The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is establishe...The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is established for the iterations of Euler family under the assumption that $\alpha \leqslant 3 - 2\sqrt 2 $ , while the strong condition thatf is analytic in Smale’s criterion α is replaced by the weak condition thatf is of finite order derivative.展开更多
In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matte...In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.展开更多
About the accurate value of ψ （ x ） = Γ′ （ x ） / Γ （ x）, we know only ψ （1）and ψ （1/ 2）.In this paper, by calculating the accurate values of some series expansion of a function and applying some skills...About the accurate value of ψ （ x ） = Γ′ （ x ） / Γ （ x）, we know only ψ （1）and ψ （1/ 2）.In this paper, by calculating the accurate values of some series expansion of a function and applying some skills of complex analysis, we prove that the expression of the ψ-function admits a finite expression in elementary function for rational number z. As an application, some examples are given.展开更多
We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic com...We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.展开更多
In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In...In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler＇s constant γ.展开更多
文摘The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is established for the iterations of Euler family under the assumption that $\alpha \leqslant 3 - 2\sqrt 2 $ , while the strong condition thatf is analytic in Smale’s criterion α is replaced by the weak condition thatf is of finite order derivative.
文摘In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.
基金Supported by the National Natural Science Foundation of China (10926128)
文摘About the accurate value of ψ （ x ） = Γ′ （ x ） / Γ （ x）, we know only ψ （1）and ψ （1/ 2）.In this paper, by calculating the accurate values of some series expansion of a function and applying some skills of complex analysis, we prove that the expression of the ψ-function admits a finite expression in elementary function for rational number z. As an application, some examples are given.
基金supported by National Basic Research Program of China (Grant No. 2011CB309705)National Natural Science Foundation of China (Grant Nos. 11229101, 11371065 and 11271184)+2 种基金Program for New Century Excellent Talents in University (Grant No. 110227)the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Fundamental Research Funds for the Central Universities
文摘We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.
基金Supported by the National Natural Science Foundation of China(11171307)
文摘In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler＇s constant γ.
