GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

LIE GROUP INTEGRATION FOR CONSTRAINED GENERALIZED HAMILTONIAN SYSTEM WITH DISSIPATION BY PROJECTION METHOD

For the constrained generalized Hamiltonian system with dissipation, by introducing Lagrange multiplier and using projection technique, the Lie group integration method was presented, which can preserve the inherent structure of dynamic system and the constraint-invariant. Firstly, the constrained generalized Hamiltonian system with dissipative was converted to the non-constraint generalized Hamiltonian system, then Lie group integration algorithm for the non-constraint generalized Hamiltonian system was discussed, finally the projection method for generalized Hamiltonian system with constraint was given. It is found that the constraint invariant is ensured by projection technique, and after introducing Lagrange multiplier the Lie group character of the dynamic system can't be destroyed while projecting to the constraint manifold. The discussion is restricted to the case of holonomic constraint. A presented numerical example shows the effectiveness of the method.

Study on the Latter Stage Evaluation to Technique Import Project

How＇s the effect of technical import actually？ The latter stage evaluation to technique import project is necessary to get the answer. Therefore, the latter stage evaluation to technique import project is not equal to the latter stage evaluation to general construction projects, it doesn＇t emphasize particularly on its economic profits but the performance of the digest, generalization, improvement and redevelopment of the imported technique.

Detection of tracheal branching with computerized tomography:The relationship between the angles and age-gender

BACKGROUND The data obtained on the anatomical knowledge of the tracheobronchial system can be used for diagnosis,treatment and interventional interventions in areas such as anesthesia,thoracic surgery,pulmonary physiology.AIM To determine the tracheobronchial branching angles in pediatric and adult populations by using the multislice computed tomography(CT)and minimum intensity projection(MinIP)technique,which is a non-invasive method.METHODS Our study was carried out retrospectively.Patients who underwent contrast and non-contrast CT examination,whose anatomically and pathophysiologically good tracheobronchial system and lung parenchyma images were obtained,were included in the study.Measurements were made in the coronal plane of the lung parenchyma.In the coronal plane,right main bronchus-left main bronchus angle,right upper lobe bronchus-intermedius bronchus angle,right middle lobe bronchus-right lower lobe bronchus angle,left upper lobe bronchus-left lower lobe bronchus angle were measured.RESULTS The study population consisted of 1511 patients,753 pediatric(mean age:13.4±4.3;range:1-18 years)and 758 adults(mean age:54.3±17.3;range:19-94 years).In our study,tracheal bifurcation angle was found to be 73.3°±13.7°(59.6°-87°)in the whole population.In the pediatric group,the right-left main coronal level was found to be higher in boys compared to girls(74.6°±12.9°vs 71.2°±13.9°,P=0.001).In the adult group,the right-left main coronal level was found to be lower in males compared to females(71.9°±12.9°vs 75.8°±14.7°,P<0.001).CONCLUSIONS Our study,with the number of 1511 patients,is the first study in the literature with the largest number of patient populations including pediatric and adult demographic data,measuring the angle values of the tracheobronchial system using multislice CT and MinIP technique.Study data will not only be a guide during invasive procedures,but it can also guide studies to be done with imaging methods.

MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow

We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number.

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.

PERT and CPM in Project Management with Practical Examples

This paper reviewed the concepts of Project Evaluation Review Technique and Critical Path Method in project management with practical examples. The methods and success of quantitative decision-making approaches in project management through the use of project evaluation review technique and the critical path method as regards project duration and critical activities of a project, were discussed. The review found that while both methods are effective in achieving success in project management, the relationship and connectivity of activities involved in a project life cycle are key aspects. The paper concludes that the project evaluation review technique is more effective when the duration of the project is uncertain, while the critical path method is effective when the project’s end time is certain. The paper, therefore, recommends that to achieve maximum operative efficiency in utilizing resources in project management, prior to commencing the execution of a project, all required resources to cover every activity must be assembled and prioritized to eliminate interruptions that could bring delay and unnecessary cost implications. Again, policies focused on improving project execution should be implemented in developing nations to minimize the many cases of failed and delayed projects. Subsequently, stakeholders in projects must be given the right, under the law, to prosecute the government, its agencies and/or the executors of projects for failure to execute a project on schedule.