Characteristic Decomposition Research Articles

Characteristic decomposition of polynomial sets

An ordered pair $(\pset{G},\,~\pset{C})$ is called the characteristic pair of a polynomial ideal if $\pset{G}$ is the reduced lexicographic grobner basis of the ideal and $\pset{C}$ is the minimal triangular set contained in $\pset{G}$. A characteristic pair $(\pset{G},\,~\pset{C})$ is said to be regular or normal if $\pset{C}$ is regular or normal; it is said to be strong if the ideal generated by $\pset{G}$ and the saturated ideal of $\pset{C}$ are the same. A strong regular or normal characteristic decomposition of a polynomial set means a decomposition of the polynomial set into finitely many (strong) regular or normal characteristic pairs with an associated zero or ideal decomposition. This paper presents two algorithms for characteristic decomposition of any given polynomial set, one producing strong normal characteristic pairs with ideal splitting according to pseudo-divisibility relations between polynomials in reduced lexicographic grobner bases and the other producing strong regular characteristic pairs by constructing nontrivial ideals that can be divided out of given ideals by using ideal quotient. Novel theorems are established for regularizing characteristic pairs and strengthening regular and normal characteristic pairs by using ideal saturation. Strong regular or normal characteristic pairs produced by the algorithms possess nice properties and furnish two representations, one in terms of lexicographic grobner bases and the other in terms of triangular sets, for the zeros of the input set of multivariate polynomials. The paper includes a brief review on triangular decompositions of various kinds and discussions about inherent connections among triangular sets, Ritt characteristic sets, and reduced lexicographic grobner bases. Examples and experimental results are also provided to illustrate the method of characteristic decomposition and its applicability and performance.

SF6 Partial Discharge Decomposition Characteristics Under Different Lengths of Wire-Type Metal Particles in Direct Current Gas Insulated Equipment

Aiming at the serious defects of wire-type free metal particles, which can cause severe partial discharge (PD) in Direct current (DC) gas-insulated equipment, the experiments on the influence of four lengths (3.0, 5.0, 7.0, and 9.0 mm) of wire-type free metal materials on SF6 decomposition under DC PD were conducted. The formation rules of four characteristic decomposition components, namely, CF4, SOF2, SO2F2 and SO2, under different lengths of wire-type free metal particles, were determined using gas chromatography. Results showed that the amounts of four kinds of SF6 DC PD characteristic decomposition components are proportional to the length of wire-type free metal particles. The long length of wire-type free metal particles increases the intensity of PD and the amount and effective generation rates of SF6 DC PD characteristic decomposition components. All these findings provide an experimental basis for the diagnosis of insulation defect types in SF6 DC gas insulated equipment.

On a degenerate hyperbolic problem for the 3-D steady full Euler equations with axial-symmetry

AbstractThe transonic channel flow problem is one of the most important problems in mathematical fluid dynamics. The structure of solutions near the sonic curve is a key part of the whole transonic flow problem. This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. By introducing a novel set of dependent and independent variables, we use the idea of characteristic decomposition to transform the axisymmetric Euler equations as a new system which has explicitly singularity-regularity structures. We first establish a local classical solution for the new system in a weighted metric space and then convert the solution in terms of the original variables.

Existence of global bounded smooth solutions for the one‐dimensional nonisentropic Euler system

We study the existence of global bounded smooth solutions to the one‐dimensional (1D) nonisentropic Euler system with large initial data. We derive a group of characteristic decompositions for the 1D nonisentropic Euler system. Using these characteristic decompositions, we find some sufficient conditions on the initial data to obtain the existence of global bounded classical solutions to the Cauchy problem. By the method of characteristic decomposition, we also give a type of large initial data to show the formation of singularity for the 1D nonisentropic Euler system.

