Non-existence of Shilnikov chaos in continuous-time systems

In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation （ODE） systems characterized by the nonexistence of homoclinic and heteroclinic orbits.

Existence and Non-Existence Result for Singular Quasilinear Elliptic Equations

We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .

Comments on "Non-existence of Shilnikov chaos in continuous-time systems"

A paper, ＂Non-existence of Shilnikov chaos in continuous-time systems＂ was published in the journal Applied Mathematics and Mechanics （English Edition）. The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.

Comments on “Non-existence of Shilnikov chaos in continuous-time systems”

Comments on 'Non-existence of Shilnikov chaos in continuous-time systems' are given.An error has been found in the proof of Theorem 1 in the paper by Elhadj and Sprott(Elhadj,Z.and Sprott,J.Non-existence of Shilnikov chaos in continuous-time systems.Applied Mathematics and Mechanics(English Edition),33(3),1-4(2012)).It makes the main conclusion of the paper incorrect,that is to say,the non-existence of Shilnikov chaos in the continuous-time systems considered cannot be ensured.Furthermore,a counter-example shows that Theorem 1 in the paper is incorrect.

肥胖儿童non-HDL-C、remnant cholesterol与亚临床动脉粥样硬化的关系

目的:了解non-HDL-C和remnant cholesterol与肥胖儿童亚临床动脉粥样硬化(AS)的关系。方法:根据甘油三酯(TG)水平将65例肥胖儿童(肥胖组)分为I组(TG≥2.3 mmol/L)32例,II组(TG<2.3 mmol/L)33例,与肥胖组儿童性别年龄相匹配的正常体质量儿童30例为III组(对照组)。比较3组儿童血脂指标,对肥胖组各项血脂指标与血浆致动脉粥样硬化指数(AIP)进行相关性分析,肥胖患儿体质指数、血脂指标与颈动脉内径、内膜-中层厚度(c-IMT)、血流参数进行相关性分析。结果:I组、II组的TG、总胆固醇(TC)、低密度脂蛋白胆固醇(LDL-C)、non-HDL-C、remnant cholesterol、AIP均较对照组升高,高密度脂蛋白胆固醇(HDL-C)较对照组降低,且I组的remnant cholesterol、AIP均较II组升高。肥胖组儿童AIP与TG、non-HDL-C、remnant cholesterol呈正相关,与HDL-C呈负相关。37例行颈动脉超声检查的肥胖儿童的c-IMT较正常儿童的增厚。结论:non-HDL-C、remnant cholesterol在肥胖儿童亚临床AS中有重要作用,在肥胖儿童血脂异常的治疗中应关注non-HDL-C、remnant cholesterol的变化。

Shenqi Fuzheng injection combined with GP chemotherapy in the treatment of advanced non-small cell lung cancer： a meta-analysis

Objective： To evaluate the clinical efficacy of Shenqi Fuzheng injection combined with gemcitabine plus cisplatin（GP） in the treatment of advanced non-small cell lung cancer （NSCLC）. Methods： we performed a systematicsearch in the electronic databases such as Cochrane Library, Pubmed, Embase, Chinese Journal Full-text Database,Chinese Biomedical Literature Database, Chinese Science and Technology Periodical Full-text Database andWanfang Database up to 30 January 2017. Randomized controlled trials （RCT） of Shenqi Fuzheng Injectioncombined with GP chemotherapy in the treatment of advanced NSCLC were searched, and all the RCTs wereconducted on methodological quality assessment. Data extraction and data analysis were according to standards ofCochrane systematic review. Results： Eight trials were included including a total of 701 patients. Meta-analysisresults： Shenqi Fuzheng injection combined with GP chemotherapy could significantly improve the functionalstatus of patients with NSCLC （OR = 3.44, 95% CI [2.26, 5.25], P 〈 0.0001） and clinical treatment efficacy （OR =（OR = 0.31, 95%CI [0.20, 0.47], P 〈 0.0001. The rate of leukopenia （OR = .31, 95%CI [0.20,0.47], P 〈 0.0001）,thrombocytopenia （OR = 0.58, 95%CI [0.37, 0.91], P = 0.020）, hemoglobin decline （（OR = 0.31, 95%CI [0.16,0.59], P = 0.0004） and incidence of gastrointestinal reactions （OR = 0.58,P 〈 0.05） could be reduced. Conclusion：Shenqi Fuzheng injection combined with GP chemotherapy in the treatment of advanced NSCLC obtainedsignificantly clinical efficacy. The quality of the literature incorporated is low, the conclusion requires high-qualityresearch to further prove.

THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE

This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum

We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that there is a global strong solution and is unique for the 2D Cauchy problem with the initial density which can allow vacuum conditions and even have compact support. Besides, the large time decay rates of the gradients of velocity, temperature and pressure can also be obtained which are also the same as those of the homogeneous case.

