BOUNDEDNESS OF GENERALIZED HIGHER COMMUTATORS OF MARCINKIEWICZ INTEGRALS

Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.

BOUNDEDNESS OF COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON WEIGHTED HERZ-TYPE HARDY SPACES

In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.

LITTLEWOOD-PALEY OPERATORS AND MARCINKIEWICZ INTEGRAL ON GENERALIZED CAMPANATO SPACES

Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.

ON GENERALIZED COMPLETE(p,q)-ELLIPTIC INTEGRALS

In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag-Leffler Function in the Kernel

In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.

Nonlinear Dynamics of Viscoelastic Pipe Conveying Pulsating Fluid Subjected to Base Excitation

Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governing partial differential equation is transformed into a nonlinear system of fourth-order ordinary differential equations by using the generalized integral transform technique(GITT).The effects of the combined excitation of base motion and pulsating internal flow on the nonlinear dynamic behavior of the pipe are investigated using a bifurcation diagram,phase trajectory diagram,power spectrum diagram,time-domain diagram,and Poincare map.The results show that the base excitation amplitude and frequency significantly affect the dynamic behavior of the pipe system.Some new resonance phenomena can be observed,such as the period-1 motion under the base excitation or the pulsating internal flow alone becomes the multi-periodic motion,quasi-periodic motion or even chaotic motion due to the combined excitation action.

First Integrals and Reduction of the Birkhoffian System

Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.

Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model

To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.

TOEPLITZ-TYPE OPERATORS ON LEBESGUE SPACES

Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...

Synchronous Vibration Suppression of Magnetic Bearing Systems without Angular Sensors

Active Magnetic Bearing(AMB)levitates rotor by magnetic force without friction,and it can provide active control force to suppress vibration while rotating.Most of vibration suppressing methods need angular speed sensors to obtain rotating speed,but in many occasions,angular speed sensor is difficult to install or is difficult to guarantee reliability.This paper proposed a vibration suppressing strategy without angular speed sensor based on generalized integrator and frequency locked loop(GI-FLL)and phase shift generalized integrator(PSGI).GI-FLL and high-pass filter estimate frequency from control current,PSGI is applied to generate compensating signal.Firstly,model of AMB system expressed by transfer function is established and effect of centrifugal force is analyzed.Then,principle and process of vibration suppressing strategy is introduced.Influence of parameters are analyzed by root locus and bode diagram.Simulation results display the process of frequency estimation and performance of displacement.Experiments are carried on a test rig,results of simulations and experiments demonstrate the effectiveness of proposed vibration suppressing strategy.

Fruit Image Classification Using Deep Learning

Fruit classification is found to be one of the rising fields in computer and machine vision.Many deep learning-based procedures worked out so far to classify images may have some ill-posed issues.The performance of the classification scheme depends on the range of captured images,the volume of features,types of characters,choice of features from extracted features,and type of classifiers used.This paper aims to propose a novel deep learning approach consisting of Convolution Neural Network(CNN),Recurrent Neural Network(RNN),and Long Short-TermMemory(LSTM)application to classify the fruit images.Classification accuracy depends on the extracted and selected optimal features.Deep learning applications CNN,RNN,and LSTM were collectively involved to classify the fruits.CNN is used to extract the image features.RNN is used to select the extracted optimal features and LSTM is used to classify the fruits based on extracted and selected images features by CNN and RNN.Empirical study shows the supremacy of proposed over existing Support Vector Machine(SVM),Feed-forwardNeural Network(FFNN),and Adaptive Neuro-Fuzzy Inference System(ANFIS)competitive techniques for fruit images classification.The accuracy rate of the proposed approach is quite better than the SVM,FFNN,and ANFIS schemes.It has been concluded that the proposed technique outperforms existing schemes.

