Orthogonalization Process Research Articles

Universal Behavior of the Corners of Orbital Beta Processes

Abstract There is a unique unitarily-invariant ensemble of $N\times N$ Hermitian matrices with a fixed set of real eigenvalues $a_1> \dots > a_N$. The joint eigenvalue distribution of the $(N-1)$ top-left principal submatrices of a random matrix from this ensemble is called the orbital unitary process. There are analogous matrix ensembles of symmetric and quaternionic Hermitian matrices that lead to the orbital orthogonal and symplectic processes, respectively. By extrapolation, on the dimension of the base field, of the explicit density formulas, we define the orbital beta processes. We prove the universal behavior of the virtual eigenvalues of the smallest $m$ principal submatrices, when $m$ is independent of $N$ and the eigenvalues $a_1> \dots > a_N$ grow linearly in $N$ and in such a way that the rescaled empirical measures converge weakly. The limiting object is the Gaussian beta corners process. As a byproduct of our approach, we prove a theorem on the asymptotics of multivariate Bessel functions.

Mechanics of Grains Size and Orientation on the Machining of AISI S-7 Steel Grade Using Numerical Technique

Two-dimensional models namely homogeneous, uniformly distributed grains and non-uniformly distributed grains were developed for AISI S-7 steel grade metal, to investigate the effect of the grains size and orientation on the chip morphology and temperature rise during the orthogonal machining process. A Johnson-Cook model was used for the simulation study. The machining was done at a medium speed of 60 ms-1 and the depth of cut was maintained at 5 mm in all the above cases. Compared to other models, results showed that nonuniformly distributed grains develop alternate low and high shear bands and generate maximum temperature in the high shear band zone, which was found to be detrimental during the machining process compared to other models. Intergranular chip segmentation was observed in the case of uniformly distributed grains. For the same material, three different chip morphologies and temperature profiles were observed during the orthogonal machining process. Detailed discussion on the mechanics of machining of the above-said models was done that may be advantageous for material and tool design scientist.

Clutter and distortion products suppression methods for code division multiple access systems

This study summarises effort to design and optimise clutter and distortion products suppression method for multi-static primary surveillance radar (MSPSR) system working with code division multiple access. Proposed methods have been designed based on clutter suppression algorithm used in frequency division multiple access systems with an emphasis on computational complexity. Further research has been focused on suppression and also other distortion products in a received signal, those are mostly caused by the phase noise of transmitters and receiver. Finally, the optimal setting of designed methods has been investigated, which is mainly focused on orthogonalisation process of base matrices and time frame length for clutter suppression. Performance of proposed algorithms is compared on both simulated and real signal from the MSPSR system and also for numerical precision single versus double.

Metabolic Diversity in Human Non-Small Cell Lung Cancer Cells.

Intermediary metabolism in cancer cells is regulated by diverse cell-autonomous processes, including signal transduction and gene expression patterns, arising from specific oncogenotypes and cell lineages. Although it is well established that metabolic reprogramming is a hallmark of cancer, we lack a full view of the diversity of metabolic programs in cancer cells and an unbiased assessment of the associations between metabolic pathway preferences and other cell-autonomous processes. Here, we quantified metabolic features, mostly from the 13C enrichment of molecules from central carbon metabolism, in over 80 non-small cell lung cancer (NSCLC) cell lines cultured under identical conditions. Because these cell lines were extensively annotated for oncogenotype, gene expression, protein expression, and therapeutic sensitivity, the resulting database enables the user to uncover new relationships between metabolism and these orthogonal processes.

Evaluation of Distortion and Residual Stresses in Dissimilar Metal Laser Welds

The distortion and residual stresses in laser weld joints play an important role in performing the intended functions. The objective of this research work is to evaluate distortion and residual stresses induced in dissimilar metal butt weld joints. The 304 L stainless steel and mild steel sheets of 0.98 mm thick are used in automobile industries. The laser welding experiments are conducted on dissimilar metals as per the L9 orthogonal array design matrix and optimal process parameters obtained using Artificial Neural Network. A mathematical model is proposed to estimate the angular distortion and longitudinal residual stresses in dissimilar weld joints. The longitudinal, transverse and twisting type distortions are evaluated using the Coordinate Measuring Machine, whereas residual stresses using an X-ray Diffractometer. The standard correction techniques are applied for background error correction and peak position was obtained using the Gaussian curve fitting technique. The outcome of the research work is useful for the evaluation of distortion and residual stress in dissimilar metal weld joints.

Numerical method and convergence order for second-order impulsive differential equations

This paper is devoted to the numerical scheme for the impulsive differential equations. The main idea of this method is, for the first time, to establish a broken reproducing kernel space that can be used in pulse models. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and have the second-order convergence. The algorithm is proved to be feasible and effective through some numerical examples.

