Gradient-Based Iterative Algorithm for a Coupled Complex Conjugate and Transpose Matrix Equations

Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.

A novel interference suppression scheme applying complex weighted matrix interleaving mapping for UFMC systems

In response to the problem of inter-carrier interference(ICI)and inter-subband interference(IBI)in the received signals of universal filtered multi-carrier(UFMC)systems,a novel interfer-ence suppression design scheme applying the method of complex weighted matrix inter-leaving map-ping(CWMIM)is proposed on the basis of the existing suppression scheme of conjugate weighted butterfly interleaving mapping(CWBIM).The proposed scheme performs matrix interleaving map-ping on the transmitted signal,which not only improves the carrier interference ratio(CIR)of the received signal by combining the original IBI and ICI terms,but also further inhibits the probability of burst error in the received signal.Meanwhile,the scheme can further decrease the impact of phase rotation errors in the received signal by increasing the number of rotation factors.Theoretical analysis and simulation results demonstrate that compared with CWBIM-UFMC,the proposed CWMIM-UFMC can obtain more effective ICI and IBI suppression and better system bit error rate(BER)performance with only a little bit increase in computational complexity.

Norms of Dual Complex Vectors and Dual Complex Matrices

In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.

Binary Image Watermarking Algorithm Using Matrix of Complexity Index

A new watermarking algorithm of binary image is proposed.The complexity index of pixels is presented to reflect the change degree of pixels and to evaluate the modifiable degree of pixels.Firstly, in a small image block, the complexity index of"jumping-change"is calculated in vertical and horizontal direction.Secondly, the matrix of the complexity index is calculated by integrating the complexity index of pixels in two directions.Finally, the matrix of the complexity index is used to embed the watermark in binary images.Experimental results show that the proposed algorithm has a good performance.

Universal peroxidase-like strategy for sensitive glucose detection in complex matrix

Glucose detection in complex matrix such as physiological fluids and drinks can provide useful information guide for people.However,traditional detection methods toward complex matrix suffer from the impurity interference or complex pretreatments.So,it is important to exploit a universal and sensitive glucose detection strategy in complex matrix.In this work,a cascade catalytic scheme based on peroxidase-like MBs@MIL-100(Fe)@Ag(MMA)is developed for sensitive glucose detection in complex solution.Using 3,3’,5,5’-tetramethylbenzidine(TMB)as an indicator,MMA can trigger catalytic cascade reactions for specific glucose sensing.In particular,the peroxidase-like MIL-100(Fe)serves as both the catalysis unit and enrichment unit.Oxidation state of TMB(oxTMB)can be effectively and specifically enriched by MIL-100(Fe)to exclude the interference of undesired impurities and macromolecules,which is suitable for complex sample matrix including colored soda and saliva.In addition,utilizing the peroxidase-like activity of MIL-100(Fe)for self-clean,the residual indicator molecules can be degraded,resulting in the recyclable use of MMA.

Complex matrix interpolation model of the S-transform for electric load movement forecast

Electric load movement forecast is increasingly importance for the industry.This study addresses the load movement forecast modeling based on complex matrix interpolation of the S-transform(ST).In complex matrix of time-frequency representation of the ST,each row follows conjugate symmetric property and each column appears a certain degree of similarity.Based on these characteristics,a complex matrix interpolation method for the time-frequency representation of the ST is proposed to interpolate each row of the complex matrix based on the conjugate symmetric property,and then to perform nearestneighbor interpolation on each column.Then with periodic extension for daily and yearly electric load movement,a forecast model employing the complex matrix interpolation of the ST is introduced.The forecast approach is applied to predict daily load movement of the European Network on Intelligent Technologies(EUNITE)load dataset and annual electric load movement of State Gird Corporation of China and its branches in 2005 and 2006.Result analysis indicates workability and effectiveness of the proposed method.

Super-resolution microscopy reveals the distribution of targeted molecules in the complex matrix

With the support by the National Natural Science Foundation of China and the Chinese Academy of Sciences,the research team led by Prof.Li Junbai(李峻柏)at the CAS Key Lab of Colloid,Interface and Thermodynamics,Institute of Chemistry,Chinese Academy of Sciences,revealed the distribution of proteins in the transformation of inorganic/protein hybrid crystals by super-resolution microscopy,which

Heterogeneous particle structure formation during post-crystallization of spray-dried powder

The formation of heterogeneous particle structure in skim milk powder has been investigated in a post- crystallization facility using experimental and a mathematical model. Various processing conditions were used to produce these heterogeneous structures. The experimental process parameters were used as initial and boundary conditions for the model. The modelled data agreed well with the experimental data. The experimental and modelling results show that the powder processed at high water activity （aw = 0.7） with low initial moisture content （X0 = 0.01 kg/kg） developed a crystalline surface layer while the core of the particle remained amorphous. This structure is referred to as an egg-shell structure. The powder that was processed at low water activity （αw = 0.1） with high initial moisture content （X0 = 0.2 kg/kg） developed a crystalline core while the surface of the particle remained amorphous. This structure is referred to as an egg-yolk structure. Understanding the dependency of particle microstructures on the processing conditions could be useful when developing procedures to control the drying equipment because the particle microstructure affects the physicochemical properties of the powder and potential applications and behaviour of the powder.

Degree dependence entropy descriptor for complex networks

In order to supply better accordance for mod eling and simulation of complex networks, a new degree dependence entropy （DDE） descriptor is proposed to describe the degree dependence relationship and corre sponding characteristic in this paper. First of all, degrees of vertices and the shortest path lengths between all pairs of ,ertices are computed. Then the degree dependence matrices under different shortest path lengths are con structed. At last the DDEs are extracted from the degree dependence matrices. Simulation results show that the DDE descriptor can reflect the complexity of degree dependence relationship in complex networks; high DDE indicates complex degree dependence relationship; low DDE indicates the opposite one. The DDE can be seen as a quantitative statistical characteristic, which is meaningful for networked modeling and simulation.