SOME NOTES ON MULTIPLE STRA TONOVITCH INTEGRALES

Tn this paper we point out some similarities of multiple Stratonovitch integrale series with Talor series and prove some properties and a convergence theorem.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

A Cauchy integral formula for(p,q)-monogenic functions withα-weight

Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.

Revised BDS test

In this paper,we focus on the BDS test,which is a nonparametric test of independence.Specifically,the null hypothesis H0 of it is that {u_(t)} is i.i.d.(independent and identically distributed),where {u_(t)} is a random sequence.The BDS test is widely used in economics and finance,but it has a weakness that cannot be ignored:over-rejecting H0 even if the length T of {u_(t)} is as large as(100;2000).To improve the over-rejection problem of BDS test,considering that the correlation integral is the foundation of this test,we not only accurately describe the expectation of the correlation integral under H_(0),but also calculate all terms of the asymptotic variance of the correlation integral whose order is O(T^(-1))and O(T^(-2)),which is essential to improve the finite sample performance of BDS test.Based on this,we propose a revised BDS(RBDS)test and prove its asymptotic normality under H0.The RBDS test not only inherits all the advantages of BDS test,but also effectively corrects the over-rejection problem of it,which can be fully confirmed by the simulation results we presented.Moreover,based on the simulation results,we find that similar to BDS test,RBDS test would also be affected by the parameter estimations of the ARCH-type model,resulting in size distortion,but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model.Besides,through some actual datasets that have been demonstrated to fit well with ARCH-type models,we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem,and the results reflect that,under the same condition,the performance of the RBDS test is more encouraging.

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant

It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.

Truly optimal semi-active damping to control free vibration of a single degree of freedom system

This paper studies a single degree of freedom system under free vibration and controlled by a general semiactive damping.A general integral of squared error is considered as the performance index.A one-time switching damping controller is proposed and optimized.The pontryagin maximum principle is used to prove that no other form of semi-active damping can provide the better performance than the proposed one-time switching damping.

Multivariate form of Hermite sampling series

In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented.

Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary

This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.

Design of integral sliding mode guidance law based on disturbance observer

With the increasing precision of guidance,the impact of autopilot dynamic characteristics and target maneuvering abilities on precision guidance is becoming more and more significant.In order to reduce or even eliminate the autopilot dynamic operation and the target maneuvering influence,this paper suggests a guidance system model involving a novel integral sliding mode guidance law(ISMGL).The method utilizes the dynamic characteristics and the impact angle,combined with a sliding mode surface scheme that includes the desired line-ofsight angle,line-of-sight angular rate,and second-order differential of the angular line-of-sight.At the same time,the evaluation scenario considere the target maneuvering in the system as the external disturbance,and the non-homogeneous disturbance observer estimate the target maneuvering as a compensation of the guidance command.The proposed system’s stability is proven based on the Lyapunov stability criterion.The simulations reveale that ISMGL effectively intercepted large maneuvering targets and present a smaller miss-distance compared with traditional linear sliding mode guidance laws and trajectory shaping guidance laws.Furthermore,ISMGL has a more accurate impact angle and fast convergence speed.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

On the global L^(1)-boundedness of Fourier integral operators with rough amplitude and phase functions

Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.

预测规则波浪中船舶运动和载荷的频域三维计算机程序

The development of an in-house computer program for determining the motions and loads of advancing ships through sea waves in the frequency domain,is described in this paper.The code is based on the potential flow formulation and originates from a double-body code enhanced with the regular part of the velocity potential computed using the pulsing source Green function.The code is fully developed in C++language with extensive use of the object-oriented paradigm.The code is capable of estimating the excitation and inertial radiation loads or arbitrary incoming wave frequencies and incidence angles.The hydrodynamic responses such as hydrodynamic coefficients,ship motions,the vertical shear force and the vertical bending moment are estimated.A benchmark container ship and an LNG carrier are selected for testing and validating the computer code.The obtained results are compared with the available experimental data which demonstrate the acceptable compliance for the zero speed whereas there are some discrepancies over the range of frequencies for the advancing ship in different heading angles.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Geomorphological responses of rivers to active tectonics along the Karahay?t Fault, Western Türkiye

Understanding the topography in active tectonic areas and assessing the rates and models of active deformation in the upper crust are primary objectives in tectonic geomorphology studies. The drainage pattern of river systems is highly sensitive to tectonically induced changes, and it often preserves the records of the formation and progression of most tectono-geomorphic processes within its boundaries. Therefore, the evolution of landforms is a consequence of the evolution of individual drainage basins in which they are formed. Assessing the rates of tectonic deformation using geomorphic data is a traditionally adopted method to characterize the nature of active faults. Globally, the Digital Elevation Model(DEM) is widely used as a crucial tool to analyze the morphotectonic features of drainage basins. In this study, some geomorphic indices were applied to investigate the impact of tectonism on landscape along the Karahay?t Fault and its associated drainage areas. These geomorphic indices are mountain front sinuosity(Smf values between 1.17-1.52), valley floor width-to-height ratio(Vf values between 0.25-1.46), basin asymmetry factor(AF values between 15-72), drainage basin shape(Bs values between 3.18-6.01), hypsometric integral and curve(HI values between 0.32-047), channel sinuosity(S values between 1-1.6), normalized steepness index(Ksn values between 1-390) and Chi integral(χ values between 200-4400). The development of drainage areas on the hanging wall and footwall block of the Karahayit Fault differs depending on the uplift. The drainage areas developed on the hanging wall present different patterns depending on the regional uplift caused by the fault. This reveals that the fault contributed significantly to the development of drainage areas and regional uplift in the region. In addition, the maximum earthquake magnitude that may occur in the future on the Karahayit Fault, whose activity is supported by geomorphic indices, is calculated as 6.23. Since an earthquake of this magnitude may cause loss of life and property in the region, precautions should be taken.

Adaptive Sensor-Fault Tolerant Control of Unmanned Underwater Vehicles With Input Saturation

This paper investigates the tracking control problem for unmanned underwater vehicles(UUVs)systems with sensor faults,input saturation,and external disturbance caused by waves and ocean currents.An active sensor fault-tolerant control scheme is proposed.First,the developed method only requires the inertia matrix of the UUV,without other dynamic information,and can handle both additive and multiplicative sensor faults.Subsequently,an adaptive fault-tolerant controller is designed to achieve asymptotic tracking control of the UUV by employing robust integral of the sign of error feedback method.It is shown that the effect of sensor faults is online estimated and compensated by an adaptive estimator.With the proposed controller,the tracking error and estimation error can asymptotically converge to zero.Finally,simulation results are performed to demonstrate the effectiveness of the proposed method.

Intelligent Fractional-Order Controller for SMES Systems in Renewable Energy-Based Microgrid

An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.