We introduce a modification of reflectron time-of-flight mass spectrometer for laser photodissociation of mass-selected ions. In our apparatus, the ions of interests were selected by a mass gate near the first space f...We introduce a modification of reflectron time-of-flight mass spectrometer for laser photodissociation of mass-selected ions. In our apparatus, the ions of interests were selected by a mass gate near the first space focus point and decelerated right after the mass gate, were then crossed by a laser beam for dissociation. The daughter ions and surviving parent ions were re-accelerated and analyzed by the reflectron time-of-flight mass spectrometer. Compared to the designs reported by other research groups, our selection-deceleration-dissociation-reacceleration approach has better daughter-parent-ions-separation, easier laser timing, and better overlapping between the ion beam and laser beam. We also conducted detailed cal- culations on the parent ion and daughter ion flight times, and provided a simplified formula for the calibration of daughter ion mass.展开更多
Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it...Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.展开更多
The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. ...The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well. [ABSTRACT FROM AUTHOR]展开更多
A generalization of the Householder transformation,renamed as elementary matrix by A.S.Householder:Unitary transformation of a nonsymmetric matrix,J.ACM,5(4),339–342,1958,was introduced by LaBudde(Math Comput 17(84):...A generalization of the Householder transformation,renamed as elementary matrix by A.S.Householder:Unitary transformation of a nonsymmetric matrix,J.ACM,5(4),339–342,1958,was introduced by LaBudde(Math Comput 17(84):433–437,1963)as a tool to obtain a tridiagonal matrix similar to a given square matrix.Some of the free parameters of the transformation can be chosen to attain better numerical properties.In this work,we study the spectral properties of the transformation.We also propose a special choice for free coefficients of that transformation to minimize its condition number.The transformation with such suitable choice of parameters is called optimal.展开更多
基金V. ACKNOWLEDGMENTS This work supported by the National Natural Science Foundation of China （No.20853001）. We thank Professor Qi-he Zhu and Professor Zhen Gao for valuable discussions.
文摘We introduce a modification of reflectron time-of-flight mass spectrometer for laser photodissociation of mass-selected ions. In our apparatus, the ions of interests were selected by a mass gate near the first space focus point and decelerated right after the mass gate, were then crossed by a laser beam for dissociation. The daughter ions and surviving parent ions were re-accelerated and analyzed by the reflectron time-of-flight mass spectrometer. Compared to the designs reported by other research groups, our selection-deceleration-dissociation-reacceleration approach has better daughter-parent-ions-separation, easier laser timing, and better overlapping between the ion beam and laser beam. We also conducted detailed cal- culations on the parent ion and daughter ion flight times, and provided a simplified formula for the calibration of daughter ion mass.
基金CNPq of Brazil and the National Natural Science Foundation of China.
文摘Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.
基金CNPq, Brazil!301035/93-8University of Macao!RG010/ 99- 00S / JXQ / FST
文摘The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well. [ABSTRACT FROM AUTHOR]
基金The work of the first and third authors was partially supported by National Council for Scientific and Technological Development(CNPq),Brazil.
文摘A generalization of the Householder transformation,renamed as elementary matrix by A.S.Householder:Unitary transformation of a nonsymmetric matrix,J.ACM,5(4),339–342,1958,was introduced by LaBudde(Math Comput 17(84):433–437,1963)as a tool to obtain a tridiagonal matrix similar to a given square matrix.Some of the free parameters of the transformation can be chosen to attain better numerical properties.In this work,we study the spectral properties of the transformation.We also propose a special choice for free coefficients of that transformation to minimize its condition number.The transformation with such suitable choice of parameters is called optimal.
