Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM

Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.

Multivariate Approach to Characterizing Soil Quality of Gabonese’s Ferralitic Soils

Assessing soil quality is essential for crop management and soil temporal changes. The present study aims to evaluate soil quality in the Ferralitic soils context countrywide. This assessment was done using multivariate soil quality indice (SQI) models, such as additive quality index (AQI), weighted quality indexes (WQIadd and WQIcom) and Nemoro quality index (NQI), applied to two approaches of indicator selection: total data set (TDS) and minimum data set (MDS). Physical and chemical soil indicators were extracted from the ORSTOM’s reports resulting from a sampling campaign in different provinces of Gabon. The TDS approach shows soil quality status according to eleven soil indicators extracted from the analysis of 1,059 samples from arable soil layer (0 - 30 cm depth). The results indicated that 87% of all provinces presented a very low soil quality (Q5) whatever the model. Among soil indicators, exchangeable K+ and Mg2+, bulk density and C/N ratio were retained in MDS, using principal component analysis (PCA). In the MDS approach, 50 to 63% of provinces had low soil quality grades with AQI, WQIadd and NQI, whereas the total was observed with WQIcom. Only 25% of provinces had medium soil quality grades with AQI and NQI models, while 12.5% (NQI) and 25% (AQI) presented high quality grades. Robust statistical analyses confirmed the accuracy and validation (0.80 r P ≤ 0.016) of AQI, WQIadd and NQI into the TDS and MDS approaches. The same sensitivity index value (1.53) was obtained with AQI and WQIadd. However, WQIadd was chosen as the best SQI model, according to its high linear regression value (R2 = 0.82) between TDS and MDS. This study has important implications in decision-making on monitoring, evaluation and sustainable management of Gabonese soils in a pedoclimatic context unfavorable to plant growth.

Assessment and Prediction of Thermodynamic Functions of Compounds in Sialon System

According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sialon materials possible.

Research on Effective Access for Strengthening and Improving the Management and Benefit use of Large Instruments

The purchasement and development as well as the benefit of utilization for the large equipment in universities of China are analyzed in this paper, the paper in dicates that in utilization of large equipment the contradictions such as urgency and necessity for the purchasement and development of large equipment and serious waste in resources since inadequacy of annual utilization rate of large equipment are existed, it also raises that the key step of giving full play to the benefit of large equipment is to strengthen management and development after the equipment are purchased, the paper regards through stressing standardized management and maintenance、opening the laboratory、improving the functions of equipment、renovating technology、fully examining and scientifically deciding before purchasement, the investment benefit for the large equipment can be raised effectively.

Low-temperature Heat Capacity and Standard Thermodynamic Functions of D-Galactose and Galactitol

The heat capacities of D-galactose and galactitol were measured on a quantum design physical property measurement system（PPMS） over a temperature range of 1.9-300 K, and the experimental data were fitted to a function of T using a series of theoretical and empirical models in appropriate temperature ranges. The fit results were used to calculate thermodynamic function values, C^θp,m, ^T0S0^θm , and △^T0H^θm from 0 K to 300 K. The standard molar heat capacity, entropy and enthalpy values of D-galactose and galactitol at 298.15 K and 0.1 MPa were determined to be C^θp,m=（227.96±2.28） and（239.50±2.40） J·K^-1·mol^-1, S0^θm = （211.22±2.11） and （230.82±2.30） J·K^-1·mol^-1 and μm = （33.95±0.34） and （36.57±0.37） kJ/mol, respectively.

MATHEMATICAL ANALYSIS OF AN IMPROVED HEPATITIS B VIRUS MODEL

A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-free and infection equilibria is discussed, respectively. Further, the existence of an orbitally asymptotically stable periodic orbit is also studied. By means of the theory of competitive systems and compound matrices, sufficient conditions are derived for the global stability of the infection-free and infection equilibria, respectively. At last, numerical simulations are carried out to illustrate the main results.