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.

Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator

This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.

Space-Time Chaos Filtering for the Incoherent Paradigm for 6G Wireless System Design from Theoretic Perspective

The following material is devoted to the generalization of the chaos modeling to random fields in communication channels and its application on the space-time filtering for the incoherent paradigm;that is the purpose of this research. The approach, presented hereafter, is based on the “Markovian” trend in modeling of random fields, and it is applied for the first time to the chaos field modeling through the well-known concept of the random “treatment” of deterministic dynamic systems, first presented by A. Kolmogorov, M. Born, etc. The material presents the generalized Stratonovich-Kushner Equations (SKE) for the optimum filtering of chaotic models of random fields and its simplified quasi-optimum solutions. In addition to this, the application of the multi-moment algorithms for quasi-optimum solutions is considered and, it is shown, that for scenarios, when the covariation interval of the input random field is less than the distance between the antenna elements, the gain of the space-time algorithms against their “time” analogies is significant. This is the general result presented in the following.

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.

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.

Identification of the Caroline Plate boundary:constraints from magnetic anomaly

The Caroline Plate is located among the Pacific Plate,the Philippine Sea Plate,and the India Australia Plate,and plays a key role in controlling the spreading direction of the Philippine Sea Plate.The Caroline Submarine Plateau(or Caroline Ridge)and the Eauripik Rise on the south formed a remarkable T-shaped large igneous rock province,which covered the northern boundary between the Caroline Plate and the Pacific Plate.However,relationship between these tectonic units and magma evolution remains unclear.Based on magnetic data from the Earth Magnetic Anomaly Grid(2-arc-minute resolution)(V2),the normalized vertical derivative of the total horizontal derivative(NVDR-THDR)technique was used to study the boundary of the Caroline Plate.Results show that the northern boundary is a transform fault that runs 1400 km long in approximately 28 km wide along the N8°in E-W direction.The eastern boundary is an NNW-SSE trending fault zone and subduction zone with a width of tens to hundreds of kilometers;and the north of N4°is a fracture zone of dense faults.The southeastern boundary may be the Lyra Trough.The area between the southwestern part of the Caroline Plate and the Ayu Trough is occupied by a wide shear zone up to 100 km wide in nearly S-N trending in general.The Eauripik transform fault(ETF)in the center of the Caroline Plate and the fault zones in the east and west basins are mostly semi-parallel sinistral NNW-SSE–trending faults,which together with the eastern boundary Mussau Trench(MT)sinistral fault,the northern Caroline transform fault(CTF),and the southern shear zone of the western boundary,indicates the sinistral characteristics of the Caroline Plate.The Caroline hotspot erupted in the Pacific Plate near the CTF and formed the west Caroline Ridge,and then joined with the Caroline transform fault at the N8°.A large amount of magma erupted along the CTF,by which the east Caroline Ridge was formed.At the same time,a large amount of magma developed southward via the eastern branch of the ETF,forming the northern segment of the Eauripik Rise.Therefore,the magmatic activity of the T-shaped large igneous province is obviously related to the fault structure of the boundary faults between the Caroline Plate and Pacific Plate,and the active faults within the Caroline Plate.

Double-Pole Solution and SolitonAntisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method

Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.

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.

A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.