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Oblique derivative problem for general Chaplygin-Rassias equations

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Science China Mathematics 2008年第1期51卷 5-36页

作者： WEN GuoChun LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China LMAM School of Mathematical Sciences Peking University Beijing China

The present paper deals with the oblique derivative problem for general second order equations of mixed （elliptic-hyperbolic） type with the nonsmooth parabolic degenerate line K1（y）uxx+|K2（x）|uyy+a（x,y）ux+b（x, y）uy+c（x,y）u=-d（x,y） in any plane domain D with the boundary D=Γ∪L1∪L2∪L3∪L4, whereΓ（■{y>0}）∈Cμ2 （01, L2, L3, L4 are four characteristics with the slopes -H2（x）/H1（y）, H2（x）/H1（y）,-H2（x）/H1（y）, H2（x）/H1（y）(H1（y）=|k1（y）|1/2, H2（x）=|K2（x）|1/2 in {y1∪L4, Im[λ（z）uz]|z=zl=bl, l=1,2, u（-1）=b0, u（1）=b3, in which z1, z2 are the intersection points of L1, L2, L3, L4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations K1（y）（M2（x）ux）x+M1（x）（K2（y）uy）y+r（x,y）u=f（x,y）, in D as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K（y）uxx+uyy=0 with the boundary condition u（z）=φ（z） onΓ∪L1∪L4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for t

关键词： oblique derivative problem equations of mixed type nonsmooth degenerate line

On the inner radius of univalency by pre-Schwarzian derivative

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Science China Mathematics 2007年第7期50卷 987-996页

作者： Tao CHENG~(1,2+) Ji-xiu CHEN~1 1 School of Mathematical Sciences,Fudan University,Shanghai 200433,China 2 Department of Mathematics,Jiangxi Normal University,Nanchang 330022,China School of Mathematical Sciences Fudan University Shanghai China Department of Mathematics Jiangxi Normal University Nanchang China

In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the l... 详细信息

关键词： pre-Schwarzian derivative inner radius of univalency universal Teichmuller space

Molecular recognition on supramolecular systems (XXXV)——Synthesis of novel β-cyclodextrin derivative bearing pyridinio group and its chiral discrimination of amino acids

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Science China Chemistry 2001年第3期44卷 260-267页

作者：刘育康诗钊 Nankai Univ Dept Chem Tianjin 300071 Peoples R China

A novel p-cyclodextrin derivative 4 bearing a pyridinio group on the primary side was synthesized by the reaction of 2-aminopyridine with 6-p-cyclodextrin monoaldehyde 3, and its complexation stability constants with several aliphatic amino acids have been determined in phosphate buffer solution ( pH = 7.2, 0.1 mol ?L^(-1)) at 25℃by using spectrofluorometric titrations. The stoichiometry is 1 : 1 for the inclusion complexation of amino acids with compound 4. Circular dichroism study indicates that the aromatic moiety was embedded shallowly into the cyclodextrin cavity. As a spectral probe, the pyridinio group in the modified cyclodextrin can recognize not only differences of the size and shape of amino acid molecules, but also the L/D-amino acid chiral iso-mer. As compared with mono-[6-(1-pyridinio)-6-deoxy]-p-cyclodextrin 5, compound 4 switched the enantiomer preference for L- to D-isomer, and showed the highest enantioselectivity of 5.4 for D/L-serine. These results are discussed from the viewpoints of

关键词： molecular recognition cyclodextrin derivative amino acid fluorescence spectrum.

Preparation of the selenome-thionine derivative of tab-toxin resistance protein

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Chinese Science Bulletin 2001年第15期46卷 1304-1307页

作者： HE Hongzhen SHAO Yu CHEN Yuhang LIU Bingbing CAO Zhenbo JIANG Fan LIU Yiwei TANG Hong LIU Jinyuan ZHAO Nanming RAO Zihe Laboratory of Structural Biology&Protein Science Laboratory of MOE School of Life Science and EngineeringTsinghua UniversityBeijing 100084China

In order to obtain phase information for the X-ray diffraction of tabtoxin resistance protein (TTR) crystal using the MAD phasing method, a selenomethionine (Se-Met) derivative of TTR was overexpressed in E. coli strain M15, with pQE-30 plasmid, through IPTG induction in M9 medium containing Se-Met. The product was purified to an estimated homogeneity of greater than 95% according to SDS-PAGE, by a Ni-NTA metal affinity followed by a Mono Q anion exchange column chromatography. The successful substitution of Se-Met for methionine (Met) was confirmed by MALDI-TOF and ESI-Quadrupole Mass Spectrometry analysis. The derivative crystal was obtained using similar conditions as those for the native.

