受外部周期激励的弱阻尼受迫KdV方程的吸引子

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎｔｈｅｐａｓｔｄｅｃａｄｅｏｒｓｏ ,ｔｈｅｅｘｉｓｔｅｎｃｅｏｆｇｌｏｂａｌａｔ ｔｒａｃｔｏｒｓａｎｄｔｈｅｅｓｔｉｍａｔｅｓｏｆｔｈｅｉｒＨａｕｓｄｏｒｆｆａｎｄｆｒａｃｔａｌｄｉｍｅｎｓｉｏｎｓｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｆｏｒｎｕｍｅｒｏｕｓｄｉｓｓｉｐａ ｔｉｖｅｎｏｎｌｉｎｅａｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｈｉｃｈａｒｅａｕ ｔｏｎｏｍｏｕｓ[1～ 4 ].Ｔｈｅｎｏｎ ａｕｔｏｎｏｍｏｕｓｉｎｆｉｎｉｔｅ ｄｙｎａｍｉ…     

Generalized Derivations in Prime Rings

Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0.     

L^p-estimates on a ratio involving a Bessel process

INTRODUCTION Throughout this paper, we shall work with a filtered complete probability space (?,F,(Ft),P) sat-isfying the usual conditions. Let B=(Bt)t≥0 be a stan-dard Brownian motion with B0=0. Denote by ú the set of all non-negative real numbers. Recall that a diffusion process X starting at x≥0 is called the square of a Bessel process of dimension δ>0 if d X t = δd t 2 | X t |d Bt , X 0= x, (1) Clearly, this equation has a unique non-negative strong solution X, i.e., …     

A general version of the Morse-Sard theorem

Let k,m,n be positive integers,and k≥2,α∈(0,1],0＜r＜min {m,n} an integer,d=r (m-r)/(k α),and iff∈ Ck,α(Rm,R″),A =Cr(f)= {x ∈ Rm ,rank(Df(x))≤r},thenf(A)is d-null.Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.     

在n维赋范空间中单位球体积及其渐进性质

Let Bnp={x ∈ Rn‖|x ‖p≤l} be the unit ball ofp norm in the n-dimensional normed space p. The formula for the volume of Bnp was obtained and its asymptotic properties were found out as n→∞and p→∞.     

一类压缩型映象的公共不动点定理

通过使用映象的广义弱交换条件,在完备度量空间中研究了更为广泛的一类压缩型映象的公共不动点的存在性,给出了一个新的公共不动点定理,从而在很大程度上改进和推广了现有文献中的一些结果．     

Regular-singular crossings on nonlinear systems with turning point

１ＩｎｔｒｏｄｕｃｔｉｏｎＤｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈｔｕｒｎｉｎｇｐｏｉｎｔｓｅｘｉｓｔｗｉｄｅｌｙｉｎｍａｎｙｐｒｏｂｌｅｍｓｏｆｍａｔｈｅｍａｔｉｃｓｐｈｙｓｉｃｓ,ｓｏｔｈｅｓｅｐｒｏｂｌｅｍｓａｒｅｖｅｒｙｉｍｐｏｒｔａ...     

Science Letters： New solutions of shear waves in piezoelectric cubic crystals

Acoustic wave propagation in piezoelectric crystals of classes?43m and 23 is studied. The crystals Tl3VS4 and Tl3TaSe4 (43m) of the Chalcogenide family and the crystal Bi12TiO20 (23) possess strong piezoelectric effect. Because the surface Bleustein-Gulyaev waves cannot exist in piezoelectric cubic crystals, it was concluded that new solutions for shear-horizontal surface acoustic waves (SH-SAWs) are found in the monocrystals using different electrical boundary conditions such as electri- cally “short” and “open” free-surfaces for the unique [101] direction of wave propagation. For the crystal Tl3TaSe4 with coefficient of electromechanical coupling (CEMC) Ke2=e2/(C×g)～1/3, the phase velocity Vph for the new SH-SAWs can be calculated with the following formula: Vph=(Va Vt)/2, where Vt is the speed of bulk SH-wave, Vt=Vt4(1 Ke2)1/2, Va=aKVt4, aK=2[Ke(1 Ke2)1/2-Ke2]1/2, and Vt4=(C44/ρ)1/2. It was found that the CEMC K2 evaluation for Tl3TaSe4 gave the value of K2=2(Vf–Vm)/Vf～0.047 (～4.7%), where Vf～848 m/s and Vm~828 m/s are the new-SAW velocities for the free and metallized surfaces, respectively. This high value of K2(Tl3TaSe4) is significantly greater than K2(Tl3VS4)～3% and about five times that of K2(Bi12TiO20).     

