In the current era of ‘big data’, scientists are able to quickly amass enormous amount of data in a limited number of experiments. The investigators then try to hypothesize about the root cause based on the observed trends for the predictors and the response variable. This involves identifying the discriminatory predictors that are most responsible for explaining variation in the response variable. In the current work, we investigated three related multivariate techniques: Principal Component Regression (PCR), Partial Least Squares or Projections to Latent Structures (PLS), and Orthogonal Partial Least Squares (OPLS). To perform a comparative analysis, we used a publicly available dataset for Parkinson’ disease patien ts. We first performed the analysis using a cross-validated number of principal components for the aforementioned techniques. Our results demonstrated that PLS and OPLS were better suited than PCR for identifying the discriminatory predictors. Since the X data did not exhibit a strong correlation, we also performed Multiple Linear Regression (MLR) on the dataset. A comparison of the top five discriminatory predictors identified by the four techniques showed a substantial overlap between the results obtained by PLS, OPLS, and MLR, and the three techniques exhibited a significant divergence from the variables identified by PCR. A further investigation of the data revealed that PCR could be used to identify the discriminatory variables successfully if the number of principal components in the regression model were increased. In summary, we recommend using PLS or OPLS for hypothesis generation and systemizing the selection process for principal components when using PCR.rewordexplain later why MLR can be used on a dataset with no correlation

This paper presents a finite element analysis of the bi-directional orthogonal model, which incorporates individual crack strain separation and tracking. The objective of the research is to expand the current shear friction model to manage bi-directional cracking at any angle, allowing for a more universal model that can be applied to intricate structures and non-proportional loading cases. The proposed model was initially developed as a total strain-based model, with the assumption that crack strains are equivalent to total strains, but was subsequently recalculated to improve accuracy by separating crack strains from total strains. Furthermore, a separate crack strain formulation was created to account for strains in the concrete's uncracked portions and locked-in crack strains. The article then discusses the testing of various convergence methods and loading programs to achieve high convergence. Comparative analyses of the generalized shear friction model with other models for crack orientation and loading cases similar to those of a reinforced concrete membrane are also presented. The MATLAB program successfully applied the bi-directional cracking model for one finite element under a uniform cyclical strain state, using a secant stiffness formulation.

This article aims to carry out experiments on water absorption by husked red rice, at constant temperatures of 28, 40 and 50 °C. The description of the absorption kinetics, as well as the analyses of water distribution and volumetric expansion of each grain, at a given instant, was done using a diffusion model. In order for the model to be as close as possible to the real physical situation, the mesh necessary to numerically solve the diffusion equation was generated from the photograph of a grain. Thus, the diffusion equation was written in Boundary-Fitted Coordinates (BFC). The solution of the diffusion equation written in generalized coordinates was then discretized in space and time, using the Finite Volume method, with a fully implicit formulation, considering variable volume and also variable mass diffusivity as a function of local moisture content. Optimizations based on Levenberg-Marquardt algorithm make it possible to determine the parameters of an exponential function relating mass diffusivity and the local moisture content for each temperature. Statistical indicators (chi-square, determination coefficient and Student’s t-test) allowed concluding that the model proposed was very satisfactory for all temperatures, making it possible to simulate water absorption, water distribution and volumetric expansion of the grain over time.

Data integration has been proven to provide valuable information. The information extracted using data integration in the form of multiblock analysis can pinpoint both common and unique trends in the different blocks. When working with small multiblock datasets the number of possible integration methods is drastically reduced. To investigate the application of multiblock analysis in cases where one has few number of samples, we studied a small metabolomic multiblock dataset containing six blocks (i.e. tissue types), only including common metabolites. We used a single model multiblock analysis method called Joint and unique multiblock analysis (JUMBA) and compare it to a commonly used method, concatenated PCA. These methods were used to detect trends in the dataset and identify underlying factors responsible for metabolic variations. Using JUMBA, we were able to interpret the extracted components and link them to relevant biological properties. JUMBA shows how the observations are related to one another, the stability of these relationships and to what extent each of the blocks contribute to the components. These results indicate that multiblock methods can be useful even with a small number of samples.

A self-propelled electric tea seed-planter is designed to address the lack of tea seed seeding equipment, low seeding efficiency, and poor seeding uniformity. Based on the physical characteristics of the tea seeds and the agronomic requirements of tea planting, the key structure of the planter is designed, and the structural parameters are determined. The motor and battery configurations are determined by calculating the power consumption of the entire machine. In a field experiment, the driving gear (A), ditching depth (B), and planting gear position (C) are used as test factors, and the acceptance index (AI), replay index (RI) and leakage index (LI) are used as test indexes. The test results showed that the driving speed and planting gear position significantly affect the acceptance index, replay, and leakage index, whereas the ditching depth has little effect on the performance indexes. When the driving speed was medium, ditching depth was 30 mm, and planting gear position was in the third gear, the corresponding acceptance index was 87.22%, the replay index was 8.89%, and the leakage index was 3.89%. The test prototype has a good working quality and can provide theoretical guidance for production practices.

The orthogonal matrix with cube be symmetric is a common class of matrices with important properties. We pay attention to this kind of matrices. By using the close relationship between the eigenvalues of a matrix and the trace of its power, we obtain the algorithm for its all possible different eigenvalues and multiplicities. The calculation formula is expressed only by the trace of a matrix and its power, avoiding solving the characteristic polynomial. The method is simple and practical. Furthermore, a new essential characterization for the sum of orthogonal matrix pairs being orthogonal is given as well.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Kronecker products of matrices have some striking operation properties, one of which is called the mixed-product property $(A \!\otimes\! B)(C \!\otimes\! D) = AC \!\otimes\! BD$. In view of this property, the two-term Kronecker product $A_1 \otimes A_2$ can be rewritten as $A_1 \otimes A_2 = (A_1 \otimes I_{m_2})(I_{m_1} \otimes A_2)$ of dilation forms of $A_1$ and $A_2$, and three-term Kronecker product $A_1 \otimes A_2 \otimes A_3$ can be rewritten as the products $A_1 \otimes A_2 \otimes A_3 = (A_1\otimes I_{m_2} \otimes I_{m_3})(I_{m_1} \otimes A_2 \otimes I_{m_3})(I_{m_1} \otimes I_{m_2} \otimes A_3)$ of the dilation forms of $A_1$, $A_2$, and $A_3$, respectively, where the matrices on the right-hand sides of the two factorizations are commutative. In this note, we approach the commutative Kronecker products on the right-hand sides of the two factorization equalities, and present a variety of new and useful analytical formulas for calculating the ranks, dimensions, orthogonal projectors, and ranges of matrices composed of these Kronecker products.

Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.