Study on ultraviolet absorption characteristics of SF6 decomposition components

Establish the UV spectrum database of the SF6 characteristic decomposition components: Based on the previous research and simulation analysis, obtain the UV spectrum of the SF6 characteristic decomposition components, and establish the corresponding database. Through the analysis of a large number of actual test data, the ultraviolet spectrum database of SO2, CS2 and H2S is obtained and established to realize the quantitative analysis of SO2, CS2 and H2S. The detection accuracy of H2S and the SO2 reaches 10−6 level, and that of the CS2 reaches 10−9 level, realizing the low concentration quantitative detection of SF6 characteristic components. The detection of SO2, CS2 and H2S in gas insulated equipment can effectively predict and diagnose the occurrence of partial discharge fault, partial overheating fault and solid insulation fault in gas insulated equipment. As the symbol gas, the generation of H2S directly indicates the occurrence of more serious partial overheating or partial discharge fault, while SO2 is the characteristic component gas. The occurrence of CS2 indicates that there may be a local fault involving solid insulating medium in the equipment. The detection of three gases can provide important conditions for on-line monitoring of gas insulated equipment.

On the rarefaction waves of the two-dimensional compressible Euler equations for magnetohydrodynamics

The expansion of a wedge of magnetic fluid into vacuum is studied in this paper. The magnetic fluid away from the sharp corner of a wedge expands into the vacuum as two plane-symmetric rarefaction waves, and the problem can be reduced to the interaction of these two rarefaction waves. In order to determine the flow in the interaction zone, we formulate a Goursat problem for the two-dimensional, self-similar Euler equations of magnetohydrodynamic. This system is of mixed type, and the type at each point is determined by the local fluid velocity and the local magneto-acoustic speed. We establish that the system is uniformly hyperbolic in the interaction zone when the half-angle of the wedge is less than some angle [Formula: see text], while the existence of a global classical solution to the Goursat problem is proven by a method of characteristic decomposition.

Mechanical Properties and Thermal Stability of Kaolinite/Emulsion Polymerization Styrene Butadiene Rubber Composite Prepared by Latex Blending Method

This study focused on the preparation method and evaluation of micro-nano composites based on emulsion polymerization styrene butadiene rubber (ESBR) and kaolinite. A novel method – latex blending was utilized to improve the dispersion of kaolinite in matrix and obtain a semi-exfoliation type clay/polymer composite. The results showed that the kaolinite particles presented a semi-exfoliation state and micro-nano scale dispersion in ESBR matrix. The micromorphology of layer-like particles in rubber matrix presented loose and blurry attributed to the interaction between kaolinite plate-like particles and rubber molecules in the latex mixing process, and thus resulted in the reduction of kaolinite crystal order degree. The maximum torque (MH), minimum torque (ML), and ΔM presented a gradually increase tendency with the increase of filler content and the reduction of kaolinite particle size. The mechanical properties of kaolinite/ESBR displayed a significant improvement, and the relative mechanical parameters increased as increasing filler content or reducing kaolinite particle size. The tensile strength and tear strength of the kaolinite/SBR composite reached at 15.1 MPa and 51.3 kN/m, respectively when the filler content at 80 phr. The thermal stability of kaolinite/ESBR composites presented a considerably improvement as decreasing kaolinite particle size or at a reasonable range of filler content. The characteristic decomposition parameters of kaolinite/SBR composite increased compared with those of pure ESBR. The above data indicating that the ESBR chains interacted with kaolinite particles by chemical interaction and the polymer molecules may be intercalated the surface group and interlayer of kaolinite, and thus resulted in the transformation of layer-like microstructure and the restriction on motion of rubber chains in the composite system.

Computing strong regular characteristic pairs with Gröbner bases

The W-characteristic set of a polynomial ideal is the minimal triangular set contained in the reduced lexicographical Gröbner basis of the ideal. A pair (G,C) of polynomial sets is a strong regular characteristic pair if G is a reduced lexicographical Gröbner basis, C is the W-characteristic set of the ideal 〈G〉, the saturated ideal sat(C) of C is equal to 〈G〉, and C is regular. In this paper, we show that for any polynomial ideal I with given generators one can either detect that I is unit, or construct a strong regular characteristic pair (G,C) by computing Gröbner bases such that I⊆sat(C)=〈G〉 and sat(C) divides I, so the ideal I can be split into the saturated ideal sat(C) and the quotient ideal I:sat(C). Based on this strategy of splitting by means of quotient and with Gröbner basis and ideal computations, we devise a simple algorithm to decompose an arbitrary polynomial set F into finitely many strong regular characteristic pairs, from which two representations for the zeros of F are obtained: one in terms of strong regular Gröbner bases and the other in terms of regular triangular sets. We present some properties about strong regular characteristic pairs and characteristic decomposition and illustrate the proposed algorithm and its performance by examples and experimental results.