Control mesh representation of a class of minimal surfaces

INTRODUCTION The problem of minimal surface is an old and active problem in the field of differential geometry. The minimal surface has been employed in many areas such as architecture, material science, aviation, ship manufacture, biology, crystallogeny, and so on. The history of minimal surface began with La- grange in 1762 (Nitsche, 1989). Many literature on the minimal surface exist in the last two hundred years (Nitsche, 1989; Osserman, 1986), but few on the minimal surface from the…     

具有转向点的非线性系统的奇异摄动

１　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｓｉｎｇｕｌａｒｌｙｐｅｒｔｕｒｂｅｄｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈｔｕｒｎｉｎｇｐｏｉｎｔｓａｒｅｖｅｒｙｉｍｐｏｒｔａｎｔｆｏｒｍａｔｈｅｍａｔｉｃｉａｎｓａｎｄｐｈｙｓｉｃｉｓｔｓｓｉｎｃｅｔｈｅｓｅｐｒｏｂｌｅｍｓｅｘｉｓｔｗｉｄｅｌｙｉｎｍａｎｙｐｒｏｂｌｅｍｓｏｆｐｈｙｓｉｃｓ．ＴｈｅｐｒｏｂｌｅｍｓｗｉｔｈｔｕｒｎｉｎｇｐｏｉｎｔｓｗｅｒｅｓｔｕｄｉｅｄｂｙＷｅｎｔｚａｌ,Ｋｒａｍｅｒｓ,Ｂｕｌｌｏｕｎｉｎ［１］,Ｌａｎｇｅｒ,Ａ…     

过冷液相区内轧制温度对Zr52.5Al10Ni10Cu15Be12.5大块金属玻璃表面形貌的影响

Surface morphologies of Zr52.5 Al10 Ni10 Cu15 Be12.5 bulk metallic glass after being rolled at both a temperature around T9 and near （ Tx - 50） K were investigated with a scanning electron microscopy. Macroscopic and microscopic observation results show that squamae, cracks, steps and wedges exist on the surface when the samples were rolled at temperatures around Ty. However, a smooth and fiat surface appears when the samples were rolled at temperatures near （ Tx - 50） K. These results indicate that the mode of deformation in the supercooled liquid region is a partially homogeneous flow at a temperature around T9, and a fully homogeneous one at temperatures near （ Tx - 50） K. According to the results, it is more feasible to roll the amorphous alloys at temperatures near （ Tx - 50） K to obtain parts with smooth and fiat surface.     

Sensitized Up—Conversion Luminescence of Ho^3＋ in Nd^3＋—Yb^3＋—Ho^3＋ Co—doped ZrF4—Based Glass

Up-conversion processes for the blue, green and red emissions were found two-photon phenomenon, known as the cooperative phenomenon. This phenomenon was assisted by Nd³⁺ → Yb³⁺ → Ho³⁺ energy transfer. The strong green emission due to the Ho³⁺ : (⁵F₄, ⁵S₂)→ ⁵I₈ transitions was observed in Nd³⁺-Ho³⁺ co-doped ZrF₄-based fluoride glasses under 800 nm excitation. As an attempt to enhance Ho³⁺ up-conversion luminescences in the Nd³⁺ – Ho³⁺ co-doped ZrF₄-based glasses, Yb³⁺ ions were added to the glasses. As a result it was found that, in 800 nm excitation of 60 ZrF₄. 30BaF2. (8-x)LaF₃. lNdF₃. xYbF₃. 1HoF₃ glasses (x=0 to 7), sensitized up-conversion luminescences are observed at around 490 nm (blue), 545 nm (green), and 650 nm (red), which correspond to the Ho³⁺ : ⁵F₃ → ⁵I₈, ( ⁵F₄, ⁵S₂)→⁵I₈ and ⁵F₅→ ⁵I₈ transitions respectively. The intensities of the green and red emissions in a 3 mol % YbF₃-containing glass were about 50 times stronger than those glasses without YbF₃. This is based on sensitization due to Yb³⁺ ions. In particular, the green emission was extremely strong and the Nd³⁺-Yb³⁺-Ho³⁺ co-doped ZrF₄-based glasses have a high possibility of realizing a green up-conversion laser glass. In this paper the up-conversion mechanism in the glasses is discussed in detail.     