Microstructural evolution and mechanical property of nanoparticles reinforced Al matrix composites during accumulative orthogonal extrusion process

In this work, microstructures of nanoparticles reinforced Al matrix composites after each accumulative orthogonal extrusion process (AOEP) pass, were characterized by scanning electron microscopy, electron backscatter diffraction and neutron diffraction techniques. The results showed that the nanoparticle clusters were completely invisible and the initial fibrous grain morphology in the Al matrix was replaced by ribbon-like and equiaxed ones after 2 passes. No change of the grain structure after 3 passes is related to the occurrences of grain boundary sliding and the saturation of particles stimulated nucleation effect. In addition, the strong β-fiber textures in the hot extruded composites (AOEP 1P) have been broken down after 2 passes of AOEP, leading to a lower texture fraction in the composites. As a result, a good combination of strength and ductility is achieved in the AOEPed composites. The mechanical anisotropy of composites is also diminished, attributed to the uniform particle distribution, homogeneous grain structures and low texture fractions.

Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay

In this paper, Reproducing Kernel Hilbert Space Method (RKHSM) based on collocation scheme is used to solve singularly perturbed second order differential-difference equations. We implement RKHSM without Gram–Schmidt orthogonalization process for singularly perturbed differential-difference equation with boundary layer behavior and also oscillatory behavior with small delay. RKHSM in this study, is based on the division of the problem domain into two subintervals, one with boundary layer and the other one without such a boundary layer. Several numerical examples are studied to demonstrate the accuracy of the present method. Results of the present scheme indicate that new algorithm has the following advantages: small computational work, fast convergence, and high precision.

Preparation of Naphthalene Dianhydride Bithiophene Copolymers by Direct Arylation Polycondensation and the Latent Pigment Approach.

An alternating naphthalene dianhydride bithiophene copolymer (PNDAT2) is prepared by a combined direct arylation polycondensation and the latent pigment approach. PNDAT2 is the first reported example of an alternating conjugated polymer containing naphthalene dianhydride, the oxo-analogue of naphthalene diimide often used in electron-acceptor conjugated polymers. PNDAT2 is resistant to organic solvents and can be generated directly as film by thermal treatment of the soluble tetraester precursor PNTET2. PNDAT2 is characterized by a LUMO level of -3.9 eV, similar to that of established naphthalene diimide containing soluble copolymers. This route to insoluble electron acceptor copolymers by thermal cleavage of soluble precursors is an alternative to classical cross-linking or orthogonal processing strategies.

A nonlinear analytical formula for forced vibration analysis of the hard-coating cylindrical shell based on the strain energy density principle

In this paper, a nonlinear analytical formulation of the forced vibration of the hard-coating cylindrical shell is developed to investigate the nonlinear resonant characteristics of the shell. The strain dependence of hard coating and the elastic constraint with continuous variable stiffness are considered in the formulation. In order to fully introduce the effects of the strain dependence of hard coating on the resonant characteristics with base excitation, a novel analytical method is presented to determine the equivalent strain of hard coating according to the principle of equal strain energy density. The nonlinear governing equations of motion and the admissible displacement function are derived based on the Love's first approximation theory and the Gram-Schmidt orthogonalization process. A unified Newton-Raphson iterative solution method is employed to solve the nonlinear resonant frequency and response of the shell. As an example to demonstrate the feasibility of the developed analytical model, the forced vibration of the cylindrical shell coated with NiCoCrAlY + YSZ hard coating is implemented numerically and experimentally. Moreover, the influences of the storage modulus, loss modulus and thickness of hard coating on the forced vibration characteristics of the hard-coating cylindrical shell are analyzed in detail.

Vibration and Buckling of Skew Plates Under Linearly Varying Edge Compression

Pre-buckling vibration and buckling behaviour of composite skew plates subjected to linearly varying in-plane edge loading with different boundary conditions are studied. The total energy functional of the skew plate mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram-Schmidt orthogonalization process. Using Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total energy functional is converted into sets of algebraic equations for static stability problems and ordinary differential equation for free vibration problem. Pre-buckling vibration frequencies of the stressed skew plate are obtained by solving associated linear eigen value problem for free vibration and solution of the eigen value problem for static case results critical buckling load. From different parametric study, it is observed that the pre-buckling vibration frequency and critical buckling load increase with the increase of skew angle and edge restraint.

