On the Existence of Periodic Solutions of a Class Nonlinear Differential Systems

One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.

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THE ROLE OF IGF-1 GENE EXPRESSION ABNORMALITY IN PATHOGENESIS OF DIABETIC PERIPHERAL NEUROPATHY

Objective. To explore the role of insulin-like growth factor 1 (IGF-1)gene expression abnormality in neurotrophic causes of diabetic peripheral neurophathy.Methods. Diabetes was induced in Sprague Dawley rats by alloxan. The parameters were measured as follows: IGF-1 mRNA by reverse transcriptase-polymerase chain reaction (RT-PCR); IGF-1 peptide by enzyme-linked immunosorbent assay (ELISA); electrophysiological parameters of nerves by evoked electromyogram; morphometric evaluation of sciatic nerves under light microscope and transmission electron microscope.Results. During early diabetic stage, IGF-1 mRNA [(0.430±0.031)vs. (0.370±0.016), P ＜0.01,(0.430 ± 0.031 ) vs. (0.280 ± 0.010) , P ＜0.001, respectively], IGF - 1 peptide contents [ (38.44 ± 3.60)ng/mgvs. (30.06±2.41) ng/mg, P ＜0.01, (38.44±3.6) ng/mgvs. (3.71 +2.70) ng/mg, P ＜0.001,respectively] in sciatic nerve tissue reduced in diabetic rats with hyperglycemia and varied with severity of diabetic state when compared with non-diabetic control rats, and further gradually down-regulated in the diabetic rats with duration of diabetes [IGF-1 mRNA (0. 320 ± 0. 021) ～ (0. 230 + 0. 060); IGF-1 peptide (28.80 ± 3.30) ～(19. 51 + 1.80)ng/mg]. Furthermore, they correlated with nerve functional (sensory nerve conduction velocity:r = 0. 741, P ＜0. 001; amplitude ofevokedpotential: r = 0. 716, P ＜0. 001, respectively)andstructuralabnormality (axonal areas r = 0. 81, P ＜ 0. 001 ) of sciatic nerve. No difference was found in the above parameters between diabetic rats with euglycemia and non-diabetic control group.Conclusion. IGF-1 gene expression in tissues was down-regulated from early diabetic stage, and varied with the severity and duration of diabetic state. The decrement in IGF-1 level might contribute to the initiation and development of diabetic neuropathy via autocrine or paracrine pathway.

Low net primary productivity of dominant tree species in a karst forest, southwestern China： first evidences from tree ring width and girth increment

Aboveground net primary productivity(ANPP)of two dominant species, one deciduous tree(Platycarya strobilacea) and one evergreen tree(Machilus cavaleriei),was estimated based on the tree-ring width and the girth increment as well as allometric functions in a karst evergreen and deciduous broadleaved mixed forest in central Guizhou Province, southwestern China. Results showed that the ANPP increased from 1961 to 2015, especially during the last 20–30 years, but with strong variations. The deciduous tree had higher ANPP than the evergreen tree according to two kinds of estimates by the tree ring and girth increment. The averaged ANPP for these two mature trees was 2.27 kg/individual/year, ca. 8 t/ha/year considering the normal stand density. Such karst forest productivity was lower than the natural subtropical forests in China and in the world.

Propagation of Smooth Pulses in Anomalously Dispersive Media

In the present letters we study the propagation of smooth pulses in anomalously dispersive media. We prove that non-analytical but smooth points in a pulse still propagate with the vacuum speed of light, c. It gives an upper limit for signal velocity as well as the non-continuous points of the envelop of a pulse or its derivatives of arbitrary order do.

Existence of Periodic Solutions About One Class Differential Equation

We discuss the existence and the number of periodic solutions of differential equation dx/dt=A_1(t)x+A_2(t)x^2+A_3(t)x^3/a_0(t)+a_1(t)x+a_2(t)x^2 (1) where A_i(t), a_j(t) (i=1,2,3;j=0,1,2) are continuous periodic functions. The results of this paper extend the work of paper [1].

Degradation process assessment of prestressed concrete continuous bridges in life-cycle

To accurately evaluate the degradation process of prestressed concrete continuous bridges exposed to aggressive environments in life-cycle,a finite element-based approach with respect to the lifetime performance assessment of concrete bridges was proposed.The existing assessment methods were firstly introduced and compared.Some essential mechanics problems involved in the degradation process,such as the deterioration of materials properties,the reduction of sectional areas and the variation of overall structural performance caused by the first two problems,were investigated and solved.A computer program named CBDAS(Concrete Bridge Durability Analysis System) was written to perform the above-metioned approach.Finally,the degradation process of a prestressed concrete continuous bridge under chloride penetration was discussed.The results show that the concrete normal stress for serviceability limit state exceeds the threshold value after 60 a,but the various performance indicators at ultimate limit state are consistently in the allowable level during service life.Therefore,in the case of prestressed concrete bridges,the serviceability limit state is more possible to have durability problems in life-cycle;however,the performance indicators at ultimate limit state can satisfy the requirements.

