Non-separative Method Research Articles

Synchronization Analysis of Discrete-Time Fractional-Order Quaternion-Valued Uncertain Neural Networks.

This article studies synchronization issues for a class of discrete-time fractional-order quaternion-valued uncertain neural networks (DFQUNNs) using nonseparation method. First, based on the theory of discrete-time fractional calculus and quaternion properties, two equalities on the nabla Laplace transform and nabla sum are strictly proved, whereafter three Caputo difference inequalities are rigorously demonstrated. Next, based on our established inequalities and equalities, some simple and verifiable quasi-synchronization criteria are derived under the quaternion-valued nonlinear controller, and complete synchronization is achieved using quaternion-valued adaptive controller. Finally, numerical simulations are presented to substantiate the validity of derived results.

Finite-time synchronization for a fully complex-valued BAM inertial neural network with proportional delays via non-reduced order and non-separation approach

This paper focuses on finite-time synchronization (FinTS) for fully complex-valued bidirectional associative memory inertial neural networks (FCV-BAM-INNs) with proportional delays via non-reduced order and non-separation approach. Firstly, a model of the FCV-BAM-INNs with proportional delays is established. Secondly, by using the non-reduced order transformation method of inertial neural networks (INNs) and the non-separation method of complex-valued neural networks (CVNNs), an adjustable complex feedback control law with memory is designed to reach the FinTS of the drive–response FCV-BAM-INNs with proportional delays. Thirdly, some new delay-independent algebraic sufficient criteria are formed to guarantee FinTS of FCV-BAM-INNs with proportional delays by applying non smooth theory and inequalities in the complex domain, which are flexible and adjustable and easy to implement in applications. Moreover, the settling time of FinTS theoretically is calculated. Finally, some numerical simulations and an application on image encryption and decryption as evidences of the validity and availability of the results.

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0<Vt⩽1 are no longer required. For the purpose of verifying the new lemmas, complex-valued fuzzy cellular neural networks (CVFCNNs) with discontinuous activation functions are studied with a nontraditional non-separation method, which could reduce the conservatism of the obtained results greatly. Besides, FXT synchronization is discussed simultaneously. When contrasted with the results of other similar prominent pioneering works nowadays, the accuracy of settling times (STs) is quite enhanced. At last, numerical simulations are conducted to demonstrate the validity and superiority of our established theoretical results.

Projective synchronization in fixed/predefined-time for quaternion-valued BAM neural networks under event-triggered aperiodic intermittent control

This study aims to solve the fixed/predefined-time projective synchronization (FTPS/PTPS) of quaternion-valued BAM neural networks (BAMNNs) through event-triggered aperiodic intermittent control (ETAIC). Firstly, a novel quaternion-valued BAMNN model is established by integrating discontinuous activations, parameter uncertainties and time-varying delays. Subsequently, under the framework of the non-separation method several concise ETAIC schemes are designed by utilizing an exponential term instead of a sign function and two power-law terms. Different from the previous time-triggered intermittent controllers, the control and rest intervals of the ETAIC strategies are determined according to the dynamics of the network rather than being pre-specified. Furthermore, several adequate conditions are acquired to guarantee the FTPS and PTPS of the considered networks by constructing auxiliary functions and applying Taylor expansion Ultimately, three simulation examples are presented to confirm the validity and usefulness of the theoretical findings.

Non-separation Method-Based Global Stability Criteria for Takagi–Sugeno Fuzzy Quaternion-Valued BAM Delayed Neural Networks Using Quaternion-valued Auxiliary Function-Based Integral Inequality

This paper focuses on the global asymptotic stability (GAS) problem for Takagi–Sugeno (T-S) fuzzy quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with discrete, distributed and leakage delays by using non-separation method. By applying T-S fuzzy model, we first consider a general form of T-S fuzzy QVBAMNNs with time delays. Then, by constructing appropriate Lyapunov–Krasovskii functionals and employing quaternion-valued integral inequalities and homeomorphism theory, several delay-dependent sufficient conditions are obtained to guarantee the existence and GAS of the considered neural networks (NNs). In addition, these theoretical results are presented in the form of quaternion-valued linear matrix inequalities (LMIs), which can be verified numerically using the effective YALMIP toolbox in MATLAB. Finally, two numerical illustrations are presented along with their simulations to demonstrate the validity of the theoretical analysis.

