We propose that the exotic meson tetraquark u<sub>d</sub>~</sup>dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition ...We propose that the exotic meson tetraquark u<sub>d</sub>~</sup>dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, d<sub>d</sub>~</sup> and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The u<sub>d</sub>~</sup>dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũd<sub>d</sub>~</sup> for the electrons and u<sub>d</sub>~</sup>d<sub>d</sub>~</sup> for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state u<sub>d</sub>~</sup>dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.展开更多
Amylose tris (phenylcarbamate) chiral stationary phase (ATPC-CSP) was prepared and used for optical resolution of clusters 1 and 2. n-Hexane/2-propanol ( 99/1; v/v) were found to be the most suitable mobile phase on ...Amylose tris (phenylcarbamate) chiral stationary phase (ATPC-CSP) was prepared and used for optical resolution of clusters 1 and 2. n-Hexane/2-propanol ( 99/1; v/v) were found to be the most suitable mobile phase on ATPC-CSP.展开更多
Locomotion and manipulation optimization is essential for the performance of tetrahedron-based mobile mechanism. Most of current optimization methods are constrained to the continuous actuated system with limited degr...Locomotion and manipulation optimization is essential for the performance of tetrahedron-based mobile mechanism. Most of current optimization methods are constrained to the continuous actuated system with limited degree of freedom(DOF), which is infeasible to the optimization of binary control multi-DOF system. A novel optimization method using for the locomotion and manipulation of an 18 DOFs tetrahedron-based mechanism called 5-TET is proposed. The optimization objective is to realize the required locomotion by executing the least number of struts.Binary control strategy is adopted, and forward kinematic and tipping dynamic analyses are performed, respectively.Based on a developed genetic algorithm(GA), the optimal number of alternative struts between two adjacent steps is obtained as 5. Finally, a potential manipulation function is proposed, and the energy consumption comparison between optimal 5-TET and the traditional wheeled robot is carried out. The presented locomotion optimization and manipulation planning enrich the research of tetrahedron-based mechanisms and provide the instruction to the successive locomotion and operation planning of multi-DOF mechanisms.展开更多
Aim of this work is to try to explain, on a Rational basis, some equations of Electro-Magnetism, which are based on Experimental data. Any Electric Field can produce a Field of many small Electric Dipoles, continuousl...Aim of this work is to try to explain, on a Rational basis, some equations of Electro-Magnetism, which are based on Experimental data. Any Electric Field can produce a Field of many small Electric Dipoles, continuously distributed in space. In a region, where the Electric Field is constant, in direction and magnitude, all the small Dipoles are parallel to the Electric Field, and are represented by a single, long, parallel to them, fixed in space, Electric Dipole, which is here called Compass. An Alternating current, in a straight Conductor, is studied, by a simple, short computer program, for step-by-step nonlinear dynamic analysis. It is found that, only an Alternating current, not a direct current, can produce an Electric Dipole, in a straight Conductor. The two above Dipoles (Compass-Conductor) are assumed with equal lengths ℓ, lying on two skew lines, perpendicular to each other, at a distance ℓ√2, thus forming, by their four ends, a Regular Tetrahedron, with side length ℓ. Repulsion, between Like Charges, obeys the simple Coulomb Electro-Static law. Whereas Interaction (Attraction or Repulsion), between Unlike Charges, obeys a more accurate Lennard-Jones law. The analysis of Dipole-Dipole (Compass-Conductor) Interaction is performed by hand calculator. The only out-of-balance forces, in the regular Tetrahedron, acting on the Rigid Conductor, are the so-called magnetic forces. Their direction is found, in a simple Rational way, with help of Regular Tetrahedron, without recoursing to a “right-hand-rule”. The proposed model is applied to 1) The force acting on an Electric Charge moving in a magnetic field. 2) The force acting on a Current carrying straight Conductor, due to a magnetic field. 3) The magnetic fields created around a Current carrying straight Conductor. In these applications, proposed model gives reasonable results. Particularly, in third application, results, obtained by proposed model, are found in satisfactory approximation with corresponding ones, obtained by an empirical formula, based on relevant Experimental observations of H.-C. Oersted and A.-M. Ampère. So, the reliability of proposed model is checked. Position and direction of magnetic field vector coincide with those of a corresponding fixed Compass of a constant Electric Field. Main point of present work is that, without introducing the concept of a magnetic field vector, by combining field of dipoles, produced by an electric field, with dipole of an alternating current carrying conductor, the magnetic forces can be determined.展开更多