In view of increasing concerns over non-renewable resource depletion and waste management, this study aimed to apply the Taguchi optimization technique to determine the process conditions for producing bricks by incorporating thin film transition liquid crystal displays (TFT-LCD) waste glass powder with reservoir sediments. An orthogonal array L₁₆(4⁵) was adopted, which consisted of five controllable four-level factors (i.e., cullet content, drying method, preheat time, sintering temperature, and error). Moreover, the analysis of variance method was used to explore the effects of the experimental factors on the density, water absorption, shrinkage ratio, loss of ignition, porosity, and compressive strength of the fired bricks. The microstructures of the fired specimens were investigated by scanning electron microscopy. Then, the large-scale production techniques for fired bricks containing recycled TFT-LCD glass cullet and reservoir sediments was developed in a commercially available tunnel kiln. The test results showed that the structure of fired specimen was loose at a sintering temperature ranged from 900–950 °C. However, the fired specimen showed a significant densification at the sintering temperature of 1050 °C. In addition, Taguchi method is a feasible approach for optimizing process condition of brick using recycled TFT-LCD glass cullet and reservoir sediments and it significantly reduces the number of tests. On the other hand, the characteristics of fired bricks developed in the tunnel kiln were in compliance with Chinese National Standards class Ι building bricks criteria.

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

Limonene is a valuable monoterpenoid that with diverse applications. Microbial biosynthesis offers a sustainable alternative to plant-based extraction, which is prone to hinderance by climate change and acreage. In the present study, the effects on limonene production of carbon source, inoculum, working volume, temperature, pH, dodecane coverage, and media were investigated with engineered strains of Rhodosporidium toruloides. Through single-factor and orthogonal experiments, the limonene titer was improved from 52.2 to 358.1 mg/L on 250-mL flask, a 586% increase. The optimized medium was MM, with a working volume of 50 mL, inoculum OD600=0.6, 22 °C, pH 6, and dodecane coverage (v/v) of 20%. The results here demonstrated that the R. toruloides could be explored as an efficient limonene producer and facilitate other monoterpenoids biosynthesis with R. toruloides.

We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

The aim of this paper is to establish a valid procedure for better understanding all the phenomena associated with the high-speed machining of Glass Fibre Reinforced Plastic (GFRP) composites. Both rectangular and circular specimens were machined at high speeds (up to 50 m/min) in order to understand what occurred for all values of fiber orientation angles during machining operations. An innovative testing methodology was proposed and studied to investigate the phenomenon of burr formation and thus understand how to avoid it during machining operations. To this end, the forces arising during the machining process and the roughness of the resulting surface, were carefully studied and correlated with the cutting angle. Additionally, the cutting surface and chip morphology formed during cutting tests were examined using a high-speed camera. Close correlations are found between the variations of the cutting forces' signals and the trends of the roughness and the morphology of the machined surface.

Smart materials represent an elegant class of (macro)-molecules endowed with the ability to react to chemical/physical changes in the environment. Herein, we prepared new photo responsive azobenzenes possessing halogen bond donor groups. The X-ray structures of two molecules highlight supramolecular organizations governed by unusual noncovalent bonds. In azo dye I-azo-NO2, the nitro group is engaged in orthogonal H···O···I halogen and hydrogen bonding, linking the units in parallel undulating chains. As far as compound I-azo-NH-MMA is concerned, a non-centrosymmetric pattern is formed due to a very rare I···π interaction involving the alkene group supplemented by hydrogen bonds. The Cambridge Structural Database contains only four structures showing the same I···CH₂=C contact. For all compounds, an ¹⁹F NMR spectroscopic analysis confirms the formation of halogen bonds in solution through a recognition process with chloride anion, and the reversible photo-responsiveness is demonstrated upon exposing a solution to UV light irradiation. Finally, the intermediate I-azo-NH2 also shows a pronounced color change due to pH variation. These azobenzenes are thereby attractive building blocks to design future multi-stimuli responsive materials for highly functional devices.

Short-circuit blowing is an important technical means to ensure the rapid surfacing of submersible. In order to study the impact of seven multiple manipulation factors of three levels on blowing, a proportional short-circuit blowing model test bench had been built and L18(37) orthogonal experiments were carried out; then, using Back propagation neural network and Pearson correlation analysis, the experimental data were trained and predicted, correlation between individual factor and blowing was further studied as supplement of orthogonal experiments. It had been proved that both multi-factor combination and individual including blowing duration, sea tank back pressure, the gas blowing pressure of the cylinder group, and sea valve flowing area had larger influence, whose correlation coefficients were 0.6535, 0.8105, 0.5569, 0.5373, of which the F-ratio of blowing duration is over critical value 3.24. And statistical evaluation indicators of Back propagation neural network were between 10e-2 and 10e-13, relative error was less than 3%, and prediction error accuracy was 100%. Based on the results above, a reasonable prediction method for submersible short-circuit blowing had been formed and suggestions on engineering design and operations were proposed, including advantage of short-circuit blowing method, initial condition settings and manipulation strategy.

This paper presents an explicit method for constructing tangential and anisotropic bases in quadratic spaces. We will also provide three theorems that allow us to explicitly calculate vectors that are orthogonal or tangent to given vectors or that provide necessary and sufficient conditions for the existence of such vectors. A classical theorem on quadratic space states that every finite-dimensional quadratic space has an orthogonal basis. A result that seems to be unanswered is under what conditions a finite-dimensional quadratic space has a basis consisting of isotropic vectors. A second problem is whether or not every finite-dimensional quadratic space has a basis consisting of mutually tangent vectors, where two vectors v,w are tangent if (u·v)2=(u·u)(v·v). In this paper, we attack these two problems.

This article is devoted to overcoming the contradiction between the problem of maximizing the extraction of wind energy as the goal of optimizing wind turbines, and the use of traditional methods based on criteria for the aerodynamic quality of the blades. A modified technique is considered in which the optimization criterion is the directly extracted flow power. It is based on pulse theory methods that use specific power as an optimization criterion. A comparative analysis of the energy efficiency of different types of turbines is carried out, and the effects of blade inversion are considered. A method for calculating multi-rotor turbines based on the concept of uniform power distribution is presented. The compatibility of proprietary and traditional methods is considered by comparing the results of numerical experiments with calculated and experimental data from sources. Optimization computational algorithms generate data from numerical experiments and determine optimal parameter configurations for the turbines under consideration. It is shown that orthogonal Darrieus turbines in high-speed mode provide energy efficiency comparable to collinear turbines, and multi-rotor turbines with power uniformly distributed over the working section are not inferior in energy efficiency to basic turbines, with linear blade velocities halved.

The valley pseudospin properties of electrons in two–dimensional hexagonal materials result in lots of fascinating physical phenomena, which opens up the new field of valleytronics. The valley-contrasting physics aims at distinguishing the valley degree of freedom based on valley–dependent effects. Here, we theoretically demonstrate that both of the valley–selective high harmonic generation and valley–selective electronic excitation can be achieved by using an orthogonal two–color (OTC) laser field in gapped graphene. It is shown that the asymmetry degrees of harmonic yields in the plateaus, cutoff energies of generated harmonics and electron populations from two different valleys can be precisely controlled by the relative phase of the OTC laser field. Thus the selectivity of the dominant valley for the harmonic radiation and electronic polarization can be switched by adjusting the relative phase of the OTC laser field. Our work offers an all–optical route to produce the valley–resolved high harmonic emissions and manipulate the ultrafast valley polarization on a femtosecond timescale in condensed matter.