CD13/APN expression in peripheral blood lymphocytes and skin lesions in patients with advanced psoriasis vulgaris

Objective： To observe the expression of CD13/APN in peripheral blood lymphocytes and skin lesions of patients with advanced psoriasis vulgaris, and discuss its effect on the pathogenesis of psoriasis. Methods： CD 13 expression in peripheral blood lymphocytes and skin lesions was detected by flow cytometry and imrnunohistochemical technique, respectively. Results were compared with those of healthy controls. Results： CD 13 expression was significantly higher in peripheral blood lymphocytes of patients with advanced psoriasis vulgaris than in that of healthy controls, and in skin lesions than in healthy skin tissues. The expression was mainly in the suprabasal layers of skin lesions, and positively correlated to PASI （R 0.78029）. Conclusion： The significantly higher expression of CD13 in peripheral blood lymphocytes and skin lesions of the patients with advanced psoriasis vulgaris probably is related to immunological abnormality, blood vessel abnormality and proliferation of keratinocyte in the pathogenic course of psoriasis. It may be a novel and effective way to treat psoriasis with specific CD13 inhibitors.

Permanent myopathy caused by mutation of SCN4A Metl592Val:Observation on myogenesis in vitro and on effect of basic fibroblast growth factor on the muscle

Objective The present study is to observe in vitro the proliferation ability of the muscle cells from permanent myopathy （PM） patients of nomokalaemic periodic paralysis （normKPP）, which is caused by mutations of Metl592Val in the skeletal muscle voltage gated sodium channel （SCN4A） gene on chromosome 17q23.1. We also evaluate the possible effect of the foreign basic fibroblast growth factor （bFGF） in preventing and curing PM. Methods The gastrocnemius muscle cells were taken from two male patients with PM of the same Chinese family with Metl592Val mutation of SCN4A, determined by gene screening. Four male patients suffering from the skeletal injury without PM were taken as control. All preparations were protogenerationally cultured in vitro. Proliferation of the cultured preparations was measured by MTT. Activities of the lactic dehydrogenase （LDH）, creatine kinase （CK）, and protein content in these cells were also detected. The effects of bFGF with different doses （10 ng/mL, 20 ng/mL, 40 ng/mL, 80 ng/mL, 120 ng/mL and 160 ng/mL） on the above mentioned parameters were also evaluated. Results Cells from both PM and control subjects were successfully cultured in vitro. The cultivation of the muscle cells from PM patients in vitro was not yet seen. Results indicated the obvious stimulation of bFGF on cell proliferation, activities of LDH and CK, protein synthesis, in a dose dependent manner. The optimal dose of bFGF was 120 ng/mL （P〈0.05）, beyond which greater dose caused a less effect. The effect of bFGF on 160 ng/mL was stronger than that on 80 ng/mL, but there was no significant difference （P〉0.05）. Conclusion Myoblastic cells from patients with PM had a weaker ability of developing into the myotubules, thus they were unable to perform effective regeneration, which resulted in a progressive necrosis. The exogenous bFGF could promote the division and proliferation of the muscle cells in vitro. These results shield a light on bFGF＇s potential role in preventing and treating PM.

The role of nonlinearities associated with air-sea coupling processes in El Nino's peak-phase locking

We use conditional nonlinear optimal perturbation （CNOP） to investigate the optimal precursory disturbances in the Zebiak- Cane El Nino-Southern Oscillation （ENSO） model. The conditions of the CNOP-type precursors are highly likely to evolve into El Nino events in the Zebiak-Cane model. By exploring the dynamic behaviors of these nonlinear El Nino events caused by the CNOP-type precursors, we find that they, as expected, tend to phase-lock to the annual cycles in the Zebiak-Cane model with the SSTA peak at the end of a calendar year. However, E1 Nino events with CNOPs as initial anomalies in the linearized Zebiak-Cane model are inclined to phase-lock earlier than nonlinear E1 Nino events despite the existence of annual cycles in the model. It is clear that nonlinearities play an important role in El Nino＇s phase-locking. In particular, nonlinear temperature advection increases anomalous zonal SST differences and anomalous westerlies, which weakens anomalous upwelling and acts on the increasing anomalous vertical temperature difference and, as a result, enhances E1 Nino and then delays the peak SSTA. Finally, we demonstrate that nonlinear temperature advection, together with the effect of the annual cycle, causes El Nino events to peak at the end of the calendar year.

