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  • Author or Editor: G. Sun x
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Abstract  

We sharpen Hua’s theorem with five squares of primes by proving that every sufficiently large integer N congruent to 5 modulo 24 can be written in the form
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N = p_1^2 + p_2^2 + p_3^2 + p_4^2 + p_5^2$$ \end{document}
with p 1
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N^{\tfrac{{49}} {{288}}}$$ \end{document}
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Summary  

We study the stability of Gabor frames with arbitrary sampling points in the time-frequency plane, in several aspects. We prove that a Gabor frame generated by a window function in the Segal algebra S 0(R d) remains a frame even if (possibly) all the sampling points undergo an arbitrary perturbation, as long as this is uniformly small. We give explicit stability bounds when the window function is nice enough, showing that the allowed perturbation depends only on the lower frame bound of the original family and some qualitative parameters of the window under consideration. For the perturbation of window functions we show that a Gabor frame generated by any window function with arbitrary sampling points remains a frame when the window function has a small perturbation in S 0(R d) sense. We also study the stability of dual frames, which is useful in practice but has not found much attention in the literature. We give some general results on this topic and explain consequences to Gabor frames.

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Abstract  

The partition of uranium(VI) between nitric acid solutions and solutions of N,N-dibutyldodecanamide (DBDA) in kerosene has been investigated at varying concentrations of nitric acid, extractant, salting-out agent LiNO3 and at different temperatures. The mechanism of extraction is discussed in the light of the results obtained.

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Abstract  

A new diamide N,N,N,N-tetrahexylsuccinylamide (THSA) was synthesized, characterised and used for the extraction of U(V) and Th(IV) from nitric acid solutions in a diluent composed of 50% 1,2,4-trimethylbenzene (TMB) and 50% kerosene (OK). Extraction distribution coefficients of U(VI) and Th(IV) as a function of aqueous nitric acid concentration, extractant concentration and temperature have been studied. The composition of extracted species, equilibrium constants and enthalpies of extraction reactions have also been calculated. The IR spectra of saturated extraction of U(VI) and Th(IV) were recorded.

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Abstract  

The extraction of U(VI) with newly synthesized alkylamide, N,N-diethyloctadecanamide (DEODA), has been studied. The dependence of the extraction on nitric acid concentration, DEODA concentration and temperature from nitric acid solution has been considered. The extracted species has also been investigated using FT-IR spectrometry. The related themodynamic functions were calculated.

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Abstract  

The extraction of U(VI) with newly synthesized long chain alkyl amide, N,N-dibutyldodecanamide (DBDA), in toluene has been studied. The dependence of the extraction on nitric acid and DBDA concentrations and temperature from nitric acid solution has been considered. The extracted species has also been investigated using FT-IR spectrometry. The related thermodynamic functions were calculated. The separation factor between U(VI) and Th(IV) is higher and there is no third phase formation under the conditions studied.

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Abstract  

N,N,N,N-tetrabutylmalonamide (TBMA) was synthesized and used for extraction of uranyl(II) ion from nitric acid media in toluene. The effects of nitric acid concentration, extractant concentration, temperature and salting-out agent (LiNO3) on distribution coefficients of uranyl(II) ion have been studied. The extraction of nitric acid is also studied. The main adduct of TBMA and HNO3 is HNO3. TBMA in 1.0 mol/l nitric acid solution. The 1:2:3 complex of uranyl(II) ion, nitrate ion and TBMA as extracted species is further confirmed by IR spectra of the extraction of uranyl(II) ion with TBMA, and found that the NO 3 in the extraction species UO2(NO3)2·3TBMA did not participate in coordination of uranyl(II) ion. The values of thermodynamic parameters have also been calculated.

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Abstract  

Prompt k 0-factors relative to chlorine and relative g-emission intensities were determined for the strong non-1/v absorbers 113Cd, 149Sm, 151Eu,155Gd and 157Gd. Measurements were performed using the SNU-KAERI prompt gamma activation analysis (PGAA) facility at the Korea Atomic Energy Research Institute (KAERI). For proper experimental determination of the prompt k 0-factors, the effective g-factor and cadmium ratio were taken into account, in consideration of the effects from the non-1/v capture cross section and neutron spectrum in the thermal and epithermal energy region. By using the actual spectrum of the neutron beam in this study, the effective g-factor was obtained by calculation, and the influence of epithermal neutrons on the capture rate was corrected by measuring the cadmium ratio for each non-1/v target isotope. The measured prompt k 0-factors were used to check the consistency between the existing dataset of the absolute g-emission intensity and the 2200 m/s capture cross section for these isotopes.

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Abstract  

Doppler broadening of a 477.6 keV line combined with a recoil of an excited Li nucleus is the characteristic of PGAA, which leads to complicated gamma-ray spectrum which is difficult to analyze. For this solution, a modified algorithm for an automated analysis of the Doppler-broadened peak spectrum is presented. The modified algorithm maintained the consistency of a Doppler-broadened peak with the finest analysis algorithm used for a Gaussian gamma-ray peak analysis in the HYPERMET code.

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Genetic structure of 142 parent lines of sorghum [Sorghum bicolor (L.) Moench] was analyzed using model-based approach based on SSR markers. Forty-one selected from 103 SSR markers were used to analyze the parent lines, which generated 189 alleles revealed by each marker ranging from 2 to 11 with an average of 4.6 per marker. The polymorphic information content (PIC) value was 0.543 with a range of 0.089 to 0.850. All the parent lines were assigned to 7 subgroups, named Kafir, Kaoliang, Feterita, Shallu, Hegari, Milo and Durra. Parent lines without clear pedigree record were clustered into their corresponding groups, and genetic components of each line were estimated by Q-values. Information of this study would be useful for breeders to conclude their genetic background and select appropriate parents for germplasm improvement and hybrid breeding, and thus improve the efficiency of breeding programs.

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