The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a...The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time ρ (the ratio of the sizes) and mass ratio τ=m/?m must be satisfied by some formulas. For any radius ratios ρ∈(0, 0.152 996 918 2) or (0.715 223 148 7, 1.398 165 037), there is only one central configuration. Otherwise, for any given mass ratio τ , there may exist more than one central configuration.展开更多
Accurate detection and imaging of adenosine triphosphate(ATP)expression levels in living cells is of great value for understanding cell metabolism,physiological activities,and pathologic mechanisms.Here,we developed a...Accurate detection and imaging of adenosine triphosphate(ATP)expression levels in living cells is of great value for understanding cell metabolism,physiological activities,and pathologic mechanisms.Here,we developed a DNA tetrahedron-based split aptamer probe(TD probe)for ratiometric fluorescence imaging of ATP in living cells.The TD probe is constructed by hybridizing two split ATP aptamer probes(Apt-a and Apt-b)to a DNA tetrahedron assembled by four DNA oligonucleotides(T1,T2,T3 and T4).In the presence of ATP,the TD probe will alter its structure from the open to closed state,thus bringing the separated donor and acceptor fluorophores into close proximity for high fluorescence resonance energy transfer(FRET)signals.The TD probe exhibits low cytotoxicity,efficient cell internalization and good biological stability.Moreover,based on the FRET“off”to“on”signal output mode,the TD probe can effectively avoid false-positive signals from complex biological matrices,which is significant for long-term reliable imaging in living cells.In addition,by changing the split aptamers attached to DNA tetrahedron,the proposed strategy may be extended for detecting various intracellular targets.Collectively,this strategy provides a valuable sensing platform for biomarkers analysis in living cells,thus having great potential for early clinical diagnosis and therapeutic evaluation.展开更多
DNA tetrahedro n nano structure (DTN) is one of the simplest DNA nano structures and has bee n successfully applied for biose nsin g, imagi ng, and treatment of can cer. To facilitate its biomedical applications and p...DNA tetrahedro n nano structure (DTN) is one of the simplest DNA nano structures and has bee n successfully applied for biose nsin g, imagi ng, and treatment of can cer. To facilitate its biomedical applications and pote ntial clinical tran slation, fun dame ntal un derstandi ng of DTN's transportation among major organs in living organisms becomes increasingly important. Here, we describe the efficient renal clearanee of DTN in healthy mice by using positron emission tomography (PET) imaging. The kidney elimination of DTN was later applied for renal function evaluation in murine models of unilateral ureteral obstruction (UUO). We further established a mathematical program of DTN to validate its changes of transportation pattern in healthy and UUO mice. We believe the establishment of pharmacokinetic profiles and mathematical model of DTN may provide in sight for future optimization of DNA nano structures for biomedical applications.展开更多
To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor,a unified framework of burning surface regression simulation has been...To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor,a unified framework of burning surface regression simulation has been developed based on minimum distance function.In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface,a fast distance querying method based on the equal size cube voxel structure was employed.An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements,achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously.The cases of star grain,finocyl grain,and non-uniform tube grain were studied to verify the proposed method.The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.展开更多
We present a numerical formulation for resin flow based on the concept of quasi-steady state situation at the flow front. To be fit for complicated product shapes,we use the four-node unstructured tetrahedron mesh bas...We present a numerical formulation for resin flow based on the concept of quasi-steady state situation at the flow front. To be fit for complicated product shapes,we use the four-node unstructured tetrahedron mesh based on which the numerical formulation of temperature and degree of cure is developed. The validity of our method is established in the case where ffexible meshes are used. The results show that the numerical procedure,tested on known data,provides numerically valid and reasonably accurate predictions.展开更多
