arXiv subjects

Ji-Gen Peng

Publications and source records attributed to Ji-Gen Peng.

5 recordsLinked to original sources

arXiv2016

Perturbations of Admissibility, Exact Controllability, Exact Observability and Regularity

This paper is concerned with the notions of admissibility, exact controllability, exact observability and regularity of linear systems in the Banach space setting. It is proved that admissible controllability, exact controllability, admissible observation, exact observability and regularity are invariant under some regular perturbations of the generators, such results are generalizations of some previous references. Moreover, the related boundary linear systems and some illustrative examples are presented.

math.FA↗

arXiv2015

A Class of Linear Boundary Systems with Delays in State, Input and Boundary Output

In this paper, we consider a class of linear boundary systems with delays in state, input and boundary output. We prove the well-posedness and derive some spectral properties of linear system with delayed boundary feedback under some regularity conditions. Moreover, we show the regularity of linear boundary systems with delays in state and boundary output. With the above results, the regularity of linear boundary systems with delays in state, input and boundary output is verified. As applications, we prove the well-posedness and the asymptotic behavior of population systems with bounded and unbounded birth processes "$B_1(t)=\int_0^\infty\int_{-r}^0β_1(σ,a)u(t-τ,a)dσda$" and "$B_2(t)=\int_0^\inftyβ_2(a)u(t-τ,a)da$", and the well-posedness of population systems with death caused by harvesting.

math.AP↗

arXiv2015

A splitting primal-dual proximity algorithm for solving composite optimization problems

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encountered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Further, we propose a preconditioned method, of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography (CT) image reconstruction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality.

math.OC↗

arXiv2015

Existence of mild solutions for Riemann-Liouville fractional differential equations with nonlocal conditions

In this paper, we are concerned with the mild solutions of Riemann-Liouville fractional differential equations with nonlocal conditions in Banach space. We use Banach contraction principle to prove the existence and uniqueness. Moreover, we derive the existence by using Krasnoselkii's theorem. An illustrative example is presented.

math.CA↗

arXiv2015

Riemann-Liouville Fractional Cosine Functions

In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $α$-order fractional cosine function is equivalent to Riemann-Liouville $α$-order fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math. Nachr. 288, No. 7, 784-797 (2015)].

math.FA↗