关键词： Se-Met TTR derivative expression purification mass spectrometry.

A new tripodal rhodamine B derivative as a highly selective and sensitive fluorescence chemosensor for copper(Ⅱ)

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Science China Chemistry 2009年第4期52卷 523-528页

作者： ZENG Xi,WU Chong,DONG Lei,MU Lan,XUE SaiFeng & TAO Zhu College of Chemistry and Chemical Engineering ,Guizhou University,Guiyang 550003,China Key Laboratory of Macrocyclic and Supramolecular Chemistry of Guizhou Province,Guizhou University,Guiyang 550025,China College of Chemistry and Chemical Engineering Guizhou University Guiyang China

A new tripodal rhodamine B derivative 2 was designed and synthesized by tripodal trialdehyde and rhodamine B hydrazide for the first time. This derivative could be used as a fluorescent chemosensor for the selective and sensitive determination of copper(II) in Tris-HCl buffer and ethanol aqueous mixed media. Under the optimum conditions described herein,fluorescence enhancement at 557/577 nm was linearly related to the concentration of copper(II) in the range of 0.10 to 10.00×10-5 mol·L-1,with a corre-lation coefficient of R2=0.9964 (n=15) and a detection limit of 1.129×10-7 mol·L-1 (the relative standard deviation for five repeated measurements at 4.00×10-5 mol·L-1 Cu(II) was 2.2%). The absorbance meas-urements at 557 nm were linearly related to the concentration of Cu(II) in the range of 0.50 to 25.00×10-5 mol·L-1,with a correlation coefficient of R2=0.9948 (n=13) and a detection limit of 3.338×10-7mol·L-1.

关键词： tripodal rhodamine B derivative copper fluorescent chemosensor

The Schwarzian derivative of C^n

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Chinese Science Bulletin 1995年第22期40卷 1873-1874页

作者：余其煌龚升 Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China Department of Mathematics USTC Hefei 23026 China

The Schwarzian derivative of holomorphic functions is an important topic in the function theory of one complex variable. The Schwarzian derivative of a holomorphic function f(z) of one complex variable z is defined

关键词： Schwarzian derivative linear fractional transformation local biholomorphic mapping.

THE SCHWARZIAN derivative IN SEVERAL COMPLEX VARIABLES (Ⅰ)

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Chinese Science Bulletin 1990年第8期35卷 697-699页

作者：龚昇 CARL H.FITZGERALD University of Science and Technology of China Hefei 280027 PRC Department of Mathematics University of California San Diego La Jolla CA 92093 USA.

The importance of the Schwarzian derivative of one complex variable is well known. It relates with the theory of differential equation theory of differential geometry,

关键词： derivative conformal Krone letter 切二 analytic invariant founded directional grateful

Novel detection approach for thermal defects:Study on its feasibility and application to vehicle cables

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High Voltage 2023年第2期8卷 358-367页

作者： Kai Liu Zhixiang Yang Wenfu Wei Bo Gao Dongli Xin Chuanming Sun Guoqiang Gao Guangning Wu School of Electrical Engineering Southwest Jiaotong UniversityChengduChina CRRC Qingdao Sifang Co. Ltd.QingdaoChina

It is important to accurately assess the thermal defect state of equipment to ensure its safe operation.A novel thermal defect detection method called the square even-order derivative method is proposed.First,the derivative functions of temperature were constructed to investigate the main-side-peak characteristics of the derivative curve,and the mathematical expressions for the position,depth,intensity of the defects,and parameters of the derivative curve were deduced,which can be used to quantitatively detect the defects.Then,numerical and experimental analyses of an example case of defected epoxy resin plates were carried out to verify that thermal defects can be effectively and accurately detected by the proposed method.Finally,the method was applied to a vehicle cable to detect its thermal defects in another example case of defected vehicle cable,which preliminarily validated the feasibility of the proposed method in practical applications.

关键词： method derivative thermal

STUDY ON PHASE TRANSITION THERMODYNAMICS OF 4-METHYL-COUMARIN derivative

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Chinese Science Bulletin 1989年第21期34卷 1844-1845页

作者：张兴康黄为钧谈夫徐广智吴正亮 National Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry Academia Sinica Beijing 100080 PRC Shanghai Institute of Optics and Fine Mechanics Academia Sinica Shanghai

This letter deals with the study on thermodynamic characteristics of phase transition for 4-methyl-coumarin derivatives, i. e. 4-methyl-7-aminocoumarin, 4-methyl-7-hydroxycoumarin, 4-methyl-7-dimethylaminocoumarin and... 详细信息

关键词： coumarin letter hereinafter thermodynamic melting bonds enthalpy deals derivative attributed