AIM: To compare the Barrett True-K formula with other formulas integrated in Lenstar 900 to predict intraocular lens(IOL) power after small-incision lenticule extraction(SMILE).METHODS: A theoretical prospective study...AIM: To compare the Barrett True-K formula with other formulas integrated in Lenstar 900 to predict intraocular lens(IOL) power after small-incision lenticule extraction(SMILE).METHODS: A theoretical prospective study was performed to predict the ratio of equivalent IOL power before and after SMILE using the SRK/T(Sanders, Retzlaff, Kraff/theoretical), Holladay 1, Haigis, and Barrett True-K formulas and compare the stability of their predictions. The study included 54 eyes(54 cases) with a manifest refraction spherical equivalent(MRSE) of-4.99±1.45 D. They were divided into two groups: 27 eyes with axial length of 24-26 mm in Group A, and 27 eyes with axial length >26 mm in Group B. All subjects enrolled in this study were examined with the Lenstar 900 before and 6 mo after SMILE including measurements of axial length, corneal curvature, and anterior chamber depth(ACD). RESULTS: The prediction of equivalent IOL power of the two groups was more stable for the Barrett True-K formula, especially in long axial length eyes(Group B). The respective percentages for the SRK/T, Holladay 1, Haigis, and Barrett True-K formulas were 7.4%, 7.4%, 85.19%, and 88.89% for a margin of error within 0.5 D;25.92%, 51.84%, 100%, and 100% for a margin of error within 1.0 D in Group A;33.33%, 40.74%, 44.44%, and 81.48% for a margin of error within 0.5 D;and 44.44%, 59.26%, 66.66%, and 92.59% for a margin of error within 1.0 D in Group B. The respective percentages for Barrett True-K formulas were 100% for a margin of error within 2.0 D in Group B.CONCLUSION: Theoretically, the Barrett True-K formula provides more stable predictions than other formulas for cataract eyes after SMILE.展开更多
We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive qua...We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.展开更多
After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first...After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.展开更多
In this paper,we discuss in detail the basic issue of green design and consider an energy efficiency function as the metric to evaluate green cellular networks.Specifically,we investigate the transmit power required f...In this paper,we discuss in detail the basic issue of green design and consider an energy efficiency function as the metric to evaluate green cellular networks.Specifically,we investigate the transmit power required for an expected transmission capacity and propose a capacity-power formula based on the energy conservation and the Shannon capacity theorem.Two novel definitions of cell interference depth and handoff dynamic model are introduced and the corresponding expression of energy efficiency function is derived.Numerical results show that the energy efficiency function is closely correlated with the transmitted/received power required and the cell radius.Our work provides a useful basis for research and evaluation on green design and technology of cellular networks.展开更多
The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a...The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.展开更多
In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for...In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.展开更多
文摘AIM: To compare the Barrett True-K formula with other formulas integrated in Lenstar 900 to predict intraocular lens(IOL) power after small-incision lenticule extraction(SMILE).METHODS: A theoretical prospective study was performed to predict the ratio of equivalent IOL power before and after SMILE using the SRK/T(Sanders, Retzlaff, Kraff/theoretical), Holladay 1, Haigis, and Barrett True-K formulas and compare the stability of their predictions. The study included 54 eyes(54 cases) with a manifest refraction spherical equivalent(MRSE) of-4.99±1.45 D. They were divided into two groups: 27 eyes with axial length of 24-26 mm in Group A, and 27 eyes with axial length >26 mm in Group B. All subjects enrolled in this study were examined with the Lenstar 900 before and 6 mo after SMILE including measurements of axial length, corneal curvature, and anterior chamber depth(ACD). RESULTS: The prediction of equivalent IOL power of the two groups was more stable for the Barrett True-K formula, especially in long axial length eyes(Group B). The respective percentages for the SRK/T, Holladay 1, Haigis, and Barrett True-K formulas were 7.4%, 7.4%, 85.19%, and 88.89% for a margin of error within 0.5 D;25.92%, 51.84%, 100%, and 100% for a margin of error within 1.0 D in Group A;33.33%, 40.74%, 44.44%, and 81.48% for a margin of error within 0.5 D;and 44.44%, 59.26%, 66.66%, and 92.59% for a margin of error within 1.0 D in Group B. The respective percentages for Barrett True-K formulas were 100% for a margin of error within 2.0 D in Group B.CONCLUSION: Theoretically, the Barrett True-K formula provides more stable predictions than other formulas for cataract eyes after SMILE.
基金the National Natural Science Foundation of China(Grant No.12061054)Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region of China(Grant No.NJYT-20A06)。
文摘We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.
文摘After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.
基金the National Science Foundation of China，the Hi-Tech Research and Development Program of China of Mobile Internet
文摘In this paper,we discuss in detail the basic issue of green design and consider an energy efficiency function as the metric to evaluate green cellular networks.Specifically,we investigate the transmit power required for an expected transmission capacity and propose a capacity-power formula based on the energy conservation and the Shannon capacity theorem.Two novel definitions of cell interference depth and handoff dynamic model are introduced and the corresponding expression of energy efficiency function is derived.Numerical results show that the energy efficiency function is closely correlated with the transmitted/received power required and the cell radius.Our work provides a useful basis for research and evaluation on green design and technology of cellular networks.
文摘The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.
基金supported by the National Natural Science Foundation of China under Grant Nos.11971341 and 12001492the Natural Science Foundation of Zhejiang Province under Grant No.LQ20A010004.
文摘In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.