Analysis of Numerical Results in High Temperature Congealment and Chemistry Non-equilibrium Flow Field

Using the air plasma ignition technique, physicochemical process of burning can be accelerated; concentration limit ofretrofires both can be extended; reliability of retrofires and stability of burning can be improved. In this paper, using internalequivalent heat area in place of electric are that created Ohm heat, the flow fields of thermodynamic equilibrium chemistry con-gealment and chemistry non-equilibrium in the plasma generator were simulated. The influences of the inlet prerotation angleof air, the inlet total pressure of air and the airflow compression angle of spray nozzle on the temperature on the surface of elec-

Turbulent Flow Action of Pulp in Wet - Laid Non - Woven Processes

The paper deals with the fluid field of web forming in wet-laid non-woven production.The influence of the turbulent flow on blending fiber and occluded fluid produced in pulp flow has been discussed in theory and practice.The suitable use of the imported velocity of pulp is very important in producing wet-laid products of good quality.

CYFRA 21-1 as an early predictor of first line chemotherapy response in advanced non small cell lung cancer

Objective： In an era of ever evolving, promising new therapies for advanced non small cell lung cancer （NSCLC）, early predictors of response to therapy, are needed. We evaluated early variations in CYFRA 21-1 serum levels of patients with advanced NSCLC receiving first line chemotherapy and correlated the results with objective tumor response. Methods： 29 consecutive, previously untreated, patients of advanced non small cell lung cancer, with measurable disease on CT scan were evaluated. All patients were treated with conventional systemic chemotherapy, although the choice of chemotherapy was left to the discretion of the treating physicians. Serum samples were obtained immediately before the start of 1st and 2nd cycles of chemotherapy. CYFRA 21-1 was measured with an electrochemiluminescense immunoassay on an automatic analyzer （Elecsys 2000; Roche Diagnostics）. Response was evaluated using Response evaluation criteria in solid tumors （RECIST） criteria. Results： 10 patients had partial response, 9 patients had stable disease and 9 had progressive disease. None of the patients had complete response. 21/29 （72%） patients had an elevated baseline value of CYFRA 21-1.62% patients （18/29） had a decrease in CYFRA 21-1 after 1 cycle of chemotherapy. The average reduction in the 2nd reading was irrespective of whether baseline value was normal or not. The average reduction was statistically significant （P = 0.002; 95% CI, from 0.8369 to 3.49464; t test）. 8 out of 10 （80%） patients with partial response had a reduction in their 2nd reading of. CYFRA （P = 0.019; 95% CI, from 0.81965 to 7.20035; t test） which was significant. We also observed that 6/9 （66%） patients whose disease remains stable also had a decrease in their subsequent reading （P = 0.0106; 95% CI, from -0.44942 to 3.82720; t test）, though it was not significant statistically. Although 5 out of 9 （55%） patients, who had an increase in their CYFRA 21-1 level, had progressive disease, but it was not statistically significant （P = 0.537; 95% CI, from -1.20021 to 2.13354; ttest）. 14 out of 19 （73%） who either had partial response or had stable disease, had a reduction in their 2nd value of CYFRA 21-1 and was significant statistically （P = 0.004; 95% CI, from 0.74792 to 3.50208; t test）. We also observed that except for 1 patient, all patients who had a decrease of 42% or more in their subsequent CYFRA 21-1 level, were those who had either responded to chemotherapy or had stable disease （P = 0.001）, which was statistically significant. Conclusion： We can conclude that monitoring of serum marker CYFRA 21-1, early dudng first-line chemotherapy may be a useful prognostic tool for evaluation of early tumor response in patients with advanced NSCLC.

MiR-16-5p plays an inhibitory role in human non-small cell lung cancer through Fermitin family member 2

Increasing evidence indicates that aberrant expressions of some microRNAs are associated with cancer progression.However,the roles and biological mechanisms of miRNA-16-5p in human non-small cell lung cancer(NSCLC)are not to be well studied.Here,we validated that the expression of miR-16-5p was decreased significantly in NSCLC samples and cell lines.The correlation between the clinicopathological features of NSCLC and the miR-16-5p expression showed that the expression of miR-16-5p in non-small cell lung cancer was linked with the advanced TNM stage,positive lymph node metastasis,with short overall survival(OS).Also,a negative correlation between miR-16-5p and Fermitin family member 2(FERMT2)was observed,implying there may be a potential link about their regulation.The hypothesis was further confirmed by in-silico analysis and dual-luciferase reporter assay.Moreover,we demonstrated that the transfections of miR-16-5p mimics could alter some biological characteristics of NSCLC cells remarkably accomplished by the expression variance of FERMT2 in vitro and in vivo assays.Summarily,this study demonstrated that miR-16-5p,as a tumor suppression factor in NSCLC by targeting FERMT2,could serve as one promising biomarker in the prediction for NSCLC patients.

