As a national cultural property,General Zhang Fei’s Temple is the largest ancient architectural complex in the Three Gorges of the Yangtze River.It was built in the Han Dynasty and has a long history of nearly 2,000 ...As a national cultural property,General Zhang Fei’s Temple is the largest ancient architectural complex in the Three Gorges of the Yangtze River.It was built in the Han Dynasty and has a long history of nearly 2,000 years.In 1994,the Chinese government launched the Three Gorges Dam project at the Yangtze River and implemented the largest relocation project for the General Zhang Fei Temple to prevent it from being submerged.The temple was relocated 32 kilometers upstream along with the local people of Yunyang County,and the historic environment was rebuilt on the opposite side of the migrant city of New Yunyang County.The temple was restored successfully and the tradition of offering sacrifices to General Zhang Fei continued in the local community.The relocation project lasted for 8 years and became the largest cultural heritage conservation project of the People’s Republic of China at the end of the 20th century.This paper comprehensively summarizes and reviews the project goals,implementation process,and project highlights of this relocation,so as to provide an important case reference for heritage conservation projects in the future.展开更多
Institute of Otolaryngology of Chinese PLA ( Key Laboratory for the Prevention of Acoustic Trauma,PLA)Key Laboratory of Hearing Impairment Science(Chinese PLA Medical School)Ministry of Education Led by four generatio...Institute of Otolaryngology of Chinese PLA ( Key Laboratory for the Prevention of Acoustic Trauma,PLA)Key Laboratory of Hearing Impairment Science(Chinese PLA Medical School)Ministry of Education Led by four generations of leadership from late Prof. JIANG Sichang (academician, Chinese Academy of Engineering), Prof.YANG Weiyan (Honorary President, Division of Otolaryngology展开更多
Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with different...Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.展开更多
Led by four generations of leadership from late Prof.JIANG Sichang(academician,Chinese Academy of Engineering),Prof.YANG Weiyan(Honorary President,Division of Otolaryngology Head and Neck Surgery,Chinese Medical Assoc...Led by four generations of leadership from late Prof.JIANG Sichang(academician,Chinese Academy of Engineering),Prof.YANG Weiyan(Honorary President,Division of Otolaryngology Head and Neck Surgery,Chinese Medical Association),Prof.HAN Dongyi(President Elected,Division of Otolaryngology Head and Neck Surgery,Chinese Medical Association)to now Prof.YANG Shiming(President,Division of Otolaryngologists,展开更多
Objective To probe into the function mechanism of penetration therapy with head electrical acupuncture on Parkinson's disease. Methods Microinjection of 6-hydroxydopamin (6-OHDA) on the left cor- pus striatum was a...Objective To probe into the function mechanism of penetration therapy with head electrical acupuncture on Parkinson's disease. Methods Microinjection of 6-hydroxydopamin (6-OHDA) on the left cor- pus striatum was adopted to prepare rotation model of Parkinson^s disease in rat. Penetration therapy with head electrical acupuncture was administered in treatment. Normal group, sham-operation group, model group and penetration therapy group were set up. (1)lmmunohistochemical (IHC) method was used to test the morphology and count of positive cell of tyrosine hydroxylase (TH). (2)RT-PCR technology was used to detect the expression of nestin mRNA of neural stem cell (NSC). Results (1)Compared with model group, in pene- tration therapy group, the expressions of TH-positive neurons in immune response were increased in areal density (AD), numerical density (ND) and integrating optic density (P〈0.05). (2)Compared with model group, in penetration therapy group, the expression of nestin mRNA was increased (P〈0. 05). Conclusion Penetration therapy with head electrical acupuncture promotes the proliferation of endogenous neural stem cells in substantia nigra of rat model of Parkinson's disease.展开更多
Objective: To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer's solution in patients during the induction of general and epidural anesthesia. Methods: The hemodilution of i.v....Objective: To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer's solution in patients during the induction of general and epidural anesthesia. Methods: The hemodilution of i.v. infusion of 1000 ml of lactated Ringer's solution over 60 min was studied in patients undergoing general (n=31) and epidural (n= 22) anesthesia. Heart rate, arterial blood pressure and hemoglobin (Hb) concentration were measured every 5 rain during the study. Surgery was not started until the study period had been completed. Results: General anesthesia caused the greater decrease of mean arterial blood pressure (MAP) (mean 15% versus 