Developing highly stable and active non-Pt oxygen reduction reaction(ORR)electrocatalysts for power generation device raises great concerns and remains a challenge.Here,we report novel truncated Pd tetrahedrons(T-Pd-T...Developing highly stable and active non-Pt oxygen reduction reaction(ORR)electrocatalysts for power generation device raises great concerns and remains a challenge.Here,we report novel truncated Pd tetrahedrons(T-Pd-Ths)enclosed by{111}facets with excellent uniformity,which have both low-coordinated surface sites and distinct lattice distortions that would induce“local strain”.In alkaline electrolyte,the T-Pd-Ths/C achieves remarkable ORR specific/mass activity(SA/MA)of 2.46 mA·cm^(−2)/1.69 A·mgPd^(−1),which is 12.3/16.9 and 10.7/14.1 times higher than commercial Pd/C and Pt/C,respectively.The T-Pd-Ths/C also exhibits high in-situ carbon monoxide(CO)tolerance and 50,000 cycles durability with an activity loss of 7.69%and morphological stability.The rotating ring-disk electrode(RRDE)measurements show that a 4-electron process occurs on T-PdThs/C.Theoretical calculations demonstrate that the low-coordinated surface sites contribute largely to the enhancement of ORR activity.In actual direct methanol fuel cell(DMFC)device,the T-Pd-Ths/C delivers superior open-circuit voltage(OCV)and peak power density(PPD)to commercial Pt/C from 25 to 80℃,and the maximum PPD can reach up to 163.7 mW·cm−2.This study demonstrates that the T-Pd-Ths/C holds promise as alternatives to Pt for ORR in DMFC device.展开更多
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are ...Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.展开更多
It is more difficult to construct 3-D splines than in 2-D case. Some results in the three directional meshes of bivariate case have been e xtended to 3-D case and corresponding tetrahedron partition has been construct...It is more difficult to construct 3-D splines than in 2-D case. Some results in the three directional meshes of bivariate case have been e xtended to 3-D case and corresponding tetrahedron partition has been constructed. The support of related Bsplines and their recurrent formulas on integration and differentiationdifference are obtained. The results of this paper can be extended into higher dimension spaces, and can be also used in wavelet analysis, because of the relationship between spline and wavelets.展开更多
文摘We propose that the exotic meson tetraquark u<sub>d</sub>~</sup>dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, d<sub>d</sub>~</sup> and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The u<sub>d</sub>~</sup>dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũd<sub>d</sub>~</sup> for the electrons and u<sub>d</sub>~</sup>d<sub>d</sub>~</sup> for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state u<sub>d</sub>~</sup>dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.
文摘Amylose tris (phenylcarbamate) chiral stationary phase (ATPC-CSP) was prepared and used for optical resolution of clusters 1 and 2. n-Hexane/2-propanol ( 99/1; v/v) were found to be the most suitable mobile phase on ATPC-CSP.
基金Supported by National Science-Technology Support Plan Projects of China (Grant No.2015BAK04B00)2015 Sino-German Postdoc Scholarship Program (Grant No.57165010)
文摘Locomotion and manipulation optimization is essential for the performance of tetrahedron-based mobile mechanism. Most of current optimization methods are constrained to the continuous actuated system with limited degree of freedom(DOF), which is infeasible to the optimization of binary control multi-DOF system. A novel optimization method using for the locomotion and manipulation of an 18 DOFs tetrahedron-based mechanism called 5-TET is proposed. The optimization objective is to realize the required locomotion by executing the least number of struts.Binary control strategy is adopted, and forward kinematic and tipping dynamic analyses are performed, respectively.Based on a developed genetic algorithm(GA), the optimal number of alternative struts between two adjacent steps is obtained as 5. Finally, a potential manipulation function is proposed, and the energy consumption comparison between optimal 5-TET and the traditional wheeled robot is carried out. The presented locomotion optimization and manipulation planning enrich the research of tetrahedron-based mechanisms and provide the instruction to the successive locomotion and operation planning of multi-DOF mechanisms.
