Cosine-modulated window function-based staggered-grid finite-difference forward modeling

The numerical dispersion and computational cost are high for conventional Taylor series expansion staggered-grid finite-difference forward modeling owing to the high frequency of the wavelets and the large grid intervals. In this study, the cosine-modulated binomial window function （CMBWF）-based staggered-grid finite-difference method is proposed. Two new parameters, the modulated time and modulated range are used in the new window function and by adjusting these two parameters we obtain different characteristics of the main and side lobes of the amplitude response. Numerical dispersion analysis and elastic wavefield forward modeling suggests that the CMBWF method is more precise and less computationally costly than the conventional Taylor series expansion staggered-grid finite-difference method.

α-times Integrated Cosine Operator Functions with Growth ω

For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.

LOCAL C-SEMIGROUPS AND LOCAL C-COSINE FUNCTIONS

This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.

STRONGLY CONTINUOUS INTEGRATED COSINE OPERATOR FUNCTIONS WITH GROWTHω

For a continuous increasing function ω ： [0, ∞） → （0, ∞） of finite exponetial type, we establish a Hille-Yosida type theorem for strongly continuous integrated cosine operator functions with O（ω）. It includes the well-known polynomially bounded and exponentially bounded cases.

Logarithmic Sine and Cosine Transforms and Their Applications to Boundary-Value Problems Connected with Sectionally-Harmonic Functions

Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.

POLYNOMIALLY BOUNDED COSINE FUNCTIONS

We characterize polynomial growth of cosine functions in terms of the resolvent of its generator and give a necessary and sufficient condition for a cosine function with an infinitesimal generator which is polynomially bounded.

Approximation Theorems for Exponentially Bounded <i>a</i>-Times Integrated Cosine Function

In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.

On Dual Cosine Operator Function

Some basic properties of daul cosine operator function are given. The concept and characterization of θ-reflexivity with respect to cosine operator function are first studied.

Perturbation Theory for Dual Cosine Function（Ⅱ）—Time－dependent Perturbation in the Sun－reflexive Case

In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.

On Local Integrated Cosine Functions

Suppose X is a Banach space, and A is a closed operator. We give some equivalent conditions between A generating a local integrated cosine functions and the existence of solutions of abstract Cauchy problems.

THE PROBABILISTIC REPRESENTATION FORMULAE FOR COSINE OPERATOR FUNCTIONS

In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae.

C-cosine算子函数的遍历性

在本文中，我们定义了 Ｃ－ｃｏｓｉｎｅ算子函数的 Ａｂｅｌ遍历性与Ｃｅｓàｒｏ遍历性，讨论了Ｃ－ｃｏｓｉｎｅ算子函数这两种遍历性的相互关系及基本性质，得到了其强Ａｂｅｌ遍历性在Ｒ（Ｃ）稠时的完全刻划．此外，我们还讨论了Ｃ－ｃｏｓｉｎｅ算子函数的轨道遍历性，并借助于Ｋ－泛函，给出了Ｃ－ｃｏｓｉｎｅ算子函数在０点以非最优化速率收敛的一个充要条件．

指数有界C-cosine算子函数扰动的一个结果

讨论了R(C)不必稠情形下C-cosine的算子函数的扰动问题,借助于C-cosine算子函数对应于的子空间∑中的一个cosine算子函数,基于已有的cosine算子函数的扰动定理,得出了C-cosine算子函数的扰动定理.

Cosine算子值函数在t＞0上一致算子拓扑连续性的特征刻划

设Ｅ是一个Ｂａｎａｃｈ空间，考虑Ｅ上的强连续Ｃｏｓｈｅ算子值函数我们研究｛Ｃ（ｔ）｝－ｘ＜ｔ＜ｘ在ｔ＞０上一致算子拓扑划问题，本文证明了：｛Ｃ（ｔ）｝－ｘ＜ｔ＜ｘ在ｔ＞０上按一致算子拓扑连续的充分必要条件是其无穷小生成元为有界线性算子。进而得知：适定的Ｅ中的非完全二阶微分方程的Ｃａｕｃｈｙ问题（＊）．（Ａ为Ｅ上的一个闭稠定的线性算子）的解算子在ｔ＞０上按一致算子拓扑连续当且仅当Ａ有界，这种特征与Ｃ０类算子半群即适定的一阶抽象线性微分方程Ｃａｕｃｈｙ问题的解算子及适定的完全二阶及阶数ｎ≥３的高阶抽象线性微分方程Ｃａｕｃｈｙ问题解算于的性质迥然不同。

(Z)条件下正则cosine函数乘积扰动下的不变性质

设A生成Banach空间X上的指数有界C cosine函数C(t) .论文将讨论在满足(Z )条件的乘积扰动下 ,C(t)的范数连续性、局部Lipschitz连续性 ,局部紧性仍然保持不变 ,并得到一个逼近结果 .同时 ,也得到 (Z)

基于伪相关函数的cosine-BOC调制信号无模糊跟踪算法

针对余弦二进制偏移载波(cosine-BOC)调制信号自相关函数的多峰特性会导致导航接收机同步阶段产生跟踪模糊度问题,提出了一种基于伪相关函数(PCF)的cosine-BOC调制信号无模糊跟踪算法。该算法通过分析cosine-BOC信号的时域模型,在本地设计两路辅助信号波形,与接收到的cosine-BOC信号进行相关运算,再将得到的两互相关函数利用伪相关函数表达式进行组合,从而消除cosine-BOC信号自相关函数的边峰。仿真结果表明,该算法能够消除cosine-BOC信号鉴相曲线中存在的误锁点,实现伪码无模糊跟踪,提高跟踪可靠性,且该算法适用于任意阶数的cosineBOC信号。

(Z)条件下Cosine算子函数的乘积扰动下的不变性质

A生成Banach空间X上的指数有界cosine函数C(t),本文讨论了在满足(Z)条件的乘积扰动下C(t)的范数连续性,局部Lipschiz连续性仍保持不变,得到了一个逼近结果.

EFFICIENT DESIGN METHOD OF COSINE-MODULATED QMF BANKS SATISFYING PR PROPERTY

In this paper the design problem of perfect-reconstruction cosine-modulated QMF banks has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constrained matrices of the QCLS optimization problem are symmetric and positive definite. A cost function which is a convex function of desired prototype filter coefficients is constructed so that this kind of QCLS optimization problems can be efficiently solved. So a global minimizer of this problem can be easily obtained. Results of two design examples are presented to support the derivations and analyses.

A Novel Radial Basis Function Neural Network Approach for ECG Signal Classification

ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals.