Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

Kinetic study of hydrolysis of xylan and agricultural wastes with hot liquid water

We investigated the kinetics of hot liquid water (HLW) hydrolysis over a 60-min period using a self-designed setup. The reaction was performed within the range 160-220 °C, under reaction conditions of 4.0 MPa, a 1:20 solid:liquid ratio (g/mL), at 500 rpm stirring speed. Xylan was chosen as a model compound for hemicelluloses, and two kinds of agricultural wastes-rice straw and palm shell-were used as typical feedstocks representative of herbaceous and woody biomasses, respectively. The hydrolysis reactions for the three kinds of materials followed a first-order sequential kinetic model, and the hydrolysis activation energies were 65.58 kJ/mol for xylan, 68.76 kJ/mol for rice straw, and 95.19 kJ/mol for palm shell. The activation energies of sugar degradation were 147.21 kJ/mol for xylan, 47.08 kJ/mol for rice straw and 79.74 kJ/mol for palm shell. These differences may be due to differences in the composition and construction of the three kinds of materials. In order to reduce the decomposition of sugars, the hydrolysis time of biomasses such as rice straw and palm shell should be strictly controlled.