The study of mechanical properties of rock mass can be effectively carried out through rock-like material model test. The similarity of mechanical properties between rock-like material and protolith is dependent on the appropriate selection of composition and content of rock-like materials. In this research, X-Ray diffraction test was conducted to analyze the composition of deep rock, which confirmed silica, quartz, and dolomite as the primary components of deep sandstone. An orthogonal design test was used to execute the ratio test of rock-like material. River sand was used as an aggregate, cement as a binder, gypsum powder as a regulator, and polystyrene foam (EPS) as rock damage simulation material. The influencing factors considered in the orthogonal mechanical tests were the proportion of aggregate and binder, ratio of binder and regulator, quantity of damage simulation material, and size of damage simulation material. Three levels were set for each factor, and mechanical parameters such as compressive strength, tensile strength, elastic modulus, axial strain, and Poisson's ratio were tested for each group of samples. The changes of those parameters with the levels of the above four factors were studied. The study revealed that adjusting the size of polystyrene foam (EPS) can adjust the values of elastic modulus, tensile strength, and Poisson's ratio of rock-like material. Similarly, changing the ratio of binder and regulator can adjust the values of axial strain and compressive strength of rock-like material. The rock-like material developed in the study can simulate the mechanical properties of different rock masses such as granite, sandstone, shale, and limestone.

The increasing amount of data transmitted through digital broadcasting and communication channels requires efficient transmission methods that make the most of limited resources such as frequency, time, and power. The layered division multiplexing (LDM) system, which is adopted by the Advanced Television Systems Committee (ATSC) 3.0 standard, is considered one of a solution for achieving efficient transmission. Additionally, the layered time-division multiplexing (LTDM) and time layered division multiplexing (TLDM) systems have been developed as well. These layered transmission systems, utilizing multiple physical layer pipes (PLPs), offer a wide range of services including mobile and rooftop TV. To compare the efficiencies of different layered transmission systems, the article introduces the concept of normalized channel capacity. This measure allows for a fair comparison among the systems by taking into account the specific channel capacity requirements of each service. By summing the normalized channel capacities, a method is proposed to select the most efficient transmission system among the four systems: LDM, LTDM, TLDM, and time division multiplexing (TDM). The Lagrange multiplier method is employed to find the parameters that maximize the sum of the normalized channel capacities in these systems. Through simulations conducted with the determined parameters, it is demonstrated that the LDM system exhibits the highest efficiency among the four systems.

The security of several full homomorphic encryption (FHE) schemes depends on the hardness of the approximate common divisor (ACD) problem. The analysis of attack and defense against the system is one of the frontiers of cryptography research. In this paper, the performance of existing algorithms, including orthogonal lattice, simultaneous diophantine approximation, multivariate polynomial and sample pre-processing are reviewed and analyzed for solving the ACD problem. Orthogonal lattice (OL) algorithms are divided into two categories (OL-$\land$ and OL-$\vee$) for the first time. And an improved algorithm of OL-$\vee$ is presented to solve the GACD problem. This new algorithm works well in polynomial time if the parameter satisfies certain conditions. Compared with Ding and Tao's OL algorithm, the lattice reduction algorithm is used only once, and when the error vector $\mathbf{r}$ is recovered in Ding et al.'s OL algorithm, the possible difference between the restored and the true value of $p$ is given. It is helpful to expand the scope of OL attacks.

Non-orthogonal multiple access (NOMA) has been investigated to support massive connectivity for Internet-of-things (IoT) networks. However, since most IoT devices suffer from limited power and decoding capabilities, it is not desirable to pair a large number of devices simultaneously, which encourages two-user NOMA grouping. Additionally, most existing techniques have not considered the diversity in the target QoS of IoT devices, which may lead to spectrum inefficiency. Few investigations have partially considered that issue by using an order-based power allocation (OPA) approach, where the power is allocated according to the order to the user's target throughput within a priority-based NOMA (PNOMA) group. However, this does not fully capture the effects of diversity in the values of the users' target throughputs. In this work, we handle both problems by considering a throughput-based power allocation (TPA) approach, that captures the QoS diversity, within a three-users PNOMA group as a compromise between spectral efficiency and complexity. Specifically, we investigate the performance of a time-division PNOMA (TD-PNOMA) scheme, where the transmission time is divided into two-time slots with two-users per PNOMA group. The performance of such TD-PNOMA is compared with a fully PNOMA (F-PNOMA) scheme, where the three users share the whole transmission time, in terms of the ergodic capacity under imperfect successive interference cancellation (SIC). The results reveal the superiority of TPA compared with OPA approach in both schemes, besides that the throughput of both schemes can outperform each other under imperfect SIC based on the transmit signal-to-noise ratio and the deployment scenarios.

This note shows that the well-known reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$ for the Moore--Penrose inverse of matrix product is equivalent to many other equalities for that are composed of multiple products $(AB)^{\dag}$ and $B^{\dag}A^{\dag}$ by means of the definition of the Moore--Penrose inverse and orthogonal projector theory.

Large scale coherent structures in atmospheric boundary layer (ABL) are known to contribute to the power generation in wind farms. In the current paper, we perform a detailed analysis of the large scale structures in a finite sized wind turbine canopy using modal analysis from three dimensional proper orthogonal decomposition (POD). While POD analysis sheds light on the large scale coherent modes and scaling laws of the eigenspectra, we also observe a slow convergence of the spectral trends with the available number of snapshots. Since the finite sized array is periodic in the spanwise direction, we propose to adapt a novel approach of performing POD analysis of the spanwise/lateral Fourier transformed velocity snapshots instead of the snapshots themselves. This methodology not only helps in decoupling the length scales in the spanwise and the streamwise direction when studying the energetic coherent modes, but also provides a detailed guidance towards understanding the convergence of the eigenspectra. In particular, the Fourier-POD eigenspectra helps us illustrate if the dominant scaling laws observed in 3D POD are actually contributed by the laterally wider or thinner structures and provide more detailed insight on the structures themselves. We use the database from our previous large eddy simulation (LES) studies on finite-sized wind farms which uses wall-modeled LES for modeling the Atmospheric boundary layer laws, and actuator lines for the turbine blades. Understanding the behaviour of such structures would not only help better assess reduced order models (ROM) for forecasting the flow and power generation but would also play a vital role in improving the decision making abilities in wind farm optimization algorithms in future. Additionally, this study also provides guidance for better understanding the POD analysis in the turbulence and wind farm community.

Red mud (RM), a bauxite residue, contains hazardous radioactive wastes and alkaline material and poses severe surface water and groundwater contamination risks, necessitating recycling. Pretreated RM can be used to make adsorbents for water treatment. However, its performance is affected by many factors, resulting in a nonlinear correlation and coupling relationship. This study aimed to identify the best formula for an RM adsorbent using a mathematical model that examines the relationship between 11 formulation types (e.g., pore-assisting agent, component modifier, and external binder) and nine properties (e.g., specific surface area, wetting angle, and Zeta potential, among others). This model was built using a back-propagation neural networks(BP) based on single-factor experimental data and orthogonal test data. The model trained and predicted the established network structure to obtain the optimal adsorbent formula. The RM particle adsorbents had a pH of 10.16, specific surface area(BET) of 48.92 m2·g−1, pore volume of 2.10 cm3·g−1, compressive strength(ST)) of 1.12 KPa, and 24-h immersion pulverization rate(η_m) of 3.72%. In the removal of total phosphorus in flotation tailings backwater, it exhibited a good adsorption capacity (Q)and total phosphorous removal rate(η) of 48.63 mg·g−1 and 95.13%, respectively.