Eigenvectors of polarization coherency matrices.

Calculation of the eigenvectors of two- and three-dimensional coherency matrices, and the four-dimensional coherency matrix associated with a Mueller matrix, is considered, especially for algebraic cases, in the light of recently published algorithms. The preferred approach is based on a combination of an evaluation of the characteristic polynomial and an adjugate matrix. The diagonal terms of the coherency matrix are given in terms of the characteristic polynomial of reduced matrices as functions of the eigenvalues of the coherency matrix. The analogous polynomial form for the off-diagonal elements of the coherency matrix is also presented. Simple expressions are given for the pure component in the characteristic decomposition.

Adsorption and gas-sensing properties of Pt2–GaNNTs for SF6 decomposition products

Partial electric discharge faults in gas-insulated switchgear (GIS) seriously affect the operational stability of power systems. In this study, H2S, SO2, SO2F2, and SOF2 were selected as characteristic SF6 decomposition products to characterize the partial electric discharge faults in a GIS. Pt cluster-modified gallium nitride nanotubes (Pt2–GaNNTs) were selected as the gas-sensing material to study their adsorption and gas-sensing performance for SF6 decomposition products H2S, SO2, SO2F2, and SOF2. Calculation results showed that Pt2 clusters presented stable doping structures on GaNNTs that greatly enhanced the surface activity for gas adsorption. The adsorption structures, adsorption energy, charge transfer, energy band, density of states, and molecular orbit were analyzed on the basis of density functional theory. Gas molecules formed stable structures on the surfaces of Pt2–GaNNTs through chemical adsorption. The order of adsorption ability was SO2 > H2S > SOF2 > SO2F2, and that of gas-sensing ability was SOF2 > SO2 > H2S > SO2F2. In this article, a new method to detect the partial electric discharge in GIS is proposed. The proposed method helps enhance the running stability of GIS.

Symmetry-preserving WENO-type reconstruction schemes in Lagrangian hydrodynamics

WENO (Weighted essentially non-oscillatory)-type reconstruction schemes are used to work as a limiter that preserves cylindrical symmetry for radial shock flows on an equal-angle polar mesh in Lagrangian hydrodynamics. These WENO-type limiters are tested with a high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method. In order to guarantee the compactness of the underlying DG methods, for strong shock problems, canonical WENO and Hermite WENO reconstructions are used for second-order DG(P1) and third-order DG(P2) respectively, using the known DG solution for the target cell as the central stencil. A salient feature of Hermite WENO lies in taking advantage of available information, namely the derivatives that are evolved with the DG method. With a local orthonormal basis or a local characteristic decomposition, the WENO-type reconstruction schemes can guarantee the cylindrical symmetry for Lagrangian hydrodynamics. A suite of challenging test problems are calculated to demonstrate the accuracy and robustness of these WENO-type schemes.

Feature Detection of Nanofibers Based on Nonlinear Mapping Pattern Recognition

To enhance the feature extraction capacity of nanofibers, a method of feature detection based on nonlinear mapping pattern recognition is proposed. The characteristic distribution model of nanofibers is constructed, and the spectral characteristic decomposition method is used to recognize the nonlinear mapping pattern of nanofibers at current density. The spatial spectrum beam forming processing of nanofiber features is carried out by using cluster–cluster hybrid molecular reconstruction method, and the association rule feature decomposition of nanofibers is carried out by recursive graph analysis method, and the nonlinear mapping pattern recognition of nanofiber features is realized. The classification and recognition of nanofiber features are carried out by combining the correlation attribute clustering method, and the characteristics detection optimization of nanofibers is realized. The proposed method has higher acurracy than other methods. The pattern recognition performance of nonlinear mapping is good, and the ability of accurate recognition of the crystal structure characteristics of nanofibers is better.

Adsorption and Gas Sensing Properties of the Pt3-MoSe2 Monolayer to SOF2 and SO2F2.