Lagrange Operational Matrix Methods to Lane–Emden, Riccati’s and Bessel’s Equations

The current study is presented to develop two approaches and methodologies to find the numerical solution of linear and non-linear initial value problems such as Lane–Emden type equation, Riccati’s equation and Bessel’s equation of order zero based on approximation. The function approximations (scheme-I and scheme-II) are presented to find the numerical solutions of linear and non-linear initial value problems by using Gauss Legendre roots as node points and random node points in the domain [0, 1]. In the scheme-I, the roots of Legendre polynomial are used as node points for Lagrange polynomials and in scheme-II, we have taken random node points in the domain [0, 1] and orthogonalize the resulting Lagrange polynomials using Gram–Schmidt orthogonalization process. Firstly, we have introduced the function approximations by using generating interpolating scaling functions (ISF) and orthonormal Lagrangian basis functions (OLBF) over the space \(L^{2}[0,1]\) then we have constructed the operational matrices of integration and product operational matrices based on newly designed approximations namely ISF and OLBF. These operational matrices convert given linear and non-linear initial value problems into the associated system of algebraic equations. Finally, we have established error bounds (Lemmas 1, 2) of both scheme-I and scheme-II including the function approximations. The efficiency of the proposed schemes has been confirmed with several test examples including numerical stability. So, the schemes are simple, efficient and produces very accurate numerical results in considerably small number of basis functions and hence reduces computational effort.

An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non‐Gaussian randomness

SummaryStochastic analysis of structure with non‐Gaussian material property and loading in the framework of polynomial chaos (PC) is considered. A new approach for the solution of stochastic mechanics problem with random coefficient is presented. The major focus of the method is to consider reduced size of expansion in an iterative manner to overcome the problem of large system matrix in conventional PC expansion. The iterative method is based on orthogonal expansion of stochastic responses and generation of an iterative PC based on the responses of the previous iteration. The polynomials are evaluated using Gram‐Schmidt orthogonalization process. The numbers of random variables in PC expansion are reduced by considering only the dominant components of the response characteristics, which is evaluated using Karhunen‐Loève (KL) expansion. In case of random material field problem, the KL expansion is used to discretize and simulate the non‐Gaussian random field. Independent component analysis (ICA) is carried out on the non‐Gaussian KL random variables to minimize statistical dependence. The usefulness of the proposed method in terms of accuracy and computational efficiency is examined. From the numerical analysis of three different types of structural mechanics problems, the proposed iterative method is observed to be computationally more efficient and accurate than conventional PC method for solution of linear elastostatic structural mechanics problems.

Image processing for GEO object with 3D rotation based on ground-based InISAL with orthogonal baselines.

While imaging geosynchronously orbiting objects with ground-based inverse synthetic aperture LADAR (ISAL), target rotation and vibration will introduce phase errors into the echo and cause the two-dimensional imaging result to be defocused. To solve this problem, one layout of the ISAL receiving channels is designed, combining the orthogonal short baselines in the inner field with the orthogonal long baselines in the external field. On this basis, an imaging method based on orthogonal interferometry processing is proposed. The proposed method estimates and compensates for the phase errors introduced by the rotation and vibration of the target such that the focus of the two-dimensional image is improved, and three-dimensional imaging results with high accuracy are obtained. The effectiveness of the proposed method is verified by simulation data.

On Number Rigidity for Pfaffian Point Processes

Our first result states that the orthogonal and symplectic Bessel processes are rigid in the sense of Ghosh and Peres. Our argument in the Bessel case proceeds by an estimate of the variance of additive statistics in the spirit of Ghosh and Peres. Second, a sufficient condition for number rigidity of stationary Pfaffian processes, relying on the Kolmogorov criterion for interpolation of stationary processes and applicable, in particular, to pfaffian sine-processes, is given in terms of the asymptotics of the spectral measure for additive statistics.

A Hybrid Multi-Objective Optimization Model for Vibration Tendency Prediction of Hydropower Generators.

The hydropower generator unit (HGU) is a vital piece of equipment for frequency and peaking modulation in the power grid. Its vibration signal contains a wealth of information and status characteristics. Therefore, it is important to predict the vibration tendency of HGUs using collected real-time data, and achieve predictive maintenance as well. In previous studies, most prediction methods have only focused on enhancing the stability or accuracy. However, it is insufficient to consider only one criterion (stability or accuracy) in vibration tendency prediction. In this paper, an intelligence vibration tendency prediction method is proposed to simultaneously achieve strong stability and high accuracy, where vibration signal preprocessing, feature selection and prediction methods are integrated in a multi-objective optimization framework. Firstly, raw sensor signals are decomposed into several modes by empirical wavelet transform (EWT). Subsequently, the refactored modes can be obtained by the sample entropy-based reconstruction strategy. Then, important input features are selected using the Gram-Schmidt orthogonal (GSO) process. Later, the refactored modes are predicted through kernel extreme learning machine (KELM). Finally, the parameters of GSO and KELM are synchronously optimized by the multi-objective salp swarm algorithm. A case study and analysis of the mixed-flow HGU data in China was conducted, and the results show that the proposed model performs better in terms of predicting stability and accuracy.

