A rigidity theorem for submanifolds in S~(n p) with constant scalar curvature

INTRODUCTION Let Mn be a connected and oriented submanifoldisometrically immersed in a space form Mc n p(c ≥ 0).We say Mn is closed if it is compact and withoutboundary. Denote by R, H and S, the normalized sca-lar curvature, mean curvature, and square of thelength of the second fundamental form of Mn, re-spectively. Application of the approach of Simons (1968)yields many rigidity results for minimal submanifoldsand submanifolds with parallel mean curvature v…     

Moebius 2- order pre- isoparametric hypersurfaces in S4

A hypersurface x: M→S^n 1 without umbilic point is called a Moebius k- order pre- isoparametric hypersurface if its Moebius form φ vanishes and k distinct eigenvalues of the Blaschke tensor A are constant. In this paper we classify all Moebius 2 - order pre-isoparametric hypersurfaces in S^4.     

Simulation on Foft—Switching PWM Converter with High Power Factor

A new PWM converter based on soft-switching is introduced.The converter uses a minimum number of devices,and requires less switching operations than conventional techniques,Switching is realized solely in a ZVS)zero voltage switching)mode,therefore the loss is reduced and EMI(electromagnetic interference)is suppressed.The paper analyzes the operation of ZVS,and discusses the methods for maintaining a unit power factor and constant DC voltage.Changing the modulation index M and the phase angle θ keeps the input current in phase with the voltage.It also keeps the current sinusoidal,and ensures a constant output voltage.     

A co-rotational updated Lagrangian formulation for a 2D beam element with consideration of the deformed curvature

A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2^＊ derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2^＊ and C2. A stiffness matrix is obtained in C2^＊; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2^＊ is transformed into that in CI. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.     

Path Planning and Tracking for Vehicle Parallel Parking Based on Preview BP Neural Network PID Controller

In order to diminish the impacts of external disturbance such as parking speed fluctuation and model uncertainty existing in steering kinematics, this paper presents a parallel path tracking method for vehicle based on preview back propagation(BP) neural network PID controller. The forward BP neural network can adjust the parameters of PID controller in real time. The preview time is optimized by considering path curvature, change in curvature and road boundaries. A fuzzy controller considering barriers and different road conditions is built to select the starting position. In addition, a kind of path planning technology satisfying the requirement of obstacle avoidance is introduced. In order to solve the problem of discontinuous curvature, cubic B spline curve is used for curve fitting. The simulation results and real vehicle tests validate the effectiveness of the proposed path planning and tracking methods.     

The homogenization of a class of degenerate quasilinear parabolic equations

1. Introduction and main results 1.1 Introduction Let 0T> and nW be an open bounded domain with with Lipschitz boundary, consider the following initial-boundary value problem : () 0div (,,)(,) in (0,)(,)0 on (0,) (0,)|()tTtuuftTPutTuuxeeeeeWWeeW-==?洞=xaxxxin the space [0,;]pXLTV=, where 1,0(,)pVWemW= is a weighted Sobolev space, p is a constant larger than 1, and e is a positive constant, t and x are variables of the functions a and u. The degenerati…     

Activation of Akt and cardioprotection against reperfusion injury are maximal with only five minutes of sevoflurane postconditioning in isolated rat hearts

It had been proved that administration of sevoflurane for the first two minutes of reperfusion effectively protects the heart against reperfusion injury in rats in vivo.Our aim was to investigate the duration of effective sevoflurane administration and its underlying mechanism in isolated rat hearts exposed to global ischemia/reperfusion(I/R) injury.Adult male Sprague-Dawley rats were randomly divided into six groups(n=12):a sham-operation group,an I/R group,and four sevoflurane postconditioning groups(S2,S5,S10,and S15).In the S2,S5,S10,and S15 groups,the duration times of sevoflurane administration were 2,5,10,and 15 min after the onset of reperfusion,respectively.The isolated rat hearts were mounted on the Langendorff system,and after a period of equilibrium were subjected to 40 min global ischemia and 120 min reperfusion.Left ventricular(LV) hemodynamic parameters were monitored throughout each experiment and the data at 30 min of equilibrium and 30,60,90,and 120 min of reperfusion were analyzed.Myocardial infarct size at the end of reperfusion(n=7 in each group) and the expression of myocardial phosphorylated Akt(p-Akt) after 15-min reperfusion were determined in a duplicate set of six groups of rat hearts(n=5 in each group).Compared with the I/R group,the S5,S10,and S15 groups had significantly improved left ventricular end-diastolic pressure(LVEDP),left ventricular developed pressure(LVDP),and the maximal rate of rise or fall of the LV pressure(±dP/dtmax),and decreased myocardial infarct size(P<0.05),but not the S2 group.After 15 min of reperfusion,the expression of p-Akt was markedly up-regulated in the S5,S10,and S15 groups compared with that in the I/R group(P<0.05),but not in the S2 group.Sevoflurane postconditioning for 5 min was sufficient to activate Akt and exert maximal cardioprotection against I/R injury in isolated rat hearts.     

Seismic response analysis of damper-connected adjacent structures with stochastic parameters

Dynamic response analysis of damper connected adjacent multi-story structures with uncertain parameters is carried out. A formula of the multi degree of freedom （MDOF） for the structure-damper system with stochastic parameters is derived. The uncertainties of mass and stiffness are taken into consideration firstly. The ground acceleration is represented by Kanai-Tajimi filtered non-stationary process. The mean square random responses of structural displacement and story drift are chosen as the optimization objective. The variations of mean square responses of top floor displacements and bottom story drifts in neighboring structures with the damper stiffness and damping coefficient are analyzed in detail. Through the parametric study, the acquiring optimum parameters of damper are regarded as numerical results. Then, a reducing order model of the MDOF system for adjacent structures with mean parameters is presented. The explicit expressions for determining optimal parameters of Kelvin model-defined damper which is used to connect adjacent single degree of freedom （SDOF） structures subjected to a white-noise excitation are employed to achieve the appropriate damper parameters, which are called theory results. Through a comparative study, it can be found that the theory values of damper parameters are consistent with the results based on extensive parametric studies. The analytical results can be obtained by using the first natural frequencies and the total mass of the adjacent deterministic structures with mean parameters. The analytical formulas can be used to find appropriate parameters of damper between adjacent structures for engineering applications. The performance of damper is investigated on the basis of mitigations of mean square random responses of inter-story drifts, displacements and accelerations in adjacent structures. The numerical results demonstrate the robustness of coupled building control strategies.     

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.     

Numerical simulation of interaction between laminar flow and elastic sheet

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.     

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.     

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.     

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.     

Semi On-line Scheduling Problem for Maximizing the Minimum Machine Completion Time on m Identical Machines

In this paper, a semi on-line version on m identical machines M1 , M2, …, Mm ( m ≥ 3 ) was considered, where the processing time of the largest job is known in advance. Our goal is to maximize the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m - 1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2 m - 1 )Pmax where pmax is the largest job‘s processing time, then the worstcase ratio is 2 - 1/m.     

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).     

局部对称共形平坦黎曼流形的伪脐点子流形

本文研究局部对称共形平坦黎曼流形的具有平行非零中曲率向量的焦脐点子流形的截面曲率和数量曲率的拼挤问题。     

局部对称黎曼流形的极小子流形

以Nn+p表示其截面曲率KN 满足 0 <δ≤KN≤ 1的n +p维局部对称完备黎曼流形 ,Mn 是Nn+ p的n维极小子流形 ,本文研究这类子流形的截面曲率的Pinching问题     

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.