An Improved Stator Flux Observation Method of Permanent Magnet Synchronous Motor

The stator flux and electromagnetic torque observation is the basis of direct torque controlled permanent magnet synchronous motor( PMSM) drive system. However,the traditional stator flux observer based on voltage model is affected by integral initial values and integral drift,that based on current model is affected by the parameters of PMSM,so a new stator flux observation method is proposed based on an improved secondorder generalized integrator( SOGI). Compared to the stator flux observation method based on the conventional SOGI,the proposed method can not only overcome the influence of integral initial values and integral drift,but also completely eliminate the DC offset's influence. Therefore,the observation accuracy of stator flux is further improved. The simulation and experimental results both show that the proposed method has a higher stator flux and electromagnetic torque observation precision.

DYNAMIC ANALYSIS TO INFINITE BEAM UNDER A MOVING LINE LOAD WITH UNIFORM VELOCITY

Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reserves moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam. The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem. Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed. Additionally, the authors also present definition of moving dynamic coefficient which reflects moving effect.

Torque Distribution Strategy for Integrated Starter/ Generator Hybrid Bus Implemented by Fuzzy Algorithm

A torque distribution strategy was designed by using fuzzy logic to realize the optimal control. The vehicle load zones were dynamically divided into several zones by several torque lines to indicate the drivers demand and the high or low efficient operating areas of the diesel engine. The fuzzy logic controller with trapezoid membership function and Mamdani rule reference mechanism was utilized. There are over 100 rules used in this fuzzy-based torque distribution strategy which are sorted into four rule-bases. The fuel economy and acceleration tests were designed to test and validate the integrated starter/generator (ISG) bus perfor-mance using fuzzy-based torque distribution strategy. The fuel economy is improved 7.7% compared with the rule-based strategy. Finally the road test results reveal that there is about 15% improvement of fuel economy. And the 0-50 km/h acceleration time is 9.5% shorter than the original bus.

EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I: APPROXIMATION:

In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.

Partially coherent nonparaxial modified Bessel-Gauss beams

The concept of partially coherent nonparaxial modified Bessel Gauss （MBG） beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m, ζ and f parameters, and to compare the difference between the paraxial and nonparaxial results.

Analysis of Phased-Mission System Reliability and Importance with Imperfect Coverage

Accounting for static phased-mission systems (PMS) and imperfect coverage (IPC), generalized and integrated algorithm (GPMS-CPR) implemented a synthesis of several approaches into a single methodology whose advantages were in the low computational complexity, broad applicability, and easy implementation. The approach is extended into analysis of each phase in the whole mission. Based on Fussell-Vesely importance measure, a simple and efficient importance measure is presented to analyze component’s importance of phased-mission systems considering imperfect coverage.

Iterative convergence of boundary-volume integral equation method

The boundary-volume integral equation numerical technique can be a powerful tool for piecewise heterogeneous media, but it is limited to small problems or low frequencies because of great computational cost. Therefore, a restarted GMRES method is applied to solve large-scale boundary-volume scattering problems in this paper to overcome the computational barrier. The iterative method is firstly applied to responses of dimensionless frequency to a semicircular alluvial valley filled with sediments, compared with the standard Gaussian elimination method. Then the method is tested by a heterogeneous multilayered model to show its applicability. Numerical experiments indicate that the preconditioned GMRES method can significantly improve computational efficiency especially for large Earth models and high frequencies, but with a faster convergence for the left diagonal preconditioning.

Predictive direct power control of three-phase PWM rectifier based on TOGI grid voltage sensor free algorithm

In predictive direct power control(PDPC)system of three-phase pulse width modulation(PWM)rectifier,grid voltage sensor makes the whole system more complex and costly.Therefore,third-order generalized integrator(TOGI)is used to generate orthogonal signals with the same frequency to estimate the grid voltage.In addition,in view of the deviation between actual and reference power in the three-phase PWM rectifier traditional PDPC strategy,a power correction link is designed to correct the power reference value.The grid voltage sensor free algorithm based on TOGI and the corrected PDPC strategy are applied to three-phase PWM rectifier and simulated on the simulation platform.Simulation results show that the proposed method can effectively eliminate the power tracking deviation and the grid voltage.The effectiveness of the proposed method is verified by comparing the simulation results.