Objective:Clinical education plays a key role in preparing students for patient care.Laparoscopy is one of the most important minimally invasive surgeries(MISs)wherein surgical technologists are responsible for camera...Objective:Clinical education plays a key role in preparing students for patient care.Laparoscopy is one of the most important minimally invasive surgeries(MISs)wherein surgical technologists are responsible for camera navigation and assistant surgeons are responsible for peg transfer.Therefore,it is necessary to improve the attitude of the operating room students toward these skills during their study period.The present study was conducted to determine the effect of simulating training in the fundamentals of laparoscopic surgery(FLS)on the attitude of the operating room students.Methods:This interventional study was conducted on 28 operating room students of Iran University of Medical Sciences in 2019.The census sampling method was used.The data-collection tool included the“Intrinsic motivation inventory(IMI)questionnaire.”The educational intervention was carried out in theoretical(booklet design)and practical(simulation)sections.Data analysis was carried out using descriptive and inferential analyses including the paired t-test,Mann–Whitney U test,and independent t-test.The collected data were analyzed using R and SPSS software.P-value<0.05 was considered as the significant level.Results:The mean±SD of the participants'age was 22.93±2.14 years,and the majority of them were women(67.9%).There was a significant difference in the mean scores of students'attitudes toward the FLS before and after the educational intervention(P<0.001)in all dimensions(interest,perceived competence,perceived choice,and tension).There was also a significant correlation between gender and interest dimension(P=0.005).Conclusions:The results of the present study showed that simulating the training FLS curriculum positively affects students'attitudes.Therefore,the researchers suggest that for creating a positive attitude,increasing students'interest in laparoscopic surgery,and ensuring a more effective presence in the operating room,this training should be considered in the operating room curriculum.展开更多
A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality co...A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality constrained optimization problems is presented.Through the detail comparison of arithmetic operations,it is concluded that the average iteration number within differential algebraic equations(DAEs)integration of quasi-sequential approach could be regarded as a criterion.One formula is given to calculate the threshold value of average iteration number.If the average iteration number is less than the threshold value,quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily.Two optimal control problems are given to demonstrate the usage of threshold value.For optimal control problems whose objective is to stay near desired operating point,the iteration number is usually small.Therefore,quasi-sequential approach seems more suitable for such problems.展开更多
Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Mos...Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Most numeral systems make use of a base,typically 10,less commonly 20,followed by a wide range of other possibilities.Higher numerals are formed from primitive lower numerals by applying the processes of addition and multiplication,in many languages also exponentiation;sometimes,however,numerals are formed from a higher numeral,using subtraction or division.Numerous complexities and idiosyncrasies are discussed,as are numeral systems that fall outside this general characterization,such as restricted numeral systems with no internal arithmetic structure,and some New Guinea extended body-part counting systems.展开更多
In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak (1-1) boundedness of...In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.展开更多
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlat...A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.展开更多
In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the...In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|~γ▽_y) and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.展开更多
We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representat...We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.展开更多
Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their...Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.展开更多
English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat’s Last Theorem which had for 358 years notoriously resisted all gallant and spirited ...English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat’s Last Theorem which had for 358 years notoriously resisted all gallant and spirited efforts to prove it even by three of the greatest mathematicians of all time—such as Euler, Laplace and Gauss. Sir Professor Andrew Wiles’s proof employed very advanced mathematical tools and methods that were not at all available in the known World during Fermat’s days. Given that Fermat claimed to have had the “truly marvellous” proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat’s time, has led many to doubt that Fermat actually did possess the “truly marvellous” proof which he claimed to have had. In this short reading, via elementary arithmetic methods, we demonstrate conclusively that Fermat’s Last Theorem actually yields to our efforts to prove it.展开更多
