Additive manufacturing(AM),interchangeably termed as3D printing(3DP),has been defined as one of the key technologies in the national development strategies of a number of countries around the world.America Makes,as th...Additive manufacturing(AM),interchangeably termed as3D printing(3DP),has been defined as one of the key technologies in the national development strategies of a number of countries around the world.America Makes,as the National Additive Manufacturing Innovation Institute,is the nation’s leading and collaborative partner in AM/3DP technology research,discovery,creation,and innovation,working efficiently to innovate and accelerate AM/3DP to increase America’s global manufacturing competitiveness(https://americamakes.us).German展开更多
This paper constructs a new type of finite-dimensional thermal coherent states (FDTCS), which differs from the proceeding thermal coherent state in construction, as realisations of SU(2) Lie algebra. Using the tec...This paper constructs a new type of finite-dimensional thermal coherent states (FDTCS), which differs from the proceeding thermal coherent state in construction, as realisations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.展开更多
A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1-F1)-dimensional Ito system is obtained. Some special types of solutions such...A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1-F1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.展开更多
In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the co...In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.展开更多
't Hooft-Veltman Wilson dimensional regularization depends crucially upon Borel summability which entails strong links to the modern mathematical theory of transfinite sets and consequently to the fractal-Cantoria...'t Hooft-Veltman Wilson dimensional regularization depends crucially upon Borel summability which entails strong links to the modern mathematical theory of transfinite sets and consequently to the fractal-Cantorian spacetime proposal of Ord-Nottale-El Naschie. Starting from the above, we interpret the main step of the mathematical analysis in terms of elementary particles interaction. Thus 't Hooft-Veltman “perturbation” parameter which measures the deviation of the regulated space from the four dimensionality of spacetime is interpreted as an elementary particle with a topological mass charge equal to 0.18033989, i.e. double the magnitude of Hardy’s quantum entanglement. In turn, Hardy’s quantum entanglement which may be interpreted geometrically as a consequence of the zero set embedded in an empty set could also be interpreted as an exchange of pseudo elementary particles with a topological mass charge equal to Hardy’s entanglement where is the Hausdorff dimension of the zero set of the corresponding 't Hooft-Veltman spacetime.展开更多
A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can gener...A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.展开更多
基金supported by the National Natural Science Foundation of China (51575267 and 51322509)the National Key Research and Development Program ‘‘Additive Manufacturing and Laser Manufacturing’’ (2016YFB1100101)+5 种基金the Top-Notch Young Talents Program of China, the NSFC-DFG Sino-German Research Project (GZ 1217)the Key Research and Development Program of Jiangsu Provincial Department of Science and Technology of China (BE2016181)the 333 High-level Talents Training Project (BRA2015368), the Aeronautical Science Foundation of China (2015ZE52051)the Outstanding Youth Foundation of Jiangsu Province of China (BK20130035)the Program for New Century Excellent Talents in University (NCET-13-0854)the Fundamental Research Funds for the Central Universities (NE2013103, NP2015206 and NZ2016108)
文摘Additive manufacturing(AM),interchangeably termed as3D printing(3DP),has been defined as one of the key technologies in the national development strategies of a number of countries around the world.America Makes,as the National Additive Manufacturing Innovation Institute,is the nation’s leading and collaborative partner in AM/3DP technology research,discovery,creation,and innovation,working efficiently to innovate and accelerate AM/3DP to increase America’s global manufacturing competitiveness(https://americamakes.us).German
基金Project supported by the National Natural Science Foundation of China(Grant No.10574060)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A23and ZR2010AQ027)the Shandong Province Higher Educational Science and Technology Program,China(Grant Nos.J09LA07and J10LA15).
文摘This paper constructs a new type of finite-dimensional thermal coherent states (FDTCS), which differs from the proceeding thermal coherent state in construction, as realisations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.
文摘A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1-F1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.
文摘In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.
文摘't Hooft-Veltman Wilson dimensional regularization depends crucially upon Borel summability which entails strong links to the modern mathematical theory of transfinite sets and consequently to the fractal-Cantorian spacetime proposal of Ord-Nottale-El Naschie. Starting from the above, we interpret the main step of the mathematical analysis in terms of elementary particles interaction. Thus 't Hooft-Veltman “perturbation” parameter which measures the deviation of the regulated space from the four dimensionality of spacetime is interpreted as an elementary particle with a topological mass charge equal to 0.18033989, i.e. double the magnitude of Hardy’s quantum entanglement. In turn, Hardy’s quantum entanglement which may be interpreted geometrically as a consequence of the zero set embedded in an empty set could also be interpreted as an exchange of pseudo elementary particles with a topological mass charge equal to Hardy’s entanglement where is the Hausdorff dimension of the zero set of the corresponding 't Hooft-Veltman spacetime.
文摘A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.