ALGEBRAIC OPERATION OF SPECIAL MATRICES RELATED TO METHOD OF LEAST SQUARES

The following situation in using the method of least squares to solve problems often occurs.After m experiments completed and a solution of least squares obtained,the ( m+1 ) th experiment is made further in order to improve the results.A method of algebraic operation of special matrices involved in the problem is given in this paper for obtaining a new solution for the m +1 experiments based upon the old solution for the primary m experiments. This method is valid for more general matrices.

Comparison of modeling methods for wind power prediction:a critical study

Prediction of power generation of a wind turbine is crucial,which calls for accurate and reliable models.In this work,six different models have been developed based on wind power equation,concept of power curve,response surface methodology(RSM)and artificial neural network(ANN),and the results have been compared.To develop the models based on the concept of power curve,the manufacturer’s power curve,and to develop RSM as well as ANN models,the data collected from supervisory control and data acquisition(SCADA)of a 1.5 MW turbine have been used.In addition to wind speed,the air density,blade pitch angle,rotor speed and wind direction have been considered as input variables for RSM and ANN models.Proper selection of input variables and capability of ANN to map input-output relationships have resulted in an accurate model for wind power prediction in comparison to other methods.

ANALYSIS ON THE COHESIVE STRESS AT HALF INFINITE CRACK TIP

The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function . The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are given.

A priori, de novo mathematical exploration of gene expression mechanism via regression viewpoint with briefly cataloged modeling antiquity

Various algorithms have been devised to mathematically model the dynamic mecha- nism of the gene expression data. Gillespie＇s stochastic simulation （GSSA） has been exceptionally primal for chemical reaction synthesis with future ameliorations. Several other mathematical techniques such as differential equations, thermodynamic models and Boolean models have been implemented to optimally and effectively represent the gene functioning. We present a novel mathematical framework of gene expression, under~ taking the mathematical modeling of the transcription and translation phases, which is a detour from conventional modeling approaches. These subprocesses are inherent to every gene expression, which is implicitly an experimental outcome. As we foresee, there can be modeled a generality about some basal translation or transcription values that correspond to a particular assay.