For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial...For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.展开更多
In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
In renewing tissues,mutations conferring selective advantage may result in clonal expansions1-4.In contrast to somatic tissues,mutations driving clonal expansions in spermatogonia(CES)are also transmitted to the next ...In renewing tissues,mutations conferring selective advantage may result in clonal expansions1-4.In contrast to somatic tissues,mutations driving clonal expansions in spermatogonia(CES)are also transmitted to the next generation.This results in an effective increase of de novo mutation rate for CES drivers5-8.CES was originally discovered through extreme recurrence of de novo mutations causing Apert syndrome5.Here,we develop a systematic approach to discover CES drivers as hotspots of human de novo mutation.Our analysis of 54,715 trios ascertained for rare conditions9-13,6,065 control trios12,14-19 and population variation from 807,162 mostly healthy individuals20 identifies genes manifesting rates of de novo mutations inconsistent with plausible models of disease ascertainment.We propose 23 genes hypermutable at loss-of-function(LoF)sites as candidate CES drivers.An extra 17 genes feature hypermutable missense mutations at individual positions,suggesting CES acting through gain of function.CES increases the average mutation rate roughly 17-fold for LoF genes in both control trios and sperm and roughly 500-fold for pooled gain-of-function sites in sperm21.Positive selection in the male germline elevates the prevalence of genetic disorders and increases polymorphism levels,masking the effect of negative selection in human populations.展开更多
In this paper,we study asymptotic power series of the composition f(x)=h(g(x)),where g(x)=∑_(n=0)^(∞)b_(n)x^(-n),b_(n)∈R,and h is a given elementary function.The asymptotic expansions have been obtained for the com...In this paper,we study asymptotic power series of the composition f(x)=h(g(x)),where g(x)=∑_(n=0)^(∞)b_(n)x^(-n),b_(n)∈R,and h is a given elementary function.The asymptotic expansions have been obtained for the composition with an exponential or logarithmic function.Using the re-cursive method,we present the asymptotic expansions for the composition with seven trigonometric functions,respectively.As an application,the asymptotic expansions of roots of some equations are given.Computational results show that our recursive formula is more efficient than the method of Lagrange's inverse theorem.展开更多
We investigate the null tests of cosmic accelerated expansion by using the baryon acoustic oscillation(BAO)data measured by the dark energy spectroscopic instrument(DESI)and reconstruct the dimensionless Hubble parame...We investigate the null tests of cosmic accelerated expansion by using the baryon acoustic oscillation(BAO)data measured by the dark energy spectroscopic instrument(DESI)and reconstruct the dimensionless Hubble parameter E(z)from the DESI BAO Alcock-Paczynski(AP)data using Gaussian process to perform the null test.We find strong evidence of accelerated expansion from the DESI BAO AP data.By reconstructing the deceleration parameter q(z) from the DESI BAO AP data,we find that accelerated expansion persisted until z■0.7 with a 99.7%confidence level.Additionally,to provide insights into the Hubble tension problem,we propose combining the reconstructed E(z) with D_(H)/r_(d) data to derive a model-independent result r_(d)h=99.8±3.1 Mpc.This result is consistent with measurements from cosmic microwave background(CMB)anisotropies using the ΛCDM model.We also propose a model-independent method for reconstructing the comoving angular diameter distance D_(M)(z) from the distance modulus μ,using SNe Ia data and combining this result with DESI BAO data of D_(M)/r_(d) to constrain the value of r_(d).We find that the value of r_(d),derived from this model-independent method,is smaller than that obtained from CMB measurements,with a significant discrepancy of at least 4.17σ.All the conclusions drawn in this paper are independent of cosmological models and gravitational theories.展开更多
A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Til...A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Tile matrix quotients are based oil the generalized inverse for a matrix, Which is found to beeffective in continued fraction interpolation. In this paper, tWo dual expansions for bivariate matrix valuedThiele-type interpolating continued fractions are presented, then, tWo dual rational interpolants are definedout of them.展开更多
基金Supported by Projects from Chongqing Municipal Science and Technology Commission(CSTB2022NSCQ-MSX0445)。
文摘For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
文摘In renewing tissues,mutations conferring selective advantage may result in clonal expansions1-4.In contrast to somatic tissues,mutations driving clonal expansions in spermatogonia(CES)are also transmitted to the next generation.This results in an effective increase of de novo mutation rate for CES drivers5-8.CES was originally discovered through extreme recurrence of de novo mutations causing Apert syndrome5.Here,we develop a systematic approach to discover CES drivers as hotspots of human de novo mutation.Our analysis of 54,715 trios ascertained for rare conditions9-13,6,065 control trios12,14-19 and population variation from 807,162 mostly healthy individuals20 identifies genes manifesting rates of de novo mutations inconsistent with plausible models of disease ascertainment.We propose 23 genes hypermutable at loss-of-function(LoF)sites as candidate CES drivers.An extra 17 genes feature hypermutable missense mutations at individual positions,suggesting CES acting through gain of function.CES increases the average mutation rate roughly 17-fold for LoF genes in both control trios and sperm and roughly 500-fold for pooled gain-of-function sites in sperm21.Positive selection in the male germline elevates the prevalence of genetic disorders and increases polymorphism levels,masking the effect of negative selection in human populations.
基金Supported by The Innovation Fund of Postgraduate,Sichuan University of Science&Engineering(Y2024336)NSF of Sichuan Province(2023NSFSC0065).
文摘In this paper,we study asymptotic power series of the composition f(x)=h(g(x)),where g(x)=∑_(n=0)^(∞)b_(n)x^(-n),b_(n)∈R,and h is a given elementary function.The asymptotic expansions have been obtained for the composition with an exponential or logarithmic function.Using the re-cursive method,we present the asymptotic expansions for the composition with seven trigonometric functions,respectively.As an application,the asymptotic expansions of roots of some equations are given.Computational results show that our recursive formula is more efficient than the method of Lagrange's inverse theorem.
基金supported in part by the National Key Research and Development Program of China (Grant No.2020YFC2201504)the National Natural Science Foundation of China (Grant Nos.12588101 and 12535002)。
文摘We investigate the null tests of cosmic accelerated expansion by using the baryon acoustic oscillation(BAO)data measured by the dark energy spectroscopic instrument(DESI)and reconstruct the dimensionless Hubble parameter E(z)from the DESI BAO Alcock-Paczynski(AP)data using Gaussian process to perform the null test.We find strong evidence of accelerated expansion from the DESI BAO AP data.By reconstructing the deceleration parameter q(z) from the DESI BAO AP data,we find that accelerated expansion persisted until z■0.7 with a 99.7%confidence level.Additionally,to provide insights into the Hubble tension problem,we propose combining the reconstructed E(z) with D_(H)/r_(d) data to derive a model-independent result r_(d)h=99.8±3.1 Mpc.This result is consistent with measurements from cosmic microwave background(CMB)anisotropies using the ΛCDM model.We also propose a model-independent method for reconstructing the comoving angular diameter distance D_(M)(z) from the distance modulus μ,using SNe Ia data and combining this result with DESI BAO data of D_(M)/r_(d) to constrain the value of r_(d).We find that the value of r_(d),derived from this model-independent method,is smaller than that obtained from CMB measurements,with a significant discrepancy of at least 4.17σ.All the conclusions drawn in this paper are independent of cosmological models and gravitational theories.
文摘A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Tile matrix quotients are based oil the generalized inverse for a matrix, Which is found to beeffective in continued fraction interpolation. In this paper, tWo dual expansions for bivariate matrix valuedThiele-type interpolating continued fractions are presented, then, tWo dual rational interpolants are definedout of them.
