Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

Boundedness for Multilinear Operators of Pseudo-Differential Operators

In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the Lp (1 p norm inequalities for the multilinear operators.

General Formulae for Two Pseudo-differential Operator

Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1（Rn） into L1（Rn） only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc.

Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation

In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.

Cyclic Operator Decomposition for Solving the Differential Equations

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.

Structural Damage Detection Method Based on Decomposition of the Operating Deflection Shapes

Full-field measurement techniques such as the scanning laser Doppler vibrometer （LDV） and the electronic speckle pattern interferometry systems can provide a dense and accurate vibration measurement on structural operating deflection shape （ODS） on a relatively short period of time.The possibility of structural damage detection and localization using the ODS looks likely more attractive than when using traditional measurement techniques which address only a small number of discrete points.This paper discusses the decomposition method of the structural ODSs in the time history using principal component analysis to provide a novel approach to the structural health monitoring and damage detection.The damage indicator is proposed through comparison of structural singular vectors of the ODS variation matrixes between the healthy and damaged stages.A plate piece with a fix-free configuration is used as an example to demonstrate the effectiveness of the damage detection and localization using the proposed method.The simulation results show that：（1） the dominated principal components and the corresponding singular vectors obtained from the decomposition of the structural ODSs maintain most of all vibration information of the plate,especially in the case of harmonic force excitations that the 1st principal component and its vectors mostly dominated in the system;（2） the damage indicator can apparently flag out the damage localization in the case of the different sinusoidal excitation frequencies that may not be close to any of structural natural frequencies.The successful simulation indicates that the proposed method for structural damage detection is novel and robust.It also indicates the potentially practical applications in industries.

Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

Helmholtz Decomposition of Vector Fields Using an Optimal Preconditioned Conjugate Gradient Algorithm

In this article, we study numerically a Helmholtz decomposition methodology, based on a formulation of the mathematical model as a saddle-point problem. We use a preconditioned conjugate gradient algorithm, applied to an associated operator equation of elliptic type, to solve the problem. To solve the elliptic partial differential equations, we use a second order mixed finite element approximation for discretization. We show, using 2-D synthetic vector fields, that this approach, yields very accurate solutions at a low computational cost compared to traditional methods with the same order of approximation.

A novel two-stage Lagrangian decomposition approach for refinery production scheduling with operational transitions in mode switching

To address large scale industrial processes,a novel Lagrangian scheme is proposed to decompose a refinery scheduling problem with operational transitions in mode switching into a production subproblem and a blending and delivery subproblem.To accelerate the convergence of Lagrange multipliers,some auxiliary constraints are added in the blending and delivery subproblem.A speed-up scheme is presented to increase the efficiency for solving the production subproblem.An initialization scheme of Lagrange multipliers and a heuristic algorithm to find feasible solutions are designed.Computational results on three cases with different lengths of time horizons and different numbers of orders show that the proposed Lagrangian scheme is effective and efficient.

Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform

In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.

A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L_(2)^(a) (R_(+);m_(a)(x)dx)

Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are defined.Estimates for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis introduced.Later product and commutators for the PDO are investigated and their boundedness results are discussed.

Bilinear Pseudo-Differential Operator and Its Commutator on Generalized FractionalWeighted Morrey Spaces

The aim of this paper is to establish the boundedness of bilinear pseudodifferential operator Ts and its commutator[b1,b2,Ts]generated by Ts and b1,b22 BMO(Rn)on generalized fractional weighted Morrey spaces Lp,h,j(w).Under assumption that a weight satisfies a certain condition,the authors prove that Ts is bounded from products of spaces Lp1,h1,j(w1)Lp2,h2,j(w2)into spaces Lp,h,j(~w),where~w=(w1,w2)2 A~P,~P=(p1,p2),h=h1+h2 and 1 p=1 p1+1 p2 with p1,p22(1,¥).Furthermore,the authors show that the[b1,b2,Ts]is bounded from products of generalized fractional Morrey spaces Lp1,h1,j(Rn)Lp2,h2,j(Rn)into Lp,h,j(Rn).As corollaries,the boundedness of the Ts and[b1,b2,Ts]on generalized weighted Morrey spaces Lp,j(w)and on generalized Morrey spaces Lp,j(Rn)is also obtained.

The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces

The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.

Multi-Parameter Design and Optimization for the Decomposition Projective Method and Its Applications

In order to solve the electromagnetic problems on the large multi branch domains, the decomposition projective method(DPM) is generalized for multi subspaces in this paper. Furthermore multi parameters are designed for DPM, which is called the fast DPM(FDPM), and the convergence ratio of the above algorithm is greatly increased. The examples show that the iterative number of the FDPM with optimal parameters decreases much more, which is less than one third of the DPM iteration number. After studying the ...

Boundedness of Hausdorff operators on some product Hardy type spaces

We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.

Integrability of the general product Hardy operators on the product Hardy spaces

In this paper,we prove that the general product Hardy operators are bounded from the product Hardy space H1n（Rm1×···×Rmn） to L1（R（∑ni=1mi）.

Getting pre-stack time migration travel times from the single square root operator

Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.

WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator

Catalytic bed slenderness ratio and ADN/methanol ratio for decomposition and combustion characteristics within ammonium dinitramide(ADN)-based green aerospace thruster

The decomposition and combustion characteristics of ammonium dinitramide (ADN) based non-toxic aerospace propellant are analytically studied to determine the effects of catalytic bed structure (slenderness ratio) and operation parameters (mass fraction ratio of ADN/CH3OH) on the general performance within the ADN-based thruster. In the present research, the non-equilibrium temperature model is utilized to describe the heat transfer characteristics between the fluid phase and solid phase in the fixed bed. We determined the fluid resistance characteristics in the catalytic bed by experiments involving the method of pressure-mass. We have done the simulation study based on the available results in the literature and found the complex physical and chemical processes within the ADN thruster. Furthermore, an optimized catalytic bed slenderness ratio was observed w让h a value of 1.75 and the mass fraction ratio of 5.73 significantly influenced the propellant performance. These results could serve as a reference to explore the combustion characteristics within the thruster and the preparation of future propellants.