Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficien...Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).展开更多
Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived ...Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.展开更多
Bronchial asthma is a chronic inflammatory disease. Allergies are intensely related to bronchial asthma and to other respiratory diseases such as chronic sinusitis, middle ear infections, and nasal polyps. Treatment c...Bronchial asthma is a chronic inflammatory disease. Allergies are intensely related to bronchial asthma and to other respiratory diseases such as chronic sinusitis, middle ear infections, and nasal polyps. Treatment can vary from inhalers to oral medications to drugs delivered in a nebulizer or breathing machine. Besides, dietary involvement was a significant tool to reduce the severity of many chronic inflammatory diseases including asthma. Randomly assigned, double blind, and placebo controlled 290 adults with mild to moderately persistent bronchial asthma concluded in this study, were subjected to alternating phases of supplementation with omega-3 fatty acids, vitamin C and Zn either singly or in combination. Subjective symptom improvement, pulmonary function, and biochemical tests were carried out at the beginning of the study and at the end of each therapeutic phase. The study findings showed that nearly half of the cases were in age between 18 years to 40 years followed by 29.6 of the cases that fall in age range between 40 years and 60 years. It was clear that all the four supplements (ogema-3 fatty acids, vitamin C and Zn, and combination) contributed more than placebo in reducing the severity of bronchial asthma. However, omega 3 fatty acids and combined supplement significantly contributed in symptomatic improvement (p < 0.05). There was a significant improvement of pulmonary function and sputum inflammatory markers with diet supplementation (p < 0.05). So, the subjects with mild and moderately persistent bronchial asthma may get benefit from their dietary supplementation with omega 3 fatty acids, Zinc and vitamin C. It is evident from this study that omega 3 fatty acids and combined supplementation significantly improved the severity of bronchial asthma.展开更多
文摘Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA17010105)National Key Research and Development Program(Grant No.2018YFC1507104)+2 种基金Science and Technology Development Plan Project of Jilin Province(20180201035SF)Flexible Talents Introducing Project of Xinjiang(2019)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(EarthLab)。
文摘Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.
文摘Bronchial asthma is a chronic inflammatory disease. Allergies are intensely related to bronchial asthma and to other respiratory diseases such as chronic sinusitis, middle ear infections, and nasal polyps. Treatment can vary from inhalers to oral medications to drugs delivered in a nebulizer or breathing machine. Besides, dietary involvement was a significant tool to reduce the severity of many chronic inflammatory diseases including asthma. Randomly assigned, double blind, and placebo controlled 290 adults with mild to moderately persistent bronchial asthma concluded in this study, were subjected to alternating phases of supplementation with omega-3 fatty acids, vitamin C and Zn either singly or in combination. Subjective symptom improvement, pulmonary function, and biochemical tests were carried out at the beginning of the study and at the end of each therapeutic phase. The study findings showed that nearly half of the cases were in age between 18 years to 40 years followed by 29.6 of the cases that fall in age range between 40 years and 60 years. It was clear that all the four supplements (ogema-3 fatty acids, vitamin C and Zn, and combination) contributed more than placebo in reducing the severity of bronchial asthma. However, omega 3 fatty acids and combined supplement significantly contributed in symptomatic improvement (p < 0.05). There was a significant improvement of pulmonary function and sputum inflammatory markers with diet supplementation (p < 0.05). So, the subjects with mild and moderately persistent bronchial asthma may get benefit from their dietary supplementation with omega 3 fatty acids, Zinc and vitamin C. It is evident from this study that omega 3 fatty acids and combined supplementation significantly improved the severity of bronchial asthma.
