Second Order Research Articles

High-order allpass cascade-connected phase-system design utilizing fractional polynomial errors

ABSTRACT This paper proposes a nonlinear optimization method for designing a high-order recursive allpass digital phase system that comprises several cascade-connected second-order (SO) allpass sections. This method first splits a given phase design specification (approximation target) into a set of equal sub-specifications, and then the equal sub-specification acts as the ideal phase for each of the SO sections. Since an SO section can be designed via employing a linear programming to minimize a linear fractional error function, this splitting process generates an excellent starting point (good initial values for the coefficients of the cascaded SO sections) for further minimizing the overall approximation error. This paper first derives a wide variety of fractional polynomial error functions for designing cascade-connected allpass phase systems of different high orders, and then shows that a high-order cascade-connected allpass phase system can be designed by utilizing a nonlinear solver to minimize the peak deviation of such a fractional polynomial error. Using the derived fractional polynomial error functions in the system design enables the system designer to find an excellent starting point for further minimizing the approximation error and thus reach a convergent design solution. This paper first derives a set of fractional polynomial errors, and then adopts the eighth-order cascade-connected phase system design to exemplify the effectiveness of the fractional-polynomial-error-based design tactic. Furthermore, the stability of the cascade-connected high-order allpass system can be readily checked via confirming that all of the cascaded SO sections have their poles inside the unit circle in the complex plane.

Efficient Optimization of a Support Vector Regression Model with Natural Logarithm of the Hyperbolic Cosine Loss Function for Broader Noise Distribution

While traditional support vector regression (SVR) models rely on loss functions tailored to specific noise distributions, this research explores an alternative approach: ε-ln SVR, which uses a loss function based on the natural logarithm of the hyperbolic cosine function (lncosh). This function exhibits optimality for a broader family of noise distributions known as power-raised hyperbolic secants (PHSs). We derive the dual formulation of the ε-ln SVR model, which reveals a nonsmooth, nonlinear convex optimization problem. To efficiently overcome these complexities, we propose a novel sequential minimal optimization (SMO)-like algorithm with an innovative working set selection (WSS) procedure. This procedure exploits second-order (SO)-like information by minimizing an upper bound on the second-order Taylor polynomial approximation of consecutive loss function values. Experimental results on benchmark datasets demonstrate the effectiveness of both the ε-ln SVR model with its lncosh loss and the proposed SMO-like algorithm with its computationally efficient WSS procedure. This study provides a promising tool for scenarios with different noise distributions, extending beyond the commonly assumed Gaussian to the broader PHS family.

Mesoporous Carbons and Highly Cross-Linking Polymers for Removal of Cationic Dyes from Aqueous Solutions-Studies on Adsorption Equilibrium and Kinetics.

This study presents the results of applying the methods of synthesizing mesoporous carbon and mesoporous polymer materials with an extended porous mesostructure as adsorbents for cationic dye molecules. Both types of adsorbents are synthetic materials. The aim of the presented research was the preparation, characterisation, and utilisation of obtained mesoporous adsorbents. The physicochemical properties, morphology, and porous structure characteristics of the obtained materials were determined using low-temperature nitrogen sorption isotherms, X-ray diffraction (XRD), small angle X-ray scattering (SAXS), and potentiometric titration measurements. The morphology and microstructure were imaged using scanning electron microscopy (SEM). The chemical characterisation of the surface chemistry of the adsorbents, which provides information about the surface-active groups, the elemental composition, and the electronic state of the elements, was carried out using X-ray photoelectron spectroscopy (XPS). The adsorption properties of the mesoporous materials were determined using equilibrium and kinetic adsorption experiments for three selected cationic dyes (derivatives of thiazine (methylene blue) and triarylmethane (malachite green and crystal violet)). The adsorption capacity was analysed to the nanostructural and surface properties of used materials. The Generalized Langmuir equation was applied for the analysis of adsorption isotherm data. The adsorption study showed that the carbon materials have a higher sorption capacity for both methylene blue and crystal violet, e.g., 0.88-1.01 mmol/g and 0.33-0.44 mmol/g, respectively, compared to the polymer materials (e.g., 0.038-0.044 mmol/g and 0.038-0.050 mmol/g, respectively). The kinetics of dyes adsorption was closely correlated with the structural properties of the adsorbents. The kinetic data were analysed using various equations: first-order (FOE), second-order (SOE), mixed 1,2-order (MOE), multi-exponential (m-exp), and fractal-like MOE (f-MOE).