The security of several fully homomorphic encryption (FHE) schemes depends on the intractability assumption of the approximate common divisor (ACD) problem over integers. Subsequent efforts on solving the ACD problem as well as its variants were also developed during the past decade. In this paper, an improved orthogonal lattice (OL) based algorithm, AIOL, is proposed to solve the general approximate common divisor (GACD) problem. The conditions for ensuring the feasibility of AIOL are also presented. Compared to the Ding-Tao’s OL algorithm, the well-know LLL reduction is used only once in AIOL, and when the error vector r is recovered in AIOL, the possible difference between the restored and the true value of p is given. The experimental comparisons towards the Ding-Tao’s algorithm and ours are also provided for validating our improvements.

We use a recently proposed formulation of quantum mechanics based, not on potential functions but rather, on orthogonal energy polynomials. In this context, the most important building block of a quantum mechanical system, which is the wavefunction at a given energy, is expressed as pointwise convergent series of square integrable functions in configuration space. The expansion coefficients of the series are orthogonal polynomials in the energy; they contain all physical information about the system. No reference is made at all to the usual potential function. We consider, in this new formulation, few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. The objective is to demonstrate the viability of this formulation of quantum mechanics and its power in generating rich energy spectra illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures.

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

Digital-Radio-Frequency-Memory (DRFM) has emerged as an advanced technique to achieve diverse jamming signals, due to its capability of intercepting waveforms within a short time. Multiple-Input Multiple-Output (MIMO) radars can transmit agile orthogonal waveform sets for different pulses to combat the DRFM-based jamming, where any two groups of waveform sets are also orthogonal. In order to design multiple groups of orthogonal waveform sets at the same time, this article formulates a group orthogonal waveforms optimal design model, whose objec-tive function is the weighted sum of the intra- and inter-group orthogonal performances metrics. To solve this optimization problem, this article proposes a group orthogonal waveforms design algorithm. Based on a primal-dual type method and proper relaxations, the proposed algorithm transforms the original problem into a series of simple sub-problems. Numerical results demonstrate that the proposed algorithm has the ability to balance the intra- and inter-group orthogonal performances by adjusting the weighting factors, which is not available using other state-of-the-art orthogonal waveform design algorithms.

In response to the structural optimization problem of PCB stator coreless disc motors, the orthogonal response surface method was used to optimize the motor structure, determine the basic parameters of the motor preliminarily, and conduct orthogonal experiments on the motor parameters based on the optimization design objectives, The optimization factors were the quantity of magnetic pole of the motor rotor, the ratio of main/auxiliary pole size, the thicknessof the permanent magnet, and the air gap length.The motor torque，the amplitude of magnetic density of the air gap and waveform distortion rateare used as optimization objectives. The motor parameters that make the motor torque reach the maximum, the air gap magnetic density maximum, and the waveform distortion rate minimum. Due to the use of PCB plates instead of motor stator cores in PCB coreless disc motors,The service life of the PCB board during motor operation will be reduced with the temperature rise generated by the stator winding To solve this problem, the response surface analysis of the motor is carried out to reduce the temperature rise of the stator windings during the operation of the motor. PCB board and stator winding are the main factors affecting the temperature rise of the motor.Taking the thickness of the PCB board, the hole diameter on the board, and the uneven width of the stator winding as optimization factors, the motor parameters with the lowest temperature rise of the motor winding are obtained. Simulation analysis is conducted using Ansys/Maxwell software, and the results prove the feasibility of optimization.

In order to solve the interference of narrowband in the ultra-wideband (UWB) system, a high isolation of multiple-input multiple-output (MIMO) antenna is investigated in this paper. The MIMO antenna consists of 2 or 4 UWB elements; and each UWB antenna element is a monopole reconstructed with 2-notched slots, a U-shaped and inverted U-shaped slots etched on the monopole patch to achieve notch characteristics in WIMAX and ITU bands. The property of a 2-element MIMO antenna is analyzed firstly, which is put into a same substrate in parallel. Two rectangular branches are located in the middle to reduce the coupling. Then a 4-element MIMO antenna is studied to meet big size space and more application scenarios. Each element is placed orthogonally on the same substrate; and the isolation is implemented by a cross-shaped branch located in the middle of elements. Both MIMO antenna samples have been tested to verify the design. Measured results show that the working bandwidth is 2.45-14.88 GHz and 2.14-14.95 GHz, the isolation is greater than 17 dB and 20 dB, the peak gain is 5.7 dB and 5.9 dB, the max-imum radiation efficiency can reach 96% and 95%, the envelope correlation coefficient is less than 0.02 and 0.05 for the 2- and 4-element UWB MIMO antenna, respectively. They both are with very good omnidirectional characteristic with notched bands such as the WIMAX and ITU, and meet the requirements of the UWB application in most cases.

We consider the second order differential equation y'' + ω^(2)ρ(x)y = 0 where ω is a positive parameter. The principal concern here is to find conditions on the function ρ^(−1/2)(x), which ensure that the consecutive differences of sequences constructed from the zeros of a nontrivial solution of the equation are regular in sign for ω sufficiently large. In particular, if c_(νk)(α) denotes the k-th positive zero of the general Bessel (cylinder) function C_(ν)(x; α) = J_(ν)(x) cos α−Y_(ν)(x) sin α of order ν, and if |ν| < 1/2, we prove that (−1)^(m)∆^(m+2)c_(νk)(α) > 0 (m = 0, 1, 2, ...; k = 1, 2, ...), where ∆a_(k) = a_(k+1) − a_(k). This type of inequalities was conjectured by Lorch and Szego in 1963. We also show that the differences of the zeros of various orthogonal polynomials with higher degrees possess the sign-regularity.

Deep neural networks (DNNs), founded on the brain's neuronal organization, can extract higher-level features from raw input. However, complex intellect via autonomous decision-making is way beyond current AI design. Here we propose an autonomous AI inspired by the thermodynamic cycle of sensory perception, operating between two information density reservoirs. Stimulus unbalances the high entropy resting state and triggers a thermodynamic cycle. By recovering the initial conditions, self-regulation generates a response while accumulating an orthogonal, holographic potential. The resulting high-density manifold is a stable memory and experience field, which increases future freedom of action via intelligent decision-making.

Based on the satellite attitude control method, this paper proposes an attitude control method based on neural network disturbance compensation. The paper firstly analyzes the neural network algorithm and proposes an orthogonal least squares algorithm to implement network learning. In this paper, a set of high-precision directional neural network compensation controllers is designed for the attitude control of acupuncture small satellites. The feasibility of the improved orthogonal least-squared algorithm combined with the neural network supplementary control method in satellite attitude control is verified by experiments.

