Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis

We present recent work of harmonic and signal analysis based on the complex Hardy space approach.

Species distribution of polymeric aluminium ferrum——timed complexation colorimetric analysis method of Al-Fe-Ferron

The effects of the calorimetric buffer solutions were investigated while the two colorimetric reactions of AI-ferron complex and Fe-ferron complex occurred individually, and the effects of the testing wavelength and the pH of the solutions were also investigated. A timed complexatian colorimetric analysis method of Al-Fe-ferron in view of the total concentration of {AI + Fe} was then established to determine the species distribution of polymeric Al-Fe. The testing wavelength was recommended at 362 net and the testing pH value was 5. With a comparison of the ratios of n(Al)/n(Fe), the standard adsorption curves of the polymeric Al-Fe solutions were derived from the experimental results. Furthermore, the solutions' composition were carious in both the molar n(Al)/n(Fe) ratios, i.e. 0/0, 5/5, 9/1 and 0/10, and the concentrations associated with the total ( Al + Fe which ranged from 10(-5) to 10(-4) mol/L..

The Space and Time Features of Global SST Anomalies Studied by Complex Principal Component Analysis

In this paper, the variability characteristics of the global field of sea surface temperature (SST) anomaly are studied by complex principal component (c.p.c.) analysis, whose results are also compared with those of real p.c. analysis. The data consist of 40 years of global SST monthly averages over latitudes from 42 5°S to 67 5°N. In the spatial domain, it is found that the distribution of the first complex loading amplitude is characterized by three areas of large values: the first one in the eastern and central equatorial Pacific Ocean, the second one in the northern tropical Indian Ocean and South China Sea, the third one in the northern Pacific Ocean. As it will be explained, this pattern may be considered as representative of El Nio mode. The first complex loading phase pattern shows a stationary wave in the Pacific (also revealed by real p.c. analysis) superimposed to an oscillating disturbance, propagating from the Pacific to Indian or the opposite way. A subsequent correlation analysis among different spatial points allows revealing disturbances actually propagating westward from the Pacific to the Indian Ocean, which could therefore represent reflected Rossby waves, i.e. the west phase of the signals that propagate disturbances of thermal structure in the tropical Pacific Ocean. In the time domain, a relation between the trend of the first complex principal component and the ENSO cycle is also established.

Complex Seismic Focus Structure and Earthquake-Triggered Landslide Distribution:Analysis of the 2014 Ludian M_w6.1 Earthquake in Yunnan

Objective The 2014 Ludian Mw6.1 earthquake in Yunnan occurred in a mountainous area with complex tectonics and topography, which caused serious damage as well as co-seismic landslides of an unusual large scale. Because the suspected seismogenic faults on the surface, distribution of aftershocks and focal mechanism solutions are not consistent, it remains difficult to determine what is the real causal fault or seismogenic structure for this event. Actually, it may imply the complicity of the seismic source at depth. In addition, the distribution of the co- seismic landslides also exhibits some diffusion that is different from general eases, likely associated with the seismic focus structure.

A ca. 2.2Ga Acidic Magmatic Event at the Northern Margin of the Yangtze Craton: Evidence from U-Pb Dating and Hf Isotope Analysis of Zircons from the Kongling Complex

Objective The Yangtze craton collisional orogeny at ca. extensional events at ca. 1 experienced Paleoproterozoic 1.95-2.0 Ga and post-orogenic 85 Ga related to amalgamation of the Columbia （Nuna） supercontinent （Zhao and Cawood, 2012）. A ca. 2.15 Ga suprasubduction zone ophiolitic melange was recongized in the Archean- Paleoproterozoic Kongling Complex of the northern Yangtze craton （Han et al., 2017）. However, the tectonic evolution in early Paleoproterozoic from 2.4 Ga to 2.2 Ga remains unclear. We report here the presence of a suite of Paleoproterozoic （2.2 Ga） granites in the Huangling dome, northern Yangtze craton, which may provide important insights into crustal growth processes in the craton prior to the assembly of Columbia.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Arrhythmia Detection by Using Chaos Theory with Machine Learning Algorithms

Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.

Optimizing Connections:Applied Shortest Path Algorithms for MANETs

This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to delve into and refine the application of the Dijkstra’s algorithm in this context,a method conventionally esteemed for its efficiency in static networks.Thus,this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm,considering adaptation to the dynamic network conditions that are typical for MANETs.This paper has shown through detailed algorithmic analysis that Dijkstra’s algorithm,when adapted for dynamic updates,yields a very workable solution to the problem of real-time routing in MANETs.The results indicate that with these changes,Dijkstra’s algorithm performs much better computationally and 30%better in routing optimization than Bellman-Ford when working with configurations of sparse networks.The theoretical framework adapted,with the adaptation of the Dijkstra’s algorithm for dynamically changing network topologies,is novel in this work and quite different from any traditional application.The adaptation should offer more efficient routing and less computational overhead,most apt in the limited resource environment of MANETs.Thus,from these findings,one may derive a conclusion that the proposed version of Dijkstra’s algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods.This paper,therefore,operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness.