SF6 acts as an insulation gas in gas-insulated switchgear (GIS), which inevitably decomposes under partial discharge caused by insulation defects. This work is devoted to finding a new gas-sensing material for detecting two characteristic SF6 decomposition products: SOF2 and SO2F2. The platinum-cluster-modified molybdenum diselenide (Pt3-MoSe2) monolayer has been proposed as a gas sensing material. Based on first-principles calculations, the adsorption properties and the mechanism were studied by analyzing the adsorption structures, adsorption energy, charge transfer, density of states, and molecular orbitals. The adsorption ability of Pt3-MoSe2 to SO2F2 is stronger than that to SOF2 due to its chemisorption property. The obvious change of conductivity of the adsorption system during the gas adsorption process shows that Pt3-MoSe2 is sensitive to both of the gas molecules. In addition, the modest adsorption energy signifies that the gas adsorption process can be reversible, which confirms the feasibility of Pt3-MoSe2-based gas sensors. Our calculation suggests that Pt3-MoSe2-based gas sensors can be employed in GIS for partial discharge detection.

Modal Tracking Based on Group Theory

Issues in modal tracking in the presence of crossings and crossing avoidances between eigenvalue traces are solved via the theory of point groups. The von Neumann-Wigner theorem is used as a key factor in predictively determining mode behavior over arbitrary frequency ranges. The implementation and capabilities of the proposed procedure are demonstrated using characteristic mode decomposition as a motivating example. The procedure is, nevertheless, general and can be applied to an arbitrarily parametrized eigenvalue problems. A treatment of modal degeneracies is included and several examples are presented to illustrate modal tracking improvements and the immediate consequences of improper modal tracking. An approach leveraging a symmetry-adapted basis to accelerate computation is also discussed. A relationship between geometrical and physical symmetries is demonstrated on a practical example.

Non-Search Mathematical Programming Algorithm for Limit Analysis

In order to improve the ability of no-search mathematical programming under limit analysis, and guide big data to optimize classification, a non-search mathematical programming model based on limit analysis model is proposed. The non-search mathematical programming of hyperbolic differential equations in the limit analysis model is analyzed, which provides a mathematical theoretical basis for solving the stability control problem of the system. The hyperbolic differential equation is constructed and the characteristic decomposition of the linear programming model is carried out by using adaptive limit analysis method. The searching delay two-degree-of-freedom control method is used at the load balancing point to adaptively optimize the searching delay parameters of the limit analysis model. In this paper, the hyperbolic differential equations in the limit analysis model are obtained, and the theorems of non-search mathematical programming are given. The mathematical analysis shows that the hyperbolic differential equations in the limit analysis model have the characteristics of non-search mathematical programming. The given theorem of non-search mathematical programming is reliable, and the characteristic solutions of differential equations are stable convergence, which can guide the stability control and improve the control accuracy and reliability. The simulation results show that the algorithm has better convergence and shorter time cost under the limit analysis.

Influence of Pd Clusters Doping on Gas Sensing Properties of TiO₂(101) Nanotubes to SF₆ Decomposition Products

Detection and analysis of sulfur hexafluoride (SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> ) decomposition components is one of the most used methods to realize online monitoring of gas insulated switchgear (GIS) faults. In this paper, Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -doped anatase TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (101) surface was constructed, and studied about its geometric and electronic properties to characteristic SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> decomposition products: SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> based on DFT calculations. Comparing with intrinsic TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (101), the conductivity of Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (101) surface decreases dramatically. Studies on adsorption energy, charge transfer, and adsorption distance show that Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (101) shows strong chemisorption to SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> molecules. Based on density of states and molecular orbital theory analysis, it is found that the adsorption of SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> can dramatically change the conductivity in different degrees. As a result, the Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (101) surface exhibits high gas sensitivity and selectivity to SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> molecules. Our calculations would be meaningful for the development of new sensing materials for SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> decomposition components detection.

