Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is...

A new fractional accumulation technique based on discrete sequence convolution transform was developed. The system, whose unit impulse response is the sequence, constructed; then, order extended to orders. accumulative grey forecasting model GMr*(1,1) established convolution. From viewpoint of convolution, we can better understand mechanism generation. Real cases were used verify validity and e...

The infimal convolution of M-convex functions is M-convex. This is a fundamental fact in discrete convex analysis that is often useful in its application to mathematical economics and game theory. M-convexity and its variant called M-convexity are closely related to gross substitutability, and the infimal convolution operation corresponds to an aggregation. This note provides a succinct descrip...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

Abstract: Reduction of singular fractional systems to standard fractional systems and decomposition of singular fractional discrete-time linear systems into dynamic and static parts are addressed. It is shown that if the pencil of singular fractional linear discrete-time system is regular then the singular system can be reduced to standard one and it can be decomposed into dynamic and static pa...

In this paper, a color image watermarking algorithm based on Redundant Discrete Wavelet Transform (RDWT) and Singular Value Decomposition (SVD) is proposed. The new algorithm selects blue component of a color image to carry the watermark information since the Human Visual System (HVS) is least sensitive to it. To increase the robustness especially towards affine attacks, RDWT is adopted for its...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

This paper presents a new algorithm for the implementation of an N-point prime-length discrete sine transform (DST) through cyclic convolution. The proposed algorithm is based on the idea of reformulating prime N-length DST into two 1 /2 point cyclic convolutions. Thus, the hardware complexity can be reduced. This cyclic convolution –based algorithm is used to obtain a simple systolic array for...