Meridional movement of northern and southern equatorial ionization anomaly crests in the East-Asian sector during 2002-2003SSW

The present paper investigates the asymmetrical variability of the location of the north and the south equatorial ionization anomaly(EIA) crests in the East-Asian sector,along with their association with simultaneous observations of equatorial electrojet(EEJ) strength,geomagnetic activity index,and solar flux index during the 2002-2003 sudden stratospheric wanning(SSW) event.Analysis of these observations indicates the existence of a large-scale quasi 16-day periodic meridional movement in both EIA crests,and also reveals a strong correlation between the quasi 16-day oscillation in geomagnetic latitudes of the EIA crest and EEJ strength.The latitude of the northern/southern EIA crest and the EEJ strength indicate that obvious synchronous periodic oscillations were in-phase in the northern and southern hemisphere when the SSW occurred.In addition,it is also found that both the EIA crest location and amplitude of the periodic movement of the EIA locations exhibit hemispheric asymmetry.The amplitude of the periodic movement of the EIA location in the southern hemisphere is larger than that of the northern hemisphere,and the southern EIA crest is further off from the equator than the north one.Understanding these asymmetries requires a combination of mechanisms that involve at least trans-equator meridional winds and the position of a sub-solar point;however,potential disturbances in neutral winds associated with the SSW may additionally complicate the equatorial ionospheric dynamics.

The Bonnesen isoperimetric inequality in a surface of constant curvature

We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.

PSEUDO ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITHPIECEWISE CONSTANT ARGUMENT

The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.

Solution procedure of residue harmonic balance method and its applications

This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no small parameter is assumed.The harmonic residue of balance equation is separated in two parts at each step.The first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent improvement.The corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method again.Three kinds of different differential equations involving general,fractional and delay ordinary differential systems are given as numerical examples respectively.Highly accurate limited cycle frequency and amplitude are captured.The results match well with the exact solutions or numerical solutions for a wide range of control parameters.Comparison with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential systems.Moreover,the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.

Circumferential Propagation of Tip Leakage Flow Unsteadiness for a Low-Speed Axial Compressor

Full-annulus three-dimensional unsteady numerical simulations were conducted for a low-speed isolated axialcompressor rotor, intending to identify the behavior of self-induced unsteady tip leakage flow within multi-bladepassages. There is a critical mass flow rate near stall point, below it, the self-induced unsteadiness of tip leakageflow can propagate circumferentially and thus initiates two circumferential waves. Otherwise, the self-inducedunsteady tip leakage flow oscillates synchronously in each single blade passage. The major findings are: 1) whilethe self-induced unsteadiness of tip leakage flow is a single-passage phenomenon, there exist phase shifts amongblade passages in multi-passage environments then evolving into the first short length wave propagating at abouttwo times of rotor rotation speed after the transient period ends; and 2) the time traces of the pseudo sensors locatedon the rotor blade tips reveal another much longer length-scale wave modulated with the first wave due tophase shift propagating at about half of rotor rotation speed. Features of the short and long length-scale circumferentialwaves are similar to those of rotating instability and modal wave, respectively.

BIFURCATIONS OF ROUGH 3-POINT-LOOP WITH HIGHER DIMENSIONS

The authors study the bifurcation problems of rough heteroclinic loop connecting threesaddle points for the case β1 ＞ 1, β2 ＞ 1, β3 ＜ 1 and β1β2β3 ＜ 1. The existence, number, co-existence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied.Meanwhile, the bifurcation surfaces and existence regions are given.

ALMOST PERIODIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

The authors study the existence of almost periodic solutions to differential equations with piecewise constant arguments which found applications in certain biomedical problems.

Phase-response synchronization in neuronal population

In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function.By numerical simulation,we have found that the phase of a neuronal oscillator undergoes periodic evolution or locked state,which is determined by the synaptic time constant.The synaptic time constant is also an important condition under which the global network is synchronized.When the synaptic time constant is relatively small,perfectly synchronized behavior quickly occurs in the neuronal population.As the synaptic time constant becomes slightly larger,periodic synchronization emerges in the neuronal population.However,synchronized activity in the neuronal population is lost for larger synaptic time constant.The external periodic stimulus can change the synchronization patterns in the neuronal population.With a weak low-frequency stimulus,the neuronal populations quick synchronized bursting;whereas a high-frequency stimulus can produce synchronized overlapping bursting.We have also found that neuronal oscillators with type-II phase response curves are more susceptible to synchronization than those with type-I phase response curves.