Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.

Parameterized Solution to a Class of Sylvester Matrix Equations

A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX - EXF = BY and its dual equation XA - FXE = YC are provided. It is also shown that the results obtained can be used easily for observer design. The method proposed in this paper is universally applicable to linear matrix equations.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

Prediction of rock brittleness using nondestructive methods for hard rock tunneling

Sand production is an undesired phenomenon occurring in unconsolidated formations due to shear failure and hydrodynamic forces. There have been many approaches developed to predict sand production and prevent it by changing drilling or production strategies. However, assumptions involved in these approaches have limited their applications to very specific scenarios. In this paper, an elliptical model based on the borehole shape is presented to predict the volume of sand produced during the drilling and depletion stages of oil and gas reservoirs. A shape factor parameter is introduced to estimate the changes in the geometry of the borehole as a result of shear failure. A carbonate reservoir from the south of Iran with a solid production history is used to show the application of the developed methodology. Deriving mathematical equations for determination of the shape factor based on different failure criteria indicate that the effect of the intermediate principal stress should be taken into account to achieve an accurate result. However, it should be noticed that the methodology presented can only be used when geomechanical parameters are accurately estimated prior to the production stage when using wells and field data.

The Industrial Production of Water Dedicated to Absorption of Gases

The paper presents a flow plasma reactor permitting modification of the properties of water/aqueous solutions by stochastic resonance amplification of vibrations of selected chemical species in water with electromagnetic noise generated during a plasma discharge. The main parameters characterizing the quality for super-pure water, tap water and water from the intake in Besko (Poland) before and after the process in the plasma reactor were presented for comparison. In addition, the 17O NMR (the full width at half maximum) and electrospray ionization mass spectrometry (ESI MS) methods were used to determine differences in physicochemical parameters between the untreated and plasma-treated water. It has been established that the water subjected to plasma treatment shows much different gas absorption properties than the untreated water samples, as a function of temperature and pressure, in this paper we report exemplary data for CO2, oxygen and acetylene. The improved gas absorption properties of the plasma-treated water make it attractive for the use in industrial processes. It is worth pointing to a great capacity of the new reactor (4000 l/h), and low energy consumption (20 MJ/h) for the treatment of the above mentioned volume flow rate of water.

Microwave synthesis of duplexα/β-SiAlON ceramic cutting inserts:Modifying m,n,z values,synthesis temperature,and excess Y_(2)O_(3) synthesis additive

Duplexα/β-SiAlON ceramic cutting inserts(30α:70β)were synthesized by microwave sintering.The effects of solid solution parameters(m,n,z),synthesis temperature,and amount of excess Y_(2)O_(3) synthesis additive on phase assemblage,microstructure,mechanical properties,and cutting performance were systematically investigated.It was found that increasing m value could improve the formation ofαphase while high z value over 1.0 resulted in the dissolution ofαphase intoβphase and intergranular phase.Increasing the amount of excess Y_(2)O_(3) could promote densification and elongatedβgrain growth;however,the excess Y_(2)O_(3) amount above 4 wt%resulted in substantial crystallization of M'SS phase,thus declining the mechanical properties and wear resistance.The microwave-synthesizedα/β-SiAlON cutting insert with modified parameters(m=1.7,n=1.0,z=0.7,and 3 wt%excess Y_(2)O_(3))was obtained with optimal comprehensive properties,whose tool life was found to increase by approximately 75%in high-speed milling of Inconel 718 superalloy compared to the commercialα/β-SiAlON cutting insert.

NLS equation wronskians Peregrine breather rogue waves

The Peregrine breather of order eleven（P_（11） breather） solution to the focusing one-dimensional nonlinear Schrdinger equation（NLS） is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given： when all parameters are equal to 0 we recover the famous P_（11） breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the（x; t） plane, in function of the different parameters.