An iterative polynomial chaos approach for solution of structural mechanics problem with Gaussian material property

A new approach for solution of Stochastic structural Mechanics problem with random coefficient in the framework of Polynomial Chaos (PC) expansion is proposed. The basic strategy of the proposed method is to iteratively construct a PC expansion with reduced numbers of unknown coefficients. The method is based on orthogonal expansion of stochastic responses and generation of an iterative PC based on the responses of the previous iteration. The polynomials are evaluated using Gram-Schmidt orthogonalization process. The number of random variables in PC expansion is reduced by considering only the dominant components of the response characteristics, which is evaluated using Karhunen-Loève (KL) expansion. In case of random material field problem, KL expansion is used to discretize the random field. The usefulness of the proposed method in terms of accuracy and computational efficiency is examined. The results of linear static structural mechanics problems are compared with MCS and PC method. The proposed method is observed to be computationally more efficient and accurate than PC method.

Double Emitting Layer Based Solution Processed WOLEDs Simultaneously with High Power Efficiency and Good Color Stability

AbstractA double emitting layer (EML) device configuration is successfully demonstrated for power‐efficient and color‐stable white organic light‐emitting diodes (WOLEDs) that are fabricated via orthogonal solvent processing. In this case, a self‐host blue dendrimer B‐G2 is independently used as the bottom EML due to its excellent nondoped device performance and perfect alcohol resistance, and an alcohol‐soluble yellow phosphor Ir(Flpy‐CF3‐EG)3 functionalized with 2‐(2‐methoxyethoxy)ethyl group is newly developed as the upper EML combined with the arylphosphine oxide‐containing electron transporting materials. Unlike single EML based white devices, the unwanted charge trap from long‐wavelength phosphors can be easily and effectively prevented by tuning the energy level alignment in the upper EML, leading to a nearly unchanged white electroluminance with a negligible Commission Internationalede l'Eclairage (CIE) variation of ΔCIE (0.008, 0.005) in a luminance range from 2.2 to 1015 cd m−2. Meanwhile, a promising power efficiency of 51.5 lm W−1 is realized, which can be further optimized to 104.5 lm W−1 at maximum and 62.0 lm W−1 at 1000 cd m−2 after the addition of an out‐coupling half‐sphere. The simultaneous achievement of high power efficiency and good color stability clearly indicates the great potential of double EML in solution processed WOLEDs.

Comprehensive stellar seismic analysis

Aims.We develop a method that provides a comprehensive analysis of the oscillation spectra of solar-like pulsators. We define new seismic indicators that should be as uncorrelated and as precise as possible and should hold detailed information about stellar interiors. This is essential to improve the quality of the results obtained from asteroseismology as it will provide better stellar models which in turn can be used to refine inferences made in exoplanetology and galactic archaeology.Methods.The presented method – WhoSGlAd – relies on Gram-Schmidt’s orthogonalisation process. A Euclidean vector sub-space of functions is defined and the oscillation frequencies are projected over an orthonormal basis in a specific order. This allowed us to obtain independent coefficients that we combined to define independent seismic indicators.Results.The developed method has been shown to be stable and to converge efficiently for solar-like pulsators. Thus, detailed and precise inferences can be obtained on the mass, the age, the chemical composition and the undershooting in the interior of the studied stars. However, attention has to be paid when studying the helium glitch as there seems to be a degeneracy between the influence of the helium abundance and that of the heavy elements on the glitch amplitude. As an example, we analyse the 16CygA (HD 186408) oscillation spectrum to provide an illustration of the capabilities of the method.

Microstructure and mechanical properties of hot pressed Ti3SiC2/Al2O3

In this work, Ti3SiC2/Al2O3 composites with various volume contents of Ti3SiC2 were fabricated under different orthogonal processes by vacuum hot pressing sintering. optimized comprehensive mechanical properties and relative density (＞97%) were obtained (the microhardness, flexural strength and fracture toughness reached the values of 16.25 GPa, 536.31 MPa and 9.3 MPa m1/2, respectively.) when the Al2O3 (60.0 vol %) and Ti3SiC2 (40.0 vol %) were sintered at 1500 °C for 0.5 h at 30 MPa, which basically correspond to the best level of after orthogonal calculation. The orientational growth behavior of Ti3SiC2 was further confirmed by EBSD, and temperature was found to play a prominent role in the growth of Ti3SiC2 to some extents, fewer columnar Ti3SiC2 grains were observed at lower temperature and weak decomposition of Ti3SiC2 was observed at 1500 °C. Meanwhile, high volume Ti3SiC2 was beneficial to the improvement of mechanical properties for the intrinsical layered structure.