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Unicity Theorems for Entire or Meromorphic Functions

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Acta Mathematica Sinica,English Series 1994年第2期10卷 121-131页

作者： Yi Hongxun Department of mathematics Shandong University jinan, 250100 {3. 1. Department of mathematics Shandong University 250100 Jinan China

In this paper, we deal with the problem of uniqueness of entire or meromorphic functions and obtain some results that are improvements over those of M. Ozawa, H. Ueda, K. Shibazaki and Yi Hongxun. An example shows tha... 详细信息

关键词： Unicity Theorems for Entire or Meromorphic Functions

Correlation of zeros of automorphic L-functions

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Science china mathematics 2008年第7期51卷 1147-1166页

作者： LIU JianYa1 & YE YangBo1,2 1 school of mathematics,Shandong University,jinan 250100, {3. 2Department of mathematics,The University of Iowa,Iowa City,IA 52242-1419,USA 1. school of mathematics Shandong University Jinan 250100 China 2. Department of mathematics The University of Iowa Iowa City IA 52242-1419 USA

We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (?A). Here the sizes of the groups GL mj (?A) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ? 4, but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture 11F70 11M26 11M41

Large deviation principle for diffusion processes under a sublinear expectation

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Science china mathematics 2012年第11期55卷 2205-2216页

作者： CHEN ZengJing 1,2 & XIONG Jie 3.4,1 school of mathematics,Shandong University,jinan 250100,{3. 2 Department of Financial Engineering,Ajou University,Suwon 443.49,Korea 3.Department of mathematics,University of Macao,PO Box 3.01,Macao,{3. 4 Department of mathematics,University of Tennessee,Knoxville,TN 3.996-13.0,USA 1. school of mathematics Shandong University Jinan 250100 China 2. Department of Financial Engineering Ajou University Suwon 443749 Korea 3. Department of mathematics University of Macau PO Box 3001 Macau China 4. Department of mathematics University of Tennessee Knoxville TN 37996-1300 USA

We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential *** an application,we establish a large deviation principle of the Freidlin and Wentzell type under the corresponding nonlinear probability for diffusion processes with a small diffusion coefficient.

关键词： large deviation principle backward stochastic differential equation g-expectation ambiguity

Sol-gel preparation and spectroscopic study of the pyrophanite MnTiO_3.nanoparticles

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Science china Chemistry 2005年第3期48卷 210-215页

作者： ZHOU Guowei1, KANG Youngsoo2, LI Tianduo1 & XU Guiying3.1. school of Light Chemicals and Environmental Engineering, Shandong Institute of Light Industry, jinan 250100, china 2. Department of Chemistry, Pukyong National University, Daeyeon-3.dong, Nam-gu, Pusan 608-73., Korea 3. Key Laboratory for Colloid and Interface of Ministry of Education of china, Shandong University, jinan 250100, china 1. school of Light Chemicals and Environmental Engineering Shandong Institute of Light Industry 250100 Jinan China 2. Department of Chemistry Pukyong National University Daeyeon-3-dong Nam-gu 608-737 Pusan Korea 3. Key Laboratory for Colloid and Interface of Ministry of Education of china Shandong University 250100 Jinan China

The nanosized xerogel of titanium dioxide (TiO2) and manganese oxides (MnO2, Mn2O3. Mn3.4) was prepared by the sol-gel method using manganese chloride (MnCl2·4H2O) and titanium isopropoxide (Ti(O-iPr)4) as precursors in cetyltrimethylammonium bromide (CTAB)/ ethanol/H2O/HCl micelle solutions, following the calcinations of the produced powders at differ-ence temperatures. The nanostructure and phase composition of these nanoparticles were characterized with X-ray powder diffraction (XRD), transmission electron microscopy (TEM), en-ergy dispersive X-ray spectroscopy (EDX) and X-ray photoelectron spectroscopy (XPS). The spectroscopic characterizations of these nanoparticles were also done with UV-Vis spectroscopy and laser Raman spectroscopy (LRS). XRD patterns show that the pyrophanite MnTiO3.phase was formed at the calcinations temperature of 900℃. The TEM images show that the nanoparti-cles are almost spherical or slight ellipose and the sizes are 50 nm on average. The UV-Vis spectra show that the nanosized MnTiO3.have significant absorption bands in the visible region. There are new absorption peaks of MnTiO3.nanoparticles in LRS compared with the pure TiO2 powder.

关键词： pyrophanite MnTiO3. nanoparticles, spectroscopy, CTAB micelle, sol-gel.

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新一轮家电“以旧换新”行动方案影响

日用电器 2024年第3期 1-2页

作者： 1.华创证券 2.光大证券 3.中信期货华创证券光大证券中信期货

国务院印发《推动大规模设备更新和消费品以旧换新行动方案》（以下简称《行动方案》），明确了5方面20项重点任务和实施设备更新、消费品以旧换新、回收循环利用、标准提升四大行动，提出积极开展家电等消费品以旧换新。《行动方案》...