At the end of last year, the editors from Power and Electrical Engineers interviewed Zhou Xiaoxin on "Fundamental Research on Enhancing Operation Reliability for Large-Scale Interconnected Power Grids", a pr...At the end of last year, the editors from Power and Electrical Engineers interviewed Zhou Xiaoxin on "Fundamental Research on Enhancing Operation Reliability for Large-Scale Interconnected Power Grids", a project of "973 Program". Mr. Zhou, the chief engineer of China Electric Power Research Institute(CEPRI) and an academician of Chinese Academy of Sciences, is the chief scientist in charge of this research project.展开更多
Numeracy is the capacity to use mathematical ideas in all facets of life.It involves activities such as adding and subtracting numbers,counting,number recognition,solving number problems involving various operations,s...Numeracy is the capacity to use mathematical ideas in all facets of life.It involves activities such as adding and subtracting numbers,counting,number recognition,solving number problems involving various operations,sorting,observing,identifying,and establishing patterns.It is one of the fundamental skills that students should have mastered by the end of their primary schooling.With the notable importance of mastery of numeracy skills,low achievement and performance of the learners were observed in this aspect.This study aimed in enhancing the numeracy skills of Grade 3 learners through authentic performance tasks.The variable in numeracy skills includes the four fundamental operations and problem solving.The quasi-experimental design was utilized wherein purposive sampling or non-randomized sampling was used.In this study,33 Grade 3 learners of Rizal Elementary School were selected to participate in the tests.Pre-test and post-test crafted by the teacher were the main instrument in the study.The result revealed that in the pre-test the learners obtained a mean percentage score(MPS)of 38.20%in four fundamental operations,which implied a non-numerate level.While in terms of problem solving,the learners obtained a MPS of 20.60%which is also in the non-numerate level.It has a grand mean of 29.40%with an interpretation of non-numerate level.In the post-test,it was observed that four fundamental operations have a MPS of 81.10%which is in average numerate level,while problem solving has a MPS of 76.30%with a grand mean of 78.70%with an interpretation of average numerate level.This implied that there is a significant difference between the pre-test and post-test in the four fundamental operations and problem solving.Thus,it can be concluded that the application of authentic performance tasks was effective to bridge the gap on numeracy skills.展开更多
New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equ...New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equations. The sole aim of this paper is to make a case for arithmetic calculus, which is lurking in conventional mathematics and science but has no identity of its own. The underlying thinking is: 1) to shift the focus from the whole sequence to any of its single elements;and 2) to factorise each element to building blocks and rules. One outcome of this emerging calculus is to understand the interconnectivity in a family of sequences, without which they are seen as discrete entities with no interconnectivity. Arithmetic calculus is a step closer towards deriving a “Tree of Numbers” reminiscent of the Tree of Life. Another windfall outcome is to show that the deconvolution problem is explicitly well-posed but at the same time implicitly ill-conditioned;and this challenges a misconception that this problem is ill-posed. If the thinking in this paper is not new, this paper forges it through a mathematical spin by presenting new terms, definitions, notations and operators. The return for these out of the blue new aspects is far reaching.展开更多
Although many methods have been applied to diagnose the gear thult currently, the sensitivity of them is not very good. In order to make the diagnosis methods have more excellent integrated ability in such aspects as ...Although many methods have been applied to diagnose the gear thult currently, the sensitivity of them is not very good. In order to make the diagnosis methods have more excellent integrated ability in such aspects as precision, sensitivity, reliability and compact algorithm, and so on, and enlightened by the energy operator separation algorithm (EOSA), a new demodulation method which is optimizing energy operator separation algorithm (OEOSA) is presented. In the algorithm, the non-linear differential operator is utilized to its differential equation: Choosing the unit impulse response length of filter and fixing the weighting coefficient for inportant points. The method has been applied in diagnosing tooth broden and fatiguing crack of gear faults successfully. It provides demodulation analysis of machine signal with a new approach.展开更多
The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the ...The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form (FFF) and the partial Noether operator's determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and fiat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.展开更多
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) =∑k=0^n akψ(k) where the constant coefficients...For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) =∑k=0^n akψ(k) where the constant coefficients ak C R may be adapted to f.展开更多