SELF-SIMILAR SOLUTIONS OF A CLASS OF NONLINEAR PAPTIAL DIFFERENTIAL EQUATION

In this paper, we investigate the following partial differential equation, ut , where a > 0 and p> 1. When n(p-1)/2 > 1 andp > 3, we obtained a nontrivial non-negative global solution. Furthermore, on Sobolev space W1,s(W2,s) with s > 1. a nonuniqueness result is established which shows that there exists a positive solution u(t,x) with u(t,x)→0 as t→0 in W1,s(W2,s). On the other hand, our result can be regarded as a generalization of conclusion of Haraux, A.and Weissler, F.B. in [5].

A NONLINEAR DEGENERATE PARABOLIC EQUATION WITH NON-LOCAL SOURCE

The global existence and finite time blow up of the positive solution for a nonlinear degenerate parabolic equation with non- local source are studied

DYNAMIC ANALYSIS OF TWO-DEGREE-OF-FREEDOM OBLIQUE IMPACT SYSTEM WITH NON-FIXED IMPACT POSITIONS

The dynamic behavior of a two-degree-of-freedom oblique impact system consisted of two pendulums with non-fixed impact positions is investigated. The relations between the restitution coefficient, the friction coefficient, as well as other parameters of the system and the states before or after impact, are clarified in this oblique impact process. The existence criterion of single impact periodic-n subharrnonic motions is deduced based on the Poincare map method and the oblique impact relations with non-fixed impact positions. The stability of these subharrnonic periodic motions is analyzed by the Floquet theory, and the formulas to calculate the Flocluet multipliers are given. The validity of this method is shown through numerical simulation. At the same time, the probability distribution of impact positions in this oblique system with nonfixed impact positions is analyzed.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

The Existence and Uniqueness of Solutions for Mean-Reverting <i>γ</i>-Process

Empirical studies show that more and more short-term rate models in capturing the dynamics cannot be described by those classic ones. So the mean-reverting γ-process was correspondingly proposed. In most cases, its coefficients do not satisfy the linear growth condition;even they satisfy the local Lipschitz condition. So we still cannot examine its existence of solutions by traditional techniques. This paper overcomes these difficulties. Firstly, through using the function Lyapunov, it has proven the existence and uniqueness of solutions for mean-reverting γ-process when the parameter . Secondly, when , it proves the solution is non-negative. Finally, it proves that there is a weak solution to the mean-reverting γ-process and the solution satisfies the track uniqueness by defining a function ρ. Therefore, the mean-reverting γ-process has the unique solution.

A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.

Construction of Non-Symmetric Balanced Incomplete Block Design through Combination of Symmetric Disjoint Balanced Incomplete Block Designs

The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing construction methods have not been able to construct these designs despite their design parameters satisfying the necessary conditions for the existence of BIBD. The study aimed to bridge this gap by introducing a new class of non-symmetric BIBDs. The proposed class of BIBDs is constructed through the combination of disjoint symmetric BIBDs. The study was able to determine that the total number of disjoint symmetric BIBDs (n) with parameters (v = b, r = k, λ) that can be obtained from an un-reduced BIBD with parameters (v, k) is given by n = r - λ. When the n symmetric disjoint BIBDs are combined, then a new class of symmetric BIBDs is formed with parameters v* = v, b* = nb, r* = nr, k* = k, λ* = λ, where 2≤ n ≤ r - λ. The study established that the non-existence property of this class of BIBD was that when is not a perfect square then v should be even and when v* is odd then the equation should not have a solution in integers x, y, z which are not all simultaneously zero. In conclusion, the study showed that this construction technique can be used to construct some non-symmetric BIBDs. However, one must first construct the disjoint symmetric BIBDs before one can construct the non-symmetric BIBD. Thus, the disjoint symmetric BIBDs must exist first before the non-symmetric BIBDs exist.

Uniqueness Theorem for the Non-Local Ionization Source in Glow Discharge and Hollow Cathode

The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The theorem is applied to wide class of electric field configurations, and to the walls of discharge volume, which have a property of incomplete absorption of the electrons. Cathode is regarded as interior singular source, which is placed arbitrarily close to the wall. The existence of solution is considered also. During the proof of the theorem many of useful structure formulae are obtained. Elements of the proof structure, which have arisen, are found to have physical sense. It makes clear physical construction of non-local electron avalanche, which builds a source of ionization in glow discharge at low pressures. Last has decisive significance to understand the hollow cathode discharge configuration and the hollow cathode effect.