We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second...We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.展开更多
In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and t...In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and the relationship between special polynomials and numbers.Also,we introduce modified degenerate unipolyCauchy polynomials of the second kind and derive some fruitful properties of these polynomials.In addition,positive associated beautiful zeros and graphical representations are displayed with the help of Mathematica.展开更多
In May of 2007,the second generation selected (SS) and control (SC) groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the...In May of 2007,the second generation selected (SS) and control (SC) groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the first generation selected group.Growth performance of the SS and SC groups were compared on the basis of measurement data at Days 8,18,60,95,195 and 365.On Day 365,100 individuals (60.0–75.0 mm at shell length) were sampled from each group and then subjected to the experiment where physiological parameters such as filtrate rate,oxygen consumption and ammonia excretion were measured at 15,20,25 and 30°C.The results show that the SS group had significantly larger mean shell length and shell height than the SC group at Days 8,18,60,95,195 and 365 (P 0.05).The genetic gains at different ages varied from 6.0% to 17.0% for shell length and 5.7% to 14.6% for shell height,respectively.At 15,20,25 and 30 ° C,the SS groups had significantly larger filtrate rate than the SC group (P 0.05).At 15 and 25 °C,the differences in oxygen consumption rate between the SS and SC groups were not significant (P 0.05).At 20 and 30 °C,however,the oxygen consumption rate of the SS group was significantly larger than the SC group (P 0.05).At 15,20,25 and 30 °C,there were no significant differences in ammonia excretion rate between the SS and SC groups (P 0.05).The present results indicate that there existed considerable genetic variability in the base population and a further selection could be likely fruitful.Mass selection for faster growth might produce animals that had higher intake of metabolizable energy by virtue of faster filtrating behavior.展开更多
Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one ...Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O(1/n|nn)展开更多
It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities (cracks, pores, foreign particles). From the theor...It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities (cracks, pores, foreign particles). From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomo- geneity. In this paper, we point out the impossibility to trans- form this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.展开更多
By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conser...By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation quantities under Gaussian (or spherical) mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed展开更多
The second phase particle dispersed in microalloyed steel has different effects on grain growth depending on their size and volume fiaction of the second phase particles which will change during welding thermal cycles...The second phase particle dispersed in microalloyed steel has different effects on grain growth depending on their size and volume fiaction of the second phase particles which will change during welding thermal cycles. The particle coarsening and dissolution kinetics model was analyzed for continuous heating and cooling. In addition, based on experimental data, the coupled equation of grain growth was established by introducing limited size of grain growth with the consideration of the second phase particles pinning effects. Using Monte Carlo method based on experimental data model, the grain growth simulation for heat-affected zone of microalloyed steel welds was achieved. The calculating results were well in agreement with that of experiments.展开更多
The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing t...The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.展开更多
Theories of the second reciprocal derivative chronopotentiometry analysis were deduced and experimentally verificated.Results in this study show that chronopotentiometry is significantly developed in both sensitivity ...Theories of the second reciprocal derivative chronopotentiometry analysis were deduced and experimentally verificated.Results in this study show that chronopotentiometry is significantly developed in both sensitivity and resolution for signals treated by the second reciprocal derivative.展开更多
First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed.Then the case with a general form of nonlinearity is considered and its global proper...First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed.Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations.As a result,sufficient conditions for estimating the critical damp are established,which improves the work by Leonov et al.展开更多
The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By a...The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.展开更多
The isospectral problem of the second mKdV equation is found out firstly. It follows that the strong hereditary symmetry and the Hamiltonian structure of the second mKdV equation are presented.
The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics.In recent years,some mathematicians have studied degenerate version of them and o...The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics.In recent years,some mathematicians have studied degenerate version of them and obtained many interesting results.With this in mind,in this paper,we introduce the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind.We derive many interesting properties and identities for them including generating functions,Dobinski-like formula,integral representations,recurrence relations,differential equation and various explicit expressions.In addition,we explore some expressions for them that can be derived from repeated applications of certain operators to the exponential functions,the derivatives of them and some identities involving them.展开更多
GENERAL INFORMATIONThe Chinese Society of Metals is pleased to announcethat The Second International Conference on HSLASteels(HSEA’90)will be held in Beijing,China inOctober 1990.Much progress in research and devel-o...GENERAL INFORMATIONThe Chinese Society of Metals is pleased to announcethat The Second International Conference on HSLASteels(HSEA’90)will be held in Beijing,China inOctober 1990.Much progress in research and devel-opment of HSLA steels has been achieved by theworld’s metallurgical and materials community sincethe previous International Conference HSLA Steels’85 was held in Beijing,The aim of the conference isto review and to consolidate the scientific,metallurgical,and economical results and to assessthe future trend of development in the fields.展开更多
Beijing / China August 2-6, 2010 Organized by The Chinese Society of Rare Earths (CSRE) Co-Organized by Peking University (PKU), Roskill Information Services Ltd., Metallurgical Council
基金This work was supported by the National Research Foundation of Korea(NRF)Grant Funded by the Korea Government(No.2020R1F1A1A01071564).
文摘We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.
