Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem

The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

Prognostic factors of refractory NSCLC patients receiving anlotinib hydrochloride as the third-or further-line treatment

Objective:Anlotinib hydrochloride is a multitarget tyrosine kinase inhibitor that targets vascular endothelial growth factor receptor,fibroblast growth factor receptor,platelet-derived growth factor receptor,c-Kit,and c-MET;therefore,it exhibits both antitumor and anti-angiogenetic activities.A phase III trial has shown that anlotinib improved progression-free survival(PFS)and overall survival(OS)in patients with advanced non-small cell lung cancer(NSCLC),who presented with progressive disease or intolerance after standard chemotherapy.This study aimed to analyze the characteristics of patients receiving anlotinib treatment to determine the dominant populations who are fit for the treatment.Methods:Data were collected from March 2015 to January 2017 from a randomized,double-blind,placebo-controlled,multicenter,phase III trial of anlotinib(ALTER0303).A total of 437 patients were enrolled and randomly allocated(2:1)to the anlotinib and placebo groups.Kaplan–Meier analysis and log-rank test were performed to compare PFS and OS.Cox proportional hazards model was adopted for multivariate prognostic analysis.Results:Multivariate analysis indicated that high post-therapeutic peripheral blood granulocyte/lymphocyte ratio and elevated alkaline phosphatase levels were independent risk factors for PFS.Meanwhile,elevated thyroid-stimulating hormone,blood glucose,and triglyceride levels;hypertension;and hand–foot syndrome were independent protective factors of PFS.High posttherapeutic peripheral blood granulocyte/lymphocyte ratio,an Eastern Cooperative Oncology Group(ECOG)score≥2,and the sum of the maximal target lesion length at baseline were independent risk factors of OS,and hypertriglyceridemia was an independent protective factor of OS.Conclusions:This study preliminarily explored the possible factors that affected PFS and OS after anlotinib treatment in patients with advanced refractory NSCLC,and the baseline characteristics of the therapeutically dominant populations were then identified.

The Status Quo of Chinese Agro-products Logistics and the Establishment of the Third-Party Logistics Mode

The status quo of Chinese agro-products logistics is analyzed from the following five aspects:the circulation mode,exchange mode,storage and transportation situation,food security.The following problems in Chinese agro-products logistics are pointed out,including excessive circulation sections,bad time efficiency,single payment,slow circulation,backward information processing,obvious bullwhip effect,low logistics efficiency,low logistics technology,inadequate professional equipments,low standardization degree,organized operation mode and low degree of scale.The third-party logistics mode of agro-products is analyzed and the advantages of the mode are analyzed as well.Firstly,establishing information network through integrating circulation section to accelerate the circulation of agro-products;secondly,making the operation norms by providing professional equipments to secure the quality of agricultural products;thirdly,improving the core competitiveness of the whole logistics chain by intensifying specialized work division in each section of the supply chain;fourthly,through forming scale economy to reduce logistics costs and increase the diversity of products;fifthly,through signing contracts to clarify duties and responsibilities and materialize the profit integration of the supply chain.The measures for establishing the third-party logistics of agro-products are put forward,including establish the awareness and concept of socialized logistics services;intensify the support on the third-party logistics enterprises of agro-products;lay stress on the cultivation of logistics talents of agro-products;and vigorously apply the modern marketing means.

Analysis of Problems and Policy Recommendations for the Third-party Evaluation in the Present Poverty Alleviation

The introduction of third-party evaluation system and the implementation of third-party evaluation system in poverty alleviation is a major innovation in the targeted poverty alleviation work in China.In order to improve the third-party evaluation mechanism,further improve the efficiency of third-party evaluation,and enhance the effectiveness of targeted poverty alleviation,this paper analyzes and summarizes the main problems existing in the current third-party evaluation practice.In view of the related problems,this paper puts forward the corresponding policy recommendations,which are believed to play a positive role in further promoting the development and improvement of the third-party evaluation of getting rid of poverty.

Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

The Third-Order Intermodulation Distortion in the AlGaAs/GaAs HBT Amplifier

在测试了ＡｌＧａＡｓ／ＧａＡｓＨＢＴ（异质结晶体管）的直流特性和Ｓ参数的基础上，建立了其微波小信号等效电路，准确的等效电路有利于其微波线性应用的分析．应用Ｖｏｌｔｅｒａ级数，计算了ＡｌＧａＡｓ／ＧａＡｓＨＢＴ放大器的三阶互调失真，计算结果和双音测试结果相当一致。

Third-order elastic, piezoelectric, and dielectric constants

The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.

Tracking of a third-order maneuvering target under an arbitrary topology

We explore the tracking problem of a maneuvering target. Tracking agents with third-order kinematics can communicate with each other via wireless network. The communication network topology is arbitrary rather than switches among several fixed topologies. The information sharing and interaction among agents are position, velocity, and acceleration. Some sufficient conditions of tracking strategy have been proposed. Finally, a numerical example is employed to demonstrate the effectiveness of proposed tracking strategy.

Third-order polynomial model for analyzing stickup state laminated structure in flexible electronics

Laminated hard-soft integrated structures play a significant role in the fabrication and development of flexible electronics devices. Flexible electronics have advantageous characteristics such as soft and light-weight, can be folded,twisted, flipped inside-out, or be pasted onto other surfaces of arbitrary shapes. In this paper, an analytical model is presented to study the mechanics of laminated hard-soft structures in flexible electronics under a stickup state. Thirdorder polynomials are used to describe the displacement field,and the principle of virtual work is adopted to derive the governing equations and boundary conditions. The normal strain and the shear stress along the thickness direction in the bimaterial region are obtained analytically, which agree well with the results from finite element analysis. The analytical model can be used to analyze stickup state laminated structures, and can serve as a valuable reference for the failure prediction and optimal design of flexible electronics in the future.