基金supported by the Iran University of Medical Science。
文摘Objective:Clinical education plays a key role in preparing students for patient care.Laparoscopy is one of the most important minimally invasive surgeries(MISs)wherein surgical technologists are responsible for camera navigation and assistant surgeons are responsible for peg transfer.Therefore,it is necessary to improve the attitude of the operating room students toward these skills during their study period.The present study was conducted to determine the effect of simulating training in the fundamentals of laparoscopic surgery(FLS)on the attitude of the operating room students.Methods:This interventional study was conducted on 28 operating room students of Iran University of Medical Sciences in 2019.The census sampling method was used.The data-collection tool included the“Intrinsic motivation inventory(IMI)questionnaire.”The educational intervention was carried out in theoretical(booklet design)and practical(simulation)sections.Data analysis was carried out using descriptive and inferential analyses including the paired t-test,Mann–Whitney U test,and independent t-test.The collected data were analyzed using R and SPSS software.P-value<0.05 was considered as the significant level.Results:The mean±SD of the participants'age was 22.93±2.14 years,and the majority of them were women(67.9%).There was a significant difference in the mean scores of students'attitudes toward the FLS before and after the educational intervention(P<0.001)in all dimensions(interest,perceived competence,perceived choice,and tension).There was also a significant correlation between gender and interest dimension(P=0.005).Conclusions:The results of the present study showed that simulating the training FLS curriculum positively affects students'attitudes.Therefore,the researchers suggest that for creating a positive attitude,increasing students'interest in laparoscopic surgery,and ensuring a more effective presence in the operating room,this training should be considered in the operating room curriculum.
基金Supported by the National Natural Science Foundation of China(20676117) the National Creative Research Groups Science Foundation of China(60421002)
文摘A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality constrained optimization problems is presented.Through the detail comparison of arithmetic operations,it is concluded that the average iteration number within differential algebraic equations(DAEs)integration of quasi-sequential approach could be regarded as a criterion.One formula is given to calculate the threshold value of average iteration number.If the average iteration number is less than the threshold value,quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily.Two optimal control problems are given to demonstrate the usage of threshold value.For optimal control problems whose objective is to stay near desired operating point,the iteration number is usually small.Therefore,quasi-sequential approach seems more suitable for such problems.
文摘Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Most numeral systems make use of a base,typically 10,less commonly 20,followed by a wide range of other possibilities.Higher numerals are formed from primitive lower numerals by applying the processes of addition and multiplication,in many languages also exponentiation;sometimes,however,numerals are formed from a higher numeral,using subtraction or division.Numerous complexities and idiosyncrasies are discussed,as are numeral systems that fall outside this general characterization,such as restricted numeral systems with no internal arithmetic structure,and some New Guinea extended body-part counting systems.
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
文摘In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.
基金supported by the National Natural Science Foundation for Excellent Young Scholars(Grant 51222502)the National Natural Science Foundation of China(Grant 11172096)the Funds for State Key Laboratory of Construction Machinery(SKLCM2014-1)
文摘A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
基金Foundation item: Supported by the Natural Science Foundation of Zhejiang Province(Y6090359, Y6090383) Supported by the Department of Education of Zhejiang Province(Z200803357)
文摘In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|~γ▽_y) and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.
文摘We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.
基金This study has received funding by the Science and Technology Plan Project of Keqiao District(No.2020KZ58).
文摘Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.
文摘English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat’s Last Theorem which had for 358 years notoriously resisted all gallant and spirited efforts to prove it even by three of the greatest mathematicians of all time—such as Euler, Laplace and Gauss. Sir Professor Andrew Wiles’s proof employed very advanced mathematical tools and methods that were not at all available in the known World during Fermat’s days. Given that Fermat claimed to have had the “truly marvellous” proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat’s time, has led many to doubt that Fermat actually did possess the “truly marvellous” proof which he claimed to have had. In this short reading, via elementary arithmetic methods, we demonstrate conclusively that Fermat’s Last Theorem actually yields to our efforts to prove it.