Relative bioavailability and pharmacokinetic comparison of two different enteric formulations of omeprazole

In order to comply with the requirements for a drug listed in China, the study was developed to compare the pharmacokinetics and relative bioavailability of two different enteric formulations of omeprazole (OPZ) in healthy Chinese subjects. A total of 32 volunteers participated in the study. Plasma concentrations were analyzed by nonstereospecific liquid chromatography/tandem mass spectrometric (LC-MS/MS) method. After administration of a single 40-mg dose of the two OPZ formulations, the comparative bioavailability was assessed by calculating individual AUC_0−t (the area under the concentration-time curve from time zero to the last measurable concentration), AUC_0−∞ (the area under the concentration-time curve extrapolated to infinity), C _max (the maximum observed concentration), and T _peak (the time to C _max) values of OPZ, 5-hydroxyomeprazole (OH-OPZ), and omeprazole sulfone (OPZ-SFN), respectively. The 90% confidence intervals (CIs) of AUC_0−t , AUC_0−∞, and C _max were 85.4%–99.0%/88.8%–98.6%/87.6%–99.4%, 85.5%–99.2%/89.0%–98.6%/88.5%–101.3%, and 72.3%–87.6%/79.6%–91.1%/88.4%–99.1% for OPZ/OH-OPZ/OPZ-SFN, respectively, and T _peak values did not differ significantly. In this study, the test formulation of OPZ in fasting healthy Chinese male volunteers met the Chinese bioequivalance standard to the reference formulation based on AUC, C _max, and T _peak.     

Structure and Magnetic Properties of Fe1-xCx Solid Solution Prepared by Mechanical Alloying

Supersaturated solid solutions Fe1-xCx （0≤x≤0.9 ） of wide composition range have been prepared by mechanical alloying process. Nanocrystalline phase was formed for 0 ≤ x ≤ 0.67 and a large grain phase for 0.75 ≤ x ≤ 0.9. The large fraction of graphite volume puts off formation of nanocrystalline phase for high carbon content. In the large grain phase, magnetization follows simple magnetic dilution, and eoereivity He is mainly due to dissolution of carbon at grain boundaries. In the nanocrystalline phase the alloying effect of carbon is revealed by a distinct reduction of average magnetic moment. The increasing lattice constant with increasing carbon content is observed for x ≤ 0.5, suggesting that the high carbon concentration may enhance diffusion of carbon into the Fe lattice. It shows a discontinuity in the Hc variation with a grain size D of nanocrystalline phase. For small grain D below the critical value, Hc increases with D. For a large grain D, Hc decreases with increasing D. The solubility limit of carbon in a-Fe extended by nanocry- stalline phase formation is discussed.     

Chemically processed Nb-doped SrTiO3 films and properties

Homogeneous, crack-free SrNb_xTi_1−x O₃ thin films on (110) silicon substrates were successfully fabricated by sol-gel processing. The optimum route and conditions were systematically investigated. Sr(OAc)₂ glacial acctic acid solution, after being refluxed and reacted with tartrate, formed Sr(OAc)₂(C₄H₆O₆)₂; Ti(OBu)₄ formed Ti(OAc)_4−x (AcAc)_x after having the ligand partially exchanged with AcAc, while Nb(OC₂H₅)₅ formed (OAc)₂Nb(AcAc) (C₄H₆O₆) by exchanging of ligand in glacial acetic acid with (CH₃CO)₂O. All the metal species after undergoing partial hydrolysis and polymerization with hydroxyl or oxygen, formed SrNb_xTi_1−x O₁₃ cluster sol. Methyl cellulose (MCL) caused SrNb_xTi_1−x O₃ sol to have polymeric structure and easily form films. SrNb_xTi_1−x O₃ films with perovskite were subsequently formed after being annealed at 650∼750 °C for 60 min in 25% N₂+75% H₂ (volume ratio) atmosphere. Resistivity of the SrNb_0.1Ti_0.9O₃ films at room temperature was 64 μω·cm, a particular T ² temperature dependence of the resistivity, from 25 K up to room temperature, was observed. Project (No. 2002CB613305) supported by the National Basic Research Program (973) of China     

