The order structure of the set of six operators connected with quadrature rules is established in the class of 3–convex functions. Convex combinations of these operators are studied and their error bounds for four times differentiable functions are given. In some cases they are obtained for less regular functions as in the classical results. Quadrature Rules, Inequalities and Error Bounds Szymo...

In a previous paper, McLean and Thomée (to appear), we studied three numerical methods for the discretization in time of a fractional order evolution equation, in a Banach space framework. Each of the methods applied a quadrature rule to a contour integral representation of the solution in the complex plane, where for each quadrature point an elliptic boundary value problem had to be solved to ...

The in-phase and quadrature modulator (IQ modulator) is a key component in modern wireless transmitter. It provides a convenient method for modulating data bits or symbols onto an RF carrier. It has become the architecture of choice for implementing transmitter signal chains for end applications such as cellular, WiMAX, and wireless point-to-point. However, there are several non-ideal aspects o...

The basis of this paper is the quadrature formula where q = exp(2A), h being a chosen step length. This formula has been derived from the Trapezoidal Rule formula by F. Stenger. An explicit form of the error is given for the case where the integrand has a factor of the form (1 — x)a(\ + x)P, a,ß> -1. Application is made to the evaluation of Cauchy principal value integrals with endpoint singula...

The subject of this work is the application of fully discrete Galerkin finite element methods to initial-boundary value problems for linear partial integro-differential equations of parabolic type. We investigate numerical schemes based on the Padé discretization with respect to time and associated with certain quadrature formulas to approximate the integral term. A preliminary error estimate i...

In this Letter we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and receiver. The application of the Gaussian noise model indicates that, where there are two or more spans, it is always beneficial to split the nonlinearity compensation. The theory is verified via numerical simulations, investigating tran...

In this paper, we focus on error estimates to smooth solutions of semi-discrete discontinuous Galerkin (DG) methods with quadrature rules for scalar conservation laws. The main techniques we use are energy estimate and Taylor expansion first introduced by Zhang and Shu in [24]. We show that, with P k (piecewise polynomials of degree k) finite elements in 1D problems, if the quadrature over elem...

In this paper, we have measured channel capacity for various communication system such as SISO, SIMO, MIMO with different modulation technique like BPSK, QPSK, 16-QAM and 64-QAM. In the proposed algorithm the Bit Error Rate (BER) is less compared to conventional algorithm. The proposed algorithm is suitable for fast speed traffic that is when the speed of the mobile is very high. We have measur...

We experimentally demonstrate compensation of nonlinear distortion caused by the Kerr effect in a 3 × 32-Gbaud quadrature phase-shift keying (QPSK) wavelength-division multiplexing (WDM) transmission system. We use optical phase conjugation (OPC) produced by four-wave mixing (FWM) in a 7-mm long silicon nanowire. A clear improvement in Q-factor is shown after 800-km transmission with high span ...

Szegő quadrature rules are discretization methods for approximating integrals of the form ∫ π −π f(e it)dμ(t). This paper presents a new class of discretization methods, which we refer to as anti-Szegő quadrature rules. AntiSzegő rules can be used to estimate the error in Szegő quadrature rules: under suitable conditions, pairs of associated Szegő and anti-Szegő quadrature rules provide upper a...