NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS

In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .

On Skew Triangular Matrix Rings

In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equations. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented.

Extended tanh-function Method for Solving Traveling Wave Solutions of Nonlinear Kundu Equation

In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.

THE BALL-COVERING PROPERTY ON DUAL SPACES AND BANACH SEQUENCE SPACES

In this paper,we prove that(X,p)is separable if and only if there exists a w^(*)-lower semicontinuous norm sequence{p_(n)}_(n=1)^(∞)of(X^(*),p)such that(1)there exists a dense subset G_(n)of X^(*)such that p_(n)is Gateaux differentiable on G_(n)and dp_(n)(Gn_(n))■X for all n∈N;(2)p_(n)≤p and p_(n)→p uniformly on each bounded subset of X^(*);(3)for anyα∈(0,1),there exists a ball-covering{B(x^(*)i,n,Ti,n)}∞i=1 of(X^(*),p_(n))such that it isα-off the origin and x_(i,n)^(*)∈Gn_(n).Moreover,we also prove that if Xi is a Gateaux differentiability space,then there exist a real numberα>0 and a ball-covering(B)i of Xi such that(B)i isα-off the origin if and only if there exist a real numberα>0 and a ball-covering B of l^(∞)(X_(i))such that(B)isα-off the origin.

THE UNIQUENESS AND EXISTENCE OF SOLUTION OF THE CHABACTERISTIC PROBLEM ON THE GENERALIZED KdV EQUATION

The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma￣[2], Ihe isolated wave in transmission line￣[3], and the isolated wave in the bound-ary surface of the divided layer fluid￣[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.

ON NECESSARY CONDITIONS FOR RESONANCE IN TURNING POINT PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.

Carrier phase-based ionospheric observables using PPP models

The ionosphere is one of the major error sources in Global Navigation Satellite System （GNSS） posi- tioning, navigation and timing. Estimating the ionospheric delays precisely is of great interest in the GNSS community. To date, GNSS observables for ionospheric estimation are most commonly based on carrier phase smoothed code measurements. However, leveling errors, which affect the performance of ionospheric modeling and differential code bias （DCB） estimation, exist in the carrier phase smoothed code observations. Such leveling errors are caused by the multipath and the short-term variation of DCB. To reduce these leveling errors, this paper investigates and estimates the ionospheric delays based on carrier phase measurements without the leveling errors. The line-of-sight ionospheric observables with high precision are calculated using precise point positioning （PPP） techniques, in which carrier phase measurements are the principal observables. Ionosphere-free and UofC PPP models are applied and compared for their effectiveness to minimize the leveling errors. To assess the leveling errors, single difference of ionospheric observables for a short baseline is examined. Results show that carrier phase- derived ionospheric observables from PPP techniques can effectively reduce the leveling errors. Furthermore, we compared the PPP ionosphere estimation model with the conventional carrier phase smoothed code method to assess the bias consistency and investigate the biases in the ionospheric observables.

Acupuncture therapy with point selection based on syndrome differentiation along the meridians for functional dyspepsia:a randomized controlled trial

Objective:To observe the difference in clinical efficacy between acupuncture with point selection based on syndrome differentiation along the meridians and acupuncture at non-meridian and non-acupoint points for functional dyspepsia(FD).Methods:A total of 74 FD patients were randomized into an observation group and a control group,with 37 cases in each group.Both groups received acupuncture treatment.Zusanli(ST 36)and Neiguan(PC 6)were selected in the observation group,with Taichong(LR 3)and Neiting(ST 44)added for excess syndrome,and Gongsun(SP 4)and Yinlingquan(SP 9)added for deficiency syndrome.Four non-meridian and non-acupoint points were selected in the control group.The treatments in both groups were performed once a day with a 2-day break after 5 consecutive treatments,which constituted one treatment course.A total of 4 courses were performed.The scores of Nepean dyspepsia index(NDI)and Leeds dyspepsia questionnaire(LDQ)were recorded before and after treatment,and during follow-up(8,12,16,20 and 24 weeks after recruitment)to assess the clinical efficacy.Results:The NDI scores in the two groups after treatment and at each time point during follow-up were higher than those before treatment(all P<0.05),and the LDQ scores were lower than those before treatment(all P<0.05).The NDI scores after treatment and at each time point during follow-up in the observation group were higher than those in the control group(all P<0.01);the total LDQ score and scores of upper abdominal pain,postprandial satiety and upper abdominal burning sensation after treatment and at each time point during follow-up in the observation group were significantly lower than those in the control group(P<0.01 or P<0.05)..Conclusion:Acupuncture with point selection based on syndrome differentiation along the meridians has a better curative effect than acupuncture at non meridian and non-acupoint points in the treatment of FD.

THEORY OF SINGULAR POINTS OF ORDINARY DIFFERENTIAL EQUATIONS IN COMPLEX DOMAIN

In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.

Existence of p-mean Almost Periodic Mild Solution for Fractional Stochastic Neutral Functional Differential Equation

A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.

Clinical study on acupuncture for primary insomnia

Objective： To observe the clinical effect of Acupuncture at Baihui（GV 20）, Sishencong（EX-HN 1） and Anmian [Extra, locates at the midpoint between Yiming（EX-HN 14） and Fengchi（GB 20）] for primary insomnia. Methods： A total of 112 patients with primary insomnia were randomized into an acupuncture group and a medication group according to the visiting sequence, 56 cases in each group. The acupuncture group was intervened by acupuncture at Baihui（GV 20）, Sishencong（EX-HN 1） and Anmian [Extra, locates at the midpoint between Yiming（EX-HN 14） and Fengchi（GB 20）], and points selected based on syndrome differentiation, while the medication group was by oral intake of zopiclone tablet. The Pittsburgh sleep quality index（PSQI） was measured before and after treatment, and the clinical efficacy was compared after 1 month of treatment. Results： After treatment, subscales of PSQI and global score in the acupuncture group were improved, and intra-group comparisons showed statistical differences（all P〈0.05）; subscales of sleep quality, sleep latency, sleep duration and global score of PSQI in the medication group were improved, showing statistical differences（all P〈0.05）. Inter-group comparison of global and subscales scores of PSQI showed statistical differences（all P〈0.05）. The total effective rate in the acupuncture group was 92.9%, higher than 67.9% in the medication group, and between-group comparison showed a statistical difference（P〈0.05）. Conclusion： Acupuncture at Baihui（GV 20）, Sishencong（EX-HN 1） and Anmian [Extra, locates at the midpoint between Yiming（EX-HN 14） and Fengchi（GB 20）] as the main treatment method can produce a better effect than oral intake of zopiclone tablet.

VARIABILITY SETS AND HAMILTON SEQUENCES

This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.

Rational maps as Schwarzian primitives

We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.