Saturated formation containment control for a heterogeneous multi-agent system with unknown perturbations

This work addresses formation containment control for a heterogeneous multi-agent system composed of first-order (FO) and second-order (SO) agents that can be either leader or follower agents. It is assumed that unknown but bounded disturbances perturb its dynamical model. An error-based version of a generalized proportional–integral observer (GPIO) is proposed to estimate these perturbations, and saturation functions, based on position measurement and estimated velocity errors, are designed to achieve the control objective. Specifically, it is shown that the leader agents converge to a desired geometric pattern following a desired trajectory simultaneously. Furthermore, the follower agents converge to the convex hull spanned by the leaders. The result applies to a group of robots in which a directed spanning tree gives the communication topology among the leaders with a root in the main leader. At the same time, each follower receives information from at least one leader agent, and the communication is directed. Real-time experiments and a comparison with a robust control technique exhibit the excellent performance of the proposed GPIO and control strategy in achieving formation containment control.

Magnetic properties and magnetocaloric effect (MCE) in the melt-spun Tm20Ho20Gd20Ni20Al20 amorphous ribbon

We fabricated the Tm20Ho20Gd20Ni20Al20 ribbons by melt-spun technology and determined its glass forming ability (GFA), magnetic properties, magnetic phase transition (MPT) character, and magnetocaloric performance. The Tm20Ho20Gd20Ni20Al20 melt-spun ribbon exhibits fully amorphous nature and excellent GFA. A second order (SO) type MPT from ferromagnetic to paramagnetic was observed around the Curie temperature of 30.3 K. Moreover, considerable MCE and magnetocaloric performance in Tm20Ho20Gd20Ni20Al20 amorphous ribbon were realized with the maximum magnetic entropy change, temperature-averaged entropy change of 10 K lift, and relative cooling powder/refrigerant capacity of 9.4 J/kgK, 9.0 J/kgK, and 527.2/422.1 J/kg under 0–5 T field change, respectively. These magnetocaloric parameters are close to most of the recently reported magnetocaloric materials, which made the Tm20Ho20Gd20Ni20Al20 amorphous HE ribbon amorphous ribbon also of potential for practical cryogenic MR applications.

Second-Order, Single-Band and Dual-Band Bandstop Frequency Selective Surfaces at Millimeter Wave Regime

This communication presents the miniaturized low-profile second-order (SO) bandstop frequency selective surfaces (FSSs) for single- and dual-band resonances. The unit cell comprises two identical first-order (FO) elements in a back-to-back configuration with the metal grid in between. Two thin dielectric substrates separate the three metal layers. The proposed FO unit cell consists of intercell-connected spiral resonators (SRs) with capacitively coupled cross loop dipole. The SO filter response of the proposed FSS exhibits a wide stopband ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{21} &lt; -10$ </tex-math></inline-formula> dB) bandwidth (BW) of 27.6%. The unit cell has the periodicity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.162\lambda _{0}$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula> is the free space wavelength at the lower passband. The novelty of the proposed work is a miniaturized simple unit cell geometry, at the millimeter-waveband but not limited to it, with polarization insensitive and high angular stable filter response up to 60° with small variations in the BW. An unconventional four-unit cell element FSS is designed for dual-band SO stopband resonances with the BWs of 8.3% and 13.8%. Prototypes of both FSSs were fabricated and their measured results were found consistent with the simulated filter responses.

General High-Order Selective Harmonic Repetitive Control for PWM Converters

In this article, a general high-order selective harmonic repetitive control (HO-SHRC) scheme is proposed, which is composed of a standard high-order repetitive controller structure and a new order-expandable SHRC. Different from conventional SHRC, the proposed new SHRC is capable of being applied into the standard high-order repetitive control (HORC) structure for generating any high-order SHRC. The proposed HO-SHRC can be used to improve the steady-state tracking accuracy of the pulsewidth modulation (PWM) converter systems and is robust to system frequency variations without changing the controller parameters online. The order expansion of the controller will lead to the increase of the implementation complexity, but it will bring the overall improvement of the controller performance, such as the improvement of frequency adaptability, steady-state tracking accuracy, and dynamic performance. Therefore, HO-SHRC can achieve a good compromise between the controller performance and the implementation complexity. Moreover, the proposed HO-SHRC provides a general structure for various repetitive controls (RCs), such as conventional RC (CRC), odd-harmonic RC (OHRC), high-order CRC (HO-CRC), and HO-odd-harmonic RC (HO-OHRC). Application examples of second-order (SO)- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6k~\pm $ </tex-math></inline-formula> 1 RC-controlled three-phase PWM inverter show the effectiveness and advantages of the proposed control scheme.