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For the Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0 and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for the Geronimus transformations.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

Floods and droughts are driven, in part, by spatial patterns of extreme rainfall. Heat waves are driven by spatial patterns of extreme temperature. It is therefore of interest to design statistical methodologies that allow the identification of likely patterns of extreme rain or temperature from observed historical data. The standard work-horse for identifying patterns of climate variability in historical data is Principal Component Analysis (PCA) and its variants. But PCA optimizes for variance not spatial extremes, and so there is no particular reason why the first PCA spatial pattern should identify, or even approximate, the types of patterns that may drive these phenomena, even if the linear assumptions underlying PCA are correct. We present an alternative pattern identification algorithm that makes the same linear assumptions as PCA, but which can be used to explicitly optimize for spatial extremes. We call the method Directional Component Analysis (DCA), since it involves introducing a preferred direction, or metric, such as `sum of all points in the spatial field'. We compare the first PCA and DCA spatial patterns for US rainfall anomalies on a 6 month timescale, using the sum metric for the definition of DCA in order to focus on total rainfall anomaly over the domain, and find that they are somewhat different. The definitions of PCA and DCA result in the first PCA spatial pattern having the larger explained variance of the two patterns, while the first DCA spatial pattern, when scaled appropriately, has a higher likelihood and greater total rainfall anomaly, and indeed is the pattern with the highest total rainfall anomaly for any given likelihood. In combination these two patterns yield more insight into rainfall variability and extremes than either pattern on its own.

The demand for improved service in mobile networks is always increasing. That means signal transmission with higher capacity is required. To achieve that goal a combined optical and wireless link using double polarization multiplexing has been developed. A high quality signal transmission is achieved by applying high polarization extinction ratio. The new concept is validated by experiments varying the bit rate and fiber length. A signal with 12 Gbit/s bit rate was transmitted over a 25 km long combined link with about 1.10-8 bit error rate. That result is much better than the already published data which were measured on links transmitting information with 2.5 Gbit/s bit rate. The polarization multiplexing technique is very practical for capacity enhancement in a specific section of an existing optical fiber by inserting a new link into it without deploying a new fiber.

This research delves into the impact of complex low-speed wake flow structures on the aerodynamic characteristics of objects downstream. It employs the proper orthogonal decomposition (POD) method and the domain precursor simulation method to compare traditional methods and validate this approach. The study generates several flow structures of parallel dual-cylinder wakes with different scales and spacing. The variations in the aerodynamic coefficient of three downstream objects at various times passing through wakes of varying scales are appropriately compared and analyzed. The study establishes that the wake with a cylinder spacing of G=1.5 has a more compact and concentrated modal structure than that with a cylinder spacing of G=0.35. Smaller objects are more responsive to the wake flow structure with a spacing of G=1.5, whereas larger objects respond more to the flow structure with a spacing of G=0.35. The achieved results also reveal that the aerodynamic force coefficients of objects passing through the wakefield at different times are closely related to the temporal characteristics of the wake flow structure with different scales.

Abstract: Interrupted-sampling repeater jamming (ISRJ) is a kind of intra-pulse coherent decep-tion jamming that can generate false target peaks in the range profile and interfere with the de-tection and tracking of real targets. In this paper, an anti-ISRJ method based on the intra-pulse orthogonal waveform is proposed, which can recognize common interference signals by com-paring sub-signal matched filtering results. For some special scenes where real targets cannot be directly differentiated from false targets, a new recognition method based on the energy discon-tinuity of the interference signal in the time domain is proposed in this paper. The method pro-posed in this paper can recognize real and false targets in all ISRJ modes without any prior in-formation, such as jammer parameters, with a small amount of calculation, which is suitable for actual radar systems. Simulation experiments using different interference parameters show that although this method has a 3dB loss of pulse compression gain, it can completely suppress dif-ferent kinds of ISRJ interference when the SNR before pulse compression is higher than -20dB, with 100 % target detection probability.

Millimeter wave wide-band imaging is widely studied for a variety of applications. However real-time millimeter wave wide-band imaging at frequencies above 30GHz for moving targets in a large field of view has not been realized commercially. A 2D sparse array with transmitter multiplexing is a promising solution to this problem. In this article, a method combining compressed sensing and orthogonal coded multiplexing was proposed, and the imaging performance was analyzed for different reconstruction algorithms and observation matrices by imaging simulation for a continuous object. Also the influence on the dynamic range of the original signal introduced by orthogonal coded multiplexing was studied. This work demonstrated that the proposed method was effective in reconstructing the image with a real-time capability. It is shown that different algorithms and matrices resulted in distinct performances, while the evaluation parameter selection also played a role. This work provided useful instructions for both the hardware and software design of a real-time 3D millimeter wave imaging system in the future.

This paper is concerned with representing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials which involve the hypergeometric functions ${}_1 F_1$ and ${}_2 F_1$.

We used light, electron microscope and teased fiber autoradiography to show that myelinating Schwann cells synthesize phospholipids and proteins in perinuclear cytoplasm and superficial cytoplasmic channels or Cajal bands (SCC/CB). Neither phospholipid nor protein syntheses occur in paranodal loops, Schmidt-Lanterman incisures or adaxonal cytoplasm. Autoradiographic studies also show that in support of local protein synthesis, RNAs move from the nucleus into perinuclear cytoplasm and out along SCC/CB. Unlike other phospholipids, phosphatidylinositol synthesis occurs extensively in axons. This finding indicates differences in the distributions of phospholipid synthesizing enzymes in smooth endoplasmic reticulum of Schwann cell processes and axoplasm.Autoradiographs of nerves at longer survival times show that tritiated phosphatidylcholine and fucose-labeled glycoproteins move from synthetic sites to outermost myelin lamellae. From there, phosphatidylcholine spreads inward reaching innermost lamellae of thicker sheaths in days. Coupled with retention of fucose glycoproteins in outer myelin lamellae is the presence of fucose glycoprotein synthesized during early myelination in inner lamellae of thicker sheaths, a result consistent with growth of myelin sheaths from inner lamellae out. In this review, we revisit these studies because they provide temporal and spatial perspectives needed in understanding dynamic aspects of myelinogenesis and how myelinating cells respond to injury and from altered gene expression.

Channel estimation is an important module to enhance the performance of orthogonal frequency division multiplexing (OFDM) systems. However, the presence of a large amount of noise in multipath fading time-varying channels significantly affects the channel estimation accuracy and thus the recovery quality of the received signals. Therefore, this paper proposes a double-threshold (DT) channel estimation method based on adaptive frame statistics (AFS). The method first adaptively determines the number of statistical frames based on the temporal correlation of the received signals, and preliminarily detects the channel structure by analyzing the distribution characteristics of multipath sampling points and noise sampling points during adjacent frames. Subsequently, a multi-frame averaging technique is used to expand the distinction between multipath and noise sampling points. Finally, the DT is designed to better recover the channel based on the preliminary detection results. Simulation results show that the proposed adaptive frame statistics-double-threshold (AFS-DT) channel estimation method is effective and has better performance compared with many existing channel estimation methods.

