This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular...This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular growth of the series is considered under the same exponent condition, and a sufficient condition of the regular growth is given.展开更多
The growth regularities of nanomaterials are often concealed by the contingency of preparation. Therefore, it is always very difficult to figure out growth regularities of nanomaterials due to the accompanying undulat...The growth regularities of nanomaterials are often concealed by the contingency of preparation. Therefore, it is always very difficult to figure out growth regularities of nanomaterials due to the accompanying undulation of products. A series of precise synthesis was performed by using an automatic nanomaterial synthesizer (ANS) in order to explore the growth regularity of complex NaREF4 (RE: rare earth) upconversion nanocrystals (UCNCs). The use of ANS significantly enhances the experimental controllability, repeatability, and success rate. Mass experimental research exhibited that the NaLu_(0.795−x)Y_(x)F_(4):Yb^(3+)/Tm^(3+) (x = 0−0.795) UCNCs can vary their sizes continuously in a wide range to accurately meet the experimenter’s design merely by controlling the concentration of Y^(3+). A notable growth regularity was obtained and intuitively shown in growth phase diagrams. Furthermore, in the case of having excellent monodispersity, pure hexagonal phase, and uniform morphology, the prepared UCNCs still retained superior upconversion luminescent (UCL) properties. The regular changes in UCL properties further confirmed the growth regularity of the UCNCs. After analyzing the experimental data, we found that NaLu_(0.795−x)Y_(x)F_(4) combined the advantages of NaYF_(4) and NaLuF_(4) hosts with desired sizes. These results provide a guidance for the exploration of growth regularities of other similar nanomaterials and also for the structure design of the required nanomaterials.展开更多
In this paper,the zeros of solutions of periodic second order linear differential equation y ＋ Ay = 0,where A（z） = B（e z ）,B（ζ） = g（ζ） ＋ p j=1 b ？j ζ ？j ,g（ζ） is a transcendental entire function of l...In this paper,the zeros of solutions of periodic second order linear differential equation y ＋ Ay = 0,where A（z） = B（e z ）,B（ζ） = g（ζ） ＋ p j=1 b ？j ζ ？j ,g（ζ） is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.展开更多
文摘This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular growth of the series is considered under the same exponent condition, and a sufficient condition of the regular growth is given.
基金This work was supported by the National Natural Science Foundation of China(NSFC)(No.11774132)the Opened Fund of the State Key Laboratory on Integrated Optoelectronics,and Tsinghua National Laboratory for Information Science and Technology(TNList)Cross-discipline Foundationthe Major Science and Technology Tendering Project of Jilin Province(No.20170203012GX).
文摘The growth regularities of nanomaterials are often concealed by the contingency of preparation. Therefore, it is always very difficult to figure out growth regularities of nanomaterials due to the accompanying undulation of products. A series of precise synthesis was performed by using an automatic nanomaterial synthesizer (ANS) in order to explore the growth regularity of complex NaREF4 (RE: rare earth) upconversion nanocrystals (UCNCs). The use of ANS significantly enhances the experimental controllability, repeatability, and success rate. Mass experimental research exhibited that the NaLu_(0.795−x)Y_(x)F_(4):Yb^(3+)/Tm^(3+) (x = 0−0.795) UCNCs can vary their sizes continuously in a wide range to accurately meet the experimenter’s design merely by controlling the concentration of Y^(3+). A notable growth regularity was obtained and intuitively shown in growth phase diagrams. Furthermore, in the case of having excellent monodispersity, pure hexagonal phase, and uniform morphology, the prepared UCNCs still retained superior upconversion luminescent (UCL) properties. The regular changes in UCL properties further confirmed the growth regularity of the UCNCs. After analyzing the experimental data, we found that NaLu_(0.795−x)Y_(x)F_(4) combined the advantages of NaYF_(4) and NaLuF_(4) hosts with desired sizes. These results provide a guidance for the exploration of growth regularities of other similar nanomaterials and also for the structure design of the required nanomaterials.
基金Supported by the National Natural Science Foundation of China (Grant No. 10871076)the Startup Foundation for Doctors of Jiangxi Normal University (Grant No. 2614)
文摘In this paper,the zeros of solutions of periodic second order linear differential equation y ＋ Ay = 0,where A（z） = B（e z ）,B（ζ） = g（ζ） ＋ p j=1 b ？j ζ ？j ,g（ζ） is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.
