Coefficient Multipliers for Polynomials

Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all p∈Q n, s*p∈Q n , where * denotes the Hadamard product. Some properties for W n and Q n are obtained.

Multipliers on Weighted Hardy Spaces over Locally Compact Vilenkin Groups

This paper is devoted to study the atomic decomposition of the weighted Hardy space on Vilenkin groups and a weighted Hp multiplier theorem.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

Nested Alternating Direction Method of Multipliers to Low-Rank and Sparse-Column Matrices Recovery

The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

As we know,thus far,there has appeared no definition of bilinear spectral multipliers on Heisenberg groups.In this article,we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness.We find some restrained conditions to separately ensure its boundedness from C0(H^(n))×L^(2)(H^(n))to L^(2)(H^(n)),from L2(H^(n))×C0(H^(n))to L^(2)(H^(n)),and from L^(p)×L^(q) to L^(r) with 2<p,q<∞,2≤r≤∞.

Fast alternating direction method of multipliers for total-variation-based image restoration

A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.

Distributed Alternating Direction Method of Multipliers for Multi-Objective Optimization

In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.

Multipliers of Hardy Spaces

本文刻划了Hardy空间H^p（1≤p≤∞）到Bloch空间的乘子，推广了前人的结果。

LITTLEWOOD-PALEY THEOREM AND MULTIPLIERS ON THE QUANTUM TORUS

The Littlewood-Paley and Marcinkiewicz＇s multiplier theorems on the quan- tum torus are established. An key ingredient of the proof is vector-valued Littlewood-Paley and noncommutative Khinchin＇s inequalities.

Dyadic Bivariate Fourier Multipliers for Multi-Wavelets in L^2(R^2)

The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(~2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ, ψ, ψ},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f(s)], where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ(s), ψ(s), ψ(s)) ~T=( g(s), g(s), g(s))~ T is a dyadic bivariate wavelet whenever(ψ, ψ, ψ) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.

Distributed MPC for Reconfigurable Architecture Systems via Alternating Direction Method of Multipliers

This paper investigates the distributed model predictive control(MPC)problem of linear systems where the network topology is changeable by the way of inserting new subsystems,disconnecting existing subsystems,or merely modifying the couplings between different subsystems.To equip live systems with a quick response ability when modifying network topology,while keeping a satisfactory dynamic performance,a novel reconfiguration control scheme based on the alternating direction method of multipliers(ADMM)is presented.In this scheme,the local controllers directly influenced by the structure realignment are redesigned in the reconfiguration control.Meanwhile,by employing the powerful ADMM algorithm,the iterative formulas for solving the reconfigured optimization problem are obtained,which significantly accelerate the computation speed and ensure a timely output of the reconfigured optimal control response.Ultimately,the presented reconfiguration scheme is applied to the level control of a benchmark four-tank plant to illustrate its effectiveness and main characteristics.

Existence Theorem of the Multipliers on Riemannian Symmetric Space SL(3,H)/SP(3)

Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.

Decomposable Multipliers on a Banach Algebra

The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].

Establishment of Automated Multi-Range Multipliers Combined with TVC

An automated multi-range multipliers（range resistors）system is established for the AC voltage measurements by using a thermal voltage converter.It is performed automatically by selecting the appropriate multiplier whose voltage range contains the voltage to be measured without changing it manually through a new designed system.It consists of control part through a micro-controller controlled by specified prepared Lab-VIEW program and switching part through electronic relays in one circuit as clearly described in this work.It is used for measuring the ac voltage in the range from 1 V to 200 V.Also,it can be used for the voltage ranges up to 1 000 V by putting some factors into consideration.The AC-DC transfer differences for these multipliers combined with thermal voltage converter are determined automatically against another standard thermal voltage converter by using another Lab-VIEW program.

MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.

Optimizing Forest Sampling by Using Lagrange Multipliers

In two-phase sampling, or double sampling, from a population with size N we take one, relatively large, sample size n. From this relatively large sample we take a small sub-sample size m, which usually costs more per sample unit than the first one. In double sampling with regression estimators, the sample of the first phase n is used for the estimation of the average of an auxiliary variable X, which should be strongly related to the main variable Y (which is estimated from the sub-sample m). Sampling optimization can be achieved by minimizing cost C with fixed var Y, or by finding a minimum var Y for fixed C. In this paper we optimize sampling with use of Lagrange multipliers, either by minimizing variance of Y and having predetermined cost, or by minimizing cost and having predetermined variance of Y.

Canonic Realizations of Voltage-Controlled Floating Inductors Using CFOAs and Analog Multipliers

New voltage-controlled floating inductors employing CFOAs and an analog multiplier have been presented which have the attractive features of using a canonic number of passive components (only two resistors and a capacitor) and not requiring any component-matching conditions and design constraints for the intended type of inductance realization. The workability and applications of the new circuits have been demonstrated by SPICE simulation and hardware experimental results based upon AD844-type CFOAs and AD633-type/MPY534 type analog multipliers.

Missile robust gain scheduling autopilot design using full block multipliers

Reduction of conservatism is one of the key and difficult problems in missile robust gain scheduling autopilot design based on multipliers.This article presents a scheme of adopting linear parameter-varying（LPV） control approach with full block multipliers to design a missile robust gain scheduling autopilot in order to eliminate conservatism.A model matching design structure with a high demand on matching precision is constructed based on the missile linear fractional transformation（LFT） model.By applying full block S-procedure and elimination lemma,a convex feasibility problem with an infinite number of constraints is formulated to satisfy robust quadratic performance specifications.Then a grid method is adopted to transform the infinite-dimensional convex feasibility problem into a solvable finite-dimensional convex feasibility problem,based on which a gain scheduling controller with linear fractional dependence on the flight Mach number and altitude is derived.Static and dynamic simulation results show the effectiveness and feasibility of the proposed scheme.

CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

In the paper,we introduce some of multipliers on residuated lattices and investigate the relations among them.First,basing on the properties of multipliers,we show that the set of all multiplicative multipliers on a residuated lattice A forms a residuated lattice which is isomorphic to A.Second,we prove that the set of all total multipliers on A is a Boolean subalgebra of the residuated lattice(which is constituted by all multiplicative multipliers on A)and is isomorphic to the Boolean center of A.Moreover,by partial multipliers,we study the maximal residuated lattices of quotients for residuated lattices.Finally,we focus on principal implicative multipliers on residuated lattices and obtain that the set of principal implicative multipliers on A is isomorphic to the set of all multiplicative multipliers on A under the opposite(dual)order.