文摘At the end of last year, the editors from Power and Electrical Engineers interviewed Zhou Xiaoxin on "Fundamental Research on Enhancing Operation Reliability for Large-Scale Interconnected Power Grids", a project of "973 Program". Mr. Zhou, the chief engineer of China Electric Power Research Institute(CEPRI) and an academician of Chinese Academy of Sciences, is the chief scientist in charge of this research project.
文摘Numeracy is the capacity to use mathematical ideas in all facets of life.It involves activities such as adding and subtracting numbers,counting,number recognition,solving number problems involving various operations,sorting,observing,identifying,and establishing patterns.It is one of the fundamental skills that students should have mastered by the end of their primary schooling.With the notable importance of mastery of numeracy skills,low achievement and performance of the learners were observed in this aspect.This study aimed in enhancing the numeracy skills of Grade 3 learners through authentic performance tasks.The variable in numeracy skills includes the four fundamental operations and problem solving.The quasi-experimental design was utilized wherein purposive sampling or non-randomized sampling was used.In this study,33 Grade 3 learners of Rizal Elementary School were selected to participate in the tests.Pre-test and post-test crafted by the teacher were the main instrument in the study.The result revealed that in the pre-test the learners obtained a mean percentage score(MPS)of 38.20%in four fundamental operations,which implied a non-numerate level.While in terms of problem solving,the learners obtained a MPS of 20.60%which is also in the non-numerate level.It has a grand mean of 29.40%with an interpretation of non-numerate level.In the post-test,it was observed that four fundamental operations have a MPS of 81.10%which is in average numerate level,while problem solving has a MPS of 76.30%with a grand mean of 78.70%with an interpretation of average numerate level.This implied that there is a significant difference between the pre-test and post-test in the four fundamental operations and problem solving.Thus,it can be concluded that the application of authentic performance tasks was effective to bridge the gap on numeracy skills.
文摘New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equations. The sole aim of this paper is to make a case for arithmetic calculus, which is lurking in conventional mathematics and science but has no identity of its own. The underlying thinking is: 1) to shift the focus from the whole sequence to any of its single elements;and 2) to factorise each element to building blocks and rules. One outcome of this emerging calculus is to understand the interconnectivity in a family of sequences, without which they are seen as discrete entities with no interconnectivity. Arithmetic calculus is a step closer towards deriving a “Tree of Numbers” reminiscent of the Tree of Life. Another windfall outcome is to show that the deconvolution problem is explicitly well-posed but at the same time implicitly ill-conditioned;and this challenges a misconception that this problem is ill-posed. If the thinking in this paper is not new, this paper forges it through a mathematical spin by presenting new terms, definitions, notations and operators. The return for these out of the blue new aspects is far reaching.
基金This project is supported by National Ministry of Education of China (No.020616)Science and Technology Project of Municipal Educational Committee of Chongqing(No.030602)Scientific Research Foundation of Chongqing Institute of Technology(No.2004ZD10).
文摘Although many methods have been applied to diagnose the gear thult currently, the sensitivity of them is not very good. In order to make the diagnosis methods have more excellent integrated ability in such aspects as precision, sensitivity, reliability and compact algorithm, and so on, and enlightened by the energy operator separation algorithm (EOSA), a new demodulation method which is optimizing energy operator separation algorithm (OEOSA) is presented. In the algorithm, the non-linear differential operator is utilized to its differential equation: Choosing the unit impulse response length of filter and fixing the weighting coefficient for inportant points. The method has been applied in diagnosing tooth broden and fatiguing crack of gear faults successfully. It provides demodulation analysis of machine signal with a new approach.
文摘The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form (FFF) and the partial Noether operator's determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and fiat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.
文摘For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) =∑k=0^n akψ(k) where the constant coefficients ak C R may be adapted to f.