An Improved Least Stochastic Entropy Algorithm for Strong Noncircular Inputs and Noise

When the noise is second-order (SO) noncircular, the least stochastic entropy (LSE) algorithm can obtain a low steady-state misalignment compared to the complex-valued least mean-square (CLMS) algorithm. However, the convergence rate of LSE will decrease if the input of the adaptive filter is SO noncircular. This letter analyzes the cause of this problem and proposes an improved LSE (ILSE), which uses a combination strategy to accelerate its convergence rate. To predict its stochastic behavior, the performance of ILSE is analyzed. Simulation results are provided to verify the effectiveness of ILSE and the accuracy of the theoretical analysis.

Second or pseudo-second-order model for adsorption kinetics?

ABSTRACT Model of second-order (SO) adsorption kinetics from solutions was described and verified for the adsorption of phenol/lead (II) on samples of natural coal and activated carbon. The model was compared with the model of pseudo-second-order (PSO) kinetics, proving that the SO kinetics satisfactorily describes particularly the initial stage of the adsorption process, while the PSO model fits well with the experimental data up to the adsorption equilibrium. Possible reason for such different fit of the models for second and pseudo-second-order kinetics to adsorption data is elucidated.

Performance Analysis of RIS-Assisted FSO Communications over Fisher–Snedecor F Turbulence Channels

The Fisher–Snedecor (F-S) F distribution has recently been introduced as a tractable turbulence-induced (TI) fading model that fits well with the experimental data. This paper provides a performance evaluation of a free-space optical (FSO) re-configurable intelligent surface (RIS)-assisted communications (ACs) link over the F-S F TI fading channels, assuming the intensity modulation–direct detection (IM–DD) technique. In particular, novel and closed-form (C-F) analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) in terms of Gaussian hyper-geometric functions are efficiently derived. Capitalizing on the obtained results, novel C-F analytical expressions for the moment generating function (MMGF), outage probability (OP), average bit error rate (BER) and ergodic channel capacity (Cγ) of the FSO RIS-ACs system over the F-S F TI fading channels are provided and numerically evaluated under the various TI fading severity conditions. Furthermore, the second-order (S-O) statistical expressions for the level crossing rate (LCR) and average fade duration (AFD) are obtained and thoroughly examined for various FSO RIS-ACs system model parameters.

Second-Order Perturbation Theory-Based Digital Predistortion for Fiber Nonlinearity Compensation

The first-order (FO) perturbation theory-based nonlinearity compensation (PB-NLC) technique has been widely investigated to combat the detrimental effects of the intra-channel Kerr nonlinearity in polarization-multiplexed (Pol-Mux) optical fiber communication systems. However, the NLC performance of the FO-PB-NLC technique is significantly limited in highly nonlinear regimes of the Pol-Mux long-haul optical transmission systems. In this paper, we extend the FO theory to second-order (SO) to improve the NLC performance. This technique is referred to as the SO-PB-NLC. A detailed theoretical analysis is performed to derive the SO perturbative field for a Pol-Mux optical transmission system. Following that, we investigate a few simplifying assumptions to reduce the implementation complexity of the SO-PB-NLC technique. The numerical simulations for a single-channel system show that the SO-PB-NLC technique provides an improved bit-error-rate performance and increases the transmission reach, in comparison with the FO-PB-NLC technique. The complexity analysis demonstrates that the proposed SO-PB-NLC technique has a reduced computational complexity when compared to the digital back-propagation with one step per span.