9%; P〈0.01) and thereby followed by a more pronounced plasma dilution, blood volume expansion (VE) and blood volume expansion efficiency (VEE). A strong linear correlation between hemodilution and the reduction in MAP (r=-0.50;P〈0.01) was found. At the end of infusion, patients undergoing general anesthesia retained 47% (SD 19%) of the infused fluid in the circulation, while epidural anesthesia retained 29% (SD 13%) (P〈0.001). Correspondingly, a fewer urine output (mean 89 ml versus 156 ml; P〈0.05) and extravascular expansion (454 ml versus 551 ml; P〈0.05) were found during general anesthesia. Conclusion: We concluded that the induction of general anesthesia caused more hemodilution, volume expansion and volume expansion efficiency than epidural anesthesia, which was triggered only by the lower MAP.展开更多
The basic unit in life is cell.?It contains many protein molecules located at its different organelles. The growth and reproduction of a cell as well as most of its other biological functions are performed via these p...The basic unit in life is cell.?It contains many protein molecules located at its different organelles. The growth and reproduction of a cell as well as most of its other biological functions are performed via these proteins. But proteins in different organelles or subcellular locations have different functions. Facing?the avalanche of protein sequences generated in the postgenomic age, we are challenged to develop high throughput tools for identifying the subcellular localization of proteins based on their sequence information alone. Although considerable efforts have been made in this regard, the problem is far apart from being solved yet. Most existing methods can be used to deal with single-location proteins only. Actually, proteins with multi-locations may have some special biological functions that are particularly important for drug targets. Using the ML-GKR (Multi-Label Gaussian Kernel Regression) method,?we developed a new predictor called “pLoc-mGpos” by in-depth extracting the key information from GO (Gene Ontology) into the Chou’s general PseAAC (Pseudo Amino Acid Composition)?for predicting the subcellular localization of Gram-positive bacterial proteins with both single and multiple location sites. Rigorous cross-validation on a same stringent benchmark dataset indicated that the proposed pLoc-mGpos predictor is remarkably superior to “iLoc-Gpos”, the state-of-the-art predictor for the same purpose.?To maximize the convenience of most experimental scientists, a user-friendly web-server for the new powerful predictor has been established at http://www.jci-bioinfo.cn/pLoc-mGpos/, by which users can easily get their desired results without the need to go through the complicated mathematics involved.展开更多
The purpose of this paper is to explore the safe and effective dose of dexmedetomidin for the prevention of agitation and delirium during the awakening period for children undergoing general anesthesia. Samples of 989...The purpose of this paper is to explore the safe and effective dose of dexmedetomidin for the prevention of agitation and delirium during the awakening period for children undergoing general anesthesia. Samples of 989 cases are collected from children with comprehensive treatment of dental caries, and were randomly divided into four groups. Group A, group B and group C were intravenously at constant speed (60 mL/h), 0.5 and 0.25 infusion with 1 μg/kg dexmedetomidine. Group D (control group) was intravenously saline at the same speed. The score of 5-point scale and the incidence of ED (emergency delirium) and EA (emergence agitation) in four groups were compared. Comparison of four groups of CHIPPS (children and infants postoperative pain) score, the amount of operation time and record seven halothane (TO), time to stop cover drug withdrawal of laryngeal anesthesia (TM), eye opening time (TE), independent records of children at the time of ICU stay after anesthesia (TP). Results show that there was no significant difference between the four groups (p 〉 0.05), among which the TM in B, C groups was significantly higher than that in A, D groups (p 〈 0.05). Group C was significantly higher than group B (p 〈 0.05). There was no significant difference in TE and TP between the A, B, D groups (p 〉 0. 05). TE in group C was significantly higher than that in groups A, D (p 〉 0. 05). The TP of group C was significantly higher than that of groups A, D (p 〈 0.05), but there was no significant difference between the B, C groups (p 〉 0.05). The incidence rates of EA and ED in groups A and B were significantly lower than those in group D (p 〈 0.05). Group C was significantly lower than group A (p 〈 0.05). There was no significant difference between group C and group C (p 〉 0.05). The CHIPPS score and sevoflurane dosage in groups A and B were significantly lower than those in group D (p 〈 0.05). Group C was significantly lower than group A (p 〈 0.05). There was no significant difference between group C (p 〉 0.05). Conclusion: the dose of dexmetomidine 0.5 μg/kg in children with general anesthesia can prevent restlessness and delirium after operation.展开更多
