Nonlinear Adaptive Wavelet Transform for Lossless Image Compression

The paper presents a class of nonlinear adaptive wavelet transforms for lossless image compression. In update step of the lifting the different operators are chosen by the local gradient of original image. A nonlinear morphological predictor follows the update adaptive lifting to result in fewer large wavelet coefficients near edges for reducing coding. The nonlinear adaptive wavelet transforms can also allow perfect reconstruction without any overhead cost. Experiment results are given to show lower entropy of the adaptive transformed images than those of the non-adaptive case and great applicable potentiality in lossless image compresslon.

REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS

This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions.

Furi-Martelli-Vignoli spectrum and Feng spectrum of nonlinear block operator matrices

We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.

THE EXISTENCE AND BLOW-UP OF THE RADIAL SOLUTIONS OF A(k_(1),k_(2))-HESSIAN SYSTEM INVOLVING A NONLINEAR OPERATOR AND GRADIENT

In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.

A NOTE ON PROBABILISTIC CONTRACTOR COUPLE AND SOLUTIONS FOR A SYSTEM OF NONLINEAR EQUATIONS IN N A MENGER PN-SPACES

The concept of (Phi, Delta)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of the solutions for a system of nonlinear operator equations with this kind of propabilistic contractor couple in N. A. Menger PN-spaces were studied. The works improve and extend the corresponding results by M. Altman, A. C. Lee, W. J. Padgett et al.

A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS

In this article thc concept of local conjugation of a C^1 mapping between two Banach manifolds is introduced. Thcn a rank theorem for nonlinear scmi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis.

An Efficient Maple Program for Calculating Adomian Polynomials

The immense quest for proficient numerical schemes for the solution of mathematical models featuring nonlinear differential equations led to the realization of the Adomian decomposition method (ADM) in the 80th. Undoubtedly, the solution of nonlinear differential equations using ADM is presided over by the acquisition of Adomian polynomials, which are not always easy to find. Thus, the present study proposes easy-to-implement Maple programs for the computation of Adomian polynomials. In fact, the proposed algorithms performed remarkably on several test functions, consisting of one- and multi-variable nonlinearities. Moreover, the introduced programs are advantageous in terms of simplicity;coupled with the requirement of less computational time in comparison with what is known in the literature.

INVARIANTS-PRESERVING DU FORT-FRANKEL SCHEMES AND THEIR ANALYSES FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH WAVE OPERATOR

Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stable scheme.However,there has been no research work on numerical solutions of nonlinear Schrödinger equations with wave operator by using Du Fort-Frankel-type finite difference methods(FDMs).In this study,a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional(1D)and two-dimensional(2D)nonlinear Schrödinger equations with wave operator.By using the discrete energy method,it is shown that their solutions possess the discrete energy and mass conservative laws,and conditionally converge to exact solutions with an order of for ofο(T^(2)+h_(x)^(2)+(T/h_(x))^(2))1D problem and an order ofο(T^(2)+h_(x)^(2)+h_(Y)^(2)+(T/h_(X))^(2)+(T/h_(y))^(2))for 2D problem in H1-norm.Here,τdenotes time-step size,while,hx and hy represent spatial meshsizes in x-and y-directions,respectively.Then,by introducing a stabilized term,a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised.They not only preserve the discrete energies and masses,but also own much better stability than original schemes.Finally,numerical results demonstrate the theoretical analyses.

Automatic spikes detection in seismogram

Data processing for seismic network is very complex and fussy,because a lot of data is recorded in seismicnetwork every day,which make it impossible to process these data all by manual work.Therefore,seismic datashould be processed automatically to produce a initial results about events detection and location.Afterwards,these results are reviewed and modified by analyst.In automatic processing data quality checking is important.There are three main problem data that exist in real seismic records,which include:spike,repeated data and

A Newton type iterative method for heat-conduction inverse problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.