ON THE BOUNDEDNESS AND PERIODICITY OF THESOLUTIONS OF A CERTAIN VECTOR DIFFERENTIALEQUATION OF THIRD-ORDER

There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.

Crystal Structure and Third-order Nonlinear Optical Property Studies on Copper(Ⅱ) Complex Containing NS Donor Ligand

A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D type comPlex (D=donor, M=metal). Single crystal X-ray diffraction analysis of the copper(Ⅱ) complex established that the geometry around Cu (Ⅱ) is square-planar with two equivalent M-N and M-S bonds. The two phenyl rings and the coordinated plane are almost in one plane fotheng an electronic delocalization system. Their thirdorder response was also studied.

Existence and Uniqueness of Positive Solution for Third-Order Three-Point Boundary Value Problems

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.

Hybrid Intelligent Approach for the Selection of Third-Party Reverse Logistics Provider under Uncertainty

A hybrid intelligent approach is proposed to help the decision maker to select the appropriate third-party reverse logistics provider. The following process is included: firstly,the evaluation team is established to determine the selection criteria and evaluate them by triangular fuzzy numbers; secondly,calculate the weight of criteria by the proposed hybrid algorithm integrating particle swarm optimization( PSO) and simulated annealing( SA); then, the performance evaluation for each supplier is predicted by the proposed self-feedback neural network( SFBNN) based on the historical data. A numerical example is also presented to interpret the methodology above.

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically.The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient.The hybrid multi-step differential transformation method(Hybrid-MsDTM) and the Crank-Nicholson method(CNM) are used to solve the partial differential equation(PDE), and a good agreement between them is observed in the results.The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered.The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries.Also, the maximum wall shear stress increases when Ag increases.

Recent progress in third-generation low alloy steels developed under M^3 microstructure control

During the past thirty years, two generations of low alloy steels(ferrite/pearlite followed by bainite/martensite) have been developed and widely used in structural applications. The third-generation of low alloy steels is expected to achieve high strength and improved ductility and toughness, while satisfying the new demands for weight reduction, greenness, and safety. This paper reviews recent progress in the development of third-generation low alloy steels with an M^3 microstructure, namely, microstructures with multi-phase, meta-stable austenite, and multi-scale precipitates. The review summarizes the alloy designs and processing routes of microstructure control, and the mechanical properties of the alloys.The stabilization of retained austenite in low alloy steels is especially emphasized. Multi-scale nano-precipitates, including carbides of microalloying elements and Cu-rich precipitates obtained in third-generation low alloy steels, are then introduced. The structure–property relationships of third-generation alloys are also discussed. Finally, the promises and challenges to future applications are explored.

A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations

In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.

Investigation on Third-Order Optical Nonlinearities of Two Organometallic Dmit2- Complexes Using Z-Scan Technique

The third-order nonlinear optical properties of two dmit organometallic complexes, [(CH3)4N] [Au(C3S5)2] (MeAu) and [(CH3)4N][Ni(C3S5)2] (Me Ni) in acetone solutions, were characterized us- ing a short pulse Z-scan technique at 1064 nm wavelength. Self-defocusing effects were found in both samples and stronger saturable absorp-tion was observed in MeNi solution comparing with that of MeAu. The origins were analyzed for the differences between the results. Two figures of merit W and T were also calculated to evalu-ate the suitability of two materials for all-optical integrated devices. The results of W=22.84 and T≈0 of MeAu make it an excellent candidate for the all-optical applications.

Work Effectiveness,Problems and Countermeasures of Third-Party Assessment Teams from Colleges and Universities for Targeted Poverty Alleviation

Conducting a third-party assessment on targeted poverty alleviation can effectively avoid the disadvantage that local government plays as both athlete(i.e.performer of poverty alleviation work)and referee(i.e.referee for poverty alleviation effect)in poverty alleviation to ensure the truth of poverty alleviation,and therefore,it is an important part of the work to win the battle against poverty.Since 2016,the thirdparty assessment teams from colleges and universities for targeted poverty alleviation have achieved good results and performance in the assessment on both the effectiveness of targeted poverty alleviation work and the exit of poor counties in China,and they have made due contributions to the cause of poverty alleviation.However,as a new thing,third-party assessment obviously has some problems,mainly including the following:subjective understanding on the long-term nature of rural poverty alleviation is insufficient,and there is a lack of long-term considerations and related mechanism for third-party assessment;affected by policies and institutions,most of the existing third-party assessment teams from colleges and universities have not regarded third-party assessment of targeted poverty alleviation as a cause,and they lack the motivation to actively study the assessment business;and the third-party assessment staff from colleges and universities for targeted poverty alleviation have low stability and high mobility,not conducive to the long-term construction of assessment teams.In order to establish long-term poverty alleviation and prevention mechanisms,these issues must be addressed squarely and relevant countermeasures need to be taken actively to effectively build a long-term mechanism for building third-party assessment teams from colleges and universities for targeted poverty alleviation.

Evaluation of Third-Order Method for the Tests of Variance Component in Linear Mixed Models

Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.