ON SOME GENERALIZED DIFFERENCE PARANORMED SEQUENCE SPACES ASSOCIATED WITH MULTIPLIER SEQUENCE DEFINED BY MODULUS FUNCTION

In this article we introduce the paranormed sequence spaces （f,A, Am,p）, c0（f,A,Am,p） and L00（f,A, Am,p）, associated with the multiplier sequence ∧ = （hk）, defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

Steganography based on wavelet transform and modulus function

In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.

SOME NEW TYPE OF DIFFERENCE SEQUENCE SPACES DEFINED BY MODULUS FUNCTION AND STATISTICAL CONVERGENCE

In this article we introduce the difference sequence spaces Wo [f, △m], W1 [f, △m],W∞[f ,△m] and S[f, △m], defined by a modulus function f. We obtain a relation between W1 【f, △m] ∩ l∞[f, △m] and S[f, △m]∩ l∞[f, △m] and prove some inclusion results.

PROPERTIES OF SOME SETS OF SEQUENCES DEFINED BY A MODULUS FUNCTION

In this article, the author introduces the generalized difference paranormed sequence spaces c （△v^m, f, p, q, s）, c0 （△v^m, f, p, q, s）, and l∞ （△v^m, f, p, q, s） defined over a seminormed sequence space （X, q）. The author also studies their properties like completeness, solidity, symmetricitv, etc.

Lacunary Invariant Statistical Convergence Of Sequences Of Sets With Respect To A Modulus Function

In this paper, we introduce and study the concept of lacunary invariant convergence for sequences of sets with respect to modulus functionfand give some inclusion relations.

Data embedding based on pixel value differencing and modulus function using indeterminate equation

An effective data hiding method based on pixel value differencing （PVD） and modulus function （MF） PVD （MF-PVD） was proposed. MF-PVD method was derived by Wang et al in which the MF was employed to adjust the remainder of two pixels for data embedding and extraction. In the proposed method, a new remainder function in a more general form is defined by selecting proper parameters, in which an indeterminate equation is constructed and an optimal solution is applied to revise the pixels. This strategy leads to a significant image distortion reduction compared with the original method. The experiment reveals that, by preserving the original embedding capacity, the method provides better embedding efficiency than both MF-PVD and PVD methods.

SOME CLASSES OF DIFFERENCE SEQUENCES OF FUZZY NUMBERS DEFINED BY A SEQUENCE OF MODULI

In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.

Exact Convergence Rates of Functional Modulus of Continuity of a Wiener Process

Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.

FUNCTIONAL MODULUS OF CONTINUITY FOR BROWNIAN MOTION IN HLDER NORM

The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.

Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.

Global Convergence of a New Restarting Three Terms Conjugate Gradient Method for Non-linear Optimizations

In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.

QUASI－FLOW CORNER THEORY ON LARGE PLASTIC DEFORMATION OF DUCTILE METALS AND ITS APPLICATIONS

A quasi -flow corner theory on lalge plastic deformation if ductile metals is proposed in this paper. From orthogonal rule of plastic flow, the theory introduces a 'modulus rethtced function' and a corner effect of yield surface into the constilulive model of elastic-plastic large deformation . Thereby, the smooth and continuous transitions from orthogonal constitutive model to non-orthogonal one, and from plastic loading to elastic unloading are realized. In addition, the theory makes it possible to connect general anisotropic yield functions with corner hardening effect. The comparison between numerical simulation and experimental observation for the uniaxial tensile instability and shear band deformation of anisotropic sheet metals shows the validity of the present quasi-flow corner theory.

Global Convergence of a New Conjugate Gradient Methods with a Modification of the Curry-Altman Step-size Rule

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman's step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.

The essential order of approximation for neural networks

There have been various studies on approximation ability of feedforward neural networks (FNNs). Most of the existing studies are, however, only concerned with density or upper bound estimation on how a multivariate function can be approximated by an FNN, and consequently, the essential approximation ability of an FNN cannot be revealed. In this paper, by establishing both upper and lower bound estimations on approximation order, the essential approximation ability (namely, the essential approximation order) of a class of FNNs is clarified in terms of the modulus of smoothness of functions to be approximated. The involved FNNs can not only approximate any continuous or integrable functions defined on a compact set arbitrarily well, but also provide an explicit lower bound on the number of hidden units required. By making use of multivariate approximation tools, it is shown that when the functions to be approximated are Lipschitzian with order up to 2, the approximation speed of the FNNs is uniquely determined by modulus of smoothness of the functions.

The essential order of approximation for nearly exponential type neural networks

For the nearly exponential type of feedforward neural networks （neFNNs）, it is revealed the essential order of their approximation. It is proven that for any continuous function defined on a compact set of Rd, there exists a three-layer neFNNs with fixed number of hidden neurons that attain the essential order. When the function to be approximated belongs to the α-Lipschitz family （0 〈α≤ 2）, the essential order of approxi- mation is shown to be O（n^-α） where n is any integer not less than the reciprocal of the predetermined approximation error. The upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only characterize the intrinsic property of approximation of the neFNNs, but also uncover the implicit relationship between the precision （speed） and the number of hidden neurons of the neFNNs.