ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB...ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.展开更多
Ti_(2)AlNb-based alloy was joined in a continuous drive friction welding machine under different rotational rates(500,1000 and 1500 r/min).The microstructure and mechanical properties of the joints were investigated.I...Ti_(2)AlNb-based alloy was joined in a continuous drive friction welding machine under different rotational rates(500,1000 and 1500 r/min).The microstructure and mechanical properties of the joints were investigated.It is shown that the weld zone(WZ) is fully composed of recrystallized B2 phase,and the grain size decreases with increasing rotational rate.The thermo-mechanically affected zone(TMAZ) suffers severe deformation during welding,due to which most of original precipitation phase is dissolved and streamlines are present.In the heat affected zone(HAZ),only the fine O phase is dissolved.The as-welded joint produced using 1000 r/min has the best mechanical properties,whose strength and elongation are both close to those of the base metal,while the as-welded joint obtained using 500 r/min exhibits the worst mechanical properties.Post-weld annealing treatment annihilates the deformation microstructure and fine O phase precipitates in the joints,consequently improving the mechanical properties significantly.Decomposed α_(2) phase is a weakness for the mechanical performance of the joint since microcracks are apt to form in it in the tensile test.展开更多
Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type in...Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type inequality is established and the sufficient condition for a.s. l 2 continuity of Y(·) is studied by means of the inequality.展开更多
基金the National Natural Science Foundation of China(61772164,61761136010)the Natural Science Foundation of Zhejiang Province(LY17F020025).
文摘ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.
基金jointly supported by the National Natural Science Foundation of China(No.22273093,No.41905018,No.21903080)the Ministry of Science and Technology of China(No.2022YFF0606500)。
基金the financial supports from the Science and Technology Special Project, China (No. K19168)the National Science and Technology Major Project of China (No. 2017-VI-0004-0075)the National Natural Science Foundation of China (No. 52231002)。
文摘Ti_(2)AlNb-based alloy was joined in a continuous drive friction welding machine under different rotational rates(500,1000 and 1500 r/min).The microstructure and mechanical properties of the joints were investigated.It is shown that the weld zone(WZ) is fully composed of recrystallized B2 phase,and the grain size decreases with increasing rotational rate.The thermo-mechanically affected zone(TMAZ) suffers severe deformation during welding,due to which most of original precipitation phase is dissolved and streamlines are present.In the heat affected zone(HAZ),only the fine O phase is dissolved.The as-welded joint produced using 1000 r/min has the best mechanical properties,whose strength and elongation are both close to those of the base metal,while the as-welded joint obtained using 500 r/min exhibits the worst mechanical properties.Post-weld annealing treatment annihilates the deformation microstructure and fine O phase precipitates in the joints,consequently improving the mechanical properties significantly.Decomposed α_(2) phase is a weakness for the mechanical performance of the joint since microcracks are apt to form in it in the tensile test.
基金Research supported by National Natural Science Foundation of China(1 0 0 71 0 2 7)
文摘Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type inequality is established and the sufficient condition for a.s. l 2 continuity of Y(·) is studied by means of the inequality.