The Maximum Dissipative Extension of Schrodinger Operator

In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.

Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term

In this paper,a nonlinear boundary value problem in a three dimensional thin domain with Tresca’s friction law is considered.The small change of variable z=x3/εtransforms the initial problem posed in the domainΩεinto a new problem posed on a fixed domainΩindependent of the parameterε.As a main result,we obtain some estimates independent of the small parameter.The passage to the limit onε,permits to prove the results concerning the limit of the weak problem and its uniqueness.

A Posteriori Parameter Choice Strategy for Nonlinear Monotone Operator Equations

In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation.

Image Encryption Application of Chaotic Sequences Incorporating Quantum Keys

Abstract This paper proposes an image encryption algorithm LQBPNN(logistic quantum and back propagation neural network)based on chaotic sequences incorporating quantum keys.Firstly,the improved one-dimensional logistic chaotic sequence is used as the basic key sequence.After the quantum key is introduced,the quantum key is incorporated into the chaotic sequence by nonlinear operation.Then the pixel confused process is completed by the neural network.Finally,two sets of different mixed secret key sequences are used to perform two rounds of diffusion encryption on the confusing image.The experimental results show that the randomness and uniformity of the key sequence are effectively enhanced.The algorithm has a secret key space greater than 2182.The adjacent pixel correlation of the encrypted image is close to 0,and the information entropy is close to 8.The ciphertext image can resist several common attacks such as typical attacks,statistical analysis attacks and differential attacks.

Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ

Some results on convergence of Newton's method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.

Lipschitz Operators and the Solvability of Non-linear Operator Equations

Let U and V be Banach spaces, L and N be non-linear operators from U into V. L is said to be Lipschitz if L 1(L) := sup{∥Lx - Ly∥ · ∥x - y∥-1 : x ≠ y} is finite. In this paper, we give some basic properties of Lipschitz operators and then discuss the unique solvability, exact solvability, approximate solvability of the operator equations Lx = y and Lx + Nx = y. Under some conditions we prove the equivalence of these solvabilities. We also give an estimation for the relative-errors of the solutions of these two systems and an application of our method to a non-linear control system.

Novel parametric optimum processing method for airborne radar

In radar target detection, an optimum processor needs to automatically adapt its weights to the environment change. Conventionally, the optimum weights are obtained by substantial independently and identically distributed (i.i.d.) interference samplings, which is not always realistic in an inhomogeneous clutter background of airborne radar. The lack of i.i.d. samplings will inevitably lead to performance deterioration for optimum processing. In this paper, a novel parametric adaptive processing method is proposed for airborne radar target detection based on the modified Doppler distributed clutter (DDC) model with contribution of clutter's internal motion. It is different from the conventional methods in that the adaptive weights are determined by two parameters of DDC model, i.e., angular center and spread. A low-complexity nonlinear operators approach is also proposed to estimate these parameters. Simulation and performance analysis are also provided to show that the proposed method can remarkably reduce the dependence of i.i.d. samplings and it is computationally efficient for practical use.

Chalcogenide photonic crystal fiber for ultraflat mid-infrared supercontinuum generation

In this Letter, we numerically simulate the generation of a 1–15 μm mid-infrared supercontinuum（SC） from a highly nonlinear Ge_（11.5）As24Se_（64.5）-based photonic crystal fiber（PCF）. This ultra-broadband SC is achieved in a100 mm long PCF pumped using 85 fs laser pulses operated at 3.1 μm and a peak pulse power of 3 k W. The proposed design offers a flat dispersion profile with two zero dispersion wavelengths. This broad and flat dispersion profile of the Ge_（11.5）As24Se_（64.5）PCF, combined with the high nonlinearity（2474 W-1km-1）, generates an ultra-broadband SC.

Homogenization of Differential Operators

In this note, we present a method of constructing the homogenized operator for a general sequence of differential operators. As an example, we construct the homogenized operator for a sequence of linear parabolic operators.