This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its general...This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em>展开更多
In accordance with the regulations as stipulated in the Pro-visions of the Customs of the People’s Republic of China on Ex-ternal Audit, the Customs officers engaged in external audit shalluse the Certificate of Exte...In accordance with the regulations as stipulated in the Pro-visions of the Customs of the People’s Republic of China on Ex-ternal Audit, the Customs officers engaged in external audit shalluse the Certificate of External Audit of the Customs (hereinafterreferred to as Certificate) as of June 5, 1997. The Certificate has ablack leather outer covering and is inlaid inside with a pierced andguilded customs emblem, which consists of the red national em-blem in its upper part, and a key and a truncheon encircled by earsof wheat in its lower part. Put in a leather covering, the Certificateis a card sealed up with plastics, on which there is a bareheadedcolour photo of the holder in the Customs uniform and with a展开更多
In the present study, we have obtained a new analytical solution of combined Einstein-Maxwell field equations describing the interior field of a ball having static spherically symmetric isotropic charged flu...In the present study, we have obtained a new analytical solution of combined Einstein-Maxwell field equations describing the interior field of a ball having static spherically symmetric isotropic charged fluid within it. The charge and electric field intensity are zero at the center and monotonically increasing towards the boundary of the fluid ball. Besides these, adiabatic index is also increasing towards the boundary and becomes infinite on it. All other physical quantities such as pressure, density, adiabatic speed of sound, charge density, adiabatic index are monotonically decreasing towards the surface. Causality condition is obeyed at the center of ball. In the limiting case of vanishingly small charge, the solution degenerates into Schwarzchild uniform density solution for electrically neutral fluid. The solution joins smoothly to the Reissner-Nordstrom solution over the boundary. We have constructed a neutron star model by assuming the surface density . The mass of the neutron star comes with radius 14.574 km.展开更多
Saussure, the greatest linguist in the 20^(th) century, is the founder of modern linguistics, semiology as well as structuralism linguistics. Moreover, his ideas have have influenced a great number of linguists in the...Saussure, the greatest linguist in the 20^(th) century, is the founder of modern linguistics, semiology as well as structuralism linguistics. Moreover, his ideas have have influenced a great number of linguists in the last ninety years. This paper aims to present and comment on some of his ideas in one of this masterworks—Course in General Linguistics. In the end, the author proposes some suggestions for further study.展开更多
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, wh...By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to ehiral perturbation theory and general relativity.展开更多
文摘As a national cultural property,General Zhang Fei’s Temple is the largest ancient architectural complex in the Three Gorges of the Yangtze River.It was built in the Han Dynasty and has a long history of nearly 2,000 years.In 1994,the Chinese government launched the Three Gorges Dam project at the Yangtze River and implemented the largest relocation project for the General Zhang Fei Temple to prevent it from being submerged.The temple was relocated 32 kilometers upstream along with the local people of Yunyang County,and the historic environment was rebuilt on the opposite side of the migrant city of New Yunyang County.The temple was restored successfully and the tradition of offering sacrifices to General Zhang Fei continued in the local community.The relocation project lasted for 8 years and became the largest cultural heritage conservation project of the People’s Republic of China at the end of the 20th century.This paper comprehensively summarizes and reviews the project goals,implementation process,and project highlights of this relocation,so as to provide an important case reference for heritage conservation projects in the future.
文摘Institute of Otolaryngology of Chinese PLA ( Key Laboratory for the Prevention of Acoustic Trauma,PLA)Key Laboratory of Hearing Impairment Science(Chinese PLA Medical School)Ministry of Education Led by four generations of leadership from late Prof. JIANG Sichang (academician, Chinese Academy of Engineering), Prof.YANG Weiyan (Honorary President, Division of Otolaryngology
文摘Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.
