Characterizations of semihoops based on derivations

In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.

New Second-Level-Discrete Zeroing Neural Network for Solving Dynamic Linear System

Dear Editor,This letter deals with a new second-level-discretization method with higher precision than the traditional first-level-discretization method.Specifically,the traditional discretization method utilizes the first-order time derivative information,and it is termed first-level-discretization method.By contrast,the new discretization method not only utilizes the first-order time derivative information,but also makes use of the second-order derivative information.By combining the new second-level-discretization method with zeroing neural network(ZNN),the second-level-discrete ZNN(SLDZNN)model is proposed to solve dynamic(i.e.,time-variant or time-dependent)linear system.Numerical experiments and application to angle-of-arrival(AoA)localization show the effectiveness and superiority of the SLDZNN model.

Input-to-State Stability of Impulsive Switched Systems Involving Uncertain Impulse-Switching Moments

Dear Editor,This letter studies the input-to-state stability(ISS)for a class of impulsive switched systems,where uncertain impulse-switching moments are involved.The robustness of ISS with respect to the perturbations of the occurrence time of impulse-switching moments is revealed by several less conservative dwell-time conditions for the uncertain impulse-switching moments combined with Lyapunov conditions.Moreover,the Lyapunov conditions have multiple coefficients at discrete time so as to handle the hybrid effect of impulse-switching moments,and the case that time derivative of Lyapunov function is indefinite is also taken into account.Finally,a numerical example is proposed to illustrate the effectiveness of the theoretical results.

Prediction and Output Estimation of Pattern Moving in Non-Newtonian Mechanical Systems Based on Probability Density Evolution

A prediction framework based on the evolution of pattern motion probability density is proposed for the output prediction and estimation problem of non-Newtonian mechanical systems,assuming that the system satisfies the generalized Lipschitz condition.As a complex nonlinear system primarily governed by statistical laws rather than Newtonian mechanics,the output of non-Newtonian mechanics systems is difficult to describe through deterministic variables such as state variables,which poses difficulties in predicting and estimating the system’s output.In this article,the temporal variation of the system is described by constructing pattern category variables,which are non-deterministic variables.Since pattern category variables have statistical attributes but not operational attributes,operational attributes are assigned to them by posterior probability density,and a method for analyzing their motion laws using probability density evolution is proposed.Furthermore,a data-driven form of pattern motion probabilistic density evolution prediction method is designed by combining pseudo partial derivative(PPD),achieving prediction of the probability density satisfying the system’s output uncertainty.Based on this,the final prediction estimation of the system’s output value is realized by minimum variance unbiased estimation.Finally,a corresponding PPD estimation algorithm is designed using an extended state observer(ESO)to estimate the parameters to be estimated in the proposed prediction method.The effectiveness of the parameter estimation algorithm and prediction method is demonstrated through theoretical analysis,and the accuracy of the algorithm is verified by two numerical simulation examples.

Design of PID controller with incomplete derivation based on ant system algorithm

A new and intelligent design method for PID controller with incomplete derivation is proposed based on the ant system algorithm ( ASA) . For a given control system with this kind of PID controller, a group of optimal PID controller parameters K p * , T i * , and T d * can be obtained by taking the overshoot, settling time, and steady-state error of the system's unit step response as the performance indexes and by use of our improved ant system algorithm. K p * , T i * , and T d * can be used in real-time control. This kind of controller is called the ASA-PID controller with incomplete derivation. To verify the performance of the ASA-PID controller, three different typical transfer functions were tested, and three existing typical tuning methods of PID controller parameters, including the Ziegler-Nichols method (ZN),the genetic algorithm (GA),and the simulated annealing (SA), were adopted for comparison. The simulation results showed that the ASA-PID controller can be used to control different objects and has better performance compared with the ZN-PID and GA-PID controllers, and comparable performance compared with the SA-PID controller.

DERIVATION AND INTEGRAL SLIDING MODE VARIABLE STRUCTURE CONTROL OF HYDRAULIC VELOCITY TRACKING SYSTEM

The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a derivation and integral sliding mode variable structurecontrol scheme (DI-SVSC) is proposed. An integral controller is introduced to avoid the assumptionthat the derivative of desired signal must be known in conventional sliding mode variable structurecontrol, a nonlinear derivation controller is used to weaken the chattering of system. The designmethod of switching function in integral sliding mode control, nonlinear derivation coefficient andcontrollers of DI-SVSC is presented respectively. Simulation shows that the control approach is ofnice robustness and improves velocity tracking accuracy considerably.

Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)disease.We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system.We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem.By utilizing the Newtonian polynomials interpolation technique,we recall a powerful algorithm to interpret the numerical findings for the aforesaid model.Here,we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to person.Fruits bats which are also known as flying foxes are one of the sources of transmission of NiV disease.Here in this work,we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and prediction.We present the approximate results for different compartments using different fractional orders.By using the piecewise derivative concept,we detect the crossover ormulti-steps behavior in the transmission dynamics of the mentioned disease.Therefore,the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.