基金supported by the Taif University Researchers Supporting Project(TURSP-2020/246),Taif University,Taif,Saudi Arabia.
文摘In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and the relationship between special polynomials and numbers.Also,we introduce modified degenerate unipolyCauchy polynomials of the second kind and derive some fruitful properties of these polynomials.In addition,positive associated beautiful zeros and graphical representations are displayed with the help of Mathematica.
基金The National Key Technology R&D Program in the 11th Five Year Plan of China under contract No. 2007BAD29B01-2National Department Public Benefit Research Foundation under contract No. nyhyzx 07-048Guangdong Marine and Fishery Bureau under contract Nos A200708C01, A200908A02 and A200908A05
文摘In May of 2007,the second generation selected (SS) and control (SC) groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the first generation selected group.Growth performance of the SS and SC groups were compared on the basis of measurement data at Days 8,18,60,95,195 and 365.On Day 365,100 individuals (60.0–75.0 mm at shell length) were sampled from each group and then subjected to the experiment where physiological parameters such as filtrate rate,oxygen consumption and ammonia excretion were measured at 15,20,25 and 30°C.The results show that the SS group had significantly larger mean shell length and shell height than the SC group at Days 8,18,60,95,195 and 365 (P 0.05).The genetic gains at different ages varied from 6.0% to 17.0% for shell length and 5.7% to 14.6% for shell height,respectively.At 15,20,25 and 30 ° C,the SS groups had significantly larger filtrate rate than the SC group (P 0.05).At 15 and 25 °C,the differences in oxygen consumption rate between the SS and SC groups were not significant (P 0.05).At 20 and 30 °C,however,the oxygen consumption rate of the SS group was significantly larger than the SC group (P 0.05).At 15,20,25 and 30 °C,there were no significant differences in ammonia excretion rate between the SS and SC groups (P 0.05).The present results indicate that there existed considerable genetic variability in the base population and a further selection could be likely fruitful.Mass selection for faster growth might produce animals that had higher intake of metabolizable energy by virtue of faster filtrating behavior.
基金Supported by the National Nature Science Foundation.
文摘Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O(1/n|nn)
基金supported by the National Natural Science Foundation of China (10872086 and 11072105)
文摘It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities (cracks, pores, foreign particles). From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomo- geneity. In this paper, we point out the impossibility to trans- form this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.
基金Project supported by the National Natural Science Foundation of China (No.10572076)
文摘By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation quantities under Gaussian (or spherical) mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed
文摘The second phase particle dispersed in microalloyed steel has different effects on grain growth depending on their size and volume fiaction of the second phase particles which will change during welding thermal cycles. The particle coarsening and dissolution kinetics model was analyzed for continuous heating and cooling. In addition, based on experimental data, the coupled equation of grain growth was established by introducing limited size of grain growth with the consideration of the second phase particles pinning effects. Using Monte Carlo method based on experimental data model, the grain growth simulation for heat-affected zone of microalloyed steel welds was achieved. The calculating results were well in agreement with that of experiments.
基金Supported by the National Natural Science Foun-dation of China(10101018)
文摘The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.
基金Project supported by the Natural Science Foundation of the Education Committee of Hunan Province.
文摘Theories of the second reciprocal derivative chronopotentiometry analysis were deduced and experimentally verificated.Results in this study show that chronopotentiometry is significantly developed in both sensitivity and resolution for signals treated by the second reciprocal derivative.
文摘First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed.Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations.As a result,sufficient conditions for estimating the critical damp are established,which improves the work by Leonov et al.
文摘The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371070, the Youth Foundation of Shanghai Education Committee and the Special Funds for Major Specialities of Shanghai Education Committee .The first author expresses her appreciations to the soliton disquisitive team of Shanghai University for their useful discussions.
文摘The isospectral problem of the second mKdV equation is found out firstly. It follows that the strong hereditary symmetry and the Hamiltonian structure of the second mKdV equation are presented.
基金supported by the Basic Science Research Program,the National Research Foundation of Korea(NRF-2021R1F1A1050151).
文摘The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics.In recent years,some mathematicians have studied degenerate version of them and obtained many interesting results.With this in mind,in this paper,we introduce the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind.We derive many interesting properties and identities for them including generating functions,Dobinski-like formula,integral representations,recurrence relations,differential equation and various explicit expressions.In addition,we explore some expressions for them that can be derived from repeated applications of certain operators to the exponential functions,the derivatives of them and some identities involving them.
文摘GENERAL INFORMATIONThe Chinese Society of Metals is pleased to announcethat The Second International Conference on HSLASteels(HSEA’90)will be held in Beijing,China inOctober 1990.Much progress in research and devel-opment of HSLA steels has been achieved by theworld’s metallurgical and materials community sincethe previous International Conference HSLA Steels’85 was held in Beijing,The aim of the conference isto review and to consolidate the scientific,metallurgical,and economical results and to assessthe future trend of development in the fields.
文摘Beijing / China August 2-6, 2010 Organized by The Chinese Society of Rare Earths (CSRE) Co-Organized by Peking University (PKU), Roskill Information Services Ltd., Metallurgical Council