文摘Led by four generations of leadership from late Prof.JIANG Sichang(academician,Chinese Academy of Engineering),Prof.YANG Weiyan(Honorary President,Division of Otolaryngology Head and Neck Surgery,Chinese Medical Association),Prof.HAN Dongyi(President Elected,Division of Otolaryngology Head and Neck Surgery,Chinese Medical Association)to now Prof.YANG Shiming(President,Division of Otolaryngologists,
基金the Excellent Discipline Leadership Fund Project of Harbin Science-Technology Administration :2006RFXYS044
文摘Objective To probe into the function mechanism of penetration therapy with head electrical acupuncture on Parkinson's disease. Methods Microinjection of 6-hydroxydopamin (6-OHDA) on the left cor- pus striatum was adopted to prepare rotation model of Parkinson^s disease in rat. Penetration therapy with head electrical acupuncture was administered in treatment. Normal group, sham-operation group, model group and penetration therapy group were set up. (1)lmmunohistochemical (IHC) method was used to test the morphology and count of positive cell of tyrosine hydroxylase (TH). (2)RT-PCR technology was used to detect the expression of nestin mRNA of neural stem cell (NSC). Results (1)Compared with model group, in pene- tration therapy group, the expressions of TH-positive neurons in immune response were increased in areal density (AD), numerical density (ND) and integrating optic density (P〈0.05). (2)Compared with model group, in penetration therapy group, the expression of nestin mRNA was increased (P〈0. 05). Conclusion Penetration therapy with head electrical acupuncture promotes the proliferation of endogenous neural stem cells in substantia nigra of rat model of Parkinson's disease.
基金Project (No. 20051899) supported by Office of Education of Zheji-ang Province, China
文摘Objective: To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer's solution in patients during the induction of general and epidural anesthesia. Methods: The hemodilution of i.v. infusion of 1000 ml of lactated Ringer's solution over 60 min was studied in patients undergoing general (n=31) and epidural (n= 22) anesthesia. Heart rate, arterial blood pressure and hemoglobin (Hb) concentration were measured every 5 rain during the study. Surgery was not started until the study period had been completed. Results: General anesthesia caused the greater decrease of mean arterial blood pressure (MAP) (mean 15% versus 9%; P〈0.01) and thereby followed by a more pronounced plasma dilution, blood volume expansion (VE) and blood volume expansion efficiency (VEE). A strong linear correlation between hemodilution and the reduction in MAP (r=-0.50;P〈0.01) was found. At the end of infusion, patients undergoing general anesthesia retained 47% (SD 19%) of the infused fluid in the circulation, while epidural anesthesia retained 29% (SD 13%) (P〈0.001). Correspondingly, a fewer urine output (mean 89 ml versus 156 ml; P〈0.05) and extravascular expansion (454 ml versus 551 ml; P〈0.05) were found during general anesthesia. Conclusion: We concluded that the induction of general anesthesia caused more hemodilution, volume expansion and volume expansion efficiency than epidural anesthesia, which was triggered only by the lower MAP.
文摘The basic unit in life is cell.?It contains many protein molecules located at its different organelles. The growth and reproduction of a cell as well as most of its other biological functions are performed via these proteins. But proteins in different organelles or subcellular locations have different functions. Facing?the avalanche of protein sequences generated in the postgenomic age, we are challenged to develop high throughput tools for identifying the subcellular localization of proteins based on their sequence information alone. Although considerable efforts have been made in this regard, the problem is far apart from being solved yet. Most existing methods can be used to deal with single-location proteins only. Actually, proteins with multi-locations may have some special biological functions that are particularly important for drug targets. Using the ML-GKR (Multi-Label Gaussian Kernel Regression) method,?we developed a new predictor called “pLoc-mGpos” by in-depth extracting the key information from GO (Gene Ontology) into the Chou’s general PseAAC (Pseudo Amino Acid Composition)?for predicting the subcellular localization of Gram-positive bacterial proteins with both single and multiple location sites. Rigorous cross-validation on a same stringent benchmark dataset indicated that the proposed pLoc-mGpos predictor is remarkably superior to “iLoc-Gpos”, the state-of-the-art predictor for the same purpose.?To maximize the convenience of most experimental scientists, a user-friendly web-server for the new powerful predictor has been established at http://www.jci-bioinfo.cn/pLoc-mGpos/, by which users can easily get their desired results without the need to go through the complicated mathematics involved.