Some results on derivations of MV-algebras

In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].

Theoretical derivation of the crystallographic parameters of polytypes of long-period stacking ordered structures with the period of 13 and 14 in hexagonal close-packed system

Based on crystallographic theory, there are 63 kinds of polytypes of 13H long-period stacking order （LPSO） structure, 126 kinds of polytypes of 14H LPSO structure, 120 kinds of polytypes of 39R LPSO structure, and 223 kinds of polytypes of 42R LPSO structure in a hexagonal close-packed （HCP） system, and their stacking sequences and space groups have been derived in detail. The result provides a theoretical explanation for the various polytypes of the LPSO structure.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

On the partial stability of nonlinear impulsive Caputo fractional systems

In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptotic uniform stability and Mittag Leffler stability.The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.Furthermore,some numerical examples are given to show the effectiveness of our obtained theoretical results.

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

(ρ, τ, σ)-Derivations of Dendriform Algebras

We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.

Fullerenes and derivatives as electrocatalysts: Promises and challenges

Carbon-based metal-free nanomaterials are promising alternatives to precious metals as electrocatalysts of key energy storage and conversion technologies.Of paramount significance are the establishment of design principles by understanding the catalytic mechanisms and identifying the active sites.Distinct from sp2-conjugated graphene and carbon nanotube,fullerene possesses unique characteristics that are growingly being discovered and exploited by the electrocatalysis community.For instance,the well-defined atomic and molecular structures,the good electron affinity to tune the electronic structures of other substances,the intermolecular self-assembly into superlattices,and the on-demand chemical modification have endowed fullerene with incomparable advantages as electrocatalysts that are otherwise not applicable to other carbon ma-terials.As increasing studies are being reported on this intriguing topic,it is necessary to provide a state-of-the-art overview of the recent progress.This review takes such an initiative by summarizing the promises and challenges in the electrocatalytic applications of fullerene and its derivatives.The content is structured according to the composition and structure of fullerene,including intact fullerene(e.g.,fullerene composite and superlattices)and fullerene derivatives(e.g.,doped,endohedral,and disintegrated fullerene).The synthesis,characterization,catalytic mechanisms,and deficiencies of these fullerene-based materials are explicitly elaborated.We conclude it by sharing our perspectives on the key aspects that future efforts shall consider.

Organic solar cells with D18 or derivatives offer efficiency over 19%

In recent years,organic solar cells(OSCs)have garnered significant attention due to their distinctive attributes,such as flexibility,lightweight,and solution processing,which position them as alternatives for next-generation solar technologies[1−5].Thanks to breakthroughs in materials development,the power conversion efficiency(PCE)for single-junction OSCs has already surpassed 19%[6−13].The development of photoactive materials is pivotal in enhancing the PCEs,and several reviews have provided insights into materials design[14−18].Herein,we highlight single-junction OSCs based on D18 and its derivatives[19,20].

Time-dependent behavior and permeability evolution of limestone under hydro-mechanical coupling

Excessively high pore water pressure presents unpredictable risks to the safety of rock tunnels in mountainous regions that are predominantly composed of limestone. Investigating the creep characteristics and permeability evolution of limestone under varying hydrated conditions is crucial for a better understanding of the delayed deformation mechanisms of limestone rock tunnels. To this end, this paper initially conducts a series of multi-stage triaxial creep tests on limestone samples under varying pore water pressures. The experiment examines how pore water pressure affects limestone’s creep strain, strain rate, long-term strength, lifespan, and permeability, all within the context of hydraulicmechanical(HM) coupling. To better describe the creep behavior associated with pore water pressure, this paper proposes a new nonlinear fractional creep constitutive model. This constitutive model depicts the initial, steady-state, and accelerated phases of limestone’s creep behavior. Finally, the proposed model is applied to the numerical realization of deformation in limestone tunnel, validating the effectiveness of the proposed constitutive model in predicting tunnel’s creep deformation. This research enhances our understanding of limestone’s creep characteristics and permeability evolution under HM coupling, laying a foundation for assessing the longterm stability of mountain tunnels.

Identification of key genes regulating the synthesis of quercetin derivatives in Rosa roxburghii through integrated transcriptomics and metabolomics

Rosa roxburghii fruit is rich in flavonoids, but little is known about their biosynthetic pathways. In this study, we employed transcriptomics and metabolomics to study changes related to the flavonoids at five different stages of R. roxburghii fruit development. Flavonoids and the genes related to their biosynthesis were found to undergo significant changes in abundance across different developmental stages, and numerous quercetin derivatives were identified. We found three gene expression modules that were significantly associated with the abundances of the different flavonoids in R. roxburghii and identified three structural UDP-glycosyltransferase genes directly involved in the synthesis of quercetin derivatives within these modules. In addition, we found that RrBEH4, RrLBD1 and RrPIF8could significantly increase the expression of downstream quercetin derivative biosynthesis genes. Taken together,these results provide new insights into the metabolism of flavonoids and the accumulation of quercetin derivatives in R. roxburghii.