国务院印发《推动大规模设备更新和消费品以旧换新行动方案》（以下简称《行动方案》），明确了5方面20项重点任务和实施设备更新、消费品以旧换新、回收循环利用、标准提升四大行动，提出积极开展家电等消费品以旧换新。《行动方案》家电直接相关内容1.到2027年废旧家电回收量较2023.增长3.%,

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Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

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Wuhan University Journal of Natural Sciences 2005年第2期10卷 339-343页

作者： HAN Hui-li 1,2 ,DU Jin-yuan 1,3.1. school of mathematics and Statistics, Wuhan University, Wuhan 43.072, Hubei, china 2. school of mathematics and Computer, Ningxia University, Yinchuan 750021, Ningxia, china 3. Department of mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, china Wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningxia University School of Mathematics and Computer Yinchuan Ningxia China (GRID:grid.260987.2) (ISNI:***) Wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Hubei Institute for Nationalities Department of Mathematies Enshi Hubei China (GRID:grid.34418.3a) (ISNI:***)

We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... 详细信息

关键词： boundary value problem singular integral equation the singularities of high order

Exponential sums over primes in short intervals

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Science china mathematics 2006年第5期49卷 611-619页

作者： LIU Jianya, Lu Guangshi & ZHAN Tao Department of mathematics, Shandong University, jinan 250100, china Department of mathematics Shandong University Jinan 250100 China

In this paper we establish one new estimate on exponential sums over primes in short intervals. As an application of this result, we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N = p12+p22+p3.+p42+p52, with |pj-(N/5)^(1/2)|≤U = N1/2-1/20+ε, where pj are primes. This result is as good as what one can obtain from the generalized Riemann hypothesis.

关键词： exponential sums over primes circle method Waring-Goldbach problems.

Large second-order optical nonlinearities of s-triazine derivatives: View from micro molecules to macro crystals

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Science china Chemistry 2005年第3期48卷 203-209页

作者： FANG Qi1, LEI Hong2, CUI Yuezhi3. HUANG Zhenli4, XUE Gang1 & YU Wentao1 1. State Key Laboratory of Crystal Materials, Shandong University, jinan 250100, china 2. school of Information Science and Engineering, Shandong University, jinan 250100, china 3. Department of Chemical Engineering, Light Industry College of Shandong, jinan 250100, china 4. Key Laboratory of Biomedical Photonics, Ministry of Education, Huazhong University of Science and Technology, Wuhan 43.074, china 1. State Key Laboratory of Crystal Materials Shandong University 250100 Jinan China 2. school of Information Science and Engineering Shandong University 250100 Jinan China 3. Department of Chemical Engineering Light Industry College of Shandong 250100 Jinan China 4. Key Laboratory of Biomedical Photonics Ministry of Education Huazhong University of Science and Technology 430074 Wuhan China

Three s-triazine derivatives have been synthesized and their structures been de-termined. These are Compound I: 2,4-dimethyl-6-(p-N,N-dimethylaminostyryl)-s-triazine (abbre-viated to NMe-1), Compound II: 2,4-dimethyl-6-(p-N,N-diethylaminostyryl)-s-triazine (to NEt-1), and Compound III: 2-methyl-4,6-bis(p-N,N-dimethylaminostyryl)-s-triazine (NMe-2). NMe-1 and NEt-1 molecules belong to the D-π-A type with a one-dimensional charge-transfer character. NMe-1 crystallizes to centrosymmetric P1 space group, while NEt-1 to non-centrosymmetric polar Cc space group with all of the molecular charge-transfer axes taking the same orientation. Under the irradiation of 1064 nm fundamental laser, NEt-1 powder crystals radiate a 2-order harmonic light with an intensity 46.8 times that of urea. The Λ typed NMe-2 molecule, which has a two-dimensional charge-transfer character, crystallizes to polar P21 space group. Its powder crystals exhibit a 2-order harmonic intensity 46.2 times that of urea. The quantum chemical cal-culations and tensor analyses have been carried out to reveal the dependence of the macro 2-order nonlinear optical (NLO) efficiency on the micro 2-order NLO coefficients (β) and on the crystalline packing styles.

关键词： s-triazine derivatives, synthesis, structure, SHG intensities of crystals, βvalues of molecules.

AN ANALYTICAL SOLUTION FOR THE MODEL OF DRUG DISTRIBUTION AND ABSORPTION IN SMALL INTESTINE

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Acta Mechanica Sinica 1990年第4期6卷 316-323页

作者： Xu Mingyu (Department of mathematics,Shandong University,jinan,250100,{3.) 1. Department of mathematics Shandong University 250100 Jinan China

According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,*** et *** a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drugby numerical *** this paper,we give a steady-state analytical solution of the above model including *** obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence pro- vides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.

关键词： drug and nutrient distribution and absorption in small intestine model and analytical solution