We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a f...We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.展开更多
Typical rotors such as those on steam turbine or generator are often supported by two bearings with two balance planes at both ends.Vibrations are monitored by a pair of proximity probes at each bearing.There are two ...Typical rotors such as those on steam turbine or generator are often supported by two bearings with two balance planes at both ends.Vibrations are monitored by a pair of proximity probes at each bearing.There are two approaches to reduce 1X vibration due to unbalance at both ends via balancing with influence coefficient method.The first approach is to treat it as a multiple-plane balancing problem involving 2x2 matrix of complex influence coefficients.The second approach is to treat it as two single-plane balance problems using static(in-phase)and couple(180 degree out-of-phase)components,respectively.Conversion equations of influence coefficients between these two approaches have been found previously by the author.The corresponding spreadsheets that convert influence coefficients between these two formats are presented in the current paper.The paper shows effectiveness of these conversion equations in dealing with real balancing problems in the field.A detailed balance case is presented to demonstrate how the conversion equations are used to reduce vibration effectively.展开更多
This article lists all possible conversion equations of influence coefficients(ICs)with different formats when some of these are known to handle two-plane balancing tasks with no or less trial weight runs.There are tw...This article lists all possible conversion equations of influence coefficients(ICs)with different formats when some of these are known to handle two-plane balancing tasks with no or less trial weight runs.There are two approaches for two-plane balancing.One can treat it as a multi-plane balance problem involving a 2×2 matrix of complex ICs where two direct ICs along with two cross-effect ICs are generated so that correction weights at one or two balance planes can be determined.One can also apply a static pare(in-phase)and/or couple pair(180 degrees out-of-phase)weights for balancing.The latter approach has been used quite often in the field,especially on steam turbine and generator rotors.Dependent on vibration mode shapes and combinations as well as balance plane accessibility,sometimes applying static or couple pair weights can be a wise choice;other times weights at one or two end planes are needed.There are totally 4 possible sets of IC data due to weights at plane 1,plane 2,static pair,and couple pair.IC data would typically be obtained by applying trial weights followed by trial weight runs.It is found,however,that all these IC data can be converted easily without trial weight runs once any two of 4 sets are known.The above findings and conversion equations have been obtained analytically and verified by experimental results.Real cases are given to demonstratetheirapplications.展开更多
The high-intensity heavy-ion accelerator facility(HIAF)is under design at the Institute of Modern Physics(IMP)and will provide an intense ion beam for nuclear physics,atomic mass measurement research,and other applica...The high-intensity heavy-ion accelerator facility(HIAF)is under design at the Institute of Modern Physics(IMP)and will provide an intense ion beam for nuclear physics,atomic mass measurement research,and other applications.As the main ring of HIAF,the BRing accumulates beams to high intensity and accelerates them to high energy.To achieve high intensities up to 1×10^(11)(^(238)U^(34+)),the injection gain of the BRing must be as high as 88.However,multiple multiturn injection supported by the electron cooling system takes a long time,causing substantial beam loss under a strong space charge effect.Hence,a two-plane painting injection scheme is proposed for beam accumulation in the BRing.This scheme uses a tilted injection septum and horizontal and vertical bump magnets to paint the beam into horizontal and vertical phase space simultaneously.In this paper,the two-plane painting injection parameters are optimized,and the resulting injection process is simulated using the Objective Ring Beam Injection and Tracking(ORBIT)code.An injection gain of up to 110.3 with a loss rate of 2:3%is achieved,meeting the requirements of BRing.展开更多
In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.
We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.
文摘We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.
文摘Typical rotors such as those on steam turbine or generator are often supported by two bearings with two balance planes at both ends.Vibrations are monitored by a pair of proximity probes at each bearing.There are two approaches to reduce 1X vibration due to unbalance at both ends via balancing with influence coefficient method.The first approach is to treat it as a multiple-plane balancing problem involving 2x2 matrix of complex influence coefficients.The second approach is to treat it as two single-plane balance problems using static(in-phase)and couple(180 degree out-of-phase)components,respectively.Conversion equations of influence coefficients between these two approaches have been found previously by the author.The corresponding spreadsheets that convert influence coefficients between these two formats are presented in the current paper.The paper shows effectiveness of these conversion equations in dealing with real balancing problems in the field.A detailed balance case is presented to demonstrate how the conversion equations are used to reduce vibration effectively.
文摘This article lists all possible conversion equations of influence coefficients(ICs)with different formats when some of these are known to handle two-plane balancing tasks with no or less trial weight runs.There are two approaches for two-plane balancing.One can treat it as a multi-plane balance problem involving a 2×2 matrix of complex ICs where two direct ICs along with two cross-effect ICs are generated so that correction weights at one or two balance planes can be determined.One can also apply a static pare(in-phase)and/or couple pair(180 degrees out-of-phase)weights for balancing.The latter approach has been used quite often in the field,especially on steam turbine and generator rotors.Dependent on vibration mode shapes and combinations as well as balance plane accessibility,sometimes applying static or couple pair weights can be a wise choice;other times weights at one or two end planes are needed.There are totally 4 possible sets of IC data due to weights at plane 1,plane 2,static pair,and couple pair.IC data would typically be obtained by applying trial weights followed by trial weight runs.It is found,however,that all these IC data can be converted easily without trial weight runs once any two of 4 sets are known.The above findings and conversion equations have been obtained analytically and verified by experimental results.Real cases are given to demonstratetheirapplications.
基金supported by the National Natural Science Foundation of China(No.11505256)
文摘The high-intensity heavy-ion accelerator facility(HIAF)is under design at the Institute of Modern Physics(IMP)and will provide an intense ion beam for nuclear physics,atomic mass measurement research,and other applications.As the main ring of HIAF,the BRing accumulates beams to high intensity and accelerates them to high energy.To achieve high intensities up to 1×10^(11)(^(238)U^(34+)),the injection gain of the BRing must be as high as 88.However,multiple multiturn injection supported by the electron cooling system takes a long time,causing substantial beam loss under a strong space charge effect.Hence,a two-plane painting injection scheme is proposed for beam accumulation in the BRing.This scheme uses a tilted injection septum and horizontal and vertical bump magnets to paint the beam into horizontal and vertical phase space simultaneously.In this paper,the two-plane painting injection parameters are optimized,and the resulting injection process is simulated using the Objective Ring Beam Injection and Tracking(ORBIT)code.An injection gain of up to 110.3 with a loss rate of 2:3%is achieved,meeting the requirements of BRing.
基金supported by National Research Foundation of Korea(NRF)(Grant Nos.2012-R1A1A3002031 and 2015-R1A2A1A-01002459)supported by KNU 2015(Bokhyun)Research Fund
文摘In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.
基金Supported by National Research Foundation of Korea(Grant No.NRF-2011-220-1-C00002)partially supported by MCT(Grant No.MTM2010-18099)supported by NRF(Grant No.NRF-2012-R1A2A2A-01043023)
文摘We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.