Preassigned-time projective synchronization of delayed fully quaternion-valued discontinuous neural networks with parameter uncertainties

This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.

Nonseparation Method for Determining Volumetric Fractions of Gas, Condensate, and Water in the Extracted Products of Gas–Condensate Wells

Nonseparation Method for Determining Volumetric Fractions of Gas, Condensate, and Water in the Extracted Products of Gas–Condensate Wells

Fixed/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations

This paper studies the fixed-time and predefined-time lag synchronization of a class of complex-valued BAM neural networks with random disturbances. Firstly, based on the non-separation method, some basic properties of sign function in complex domain are introduced. Then, two simple complex-valued controllers are designed to achieve the fixed/predefined-time lag synchronization of considered stochastic systems. Compared with the results of existing works, the designed complex-valued controllers do not contain the linear term −λiei(t), which makes the controller more simpler and efficient. Finally, two numerical examples are provided to verify the feasibility of our results through MATLAB simulation.

Fixed/Predefined-Time Synchronization of Complex-Valued Stochastic BAM Neural Networks with Stabilizing and Destabilizing Impulse

This article is mainly concerned with the fixed-time and predefined-time synchronization problem for a type of complex-valued BAM neural networks with stochastic perturbations and impulse effect. First, some previous fixed-time stability results on nonlinear impulsive systems in which stabilizing and destabilizing impulses were separately analyzed are extended to a general case in which the stabilizing and destabilizing impulses can be handled simultaneously. Additionally, using the same logic, a new predefined-time stability lemma for stochastic nonlinear systems with a general impulsive effect is obtained by using the inequality technique. Then, based on these novel results, two novel controllers are implemented to derive some simple fixed/predefined-time synchronization criteria for the considered complex-valued impulsive BAM neural networks with stochastic perturbations using the non-separation method. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.

Polynomial synchronization of complex-valued inertial neural networks with multi-proportional delays

This paper investigates the polynomial synchronization (PS) problem of complex-valued inertial neural networks with multi-proportional delays. It is analyzed based on the non-separation method. Firstly, an exponential transformation is applied and an appropriate controller is designed. Then, a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques. In the end, a numerical example is given to illustrate the effectiveness of the obtained result.

Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts’ absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.

Gas Condensate Wells: Challenges of Sampling, Testing and Production Optimization

The main problem of fluid sampling during well testing of reservoirs with near-critical fluids (gas condensate and volatile oil) is due to the fact that even a small pressure drawdown usually leads to the formation of a two-phase mixture in the bottom hole area, and it is almost impossible to take representative samples with downhole samplers or a formation tester. Sampling via test-separator and the current non-separation methods are also imperfect. An alternative method—MIKS (Multiphase IsoKinetic Sampling)—of gas condensate well testing was proposed, which is based on emulsifying a multiphase flow to particles of about 1–10 μm. Thereby MIKS would eliminate the problem of particle slippage in a homogeneous flow and enables high-quality sampling directly from the flowmeter line. The initial formation fluid is characterized by the maximum value of the condensate-gas ratio (CGR). Therefore, first, the well effluent would be adjusted to the mode with the maximum CGR using a choke manifold and a multiphase flow meter. Then the flow mixture is transferred to a by-pass line with an emulsifier to achieve an isokinetic flow. Thereafter, pressure samples can be taken into pressurized sampling bottles, in which thermodynamic conditions are preset according to the flow line. The efficiency of sampling and recombining procedures allows for conducting a study of reservoir samples in the field laboratory directly on the rig and obtaining a complete PVT report even before the completion of drilling and abandonment of the well. An additional economic effect is achieved by reducing the costs of transporting and samples storage. Well test equipment setup becomes much more compact and less weight; the costs of drilling time are reduced, which is viably important for well testing on the Arctic conditions. Another major problem in the development of gas condensate reservoirs is avoiding the condensate banking around producing wells. Optimization of condensate production can be achieved by maintaining the well operation mode at maximum CGR level by means of multiphase flowmeters. The formed condensate bank can be destroyed by a combination of methods—hydraulic fracturing, followed by cycling process—purging the formation with dried gas and/or injection of methanol into the formation. Methanol can be obtained from synthesis gas as a by-product in the utilization of associated gas also at the field. The specified set of measures will allow to revive the GC wells that are losing productivity, as well as to extend the period of high productivity of new wells.