Strong metal-support interactions between highly dispersed Cu^(+) species and ceria via mix-MOF pyrolysis toward promoted water-gas shift reaction

The modulation of metal-support interfacial interaction is significant but challenging in the design of high-efficiency and high-stability supported catalysts.Here,we report a synthetic strategy to upgrade Cu-CeO_(2)interfacial interaction by the pyrolysis of mixed metal-organic framework(MOF)structure.The obtained highly dispersed Cu/CeO_(2)-MOF catalyst via this strategy was used to catalyze water-gas shift reaction(WGSR),which exhibited high activity of 40.5μmolCOgcat^(-1).s^(-1)at 300℃and high stability of about 120 h.Based on comprehensive studies of electronic structure,pyrolysis strategy has significant effect on enhancing metal-support interaction and then stabilizing interfacial Cu^(+)species under reaction conditions.Abundant Cu^(+)species and generated oxygen vacancies over Cu/CeO_(2)-MOF catalyst played a key role in CO molecule activation and H2O molecule dissociation,respectively.Both collaborated closely and then promoted WGSR catalytic performance in comparison with traditio nal supported catalysts.This study shall offer a robust approach to harvest highly dispersed catalysts with finely-tuned metal-support interactions for stabilizing the most interfacial active metal species in diverse heterogeneous catalytic reactions.

Discovery and structure-activity relationship studies of novel tetrahydro-β-carboline derivatives as apoptosis initiators for treating bacterial infections

Developing and excavating new agrochemicals with highly active and safe is an important tactic for protecting crop health and food safety.In this paper,to discover the new bactericide candidates,we designed,prepared a new type of1,2,3,4-tetrahydro-β-carboline(THC)derivatives and evaluated the in vitro and in vivo bioactivities against the Xanthomonas oryzae pv.oryzae(Xoo),Xanthomonas axonopodis pv.citri(Xac),and Pseudomonas syringae pv.actinidiae(Psa).The in vitro bioassay results exhibited that most title molecules possessed good activity toward the three plant pathogenic bacteria,the compound A17 showed the most active against Xoo and Xac with EC50 values of 7.27 and 4.89 mg mL^(-1)respectively,and compound A8 exhibited the best inhibitory activity against Psa with EC50value of 4.87 mg mL^(-1).Pot experiments showed that compound A17 exhibited excellent in vivo antibacterial activities to manage rice bacterial leaf blight and citrus bacterial canker,with protective efficiencies of 52.67 and 79.79%at 200 mgmL^(-1),respectively.Meanwhile,compound A8 showed good control efficiency(84.31%)against kiwifruit bacterial canker at 200 mg mL^(-1).Antibacterial mechanism suggested that these compounds could interfere with the balance of the redox system,damage the cell membrane,and induce the apoptosis of Xoo cells.Taken together,our study revealed that tetrahydro-β-carboline derivatives could be a promising candidate model for novel broadspectrum bactericides.

Development and identification of two novel wheat-rye 6R derivative lines with adult-plant resistance to powdery mildew and high-yielding potential

Powdery mildew,caused by Blumeria graminis f.sp.tritici(Bgt),is a devastating disease that seriously threatens wheat yield and quality.To control this disease,host resistance is the most effective measure.Compared with the resistance genes from common wheat,alien resistance genes can better withstand infection of this highly variable pathogen.Development of elite alien germplasm resources with powdery mildew resistance and other key breeding traits is an attractive strategy in wheat breeding.In this study,three wheat-rye germplasm lines YT4-1,YT4-2,and YT4-3 were developed through hybridization between octoploid triticale and common wheat,out of which the lines YT4-1 and YT4-2 conferred adult-plant resistance(APR)to powdery mildew while the line YT4-3 was susceptible to powdery mildew during all of its growth stages.Using genomic in situ hybridization,multi-color fluorescence in situ hybridization,multi-color GISH,and molecular marker analysis,YT4-1,YT4-2,and YT4-3 were shown to be cytogenetically stable wheat-rye 6R addition and T1RS.1BL translocation line,6RL ditelosomic addition and T1RS.1BL translocation line,and T1RS.1BL translocation line,respectively.Compared with previously reported wheat-rye derivative lines carrying chromosome 6R,YT4-1 and YT4-2 showed stable APR without undesirable pleiotropic effects on agronomic traits.Therefore,these novel wheat-rye 6R derivative lines are expected to be promising bridge resources in wheat disease breeding.