On Second-Order Statistics of the Composite Channel Models for UAV-to-Ground Communications With UAV Selection

Unmanned-aerial-vehicles (UAVs) are intended to be a vital part of beyond 5G (B5G) and 6G communication networks. UAV-to-ground communications in urban and populated areas are usually exposed to highly variable propagation conditions that can be often characterized by composite fading channels. This paper provides mathematical framework for the performance evaluation of UAV-to-ground communications over double-scattered single-shadowed (DS-SS), and double scattered double shadowed (DS-DS) fading channels. To analyse in details we provide probability density function (PDF), cumulative distribution function (CDF), average fade duration (AFD) and level crossing rate (LCR) of the product of double Nakagami-m (DN) and single inverse Gamma (SIG) random processes (RPs), as well as the product of DN and double inverse Gamma (DIG) RPs. Furthermore, the derived integral-form formulas for the second order (SO) statistical measures are approximated by Laplace integration (LI) and exponential LI in order to provide closed-form expressions. The impact of DS-SS and DS-DS fading types on the SO statistics of UAV-to-ground propagation scenario are thoroughly examined. Moreover, the impact of different values of DS-SS and DS-DS fading severities on the SO statistics are also taken into investigation. Lastly, the proposed UAV-to-ground model is extended to include the SO performance analysis of L-number of UAVs. All the analytical results for the SO statistics are confirmed by Monte-Carlo simulations.

A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.

Kinetics models of transesterification reaction for biodiesel production: A theoretical analysis

The kinetics of the transesterification reaction has been explored theoretically. A general rate equation (GRE) was obtained for kinetics modeling of transesterification at the entire time of reaction based on a three-step mechanism. It has been shown that the GRE model converts to a Second-Order (SO) model at short initial times of reaction and it converts to Pseudo-First-Order (PFO) model at short initial times of reaction and high concentration of alcohol. Also, a modified form of the Second-Order model (MSO) was derived when the reaction is spontaneous (at ΔrG≪0 conditions or at short initial times of reaction). The accuracy of theoretical models and our assumptions was evaluated by three sets of experimental data selected at literature. It has been shown that the accuracy of PFO, SO, and MSO models followed the order of MSO > SO > PFO at short initial times while the GRE model is a suitable kinetics model at the entire times of reaction. Also, our research, contrary to what has been reported so far in published papers, shows that pseudo-first-order and second-order models are only accurate for kinetics modeling of the transesterification reaction at short initial times of reaction.

Dorsolateral striatum dopamine-dependent cocaine seeking is resistant to pavlovian cue extinction in male and female rats

Cue exposure therapy (CET) reduces craving induced by drug-associated cues in individuals with substance use disorders. A preclinical model of CET, cue extinction, similarly reduces cue-induced cocaine seeking in rodent self-administration models; however, those models may not capture the habitual or compulsive aspects of drug use. Thus, the effectiveness of cue extinction was tested in male and female rats trained to self-administer cocaine using second-order (SO) or fixed-ratio (FR) schedules of reinforcement to facilitate dorsolateral striatum (DLS) dopamine-dependent or -independent response strategies, respectively. Cue extinction significantly reduced drug seeking in FR-trained rats, replicating prior results, but was ineffective in SO-trained rats. SO-trained rats also showed increased indices of glutamate signaling in the DLS relative to FR-trained rats, despite comparable levels of cocaine intake. Furthermore, in SO-trained rats, antagonism of AMPA receptors in the DLS rescued the efficacy of cue extinction to reduce drug seeking. Finally, the effectiveness of cue extinction was also revealed in SO-trained rats when they were taught to perform a new, non-habitual response for cocaine cue presentation. Overall, our findings indicate that habit-like drug seeking leads to plasticity in the DLS and behavior that is resistant to cue extinction, but that the effects of cue extinction are restored when DLS glutamatergic signaling is blocked. These results have implications for the effectiveness of clinical cue exposure therapy.

Image super resolution via nonlocal and second-order feature fusion network

Recently, deep neural networks have made remarkable performance in the image super-resolution (SR) field. However, they mainly focus on wider or deeper architectural design, neglecting to capture the inherent property of natural images, hence hindering the representational ability of convolutional neural networks. To address this issue, we propose a deep network based on nonlocal (NL) and second-order (SO) feature fusion for image SR. In particular, we draw the observation that a SO attention mechanism could achieve more powerful feature expression and feature correlation learning. On the other hand, NL module is proved to be an effective prior to explore spatial contextual information. Thus, we introduce an SR network architecture by embedding NL operations and SO feature to capture intrinsic statistical characteristics of images. Furthermore, long skip connection is applied in the network to pass more abundant low-frequency information from low-resolution images and ease the network training. Experimental results on a variety of images demonstrate that our proposed method can achieve more desirable performance over several state-of-the-art methods in terms of quantitative metrics and visual quality.

