开更多
In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard ...In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.展开更多
文摘We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.
基金Supported by Natural Science Foundation of Guangdong Province (No.8451051501000501)the Science and Technology Projects of Guangdong Province (No.2009B-010800029)
文摘Concave vertex of an object is an important parameter for analyzing an object’s shape. A new algorithm for searching concave vertex is proposed in this paper. The new algorithm requires tracking the border firstly,and then uses sampling border to obtain coordinates sequence of discrete boundary points. Each sampling point of the discrete border is determined to be either concave or convex according to the value of vector product. Two inflexions can be searched by the change of concavo-convex trend. The region between two inflexions is defined as concave area. The values of distance are calculated between all boundary points on the concave area and a straight line connected by two inflexions. The boundary point corresponding to the greatest distances is max concave vertex,or the object’s concave vertex. Experimental results have proved that the new algorithm can extract the max concave vertexes of an object accurately and reliably.
基金supported by the National Key R&D Program of China(Grant No.2024YFA1611004)the National Natural Science Foundation of China(Grant Nos.12175117,12475084,and 12321005)the Shandong Province Natural Science Foundation(Grant Nos.ZFJH202303 and ZR2024MA012)。
文摘The transverse single-spin asymmetry forρ^(0) production in semi-inclusive deep inelastic scattering was recently reported by the COMPASS Collaboration.Using the Sivers function extracted from pion and kaon productions,we perform a calculation of the Sivers asymmetry within the transverse momentum-dependent factorization.Our results are consistent with the COMPASS data,supporting the universality of the Sivers function in the semi-inclusive deep inelastic scattering process for different final-state hadrons within current experimental uncertainties.While different parametrizations of the Sivers function from global analyses allow describing the data equally well,we obtain very different predictions on the Sivers asymmetry ofρand K^(*)productions at electron-ion colliders,which therefore are expected to provide further constraints.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
文摘A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second, a summation process of term by term integrated results and a formula of the bulging were introduced, and an analytical solution of stress effective factor was obtained. It is proved that the expression of power by the above linear integration is the same as that of traditional immediate integration. Also, the solution was simplified by series expansion and compared by slab forging test with the others. It turns out that the calculated result of total forging pressure is basically in agreement with measured value in the actual press test.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金Project(50474015) supported by the National Natural Science Foundation of China
文摘A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined by the ratio of coordinate increments.Furthermore,inner-product of the vector for plastic power was term integrated by term and summed.Thereafter,through a formula for determination of bulge an analytical solution of stress effective factor was obtained.Finally,through compression tests,the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine.It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%.However,when the reduction gets up to 25.34% and 33.12%,the corresponding errors between the calculated and measured results also get up to 6% and 13.5%,respectively.
基金supported by the Major Program of the National Natural Science Foundation of China (Grant 51490662)the Funds for Distinguished Young Scientists of Hunan Province (Grant 14JJ1016)+1 种基金the State Key Program of the National Science Foundation of China (11232004)the Heavy-duty Tractor Intelligent Manufacturing Technology Research and System Development (Grant 2016YFD0701105)
文摘Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China(No.70890083) the Project of National Innovation Fund for Technology Based Firms (No.09c26222123243)
文摘For the task of visual-based automatic product image classification for e-commerce,this paper constructs a set of support vector machine(SVM) classifiers with different model representations.Each base SVM classifier is trained with either different types of features or different spatial levels.The probability outputs of these SVM classifiers are concatenated into feature vectors for training another SVM classifier with a Gaussian radial basis function(RBF) kernel.This scheme achieves state-of-the-art average accuracy of 86.9%for product image classification on the public product dataset PI 100.
文摘The comprehension of Prof. Tai's symbolic vector method in vector analysis presented, some problems are found and some suggestions are provided to solve them. Some defenses for Gibbs' symbol have been made as well. Key words: symbolic vector(? ?; operator; vector product model
基金supported by the National Natural Science Foundation of China(10871025)
文摘By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.
文摘Kamaugh maps are widely used in the logic synthesis. However, the number of the variable it can deal with is limited. In this paper, two kinds of function shrinking techniques are proposed, and a fast algorithm to configure a truth vector into a XOR function is realized. There is no variable number limitation for this algorithm.
文摘Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.
文摘Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR4. One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures, if the rotations are compared in spaces of three and four dimensions.
文摘In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.