文摘The purpose of this paper is to explore the safe and effective dose of dexmedetomidin for the prevention of agitation and delirium during the awakening period for children undergoing general anesthesia. Samples of 989 cases are collected from children with comprehensive treatment of dental caries, and were randomly divided into four groups. Group A, group B and group C were intravenously at constant speed (60 mL/h), 0.5 and 0.25 infusion with 1 μg/kg dexmedetomidine. Group D (control group) was intravenously saline at the same speed. The score of 5-point scale and the incidence of ED (emergency delirium) and EA (emergence agitation) in four groups were compared. Comparison of four groups of CHIPPS (children and infants postoperative pain) score, the amount of operation time and record seven halothane (TO), time to stop cover drug withdrawal of laryngeal anesthesia (TM), eye opening time (TE), independent records of children at the time of ICU stay after anesthesia (TP). Results show that there was no significant difference between the four groups (p 〉 0.05), among which the TM in B, C groups was significantly higher than that in A, D groups (p 〈 0.05). Group C was significantly higher than group B (p 〈 0.05). There was no significant difference in TE and TP between the A, B, D groups (p 〉 0. 05). TE in group C was significantly higher than that in groups A, D (p 〉 0. 05). The TP of group C was significantly higher than that of groups A, D (p 〈 0.05), but there was no significant difference between the B, C groups (p 〉 0.05). The incidence rates of EA and ED in groups A and B were significantly lower than those in group D (p 〈 0.05). Group C was significantly lower than group A (p 〈 0.05). There was no significant difference between group C and group C (p 〉 0.05). The CHIPPS score and sevoflurane dosage in groups A and B were significantly lower than those in group D (p 〈 0.05). Group C was significantly lower than group A (p 〈 0.05). There was no significant difference between group C (p 〉 0.05). Conclusion: the dose of dexmetomidine 0.5 μg/kg in children with general anesthesia can prevent restlessness and delirium after operation.
文摘This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em>
文摘In accordance with the regulations as stipulated in the Pro-visions of the Customs of the People’s Republic of China on Ex-ternal Audit, the Customs officers engaged in external audit shalluse the Certificate of External Audit of the Customs (hereinafterreferred to as Certificate) as of June 5, 1997. The Certificate has ablack leather outer covering and is inlaid inside with a pierced andguilded customs emblem, which consists of the red national em-blem in its upper part, and a key and a truncheon encircled by earsof wheat in its lower part. Put in a leather covering, the Certificateis a card sealed up with plastics, on which there is a bareheadedcolour photo of the holder in the Customs uniform and with a
文摘In the present study, we have obtained a new analytical solution of combined Einstein-Maxwell field equations describing the interior field of a ball having static spherically symmetric isotropic charged fluid within it. The charge and electric field intensity are zero at the center and monotonically increasing towards the boundary of the fluid ball. Besides these, adiabatic index is also increasing towards the boundary and becomes infinite on it. All other physical quantities such as pressure, density, adiabatic speed of sound, charge density, adiabatic index are monotonically decreasing towards the surface. Causality condition is obeyed at the center of ball. In the limiting case of vanishingly small charge, the solution degenerates into Schwarzchild uniform density solution for electrically neutral fluid. The solution joins smoothly to the Reissner-Nordstrom solution over the boundary. We have constructed a neutron star model by assuming the surface density . The mass of the neutron star comes with radius 14.574 km.
文摘Saussure, the greatest linguist in the 20^(th) century, is the founder of modern linguistics, semiology as well as structuralism linguistics. Moreover, his ideas have have influenced a great number of linguists in the last ninety years. This paper aims to present and comment on some of his ideas in one of this masterworks—Course in General Linguistics. In the end, the author proposes some suggestions for further study.
基金The project supported in part by National Natural Science Foundation of China
文摘By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to ehiral perturbation theory and general relativity.