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…     

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…     

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., …     

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).     

Estimation method for mixed-effect coefficient semiparametric regression model

Consider the mixed-effect coefficient semiparametric regression modelZ=X'α+Y'β+g(T)+e, whereX, Y andT are random vectors onR ^p×R ^q×[0, 1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=Σ),g(.) is an unknown function on [0, 1], e is a random error with mean zero and variance σ², and (X, Y, T) and (β,e), β ande are mutually independent. We estimate α,b andg(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α,b have asymptotic normality and obtain the best convergence raten ^−1/3 for the estimation ofg(.). Project supported by the NSFC and the Natural Science Foundation of Zhejiang Province.     

Infrared Absorption Spectra of Serpentine Cat＇s Eye from Sichuan Province of China

Infrared （IR） absorption spectra and X-ray powder diffraction （XRD） patterrns of sexpenfine cat＇s eye from Sichuan Province have been investigated, and infrared absorption bands of the serpentine have been assigned in this paper. The results indicate that the bands near 3 600 - 3 700 cm^-1 belong to the stretching absorption band VOH, the bands in 948 - 1 100 cm^-1 axe assigned to the stretching vibraling band Usvo, and the bands at 600 570 and 440 cm^-1 respectively belong to the bending vibration band VOH, δMg-O and δSi-O. The serpentine cat＇ s eye includes two types： chrysotile and antigorite. Chrysotile has a sharp and intensive band at 3 688 cm^-1 and a weak band at 3 643 cm^-1 , while antigorite has only one intensive band in the region. At vibration band VSi-O, chrysotile and antigorite have a similar feature at 1 071 cm^-1, but the band at 980 cm^-1 in anfigorite has been split into two bands in chrysotile - a strong one at 1 027 cm^-1 and a weak one at 949 cm^-1. In addition, antigorite has a characteristic bending vibrating band δMg-O at 570 cm^-1. Based on the analysis of the feature of crystal structure, their IR differences axe well explained.     

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).     

Projectively flat Asanov Finsler metric

In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.     

On some projectively flat polynomial （α,β）-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

A class of not max-stable extreme value distributions

The sequences {Zi,n, l≤i≤n}, n≥l have multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i,u≥l }, …, {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of i.i.d, random variables Z1,n, Z2Zn,n is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) Gz(x) = r-1∏i=1ФAiαi(x) × Фαr (x);ii) Gz (x) = r-1∏i=1ψAiαi (x) × ψαr (x); iii) Gz (x) = r-1∏i=1 ∧Ai (λix) × A(x), r≥2, 0＜α1≤α2≤…≤αr and λi∈ (0,1] for i, l≤i≤r-1 which occur if Fj, …, Fm belong to the same MDA.     

Study of the behaviour of the dielectric constant in Cu,Fe：BaTiO3

In this work we study the behaviour of the dielectric constant of BaTiO3 single crystals doped with Cu and Fe for different ion percentages, particularly, the influence of these hetemvalent substitutions on the ferroelectric-paraelectric phase transition whose temperature is found at Tc=120℃ for pure samples. The dielectric constant e in terms of temperature shows that the Curie temperature decreases when the quantity of impurities increases and presents a broadening and flattering of the maximum oft（T） within higher values, with the transition becoming more and more diffuse. It is interesting to have a material with very high permittivity （high-k） because of its capacity to store an important quantity of electric charges. The t anisotropy and the Curie-Weiss law are also verified with a good ratio between the slopes ofε^-l（T） from both sides of the transition, leading to a Curie constant： C= 13 × 10^4 K for BaTiO3：1.6%Fe in the polar phase. BaTiO3 is a displacive ferroelectric going through a first-order phase transition. The substitutions have an effect on the dynamics of the perovskite lattice. They induce charges transfer to Ti and a diminution of elastic forces in BaTiO3. Then we discuss the transition but on the nature of the material. fact that the maximum of permittivity does not depend on the phase     

On Turán type inequality with doubling weights andA * weights

LetH _n be the set of real algebraic polynomials of degreen, whose zeros all lie in the interval [−1,1]. The well known Turán type inequalities tell us that forf(x)∈H _n , it holds ‖f′‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities underL ^p norm for 0<p≤∞. Our results essentially extend the result of Wang and Zhou (2002), and the method used in this paper is simpler and more direct than that of Wang and Zhou (2002). The results and methods have their own values in approximation theory and computation.     