In order to solve the interference of narrowband communication system to ultra-wideband (UWB) system and meet the design requirements of high isolation of multiple-input multiple-output (MIMO) antenna, two MIMO antennas with double notch structures are designed. Firstly, a two-element antenna was placed symmetrically in parallel, and two rectangular branches were loaded to improve the isolation. U-shaped slots and inverted U-shaped slots are etched on the radiating patch and feeder to achieve notch characteristics in WIMAX and ITU band, respectively. Then, in order to meet more application scenarios, a four-element MIMO antenna is designed, where each element is placed orthogonally to each other, and the isolation is improved by loading a cross-shaped branches in the middle of elements. Both antenna samples are tested to verify the design. Measured results show that the working bandwidth of the two-element UWB MIMO antenna is 2.45-14.88 GHz, the isolation is greater than 17 dB, the peak gain is 5.7 dB, the maximum radiation efficiency can reach 96%, the envelope correlation coefficient (ECC)is less than 0.02. Meanwhile, the working bandwidth of the four-element antenna is 2.14-14.95 GHz, the isolation is greater than 20 dB, the peak gain is 5.9 dB, the maximum radiation efficiency can reach 95%, the ECC is lower than 0.05. They both are with very good omnidirectional characteristic, and meet the requirements of the UWB application.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

We compare several different measures of non-Gaussianity for two families of four-photon superpositions of the Fock states: even vacuum squeezed states and orthogonal-even coherent states.

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

To study the heat and mass transfer characteristics of an evaporative cooler for cooling high-temperature working fluids such as supercritical carbon dioxide, an experimental device of the evaporative cooler was built, and a corresponding test system was constructed. Then, the experimental study was carried out based on the orthogonal test method, and the law and extent of the influence of water flow in the tube, spray water flow rate, inlet water temperature in the tube, and air flow rate on heat dissipation, cooling efficiency, and heat and mass transfer coefficients have been obtained. The correlation equations of the heat and mass transfer coefficients were obtained by fitting the orthogonal experimental data, and the validity of the correlation equations was confirmed by the verification experiment.

The article features the structure and functions of plant synthetic promoters frequently exercised to precisely regulate complex regulatory routes. The composition of plant native promoters together with interacting proteins is presented to provide a better understanding of tasks associated with synthetic promoter development. The production of synthetic promoters is conferred on relatively small libraries produced generally by basic molecular or genetic engineering methods such as cis-element shuffling or domain swapping. Moreover, the preparation of large-scale libraries supported by synthetic DNA fragments, directed evolution, and machine or deep learning methodologies is presented. A particularly interesting group of synthetic promoters are bidirectional forms that enable the putative expression of up to 6–8 genes by one regulatory element. The introduction and controlled expression of several genes after one transgenic event strongly decreases the frequency of such problems as complex segregation patterns and random integration of multiple transgenes. These complications are commonly observed during transgenic crop development through traditional, multistep transformation by genetic constructs containing a single gene. Another path to solving problems associated with the low complexity and homology of already tested DNA fragments is through orthogonal expression systems composed of synthetic promoters and trans-factors that do not occur in nature or arise from different species. Their structure, functions, and applications are rendered in the article.

In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, M\"{o}bius, Proper Velocity, and Chen's gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite-dimensional subspace. As a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (cogyrolines) together with automorphisms of the subgyrogroup. With the algebraic structure of the decompositions, we study fiber bundles and sections inherited by the gyroprojectors. Finally, the general theory is exemplified for the aforementioned gyrogroups.

Differential Evolution (DE) is an evolutionary algorithm that has become increasingly popular due to its effectiveness and efficiency. However, its adaptation for multi-objective optimization requires further investigation. To address this issue, a novel algorithm called ILSDEMO has been proposed, which incorporates indicator-based selection and local search into a self-adaptive DE. ILSDEMO employs an archive population to store non-dominated solutions, generating an initial population uniformly distributed over the feasible solution space using orthogonal design. Additionally, two variants of DE are used to expedite convergence, while q-Gaussian mutation is utilized to exploit better trial individuals. The k-nearest neighbor rule is used to eliminate crowded solutions, and indicator-based selection is employed to generate a new parent population without diversity preservation. The performance of ILSDEMO was investigated on the test instances from the ZDT series and DTLZ series in terms of the selected indicators. The results suggest that ILSDEMO accurately and evenly approximates the true Pareto front compared to NSGAII, IBEA, and DEMO.

A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank-Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear Extended Fisher-Kolmogorov (EFK) equation is proposed. The method reduces CPU runtime and error accumulation by reducing the dimension of the unknown CNMFE solution coefficient vectors. For this purpose, The CNMFE scheme of the EFK equation is established and the uniqueness, stability and convergence of the CNMFE solutions are discussed. Subsequently, the matrix-based RDCNMFE scheme is derived by applying the POD method. Furthermore, the uniqueness, stability and error estimates of the linearized RDCNMFE solution are proved. Finally, numerical experiments are carried out to validate the theoretical findings. In addition, we contrast the RDCNMFE method with the CNMFE method, highlighting the advantages of the dimensionality reduction method.

With the proliferating of video surveillance system deployment and related applications, real-time video analysis is very critical to achieve intelligent monitoring, autonomous driving, etc. It is non-trivial to achieve high accuracy and low latency video stream analysis through the traditional cloud computing. In this paper, we propose a non-orthogonal multiple access (NOMA) based edge real-time video analysis framework with one edge server (ES) and multiple user equipments (UEs). A cost minimization problem composed of delay, energy and accuracy is formulated to improve the QoE of UEs. In order to efficiently solve this problem, we propose the joint video frame resolution scaling, task offloading, and resource allocation algorithm based on the Deep Q-Learning Network (JVFRS-TO-RA-DQN), which effectively overcomes the sparsity of the single-layer reward function and accelerates the training convergence speed. JVFRS-TO-RA-DQN consists of two DQN networks to reduce the curse of dimension, which respectively select the offloading and resource allocation action, the resolution scaling action. Experimental results show that JVFRS-TO-RA-DQN can effectively reduce the cost of transmission and computation, and have better performance in convergence compared to other baseline.

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and triggered the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

Ultra-large cold-water pipes (CWP) may present structural instability phenomenon under complex and variable operating conditions, and the current theoretical analysis rarely takes into account the influence of multiple key parameters at the same time, resulting in some errors between the prediction results and the actual deformation behavior of the pipe. Considering this issue, this paper establishes a computational analysis model of the mechanical performance of the CWP based on the Euler-Bernoulli beam theory, considering the effect of waves, the clump weight at the bottom, internal flow and sea current, and gives a time-dependent solution of the mechanical response of the pipe with the action of multiple key parameters using the differential quadrature method (DQM). Additionally, the correctness and validity of the theoretical model are well verified by comparing the numerical solution with the theoretical results. Finally, to study the effects of operating conditions on the mechanical response of the pipe, the effects of waves, the clump weight, internal flow and sea current on the lateral deflection and maximum bending moment of the pipeline are discussed based on numerical simulation and orthogonal experimental method. The results show that changing the wave strength and internal flow velocity has little effect on the lateral deflection of the CWP, and the clump weight at the bottom can effectively suppress the lateral deflection of the pipeline, but increasing the current velocity can significantly increase the lateral deflection of the pipeline, which can lead to the instability of the pipe. Nevertheless, the effects of waves, the clump weight, internal flow and sea current on the maximum bending moment of the pipeline are basically the same, all of them increase sharply at first, and then decrease gradually until they level off, and the differences in the effects are mainly reflected in the different locations of the pipe sections. This paper suggests the design guidance of CWP in aspect of dynamic response depending on the operating condition.

