Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2×2 linear hyperbolic systems

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order 2×2 linear hyperbolic systems. The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem.

New application of non-binary Galois fields Fourier transform: digital analog of convolution theorem

It is shown that the use of the representation of digital signals varying in the restricted amplitude range through elements of Galois fields and the Galois field Fourier transform makes it possible to obtain an analogue of the convolution theorem. It is shown that the theorem makes it possible to analyze digital linear systems in same way that is used to analyze linear systems described by functions that take real or complex values (analog signals). In particular, it is possibile to construct a digital analogue of the transfer function for any linear system that has the property of invariance with respect to the time shift. It is shown that the result obtained has a fairly wide application, in particular, it is of interest for systems in which signal processing methods are combined with the use of neural networks.

Estimates and properties of certain q-Mellin transform on generalized q-calculus theory

This paper deals with the generalized q-theory of the q-Mellin transform and its certain properties in a set of q-generalized functions. Some related q-equivalence relations, q-quotients of sequences, q-convergence definitions, and q-delta sequences are represented. Along with that, a new q-convolution theorem of the estimated operator is obtained on the generalized context of q-Boehmians. On top of that, several results and q-Mellin spaces of q-Boehmians are discussed. Furthermore, certain continuous q-embeddings and an inversion formula are also discussed.

Gupta Transform Approach to the Series RL and RC Networks with Steady Excitation Sources

The analysis of electric networks circuits is an essential course in engineering. The response of such networks is usually obtained by mathematical approaches such as Laplace Transform, Calculus Approach, Convolution Theorem Approach, Residue Theorem Approach. This paper presents a new integral transform called Gupta Transform for obtaining the complete response of the series RL and RC networks circuits with a steady voltage source. The response obtained will provide electric current or charge flowing through series RL and RC networks circuits with a steady voltage source. In this paper, the response of the series RL and RC networks circuits with steady excitation source is provided as a demonstration of the application of the new integral transform called Gupta Transform.

More Properties of Fractional Proportional Differences

The main aim of this paper is to clarify the action of the discrete Laplace transform on the fractional proportional operators. First of all, we recall the nabla fractional sums and differences and the discrete Laplace transform on a time scale equivalent to $h\mathbb{Z}$. The discrete $h-$Laplace transform and its convolution theorem are then used to study the introduced discrete fractional operators.

The q-Sumudu transform and its certain properties in a generalized q-calculus theory

In this paper we consider a generalization to the q-calculus theory in the space of q-integrable functions. We introduce q-delta sequences and develop q-convolution products to derive certain q-convolution theorem. By using the concept of q-delta sequences, we establish various axioms and set up q-spaces of generalized functions named q-Boehmian spaces. The new assigned spaces of q-generalized functions are acceptable and compatible with the classical spaces of the ordinary functions. Consequently, we extend the generalized q-Sumudu transform to the sets of q-Boehmian spaces. On top of that, we nominate the canonical q-embeddings between the q-integrable sets of functions and the q-integrable sets of q-Boehmians. Furthermore, we address the general properties of the generalized q-Sumudu transform and its inversion formula in some detail.