Synergistic interaction of NaCl and Cd on growth and photosynthetic parameters in soybean genotypes differing in salinity tolerance

The effects of salinity(50 mmol/L NaCl) and Cd(1 μmol/L CdCl2) as sole and combined on growth and photosyn-thetic parameters were studied using two soybean genotypes,Huachun 18 and NGB.The concentrations of Cd2 ,Zn2 ,Ca2 ,Mg2 ,K and Na were also determined in seeds and pods.Huachun 18 suffered a more serious decrease than NGB in net photosynthetic rate(Pn) in the treatments of salinity stress alone and combined stress(NaCl Cd),showing that it is relatively sensitive to salinity.The decrease in Pn caused by salt stress in Huachun 18 was mainly due to the reduced total chlorophyll content and photosynthetic efficiency(the ratio of variable fluorescence to maximal fluorescence,Fv/Fm),whereas the decease in NGB was mainly related to reduced stomatal conductance(Gs).The combined stress of both Na and Cd did not induce further decrease in photosynthesis and fluorescence in the two genotypes relative to salt or Cd stress alone.Greater change in the pod concentrations of Zn2 ,Ca2 ,Mg2 ,K and Na was detected under salt stress for Huachun 18 than for NGB.The results suggested that the interactive effect of NaCl-Cd on growth and nutrient uptake differs between the two soybean genotypes.     

Sap flow response of Eucaylyptus (<Emphasis Type="Italic">Eucalyptus urophylla</Emphasis>) to environmental stress in South China

Sap flow and environmental conditions were monitored at two Eucalyptus (Eucalyptus urophylla S.T. Blake) plantations at Hetou and Jijia, located in Leizhou, Zhanjiang, Guangdong Province. It was found that daily sap flux density (SFD) of Eucalyptus was closely related to daily atmospheric vapor pressure deficit (VPD) (R ²=0.76, P=0.01 at Hetou and R ²=0.7021, P=0.01 at Jijia) at both sites. No significant relationship existed between daily SFD and mean daily air temperature at both sites. Daily SFD varied with wind speed Y=−17585X ³+15147X ²−1250.7X+2278.4 (R ²=0.68; P=0.01) at Hetou and Y=−101.67X ³−1.65X ²−376.4X+1914.8 (R ²=0.40, P=0.05) at Jijia, where Y was daily SFD, X was daily wind speed. Experimental observations yielded the following data: (1) the critical lower and upper daily VPD threshold were 0 and 2 kPa, within which daily SFD varied from 540±70 L/(m²·d) to 4739±115 L/(m²·d) at Hetou site, from 397±26 L/(m²·d) to 3414±191 L/(m²·d) at Jijia site; (2) Diurnal SFDs at Hetou site were much higher under low relative humidity (<30%) and slightly lower under high relative humidity (>80%) compared with those at the Jijia site; (3) The upper and lower threshold of daily and diurnal RAD for the optimal water use of E. urophylla plantations were 18±2.7 and 2±1 MJ/(m²·d), 669 and 0 J/(cm²·h) during the observation period. Project supported by Knowledge Innovation Funds from Chinese Academy of Sciences (Nos. KSCX2-SW-120, KZCX1-SW-01-01A3) and the Key Project of Guangdong Natural Science Foundation (No. 010567), China     

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

Consider the positive d-dimensional lattice d (d≥2) with partial ordering ≤, let {XK; K ∈ d } be i.i.d. random vari- ables taking values in a real separable Hilbert space (H, ||·||) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K , N ∈ d . Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε 0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).     

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.     

Projectively flat exponential Finsler metric

INTRODUCTION One century ago, Hilbert announced his famous 23 problems. The Hilbert’s Fourth Problem is to characterize the (not-necessarily-reversible) distance functions on an open subset in ún such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Thus Hilbert’s Fourth Problem in the smooth case is to characterize Finsler metric on an open subset in ún whose geodesics are straight lines. Finsler metric on an ope…     

Determination of Trace Molybdenum（VI） by Oscillographic Potentiometric Catalyzing Kinetic Method of Simplex Optimization

1　Introduction　Ahugeamountofliteratureexistsonthestudyofi dentifyingtracemetalionsbymeansofspectropho tometry[1 3] ,fluorimetry[4 6 ] aswellas polarogra phy[7 9] ,whichhaveactiononlocatingtheendpointoftheindicatingreaction .Howeverbothspectropho tometryandfluorimetryareeasytobeinterferedbycolororprecipitation ,whilepolarographyhasanissueofmercurypollution .Thecatalyzingkineticanalysishasthecharacteristicsofhighsensitivityandspeedi ness.Oscillographicpotentiometryisasimpleintu itionisticanal…     

Congruences for finite triple harmonic sums

Zhao (2003a) first established a congruence for any odd prime p>3, S(1,1,1;p)≡-2Bp-3 (mod p), which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S(α,β,γ;p) (mod p) is considered for all positive integers α,β,γ. We refer to w=α β γ as the weight of the sum, and show that if w is even, S(α,β,γ;p)≡0 (mod p) for p≥w 3; if w is odd, S(α,β,γ;p)≡rBp≥w (mod p) for p≥w, here r is an explicit rational number independent of p. A congruence of Catalan number is obtained as a special case.     

几乎正则图的全符号控制

1IntroductionFor notation and graph theory terminology we ingeneral follow[1].LetG=(V,E)be a graph with thevertex setVand the edge setE,andletvbe a vertexinV.The open neighborhood ofvisN(v)={u∈V|uv∈E}and the closed neighborhood ofvisN[v]={v}∪N(v).The d…