Adaptive Sliceable-Bandwidth Variable Transceivers (S-BVTs) are key enabler for future optical networks. In particular, those based on Discrete MultiTone (DMT) modulation and Direct Detection (DD) can be considered a flexible solution suitable to address the cost efficiency requirement of optical metro networks. In this paper, we propose to use this cost-effective S-BVT option/implementation in optical metro networks adopting switching nodes based on Semiconductor Optical Amplifier (SOA) technology. Bit loading (BL) and power loading (PL) algorithms are applied to the Digital Signal Processing (DSP) modules, to maximize the performance and/or the capacity as well as enhance the flexibility and adaptability of the system. Our analysis considers switching nodes based on SOAs with and without filtering elements and fiber spans of 25 km. We present the results up to 100 km, with and without SOA-based nodes. Firstly, we analyze the adaptive BVT transmission using the Margin Adaptive (MA) BL/PL algorithm at a fixed bit rate of 28 Gb/s. The possibility of controlling the SOAs current is a key factor to face the transmission impairments due to the fiber and the filtering elements. We also analyze the system considering Rate Adaptive (RA) transmission at a fixed target BER of 3.8·10⁻³, showing that a maximum capacity above 34 Gb/s can be achieved for a single span of 25 km. Although the cascading of filtering elements still constitutes a limiting factor, we show that an improvement of the net bit rate performance can be obtained thanks to the combined use of S-BVT and SOA technology at the switching nodes, resulting in a promising approach for designing future optical metro networks.

The extensive use of engineered nanoparticles (ENPs) such as zinc oxide nanoparticles (ZnO NPs) in various commercial fields has spurred significant concern about its possible toxicological effects of ZnO NPs on human health and eco-system. Therefore, it is substantial to understand the aggregation phenomena which could attenuate this effect. This data article provides information on aggregation of ZnO NPs under the influence of various parameters of water chemistry. Moreover, Taguchi orthogonal array L27(313) design matrix was used to evaluate the effect of multiple parameters in aqueous solution. The data were obtained from single beam UV-Vis spectrophotometer (Optizen 2120 UV, Mecasys, Korea) using Optizenview 4.2.5 PC interference software, Fourier transform infrared spectrometer (FT/IR-4700, spectroscopy, JASCO Analytical Instruments, Easton, USA) and particle electrophoresis (NanoZS, Zetasizer, Malvern Instruments Ltd, Worcestershire, UK). The dataset draws attention on dominant parameters influencing aggregation of ZnO NPs in water. The analysis of variance (ANOVA) data revealed that electrolyte concentration, type and natural organic matter (NOM) concentration were the most significant parameters. Furthermore, FT-IR data presents a possible mechanism of ZnO NPs stabilization in the presence of different NOM. This data will be helpful for the development of environmental risk assessment strategies and prediction of fate and mobility of other ENPs in the aquatic environment.

This paper presents a) the novel hybrid learning method to train the type-1 non-singleton interval type-3 (IT3) fuzzy logic systems (IT3 NSFLS-1) and b) the novel method named enhanced Wagner-Hagras (EWH) IT3 NSFLS-1 fuzzy systems which includes the level alpha 0 output to calculate the output y alpha using the average of the outputs y alpha k instead of their weighted average. The development of the proposed methodology uses the orthogonal least square (OLS) method to train the consequent parameters and the back propagation (BP) method to train the antecedent parameters. This proposal dynamically changes the parameters of only the level alpha 0 minimizing some criterion function as new information becomes available to each level alpha k. The antecedent sets are type-2 fuzzy sets, the consequent sets are fuzzy centroids, the inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations, and the secondary membership functions are modeled as two Gaussians with uncertain standard deviation and the same mean. Based on the firing set of the level alpha 0, the proposed methodology calculates each firing set of each level alpha k to dynamically construct and update the EWH IT3 NSFLS-1 (OLS-BP) system. The algorithm was tested in a hot strip mill facility to predict the transfer bar surface temperature showing its superior capability to obtain the industrial pyrometer’s knowledge uncertainty for tuning and its better performance when compared with IT2 SFLS, IT2 NSFLS-1, GT2 SFLS, GT2 NSFLS-1, IT3 SFLS, and IT3 NSFLS-1 trained with the BP-BP algorithm.

Interdisciplinary research consists of many levels and pathways. One research level that has emerged since the early 21st century is called integration science. Specifically, we focus on a research pathway that structurally integrates social sciences with theoretical physics from perspectives of dynamic analysis. Building on nearly 20 years of prior work, this paper proposes a basic theory of integration science, laying the theoretical foundation for its subsequent development. The significance of integration science operates on three levels. First, identifying structural connections between different disciplines helps in our holistic understanding of natural and social phenomena. Second, generally speaking, the current level of conceptualization and modeling in natural sciences, especially physics, is ahead of social sciences. Integration science research can help elevate the level of conceptualization and modeling in social sciences. Third, the structural similarity across different disciplines reflects the shared thinking of scientists from various fields. Integration science is not simply a synthesis of knowledge from different disciplines. The standard of integration science is to enable social sciences and natural sciences to share the same mathematical structures, thereby possessing a unified mathematical language for description. The empirical basis of integration science is discussed, proposing a unified theory of interdisciplinary scientific observation. This includes concepts like the directionality of scientific observation and the orthogonal principle, the concept of observational disturbance and the diagonal law, defining low and high disturbance quadrants, and discussing why different disturbance quadrants follow their respective mathematical paths. The basic theory of integration science is proposed. The application of category theory in integration science is introduced, along with the necessary semantic supplements. The fundamental concepts of integration mathematics are proposed, defining concepts like integration points, lines, plans, and bulks, and discussing their algebraic and functional analysis methods, thereby laying the mathematical foundation for the integration science. The structural force hypothesis is proposed, along with an axiomatic system of structural forces, thereby laying the philosophical foundation for integrative science. Based on prior work, specific cases of integrative points, lines, plans, and bulks are provided.

Cooperative non-orthogonal multi access communication is a promising paradigm for the future wireless networks because of its advantages in terms of energy efficiency, wider coverage and interference mitigating. In this paper, we study the secrecy performance of a downlink cooperative non-orthogonal multi access (NOMA) communication system under the presence of an eavesdropper node. Smart node selection based on feed forward neural networks (FFNN) is proposed in order to improve the physical layer security (PLS) of a cooperative NOMA network. The selected cooperative relay node is employed to enhance the channel capacity of the legal users, where the selected cooperative jammer is employed to degrade the capacity of the wiretapped channel. Simulations of the secrecy performance metric namely the secrecy capacity ($C_S$) are presented and compared with the conventional technique based on fuzzy logic node selection technique. Based on our simulations and discussions the proposed technique outperforms the existing technique in term the of secrecy performance.