Core acupoints of acupuncture for hyperplasia of mammary gland: a network analysis

Backgroud:Clinical studies on acupuncture treatment of hyperplasia of mammary gland(HMG)have proved its effectiveness,but most studies have paid little attention to acupoints prescription and acupoint compatibility.The clinical prescription is not identical,the curative effect also has the difference.Therefore,through data mining and network analysis,this study explored the core acupoints and the compatibility law of acupoints in acupuncture treatment of HMG.Methods:To search and select qualified literature according to inclusion and exclusion criteria for relevant clinical research literature on acupuncture treatment of HMG in CNKI,VIP database,WanFang database and PubMed,etc.Then extract relevant information and establish a database.Using the method of statistical and complex network analysis,this paper studies the core acupoints and the law of acupoint compatibility.Results:A total of 104 Chinese literatures and 0 English literatures were included and 106 acupuncture prescriptions were extracted.The core acupoints in the treatment of HMG are Danzhong(CV 17),Wuyi(ST 15),Zusanli(ST 36),Jianjing(GB 21).Danzhong(CV 17)and Zusanli(ST 36),Danzhong(CV 17)and Wuyi(ST 15),Jianjing(GB 21)and Tianzong(SI 11),Jianjing(GB 21)and Wuyi(ST 15)have the highest correlation degree.The method of acupoint matching mainly consists of local-remote acupoints,upper-lower acupoints and front-rear acupoints.Conclusion:The results of a network analysis substantially accord with the general rules of acupuncture theories in traditional Chinese medicine,able to reflect the points-selection principles and features in acupuncture treatment of HMG and provide evidence for the acupoints selection in the treatment of HMG in acupuncture clinic.

COMPLEX NUMBER MODE APPROACH FOR REDUCING VIBRATION OF STRUCTURAL FLEXIBLE REDUNDANT ROBOT MANIPULATORS

A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify the modal exciting force of flexural motion, and the approach can be freely used when the degree of freedom of flexural motion is much greater than the available degree of reundancy. The availability and effectiveness of the proposed approach are demonstrated through numerical simulation with a four link spatial robotic manipulator possessing an end flexible link.

SPECTROSCOPIC STUDY AND APPLICATION ON THE INCLUSION COMPLEXATION β-CYCLODEXTRIN WITH ESTRADIOL BENZOATE IN AQUEOUS SOLUTION

The inclusion complexation reaction of β-cyclodextrin with estradiol benzoate (EB) in the presence ofcetyltrimethylammonium bromide has been studied by means of UV absorption and fluorescent spectrometry. The reaction conditions, the formation constant, the mechanism of the host-guest inclusion complexhave been studied and a simple, highly sensitive fluorescent synergistic method for the determination of EBhas been established with satisfactory results.

Evolution of IPv6 Internet topology with unusual sudden changes

The evolution of Internet topology is not always smooth but sometimes with unusual sudden changes. Consequently, identifying patterns of unusual topology evolution is critical for Internet topology modeling and simulation. We analyze IPv6 Internet topology evolution in IP-level graph to demonstrate how it changes in uncommon ways to restructure the Internet. After evaluating the changes of average degree, average path length, and some other metrics over time, we find that in the case of a large-scale growing the Internet becomes more robust; whereas in a top–bottom connection enhancement the Internet maintains its efficiency with links largely decreased.

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

Complexity Analysis and Algorithm Design of Pooling Problem

The pooling problem,also called the blending problem,is fundamental in production planning of petroleum.It can be formulated as an optimization problem similar with the minimum-cost flow problem.However,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general case.They also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of qualities.In this paper,we prove that the pooling problem is still strongly NP-hard even with only one quality.This means the quality is an essential difference between minimum-cost flow problem and the pooling problem.For solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming method.Global convergence of the algorithm is established.The numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local minimizer.Our results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