NAO Robot Walking Control System Based on Motor Imagery

Brain-computer interface (BCI) technology refers to the spontaneous imagination of a certain mode of movement in the brain to communicate with the computer or control external equipment. This technology helps the limb rehabilitation of paralysed and stroke patients. BCI system will fix electrodes on the experimenter’s brain. This paper designs a brain-computer interface system based on motor imagery, and uses it to control the movement of NAO robot. The system is mainly divided into three modules: signal acquisition, signal processing and robot control. In the aspect of signal acquisition, EEG cap, conductive paste, EEG amplifier and the designed upper computer software system are used to realize the design. Computer storage and processing of data. In signal processing, this paper designs a signal feature method based on Common Spatial Pattern (CSP) and Local Characteristic Scale Decomposition (LCD), and then classifies the features into commands to control NAO robots. In the aspect of communication control, the instruction coding is set in advance, and the classification result is set as the instruction to control the different actions of the robot. Socket communication is carried out by client-server mode using UDP protocol. The experimental results of the study also obtained a high accuracy.

Research on network intrusion detection security based on improved extreme learning algorithms and neural network algorithms

In order to improve the ability of network fuzzy intrusion detection, a network intrusion detection method based on improved extreme learning algorithm and neural network algorithm is proposed to improve the security of the network. ARMA and other linear detection methods are used to construct the network intrusion signal model, and the nonlinear time series and chaos analysis methods are used to extract the feature of network intrusion and big data information analysis. The limit learning method is used for active detection of network intrusion; the adaptive learning method is used for iterative analysis of network intrusion detection, and the correlation characteristic decomposition method is used to improve the convergence of network intrusion detection. The fuzzy neural network algorithm is used to classify the network intrusion features to improve the intrusion detection performance. The simulation results show that this method has high accuracy and strong anti-jamming ability; it has good application value in network security.

Decomposition Characteristics of SF6/N2 Under Partial Discharge of Different Degrees

SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas mixture can not only reduce the consumption of SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> in power system, but also effectively alleviate SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> greenhouse effect. Since SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> can decompose under the alternating current partial discharge(PD), its decomposition characteristics are closely related to PD attributes. Therefore, the fault diagnosis method can be established through its PD decomposition characteristics. However, at present, the decomposition characteristics of SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> mixed gas under PD have not been fully grasped, and the correlation characteristics between decomposition characteristics and PD intensity have not been obtained. To this end, this article uses pin-plate electrodes to simulate the typical metal protrusion insulation defects in GIS equipment. SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> decomposition experiments are conducted at different PD intensity to study the correlation between the PD decomposition characteristics of SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> mixed gas and PD intensity. The results show that: the generation rate of characteristic decomposition components such as SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , NO, NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and NF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> are positively correlated with PD intensity; NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and (SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> +SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> +SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> +SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) can be used as the characteristic quantity to judge the whole process of PD, SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> can be used as the feature to judge the early PD, and SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and SOF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> can be used as the features to judge the severe PD. The results of this article will lay the foundation for the monitoring of equipment insulation status using SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> decomposition characteristics in the future.

Vertebral Tumor Detection and Segmentation Using Analytical Transform Assisted Statistical Characteristic Decomposition Model

Recently, vertebral tumor prediction using image-based vertebral bio-mathematical modeling with accurate segmentation has been considered as a significant area of research. Further, precise lumbar spinal segmentation is essential to the clinicians for tumor analysis. Therefore, precise and reliable segmentation process is required to help radiologists and doctors to identify different vertebrae tumors with better prediction ratio. The exact vertebral disks segmentation of spinal bones from medical images is a complex process in dealing with different deformities and pathologies in accordance to the conventional techniques such as Deep Convolutional Neural Network (DCNN), Finite Element Analysis (FEA), Principal Component and Factor Analysis (PCFA), Multi-Parameter Ensemble Learning (MPEL), Hierarchical Conditional Random Forest (HCRF), and Deep Siamese Neural Network (DSNN). Therefore, to overcome the present drawbacks, Analytical Transform Assisted Statistical Characteristic Decomposition Model (ATS-CDM) is proposed in this paper for the accurate prediction of vertebral tumor detection and segmentation. This technique is used for the calibration of the segmentation procedures in vertebral tumor image prediction and Receiver Operating Curve (ROC) grading for the lumbar spines. The significant objective of the model-fitting algorithm iterates the tumor regions and measures the current region's variance for the accurate identification of tumor. The outcomes show potential and promising results at lab scale evaluation through analyzing the vertebral datasets with Intra-Discal Pressure (IDP) images for experimental validation with 98.7% bending and 98.88 % segmentation accuracy leads to 94.2 ± 0.2 % to 97.02 ± 0.2 % average ROCgrading.