文摘Aim of this work is to try to explain, on a Rational basis, some equations of Electro-Magnetism, which are based on Experimental data. Any Electric Field can produce a Field of many small Electric Dipoles, continuously distributed in space. In a region, where the Electric Field is constant, in direction and magnitude, all the small Dipoles are parallel to the Electric Field, and are represented by a single, long, parallel to them, fixed in space, Electric Dipole, which is here called Compass. An Alternating current, in a straight Conductor, is studied, by a simple, short computer program, for step-by-step nonlinear dynamic analysis. It is found that, only an Alternating current, not a direct current, can produce an Electric Dipole, in a straight Conductor. The two above Dipoles (Compass-Conductor) are assumed with equal lengths ℓ, lying on two skew lines, perpendicular to each other, at a distance ℓ√2, thus forming, by their four ends, a Regular Tetrahedron, with side length ℓ. Repulsion, between Like Charges, obeys the simple Coulomb Electro-Static law. Whereas Interaction (Attraction or Repulsion), between Unlike Charges, obeys a more accurate Lennard-Jones law. The analysis of Dipole-Dipole (Compass-Conductor) Interaction is performed by hand calculator. The only out-of-balance forces, in the regular Tetrahedron, acting on the Rigid Conductor, are the so-called magnetic forces. Their direction is found, in a simple Rational way, with help of Regular Tetrahedron, without recoursing to a “right-hand-rule”. The proposed model is applied to 1) The force acting on an Electric Charge moving in a magnetic field. 2) The force acting on a Current carrying straight Conductor, due to a magnetic field. 3) The magnetic fields created around a Current carrying straight Conductor. In these applications, proposed model gives reasonable results. Particularly, in third application, results, obtained by proposed model, are found in satisfactory approximation with corresponding ones, obtained by an empirical formula, based on relevant Experimental observations of H.-C. Oersted and A.-M. Ampère. So, the reliability of proposed model is checked. Position and direction of magnetic field vector coincide with those of a corresponding fixed Compass of a constant Electric Field. Main point of present work is that, without introducing the concept of a magnetic field vector, by combining field of dipoles, produced by an electric field, with dipole of an alternating current carrying conductor, the magnetic forces can be determined.
基金The project supported by the SpeciaLized Research Fund for the DoctoraL Program of Higher Education under Grant No. 20050285002 .
It is our pleasure to thank Yin-Sheng Ling and JianXing Fang for their helpful discussions.
基金Funded by Natural Science Foundation of China (No. 10231010)KJ of Chongqing Educational Committee (No.KJ071105)and Chongqing Three Gorges University (No. SXXYYB07004).
文摘The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time ρ (the ratio of the sizes) and mass ratio τ=m/?m must be satisfied by some formulas. For any radius ratios ρ∈(0, 0.152 996 918 2) or (0.715 223 148 7, 1.398 165 037), there is only one central configuration. Otherwise, for any given mass ratio τ , there may exist more than one central configuration.
基金supported by the Natural Science Foundation of China(Nos.21877030,21735002,21778016 and 21521063)。
文摘Accurate detection and imaging of adenosine triphosphate(ATP)expression levels in living cells is of great value for understanding cell metabolism,physiological activities,and pathologic mechanisms.Here,we developed a DNA tetrahedron-based split aptamer probe(TD probe)for ratiometric fluorescence imaging of ATP in living cells.The TD probe is constructed by hybridizing two split ATP aptamer probes(Apt-a and Apt-b)to a DNA tetrahedron assembled by four DNA oligonucleotides(T1,T2,T3 and T4).In the presence of ATP,the TD probe will alter its structure from the open to closed state,thus bringing the separated donor and acceptor fluorophores into close proximity for high fluorescence resonance energy transfer(FRET)signals.The TD probe exhibits low cytotoxicity,efficient cell internalization and good biological stability.Moreover,based on the FRET“off”to“on”signal output mode,the TD probe can effectively avoid false-positive signals from complex biological matrices,which is significant for long-term reliable imaging in living cells.In addition,by changing the split aptamers attached to DNA tetrahedron,the proposed strategy may be extended for detecting various intracellular targets.Collectively,this strategy provides a valuable sensing platform for biomarkers analysis in living cells,thus having great potential for early clinical diagnosis and therapeutic evaluation.
基金University of Wisconsin-Madison, the National Institutes of Health (NIBIB/NCI P30CA014520, T32CA009206)the American Cancer Society (125246-RSG-13- 099-01-CCE), the National Natural Science Foundation of China (Nos. 51573096, 51703132, 31771036, and 81630049)+2 种基金the Basic Research Program of Shenzhen (Nos. JCYJ20170412111100742 and JCYJ20160422091238319)the Guangdong Province Natural Science Foundation of Major Basic Research and Cultivation Project (No. 2018B030308003)Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (No. 161032).