一类广义压缩条件下自映象的不动点定理

给出了一类广义KANNAN型压缩映象及其不动点定理 ,推广并改进了文 [1- 6 ]的一些重要结果。     

A class of Marcinkiewicz integral operators on product domains

In this paper, the author proves that theL ^p-boundedness of the Marcinkiewicz integral μ_Ω on product domainsR ⁿ×R^m; for Ω∈(1)∩(5) improves the result of Chen et al. (2000). Project supported by Major Project of NSFC (No.19631080) and NSF of Zhejiang province (No. RC97017).     

Fabrication of LaAlO<Subscript>3</Subscript> film by sol-gel process with corresponding inorganic

Well-cubic perovskite lanthanum aluminate (LaAlO₃) film on (110) silicon substrate was fabricated by sol-gel method with corresponding inorganic salts. Lanthanum acetate and aluminum acetate glacial acetic acid solutions were prepared via ligand exchange starting from lanthanum nitrate hexahydrate and aluminum nitrate hexahydrate after being refluxed. (CH₃CO)₂O removed nitrates and the crystallized H₂O completely, acetylacetone (AcAc) was partially bidentated with metallic ion of the metallic acetates and formed La(OAc)_3−x (AcAc) _x which were hydrolyzed into La(AcAc)_3−x(OH) _x by adding 10 ml 0.4% methyl cellulose (MCL) solution. The La(AcAc)_3−x (OH) _x , polymerizing and combining with MCL, formed the LaAlO₃ sol precursor with heteropolymeric structure and formed film easily. The epitaxial LaAlO₃ film on Si(110) substrate was crystallized after being annealed in thermal annealing furnace for 650–750 °C/30 min. The morphologies and microstructures were characterized. The refractive index of the LAO film was 1.942 to 2.007; the dielectric constant and the dissipation factors were estimated to be 23–26 and 2.1×10⁻⁴−2.4×10⁻⁴ respectively. Project (No. 2002CB613305) supported by the National Basic Research Program (973) of China     

Extreme value distributions of mixing two sequences with the same MDA

Suppose {Xi,i≥1} and {Yi, i≥1} are two independent sequences with distribution functions and , respectively. Zi,n is the combination of Xi and Yi with a probability for each I with 1≤ i≤n. The extreme value distribution GZ(x) of this particular triangular array of the i.i.d. Random variables Z1,n,… Z2,n, Zn,n is discussed. We found a new form of the extreme value distributions i)ΦAα1(x)Φα2 and ii) ψAα(x)ψα2(x)α1<α2), which are not max-stable. It occurs if FX and FY belong to the same MDA(Φ) or MDA(Ψ).     

Pharmacokinetics of mycophenolic acid in Chinese kidney transplant patients

To assess the influence of cyclosporin A (CsA) and tacrolimus (FK506) on mycophenolic acid (MPA) and correlation analysis of the pharmacokinetic parameters and patient characteristics, clinical outcome in Chinese kidney transplant recipients, the pharmacokinetics of 1000 mg mycophenolate mofetil (MMF) twice daily was measured by high-performance liquid chromatography (HPLC). PKS (Pharmaceutical Kinctics Software) 1.0.2 software package was used for the calculation of pharmacokinetic parameters. The meanC _max,t _max, and AUC_(0–12) were (21.88±10.52) μg/ml, (1.20±0.95) h, and (52.546±13.215) μg·h/ml, respectively. The level of AUC_(0–12) in the FK506 group was significantly higher than that in the CsA group. MPA appeared not to be affected by renal function. MPA AUC_(0–12) showed statistically significant difference according to the patient's gender. Project (No. 20040462) supported by the Foundation of Education Bureau of Zhejiang Province, China