Robust second‐order finite‐time formation control of heterogeneous multi‐agent systems on directed communication graphs

This study concentrates on the finite-time (FT) formation control problem for a class of heterogeneous second-order (SO) multi-agent systems (MASs), where disturbance may exist in the dynamics of each agent and the communication graph is directed. First of all, a basic FT formation control protocol is proposed for the nominal SO MAS and the finite convergence time is calculated. To solve the FT formation control for a class of heterogeneous SO MASs without using global information, an adaptive FT formation control is then proposed. Finally, two numerical examples are presented to validate the theoretical results.

MCSCF optimization revisited. II. Combined first- and second-order orbital optimization for large molecules.

A new orbital optimization for the multiconfiguration self-consistent field method is presented. This method combines a second-order (SO) algorithm for the optimization of the active orbitals with the first-order super configuration interaction (SCI) optimization of the remaining closed-virtual rotations and is denoted as the SO-SCI method. The SO-SCI method significantly improves the convergence as compared to the conventional SCI method. In combination with density fitting, the intermediates from the gradient calculation can be reused to evaluate the two-electron integrals required for the active Hessian without introducing a large computational overhead. The orbitals and CI coefficients are optimized alternately, but the CI-orbital coupling is accounted for by the limited memory Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method. This further improves the speed of convergence. The method is applicable to large molecules. The efficiency and robustness of the presented method is demonstrated in benchmark calculations for 21 aromatic molecules as well as for various transition metal complexes with up to 826 electrons and 5154 basis functions.

Time-varying parameter model reference adaptive control and its application to aircraft

A new Second Order (SO) adaptive control approach, that accounts for both matched and unmatched unknown time-varying uncertainties, is proposed in this paper. It is developed based on the Predictor based Model Reference Adaptive Control (PMRAC) structure. In this approach, the estimated parameter dynamics is composed of a σ-modified PMRAC update law and a predicted parameter dynamics, with projection operator. The predicted parameter dynamics consists of a stable known eigendynamics, a feedback of an approximate parameter error, and the remaining part linearly parameterized by a set of known regressor functions combined with an adaptive estimate of unknown second-order parameters, which are updated by a Lyapunov design. Due to the estimation of time derivatives of the parameters, the proposed predictor based SO-MRAC is hence capable of capturing the rapid parameter variations in system dynamics. Furthermore, a generalized ultimate boundedness formulation based on the Lyapunov theory is presented for its stability analysis. This formulation provides separate bounds for each of the state vector partitions, mainly tracking and parameter estimation errors. Finally, this proposed approach is applied to control of lateral dynamics of an unmanned aircraft to illustrate the usefulness of the proposed approach. The simulation results are found to be quite satisfactory both in terms of tracking and adaptation performance.

Transport and Retention of Molybdenum(VI) in Soils: Kinetic Modeling

Core Ideas Mo(VI) sorption was kinetically controlled and highly nonlinear in two different soils. Mo(VI) retention mechanism in Windsor sand was different from Webster loam. Rate‐limited processes greatly influenced Mo(VI) transport in soils. Mo(VI) transport was well described using a second‐order model. Understanding the mechanisms and kinetics controlling the retention and transport of molybdenum [Mo(VI)] is a prerequisite in the effort to evaluate environmental risk of groundwater contamination. In this study, kinetic batch and miscible‐displacement experiments were performed to investigate Mo(VI) adsorption–desorption and transport behaviors on a neutral soil (Webster loam) and a slightly acidic soil (Windsor sand). Batch results indicated that adsorption of Mo(VI) was kinetically controlled and highly nonlinear in both soils. The Mo(VI) maximum adsorption and kinetic rate for acidic Windsor sand was much higher than for neutral Webster loam. Mo(VI) breakthrough curves (BTCs) were asymmetrical and exhibited extensive tailing with incomplete recovery in the effluent: these features demonstrate that rate‐limited or non‐equilibrium process influenced Mo(VI) transport behavior. To better understand the controls on the nonlinear kinetic behavior of Mo transport in these soils, a second‐order (SO) model which accounts for equilibrium, reversible, and irreversible retention mechanisms was used to describe Mo(VI) retention and transport in soils. Based on optimized and predictive modeling results, a fully reversible equilibrium‐kinetic SO model successfully described the time‐dependent Mo(VI) sorption for Webster loam. However, for Windsor sand, which exhibited strong affinity and low mobility for Mo(VI), an additional consecutive irreversible reaction phase was necessary to describe Mo(VI) retention and transport with time.