Lagrange Interpolation on a Sphere

In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.

An Innovative Method to Accommodate Chinese Medicine Pattern Diagnosis within the Framework of Evidence-Based Medical Research

Pattern diagnosis is an integral aspect of Chinese medicine （CM）. CM differentiates biomedical diseases into patterns, based upon the patient＇s symptoms and signs. Pattern identification （PI） is used to diagnose, direct the treatment principle and determine the treatment protocol. Most CM research has used fixed formula treatments for Western-defined diseases with outcomes measured using objective biomedical markers. This article presents an innovative method used in a randomised controlled pilot study using acupuncture for participants with hepatitis C virus. Each participant＇s CM patterns were identified and quantified at baseline which directed the treatment protocol for the treatment group. Data identified that while each participant expressed different patterns at baseline all participants displayed multiple patterns. Six patterns showed some expression by all 16 participants; Liver （Gan） yin vacuity expressing a group aggregate mean percentage of 47.2, binding depression of Liver qi 46.9, and Liver Kidney （Shen） yin vacuity 45.1. Further sub category gender grouping revealed that pattern ranking changed with gender; Liver yin vacuity （male 53.4%, female 51.93%）, binding depression of Liver qi （male 50.0%, female 42.86%） and Liver Kidney yin vacuity （male 42.9%, female 47.96%）. The quantification of CM patterns described in this article permitted statistical evaluation of presenting CM patterns. Although this methodology is in its infancy it may have potential use in the integration of PI with rigorous evidence based clinical research. Biomedical markers often do not relate to symptom/signs and therefore this innovative measure may offer an additional CM evaluation methodology and further CM PI understanding.

The uncoupled microbial fed-batch fermentation optimization based on state-dependent switched system

In the actual microbial fermentation process,excessive or insufficient substrate can produce inhibitory effects on cells growth.The artificial substrate feeding rules by past experiences have great blindness to keep substrate concentration in a given appropriate range.This paper considers that alkali feed depends on pH value of the solution and glycerol feed depends on glycerol concentration of the solution in the uncoupled microbial fed-hatch fermentation process,and establishes a state-dependent switched system in which the flow rates of glycerol and alkali,the number of mode switches,the mode sequence and the switching times are prior unknown.To maximize the yield of target product 1,3-Propanediol(1,3-PD),we formulate a switching optimal control problem with the flow rates of glycerol and alkali,the number of mode switches,the mode sequence and the switching times as decision variables,which is a mixed-integer dynamic programming problem.For solving the mixed-integer dynamic programming problem,the control parametrization technique,the time scaling transformation and the embedded system technology are used to obtain an approximate parameter optimization problem.By using a parallel optimization algorithm,we obtain the optimal control strategies.Under the obtained optimal control strategies,the 1,3-PD yield at the terminal time is increased significantly compared with the previous results.