Synchronization in fixed/preassigned-time of delayed fully quaternion-valued memristive neural networks via non-separation method

This paper mainly centers on investigating issues of synchronization of delayed memristive quaternion-valued neural networks (MQVNNs), which are first studied with an unconventional non-separation approach for the fully quaternion-valued (QV) parameters (i.e. state vectors, weights, inputs and outputs). First, QV sign function and norms are introduced and new properties of quaternions are established, which are the basis of the non-separation approach. Next, more relaxed conditions with a new pure lemma are explored to guarantee fixed-time (FXT) or preassigned-time (PST) synchronization and the settling times (STs) are measured. Specially, the ST of PST synchronization is pre-specified and irrelevant to any parameter of the systems or controllers, which is more independent. Subsequently, controller strategies are given to realize FXT and PST synchronization of the discussed systems. Lastly, the effectiveness and superiority of the achieved theoretical results are illustrated by numerical examples.

Synchronization in Fixed/Preassigned-Time of Delayed Fully Quaternion-Valued Memristive Neural Networks Via Non-Separation Method

Synchronization in Fixed/Preassigned-Time of Delayed Fully Quaternion-Valued Memristive Neural Networks Via Non-Separation Method

Separation and non-separation methods for the analysis of cannabinoids in Cannabis sativa L.

Cannabis sativa L. is a plant known all over the world, due to its history, bioactivity and also social impact. It is chemically complex with an astonishing ability in the biosynthesis of many secondary metabolites belonging to different chemical classes. Among them, cannabinoids are the most investigated ones, given their pharmacological relevance. In order to monitor the composition of the plant material and ensure the efficacy and safety of its derived products, extraction and analysis of cannabinoids play a crucial role. In this context, in addition to a conventional separation method based on HPLC with UV/DAD detection, a new strategy based on a non-separation procedure, such as 13C-qNMR, may offer several advantages, such as reduced solvent consumption and simultaneous acquisition of the quali/quantitative data related to many analytes. In the light of all the above, the aim of this work is to compare the efficiency of the above-mentioned analytical techniques for the study of the main cannabinoids in different samples of cannabis inflorescences, belonging to fibre-type, recreational and medical varieties. The 13C-qNMR method here proposed for the first time for the quantification of both psychoactive and non-psychoactive cannabinoids in different cannabis varieties provided reliable results in comparison to the more common and consolidated HPLC technique.

Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks

In this paper, robust finite-time synchronization (F-TS) issue is addressed for a class of uncertain fractional-order quaternion-valued neural networks by employing non-separation method instead of separation method. First, a general fractional differential inequality is developed to provide new insight into the research about finite-time stability and synchronization of fractional-order systems. Next, quaternion-valued feedback controller and quaternion-valued adaptive controller are designed. On the basis of the newly developed inequality, quaternion inequality techniques, together with the properties of fractional calculus and reduction to absurdity, some easily-verified algebraic criteria for robust F-TS are established, and the settling time for robust F-TS is explicitly reckoned, which depends on not only the controller parameters but also the initial values and order of the considered systems. Eventually, numerical results are provided to substantiate our robust F-TS criteria.

Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order

Abstract Based on the non-separation method, the finite-time projective synchronization of fractional-order quaternion-valued memristive networks with discontinuous activation functions is investigated in this paper. Firstly, the sign function related to quaternion is introduced and some properties concerning it are developed. Secondly, two different quaternion-valued controllers are designed by feat of the proposed sign function. Subsequently, several synchronization conditions are derived and the settling times are evaluated validly by the established finite-time fractional-order inequality. Especially noteworthy is that the addressed networks are converted into systems with parametric uncertainty in the framework of differential inclusion and measurable selection. Finally, a numerical example is given to demonstrate the correctness of theoretical analyses.

Sparse Bayesian learning algorithm for separable dictionaries

Dictionaries with separable structure reduce the computational load of sparse coding and learning algorithms and ensure that patterns present in 2D data are not broken by vectorization. We propose an adaptation of the sparse Bayesian learning (SBL) framework for sparse approximation to the 2D separable case. Our algorithm has two stages. In the first, the hierarchical prior model targets the sparsity patterns occurring in each dimension, therefore focusing on the representation structure. The underlying 2D row-column structure of the sparse support is thus recovered via two separate SBL processes. Simulations show that this recovery is obtained in considerably less iterations than the non-separable method, especially in noisy setups. Since we take advantage of the separable structure, each iteration is considerably faster. In the second stage, only few iterations of standard SBL on the reduced support are needed to obtain the signal representation.In addition to this significant improvement over SBL in numerical complexity, we demonstrate, in a series of tests carried out on synthetic data and images, that the separable formulation results also in comparable accuracy.

Application of Variable Projection Method based on Gram-Schmidt Orthogonalization in Spatial Cartesian Coordinate Transformation Model

For the linear and nonlinear parameters that can be separated in the spatial Cartesian coordinate transformation model, we use the variable projection algorithm in this paper to represent the linear parameters with nonlinear parameters, which are transformed into least squares problems with only nonlinear parameters. We simplify the matrix of the nonlinear function by the Gram-Schmidt orthogonalization method, and combine the nonlinear least squares iterative method with the Levenberg-Marquardt (LM) algorithm to solve for the coordinate transformation parameters. Experiments are carried out by solving for the coordinate transformation parameters of the independent spatial Cartesian coordinate system and the CGCS2000 coordinate system. We compare the solution results of the four methods (parameter non-separation method, traditional variable projection method, variable projection method based on QR decomposition, and variable projection method based on Gram-Schmidt orthogonal decomposition) with respect to the calculated results, the number of iterations and the computation time. The experimental results show that the proposed method in this paper requires a lower computation time and achieves higher computational efficiency when obtaining the same solution results and with the same number of iterations.

Non-separative method based on a single quadrupole mass spectrometer for the semi-quantitative determination of amino acids in saliva samples. A preliminary study

Amino acids have been of great interest in clinical studies since variation in their concentration may provide information about different disorders. For the first time, a non-separative method based on single quadrupole mass spectrometry (qMS) for the simultaneous semiquantitative determination of sixteen amino acids in saliva samples has been developed. The method includes derivatisation of amino acids with ethyl chloroformate-pyridine-ethanol to obtain volatile products, liquid-liquid extraction (LLE) and further analysis using a programmed temperature vaporizer (PTV) coupled to qMS. This method could be applied to the analysis of a great number of saliva samples, limiting the use of separative methods only when abnormal concentrations of amino acids were found, reducing analysis time and cost. The results obtained in the determination of amino acids using the non-separative method were compared to those obtained when a separative method based on gas chromatography (GC) was used, providing values of average relative predictive error (E %) ranging between 2 and 48%. Repeatability and reproducibility were tested, obtaining relative standard deviation (RSD) values equal to or lower than 11% and 16%, respectively. Detection limits were in the range of 0.076–8.747 mg L−1 for the non-separative method.