Dynamic Response of Truss Adaptive Structures

It is pointed out that the damping matrix deduced by active members in the finite element vibration equation of a truss adaptive structure generally can not be decoupled, which leads to the difficulty in the process of modal analysis by classical superposition method. This paper focuses on the computational method of the dynamic response for truss adaptive structures. Firstly, a new technique of state vector approach is applied to study the dynamic response of truss adaptive structures. It can make the coeffic lent matrix of first derivative of state vector a symmetric positive definite matrix, and particularly a diagonal matrix provided that mass matrix is derived by lumped method, so the coefficient matrix of the first derivative of state vector can be exactly decomposed by CHOLESKY method. In this case, the proposed technique not only improves the calculation accuracy, but also saves the computing time. Based on the procedure mentioned above, the mathematical formulation for the system response of truss adaptive structures is systematically derived in theory. Thirdly, by using FORTRAN language, a program system for computing dynamic response of truss adaptive structures is developed. Fourthly, a typical 18 bar space truss adaptive structure has been chosen as test numerical examples to show the feasibility and effectiveness of the proposed method. Finally, some good suggestions, such as how to choose complex mode shapes practically in determining the dynamic response are also given. The new approach can be extended to calculate the dynamic response of general adaptive structures.

Vibration of axially moving beam supported by viscoelastic foundation

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton＇s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

Synthesis, Crystal Structure and Spectroscopic Properties of Zn(Ⅱ) with N-carbamylglutamate Ligand

ZnC6HsN2O5H2O （NCGZn） has been synthesized, and its functional groups present in the title compound were confirmed by elemental analysis, TG and IR spectral studies. Meanwhile, the crystal of NCGZn was obtained by slow evaporation of a saturated aqueous solution at room temperature and confirmed by single-crystal X-ray diffraction analysis. It crystallizes in triclinic, space group P21 with a = 5.03220（1）, b = 13.3747（4）, c = 12.9944（4） A, β = 92.987（2）°, V= 873.39（4） A3, Z = 2, CI2H20NaOI2Zn2, Mr = 543.10, Dc = 2.065 g/cm3, F（000） = 552,μ（MoKa） = 2.826 mm-1, R = 0,0422 and wR = 0.1142. In NCGZn, Zn（l） and the symmetry formed Zn（l） ions are connected by five atoms from four NCG.2H anions and a water molecule. A NCG ligand has two carboxylate groups, one connecting a Zn ion, and the other bridgiong two Zn ions. The NCG ligand bridges four Zn ions through the amino group and two carboxylate groups with a water molecule to yield a 3D coordination polymer structure with hydrogen bonds.

Progress of Studies on Traditional Chinese Medicine Based on Complex Network Analysis

Traditional Chinese medicine(TCM) is a distinct medical system that deals with the life-health-disease-environment relationship using holistic, dynamic, and dialectical thinking. However, reductionism has often restricted the conventional studies on TCM, and these studies did not investigate the central concepts of TCM theory about the multiple relationships among life, health, disease, and environment. Complex network analysis describes a wide variety of complex systems in the real world, and it has the potential to bridge the gap between TCM and modern science owing to the holism of TCM theory. This article summarizes the current research involving TCM network analysis and highlights the computational tools and analysis methods involved in this research. Finally, to inspire a new approach, the article discussed the potential problems underlying the application of TCM network analysis.

Synthesis, Crystal Structure and Spectroscopic Properties of Zn(II) with N-carbamylglutamate Ligand

ZnC6HsN2O5·H20 （NCGZn） has been synthesized, and its functional groups present in the title compound were confirmed by elemental analysis, TG and IR spectral studies. Meanwhile, the crystal of NCGZn was obtained by slow evaporation of a saturated aqueous solution at room temperature and confirmed by single-crystal X-ray diffraction analysis. It crystallizes in triclinic, space group P21 with α= 5.03220（1）, b = 13.3747（4）, c = 12.9944（4） A,β= 92.987（2）°, V= 873.39（4） A^3, Z = 2, C12H20N4O12Zn2, Mr = 543.10, Dc = 2.065 g/cm^3, F（000） = 552,μ（MoKα） = 2.826 mm^-1, R = 0.0422 and wR = 0.1142. In NCGZn, Znl and the symmetry formed Znl ions are connected by five atoms from four NCG-2H anions and a water molecule. A NCG ligand has two carboxylate groups, one connecting a Zn ion, and the other bridgiong two Zn ions. The NCG ligand bridges four Zn ions through the amino group and two carboxylate groups with a water molecule to yield a 3D coordination polymer structure with hydrogen bonds.

Design and analysis of superlens based on complex two-dimensional square lattice photonic crystal

We theoretically demonstrate the imaging properties of a complex two-dimensional(2D) face-centered square lattice photonic crystal(PC) made from germanium cylinders in air background. The finitedifference time-domain(FDTD) method is employed to calculate the band structure and simulate image construction. The band diagram of the complex structure is significantly compressed. Negative refraction occurs in the second energy band with negative phase velocity at a frequency of 0.228(2πc/a), which is lower than results from previous studies. Lower negative refraction frequency leads to higher image resolution. Numerical results show that the spatial resolution of the system reaches 0.7296λ, which is lower than the incident wavelength.