文摘DNA tetrahedro n nano structure (DTN) is one of the simplest DNA nano structures and has bee n successfully applied for biose nsin g, imagi ng, and treatment of can cer. To facilitate its biomedical applications and pote ntial clinical tran slation, fun dame ntal un derstandi ng of DTN's transportation among major organs in living organisms becomes increasingly important. Here, we describe the efficient renal clearanee of DTN in healthy mice by using positron emission tomography (PET) imaging. The kidney elimination of DTN was later applied for renal function evaluation in murine models of unilateral ureteral obstruction (UUO). We further established a mathematical program of DTN to validate its changes of transportation pattern in healthy and UUO mice. We believe the establishment of pharmacokinetic profiles and mathematical model of DTN may provide in sight for future optimization of DNA nano structures for biomedical applications.
基金the National Natural Science Foundation of China(No.11202224)。
文摘To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor,a unified framework of burning surface regression simulation has been developed based on minimum distance function.In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface,a fast distance querying method based on the equal size cube voxel structure was employed.An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements,achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously.The cases of star grain,finocyl grain,and non-uniform tube grain were studied to verify the proposed method.The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.
文摘We present a numerical formulation for resin flow based on the concept of quasi-steady state situation at the flow front. To be fit for complicated product shapes,we use the four-node unstructured tetrahedron mesh based on which the numerical formulation of temperature and degree of cure is developed. The validity of our method is established in the case where ffexible meshes are used. The results show that the numerical procedure,tested on known data,provides numerically valid and reasonably accurate predictions.
基金the National Natural Science Foundation of China(No.21571038)Education Department of Guizhou Province(No.2021312)+4 种基金Foundation of Guizhou Province(No.2019-5666)Science Foundation for Aftergraduated Students of Guizhou Province(No.YJSCXJH2020045)State Key Laboratory of Coal Mine Disaster Dynamics and Control(Chongqing University,No.2011DA105287-ZR202101)State Key Laboratory of Physical Chemistry of Solid Surfaces(Xiamen University,No.202009)the Open Fund of the Key Lab of Organic Optoelectronics&Molecular Engineering(Tsinghua University)。
文摘Developing highly stable and active non-Pt oxygen reduction reaction(ORR)electrocatalysts for power generation device raises great concerns and remains a challenge.Here,we report novel truncated Pd tetrahedrons(T-Pd-Ths)enclosed by{111}facets with excellent uniformity,which have both low-coordinated surface sites and distinct lattice distortions that would induce“local strain”.In alkaline electrolyte,the T-Pd-Ths/C achieves remarkable ORR specific/mass activity(SA/MA)of 2.46 mA·cm^(−2)/1.69 A·mgPd^(−1),which is 12.3/16.9 and 10.7/14.1 times higher than commercial Pd/C and Pt/C,respectively.The T-Pd-Ths/C also exhibits high in-situ carbon monoxide(CO)tolerance and 50,000 cycles durability with an activity loss of 7.69%and morphological stability.The rotating ring-disk electrode(RRDE)measurements show that a 4-electron process occurs on T-PdThs/C.Theoretical calculations demonstrate that the low-coordinated surface sites contribute largely to the enhancement of ORR activity.In actual direct methanol fuel cell(DMFC)device,the T-Pd-Ths/C delivers superior open-circuit voltage(OCV)and peak power density(PPD)to commercial Pt/C from 25 to 80℃,and the maximum PPD can reach up to 163.7 mW·cm−2.This study demonstrates that the T-Pd-Ths/C holds promise as alternatives to Pt for ORR in DMFC device.
基金supported by the National Natural Science Foundation of China(Nos.11471097,11271257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20121303110005)+1 种基金the Natural Science Foundation of Hebei Province(No.A2013205021)the Key Fund Project of Hebei Normal University(No.L2012Z01)
文摘Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.
基金This work was partly supported by the Major Basic Project of China (Grant No. G19990328) the National Natural Science Foundation of China (Grant No. 69883006)+1 种基金 partly supported by NKBRSF (Grant No. G1998030600) the Doctoral Program Foundation of E
文摘It is more difficult to construct 3-D splines than in 2-D case. Some results in the three directional meshes of bivariate case have been e xtended to 3-D case and corresponding tetrahedron partition has been constructed. The support of related Bsplines and their recurrent formulas on integration and differentiationdifference are obtained. The results of this paper can be extended into higher dimension spaces, and can be also used in wavelet analysis, because of the relationship between spline and wavelets.
