EXISTENCE THEOREMS FOR A SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH IMPULSES

In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).

The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

INTERSECTION POINT RULE OF THE RETENTION VALUE AND NORMAL BOILING POINT OF THE HOMOLOGUES IN REVERSED-PHASE HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY

In this paper, a linear relationship between the logarithm of capacity factor k and normal boiling point to of the homologues has been derived, based on the basic retention equation of liquid chromatography according to statistical thermodyoamics proposed by professor Ln Peizhang and others, This equation has been verified by a large number of experimental data, all the strsight lines of lnk- of bumologues for different mobile phass coaiposltion cross each other at the same point, So the intereection point equation van proposed, wbich was used to prodict the retention valu, the result was satisfactory.

INTERSECTION POINT RULE OF THE RETENTION VALUE AND MOBILE PHASE COMPOSITION OF THE HOMOLOGUES IN REVERSED-PHASE HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY

Based on the intersection point rule of the retention value and normal boiling point of homologues in reversed-phase high-performance liquid chromatography(RPLC), the intersection point rule of the retention value of homologues and mobile phase composition has been derived, and was testified by a lot of experimental data from the literature. With this newly proposed equation, we can use the retention value of the compound in one mobile phase composition to predict its retention value in any other mobile phase composition. For fourteen groups of homologues in five mobile phase compositions on five Kinds of columns, the overall average absolute error of 721 data sets is 2.8%.

Existence of solutions for fourth-order boundary value problem with parameter

This paper is a sequel to a previous paper （Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69（2）, 1364-1375 （2008）） in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.

POSITIVE SOLUTIONS FOR SOME 1-DIMENSIONAL BOUNDARY VALUE PROBLEMS OF LAPLACE-TYPE

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.

BIFURCATIONS OF A CUBIC SYSTEM PERTURBED BY DEGREE FIVE

In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and ob-tained the system that can have 17 limit cycles giving their two kinds of distributions (see Fig.5).

ON THE ORDER OF SUMMABILITY OF THE FOURIER INVERSION FORMULA

In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.

Preparation of special silicon steel grade MgO from hydromagnesite

A preparation technology of MgO powder used in special silicon steel from hydromagnesite mineral has been developed. The preparation technology includes the following steps： （1） calcining the hydromagnesite at 700-750°C for 1.5-2 h; （2） hydrating the calcined hydromagnesite to be slurry containing the solid-liquid ratio of 15-20 g？L？1; （3） acquiring Mg（HCO3）2 solution by carbonating the slurry, the carbonation temperature, CO2 pressure, and end point PH value of carbonation are less than 40°C, 0.4-0.6 MPa, and 7 respectively during the carbonation process; （4） preparing precipitated basic magnesium carbonate by thermally decomposing the Mg（HCO3）2 solution at 90-100°C; （5） obtaining the MgO product by calcining the precipitated basic magnesium carbonate at 850-950°C for 30-60 min, and adopting flowing nitrogen during the cooling process. By using this technology, more than 80wt% magnesium in hydromagnesite mineral can be extracted, and high-performance MgO products used in special silicon steel can be ob- tained.

Another Approach to Multiobjective Programming Problems with V-invex Functions

In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.

POSITIVE SOLUTION TO SECOND-ORDER FOUR-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY

This paper considers the positive solution to a class of second-order four-point boundary value problem, in which the first order derivative is involved in the nonlinear term explicitly. By the fixed point theorem in cone, sufficient conditions ensuring the existence of positive solution to the problem are obtained. An example is given to illustrate the feasibility of the main results.

Effects on Sum and Difference Patterns by Adaptive Null

This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result that the increment value of the envelope of the sidelobe level under the effect ofa null is less than l.6dB is proved. The formula about shift value of the pointing null which is thefunction of the jammer direction and array parameters is given in the paper.

Removal of residual CuO particles on the post CMP wafer surface of multi-layered copper

This article introduces the removal technology of CuO particles on the post CMP wafer surface of multi-layered copper. According to the Cu film corrosion curve with different concentrations of HEO2 and the effect curve of time on the growth rate of CuO film, CuO film with the thickness of 220 nm grown on Cu a surface was successfully prepared without the interference of CuC12.2H20. Using the static corrosion experiment the type of chelating agent （FA/O II type chelating agent） and the concentration range （10-100 ppm） for CuO removal was determined, and the Cu removal rate was close to zero. The effect of surfactant on the cleaning solution properties was studied, and results indicated that the surfactant has the effect of reducing the surface tension and viscosity of the cleaning solution, and making the cleaning agent more stable. The influence of different concentrations of FA/O I type surfactant and the mixing of FA/O II type chelating agent and FA/O I type surfactant on the CuO removal effect and the film surface state was analyzed. The experimental results indicated that when the concentration of FA/O I type surfactant was 50 ppm, CuO particles were quickly removed, and the surface state was obviously improved. The best removal effect of CuO on the copper wiring film surface was achieved with the cleaning agent ratio of FA/O II type chelating agent 75 ppm and FA/O I type surfactant 50 ppm. Finally, the organic residue on the copper pattern film after cleaning with that cleaning agent was detected, and the results showed that the cleaning used agent did not generate organic residues on the film surface, and effectively removes the organic residue on the water.

Alternating Direction Implicit Orthogonal Spline Collocation on Non-Rectangular Regions

The alternating direction implicit(ADI)method is a highly efficient technique for solving multi-dimensional time dependent initial-boundary value problems on rectangles.When the ADI technique is coupled with orthogonal spline collocation(OSC)for discretization in space we not only obtain the global solution efficiently but the discretization error with respect to space variables can be of an arbitrarily high order.In[2],we used a Crank Nicolson ADI OSC method for solving general nonlinear parabolic problems with Robin’s boundary conditions on rectangular polygons and demonstrated numerically the accuracy in various norms.A natural question that arises is:Does this method have an extension to non-rectangular regions?In this paper,we present a simple idea of how the ADI OSC technique can be extended to some such regions.Our approach depends on the transfer of Dirichlet boundary conditions in the solution of a two-point boundary value problem(TPBVP).We illustrate our idea for the solution of the heat equation on the unit disc using piecewise Hermite cubics.