Previous research has indicated that ultra-high pressure (UHP) technology is useful in speeding up the extraction process of cold brew (CB) coffee. However, the impact of different degrees of roasting on UHP CB coffee is still unclear. Therefore, this study aimed to investigate the effects of three different degrees of roasting (light, medium, and dark) on the physicochemical and flavor characteristics of UHP CB coffee. The results of this study showed that most physicochemical characteristics of UHP coffee were similar to those of conventional CB coffee, regardless of the degree of roasting. However, the majority of physicochemical characteristics, non-volatile components, and sensory evaluation significantly increased with an increase in roasting degree. The HS-SPME-GC/MS analysis showed that most volatile components, such as pyrazines, furans (except furfural), esters, pyrrole, pyridine, and most aldehydes, increased from light to dark roasting, and this was significantly evident in CB coffee compared with UHP. The content of volatile components in UHP coffee was significantly (P<0.05) higher than that in CB coffee at the same degree of roasting, especially with dark roasting. The combination of orthogonal partial least squares-discriminant analysis (OPLS-DA) and principal component analysis (PCA) indicated that the distance between coffee samples at different degrees of roasting under CB coffee was greater than that under UHP coffee. However, the distance between these two extraction methods at medium roasting was evidently closer than that at light and dark roasting. Moreover, 15 representative differential compounds, such as were Hazelnut pyrazine, linalool, butane-2,3-dione, 3- methylbutanal found by the calculation of odor-active values (OAVs) indicating the main contributing compounds to odor. Overall, the effect of roasting degrees on UHP coffee was less than that on CB coffee, which was consistent with the results of physicochemical characteristics, volatile components, and sensory evaluation.

For the in-house validation of a droplet digital PCR method, a factorial experimental design was implemented. This design serves different purposes. On the one hand, it is an efficient design in relation to the workload involved in achieving a desirable level of reliability of variance estimates. On the other hand, it allows a partitioning of total variance into different components, thus providing information regarding the dominant sources of random variation. The statistical modelling reflects the actual measurement mechanism, establishing relationships between nominal target DNA copies per well, the range of variation of copy numbers per droplet, probability of detection values, and estimated numbers of copies.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

Flaxseed oil is one of the best sources of n-3 fatty acids, thus its adulteration with refined oils can lead to a reduction in its nutritional value and overall quality. The purpose of this study was to use the differential scanning calorimetry (DSC) technique to detect adulterations of cold-pressed flaxseed oil with refined rapeseed oil (RP). Based on the melting phase transition curve, parameters such as peak temperature (T), peak height (h), and percentage of area (P) were determined for pure and adulterated flaxseed oils with a RP concentration of 5, 10, 20, 30, 50% (w/w). Significant linear correlations (p ≤ 0.05) between the RP concentration and all DSC parameters were observed, except for h1. In order to assess the usefulness of the DSC technique for detecting adulterations, three chemometric approaches were compared: 1) classification models (Linear Discriminant Analysis, LDA Adaptive Regression Splines, MARS, Support Vector Machine, SVM, Artificial Neural Networks, ANNs); 2) regression models (Multiple Linear Regression, MLR, MARS, SVM, ANNs, PLS) and 3) a combined model of Orthogonal Partial Least Squares Discriminant Analysis (OPLS-DA). With the LDA model, the highest accuracy of 99.5% in classifying the samples, followed by ANN&gt; SVM &gt; MARS was achieved. Among the regression models, the ANN model showed the highest correlation between observed and predicted values (R= 0.996), while other models showed goodness of fit as following MARS&gt; SVM&gt; MLR. Comparing OPLS-DA and PLS methods, higher values of R2X(cum) =0.986 and Q2 =0.973 were observed with the PLS model than OPLS-DA. These results demonstrate the usefulness of the DSC technique combined with chemometrics for predicting the adulteration of cold-pressed flaxseed oil with refined rapeseed oil.

Empirical Orthogonal Functions (EOF) analysis between the anomalies of Lake Titicaca water levels (WLs) and the Pacific Interdecadal Oscillation (IPO) reveals a correlation coefficient of 0.71 between the WLs and the principal component (PC1). These findings demonstrate the high accuracy of the IPO in representing the positive and negative phases of the water levels. By utilizing wavelet functions, we identified multi-decadal variability with periods ranging between 20 and 30 years. The statistical techniques employed indicate a relationship between IPO and ENSO; however, they operate on different timescales of climate variability. The IPO exhibits longer-term variability, typically spanning 20-30 years, while ENSO events occur on average every 2-7 years. Nevertheless, the IPO has the ability to modulate the strength and frequency of El Niño and La Niña events, and vice versa. During the positive phase of the IPO, there is a tendency for more frequent and intense El Niño events, accompanied by fewer La Niña events. This can be attributed to warmer sea surface temperatures in the central and eastern Pacific, which create favorable conditions for El Niño development. Conversely, during the negative phase of the IPO, there is a tendency for more frequent and intense La Niña events, with fewer occurrences of El Niño events, due to cooler sea surface temperatures in the central and eastern Pacific.

Compressive sensing (CS) is a technique that allows a signal vector to be reconstructed with a number of linear measurements far fewer than its size. In this study, optical hybrid cryptography with simultaneous compressive sensing based on orthogonal matching pursuit (OMP) is proposed as an alternative solution to the two important problems in communications, namely, effective / efficient / signal processing and secure encryption/decrypton. The whole system is able to both compress and encrypt data with attack immunity.

The next-generation communication systems demand integration of sensing, communication, and power transfer (PT) capabilities, requiring high spectral efficiency, energy efficiency, and low cost, while also necessitating robustness in high-speed scenarios. Integrated sensing and communication systems (ISACS) exhibit the ability to simultaneously perform communication and sensing tasks using a single RF signal, while simultaneous wireless information and power transfer (SWIPT) systems can handle simultaneous information and energy transmission, and orthogonal time frequency space (OTFS) signals are adept at handling high Doppler scenarios. Combining the advantages of these three technologies, a novel cyclic prefix (CP) OTFS based integrated simultaneous wireless sensing, communication, and power transfer system (ISWSCPTS) framework is proposed in this work. Within the ISWSCPTS, the CP-OTFS matched filter (MF) based target detection and parameters estimation (MF-TDaPE) algorithm is proposed to endow the system with sensing capabilities. To enhance the system’s sensing capability, a waveform design algorithm based on CP-OTFS ambiguity function shaping (AFS) is proposed, which is solved by iteratively method. Furthermore, to maximize the system’s sensing performance under communication and PT Quality of Service (QoS) constraints, a semidefinite relaxation (SDR) beamforming design (SDR-BD) algorithm is proposed, solved using through SDR technique. Simulation results demonstrate that the ISWSCPTS exhibits stronger parameter estimation performance in high-speed scenarios compared to orthogonal frequency division multiplexing (OFDM), waveform designed by CP-OTFS AFS demonstrates superior interference resilience, and beamforming designed by SDR-BD strikes a balance in the overall performance of the ISWSCPTS.