Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Evaluation of Non Crystalline Phase in AZS Refractories by XRD Methods

The relation between the atomic structure and the macroscopic properties and behaviors of a material constitute one of the objectives of the materials science, particularly in the design and development of ceramic materials.Crystalline and non crystalline phases together with pores, grain boundaries, etc. affect mechanical and fracture properties as well as chemical resistance and electric properties. These aspects will be bonded to the raw materials chosen and the whole processing route.In glass industry, although there are other electrofused refractories such as the alumina ones used in the feeding of the fusion kilns, probably the most used refractories in contact with the melted glass are electrofused materials that belong to the Al2O3-SiO2-ZrO2 system commonly named AZS.Exceptionally for refractory materials the amount of the glassy phase in a AZS material is important and appreciable;and makes them particularly adequate for containing fussed glass. The glass proportion will define much of their properties and behaviors.In the present work the results of the non crystalline phase quantification of two samples of commercial AZS materials are presented and compared. These were obtained by three different methods using in the X ray powder diffraction (XRD) techniques. The first method consists in the linear interpolation of the base lines of the diffractograms compared to the amorphous silica and the fully crystalline quartz. The other two methods are based in the application of the Rietveld method. One is the internal standard method with quartz as fully crystalline standard and the other one consist in the inclusion of the glassy phase to the refinement with a structural model that can be understood as the widening of the peaks consequence of an extreme decrease in the crystallite size of a quartz phase.The three methods showed equivalent results (with differences less than 3%) for the two samples and demonstrated that are adequate for the quantification of the non crystalline phase in this kind of materials.

Generation of Transgene-free Induced Pluripotent Stem Cells with Non-viral Methods

Induced pluripotent stem(iPS) cells were originally generated from mouse fibroblasts by enforced expression of Yamanaka factors(Oct3/4,Sox2,Klf4,and c-Myc).The technique was quickly reproduced with human fibroblasts or mesenchymal stem cells.Although having been showed therapeutic potential in animal models of sickle cell anemia and Parkinson's disease,iPS cells generated by viral methods do not suit all the clinical applications.Various non-viral methods have appeared in recent years for application of iPS cells in cell transplantation therapy.These methods mainly include DNA vector-based approaches,transfection of mRNA,and transduction of reprogramming proteins.This review summarized these non-viral methods and compare the advantages,disadvantages,efficiency,and safety of these methods.

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.

The global convergence of the non-quasi-Newton methods with non-monotone line search

The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved. Numerical experiments showed that the non-monotone line search was more effective.

Determination of Bonding Failures in Transparent Materials with Non-Destructive Methods—Evaluation of Climatically Stressed Glued and Laminated Glass Compounds

As part of an international research project—funded by the European Union—capillary glasses for facades are being developed exploiting storage energy by means of fluids flowing through the capillaries. To meet highest visual demands, acrylate adhesives and EVA films are tested as possible bonding materials for the glass setup. Especially non-destructive methods (visual analysis, analysis of birefringent properties and computed tomographic data) are applied to evaluate failure patterns as well as the long-term behavior considering climatic influences. The experimental investigations are presented after different loading periods, providing information of failure developments. In addition, detailed information and scientific findings on the application of computed tomographic analyses are presented.

Variational Methods to Nonlinear Differential Equations with Non-instantaneous Impulses

The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.

Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method

A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

Estimation of non-point source pollution loads with flux method in Danjiangkou Reservoir area,China

The estimation of non-point source pollution loads into the Danjiangkou Reservoir is highly significant to environmental protection in the watershed. In order to overcome the drawbacks of traditional watershed numerical models, a base flow separation method was established coupled with a digital filtering method and a flux method. The digital filtering method has been used to separate the base flows of the Hanjiang,Tianhe, Duhe, Danjiang, Laoguan, and Qihe rivers. Based on daily discharge, base flow, and pollutant concentration data, the flux method was used to calculate the point source pollution load and non-point source pollution load. The results show that:(1) In the year 2013, the total inflow of the six rivers mentioned above accounted for 95.9% of the total inflow to the Danjiangkou Reservoir. The total pollution loads of chemical oxygen demand(CODMn) and total phosphorus(TP) from the six rivers were 58.20 103 t and 1.863 10~3 t, respectively, and the non-point source pollution loads were 39.82 10~3 t and 1.544 10~3 t, respectively, indicating that the non-point source pollution is a major factor(with a contribution rate of 68.4% for CODMnand 82.9% for TP).(2) The Hanjiang River is the most significant contributor of pollution loads to the Danjiangkou Reservoir, and its CODMnand TP contribution rates reached 79.3% and 83.2%, respectively. The Duhe River took the second place.(3) Non-point source pollution mainly occurred in the wet season in 2013, accounting for 80.8% and 90.9% of the total pollution loads of CODMnand TP, respectively. It is concluded that the emphasis of pollution control should be placed on non-point source pollution.

On the field method in non-holonomic mechanics

This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized Lagrange equa-tions of the second kind.Two examples are given to illustratethe theory.

An Analytical Method for Predicting Chaos in Perturbed Planar Non-Hamiltonian System

An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed system was found by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.

Free vibration of non-uniform axially functionally graded beams using the asymptotic development method

The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.

Research on control method for machining non-cylinder pin hole of piston

The control method for machining non-cylinder pin hole of piston was studied systematically. A new method was presented by embedding giant magnetostrictive material (GMM) into the tool bar proper position. The model is established to characterize the relation between control current of coil and deformation of tool rod. A series of tests on deformation of giant magnetostrictive tool bar were done and the results validated the feasibility of the principle. The methods of measuring magne- tostrictive coefficient of rare earth GMM were analyzed. The measuring device with the bias field and prestress was designed. A series of experiments were done to test magnetostrictive coefficient. Experimental results supplied accurate characteristic pa- rameter for designing application device of GMM. The constitution of the developed control system made up of displacement detection and temperature detection for thermal deformation compensation was also introduced. The developed machine tool for boring the non-cylinder pin hole of piston has the micron order accuracy. This control method can be applied to other areas for machining precision or complex parts.

Numerical Simulation of Independent Advance of Ore Breaking in the Non-pillar Sublevel Caving Method

The mechanism of stress generation and propagation by detonation loading in five separate independent ad-vance of ore breaking patterns is discussed in the paper. An elastic numerical model was developed using AN-SYS/LS-DYNA 3D Nonlinear Dynamic Finite Element Software. In this package ANSYS is the preprocessor and LS-DYNA is the postprocessor. Numerical models in the paper to actual were 1:10 and the element mesh was dissected in scanning mode utilizing the symmetry characteristics of the numerical model. Five different advance rates were stud-ied. Parameters,such as the time required to maximum stress,the action time of the available stress,the maximum ve-locity of the nodes,the stress penetration time,the magnitude of the stress peak and the time duration for high stress were numerically simulated. The 2.2 m advance appeared optimum from an analysis of the simulation results. The re-sults from numerical simulation have been validated by tests with physical models.

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.

GLOBAL COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.